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VACUUM SCIENCE ANDENGINEERINGProperties of Gases at Low Pressure;

Vacuum Measurements;

Design and Operating Features of

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VACUUM SCIENCEAND ENGINEERING

Properties of Gases at Low Pressure;

Vacuum Measurements ; Design and OperatingFeatures of Vacuum Pumps and Systems

C. M. VAN ATTAConsultant on Vacuum Technology

McGRAW-HILL BOOK COMPANYNew York San Francisco Toronto London Sydney

FOREWORD

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HARRIS 'X

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VACUUM SCIENCE AND ENGINEERING

Copyright © 1965 by McGraw-Hill, Inc. All Rights Reserved.Printed in the United States of America. This book, or partsthereof, may not be reproduced in any form without permission ofthe publishers. Library of Congress Catalog Card Number 65-17497

The dynamic character of the vacuum industry caused by the

ever -increasing variety of applications, as well as advances in tech-

nology, clearly presents the need for a current text on vacuum science

and engineering. On two other occasions in the past the author,

Dr. C. M. Van Atta, in conjunction with the Kinney Vacuum Division

of The New York Air Brake Company, saw this need and supplied the

industry with The Design for High Vacuum Systems in 1945 and a

revised edition under the same title in 1958. The presence of manyof these worn, dog-eared manuals on engineers' and scientists' desks,

as well as the great demand for new and replacement copies, stands

as testimony to Dr. Van Atta's success in meeting the needs of prac-

titioners in the field.

By comparison, this new effort

—

Vacuum Science and Engineering—is far superior to and is certainly much more comprehensive than the

prior book. We believe that Dr. Van Atta has achieved in this new

writing a complete and up-to-date coverage of his subject, which

should again meet the needs of the industry and become a standard

text and reference for all those who wish to study or practice in the

field of vacuum science and engineering.

It has been a privilege for the Kinney Vacuum Division to encourage

and support this work. It is with admiration and respect for the

eminently qualified author that we submit this book for your use.

J. E. Chappell, General Manager

Kinney Vacuum Division

The New York Air Brake Company

66854

23456789-MP-9876

PREFACE

Over the past forty years vacuum technology has evolved from an

incidental but essential tool of scientific research to a rapidly growing

branch of engineering. In the 1930s the principal engineering appli-

cation of vacuum technology was in the manufacture of light bulbs

and radio tubes, for which processes ingenious equipment wasdeveloped largely by an empirical approach to the problems of evacu-

ating and surface conditioning. The transition from a research tool

to engineering application was greatly accelerated during WorldWar II, particularly by the multilateral attack on the release of

atomic energy by the Manhattan Project. Many divisions of that

project required the development of vacuum equipment of morediverse and greater capabilities than had ever been contemplated

previously. Subsequently the design and construction of large

particle accelerators for nuclear and high-energy physics and the

development of such processes as vacuum coating, distillation, andmetal degassing made further engineering applications of the vacuumtechnology developed during the war. More recently the require-

ments of controlled thermonuclear research and space simulation have

converted to an engineering scale the techniques of ultrahigh vacuumwhich had previously been applied only to small scale laboratory

experiments.

The process of evolution and growth of vacuum engineering is by nomeans complete. Requirements in many fields of research andmaterials processing are even now inadequately met, either becausethe desired vacuum conditions cannot be reliably attained, or becausethe cost of doing so is excessive. Improved methods of vacuumpumping, surface degassing, and the measurement of low pressuresare needed to meet these present requirements. The role of sorption

(adsorption, absorption, and chemisorption) on surfaces is imperfectly

understood, so that significant further progress will depend upon aconcerted experimental and theoretical effort to understand the basic

phenomena involved in the interaction between gases and surfaces atlow pressure.

Vlll PREFACE

In Vactmm Science and Engineering the objectives are to give in

fairly classical form the scientific basis of vacuum technology, to

describe in some detail the performance characteristics and limitations

of vacuum pumps, gauges for measuring gas pressure, and other

components of vacuum systems, and finally to provide design criteria

in sufficiently general form to be useful in designing vacuum systems

for a wide range of applications. Throughout the text an effort has

been made to describe in some detail the physical processes which

determine the operating features of the various devices which are

discussed. The object in doing so has been to give the reader not

merely a catalogue of typical vacuum components and perform^ance

data, but in addition a basis for judging the importance of various

phenomena which occur in vacuum systems. It is my belief that only

by this approach can one provide guidance for the optimization of

the design of vacuum systems for a variety of uses.

Aside from my own experience in large scale experimental research

and industrial vacuum development, I have drawn heavily upon the

expanding technical literature dealing with vacuum technology.

The emergence of the published proceedings of the American VacuumSociety and its predecessor organizations, and those of the Inter-

national Organization for Vacuum Science and Technology, as well

as such journals as Vacuum (Pergamon Press, London), Le Vide (la

Societe Francaise des Ingenieurs et Techniciens du Vide, Nogent-sur-Marne (Seine) France), and Vakuum-Technik ( Springer-Verlag

OHG, Berlin) has greatly eased the task of locating literature on newdevelopments in vacuum technology. With the kind cooperation of

Dr. J. H. Leek, I have found his excellent book. Pressure Measure-ment in Vacuum Systems (published for the Institute of Physics andthe Physical Society by Chapman and Hall, Ltd., London), most help-

ful in writing Chapter 3 of the text.

It is with deep appreciation that I acknowledge the incentive andsupport provided by the New York Air Brake Company for under-taking the task of writing a book of this character. The critical

comments of R. R. Cyr and Z. C. Dobrowolski of the Kinney VacuumDivision of the company contributed significantly to the final version,

particularly of Chapters 5, 6, 7, and 8 of the text. I am deeplyindebted to Miss Margaret R. Thomas, who not only typed the manu-script with its many revisions, but also maintained order in the grow-ing lists of references, permissions, and credits. I also wish to thankthe many authors, publishers, and vacuum equipment manufacturerswho have responded so generously to requests to use illustrative

material and who, in many cases, have provided the glossy printsnecessary to reproduce photographic illustrations.

C. M. Van Atta

CONTENTS

Foreword

Preface

Chapter 1. The Nature and Behavior of Gases

1-1. The General Gas Law ......1-2. Molecular Constitution and Kinetic Theory of Gases

1-3. Pressure Related to the Average Molecular Kinetic Energy1-4. The Maxwell-Boltzmann Distribution Law1-5. Velocity of Sound in a Gas1-6. Flow of Molecules through a Hole1-7. Molecular Mean Free Path .

1-8. Van der Waals' Equation of State

1-9. Dependence of Viscosity on Molecular Diameter

BEFEBENCES ......Chapter 2. Gas Flow

2-1. Gas Flow in Vacuum Systems2-2. Pumping Speed and Conductance2-3. Viscous Flow—Poiseuille's Law .

2-4. Pressure Drop Formula2-5. Turbulent Flow in Vacuum Systems2-6. Correction to Poiseuille's Law Due to Surface Slip

2-7. Gas Flow in the Transition Pressure Range .

2-8. Gas Flow at Low Pressure ....2-9. Conductance of a Long Tube at Low Pressure

2-10. Conductance of an Aperture2-11. Conductance of a Tube at Low Pressure Corrected for End Effect

2-12. Clausing and Monte Carlo Corrections to the Knudsen Conductance

Formulas .........2-13. Summary of Gas-flow and Conductance Formulas

RErEBENCES .........t^* Chapter 3. Pressure Measurement in Vacuum Systems

3-1. Liquid Manometers ........3-2. The Diaphragm Manometer ......

v

vii

1

4

5

8

11

12

13

15

18

22

23

23

26

30

31

34

36

43

44

47

49

51

57

62

63

65

X CONTENTS

3-3. The Dubrovin Gauge

3-4. The McLeod Gauge .

* 3-5. Thermal Conductivity Gauges

3-6. Hot-cathode Ionization Gauge

)C_3-7. The Bayard-Alpert Ionization Gauge3-8. Hot-cathode Magnetron Ionization Gauge

3-9. Magnetically CoUimated Electron Beam Ionization

3-10. Cold-cathode Ionization Gauges .

3-11. The Alphatron Gauge ....^3-12. The Knudsen Radiometer Gauge

3-13. Calibration of Vacuum Gauges

3-14. General Remarks on Ambiguities of Pressure

Vacuum Systems ....KEFBBBNCES ......

Gauge

Measurement in

Chapter 4. Vacuum Analyzers and Leak Detectors

4-1. Magnetic-deflection Mass Spectrometers

4-2. The Omegatron Mass Spectrometer

4-3. Linear High-frequency Mass Spectrometers

4-4. Halogen Leak Detector

4-5. Leak-detection Techniques .

BErBBBNCES .....Chapter 5. Mechanical Vacuum Pumps

5-1. Functions of Mechanical Pumps ......5-2. General Features of Oil-sealed Mechanical Pumps .

5-3. Pumping Speed of Oil-sealed Mechanical Pumps5-4. The Effect of Condensable Vapor upon Mechanical Pump Perform

ance .........5-5. Gas Ballast .........5-6. Other Methods of Preventing Contamination by Condensables

5-7. Mechanical Booster Pumps ......5-8. Analysis of Mechanical Booster-pump Performance

5-9. Computed Performance Curves for Mechanical Booster Pumps5-10. Measured Performance Curves for Mechanical Booster Pumps5-11. Overheating of Mechanical Booster-pump Rotors .

5-12. Vapor Compressor Action of a Mechanical Booster Pump5-13. Molecular-drag Pumps ......5-14. Axial-flow Molecular Turbine Pump ....

RErBBENCBS ........Chapter 6. Vapor-jet Vacuum Pumps

,6-1. The Steam Ejector

6-2. Diffusion Pumps . . .

6-3. Theoretical Compression Ratio for a Vapor-jet Pump6-4. Working Fluids for Diffusion Pumps

69

78

90

103

107

111

113

122

123

124

128

131

133

143

152

159

161

167

169

169

172

177

179

183

185

186

194

199

202

204

205

214

218

219

227

230

240

CONTENTS XI

6-5. Pumping Speed of Diffusion Pumps 249

6-6. Limiting Forepressure for Diffusion Pumps ..... 254

6-7. Factors Contributing to the Ultimate Pressure of a Diffusion Pump 257

6-8. Fractionation and Purging........ 268

6-9. Resume of Diffusion-pump Performance ..... 272

BBFERENCBS .......... 272

Chapter 7. The Measurement of Pumping Speed

7-1. Alternative Definitions of Pumping Speed ..... 274

7-2. Measurement of Gas Flow ....... 277

7-3. Mechanical Pump Speed Measurements .... 291

jfJ:"^-Measurement of the Pumping Speed of Diffusion Pumps 293

RBFBBENCES . . . . 302

^^-1.

Chapter 8. The Design of Vacuum Systems

The Vacuum Vessel ......... 303

8-2. Demountable Seals 307

8-3. Motion Seals 313

8-4. Vacuum Valves 318

8-5. Vapor Baffles and Traps 328

8-6. Absorption Traps 341

8-7. The Pumpdown Time 348

8-8. Selection of Vacuum Components 358

BEFEBENCES . 362

Chapter 9. Ultrahigh Vacuum

9-1. The Dominance of Surface Phenomena ..... 363

9-2. High-temperature Bakeout . 365

9-3 Metal Gaskets ..... . 370

9-4 Bakeable Valves .... . 378

9-5 Two -region Vacuum Systems . 382

9-6 Getter-ion Pumping .... . 385

9-7 Absorption Pumping.... . 398

9-8 Evaporative Deposition of Reactive Metals . 401

9-9 Cryogenic Pumping .... . 408

9-10 Ultrahigh-vacuum Systems

BEFEBENCES .....APPENDIX I . . . •

APPENDIX II . . .

APPENDIX III .....APPENDIX IV . . . •

APPENDIX V . . . • •

. 434

. 435

. 439

. 440

. 441

. 442

. 445

Author Index.. . 447

Suhject Index . . . . 451

COMMONLY USED SYMBOLS

In some cases it has not been convenient to avoid the use of a symbol for

more than one purpose. The most prevalent meaning of each commonly

used symbol is defined in the following list. Exceptions are clearly indicated

in the text.

a radius of aperture or tube

A area

B magnetic flux density

c nozzle coefficient

C conductance

Cj, specific heat at constant pressure

C^ specific heat at constant volume

D diameter of aperture or tube

e electronic charge

E energy, electric field intensity

/ molecular sticking coefficient, frequency

¥ force

h, height of a column of liquid

R Ho coefficient

ij^ positive ion current

i_ electron current

1 electrical current

Ic gas constant per molecule (Boltzmann constant)

/v conductance factor

L length

m mass of molecule

M molecular weight

n number of molecules per unit volume

Wmoi number of molecules in one mole

N total number of molecules present

p probability of ionization

pressure

gas flow in molecules per second

P

COMMONLY USED SYMBOLS

QRRg

Res

S

t

gas throughput, PdVjdtgeneral gas constant

gas constant per mole, w,,,^]/^

Reynolds numbersensitivity

pumping speed

displacement speed of a mechanical pumppumping speed at the inlet of a pumptime

T temperature

u drift velocity of a gas

U velocity

V velocity

F volume

w mass flow

W power, mass of gas

z number of electronic charges per ion

Z atomic number

a accommodation coefficient

y ratio GJC^e slip coefficient, efficiency

r] viscosity

A mean free path

A free molecular heat conductivity

V number of molecules impinging on one square centimeter of surface in

one second

I molecular diameter

p density, mass per unit volumea collision cross section

T period


I

CHAPTER 1

THE NATURE AND BEHAVIOR OF GASES

1-1. The General Gas Law. Our understanding of the behaviorof permanent gases is based upon the experiments of Boyle, Charles,and Gay-Lussac which lead to the general gas law. Experiments byBoyle resulted in the conclusion that the volume of a body of gas atconstant temperature is inversely proportional to the pressure, whichis equivalent to the expression

PV = const (1-1)

where the pressure is defined as the force per unit area exerted by thegas on the walls of the containing vessel. Charles and Gay-Lussacobserved that if the volume of a body of gas is kept constant and itstemperature varied, the pressure increases linearly with the temper-ature, so that

^1 = -Po(l + aT) (i_2)

in which T is the temperature on any chosen scale, such as centigradeF^is the pressure of the body of gas at zero on the same temperaturescale, and « is a constant. If Eq. (1-2) is multiplied by V^, the initialstandard volume of the gas sample,

PiFo = PoFo(l + ocT) (1.3)

Then if the volume is changed to some other value, such as V, we haveaccordmg to Boyle's law

PV = P„F„(1 + aT) (1.4)

which can be written as

PV = P.V^T + 1/a) (1.5)

The experimental fact is that if the temperature is measured on thecentigrade scale, 1/a = 273.I6°C, that is, the volume of a body of

T^^o^''?*^^^ changes by an amount equal to 1/273.16 of its value

at C for each degree change in temperature. This constant isessentially the same for a large number of gases (hydrogen, helium

2 VACUUM SCIENCE AND ENGINEERING

nitrogen, oxygen, and others) and therefore has very broad signifi-

cance. If one chooses a new temperature scale such that —273.16 C

is zero, then one can write

PV = PoFoaT (1-6)

where now the temperature is measured on the absolute centigrade,

or Kelvin, scale.

The implication of Eq. (1-6) is that the pressure exerted by a gas

at constant volume approaches zero as the temperature approaches

0°K. Although many common gases follow Eq. (1-6) over a wide

Table 1-1. Molecular Weights of Some Common Gases*

Chemical Scale

Chemical formula Molecular weight

Ha 2.016

He 4.003

Xe 20.18

^'2 28.02

Air (mean) 28.98

O2 32.00

Ar 39.94

CO2 44.01

CL 70.91

* See, for example, American Institute of Physics Handbook (McGraw-Hill

Book Company, New York, 1957), pp. 7-9-7-12.

range of temperature and pressure, all real gases depart from this

relationship at sufficiently large values of the pressure and low values

of the temperature. Thus only for an ideal gas would the pressure

actually approach zero as the temperature approaches absolute zero.

Returning to Eq. (1-6), since at constant temperature the product

PV for a given body of gas is constant for a given mass of gas, andsince twice the volume at the same pressure contains twice the mass,

the product PF is proportional to the mass of the body of gas. Thusthe product PF in Eq. (1-6) is proportional not only to the absolute

temperature but also to the mass of the body of gas W, and we maywrite

PV = P,V„^T WRT (1-7)

where i? is a constant of proportionality. Equa,tion (1-7) is one formof the general gas law which describes the behavior of an ideal gas

and is approximately correct for many common gases over a widerange of practical conditions.

Further understanding of the nature of gases was contributed byAvogadro, who demonstrated experimentally that at the same

THE NATUEE AND BEHAVIOR OF GASES 3

temperature and pressure the mass of a standard volume of gas is pro-portional to its chemical combining (or molecular) weight. Consistentwith Avogadro's law, precise experiments have shown that understandard conditions of temperature (0°C or 273.16°K) and pressure(normal atmospheric pressure defined as 760 torr) 1 gram molecularweight of any gas occupies a volume of 22,415 cm^. This is the volumeoccupied by 32.00 g of oxygen (0^) at STP standard temperature andpressure, which is the arbitrary standard on the chemical scale ofmolecular weights. A partial list of molecular weights of somecommon gases is given in Table 1-1. A more comprehensive table ofmolecular weights of gases is given in Appendix I.

By referring to Eq. (1-7) we can now write the general gas law interms of the molecular weight of the gas, as follows:

^^=|^oT (1-8)

where W = mass of the sample of gasM = molecular weight of the gasB„ = universal gas constant per mole

The ratio W/M is the number of moles (gram molecular weights) ofthe gas present. The numerical value of E^ depends upon the unitsof mass, pressure, volume, and temperature used. If the pressure is

measured in torr, the volume in liters (1 hter = 1,000.027 cm^), andthe temperature in degrees Kelvin, then for 1 mole (W/M = 1) of gas

PV = R,T (i-sa)

Under standard conditions

so that E(, =

P = 760 torr

F = 22,415/1,000.027 = 22.415 liters

T = 273.16°K = 0°C

PV 760 X 22.415

T 273.16= 62.364 torr liters/°K g mole

For the common choices of units the numerical value of E^ is given inTable 1-2. In many situations the mass of a body of gas is of noconcern, but the changes in pressure, volume, and temperature are ofinterest. In this case a convenient form of the general gas law is

PiFi P2F,(1-9)

which follows directly from Eq. (1-8), since for a given body of gasPVjT is a, constant.

4

Table 1-2.


KuMERicAL Values of Bg Gas Constant peb Mole fob Vabious

Systems of Units* f

p V T i?„

dynes/cm^ cm^ "K 8.314 X 10' ergs/°K

newtons/m^ mS °K 8,314 joules/°K

torr cm^ °K 62,364 torr cm'/°K

torr liters °K 62.364 torr liters/°K

atm cm' "K 82.057 atm cm'/°K

psi ftS "R 1,546 lb ft/°R

* In engineering units, 1 lb mole of gas occupies 359 ft' at 32°F and atmos-

pheric pressure (14.67 psi). The Bankine absolute temperature scale is based

upon the Fahrenheit scale for which absolute zero temperature is — 459.69°F.

Thus T °R = T °F + 459.69 just as T °K = T "C + 273.16.

t Sources: W. E. Forsythe, Smithsonian Physical Tables (Smithsonian Insti-

tution, Washington, D.C., 1954, 9th rev. ed.; T. Baumeister (ed.), Marks'

Mechanical Engineers' Handbook (McGraw-Hill Book Company, New York,

1958), 6th ed.

1-2. Molecular Constitution and Kinetic Theory of Gases.

From the time of the Greek philosophers the concept that all matter

is made up of tiny indivisible particles called molecules had been

sporadically put forward to explain one or another of the observed

properties of matter . On the basi s of the experimental results reported

by a number of independent investigators, Avogadro concluded that

equal volumes of all gases under the same conditions of temperature

and pressure contain equal numbers of molecules.

We have already seen that under standard conditions (760 torr

pressure and 0°C) a gram molecular weight of any gas fills a volume of

22.415 hters. The number of molecules contained in this standard

sample of gas is obtained from the precise measurement of the faraday,

F = 96,488 coulomb

the electrical charge necessary to deposit a gram equivalent of a

substance in electrolysis, and the charge on an electron,

e = 1.602 X 10-19 coulombs

which is the unit of ionic charge,

determined quantities

96.488''mol"^.^i —

1.602 X 10-1-

The ratio of these experimentally

6.023 X 1023

is known as Avogadro's number; it is the number of molecules in a

gram molecular weight of a substance, and is therefore the number of

THE NATURE AND BEHAVIOR OF GASES 5

molecules present in 22.415 liters of any gas under normal conditions.The number of molecules in a unit of volume of gas under normalconditions is therefore

ti,

6.023 X 1023=^^^Y5 = ^-^^^ ^ ^^" molecuIes/cm3

It is worthwhile pausing to note the magnitude of this number. Itsmeaning can perhaps be visualized best by noting that if the moleculesin a cubic centimeter of gas under standard conditions were arrangedat the corners of tiny cubic cells, the number of such cells in a centi-meter length would be

(2.687 X lO^")!^ <^ (27 X 10i8)'/iS = 3 x 10"

sothatthedistancebetweenmolecules would be about 3.3 x 10"' cm,which is approximately the average distance between molecules for agas under standard conditions.

Actually, in a gas the molecules are not arranged in a simple patternbut are moving randomly relative to one another. During theirmotion the molecules suffer collisions between themselves and bounceoff one another. The average distance which the molecules movebetween collisions is called the mean free path (A). The moleculesalso impinge on the walls of the confining vessel and bounce back (orare reemitted) from the wall. The momentum transfer from themolecules to the walls of the vessel produces the outward forceexerted by the gas upon the walls of the vessel. This force per unitarea is precisely the pressure which appears in the general gas lawdiscussed in the previous section.

The molecules of an ideal gas may be considered as a first approxi-mation to be elastic spheres about 10"* cm in diameter. The randommotion of the molecules consists of motion in all possible directionswith various individual molecular velocities. As will be shown, thetemperature of the gas determines the mean square velocity (i.e., theaverage value of the square of the velocity) for any particular type ofmolecule and the average kinetic energy for molecules of all types ina mixture of gases. The kinetic theory of gases consists of thestatistical mechanical treatment of the microscopic molecular motionsand leads to a basic understanding of the gross behavior of a gas interms of molecular motions.

1-3. Pressure Related to the Average Molecular KineticEnergy. Consider a box of rectangular cross section filled with apure gas such that the density in the box is n molecules/cm', eachmolecule having a mass of m grams. The two walls of the boxperpendicular to the x axis suffer collisions by molecules by reason of


their x component of velocity v^. If the molecules in the box are

moving in a random manner, half will be moving with positive v^

and half with negative v^. Those moving in the positive x direction

with a specific value of v^ will strike the wall in a time ht if they are

contained in a sheet of thickness v^ dt adjacent to the wall. The

number striking a unit area of the surface in the time dt is thus

n^v^ ?)tj2, so that the number striking a unit area in a unit of time is

If each molecule on striking the surface of the contamer experiences

an elastic collision, the magnitude of v^ does not change on collision

with the wall but the direction reverses. The other components of

velocity, f„ and v^, are not changed in the collision since the surface

under consideration is parallel with the yz plane. The change in

momentum of a molecule on striking the wall is thus 2mv^. If in the

above discussion n^ is the number of atoms with x components of

velocity in the range between v^ and v^ + dv^, then the number

striking a unit area each second with the velocity in the range dv^ is

n^v^ dvj2. Therefore the rate of change of momentum for this group

of molecules is

n„v^ dv^[2mv^ n.mvj dv^

For the entire distribution in v^, the total rate of transfer ofmomentum,

and therefore the force per unit of area, is

f*CC

Jo

2 dv^ = nmv^^ (1-10)

where v^^ is the mean square velocity in the x direction. Similarly

P,

nmVy^

and nmv.

Since the motion is random there is no difference in the average

motion in the various coordinate directions, so that

«,/ = V,

V^ = VJ' + V^'' + V,

Vj = }/3V^

Also since

then

and the pressure measured in any direction

P = P^ = P^ = P,= y^nmv^ (1-11)

From this result it is evident that the pressure exerted by a gas is


proportional to the kinetic energy of the molecules contained in aunit volume nmv^j2. If the mass of the molecules is measured ingrams and their velocities in centimeters per second, the pressure is

measured in dynes per square centimeter.

Comparing the expression for the pressure given in Eq. (1-11) withthat of the general gas law given in Eq. (1-8), one concludes that

P = WVM R.T ^/snmv^

If this expression is divided by 2w/3 the result is

since

Introducing

y^mv' = -

i?n

2 VM n 2 Wmoi

Wmol = K —: Ww

k = —- = 1.3805 X 10-i«erg/°K

(1-12)

(1-13)

(1-14)

known as the Boltzmann constant, which is the gas constant permolecule, Eq. (1-13) yields

E = Yzniv^ = %kT (1-15)

i.e., the average kinetic energy of a molecule is proportional to thetemperature, and the energy associated with each coordinate direction(x, y, z) in its motion is therefore A;T/2. Combining (1-15) with (1-12)results in the important fundamental expression

P = %n(}4mv^) = 34n(%kT) = nkT dynes/cm^ (/^bar)

(1-16)

The derivation of the preceding relationships from elementarykinetic theory does not depend upon the molecular mass of the gasinvolved. Remembering that from Avogadro's law equal volumesof gas under the same conditions of temperature and pressure containequal numbers of molecules, it follows that for two different gases

y2miV^^ = J^ma^a^ = /4kT (1-17)If we now define

V, = («;2)'^ (j.jg)

as the root-mean-square velocity, then

^ =W = [m-J(1-19)

Thus, in general, the root-mean-square velocities of molecules of


different gases at the same temperatures are inversely proportional

to the square roots of their molecular masses, or of their gram molecular

weights.

From Eq. (1-11) P = nrnv^fZ, so that the value of the root-mean-

square velocity of the molecules in terms of macroscopic parameters is

(V i\M\nml \ p

(1-20)

where p =nm\s the density of the gas in grams per cubic centimeter

and the pressure is in dynes per square centimeter or microbars

(see Sec. 3-1).

1-4. The Maxwell-Boltzmann Distribution Law. In the

discussion of the previous section it was not necessary to inquire into

the distribution in velocity which the molecules of a gas might assume

as a result of mutual collisions. It is clear that even if the molecules

of a gas were to have equal but randomly directed velocities the sub-

sequent elastic collisions would quickly introduce a wide distribution

in velocity. Since in an elastic collision the total kinetic energy of the

particles is preserved, the quantity m{v^^ + v^)l2 is the same before

and after each molecular collision, even if v^ and v^ must change to

satisfy the conservation of momentum. For a body of gas composed

of a large number of molecules, therefore, (m/2) ^ «' remains constantn

even though the individual molecular velocities change because of

mutual collisions. The root-mean-square velocity and therefore also

the pressure exerted by the gas are independent of the velocity

distribution which may result from mutual collisions. Some features

of gas behavior, however, do depend upon the form of the equilibrium

distribution in velocities which gas molecules assume, so that a

knowledge of the velocity distribution is essential to a complete

understanding of the properties of a gas.

The actual distribution in velocity of the molecules of a gas was

deduced by Maxwell and Boltzmann by arguments beyond the scope

of this text. The Maxwell-Boltzmann distribution law expressed in

terms of the velocity in a randomly chosen direction is

^ dn _ 4

\2kTjl.-mv'ltkT (1-21)

The quantity dnfn is the fraction of the total number of molecules in

the velocity range between v and v + dv, bo that dnjn dv is the frac-

tional number of molecules in this velocity range per unit of velocity

range. A plot of /^ is shown in Fig. 1-1. The distribution function

f^ goes to zero at v = because of the w^ term, since at « = the


exponential term is e» = 1. It also goes to zero as v approachesinfinity because of the dominance of the exponential term. For all

values of v between zero and infinity /^ is positive and therefore musthave a maximum value, which is the most probable value of thevelocity.

0.2 0.4 0.6 08 1.0 1.2 14 16 1.8 2.0 22 24 26 2.8 30

V in units of vp

Fig. 1-1. A plot of/„, the Maxwell-Boltzmann velocity distribution function.

By differentiating /^ with respect to v and setting the result equalto zero, the most probable value of the velocity can be determined.

dv

4 / mY"

^\2fcy/ kT ^ '

so that _ l2kTY* \ TO /

(1-22)

The meaning of the most probable value of the velocity is that moremolecules have this value than any other value of the velocity. Themost probable velocity is not, however, the arithmetic average valueof the velocity, which is calculated as follows

/•oo

dv2 l2kT\^

1.128t;.„ (1-23)

Finally, the mean square velocity is obtained from the Maxwell-Boltzmann distribution function by a similar averaging process.

W =:

J»oo

dv

= 3kTTO

(1-24)

IQ VACUUM SCIENCE AND ENGINEEBING

from which the average molecular kinetic energy is

(1-25)

consistent with Eq. (1-15), which was arrived at without consider-

ation of the details of the distribution law. Also from Eq. (1-25)

we have for the root-mean-square velocity

Which of the above velocities is of interest as representing the average

behavior of a gas depends upon the process under consideration.

Table 1-3 provides a convenient summary of these representative

velocities and the numerical factors for converting from one to another.

Table 1-3. Most Pbobable, Average, and Root-mean-squarb Velocities

Equation

2 /2J;TV^^av = —A

1

1.128

1.225

0.887

1.086

XV.

0.816

0.921

The conversion factors in Table 1-3 are so near unity that for many

approximate calculations, it is not necessary to distinguish between

the most probable, the average, and the root-mean-square velocities.

The basic factor (2A;T/m)« appears in all three with numerical factors

which are not very different from one. The average molecular weight

of air (28.98 g/mole) divided by Wmoi, the number of molecules in a gram

molecular weight, gives for the average mass of an air molecule

28.98

6.023 X 10^34.81 X 10-" g

Using this average molecular mass and the value of h given in Eq.

(1-14), the most probable velocity of an air molecule at 68°r ( = 20°C

= 293°K) is

^ (

2 X 1.371 X 10-^- X 293f ^^^ ^ ^^,

\ 4.81 X 10-23 /


Correspondingly for this case

v^y = 1.128 X 4.09 X 10* = 4.61 x 10* cm/sec

and V, = 1.225 x 4.09 x 10* = 5.01 x 10* cm/sec

In general, the above basic factor may be written in terms of the massof a molecule of unit molecular weight, m^ = 1.66 x 10-^*

g

/2kTY_ /2kY( TY

2 X 1.38 X io-i«\^/y

1.66 X 10-2*

•vA/ y Y^

( T\A= 1.29 X 10*177) cm/sec (1-27)

when T is expressed in degrees Kelvin and M in grams per mole.1-5. Velocity of Sound in a Gas. A velocity closely related to

those discussed above is the velocity of sound in a gas, which accordingto elementary texts on sound is given by

(t7

in which

(1-28)

(1-29)

where C^ is the specific heat of a gas at constant pressure and G^ is

the specific heat at constant volume. According to the kinetic theoryof gases the value of y is simply related to the number of degrees offreedom of the molecule in terms of the independent coordinates ofmotion (three represented by x, y, and 2), the axes of rotation, and themodes of vibration. The result is that for the common gases, themolecules of which are monatomic (one atom per molecule), diatomic(two atoms per molecule), or polyatomic (more than two atoms permolecule), the predicted values of y are respectively % = 1.66, % =1.40, and % = 1.33. The observed values of y for a number ofcommon gases are given in Table 1-4. The velocity of sound is

_ lykTf\ m I

- (ir- (1-30)

J2 VACUUM SCIENCE AND ENGINEEKING

For air at 68°F = 20°C, therefore,

v^ = 0.837 X 4.09 X 10* = 3.43 X 10* cm/sec

= 1121 ft/sec = 770 mi/hr

and in general the speed of sound in a gas is of the order of three-

fourths the average speed (vav) of the gas molecules. It is evident

from Eq. (1-30) that the sound speed is independent of the density (n)

of the gas, but is proportional to the square root of the temperature

as is the average molecular velocity.

Table 1-4. Observed Values of y fob Common Gases

Diatomic

Air 1-401

Hydrogen 1-408

Nitrogen 1-402

Oxygen 1-400

Carbon monoxide ... . 1.401

Monatomic

Helium 1-63

Argon 1.667

Krypton 1-66

Mercury (vapor) . . 1.66

Polyatomic

Ozone 1-29

• Water (vapor) .... 1.305

Carbon dioxide ... . 1.300

Ammonia 1.336

1-6. Flow of Molecules through a Hole. A quantity of some

interest in vacuum technology is the number of molecules which

strike a surface in a unit of time. It can be shown that the number

of gas molecules which impinge on each unit of surface area of the walls

of a containing vessel during a second is given by^-*

V = yinvav ~ 2^1 m /

molecules/cm^ sec (1-31)

in which the value of v^y given in (1-23) is substituted. The above

result can be applied to the calculation of the rate of flow of molecules

through a tiny hole in a very thin plate. If a tiny hole of area, A is

cut in the thin wall of the vessel beyond which the gas density is

zero, the rate at which molecules of gas leave the vessel is

^ = ''^=2^1"-^)nA /2kT\

2^\~m"j

= 3.64 X W^iTIMY'^nA molecules/sec (1-32)

References indicated by superscript numbers are listed at the end of the

chapter.

THE NATURE AND BEHAVIOB OF GASES 13

by reference to Eq. (1-27) when n is in molecules per cubic centimeterand A is in square centimeters. The volume of gas at the pressure

in the vessel escaping each second is obtained by dividing the molec-ular flow rate q by the density n, so that

dV q Av JT\^= 3.64 X 10^ — A

dt n n \M cm^/see (1-33)

which for air at 0°C would be

dV_

11= 3.64 X 10^

/ 273 \^

\28.98/

11.2^ liters/sec (1-34)

For the flow rate through a hole to agree with this value the thicknessof the wall at the point where the hole perforates the wall and thediameter of the hole must be small as compared with the mean freepath for collisions between the molecules, a dimension to be definedand evaluated in the next section.

1-7. Molecular Mean Free Path. The concept of the mean free

path of the molecules in a gas is of considerable practical importancein defining the behavior of a gas in a vacuum system. As waspreviously mentioned, the molecules of a gas may be considered to

act in a first approximation as if they were elastic spheres of diameterof the order of 10-^ cm. Let us designate the molecular diameter ofa particular gas as | and attempt to calculate the distance a moleculewill travel on the average before undergoing a collision with anothermolecule.

A molecule having a velocity v moves a distance v dt in the time dt.

The molecule under consideration suffers a collision with anothermolecule if anywhere its center is within the distance f , the moleculardiameter, of the center of another molecule and therefore sweeps outthe volume

dV=TTPvdt (1-35)

Since there are n molecules/cm', the volume associated with onemolecule on the average is l/n cm^. Thus when the volume in Eq.(1-35) becomes equal to l/n, it must contain on the average one othermolecule and a collision has occurred. That is, for a collision to occuron the average

1- = TTi^VT, (1-36)

when dt = t„, the average time between collisions.


The mean free path is the distance traveled, that is, A = vt^

corresponding to Eq. (1-36) and is therefore

A =TTWl*

(1-37)

Although the above derivation gives the correct general dependence

of the mean free path on the density and molecular diameter, it is

oversimplified by not taking into consideration the fact that the

molecules have a distribution in velocity and that not only the refer-

ence molecule but also all others are in motion. The exact calcu-

lation, ^ which will not be given here, introduces a factor of 25^ in the

denominator so that the corrected value for the mean free path is

kT

P =nkT

(1-38)

since from (1-16)

The mean free path is thus inversely proportional to the molecular

density and to the square of the molecular diameter. Alternatively,

it is proportional to the temperature and inversely proportional to

the pressure. As the pressure in a vacuum system decreases during

pumpdown, the mean free path changes from the order of 7 x 10"* cm

at atmospheric pressure to about 5,000 cm at a pressure of 10"* torr.

Values of the mean free path for various gases, determined from Eq.

(1-38) using values of the molecular diameter f deduced from two

different types of measurement, are given in Appendixes II and III.

The mean free path is a parameter which enters into the determina-

tion of the flow of gases under the influence of pressure difference. If

the mean free path is short as compared with the diameter of a tube

through which the gas is flowing, collisions between molecules will

predominate and collisions with the walls of the tube will occur only

for those molecules which are close to the walls. The flow dominated

by intermolecular collision is referred to as viscous flow because the

flow pattern is that of a viscous fluid. However, if the mean free

path is long as compared with the diameter of the tube, collisions of

the molecules with the walls predominate and intermolecular col-

lisions are not important. In this latter regime the molecules moveindependently of one another and nothing like viscous flow occurs.

The molecules move randomly in straight lines, colliding with the

walls of the tube and proceeding in a chaotic manner. On the

average, more molecules move from a region of higher density (or

pressure) to a region of lower density for purely statistical reasons.

This process is referred to as molecular flow. When the mean free


path is of the same order as the dimensions of the tube, both types of

collisions are important and the flow is of intermediate character.

The range of pressure over which the flow is not strictly viscous or

molecular is referred to as the transition region. Flow rates for this

pressure regime will be discussed in a later section.

1-8. Van der Waals' Equation of State. From the general gas

law as stated in Eq. (1-8) one concludes that at T = 0°K and finite

pressure the volume of the gas becomes zero. This conclusion is in

contradiction to the concept of a definite molecular diameter, i,

discussed in the previous section. Clearly the gas cannot be compressedto a volume smaller than that occupied by the

tightly packed molecules without destroying the __

structure of the molecules themselves. Even be-

fore this extremely compact arrangement of the

molecules is reached the assumption of entirely

random motion would no longer be valid because

of the restrictive effect of collisions between closely

spaced molecules. Moreover, the finite size of

each molecule eliminates a certain amount of

volume which cannot be occupied by anothercolliding molecule, no matter how low the molecu-lar density may be. Consider a molecule A whichundergoes a collision by molecule B moving in a given direction, asshown in Fig. 1-2. The center of the molecule B can lie anywhereoutside the hemisphere of radius |, the molecular diameter, but can-not lie inside this hemisphere because of the collision process. Thecenter of molecule B is therefore excluded from the volume

Fig. 1-2. Exclusionvolume in molecular

collisions.

V^ = %7Ti^ (1-39)

Such an exclusion volume is associated with each molecule so that thevolume available for random motion of the molecules is not V, thevolume of the vessel, but is V - b where

b = VzttNP (1-40)

which is a volume four times that of the N molecules present.The general gas law is also based upon the assumption that there are

no forces acting between the molecules of a gas until a collision occursand that the force acting between the molecules during impact is anelastic force similar to that between two colliding billiard balls. How-ever, it is known, for example, from the behavior of condensed gasesthat definite attractive forces act between molecules. Surface tensionIS an evidence of the existence of such forces. The origin of the


attractive force is the mutual electrical polarization of one molecule

by another and the attraction between the resulting electrical dipoles.

This attractive force is relatively long-range in terms of the molecular

separation distances over which it remains effective and is referred to as

the Van der Waals force.

Van der Waals, largely on an empirical basis, had proposed an

equation of state for gases of the form

{^-v)^^b) = RT (1-41)

which differs from the general gas law for perfect gases in the correction

term AjV^ added to the pressure due to the attractive forces between

the molecules and the subtraction of b from the volume to allow for the

region in space from which the molecules are excluded by one another

because of their finite dimensions. By multiplying out Van der Waals'

equation and rearranging terms one has

PV / A\A \ 1_

V(1-42)

plus terms of higher order such as b^jV, etc., which are negligible.

It has been shown* that Van der Waals' empirical equation (1-41) is

consistent with the equation of state for an imperfect gas calculated

from basic assumptions about the intermolecular forces to terms of as

high an order as we normally need to consider.

For our present purposes it is instructive to write Van der Waals'

equation (1-41) in descending powers of F as follows

F3 V^ + jVAb = (1-43)

This is a cubic in V for any given values of T and P. In Fig. 1-3 are

plotted typical isothermal curves (pressure versus volume) for various

values of temperature. For sufficiently small values of the pressure

and temperature there are three values of the volume, corresponding

to Eq. (1-43), for a given value of the pressure as represented by the

horizontal dotted line in Fig. 1-3 passing through the points i,j, and k.

However, when the temperature is sufficiently high the isothermal curve

has only one root. The critical point is that indicated at c where for

specific values of temperature, pressure, and volume all three roots of

the equation are equal. At this point

(7 _ 7^)3 = F* - 37^7, + 3FF,2 _ F/ = (1-44)


in order that all three roots be equal. Comparing the coefficients of

(1-44) with those of (1-43) we see that

3F. = 6RT.

3F.2 F„3:Ab

Po"

P,'

P,

from which the critical point is defined as that for which

F„ = 36A

27627'.=

8t7

276^(1-45)

Conversely, one can solve for A, b, and R in terms of the "triple point"

parameters and find that

F 8P F^ = 3F,''P, 6=-!-^ -R = ^7^' ° 3 3T,

(1-46)

Returning to the form of Van der Waals' equation given in (1-42),

it is evident that for large values of the temperature the term b in the

coefficient (6 — AjRT) dominates and the pressure is higher than that

of a perfect gas. Alternatively, when the temperature is very low,

the term AjRT dominates and the

pressure is less than that for a per-

fect gas.

In Fig. 1-3 the behavior of the

isothermal curves (dependence of

pressure on volume for a constant

value of the temperature) above

and below the critical temperature

is shown. Curves for tempera-

tures below the critical tempera-

ture represent three domains. Atthe high-pressure end of the curve

the substance is condensed in the

form of a liquid. When the pres-

sure has been reduced to a critical

value, some of the substance evap-

orates to form a vapor. From the

point i to the point k on the iso-

thermal curve the actual behaviorof the substance does not follow

the Van der Waals equation witha minimum and a maximum in the

pressure. In the mixture domain „ i o rr, •i it j nr i

• „,, Fig. 1-3. Typical Van der Waals iso-the pressure remams constant as thermal curves for various values ofthe volume is increased until all the temperature.


the liquid is converted into vapor. This is illustrated by the horizontal

straight line from i to k. After the liquid is all evaporated, the pressure

decreases as the volume is further increased in a manner somewhat

similar to the behavior of a permanent gas. In this third, or vapor,

domain the behavior differs from that of a permanent gas in that it does

not quite follow the general gas law since the Aj V^ and b terms of Eq.

(1-41) do not become negligible until the volume has become quite

large and the pressure small as compared with their values at the

point k.

At the critical temperature the isothermal curve passes through the

triple point where the region of liquid-vapor mixture has narrowed

down to a zero range in pressure. At all values of the temperature

above the critical temperature there is no condensation of the substance

into a liquid so that for all values of the pressure, no matter how large,

no condensation occurs. This is the condition in which the substance

is called a permanent gas. The higher the temperature above the

critical temperature the more nearly does the PV curve approach that

of a perfect gas as represented by the general law, Eq. (1-8).

All substances conform approximately to the behavior described

above, the difference being in the values of the parameters given in

Eqs. (1-45) and (1-46).

In Appendix II values of the critical temperature, the Van der Waals

parameters A and b, the molecular diameter | calculated by Eq. (1-40),

and the mean free path calculated by Eq. (1-38) are given for several

gases and vapors.

1-9. Dependence of Viscosity on Molecular Diameter.Because the molecules of a gas have an appreciable cross section for

collision determined by the molecular diameter discussed in Sec. 1-7,

the flow of a gas through a tube or hole due to a pressure difference is

characterized by a viscous drag. The viscosity of a gas can be derived

in terms of the molecular diameter, which also determines the meanfree path and the correction to the volume term in Van der Waals'

equation of state.

Viscous forces appear when there is a variation in the drift or flow

velocity of a gas from point to point. Such variations will occur

whenever gas flows through a tube because of the maintenance of a

pressure difference, the gas flowing from a region of high pressure to one

of low pressure. Our quantitative understanding of viscosity origi-

nated in the work of Newton, who assumed that the internal viscous

forces are directly proportional to the velocity gradient in the fluid.

Consider a body of gas, as shown in Fig. 1-4, between two parallel

plates separated by a distance w, with the lower plate at rest and the

upper plate pulled to the right with a force F. The drift velocity of


the gas in contact with the lower plate is zero, whereas that in contact

with the upper plate is m„, the velocity of the upper plate. The drift

velocity of the gas u at some intermediate point is proportional to the

distance y from the stationary plate, so that

- = — ory w w

(1-47)

The drift velocity u is superimposed upon the random velocity of the

molecules and in most physical situations is much less than the average

molecular velocity.

The assumption of direct proportionality for the above equation is

consistent with that of Newton and has been confirmed experimentally

for gases over a wide range of pres-

sure and for liquids. In the case

of a gas the uniform velocity gra-

dient can be understood in terms

of the transfer of momentum from

one layer of gas to the adjacent

layer. In order to approximate

the momentum transfer we note

that molecules on the average

move up or down because of their

random motions a distance A, the

mean free path. Molecules from a distance A above move down into

the layer under consideration with a momentum given by

y + ^(mu). = m Wy

w

'

W/^^X^^W^^^/^^X^/^/Z/W//^1 u. ^y

11/j%mMm^^^%^^%^^^%;^^,Fig. 1-4. Drift velocity distribution

due to viscous forces.

(1-48)

However, molecules from the layer at the height y — ^ also move into

the higher layer at y with a momentum

(mu)_ = m u„w

(1-49)

In the random motion one-third of the molecules may be regarded as

moving in the vertical direction and one-third each in the directions

parallel and perpendicular to the motion. Only the one-third movingm the vertical direction contribute to a transfer of momentum betweenthe layers. Of these one-half are moving upward and one-half down-ward. If Va,v is the average random velocity of the molecules, thenumber crossing an area A is the number contained in the volumeAva.yt and moving in the required direction. If the total number ofmolecules per cubic centimeter is n, then the number crossing from


above during the time A< is KnAv^v M and the momentum transfer is

I 3

Ap_^ = HnAva,v('mu)+ A< = Hnm Ave.yU„ A< (1-50)

Similarly, the transfer upward across the boundary due to molecules

moving upward is

A2)_ = }4nAva,y(mu)_ M = Hnm Avs.yU„ M (1-51)

The total increase in the momentum of the gas below the boundary is

the difference between these two quantities, so that

nmXAva,yU„,^p = ^p+ - AiJ_ =——— M (1-52)

Since the rate of change in momentum is the force acting on the gas

below the boundary by that above.

F = -r- = }/inmVa,\X—-

A< w(1-53)

By definition the coefficient of viscosity is the ratio between the

tangential force per unit area divided by the resultant velocity gradient

dujdy of the shear motion in the fluid. In this case

»?=

which according to (1-53) is

FjA FjA

dujdy ujw

rj = HnmVavX

(1-54)

(1-55)

Substituting the value of the mean free path A given in (1-38), we find

the viscosity of a gas is

' 3(2)'^77|2

in which f is again the molecular diameter. According to Eq. (1-23)

the average molecular velocity is

2 /2fcT\^'av =-u—Va,y

tt'-^V m /

so that n2 /mjfcn^_ 0.667 /mfen^^

37Tf'\—) ^1^ I—) (1-57)

From Eq. (1-56) it can readily be seen that the dimensions of viscosity

are mass/length x time. In the cgs system the unit of viscosity is

1 poise = 1 g/cm sec = 1 dyne sec/cm^.


The above calculation of the viscosity is only approximate since the

ndom motion of the molecules is treated inexactly by assuming

that the molecules all move in their random motion with the average

thermal velocity and since every molecule is assumed to travel a

distance equal to the mean free path between collisions. When the

distribution in random velocities and the distribution in free paths are

taken into account, the problem becomes much more complicated and

the solution can be arrived, at only by successive approximations.*'^

The result of the calculation for rigid, elastic, spherical molecules is

that the viscosity is

, 0.499 mvav 0.499 pvav ,, ,„,, = 0.499 «vA ^ -^^p;j^ =^^^ (1-58)

where p = nm is the density in g/cm*. Accepting this latter result we

then have instead of Eq. (1-57)

0.998 /mA;T\^(1-59)

Equation (1-59) provides another basis for measurement of the

molecular diameters of various gases. Solving for the molecular

diameter,

_ 0.999 /mkTY'i\i4

(1-60)

from which the cross section for collisions between the molecules of a

gas is

0.998 /mA;T\'^a= 77|2

r] \ TT-) (1-61)

Substituting numerical values for k and tt and the molecular weight Mfor Wmoim = 6.023 x lO^* ^ ^^ ^j^g following numerical results are

obtained

:

5.22 X 10-11M

and 8.52 X 10-21

iv)

(MT)H

cm

cm'

(1-62)

(1-63)

Experimental values of the viscosity for several gases are given in

Appendix III together with computed values of the molecular diameterf from Eq. (1-62) and of the mean free path A from Eq. (1-38). Thesevalues of f and A based upon viscosity measurements should becompared with those given in Appendix II based upon the experimentalvalues of the Van der Waals parameter b.

22 VACXJUM SCIENCE AND BNGINEEBING

The above result is rather surprising in two respects. The viscosity

of a gas is predicted to be independent of the density and to increase

as the square root of the temperature, whereas in the case of common

liquids the viscosity is known to decrease as the temperature is

increased. Also for two different gases the viscosities at some standard

temperature should be proportional to the square roots of their molec-

ular weights. As surprising as these results may be, experimental

measurements of the viscosity of gases confirm them for a wide range

of temperatures and pressures. However, at extreme values of the

pressure, both high and low, the viscosity of a gas departs from this

prediction. At very high pressure the average distance between the

molecules is so small that the intermolecular forces become important

and the momentum transfer differs markedly from that assumed above.

At values of the pressure which are so low that the mean free path

exceeds the distance between the walls, colUsions between molecules

only rarely occur so that collisions with the walls predominate. In this

case there is no transfer of momentum directly from one layer of gas to

another, but only between the moving gas and the walls of the tube or

vessel. Thus, as mentioned in Sec. 1-7, the mean free path is a

characteristic dimension which determines the behavior of a gas and

in particular determines whether the gas exhibits the property of viscous

or of molecular flow.

The flow of gas due to a pressure difference will be discussed in the

next chapter. In that discussion the relative magnitude of the mean

free path as compared with the dimensions of the tube or passage

through which the flow occurs will be of basic importance.

REFERENCES

1. L. B. Loeb, Kinetic Theory of Gases (McGraw-Hill Book Company, New York,

1927), pp. 94-96.

2. Ibid., pp. 86-88.

3. J. C. Slater and N. H. Frank, Introduction to Theoretical Physics (McGraw-

Hill Book Company, New York, 1933), pp. 462-465.

4. S. Chapman, Phil. Trans. Roy. Soc. London 211 A, 433 (1912); 216A, 279

(1916); 217A, 115 (1918).

5. D. Enskog, Kinetische Theorie der Vorgange in massig verdilnnten Gasen,

Dissertation, Uppsala, 1917.

CHAPTER 2

GAS FLOW

2-1. Gas Flow in Vacuum Systems. An understanding of gas

flow over a very wide range of pressure is essential to an intelligent

approach to vacuum-system design. A system is generally at atmos-

pheric pressure initially, is then "roughed out" by mechanical vacuum

pumps, and is flnally evacuated to the desired limiting pressure by

diffusion pumps with an appropriate arrangement of water-cooled

baffles or cold traps. The mean free path of the gas in the system is

initially very smaU (about 7 x 10-" cm), as discussed in Sec. 1-7,

so that the dimensions of the pipes and manifolds are many times the

mean free path and the flow of gas is limited by viscosity. When very

low pressures are finally attained, the mean free path may be large

(perhaps hundreds or thousands of centimeters, depending upon the

pressure attained), so that the dimensions of the pipes and manifolds

are then a very small fraction of the mean free path of the molecules.

Viscosity then no longer characterizes the gas flow, which is then

referred to as molecular flow. At some value of the pressure, depending

upon the cross-sectional dimensions of the particular part of the system

under consideration, the molecular mean free path is about equal to

those dimensions and the flow is neither purely viscous nor purely

molecular in character. This is the transition region for which the

equations for gas flow are rather complex.

The characteristics of viscous and molecular flow will be developed

in some detail in this chapter, and a number of formulas of practical

interest given. The transition region will be discussed qualitatively

to illustrate the approximate behavior of gas flow in this range of

pressure. In addition, the conductance formulas so essential for the

design of vacuum systems to meet specifications will be developed.

Applications to typicd vacuum-system situations will be made in Chap.

8, dealing with vacuum-system design.

2-2. Pumping Speed and Conductance. Before proceedingWith a detailed discussion of the characteristics of gas flow it will beuseful to define the terms pumping speed and conductance as used in

"Vacuum-system design.

23


The prime movers in vacuum systems are the mechanical vacuum

pumps, steam or oil vapor ejectors, diffusion pumps, and a variety of

specialized pumping devices, such as ion and getter pumps. These

devices all remove gas from the system to be evacuated at a rate which

is measured by the pumping speed Sj,, which is defined as the volume of

gas per unit of time dVldt which the pumping device removes from the

system at the pressure existing at the inlet to the pumping device.

The common units of pumping speed are liters per second, cubic feet

per minute (cfm), and cubic meters per hour; several other combinations

of volume and time are used occasionally. A convenient table of

conversion factors for these units is given in Appendix IV.

The gas flow into a pumping device, called the throughput, is

defined as the product of the pumping speed and the inlet pressure,

I.e.

Q = P,A = ^idV~di

(2-1)

Q = ^'7dt

d

"dtiW)^BoTdWM dt

by reference to (1- 8). Thus the mass flow is

dWdt

for which the common units are torr liters per second, torr cubic feet

per minute, // liters per second (n = micron = 10"^ torr), listed with

conversion factors in Appendix IV. The throughput is proportional to

the mass flow of gas since under conditions of steady flow such that the

pressure is constantdV rl /W \ R.TdW

(2-2)

(2-3)

The flow of gas entering the pump from the vessel being evacuated

generally passes through a series of pipes or conduits which present a

resistance to flow, so that between any two points along the flow path

(e.g., between the ends of a pipe leading to the pump) a pressure

difference will exist. In fact, a net flow will occur only if such a

pressure difference does exist. By analogy with an electrical circuit,

the conductance between two points along the flow path is so defined

that the quantity of gas flowing through the system is the product of

the conductance and the pressure diff'erence, i.e.,

Q = (P,- P,)G (2-4)

Since Q is the quantity of gas per unit of time entering the pipe or

conduit at the pressure Pj, then if no additional gas leaks into or is

removed from the pipe between the points of interest this same quantityof gas comes out the pipe at pressure P^.

GAS FLOW 25

The pumping speed of a vacuum pump according to (2-1) is 8^, =QlPm- By analogy with this expression it is convenient to define the

pumping speed at any point in a vacuum system as

S = Q(2-5)

where Q is the gas flow in the system and P is the gas pressure at the

point at which the pumping speed is defined. In the case of an opening

or pipe through which the quantity of gas Q is flowing from a region at

pressure Pi to a region at Pj, the pumping speeds at the two points in

the system are given by

so that P -^

and

and

Sn = T^

QP = — (2-6)

Substituting these values of P^ and Pa into (2-4), the result is

Dividing through by Q and rearranging terms leads to

1

8,

1 1

c(2-7)

Thus the pumping speed at any point in the system can be obtained fromthe known pumping speed at some other point and the conductance of

the portion of the system (pipes, holes, or passages) in between. Inparticular, for the combination of a pump of pumping speed 8„ and a

pipe of conductance G the combined pumping speed is, by analogy.

or

1

8^

8 =

1 1

8, + C(2-8)

By reasoning similar to that given above, it can easily be shown thatlor several openings, pipes, or conduits in series, each with individual

conductances G^, G^, C3, etc., the combined conductance is given by

- (series) = — + —G G\ Cj C,

+ (2-9)


Also for several openings or pipes in parallel, so that the gas flow divides

between them, the combined conductance is

C (parallel) = Ci + C^ + C3 (2-10)

The analogy with the conductance in an electrical circuit is obvious.

The performance of a vacuum system is normally calculated by first

determining or assuming the total gas flow Q to be expected, then

choosing a combination of pumping speed and conductance such that

the desired working pressure can be maintained. The individual

conductances of components {G^, C^, C^, etc.) are first determined, then

the combined conductance is calculated by some combination of Eqs.

(2-9) and (2-10), and finally the pumping speed is calculated by (2-8).

This resulting pumping speed 8 for the system must then satisfy (2-5)

when Q is the gas flow expected from the vacuum process concerned and

P is the specified pressure to be maintained. The definition of

pumping speed under more complex conditions involving the out-

gassing of surfaces at reduced pressure, residual leaks into the system,

and variation of the pressure with time is discussed in Chap. 7.

2-3. Viscous Flow—Poiseuille's Law. The characteristics of

flow of highly viscous liquids, such as "heavy" oil or molasses, have

been observed qualitatively by nearly everyone. The flow rate of such

a hquid through a tube is proportional to the pressure difference causing

the flow and to a high power of the diameter of the tube. This same

tj^e of behavior occurs for gas flow at relatively high density. The

formulas governing gas flow under these conditions will now be

discussed.

Consider the flow of gas through a long tube of uniform circular

cross section (see Fig. 2-1). Between the ends of a segment of this

tube a pressure difference Pj — P^ exists, and gas flow occurs along

the tube from the region of higher to that of lower pressure, i.e., from

Pj to Pj. The gas contained within a thin-walled cylinder of radius

r and wall thickness dr, and within a differential length dx of the tube,

experiences a force in the direction of flow given by the cross-sectional

area 2Trr dr multiplied by the pressure difference 8P, so that

^F = 2^r8PJ^r (2-11)

The flow quickly reaches a steady

state in which an equilibrium

. I exists between this force and the

L viscous forces from the gas, both

at smaller and larger values of

Fig. 2-1. Viscous flow through a tube, the radius. The gas nearer the

GAS FLOW 27

center moves faster, and that farther from the center, and thus nearer

the wall, moves more slowly than that in our sample cylinder. Thecomponent of force due to the faster-moving gas just inside the

cylinder under consideration can be written by reference to the defini-

tion of viscosity given in Eq. (1-54) as

P,dv

where rj = coefficient of viscosity of the gas

;Sf = surface area of the cylinder

dvjdr = velocity gradient

S = 277r Sx is the area of interest, and the viscous force due to the

inside gas is thus

^ „ dvFf = -27T7]r dx— (2-12)

where the negative sign arises because the velocity v decreases as r

increases. The corresponding viscous force due to the more slowly

moving gas outside the cylinder under consideration is

P„ = 27Tw(r + 8r) 8x(^]\dr/r+ar

However, a,t r + dr the value of the velocity is i; + (dvjdr) dr, so that

v\ d I ^^s \

r/r+ir dr\ dr I

dv\

Tr)

and P, = 27Tri{r + dr) dx—\v+^drdr\ dr

(2-13)

Equilibrium will occur when the force due to the pressure difference

given in Eq. (2-11) is just balanced by the sum of the viscous forcesF^ and P„ given in Eqs. (2-12) and (2-13), so that

277r dP dr = -27Tri dx

which yields

rdP

dv, , , d ( dv \

'dr-^"^^-^drV^dr^n.

^ I , dv , d^v d^v „— ZTTf) dx\dr-—y r dr 1- ^— dr^\ dr dr^ dr^

,(dv d^v d^v \


If we drop {d^jdr^) dr as being a small term of higher order than the

remaining terms we have

1 dP dH \dv ,„ , .-• =

1(2-14)

r] dx dr^ r dr

It is easily seen that a solution of (2-14) is of the form v = A + Br^

and that the particular solution of interest is

A - 1 dP.

(2-15)

4jy ox

in which ^ is a constant determined by the boundary conditions. In

the event that there is no motion of the gas

in contact with the wall of the tube then

?; = at r = a, and in this case

4:r) ox(2-16)

Fig. 2-2. Velocity as a

function of the radius in

viscous flow through a

tube.

According to (2-16) the gas velocity as a

function of the radius is parabolic with maxi-

mum velocity Vraa.y. = {\r)){dPldx)a^ on the

axis (r = 0) and zero velocity at the wall

(r = a) as illustrated in Fig. 2-2.

The volume of gas flowing through the

cross section of the tube each second is obtained by integrating Eq.

(2-16) across the cross section of the tube, so that the flow in volume F

of gas per unit of time is

—- = 2iTrvdr =——-] (a^

dt Jr=0 ^n dxJr=0

If we define the gas flow as in (2-2), then from Eq. (2-17) we have for

the gas flow through the cross section of the tube

r^)rdr=^'-^ (2-17)8?^ ox

^dt 8r] dx

(2-18)

If we now extend the pressure drop under consideration to a length Lof the tube, where L = j dx, then

Q =na^j^ri P(dPjdx) dx

fJodx

na*

l6r]L(Px' - P^') (2-19)

This is one form of Poiseuille's law describing the flow of a viscous,

compressible fluid through a tube of circular cross section.

GAS FLOW 29

Since Pj^ - P^^ = (Pj - P2)(Pi + Pa), and since we define Pay =(Pj + P2)/2, Poiseuille's law can also be written as

QTra*

-* av(Pi ParZ)*

Pav(Pi (2-20)8rjL "'' ' " 128»;L

where D = 2a is the diameter of the tube. As this equation is written

the pressure is measured in dynes per square centimeter and the radius

(or diameter) and length of the tube in centimeters. The quantity Qis thus measured in (dynes/cm^)(cm^/sec) = microbar cm^/sec, since

10* djrnes/cm^ by definition is equal to 750.06 torr = 1 bar.

Referring to the definition of conductance given in Eq. (2-4), it

follows from (2-20) that the conductance of a tube of circular cross

section at high gas pressure is

C(cm3/sec)=^-^^=^Pa. (2-21)

in which the quantities are all in basic (cgs) units, i.e., the dimensions

D and L are in centimeters, -q is in poises, and Pav is measured in

dynes per square centimeter. Since 10* dynes/cm^ = 750.06 torr

(mm Hg), the expression for the conductance in (2-21) becomes

ttD* 10* D*^ (^«^^/^^^) = m^ ^- ^ 7^6 = ^'' ^ ^- ^^-''^^

when the pressure Pav is measured in torr. A more usual unit of

conductance is liters per second, for which (2-21) becomes

C (liters/sec) = lO-V (cm^/sec) = 3.27 x IO-2— PavriL

(2-226)

in which the pressure is again in torr, the dimensions L and D are in

centimeters, and the viscosity is in poises. Finally, since 1 ft^ =28.3 liters, 1 in. = 2.54 cm, and 12 in. = 1 ft,

C (cfm) = 3.27 X 10-^^ Pav X^^rjL 1 min

2.54 cmVlin.

Ift^ 1ft

28.3 liters 12 in.

= 9.46 X 10-2— Pav (2-22c)

m which the diameter is measured in inches, the length of the tube infeet, the viscosity in poises, and the pressure in torr.

The viscosities of various gases at a temperature of 20°C are givenin Appendix III. For the particular case of air at 20°C = 68°F the

30 VACUUM SCIENCE AND ENGINEEKING

viscosity is 1.829 X lO"* poise, so that in this case (2-226) becomes

C (liters/sec)(air at 20°C) = 179— Pav (2-23a)

in which the pressure is in torr and D and L are in centimeters. Corre-

spondingly, (2-22c) becomes

C (cfm)(air at 20°C) = 517— Pav (2-236)Ij

in which the pressure is in torr, D in inches, and L in feet.

2-4. Pressure Drop Formula. From Eqs. (2-23a) and (2-236)

a convenient "pressure drop" formula can be derived which provides

guidance in the selection of a pipe size to be used for pumping air with

a mechanical vacuum pump. Since by definitions (2-1) and (2-4)

Q = PmS^ and Q = (Pi - P,)G,

P -P,^^ = ±-9Il. (2-24)

for air at 20°C, according to (2-23a). If a pipe of diameter D is

connected to a mechanical vacuum pump of pumping speed Sj,, then,

since the pressure at the pump inlet is the same as P^, the gas flow into

the pump is Q = PiSj,, so that

If for the efficient utilization of the pump capacity the rule is adopted

that the pressure drop in the pipe must not be greater than one-fifth

the pump inlet pressure, since Pav = (Pi + P2)/2, then the quantity

2P,0.9 to 1.0 (2-26)

Pav Pi "T P2

is approximately unity, as long as the rule stated for selection of pipe

sizes is followed. Thus (2-25) yields for the approximate value of

Pressure drop (torr) =1 S^

5.6X10-"%^179 D*

when Sj, is in liters per second and D andL are in centimeters

Pressure drop (torr)517 D*

1.9 X 10-»

(2-27a)

Similarly

(2-276)

if Sj, is in cubic feet per minute, D in inches, and L in feet. These

expressions provide a means of obtaining a rough check on the selection

of the proper size for a given operating pressure range. If the pressure

drop so calculated is not small as compared with the desired operating

pressure, a larger pipe size must be selected.

GAS FLOW 31

2-5. Turbulent Flow in Vacuum Systems. The flow of a fluid

through a tube may be characterized by the dimensionless number

pvDRe

V(2-28)

where p = density of the fluid

V = flow velocity

D = diameter of the tube

rj = viscosity of the fluid

This is known as the Reynolds number. As the fiow velocity increases,

the Reynolds number increases and the pressure difiference betweentwo points along the tube increases consistently with Eq. (2-20) (where

Q = ttD^PvI4:) until the Reynolds number exceeds a critical value.

When Re > 2,000 (approximately), then the character of the flow

changes. Instead of flowing in a smooth pattern of continuous flow

lines characterized by viscous flow, the fluid becomes turbulent anderratic with the appearance of eddies and oscillations . This is turbulent

flow, the onset of which can be predicted for any fluid by evaluating

the Rejmolds number. The transition from viscous to turbulent flowwill occur for any fluid approximately in the range 1,000 > Re < 2,000.

For Re < 1,000 the flow is nearly always viscous in character andfollows Poiseuille's law. When Re > 2,000 the flow is nearly alwaysturbulent in character, in which case the pressiire difference betweentwo points along the tube no longer is given by Poiseuille's law (2-20),

but becomes erratic in value and greater than that corresponding to

viscous flow. At what exact value of the Reynolds number the flow

becomes turbulent depends upon the roughness of the surface of thetube and other factors, but in any case is in the range 1,000 to 2,000.

The throughput may be expressed in terms of the Reynolds numberas follows

:

QtD^

PvttD^ fjHe rjl

But since from (1-8) p = WjV

pD

PMjR^T

77,?P„T

ReZ)

(2-29)

For air at 20°C, r] = 1.829 x lO^* poise, R^ = 62.364 torr liters/°K,T = 293.16°K, and M = 28.98 so that

Q (air 20°C) = "L(1-829 x 10-^)(62.364)(293.16)

^^ ^4 .28.98

= 9.06 X 10-2 Re D torr liters/sec (2-30)

when D is measured in centimeters.


If we assume that turbulence sets in at Re = 2,000, then the critical

throughput above which the flow will be turbulent is

Q, = ISlDtorr liters/sec (2-31)

Situations do develop in vacuum practice in which turbulence occurs.

Consider the case in which a vacuum tank has been evacuated to a very

low pressure, and then air is admitted by opening a valve to atmospheric

pressure. To be specific, assume that the valve is connected to the

vacuum tank by a tube 1 cm in bore diameter and 10 cm in length.

According to (2.19) and (2-23a) the throughput will be

Q179 Z)*

(P,^ - p^)

Initially P^* < Pi'' so that according to Poiseuille's law

Q = i7^Ho(760)2 = 5.17 X 10' torr liters/sec

whereas according to (2-31) turbulence occurs for any value of through-

put greater than Q„ which for our chosen example is just 181 torr liters/

sec. Thus initially, when the pressure Pj in the tank is low, the in-

rushing air will experience turbulent flow. The flow will continue to

be turbulent until the internal pressure has reached a value such that

e = Oo or

1^^0(7602 - Pa^) = 181

that is, until Pj = 759.5 torr, so that turbulent flow occurs essentially

for the entire period of admitting air to the vacuum tank since the

throughput does not drop below the critical value for turbulent flow

until the pressure in the tank is within about 0.5 torr of atmospheric

pressure.

However, when pumping situations are considered, the occurrence

of throughput in excess of the critical value for turbulence is not usual

and in any case does not lead to the need for design alterations. At

low pressure, the throughput is automatically low since in the region of

viscous flow the throughput depends upon the square of the pressure.

The question is then whether the flow during the roughing-down period

of a system is turbulent during the early (high-pressure) portion of the

pumpdown cycle when a reasonable combination of mechanical pumpdisplacement and connecting pipe is used. According to the criterion

suggested in Sec, 2-4, the pressure drop in the pipeline should not

exceed one-fifth of the pump inlet pressure when the system is at the

operating level. Consider a system for which the mechanical pumpmust maintain a base pressure of 0.05 torr, so that the pressure drop in

the pipeline should not exceed 0.01 torr. To be ouite specific, let us

GAS FLOW 33

assume that a mechanical pump of 110 cfm or about 50 liters/sec

displacement speed is to be used and the connecting pipe length is 2 m.The pumping speed of such a mechanical pump at a pressure of 0.05 torr

is about 38 liters/sec. (See Chap. 5 for mechanical vacuum-pumpcharacteristics.) Then according to (2-27a)

0.01 = 1 38 X 200

179 D*

so that the appropriate internal pipe diameter is

D = 8.1 cm = 3.3 in.

Now assuming that the connecting pipe has an inside diameter of

8.1 cm and length of 200 cm, the question is whether pumping downthe system from atmospheric pressure will result in turbulent flow for

some portion of the pumpdown cycle. Since at high pressure thepumping speed will be nearly equal to the theoretical displacementspeed of the pump, the pumping speed S^ s» 50 liters/sec. From Eq.(2-23a)

Z)<Q = S,P = C(P, - Pi) = 179— P,y(P, - P,)

D*= 179— P(O.Ol)Ij

for the conditions described above. From (2-31) the critical throughputis

Z)<Q, = 1812) = 179 -— P,(0.01)

jj

so that turbulence will be present during the pumpdown until thepressure

181 LP^= ^- 102 = 38.5 torr

179 Z)3

is reached, below which the flow will be viscous. At this value of thepressure the pipe conductance, according to (2-23a), is

D*C (at P = 38.5 torr) = 179 -— (38.5)

(8.1)*= 1'79^177T7^(38.5)200'

= 1.46 X 10^ liters/sec


The conductance of the connecting pipe at this value of the pressure is

so much larger than the pumping speed of the pump that the speed of

evacuation is not affected by the very small pressure drop (0.01 torr)

in the pipe. Even though turbulence creates a pressure difference

significantly greater than 0.01 torr at higher pressures, from 760 down

to 38.5 torr, the actual speed of evacuation is not measurably decreased

by the presence of turbulence. Thus, as long as the criterion in Sec.

2-4 is followed in the design of the connecting pipe, the occurrence of

turbulent flow during pumpdown does not present any need for altering

the choice of pipe size. Although turbulent flow may be expected to

occur during the early phase of the pumpdown cycle in almost any

vacuum system, the design parameters based upon viscous flow in the

low-pressure range, where the performance is critically dependent upon

the dimensions of the connecting pipe, need not be altered by the

occurrence of turbulent flow in the high-pressure portion of the pump-

down cycle. Turbulent flow therefore does occur in vacuum systems,

but not in a way which imposes any additional design requirement.^

2-6. Correction to Poisseuille's Law Due to Surface Slip.

Poiseuille's law for viscous flow as given in Eq. (2-20) has been confirmed

experimentally over a wide range of gas pressure and tube diameter.

However, as the pressure is decreased for a given diameter of tube, the

flow rate eventually begins to deviate from that predicted by Poiseuille's

law. In the derivation of Poiseuille's law it is assumed that the gas

velocity drops to zero at the tube wall. If this is not the case, but

instead if the gas next to the wall has an appreciable velocity, referred

to as surface slip, then the flow is given by an expression of the form

Q = -^Pav(P.-Pi)(l +128»yL

Pi)( D16^

(2-32)L \l28rj

in which e is the coefficient which determines the velocity of the gas

at the inner surface of the tube.

The interaction of the gas with the walls can be analyzed in terms of

two distinct processes. Some gas molecules in striking the wall

experience specular reflection and thus retain the same component of

velocity in the direction of flow as before the impact. If all molecules

striking the tube wall were to experience specular reflection there

would be no "drag" effect at the wall and the gas velocity would be

uniform over the cross section of the tube. Other molecules strike

microscopic irregularities in the wall and bounce several times. Under

these conditions a molecule may be absorbed by the wall and then

reemitted later with a random distribution in angle and velocity.

GAS FLOW 35

Molecules experiencing absorption and reemission represent a layer ofgas which is at rest next to the wall and provide the viscous dragdiscussed above. It can be shown that the coefiicient e, which definesthis effect, is given by

U R^Tl 2 - /(2-33)

where / is the fraction of molecules which are absorbed and reemitted,and 1 — / is the fraction which are specularly reflected. By substi-tuting this expression into Eq. (2-32) one obtains for the gas flowthrough a tube of circular cross section

Q-128»j

CiPavi>*

16\2 M I

Pl-P2

-f

fD^

Pi

c,D^) (2-34)

where

and

c, =128>;

'^^ ~ 16\2 lW~/ ~ /

(2-35)

(2-36)

When the pressure Pav is sufficiently high, the term c^P^yD^ domi-nates the term c^D^ and the flow follows Poiseuille's law as given inEq. (2-20). When the value of the pressure is such that in (2-34) theterm CiPav-D* is equal to the term c^D^, the character of the flow departssignificantly from that of Poiseuille's law. The pressure for whichthis condition occurs will be referred to as the transition pressure Pjand is given by

c,P,D* = c,D3

or P.=c^D

(2-37)

At pressures significantly below P^ the viscous flow term c^Ps^vD* is

of decreasing importance and the nonviscous term CjD^ dominates.The correction to Poiseuille's law due to slip is therefore negligible atvalues of the pressure which are large as compared with the transitionpressure, but becomes so important below the transition pressure thatthe character of the flow is completely altered.

From (2-34) and the definition for conductance

C = Q C^P^yD* + CaD^

P. -P. (2-38)


where Cj and c^ are given by Eqs. (2-35) and (2-36). From the dis-

cussion above and the form of Eq. (2-38), the character of the conduct-

ance of a tube can be seen to change radically, depending upon the

pressure.

1. If the pressure is large compared with P(, the conductance is

given by Eq. (2-21) and is (a) proportional to D*, (6) proportional to

the pressure, and (c) inversely proportional to the viscosity.

2. If the pressure is small compared with P„ the conductance is

(a) proportional to D^, (6) independent of the pressure, and (c) inde-

pendent of the viscosity.

2-7. Gas Flow in the Transition Pressure Range. An exact

treatment of gas flow in the pressure range in which both viscous and

molecular flow are important is difficult and unsatisfactory because the

coefficient of slip, the e which appears in (2-32) and is defined in (2-33),.

is not calculable from first principles. An empirical approach to this

problem was offered by Knudsen^* based upon a series of carefully

controlled experiments on gas flow. Knudsen found experimentally

that the coefficient Cj given in (2-36), which determines the magnitude

of the nonviscous term in the corrected form of Poiseuille's law (2-34),

can be expressed in the form

1 -f fciPav= Kkari

(2-39)2^ av

in which

A-=-«., ^x4(5^f. 3.81X10.(1)" (2-40)12 n^X m J \M]

by substituting the value of Vav given in Eq. (1-23) and the numerical

value for {2kTlm)''^ given in (1-27). The values

and k. 5(i!L)"=1.38xlO-.:?(||n \kT/ rj \ TJ

1.24

(2-41)

(2-42)

were obtained by fitting the experimental results ofmany measurementsof gas flow and pressure difference. At sufficiently small values of

the pressure the terms JfcjPav and AjaPav are both negligible compared

with unity, and1 + fciPa

1 + fc^Pa1

* References indicated by superscript numbers are listed at the end of the

chapter.

GAS FLOW 37

so that K = 3.81 X 103 MIf the empirical expression for c^ at very low pressure given in (2-39)

is compared with the theoretical expression given in (2-36), one finds

that the value of / (the fraction of molecules which are absorbed andreemitted randomly when they hit the wall) is approximately 0.74, andtherefore the fraction specularly reflected is about 0.26. If the

pressure is sufficiently, high the terms k^Pa,^ and k^P&Y are very large

compared with unity and c^ ^ Kikjk^) = 3.07 x lO^TIM)'^. Thecorresponding value of/ is then about 0.85. Thus Knudsen's results

imply that the fraction of molecules absorbed and reemitted, as con-

trasted with those which are specularly reflected, changes slowly in

the transitional pressure region. Including Knudsen's results in the

complete expression for the conductance of a tube given in (2-38), the

final result is

C (cm3/sec) =^ Pav^ + 3.81 x M^f ^-^1^5^^ (2-43)128?? k^Pav L'

in which the values for k^ and fcj are those given in (2-41) and (2-42),

the viscosity is measured in poises, the dimensions in centimeters, the

pressure in dynes per square centimeter {fi bars), the temperature in

degrees Kelvin, and the mass in grams, so that the conductance is

measured in cubic centimeters per second. Converting units to torr

for pressure and to liters for volume, the above expression becomes

C (liter/sec)P Z)*

3.269 X 10-2-^—rj L

3.81T\^ 1 + 1.333 X 103A;iPav D^

333 X lO^jfcoPav i"

ITV^l + 1.

\m) 1 + 1.(2-44)

This latter expression can be written

C- =3.269 10-PavJ>

n3.81

/TWl + 0.1

\m) 1 +0.1

.liliMITf^iP^^DIr])

81(MITf^{P^^DIrj)

(2-45)

The quantity on the left side of (2-45), the conductance multiplied bythe length divided by the cube of the diameter of the tube, is thereforea simple function of the variable Pav-D/»? as shown graphically in Fig.2-3.

Equation (2-45) is of the form

y = ax -\- bex

I + dx(2-46)

38

where


Ly=^C-

X =n

a = 3.269 X 10-2 ^ = 0.181

/MY'

(ff

Differentiating (2-46) with respect to x and setting the resultant

derivative equal to zero determines the value of x at which y has a

minimum value. The result is

3^Tnin — ,.

'b(d 14

(2-47)

Substituting the values of the various quantities into (2-47) yields

(E^) =5.47(^f (2-48)

\ ri /mm \M/

This is the value of Pav£>/»? at which CLjD^ has a minimum value.

According to (1-58) the viscosity is given by

VavT] = 0.499 wmUavA = 1.497 — XP (2-49)

by substituting from (1-11). Thus from (2-49), (1-27), and Table 1-3

1

1.497 «av A

^ ^ = 1.145 X 10^\m) 'l

(2-50a)

when the pressure is measured in dynes per square centimeter (/xbars)

Since 10* dynes/cm^ = 750.06 torr,

1.145 X 10* X 750 X 10"'l]^l \

''Am) \(2-506)

when the pressure is measured in torr. From (2-48) and (2-49) it

follows that at the point of minimum conductance

so that „,n = 1.57i)

-^ (2-51)

(2-52)

That is, when the mean free path of the molecules is 1.57 times the

diameter of the tube, the parameter GLjD^, and therefore also

GAS FLOW 39

the conductance, reaches a minimum. For pressures less than Pminthe conductance increases asymptotically toward the low-pressure value

to be discussed in the next section, and at pressures greater than Pminthe conductance increases with increasing pressure and eventuallybecomes proportional to the pressure as given by Poiseuille's law (2-21).

In (2-37) the transition pressure P, is defined as that value of thepressure for which the viscous term CjD^Pav in the expression for theconductance of a tube given in (2-38) is equal to the nonviscous termC2D^. When (2-38) is compared with (2-45) and (2-46) it is evident

that in the notation of (2-46) when Pav = P(,

exax

dx

Solving this expression for x yields

1

2ad{(be -a) ± [(be - ay + iabdf"'} (2-53)

in which the negative sign leads to a meaningless negative value for x.

Using the positive sign, substituting the values for x, a, b, e, and d given

above into (2-53), and noting that Pav is now the transition pressure

Pj, we have

P.D I T\^^ = ''-Am)^'-''^

By combining (2-54) with (2-506) we obtain

Thus at the transition pressure

8.59

96?7D

D11.14

(2-56)

That is, at the transition pressure the diameter of the tube is about 11

times the molecular mean free path.

Since for air at 20°C the viscosity r] = 1.829 x 10"* poise, the meanfree path according to (2-506) is

A = 8.59/ 293 Y 1

\28.98/

829 X 10-* 5 x 10-3(2-57)P P

where A is given in centimeters and P in torr. Thus for air at roomtemperature the minimum value of the conductance of a tube occursat a pressure

5 X 10-3 5 X 10-3 3.18 X 10-3-i min —

1.57Z> D

40 VACUUM SCIENCE AND ENGINEBBING

in which the pressure is given in torr and the tube diameter in centi-

meters. Correspondingly, in the case of air at room temperature the

transition pressure occurs at

5.57 X 10-2

Ft-5 X 10-3 5 X 10-3 X 11.14

K D D(2-58)

so that, for example, the transition pressure for a tube of i) = 1 cm is

5.57 X 10-2 torr or 55.7 fi. . r

At the transition pressure as defined above, the dependence ot

conductance on pressure is inconveniently complex. The pressure

region over which the conductance changes from predominantly viscous

to predominantly molecular in character can be defined in terms of

(2-45) and (2-46) and is bracketed between an upper limit P„ and a lower

limit Pi. If the first term on the right is much greater than the second

term, the flow is predominantly viscous in character. For convenience

let us require that the first term be greater by a factor of 10. Then

(2-59)ax = 106I + ex

I + dx

Solving this expression for x yields

X = —-{(106c -a) ± [(106c - a)'

2ad40abdf^}

in which, as before, the negative sign leads to a meaningless negative

value of X. Using the positive sign and the values for a, 6, c, and d,

the result is ^ = 948(^f (2-60)

so that, by comparison with (2-55),

P„ = 9.91P, (2-61)

Correspondingly, if the second term on the right side of (2-46) is 10

times the first, then the flow is predominantly molecular in character.

That is,

1 + cx^2-62)lOax = b

I + dx

Solving for the value of x yields

= 10.99rfsM

so that, by comparison with (2-55),

Pi = 0.114P,

(2-63.)

(2-64)

GAS FLOW 41

so that the transition pressure range within which the character of the

flow changes ranges essentially from P„ = lOP, to P, = O.IP,.

For air at 20°C = 293°K,M = 28.98 g, and rj = 1.829 x 10^* poise,

the transition pressure from (2-55) is

293 V-^ 1.829 X 10-4P, (air 20°C) = 95.7 -

28.98,

5.57 X 10-2

D

so that

and

D

lOPt0.557

O.IP,

D

5.57 X 10-3

D

(2-65)

(2-66)

(2-67)

when the pressure is given in torr and the pipe diameter in centimeters.

In Table 2- 1 is given the range of pressure for the transition region for

various pipe sizes in the case of air at 20°C.

Table 2-1. Transition Pressure Ranges for Various Pipe Sizes fob AirAT 20°C

Pipe diameter Transition pressure range, torr

Centimeters Inches Pi Pt Pu

0.254

0.635

1.27

2.54

5.08

10.16

20.3

40.6

0.1

0.25

0.5

1.0

2.0

4.0

8.0

16.0

2.2 X 10-2

8.8 X 10-3

4.4 X 10-3

2.2 X 10-3

1.1 X 10-3

5.5 X 10-4

2.8 X 10-4

1.4 X 10-4

0.22

8.8 X 10-2

4.4 X 10-2

2.2 X 10-2

1.1 X 10-2

5.5 X 10-3

2.8 X 10-3

1.4 X 10-3

2.20

0.88

0.44

0.22

0.11

5.5 X 10-2

2.8 X 10-2

1.4 X 10-2

Also for air at 20°C the conductance of a long tube in the transition

pressure range is obtained bj^ substituting the above constants into

(2-45), with the result

C (liters/sec) = 178.7Pa1)4

12.12252.lPavi)-D3

311.7Pavi)T(2-68)

when the pressure is measured in torr and the dimensions in centimeters.

Note that the first term on the right side of (2-68) is identical to (2-23a)

and is therefore the viscous-flow term. Equation (2-68) may also be


written in the formD'

C (liters/sec) = 12.12 ^|l4.74Pav-D +^

1 + 252.lPav-D

311.7Pav£>

where

= 12.12—

G

G = 14.74Pav^ +1 + 252.lPav-P

1 + 311.7Pav-D

(2-69)

(2-70)

At sufficiently large values of the parameter Pav-D the fraction

1 + 252.1 PayJ> 252.1

1 + 311.7Pavi>~ 311.7

= 0.808

which is then negligible as compared with 14.74Pavi>. The first term

in the bracket then dominates, and (2-69) reduces to (2-23a) for viscous

flow. However, when P^^D is very small, the first term becomes

negligible as compared with the second, which approaches unity for

sufficiently small values of the parameter. The value of G is then 1 and

the conductance is given simply by 12.12D3/L, the low-pressure limiting

value of the conductance to be discussed in the next section. In

Table 2-2 are given values ofG from (2-70) as a function of the parameter

Table 2-2. Values of the Factor O fob Vaeious Values

OF THE PaBAMETER P^yD

Air at 20°C

Pe^yD,

torr cm

10-5 0.9994

io-« 0.9957

10-3 0.969

10-2 1.002

10-1 2.289

1 15.55

10 148.2

102 1,475

103 14,740

Pav-D. These values may be obtained from Fig. 2-3 by dividing the

values of the term CL/D» plotted in the graph by the factor 12.12.

In designing a vacuum system in which prolonged operation is

expected to occur in the transition pressure range, calculation of con-

ductances by (2-45) or (2-68) may be justified. However, in most

practical systems the pressure in the forevacuum portion of the system

remains in the viscous-flow regime during the crucial period of opera-

tion, whereas the piping and main chamber beyond the diffusion pump

GAS FLOW 43

pass through the transition region rapidly as the system is pumpeddown. In such cases the laborious calculation of conductance in the

transition pressure range is not justified and the operation of the

system is sufficiently well represented by using the viscous-flow or

Poiseuille form of conductance given in (2-23a to c) from atmospheric

pressure down to the transition pressure P^ and the molecular-flow

form of conductance to be discussed in the next section for values of

the pressure below P^.

r" r rr r rConductance curve from Eqs.(2-45) and (2-68)

[

viscous Term only, as given in t%\Z-Zt^]

/1 1 1 [ill /

/

180

160

140

120

100

80

11

/1

11

/ /00

rrJ

ll J

f

/ /1

1 yf ;

;

1 / 12.12;

/;60

7154"_ ^ 1 , rt: -

iyj 40

1

20^'.-'

LK**

1

'11 _ ^ji

IQ-52 3 5 7jQ-4 2 3 5 7|q-3 2 3 5 7 jq-2 2 3 5 7 ]q-I 2 3 5 7 1

Fig. 2-3. Conductance of a tube as a function of the pressure.

2-8. Gas Flow at Low Pressure. At low pressure, i.e., at valuesof the pressure at which the mean free path for collisions betweenmolecules is long as compared with the dimensions of the tube orconduit through which gas flows, the mechanics of flow are entirely

diff"erent from those at high pressure. The gas molecules move in

random directions with a velocity distribution characteristic of thetemperature as given by the Maxwell-Boltzmann distribution law(1-21), and by pure chance individually progress from one point in thesystem to another. Collisions between molecules are very rare events,whereas collisions with the walls of the system dominate so that themolecules, instead of jostling each other by collision processes, moveindependently of one another. Pressure is not transmitted from one


region in the system to another by direct transfer of momentum from

molecule to molecule, thus producing a flow toward the region of lower

pressure; instead, the transfer of momentum is between the molecules

and the walls of the system. In spite of the independent character of

motion of the individual molecules, net flow does nevertheless occur

from the region of higher density (or pressure) to the region of lower

density. Net flow results because the number of molecules leaving a

unit volume of any given region in the system is proportional to the

density in that region, whereas the number arriving in the unit of

volume from elsewhere is proportional to the density in those other

regions. By a purely statistical effect, therefore, net flow is always in

the direction tending to equalize the density everywhere and thus from

regions of higher to regions of lower density or pressure. In the pressure

regime for which the above conditions hold the flow process is called

molecular flow. Approximate formulas for molecular-flow rates

through tubes and apertures of various shapes were developed princi-

pally by Knudsen.^

2-9. Conductance of a Long Tube at Low Pressure. In a

tube through which gas is flowing at very low pressure (see Fig. 2-4)

the molecules move in random straight lines, striking the wall at the

end of each free flight. If the molecules have the Maxwell-Boltzmann

distribution of velocities [Eq.

(1-21)], then the number of gas

molecules impinging on a square

centimeter of surface area each

second is given by Eq. (1-31) as

Fig. 2-4. Motion of molecules at low

pressure.V =

WWav

2n^

1 /2)fcT\^

Thus the number striking the wall each second in the length Az of the

tube is

dn ^n /2kTf

dt Stt'-^V m /

in which s is the periphery of the cross section of the tube, which might

be circular or have any other shape.

If each molecule is completely stopped by the impact at the surface

and then reemitted randomly, there is a net momentum transferred to

the wall of the tube, provided that there is a mean drift velocity u in

the direction of flow. The momentum transferred to the increment of

length Az of the tube will therefore be mu on the average for each

molecule hitting the wall in the segment Az. This momentum transfer

GAS FLOW 45

per second is thus

dp

'di

dnmu—- =

dt

mn (2kT\^^m I 1 su Az2tt^\ m J

(2-72)

Since the rate of change of momentum represents a force exerted bythe gas molecules on the tube A/ = dpjdt, the tube reacts with a

retarding force on the flow of gas of this same magnitude. This

retarding force acts over the cross section of the tube so that the changein pressure is

1 dp(2-73)A A dt

where A is the cross-sectional area of the tube. Combining (2-73) with

(2-72) we have for the change in pressure

mnl2hT\^s277-^ \ m I A

(2-74)

Since, according to Eq. (1-16)

AP"a7

nkT, the pressure gradient is

nkTI m \'^g_ _ P

~i^\^kT) a'^~m \-^i

-^1(2-75)

7T'^\2kT/

The quantity of gas flowing through the tube is

Q = PAu /jh&T cm*/sec (2-76)

from which Pu = QjA. Substituting this expression into (2-75) yields

For an extended section of a tube of uniform cross section

AP/Az = (Pi - Pa)/^

in which Pj and Pj are the values of the pressure at the ends of asection of tube of length L. Substituting this value of AP/Az into

(2-77) and solving for Q gives for the gas flow through a tube of uniformcross section

\ m I

P,A^(2-78)

The above derivation contains the implicit assumption that a uniformdrift velocity u is superimposed upon the random Maxwell-Boltzmanndistribution of the molecules. Knudsen has shown that one shouldmore reasonably assume that the superimposed drift velocity of amolecule is proportional to its thermal or random velocity. On this


modified assumption Knudsen found that the numerical factor in

(2-78) must be multiphed by S/Stt, so that the flow along a tube of

uniform cross section is given correctly by

_ _8_ (2JcTf P^ -Pi A^(2-79)

which proves to agree with experimental results. The conductance of

a segment of a long, straight tube of uniform cross section is therefore

Q 8 /2fcr\^^^

'P^^Hp^~ 3^\ m J sLC =

= ^,(1.29xl0^)y ^3.44 X 10V?'\'^^'

_34^/T\^£^liters/:

cm^/sec

(2-80)

by substttuting from (1-27). The conductance of a tube of uniform

circular cross section, for which A^js = ttD^JW, is therefore

C

3.81 X 103[mJ T cm^/sec

IPliters/sec

when D and L are measured in centimeters, and

C = 4.34 cfm

(2-81)

(2-81a)

when B is measured in inches and L in feet. For air at room temper-

ature (20°C)

Ml \ 28.98/

so that

.if,

(7air = (3,810)(3.181)Z)3

i)312.12 X 10^^^

= 12.12-—Li

cm^/sec

liters/sec (2-82)

GAS FLOW 47


Cair = 13.82-— cfm (2-82a)

when D is in inches and L in feet. Equations (2-80) to (2-82) apply to

a segment of length L of a long, straight tube well removed from theends. They also apply to the case of a tube for which the length is

very large as compared with the diameter so that the end effect is

small. If the tube is short, how-ever, an end correction is required

to obtain results which are even

approximately correct.

Consider a tube of circular cross

section and finite length L connect-

ing two regions, one at pressure P^

and the other at pressure P^, as

indicated in Fig. 2-5. If the length

of the tube is decreased to zero,

the result is an aperture of cross-

sectional area A = ttDÎ^. Theformula for the conductance of the tube must become equal to that of

the aperture as the length of the tube shrinks to zero. In order to com-plete the derivation of the conductance of a short tube, including endeffects, it is necessary first to derive the conductance of the aperture.

2-10. Conductance of an Aperture. In accordance with (1-32)

the number of molecules which pass through a circular aperture fromthe region at the left is

% (2kTY^ ttD'^

1i = M =im\—) -^

Fig. 2-5. Tube end effects.

277^^

i2kT^

m

\ mD^ molecules/sec (2-83)

Similarly, the number of those which pass through the aperture fromthe region at pressure P^ on the right is given by

, n^7T''^(2kTYq^=vÂ=-i--\ Z)2 molecules/sec (2-84)

The net flow from the region at Pj to the region at Pg is then

9' = g-i- ^2 = — I

-:- ) (wi - n^)D^

277 Y D"^

8 \ m /

î\mkTI

since in each region n = PjkT

(Pj — Pj) molecules/sec (2-85)

48 VACUUM SCIENCE AND ENGINEEBING

If this net flow is put in terms of the volume of gas leaving the

region of higher pressure Pj from which the net flow occurs, then

q (molecules/sec) ^ ^JcT ^^.^^^^

n^ (molecules/cm^) Pi(2-86)

The flow in quantity of gas is defined as Q = (dldt)PV(fihaT cm'/sec)

and in this case from (2-86) is given by

Q = P,±=qkTn.

= !^(?^fZ).(P, _ P„8 \ m /

:)(2-87)

by substitution from (2-85). Referring to (1-27), one finds that this

expression becomes

Q=!^(1.29xlO*)(|)V(Pi-P.)

= 2.86 X 10^ (-^) D%Pi - P2) /^bar cm^/sec (2-88)

The conductivity of a circular aperture is thus

C = QP,-P

= 2.86 X lOM-— I D^ cm^/sec

/ TY2 86 — D^ liters/sec

\MI(2-89)

when D is measured in centimeters, and

C = 39.i/-|f Z)2 cfm (2-89a)

when D is measured in inches. For air at 20°C, since (TIM)'-^' = 3.181,

C = 9.16Z)2 liters/sec (2-90)

when D is measured in centimeters, and

C = 125.31)2 cfm (2-90a)

when D is measured in inches.

Note that the above derivation could have been carried out for an

aperture of any shape since the result given in (2-89) depends only on

the cross-sectional area. In general, the net flow through an aperture

GAS FLOW 49

of area A at low pressure is

q = _L-I 1 J(Pi - Pa) molecules/sec (2-91)

of which (2-85) is a special case. Correspondingly, the gas flow through

an aperture is

= 3.64 X lO'(^) '^(Pi - P2) /^laar cm^/sec (2-92)

Thus the conductivity of an aperture of any shape at low pressure is

/ T'YC = 3.64 X lOH T7I ^ cm^/sec

I TY= 3.641— 1 A liters/sec (2-93)

when A is measured in square centimeters, corresponding to (2-89) for

a circular aperture. Also

C = 49.

i

rp\Vi

cfm (2-93a)

when A is measured in square inches. Again, as in (2-90), for air at

20°C these expressions become

C = 11.6^ liters/sec

when A is measured in square centimeters, and

C = 159A cfm

(2-94)

(2-94a)

when A is measured in square inches.

2-11. Conductance of a Tube at Low Pressure Corrected for

End Effect. Let us return now to the conductance of a tube of

circular cross section and limited length, as shown in Fig. 2-5. Joining

two regions at pressures Pj and Pj respectively, the tube may be

considered as an aperture, the two sides of which are separated and the

tube of length L connected between them. The result is a combination

of two conductances in series, that of the tube C^ and that of the

aperture Co, so that according to (2-9) the resultant conductance is

- =\

or C = 7;——

^

(2-95)


in which C^ is given by (2-81) and Cq is given by (2-89). Thus for a

tube of limited length L the conductance at low pressure is

C(3.810)(2.86) X 10<'(TIM)(D^IL)

2.86 X 103(T/Jf)'^Z)2 -f 3.810 X \0^{T jM)'^^ {D'' jL)

= 3.810 X lO''(—1*AD

cm^/sec

3.810y\!^ 2)3

(I)liters/sec (2-96)


when D is measured in inches and L in feet. Comparing this expression

with (2-82) we see that for air at 20°C the conductance of a tube with

the correction for the end effects is

Z)3cm^/secC = 12.12 X 109

L + %

12.12Z>3

liters/secL + %D


7)3

C = 13.82O.llD

cfm

(2-97)

(2-97a)

when D is measured in inches and L in feet.

The above calculation was carried out for a tube of circular cross

section. The conductance of a tube or conduit of uniform cross

section of any shape can be derived by combining the conductances

given in (2-80) and (2-93) in accordance with (2-95), using the appro-

priate values for the cross-sectional area A and the periphery s. Thus,

for a channel of rectangular cross section with sides a and h and length

L, the conductance at low pressure is made up of the two components

C, 9.71 X 103TV a^ft^

and

Ml {a + b)L

rpVA/rpVA

Co = 3.64 X lO^I— I ab

(2-98)'

(2-99)

GAS FLOW 51

which, when combined according to (2-95), yield

a262C 9.71 X 103

' j'VA

W) (a

9.71

(a + b)L

MI (a +b)L +% ab

% ab

liters/sec

cm3/sec

(2-100)

In the case of a long slot in which a ^ b and in which the length L of

the slot in the direction of flow is not necessarily very large as compared

with the width b of the slot,

C 9.71ab^T

Ml L + %bliters/sec (2-101)

Finally, for a long, narrow slot a '^ b, in which the length in the

direction of flow is also large {L > 6), the conductance is

C »"lsab''

liters/sec (2-102)

In Eqs. (2-100) to (2-102) the conductance for air at 20°C is obtained

by setting 9.7l(TjMy-^^ = 30.9, so that, as an example, the conductance

of a slot from (2-102) is

ab^C = 30.9 -— liters/sec (air at 20°C) (2-103)

Ij

Another geometrical form of interest is the annular region betweentwo coaxial tubes, of which the inside diameter of the outer wall is

Dj, and the outside diameter of the inner wall is D2. Considering the

periphery to be made up of the sum of the circumferences of the inner

and outer walls and following a procedure similar to that for a tube as

developed in (2-71) through (2-96), the conductance of an annulus is

found to be

which for air at 20°C is

C = 12.12{D,'

Hi (D, - D,)

D,^)(D, - D,)

liters/sec (2-104)

liters/sec (2-105)

2-12. Clausing and Monte Carlo Corrections to the KnudsenConductance Formulas. The method of Knudsen, by which theabove formulas for conductances at low gas pressure were derived, is

only approximately correct, even for simple tubes and conduits ofuniform cross section. Clausing3 has carried out a much more exact


calculation for tubes of circular cross section and has shown that

Knudsen's formula (2-96) gives conductances which are too large for

short tubes (i.e., tubes for which the length is not very much larger

than the diameter). For more complicated configurations, such as

occur in manifolds, baffles, and vapor traps, only very crude approxi-

mations can be made of the conductance using Knudsen's method. In

this case the procedure is to represent the system by a combination of

tubes, slots, and apertures. The individual conductances are computed

and then combined in series or parallel by use of (2-9) or (2-10).

Recently, progress has been made in computing conductances at low

pressure by applying Monte Carlo methods, i.e., by tracing individual

molecules through the system analytically. The availability of large

electronic computing machines has made it possible to trace large

numbers of randomly selected molecules and thereby determine the

conductance from the net behavior of a large sample of molecules.

Davis, Levenson, and Milleron*-^ have carried out a series of Monte

Carlo calculations for the configurations shown in Figs. 2-6 through

2-13 and have compared the computed conductances with carefully

measured values. In the computation a randomly selected entering

molecule is followed by numerical computation. At each collision

with the wall the molecule is assumed to be effectively absorbed and

promptly reemitted. The molecule is then assigned random numbers

to specify the velocity and direction after leaving the wall. The

velocity selection is based on the assumption of a Maxwell-Boltzmann

distribution at the temperature of the wall. The selection of direction

is based upon Lambert's law of emission, i.e., the molecules leaving a

unit area of the wall are distributed in angle according to Ig = /„ cos Q,

where I^ is the number per second leaving at the angle Q with respect

to the normal to the surface and /„ is the number per second leaving

normal to the surface.

Davis, Levenson, and Milleron adopt as a reference the conductance

Co of an aperture of area equal to that of the opening into the geo-

metrical configuration (tube, elbow, baffle system, etc.) being investi-

gated. The computed and measured conductance C is related to Co

by a geometrical factor K such that

C = ZCo (2-106)

The assumptions made in the calculations and the conditions provided

in the experimental arrangement are

:

1. The flow is steady-state with the molecular mean free path long-

as compared with the dimensions of the system.

2. The geometries under study connect effectively infinite volumes,

i.e., volumes large enough so that diffuse flow is not inhibited.

GAS FLOW 53

3. The walls of the geometries are microscopically rough so that

molecules are diffusely reflected according to the cosine law.

For some of the configurations investigated conductances can be

calculated either directly by the formulas developed above or by

combining conductances calculated from these formulas in accordance

with (2-9) and (2-10). As an example, consider the first geometry

investigated, that of a tube of circular cross section, the conductance

of which is given according to Knudsen's method by (2-96). The value

Table 2-3. Knudsen and Clausing Conductance Factors and Ebbor in

Knudsen Factor for Tubes of Vaeious LjD Ratios

L/D Kk Kc Per cent error

1.000 1.000

0.5 0.727 0.672 8.2

1 0.571 0.514 11.1

2 0.400 0.359 11.4

3 0.307 0.281 9.3

4 0.250 0.232 7.8

6 0.182 0.172 5.8

10 0.117 0.114 2.6

20 0.0625 0.0613 2.0

30 0.0425 0.0420 1.2

40 0.0322 0.0319 0.9

50 0.0260 0.0258 0.8

of Co in this case is the conductance of a circular aperture as given in

(2-89). Thus the value of K obtained from Knudsen's formulas for

this case is

C 3.810 Z»3 1

c:Kr

2.86 L

4 D3L +y3D Dl

(2-107)

Clausing's corrected values of this factor K^, arrived at by moreelaborate methods, cannot be expressed analytically but can becompared numerically with values computed from (2-107) as given in

Table 2-3.

In Fig. 2-6 the factors Kj^ and K^ are plotted as a function of the

parameter LID for a simple tube. The values of K computed by theMonte Carlo method and the measured values are also shown onthe graph. For this case it will be noted that the Clausing and Monte<-^arlo computed values are in excellent agreement and that the measuredvalues approximate these results very closely, but are generally lower


than those obtained from the Knudsen formula by as much as 11 per

cent. The good agreement obtained in this simple case between the

Monte Carlo and Clausing calculated K factors and the measured values

lends confidence in the results obtained by Davis, Levenson, andMilleron in the more complicated geometries for which the Knudsenand Clausing methods are not so easily applied.

The second geometry investigated by Davis, Levenson, and Milleron

is a 90° elbow, the conductance factor K of which, calculated by the

:oh-A-H

Knudsen Kk

Clausing KcX X Monte Carlo calculations

\ \ Measured values

Calculated byClousing tor tube

Monte Carlo colculotion tor elbow

J Experimental points for elbow

I I I I I I I L.

I 3 5 7

(A + B)/R = L/R

Fig. 2-6. Molecular-flow factors for a

tube. [Taken with permission fromL. L. Levenson, ^N". Milleron, andD. H. Davis, in 1960 Vacuum Sym-posium Transactions (Pergamon Press,

London, 1961).]

Fig. 2-7. Molecular-flow factors for

90° elbow. [Taken with permission

from L. L. Levenson, N. Milleron,

and D. H. Davis, in 1960 Vacuum,Symposium, Transactions (Perga-

mon Press, London, 1961).]

Monte Carlo method, is compared in Fig. 2-7 with that of a tube for

which the length L is equal to the axial length of the elbow A + B.

The computed values of K do not differ significantly from those of a

straight tube such that LjD of the tube is equal to (A + B)ID of the

elbow. (Note that R = Dj2 is used in plotting the figure.) Theconductance measurements are in good agreement with this conclusion.

The importance of this result is that in the low-pressure or molecular-flow regime very little additional resistance to flow is introduced bythe presence of bends in the pipeline. The conductance for a tube withbends is the same as that for an equivalent straight tube with length'

equal to the axial length of the bent tube.

Results for the conductance of a cylindrical annulus are shown inFig. 2-8. In this case the conductance of the aperture calculated

GAS FLOW 55

from (2-93) is

= 2.86 (-j (D,^ - D,^)

(2-108)

The conductance for the annulus

according to the Knudsen method

is given in (2-104). The conduct-

ance factor in this case is then

KkC_ D,-D,

3L Vz{D, - D,)

(2-109)

If the ratio between the inner and

outer diameters of the annulus is

denoted by k = DJD2, then

(2-109) becomes

1 k

L/Dz


an annulus. [Taken with permission

from L. L. Levenson, N. Milleron, andD. H. Davis, Le Vide 18, 42 (1963).]

K {\-k)+ HiLjD,)

(2-110)

Values of Kj^ computed for various

values of the parameters k andL/Dj a-re given in Table 2-4 andare shown graphically in Fig. 2-8,

together with values of K com-puted by the Monte Carlo method.It will be noted that deviations of the order of 10 per cent occur betweenthe two calculations, but that the Knudsen formula for the conductivityof an annulus is surprisingly good.

In Figs. 2-9 and 2-10 the molecular-flow factors for various louverand chevron types of baffles are plotted as a function of the ratio oflength to the width of the slots for various baffle angles. Baffles of thechevron type are frequently used in vapor-trap design, the mainlunction of which is the trapping of condensable vapor in vacuum^y^*®nis as is discussed in Chap. 8. The experimental and theoretical(Monte Carlo) results of Davis, Levenson, and Milleron are given in thegures. The 45° chevron is most frequently used in vapor-trap design.he value of Kj^ = CjC^ for such a baffle can be computed according


Table 2-4. Knudsen Conductance Factors fob Annuli op Various L/D^AND -Dj/Dj Ratios

LID2k = DJD2

0.25 0.5 0.75 0.90

1.000 1.000 1.000 1.000 1.000

1 0.571 0.500 0.400 0.250 0.118

2 0.400 0.333 0.250 0.143 0.0625

3 0.307 0.250 0.182 0.100 0.0426

4 0.250 0.200 0.143 0.0769 0.0323

6 0.182 0.143 0.100 0.0526 0.0217

10 0.117 0.0909 0.0625 0.0323 0.0132

to Knudsen's formula for the conductance of a long, narrow slot as

given in (2-101), which is applicable if a > rf in Fig. 2-10. The area oi

the aperture is A = ad so that the conductance of the unobstructed

aperture is, according to (2-93),

C„ = 3.64(r- (2-111)

The perpendicular distance between the chevron plates is b = dj2^^

I.O

0.6

04

0.2

• Calculated points

Experimental points

" 60° louver

• 45° louver

• 30° louver

0.4

0.3-

0,2

01

-^ d t~• Calculoted points A A a

Experimental points / / \

° 60° chevron \iV^•45° chevron N \

»30°chevrane=60'

o/d

00 Cole.

10 Exp.o/d

00 Cole.

10 Exp.

Fio. 2-9. Molecular-flow factors for

louver geometries. [Taken with per-mission from L. L. Levenson, N.Milleron, and D. H. Davis, in 1960Vacuum Symposium Transactions(Pergamon Press, London, 1961).]


chevron baffle geometries. [Takenwith permission from L. L. Levenson,-

Jf. Milleron, and D. H. Davis, in

1960 Vacuum Symposium Trans-

actions (Pergamon Press, London,1961).]

GAS FLOW 57

and is the width of the slot required for application of the slot formula(2-101). The length of the flow path is iy = 2'-^ d, so that on substi-

tuting into (2-101) the conductance is

^ = ''Am) 2y^d + %m^) = ''''''' (2-112)

The conductance factor is thus computed to be

1.030^K

3.640.28 (2-113)

It is interesting to note that this result is not drastically diff'erent fromthe value 0.25 calculated for a long 45° chevron slot by the MonteCarlo method and shown in the solid curve in Fig. 2-10. The measuredvalues of conductances reported by Levenson and Milleron for the45° chevron baffle are generally about 20 per cent below those computedby the Monte Carlo method. Furthermore, in a practical case cooling

tubes for liquid nitrogen or other refrigerant will be attached to the

baffles with the result that the effective area will be somewhat reduced.

Considering these factors, a realistic value ofK for a carefully designed

chevron baffle is about 0.20. The result given in (2- 1 13) is independentof the number of 45° chevron baffle plates used to fill an aperture of

area A . Since for such a baffle arrangment the length of the flow pathdecreases as the spacing between the plates decreases (and therefore

their number increases), this result is to be expected as long as the

thickness of the plates is inappreciable as compared with their spacing.

In a practical situation it is therefore important to choose a baffle

thickness not more than 5 per cent of the perpendicular spacing betweenthe plates. In Figs. 2-11 through 2-13 the molecular-flow factors

obtained by Davis, Levenson, and Milleron for a variety of useful

geometrical shapes are shown.2-13. Summary of Gas-flow and Conductance Formulas.

The following summary of the gas-flow and conductance formulasderived and discussed in this chapter is provided for convenientreference. The gas flow in vacuum systems is usually maintained bya pump for which the pumping speed <Sj, is defined as the volume perunit of time which the pump removes from the system at the inlet

pressure to the pump. Conversion factors between the various commonunits of pumping speed are given in Appendix IV. The gas flow, orthroughput, into the pump is defined as

Q = PinS, (2-1)

-The common units and conversion factors for throughput are given inAppendix IV.


The conductance C between two points in a vacuum is defined such

that

g = (Pi - P,)C (2-4)

in which P^ and P^ are the values of the pressure at the two points in

question. The pumping speed at any point in the system is defined as

'^ = p(2-5)

where P is the pressure at the point where S is defined.

If Si and ^2 are the pumping speeds at points where the pressure

is respectively Pj and Pg, then

1 1

s«

1

c(2-7)

The units for conductance are the same as those for pumping speed.

The pumping speed of a system consisting of a pump of speed S^ with

an interconnecting conductance (a pipe or conduit) of conductance C

is given by 11 1

s >s„ c

or S = (2-8)

If several conductances are connected in series the resultant con-

ductance of the combination is given by

1 11 1- (series) =—+—+ —O Oj (^2 ^S

(2-9)

If several conductances are connected in parallel the resultant con-

ductance is

C(parallel) = Ci + C2 -f C3 + • •• (2-10)

High-pressure or Viscoiis Flow. The pressure region of viscous flow

is that for which the molecular mean free path is short as compared

with the diameter of the pipe or conduit. For these conditions the

conductance of a tube of circular cross section is

C (liters/sec) = 3.27 x 10"rjL

(2-226)

if D and L are measured in centimeters, the viscosity rj is in poises,

and the pressure is in torr, where Pav = (Pi + P2)/2, in which Pj and

GAS ELOW 59

P2 are the values of the pressure at the ends of the tube. It follows

that

C (cfm) = 9.46 X 10~2 _, p^^ (2-22c)rjL

if D is measured in inches, L in feet, rj in poises, and the pressure in

torr. The viscosity for several gases is given in Appendix III.

For air at 68°F = 20°C the viscosity rj = 1.829 x 10-« poises so

that

D*C (liters/sec) = 179 -— Pav (2-23a)

and C (cfm) = 517 —- Pav1j

(2-236)

The following approximate expression for the pressure drop in air along

a pipeline is applicable if the pressure drop is small (say not more

than 20 per cent) as compared with the pressure

:

o r

Pressure drop (torr) = 5.6 x 10~^ -y-^ (2-27a)

when Sj, is measured in liters per second and D and L are measured in

centimeters

;

.S„LPressure drop (torr) = 1.9 x 10"

D*(2-276)

when Sp is measured in cubic feet per minute, D in inches, and L in

feet.

Flow in the Transition Pressure Region. When the gas pressure is

such that the mean free path is of the same order as the cross-sectional

dimensions of the pipe or conduit through which it flows, the con-

ductance of a tube of circular cross section is then given by

C— = 3.269 X 10-2(^)--O^T\^ 1 + 0. 147(J//r)''^ P^yDIv

181(J//T)'^ Pavi>/»?

(2-45)

in which G is measured in liters per second, L and D are in centimeters,

Pav is in torr, T is in °K, M is in grams, and r] is in poises. For air at

20°C the conductance is

7)3/ \ _j_ 252 1 P D\C (liters/sec) ^ 12.12 .^(l4.74 P..D +

^ ^ 3,/,^J (2-69)

For accurate calculation of the conductance of a long tube, these

formulas should be applied over a range of pressure from lOP^ to 0.1 Pj,


where P; is the transition pressure given by

P, = 95.7

which for air at 20°C is

MI D

5.57 X 10-2

D

(2-55)

(2-58)

Calculation of conductances by the transition formulas (2-45) and

(2-69) is seldom justified in practice. It generally suffices to use the

viscous-flow value of the conductance as given in (2-22) and (2-23)

from atmospheric pressure down to the transition pressure given in

(2-58) and the molecular-flow conductance such as that given in (2-97)

from the transition pressure on down.

Molecular Flow at Low Pressure. At sufficiently low pressure, i.e.,

when the mean free path is large as compared with the cross-sectional

dimension of the tube or conduit, the conductance is independent of the

pressure. For most purposes the conductance formulas derived partly

empirically by Knudsen are sufficiently accurate. In the following

formulas the linear dimensions are measured in centimeters, areas are

in square centimeters, conductances are in liters per second, temperature

is in degrees Kelvin, and mass is in grams. The values for air are given

at 20°C. The less frequently needed equivalents for conductance in

cubic feet per minute and dimensions in inches and feet are given in the

text.

Circular Aperture

C

C(air) = 9.16i)2

in which D is the diameter of the aperture.

Aperture of Any Shape

C ^ ZM{^fA

C (air) = 11.6^

in which A is the area of the aperture.

Tube of Circular Cross Section

'pVA 2)3

C ^ 3.810(-)

C (air) = 12.12

(2-89)

(2-90)

(2-93)

(2-94)

(2-96)

(2-97)

in which D is the diameter and L the length of the tube.

gas flow

Conduit of Rectangular Cross Section

a^b^C = 9.71

G (air)

[mJ 1m,

30.9-

(a + h)L + %ab

a%^

61

(2-100)

(2-lOOa)(a + b)L + y^ab

in which a and b are the dimensions of the cross section and L is the

length in the direction of flow.

1.0


a tube with two restricted ends.

[Taken with permission from L. L.

Levenson, K. Milleron, and D. H.Davis, Le Vide 18, 42 (1963).]

o1 T_.1 I n I /

. _. • Calculated points

I

' —ll-^^ L ° Expenmentol points

U Ll_L_L fnr(R/R/ =

L/Ro


a tube with two restricted ends and acircular blocking plate. [Taken with

permission from L. L. Levenson, N.Milleron, and D. H. Davis, in 1960Vacuum Symposium Transactions

(Pergamon Press, London, 1961).]

Slot of Long, Narrow Cross Section a > 6

ab^C = 9

\m]

C (air) = 30.9

L + %b

ab^

L +%bLong, Narrow Slot with a > 6 and L ^b

T

~L

C 9.71IT\M.

C (air) = 30.9

(2-101)

(2-lOla)

(2-102)

(2-103)


Annulxjs between TwoConcentric Tubes

G =

3.810T\^ {D/ - D,^)(D, - D,)

\MI

C (air)

12.12


a tube with one restricted end and a

circular blocking plate. [Taken with

permission from L. L. Levenson, N.

Milleron, and D. H. Davis, in 1960

Vacuum Symposium Transactions


lations and measurements for someFigs. 2-6 through 2-13.

L + %{D^ - A)(2-104)

{D^ - D,')(D, - -Di)

L + %{D, - D,)

(2-105)

By combinations of the above

formulas the conductances of manycomphcated shapes, such as baffle,

structures, can be roughly approxi-

mated. The Knudsen formulas are

generally only approximate and

for short tubes give conductances

which may be greater than the true

value by as much as 11 per cent.

The results of more accurate calcu-

shapes are given in the text and in

REFERENCES

1. M. Knudsen, Ann. Physik 28, 75 (1909).

2. M. Knudsen, Ann. Physik 28, 999 (1909).

3. P. Clausing, Ann. Physik 12, 961 (1932).

4. D. H. Davis, J. Appl. Phys. 31, 1169 (1960).

5. L. L. Levenson, N. Milleron, and D. H. Davis, in 1960 Vacuum SymposiumTransactions (Pergamon Press, London, 1961), p. 372.

6. L. L. Levenson, N. Milleron, and D. H. Davis, Le Vide 18, 42 (1963).

r

CHAPTER 3

PRESSURE MEASUREMENT IN VACUUM SYSTEMS

The most important parameter to be measured in a vacuum system

is the gas pressure. The pressure of interest may be the total pressure,

including both the easily condensable and the permanent gas compo-

nents present, either the condensable or permanent gas components

separately, or finally the partial pressure of each of the constituents,

such as oxygen, nitrogen, hydrogen, carbon dioxide, etc. The range of

pressure over which reasonably accurate measurements are of interest

extends from atmospheric pressure down to 10"^^ torr or lower. Gauges

and techniques have been developed by which any of the various types

of pressure mentioned above can, in principle, be measured with the

necessary sensitivity; but particularly for values of the pressure

below about 10~* torr ambiguity and error arise from parasitic effects

within existing gauges which make accurate determination of the

pressure difficult.

3-1. Liquid Manometers. A liquid manometer consists of a

U tube partly filled with liquid. One end of the U tube is connected

to the system in which the pressure

is to be measured. The other endis either open to some reference

pressure, such as atmospheric, or is

closed off with the volume abovethe liquid level evacuated. Openand closed manometers are illus-

trated in Fig. 3-1.

Open manometers are generally

used to measure pressure relative to

atmospheric pressure and may befilled with any liquid, ofwhich water,oil, and mercury are commonlyused. The engineering term gaugepressure and units such as inches ofwater and millimeters of Hg for thepressure difference grew naturallyfrom the use of open manometers.

63

To the

system

Open

To the

system

Closed

Fig. 3-1. Liquid manometer.


Closed manometers are more generally used for measurement of

pressure small as compared with atmospheric. An exception to this

statement is the mercury barometer, which is in fact a closed manom-eter designed specifically to measure atmospheric pressure in absolute

units, i.e., relative to zero pressure. A closed manometer is first

thoroughly evacuated and then filled to the proper level while still

under vacuum so that the gas pressure over the liquid in the closed

arm is negligible as compared with any pressure to be measured.

The open end is connected to the system so that a difference in level

or head between the surfaces of the liquid in the two arms will be just

proportional to the total pressure in the system. The difference in

level h is related to the pressure according to

P=gph (3-1)

in which the pressure P is in dynes per square centimeter or /<bars when

the density p of the liquid is measured in grams per cubic centimeter,

the head in centimeters, and g = 981 cm/sec^. When the liquid is

mercury the difference in level in millimeters is by definition equal to

the pressure in torr. Since the density of mercury at 0°C is 13.59 g/cm^,

we have from (3-1)

10 X P(ubar)P(torr) = ft(mm)

981 X 13.59

7.50 X 10-«P fibaur (3-2)

thus 10* /^bar = 750 mm Hg, which is the range of atmospheric pressure

and is defined for some purposes as the standard atmosphere.

With some care in the arrangement of a mercury manometer, a

pressure of 0.1 torr can just be detected and a pressure of 1.0 torr can

be read with the unaided eye with a probable error of about 10 per cent.

For lower values of the pressure, differences in capillarity and sticking

in the tube tend to produce significant errors. However, if the tube

diameter is sufficiently large (---1 cm) and the tube and mercury kept

clean, a manometer can give accurate readings down to 10~^ torr by the

use of optical means of magnifying small differences in level.

The sensitivity of a manometer can be increased by about a factor

of 15 by using a diffusion-pump oil instead of mercury. However,organic fluids are much more susceptible of contamination by dissolving

gases than is mercury. For accurate reading of low pressures the oil

used in a manometer must be purified frequently by-vacuum distillation

and outgassing.i*

* References indicated by superscript numbers are listed at the end of thechapter.

PRESSURE MEASUREMENT IN VACUUM SYSTEMS 65

Over the range for which it is effective the liquid manometer respondsdirectly to the total pressure in the system and is therefore an excellentabsolute standard of total pressure. However, since the readingdepends upon the density of the fluid, which in turn depends upon thetemperature, some care must be taken to control the temperature ofthe gauge when highly precise measurements are required. As anexample, the density of mercury changes about 0.5 per cent over thetemperature range from to 30°C.

3-2. The Diaphragm Manometer. The principle of the dia-phragm manometer for the measurement of low gas pressures is shownin Fig. 3-2, which is a cutaway view of a gauge manufactured byWallace and Tiernan.^

The diaphragm type of gauge is a very common device for themeasurement of pressure differences, such as the "gauge" pressurerelative to atmospheric pressure in many engineering applications.For the measurement of absolute pressure in the range of interest invacuum technology, the reference pressure of interest is zero absolutewithin the range of sensitivity of the gauge. In the Wallace andTiernan gauge an evacuated beryllium-copper capsule is used as thepressure-sensitive element. The capsule is mounted in the gaugechamber, which is connected to the system within which the pressureis to be measured. Distortion of the capsule due to the pressure is

transmitted through a mechanical linkage to a rotating pointer, whichindicates the pressure on a circular dial viewed through a sealed windowin the front of the gauge chamber. Standard models of this gaugeare available with scale divisions of 0.2 torr and pressure range fromto 50 torr.

A large variety of diaphragm gauges have been developed withsensitive means for detection of small displacements of the diaphragmfor measuring much lower pressures than can be measured mechanically.In the manometer of East and Kuhn^ the diaphragm is in the form ofa bellows, into the interior of which the pressure to be measured isadmitted. Elongation of the bellows due to the pressure is amplifiedby a light beam reflected by a small mirror which is tilted by motionof the bellows. By this means pressure changes of 5 x 10^* torr weredetected.

By using electrical methods of detecting changes in the position of adiaphragm, highly sensitive vacuum manometers have been developed.One such method, as illustrated in Fig. 3-3, depends upon the capaci-tance between a diaphragm and a fixed electrode. Movements of thediaphragm in response to the pressure changes the spacing, and there-lore the capacitance, which can be measured with a capacitance bridgeor made a part of a resonant circuit, the frequency of which is measured.


GEAREDSECTOR

ZERO SETTIN6 ADJUSTMENT


Fig. 3-2. Diaphragm manometer with mechanical indication. [Reproduced

through the courtesy of Wallace and Tiernan, Inc., 25 Main Street, Belleville 9,

N.J.]

Connecting wire Insulator

Electrode

Diaphragm

2A

In either case the reading is a function

of the pressure, which may be linear

over a sufficiently wide range to beconvenient in use. The construction

of a gauge of this type, in which aplane diaphragm was used, is described

by Pressey* and is illustrated in Fig.

3-4. The range of linear response wasabout 1 torr with a sensitivity of 10-^

torr limited by fluctuations due to

temperature. More sensitive gaugesof this t5rpe have corrugated instead

of plane diaphragms, the corrugations

being concentric rings about a central

plane section. By this construction

the sensitivity to pressure changes is

increased by about a factor of 10 with no significant change in the re-

sponse to temperature variations so that sensitivity of about 10^* torr

Fig. 3-3. Diaphragm manometerfor electrical sensing of pressurechanges. [Taken with permissionfrom J. H. Leek, Pressure Meas-urement in Vacuum Systems (Pub-lished for the Institute of Physicsand the Physical Society byChapman and Hall, Ltd., London,1964), 2nd ed.]

,

Pig. 3-4. Cross section of diaphragm manometer designed for capacitance meas-urement of the differential pressure. [Taken with permission from J. H. Leek,Pressure Measurement in Vacuum Systems (Published for the Institute of Physicsand the Physical Society by Chapman and Hall, Ltd., London, 1964), 2nd ed.]


Gloss tube

is achieved. However, in a panel discussion on the subject of vacuum

gauges held at the 1960 annual symposium of the American Vacuum

Society, P. A. Redhead fexpressed the opinion that mechanical manom-

eters have a lower limit of about IQ-^ torr because of effects, such as

that of vapor molecules with dipole moments on capacitance gauges,

which cannot be controlled.

Because the sensitivity of the diaphragm manometer depends

critically upon the mechanical properties of the diaphragm, such a

gauge cannot beregarded as a primary stand-

ard in the sense that a liquid manometer

may be. For this reason diaphragm ma-

nometers must be calibrated with reference

to a liquid manometer. It is also necessary

to have some convenient method of checking

and adjusting the zero reading periodically.'

3-3. The Dubrovin Gauge. The Du-

brovin gauge ^ is a type ofmanometer which

utilizes the displacement of mercury in such

a manner as to produce a sensitivity of the

order of 10 times greater than that of the

simple mercury U-tube manometer. The

gauge consists of a glass cylinder partly

filled with mercury and a stainless steel

tube, closed at the upper end and open at

the bottom, floating vertically in the mer-

cury. The gauge is prepared for use by

laying it on its side so that the open end of

the steel tube is exposed and evacuating

the gauge so that the residual pressure

throughout the gauge, including the region

inside the steel tube, is very low. While

still evacuated the gauge is returned to the

vertical position with the steel tube floating in the mercury, as shown

in Fig. 3-5. When gas is admitted through the connection at the top

of the gauge, the steel tube is pushed down by the pressure more deeply

into the mercury. For some pressure P in the gauge the balance is

reached when the weight of the tube plus the force exerted on the

closed end of the tube by the gas pressure is equal to the change in

weight of the displaced mercury. If d^ and d^ are respectively the inner

and outer diameters of the steel tube and p, its density, then

Thin-wall

steel tube

Mercury

\J>

Fig. 3-5. The Dubrovingauge.

Tdi2 n

4^ + 7 {d^ di^)ps9L =

JW d^')Pm9{^ - h) (3-3)

7


in which p„ is the density of mercury, L the length of the steel tube,and h the length of the steel tube protruding above the mercury. Then

„ d^^ - (^2

P = ^- glpJL ~h)- p^L]d,^

d^-d,^ lp„gpm\—

d,'h (3-4)

The zero position of the steel float is obtained by setting f = in (3-4)from which

K = (3-5)

is the length of steel tube protruding above the mercury level at zeropressure and (3-4) may be written as

P = d. d,^

d,^9Pm(K - h) (3-6)

(3-7)

The sensitivity of the Dubrovin gauge from (3-6) is

dh _ dj^ 1

dP~d^-d,^'^which is to be compared with (3-1) for the mercury U-tube manometerfor which the sensitivity is l/gp^. The sensitivity of the Dubrovingauge is thus greater than that of the mercury U-tube manometer bythe factor

dx'(3-8)F

d^^ - dj^

For a factor F = 10 and d^ = 1 cm one finds from (3.8) that d^ = 1.05cm so that the wall thickness of the steel tube must be about 0.025 cm,or 0.010 in. For such a gauge a change in A of 1 cm represents achange in pressure of 1 torr, so that pressure changes of 0.1 torr can bedetected with ease. With a sensitivity of this order the Dubrovingauge is a convenient instrument for the measurement of pressure in therange below that easily read on a manometer, but above that normallyreserved for the McLeod gauge discussed below.

3-4. The McLeod Gauge. By combining a liquid manometerwith means of compressing a sample of gas as is done in the McLeod*gauge, the range over which the pressure can be measured can beextended considerably below the practical limit of about 10-^ torr forthe mercury manometer. The essential elements of a McLeod gaugeare shown in Fig. 3-6, and consist of a glass bulb with a capillary tubeextension on the top, a side arm connnecting to the vacuum system,and some means of raising and lowering the liquid level within the


gauge. The fluid normally used in McLeod gauges is

mercury, although in a few exceptional instances

organic fluids of low vapor pressure have been used.

When the mercury level in the gauge is lowered below

the branch point A the bulb of volume V is connected

to the system through side arm B. The gas in the

bulb is then at the same pressure as that in the

system. When the mercury level is raised, the bulb

is cut off from the side arm and the sample of gas

compressed into the capillary Cj. The capillary C^

is in parallel with a section of the side arm B and

has the same bore as C^ so that the surface tension

or capillary effect is the same. The difference in level

of the mercury in G^ and Cg is therefore due to the

pressure difference resulting from compression of the

sample from the large volume V into the small

-'volume of Cj above the mercury level.

The pressure of the compressed gas in the closed

capillary is proportional to (Ag — ^i) + ^O' ^^ which

hi and h^ are the heights in millimeters of the mercury

in capillaries G^ and C^, and P^ is the pressure in

the system still present in Cg. Since the compression

ratio is typically very large, P„ is negligible as com-

pared with A.2 — K- The pressure of the compressed sample of gas is

thus just equal to h^ — K torr within the limit of reading error when

hi and ^2 are measured in millimeters. If the system contains per-

manent gas only during the compression cycle, according to the general

gas law (1-1)

PV = P'V (3-9)

in which P and P' are the pressures before and after compression,

respectively, V is the volume of the bulb (i.e., the volume of the closed

portion of the gauge above the cutoff point A), and V, the volume

of the closed capillary above the mercury level h^, is given by

Fig. 3-6

gauge.

McLeod

F' =

(^0 - hi)a

1,000(3-10)

where h^ is the effective height of the closed end of capillary Cj and a

is its cross-sectional area in square millimeters. Then

PV = (^2 — hi){ho — hi)a

1,000(3-11)

PRESSUBE MEASUREMENT IN VACUUM SYSTEMS 71

which holds for all values of h^ and h^ as the mercury is raised in the

system. From (3-11) it is evident that

{K - K){K - h)-1,000

PV = const (3-12)

provided that the pressure is due to a permanent gas as defined by(3-9). In using a McLeod gauge this point should be periodically

checked, i.e., the mercury should be raised to two or more levels, the

values of A.2 a-nd h^ measured, and the criterion given in (3-12) checked.

In an extreme case the remaining gas present in the system may be dueto a substance for which the vapor pressure at room temperature is

P^. In that case the pressure will increase during compression only

to the point at which P = P^, beyond which condensation will occur

and the pressure will be independent of the volume of the sample. Inthat case for a condensable vapor

h^-hi = P^ = const (3-13)

which is in considerable contrast with the criterion in (3-12). If the

vapor pressure of the contaminant in the system is fairly low and somepermanent gas is also present, a behavior somewhat in between that of

(3-12) and that of (3-13) will result. The important point is that if

criterion (3-12) is not obeyed, the pressure readings as determined bya McLeod gauge will not be valid. One can then conclude that the

system or the gauge itself is contaminated by a condensable material,

the room-temperature saturated vapor pressure of which is givenapproximately by (3-13).

Returning to the measurement of permanent gas pressure with a

McLeod gauge we find that the pressure from (3-11) is

P = (^2 — hi){h„—hi)a

1,000F(3-14)

A McLeod gauge may conveniently be read by bringing the mercurylevel up to the point where ^2 = h^ (i.e., the level in the open capillary

opposite the end of the closed capillary) or the mercury level can be set

at some standard level h^ in the closed capillary. In the first methodwith ^2 = ^0 the pressure is

1,000F{h, - h,Y = ki(M)i^ (3-15)

in which the constant of the gauge k^ = a/l,000F. In the secondmethod with h^ = h.

„ a(h„ — h,)

^ = 1,000F ^^' ~ ^^^ = ^^^^^^' (3-16)


in which the constant of the gauge k^ = a(^o - h^)j\,()()QV. In each

method A^ is the difference in mercury level in the open and closed

capillary when the mercury level is set in the prescribed manner. The

first method leading to the formula (3-15) results in a pressure reading

proportional to the square of the reading, whereas the second method

leads to (3-16), in which the pressure is proportional to the first power

of the reading. The sensitivity can perhaps best be defined from (3-15)

when AA = 1 mm, which is about as small a value as can be estimated

with reasonable accuracy. On this basis the sensitivity of the McLeod

gauge is

P. =4,000 X 200

3.9 X 10-« torr (3-17)

which is a practical and useful sensitivity for vacuum measurements.

The McLeod gauge has a unique role in the measurement of pressure

in vacuum systems and is frequently used as the standard gauge for

calibrating most other types of low-pressure gauges.* As can be seen

from Eqs. (3-15) and (3-16), the cahbration of a McLeod gauge depends

only upon the measurement of the volume V of the bulb and the cross-

sectional area of the capillary tube. The volume of the bulb can be

measured with great precision by inverting the gauge, filling the bulb

and tubing up to the branch point A with mercury, and weighing the

mercury. The cross-sectional area of the capillary can best be measured

by filling a measured length of the capillary with mercury and weighing

the small sample of mercury. Since capillary tubing is not necessarily

of uniform cross section, a length of tubing must be tested and a section

of sufficiently uniform diameter chosen. By placing a drop of mercury

in the tubing, moving it along the tube, and measuring the length of

the mercury column formed at several positions along the tube, the

variations in diameter can be easily determined and an acceptable

section found for making both the open and closed capillaries Cj

and C2.

Experience has shown that a bore diameter less than 1 mm is im-

practical because of the tendency for the mercury column in a finer

capillary to separate, leaving a bead of mercury plugging the closed

capillary after a reading has been taken and the mercury level lowered

to empty the bulb. For high sensitivity it is therefore necessary to

increase the volume F of the bulb rather than to decrease the capillary

bore to less than 1 mm. The end of the closed capillary must be

sealed off as squarely as possible in order that the zero point of the gauge

* Note: See Sec. 3-13 for discussion of the use of a McLeod gauge with a

refrigerated vapor trap for calibrating ionization gauges, and Ref. 51 for a report

on observed discrepancies.


1

^0 can more easily be determined and also to avoid an exaggeratedtendency of the mercury column to stick whenever the mercury levelcomes within a millimeter or so of the closed end of the capillary. Theeffective height of the closed end of the capillary cannot, in general, bedetermined accurately by eye because of irregularities near the end ofthe capillary produced in sealing the end. The true value of h^ can bedetermined by applying criterion (3-12) to the gauge, which is thor-oughly trapped to eliminate condensable vapors, and choosing a valueof h^ which fits (3-12) best for several values of h^ and h-^.

The McLeod gauge is inherently a cumbersome instrument to use inthe pressure range from 10-3 to 10-« torr, in which it is most neededas an absolute gauge. Since it must be made at least partly of glass,it is a fragile device in which the shifting load of mercury must becarefully supported or disastrous breakage will occur. The interior ofthe McLeod gauge and the mercury used must be scrupulously cleanand particularly free of oil and grease, otherwise readings are meaning-less and the mercury sticks in the capillary, refusing to come down whenthe mercury level is lowered.

The connecting tubing for a portable McLeod gauge is frequently asource of error since to be convenient in use its diameter must befairly small and its length typically a meter or more.The conductance of such a connecting tubing is very small, usually

not more than 0.1 liter/sec, so that a small leak at the gauge end of thetubing can give rise to an unexpectedly large discrepancy between thepressure in the system and that seen by the gauge. Such an error caneasily be detected and estimated if the gauge connection can be closedoff next to the system and the pressure rise in the gauge due to leakagemeasured for a specific time interval, such as 5 min. The procedure is

to take a normal reading P^ with the gauge, then close off the line nearthe system and wait several minutes and take a second reading P^.Any appreciable increase of P^ over P^ is an indication that the gaugeerror due to leakage may be serious. To evaluate the gauge error thetotal volume being filled by the leak must be estimated. This totalvolume consists of the gauge volume (the bulb and side tube) and thevolume of the connecting line up to the cutoff point. As an example,assume that

Pj = 10-3 torr

P2 = 10-2 torr

< = 5 min = 300 sec

ic (the length of the connecting line) = 100 cmd^ (the diameter of the connecting line) = 0.5 emF„ = 300 cm3


then the volume of the connecting line is

^ , =—- L cm^" 4

The leakage rate is the volume filled by the gas multiplied by the

pressure rise divided by the time, or

P — PQ^ = — i {V, + Fe) torr cmS/sec

Pt-P^(7 4-7^)10-3 torr liters/sec

The conductance of the connecting line is, according to (2-82),

d ^

G =12.12-^ liters/sec

By the definition of conductance in (2-4) the flow rate and conductance

are related byQ. = G,{P, - Ps) = C, AP

in which P, is the pressure in the system when the gauge reading Pj is

taken, so that the difference between these values of the pressure is

the gauge error, which is

^0AP =C.

For the above example

77 X 0.25F„ =

Q.=

4

9 X 10-^

300

(100) = 19.6 cm^

(319.6)10-^ = 9.6 X 10-« torr liter/sec

125(7 = 12 X — = 1.5 X 10-2 Hter/sec

100

and the gauge error is

_ 9-^ X IQ"" = 0.64 X 10-3 torr1.5 X 10-2

Thus, for the example given of the reading Pj = 1 X 10-^ torr, the

greater part, or 0.64 x 10-^ torr, is the gauge error. Errors of this

magnitude and sometimes much greater frequently appear when this

simple test is carried out. The need for truly leakage-free connections

to a McLeod gauge and connecting tubing of reasonably large-bore


diameter can hardly be overemphasized. Other types ofvacuum gaugesare also sensitive to small air leaks, but the McLeod gauge is particularlyvulnerable because of the low conductance of the line with which it is

connected to the system in many applications. In systems built for thecalibration of other types of gauges, such as ionization gauges, in thepressure range 10-^ to 10-^ torr no compromises for reasons of conven-ience should be tolerated in the manner of connecting the McLeod

Set mark

760 mm

q)

-Flexible

hose

1

Fig. 3-7. Methods of controlling the mercury level in McLeod gauges.

gauge.

The system should be made of fairly large-diameter glass tubingwith a high-conductance liquid-nitrogen trap between the McLeodgauge and the gauges to be calibrated, and no questionable connectorswith rubber or other organic materials should be used.

Several methods, as illustrated in Fig. 3-7, have been devised for

raising and lowering the mercury level in McLeod gauges. For con-sistent readings it is important that the mercury be raised smoothly tothe proper level, but not beyond, since there is always a slight mechani-cal hysteresis in the response of the mercury in the closed capillary dueto surface effects.

The simplest method for controlling the mercury level is illustratedin Fig. 3-7a. A reservoir filled with mercury is connected to theMcLeod gauge just below the branch point with a length of rubbertubing. The mercury level in the gauge, riding at about a barometricheight above that in the reservoir, is adjusted to the proper height byraising and lowering the reservoir. This simple method has been usedfor many years although its disadvantages are the contamination of the

75 VACUUM SCIENCE AND ENGINEBEING

mercury by the rubber tubing and frequent loss of mercury by the

rubber tubing shpping off or rupturing..

A somewhat better arrangement for lifting the mercury level is

shown in Fig. 3-76 in which the reservoir, which in this case can be made

of steel, is coaxial with a long vertical tube extending below the branch

point a distance slightly greater than the barometric height of about

760 mm. The top of the reservoir can be made with relatively small

clearance at the top so that contamination of the mercury is not a

serious problem. For sensitive gauges, however, methods a and h

are cumbersome, even when combined with counterbalancing to reduce

the effort required to lift the heavy mercury load.

In Fig 3-7c a fixed mercury reservoir is located sufficiently below

the McLeod gauge that a barometric height for mercury places the level

below the branch point when the gauge is connected to a high vacuum.

The reservoir is in the form of a cylinder with a loosely fitting wooden

or hollow steel plunger which can be thrust down to displace most of the

mercury in the reservoir, raising the level. Relatively fine control can

be provided by clamping a threaded collar on the plunger near the top

arranged to mesh with threads at the top of the reservoir housing so

that the final inch or so of the stroke is controlled by rotating the

plunger.. -, , xu

In Fig. 3-7d a compact form of McLeod gauge is achieved by the use

of an auxiliary vacuum reservoir to control the mercury level. The

mercury in the gauge is lowered by pumping air out of the reservoir

above the mercury and raised by admitting atmospheric air, usually

through a tube partly filled with a drying agent, such as activated

alumina or silica gel. A two-way stopcock type of valve is a conven-

ient means of switching from admitting to removing air from the reser-

voir. Fine control in raising the mercury level can be provided by

notching the inner member of the stopcock with a file at both ends of

the hole through which air is admitted. With the development of

some skill an operator can then reduce the flow rate as the mercury

level approaches the zero mark and stop the flow without overshooting

the mark. Tapping the closed capillary with a finger or applying a

small mechanical vibrator will help to compensate for the tendency of

the mercury to stick and advance erratically.

The use of a flexible metallic diaphragm for raising and lowering the

mercury in a compact form of McLeod gauge is illustrated in Fig. 3-7e.

The particular model shown is an unusually compact form of McLeod

gauge and has the added feature of a dual range achieved by the use of

two closed capillaries connected to the same reservoir.

The pressure range of a McLeod gauge is determined by the length

of the capillary tube, which is limited to about 15 cm by practical


considerations. A gauge with a bulb volume of 300 cm^ and a closed

capillary of 15 mm length and 1 mm bore has a range as given by (3-9)

from

2.26 X 10-« torr for ^i = 1 mmto 5.9 X 10-2 torr for \ = 150 mm

Fig. 3-8. McLeod gaugewith several scales for

an extended pressure

range.

Fig. 3-9. Dual-range

McLeod gauge. [Takenwith permission fromJ. H. Leek, Pressure

Measurement in VacuumSystems (Published for

the Institute of Physics

and the Physical Society

by Chapman and Hall,

Ltd., London, 1964),

2nd ed.l

In many applications it is desirable to extend the range of the gaugeto appreciably higher pressure. One way in which this can be done is

to make the closed capillary out of short lengths of tubing of different

bore diameters and for each such section provide a Cg capillary, all in

parallel with the side arm, as illustrated in Fig. 3-8. An alternative

design due to Romann' is shown in Fig. 3-9 in which a small bulb is

inserted between the main bulb and the base of the closed capillary

with a second closed capillary tubing connected between the two bulbs.

The sensitivity for the second capillary is VijV[ of that for the main


capillary so that the pressure range is increased by about the inverse

of this ratio.

3-5. Thermal Conductivity Gauges. The thermal conductivity

K oi a. substance is defined by the expression

H = -K—-ds

(3-18)

in which H is the amount of heat flowing per unit area per second in the

direction parallel to s, and dTjds is the temperature gradient in this

same direction. For rarified gases the kinetic theory of gases provides

a derivation* of an expression for the thermal conductivity by methods

similar to that given for the viscosity in Sec. 1-9. The derivation leads

to the conclusion that the thermal conductivity of a rarified gas is

given byK = M(9y - 5)riC, (3-19)

in which y = CJC^ is the ratio of the specific heat of the gas at constant

pressure to that at constant volume, and r] is the coefficient of viscosity.

But the expression (1-59) for the viscosity is independent of the pressure

so that the thermal conductivity is also independent of the pressure

over the same range for which the viscosity is given by (1-59). How-

ever, as was pointed out in the discussion of that expression, when the

gas pressure is so low that the molecular mean free path is about equal

to or greater than the distance between the walls of the containing

vessel, the gas is no longer characterized by a viscosity. In that case

the expression (3-19) is no longer valid and the conductivity is then

found to depend upon the pressure. Therefore, in the pressure range

for which the mean free path is comparable with or greater than the

dimensions across which the flow of heat occurs, the variation of the

thermal conductivity of the gas with the pressure can be used for the

measurement of the pressure. The process of heat flow under these

conditions is called free molecular conduction.

Consider a cylindrical tube with a heated filament of circular cross

section running along its axis. According to (1-31) the number of

molecules per second striking each square centimeter of the surface of

the filament is

V = yinva,T/

_ n/2kTY2\ 77m;

n/2RoTY'2\ uM !

(3-20)

PEESSUEE MEASUREMENT IN VACUUM SYSTEMS 79

from (1-23) and Table 1-3. If the diameter of the filament is very smallas compared with that of the tube, each molecule will strike the wallseveral times before finally hitting the filament and will therefore bein good thermal equilibrium with the wall temperature T^ beforehitting the filament. At the low pressure here assumed, however, eachmolecule which strikes the filament will do so only once before againcolliding with the wall. The molecules leaving the filament, therefore,

will not be in equilibrium with the temperature T, of the filament, butwill be characterized by some lower temperature T'^.

Under conditions of temperature equilibrium with both surfaces, the

kinetic theory of gases gives for the energy transferred by a monatomicmolecule

E = 2k{Tf - TJ {k = the Boltzmann constant)

which in this case can only be in the form of kinetic energy. However,more generally for diatomic and polyatomic molecules which acquire

vibrational and rotational as well as translational energy, the energytransferred is greater by the factor (y + l)/4(y — 1) where y = Cj,/C^,

the ratio of specific heats of the gas. Thus, in general, the energytransferred per molecule under the conditions of thermal equilibrium

with both surfaces is

^^)HT,-TJ (3-21)E

However, the situation of interest is one in which the molecules donot come into equilibrium with the temperature of the hot filament

so that the energy transfer per molecule is given by a similar expression

with T'f substituted for T, where T'f < Tf. Thus, in the case of

interest,

5^7^ ^(^-^J (3-22)E

Knudsen defines the accommodation coefficient a as the ratio of these

two quantities; i.e..

^ f -> w

so that the energy transferred per molecule is

(3-23)

(3-24)

Combining (3-20) with (3-24) one then obtains for the rate of energy


transfer from 1 cm^ of filament surface

_ g y + 1 / -Rq \^ (rp T )P ergs/sec cm^ (3-25)

2y - 1\27tMTJ ^ '

since from (1-16) nifc = P/T and since by our assumption regarding

the ratio of diameters of the filament and the tube, the gas molecules

hitting the filament will be in equilibrium with the temperature T„

of the tube wall. For numerical evaluation Eq. (3-25) may be written

in the form

w _«L±i/_^2_f(—f(T -T~27 - l\277i/(273)/ \T„/

..m\^, T^)P ergs/sec cm'' (3-26)

in which Ao is the free molecular conductivity at 0°C given by

Ao = Y + 1 Rn J}A

2(y - l)\277i/(273)/

llOy + 1

ilf'^ 7 - 1

1.47 X 10-2 y + 1

ergs/sec cm^ °C ^bar

jfVi y-1watts/cm^ °C torr (3-27)

The free molecular conductivity at 0°C for a given gas can be calculated

by (3-27) and the resulting value inserted in (3-26). However, the

accommodation coefficient a cannot be calculated since its value depends

not only upon the gas involved but also upon the material and surface

condition (roughness and adsorbed gas layer) of the filament. For

clean metallic surfaces exposed to air, the value of a is in the vicinity

of 0.9, whereas for hydrogen the value of a is generally quite low

(0.2 to 0.5). For roughened or blackened surfaces a approaches unity

for all gases. Since surfaces are generally not highly polished nor

completely free of adsorbed gas layers, the value a = 0.7 may be used

for rough approximation.

As an example, for air

1.47 X 10-2 2.401

(28.98)'-^ 0.401= 1.64 X 10-2 watt/cm2°C torr

so that the heat conduction per unit area from a filament at a temper-

ature of 100°C to the surrounding tube walls at room temperature


(20°C) in which the pressure of air is 10^ (0.01 torr) is

(273\!-2-—I (100 - 20)(0.01)

= 8.87 X 10-3 watt/cm2

If the filament is 1 mil (0.0025 cm) in diameter and 4 in. (10 cm) long,

the surface area is about 7.9 x 10"^ cm 2 and the gas heat conduction

will be of the order of 6.9 x 10-* watt.

Even under conditions of perfect vacuum (P = 0) in the tube, heat

will be lost from a hot filament by thermal radiation. If the surfaces

were perfectly absorbing to radiation of all wave lengths, the rate of

energy loss would be given by the Stefan-Boltzmann law for "black

body" radiation^^ ^ ^^^^, _ ^^,^ ^3^^)

in which a = 5.673 x IO-12 watt/cm2 (3-29)

All real surfaces, however, are not perfectly absorbing and are character-

ized by the emissivity e with the result that the rate of radiation of

energy becomes^^ ^ ^^^^^^, _ ^^^^,^

'

^33^^

If loss of heat from the filament due to radiation is large as comparedwith that due to gas conduction, the latter cannot be used as a means of

measuring the pressure because of the large background effect.

For the example above, the heat loss by radiation for perfectly

"black" surfaces would be

W, = 5.67 X 10-12(373* - 293*)

= 6.80 X 10-» watt/cm2

Since the surface area of the filament is 7.9 x IO-2 cm2, this wouldresult in a power loss due to radiation of 5.37 x 10-* watt, which is

comparable with the loss calculated above due to free molecular con-

duction at P = 10-2 torr. However, since the emissivities of sm^faces

of clean metals at temperatures in the range of to 100°C are generally

of the order of 0.1, the true loss due to radiation would be of the order

of 5 X 10-^ watt, so that radiation loss and gas-conduction loss wouldbecome about equal at a pressure of about [(5 x 10-^)/(6.9 x 10"*)]

X 10-2 <=» 7 X 10-* torr.

Inspection of Eqs. (3-26) and (3-30) shows that radiation increases

much faster with increasing temperature because of the T* dependencethan does gas conduction, so that an equality between radiation and gas

conduction occurs at higher pressure as the temperature is raised.

Therefore, for measurement down to lowest pressure, the filament should

be operated at the lowest temperature for which the heat loss due to

gas conduction can be measured. Because of the competition with


radiation loss, thermal conductivity pressure gauges are not normally

used for pressure measurements below about 10~^ torr.

There is a third process by which a hot filament may lose heat to

its surroiuidings, i.e., by thermal conduction along the filament to the

end mountings. However, this loss can be kept sufficiently small byusing a filament of small cross section and heat conductivity. As an

Thermocouple

^Millicmmeter

Filament

:=: Battery

Microommeter

(low-resistance

type)

Rheostat for

current

adjustment

ID)

Fig. 3-10. (a) Thermocouple gauge; (6) simple electrical circuit diagram.[Taken with permission from Saul Dushman, Scientific Foundations of VacuumTechnique (John Wiley and Sons., Inc., New York, 1949).]

example nickel has a nearly constant heat conductivity of k <=« 0.14 gcal cm/°C in the temperature range from to 200°C. Exact calculation

of the heat-conduction loss along the wire is a bit tedious because of the

temperature variation along the wire. A crude estimate can be made,however, by assuming the central third of the wire to be at the

maximum temperature and the third at each end to have a uniform tem-perature gradient 3(T^ — TJjL. By this approximation the heat

conducted out both ends to the mountings is

dTW, = 2(0.239)jfc^

dL

= 2(0.239)(0.14)(4.9 x 10-«) X3(100 - 20)

10

= 7.9 X 10-« watt

in which A is the cross-sectional area of the 1-mil wire in squarecentimeters and the factor (0.239) converts from gram calories per

PKESSUEE MEASUREMENT IN VACUUM SYSTEMS 83

a- 10

second to watts. For this choice of dimensions the heat lost out to

the end mountings by heat conduction along the wire is smaller than

that lost by radiation, as calculated above, by a factor of about 750.

In general, therefore, the balance between free molecular conduction andradiation is all that needs to be considered as long as the cross-sectional

area of the filament is sufficiently small. As we have seen, this balance

occurs at a pressure of about 10~^ torr

or a bit less for the example chosen.

Since these two processes of energy loss

are both proportional to the surface

area of the hot filament, the balance

point is approximately independent of

the diameter of the filament.

The thermocouple vacuum gauge is

a thermal conductivity pressiu-e gauge

in which the temperature of the hot

filament is measured by a thermo-

couple. The heating current which is

passed through the hot filament is kept

constant at a standard value inde-

pendent of the temperature of the

filament. As the pressure increases

the heat conduction through the gas

increases and the temperature of the

filament decreases until the tempera-

ture corresponding to the high-pressure

value of the heat conduction through

the gas is reached. The thermocouple

responds to the temperature of the

filament and provides a direct reading

which can be calibrated against the

pressure in the gauge tube. Thethermocouple type of gauge was first developed by Voege' and has

been refined by a number of other investigators. ^"'^^

The thermocouple gauge manufactured for many years by General

Electric Company is shown in Fig. 3-10 together with the simple

electric circuit frequently used to heat the filament and record the

output of the thermocouple. The gauge element consists of a platinum-

iridium ribbon 0.0234 by 0.0078 cm in cross section and 3.66 6m in

length with a Nichrome-Advance thermocouple welded to its midpoint.

The heating current passing through the platinum-iridium element is

held constant in the range 30 to 60 mA depending upon the pressure

range of interest. In Fig. 3-11 are shown calibration curves of pressure

16 24 32 40 48 56

Scale reading

Fig. 3-11. Calibration curve for

General Electric thermocouple

gauge for Hg, Nj, and Xe. [Taken

with permission from Saul Dush-

man, Scientific Foundations of

Vacuum Technique (John Wiley

and Sons., Inc., New York, 1949).]


plotted against the thermocouple ciirrent for hydrogen, nitrogen, and

xenon. About two-thirds of the total deflection occurs in the pressure

range from 0.1 to 0.01 torr. Characteristically the curve becomes

very steep at 5 x 10-» torr, below which the accuracy of the gauge is

rather poor.

Triode

Clevite

CDT1349A

45 ohms

1wottl7o

WW

20ohmsPot WWCCW

Gouge

tube

Fig. 3-12. Schematic circuit diagram of Kimiey thermocouple gauge.

Thermocouple gauges are very useful and convenient in a variety of

applications. A number of commercial designs are available, of which

that manufactiu-ed by the Kinney Vacuum Division of The New York

Air Brake Company is of special interest. The gauge tube is of steel

construction and is both compact (length of 4 in. and outer diameter

of iK in.) and relatively sturdy. The thermocouple elements are

Chromel and Cupron, and the heater element is a timgsten wire.

A special feature of the Kinney thermocouple gauge is that the tubes

are all matched so that the circuit need not be reset for proper cali-

bration when tubes are changed. This is particularly convenient in

multistation installations in which a number of thermocouple gauge-

tubes are connected to a single control circuit through a selector switch.

The Kinney control unit is fully transistorized and features a printed

circuit, a simplified diagram for which is shown in Fig. 3-12. The

PEESSUKE MEASUREMENT IN VACUUM SYSTEMS 85

multistation control unit has an auxiliary heating circuit which keeps

the elements of all the gauge tubes in the system warm when they are

not connected to the pressure-reading circuit, so that there is no delay

in obtaining a pressure reading as the control unit is switched from one

tube to another.

Cufrent

Current

Gauge tube

Fig. 3-13. Hastings thermocouple

gauge schematic. [Taken with per-

mission from J. M. Benson, in 1956



Gouge tube

Fig. 3-14. Equivalent circuit of

Hastings thermocouple gauge.

[Taken with permission from J. M.Benson, in 19S6 Vacuum, Sym,pos-

ium, Transactions (Pergamon Press,

London, 1957).]

A very successful design of thermocouple gauge manufactured byHastings-Raydist, Inc., is described by Benson. ^^ The sensitive element

of the Hastings gauge consists of two thermocouples acting in parallel

and a third thermocouple in series

to compensate for variations in

ambient temperature. The gauge

elements and circuit diagram are

shown in Fig. 3-13. The two thermo-

couples (A) and (B) are heated in

series by alternating current froma transformer. Thermocouple (C)

connected from the midpoint be-

tween {A) and {B) to the center tapon the transformer provides temper-ature compensation. Since thermo-couples {A) and {B) are connected"back to back" in the a-c circuit,

they act as parallel sources of electromotive force for the d-c circuit

for which the lead from (C) through the d-c meter to the center tap is

the common return path. The equivalent circuit for the gauge is

illustrated in Fig. 3-14, and a cutaway view of the metal gauge tuberevealing the thermocouple arrangement is shown in Fig. 3-15. Mul-tiple thermocouple or thermopile gauges are made for several ranges of

Fig. 3-15. Cutaway view of Hastings

gauge showing thermocouple arrange-

ment. [Taken with permission from

J. M. Benson, in 1956 VacuumSymposium. Transactions (Pergamon

Press, London, 1957).]


pressure determined mainly by the dimensions of the thermocouple

wires and the temperature at which they are operated. The ranges

for which commercial units are available are 0.1 to 20 torr, 5 to

1,000fj,and 1 to 100

fj.,approximately. Calibration curves for several

gases are shown in Fig. 3-16. An outstanding feature of the Hastings

thermocouple gauge is the speed of response, which is significantly

shorter than for most other commercially available gauges. The metal

envelope and generally rugged construction are also features of practical

interest.

10 —

'

= "=::: i:r- ^^

s.8

"^<^ .

^^:wr2=-Argo 1

f, 6^^.

> ^s ^Carbon dioxide

::^N Mil

S 1Acetylene ^5^Xv^^ Freon

s ...^^2^:UJII2

Air- *C-^T-1pi<-:::='

i

10 50 100

Pressure, microns

500 1,000

Fig. 3-16. Calibration curves for Hastings gauge of intermediate sensitivity.

[Taken with permission from J. M. Benson, in 7956 Vacuum Symposium Trans-actions (Pergamon Press, London, 1957).]

About concurrently with the first appearance of the thermocouplegauge, Pirani^* developed a thermal-conductivity pressure gauge in whichthe resistance of the hot filament was calibrated as a function of the

gas pressure. As the pressure in the gauge tube increases, the thermalconduction of the gas surrounding the hot filament increases, and the

temperature of the filament and therefore also its electrical resistance

tend to decrease. The usual control circuit for a Pirani gauge is the

Wheatstone bridge, in which one leg of the bridge is the filament of the

gauge tube and the other three legs have resistances nearly equal to

that of the gauge tube, as shown in Fig. 3-17. It is sometimes ad-

vantageous to use two identical gauge tubes in the circuit, one of whichis evacuated to a low pressure and sealed ofi". If the sealed-off dummytube is mounted adjacent to the gauge tube, fiuctuations due to changesin ambient temperature and bridge voltage are to some degree com-pensated. In the circuit-in Fig. 3-17 the gauge tube is represented by'R„ and the compensating tube, if it is used, takes the place of R^.The Wheatstone bridge circuit can be operated in any of three ways

to provide an indication of the pressure

:


1. The constant-temperature bridge, in which the temperature of the

gauge filament is kept constant by adjusting the bridge voltage to

maintain a bridge balance as indicated by zero current through G in

Fig. 3-17. In this mode of operation the pressure is approximately a

linear function of the square of the

bridge voltage

P = (3-31)

Fig. 3-17. Wheatstone bridge circuit

for Pirani gauge control. [Taken

with permission from J. H. Leek,

Pressure Measurement in VacuumSystems (Published for the Institute

of Physics and the Physical Society

by Chapman and Hall, Ltd., London,

1964), 2nd ed.]

in which Fq is the voltage neces-

sary to balance the bridge when

the pressure in the tube is nom-

inally zero. The constant Bdepends upon the operating tem-

perature of the filament, the chem-

ical makeup of the gas, and the

geometrical parameters of the

gauge tube.

2. The constant-current bridge,

in which the current through the

hot filament of the gauge tube is

maintained at a steady value.

The bridge is balanced when the

pressure in the gauge tube is very

low, and the imbalance current registered on the meter designated

by G in Fig. 3-17 is used as an indication of the pressure.

3. The constant-voltage bridge, in which the voltage across the bridge

is kept constant, e.g., by means of a regulated power supply. Because

of the simplicity of the constant-voltage circuitry and because the

pressure is approximately a linear function of the imbalance current

over a limited range in pressure in this mode of operation, the constant-

voltage bridge has been widely adopted in commercial Pirani gauge

circuits. The bridge circuit is balanced as in the constant-current

bridge when the pressure in the gauge tube is very low (below the range

of detectable response) and the pressure observed as a function of

the imbalance current. A typical constant-voltage bridge circuiti^ is

shown in Fig. 3-18. Typical calibration curves" for constant-tem-

perature and constant-voltage-bridge operation are shown in Fig.

3-19. Although, with special precautions to ensure a constant ambient

temperature for the gauge tube, the Pirani gauge can be designed for

operation at much lower pressure, commercial Pirani gauges are useful

primarily in the range from 10"^ to 1 torr.

A thermistor is a semiconductor element which has a high negative

*105

Fig. 3-18. Typical constant-voltage bridge circuit for Pirani gauge. [Takenwith permission from C. M. Schwarz and R. Lavender, Rev. Sci. Instr. 19, 814(1948).]

88


100

10

„-i.o

0.10

temperature coefficient of resistance.

The use of a thermistor instead of a

wire as the heated element in a

Pirani gauge has been well knownin the literature for many years.

Becker, Green, and Pearson^' have

described the properties of therm-

istors and their use in vacuumgauges. The principal advantage of

the thermistor type of Pirani gauge

is that the response curve of the

bridge current as a function of the

pressure may be essentially linear

over a very wide pressure range bythe proper choice of circuit con-

stants. In spite of this very use-

ful feature, thermistor-type Pirani

gauges have not until quite recently

been successful commercially because

of the rather wide variation in prop-

erties of thermistors. This produc-

tion problem has recently been solved

so that thermistors of sufficiently

uniform properties can now be ob-

tained. Because of this improve-

ment in technology, the thermistor

gauge shown in Fig. 3-20 is nowcommercially available. The circuit diagram for this gauge is shownin Fig. 3-21, and a calibration curve is given in Fig. 3-22. The rela-

tively linear response is characteristic of thermistor-type Pirani gauges.

However, the special feature of this particular gauge is the extension of

the useful range to relatively high values of the pressure by the

0.010

/

>///

1

1

/

(

;

;

///

B,•

I

//

/

// /

/ /

ll1/

1/

//

/

20 40 60 80

Relative meter reading

100

Fig. 3-19. Pressure-sensitivity

curves for {A) constant-temperature

operation, and (B) constant-voltage

bridge operation. [Taken with per-

mission from A. R. Hamilton, Rev.

Sci. Instr. 28, 693 (1957).]

Insulator

Connector pins

Thermistor bead

Support wires

Fig. 3-20. Cross-sectional view of Kinney thermistor vacuum gauge.


lOOohms lOwatts

Ohmite Brown-Devil

Victory 25 A 4 5,000 ohmsor

Fenwal GB 35LI 5,000 ohms

Fig. 3-21. Circuit diagram of Kinney thermistor vacuum gauge.

enclosure of the thermistor element in a metallic cylinder with small

clearances. The heat flow through the gas from the thermistor element

to the cylinder therefore occurs along a very short path so that the

conditions for free molecular conduction discussed at the beginning of

this section are realized at relatively high pressure.

3-6. Hot-cathode Ionization Gauge. The hot-cathode ioni-

zation gauge consists basically of three elements in a gastight tube :a

thermionic cathode, an electrode usually in the form of a grid for

extracting electrons from the cathode, and a positive ion collector or

plate. Any ordinary triode-type electronic tube has these elements

and can be used as an ionization gauge by opening the tube envelope

and sealing on a tubulation by which it can be connected to a vacuum

system.

The operation of an ionization gauge is illustrated in Fig. 3-23.

Electrons from the cathode are accelerated by the electrostatic field

through the grid of radius r^, which for this purpose is set at a positive

potential Vg relative to the cathode. The plate of radius r^ is set at a


negative potential V^ relative to the cathode to ensure that electrons

emitted by the cathode or created by collision processes in the annu-

lar space between the grid and plate are prevented from reaching

the plate and are essentially all attracted to the grid, which is

the most positive electrode. If the grid is made of fine wire, mostof the electrons from the cathode miss the grid wires as they are

propelled outward by the field and continue toward the plate until

they reach a point in the grid-to-plate region at which the electrical

potential is the same as that of the cathode; they are then turned

back to oscillate radially, passing through the holes between the

wires of the grid repeatedly until they finally strike a grid wire andare captured. As the electrons pass through the grid they reach their

maximum kinetic energy of eVg, in which e is the electronic charge

(-4.80 X 10-1" esu = -1.60 x 10"" coulomb) and F„ is the grid

potential. The kinetic energy is either in ergs or joules, depending

upon the units (cgs or practical) in which e and V^ are expressed.

Alternatively, this kinetic energy can be expressed in units of electron

volts in which case the maximum kinetic energy of the electrons is equal

to Vg electron volts, by which one simply means that kinetic energy

acquired by a particle with one electronic charge e falling through

a difference of potential equal to F, volts. In atomic and nuclear

50

J^ \rnV/ X ^ R

^s \ "iohms/

^40 k R?\/^"/ir

k.100 Nohms ^°°°(mAJ

ohms^CLiJ/

\30

\volts

20

\s

\10 \,\

N,V,^--

0.001 2 5 0.01 2 5 0.1 2 5 12 5 10 2 5 100

Torr

Fig. 3-22. Calibration curve of Kinney thermistor vacuum gauge for air.


Grid

Plate

structure as well as in electronics both kinetic and potential energies are

commonly quoted in electron volts, for which the following conversion

factors are useful

:

1 electron volt (eV) = 1.60 x 10"" coulomb x 1 V= 1.60 X 10-" joule

= 1.60 X 10-12 erg

or conversely 1 joule = 6.24 x 10^* eV

1 erg = 6.24 x 10" eV

As shown in Fig. 3-23, electrons oscillating in and out through the

grid will eventually collide with gas molecules if any are present in

the tube. If the kinetic energy of

the electron at the time of collision

with a molecule is greater than the

ionization potential of the molecule,

an electron may be knocked off the

molecule, leaving it in an ionized

state. Each such impact decreases

the energy of the electron and de-

flects it from its otherwise purely

radial path so that the electron loses

energy during its oscillatory motionand becomes more random in its

motion. In any case, it eventually

falls into one of the grid wires and is

captured. Electrons knocked out of

molecules in ionizing collisions mayalso gain sufficient kinetic energy to

cause some additional ionization, de-

pending on the electrical potential at

the point at which they are created,

but eventually they also fall into one

of the grid wires because the grid, being positive relative to both the

cathode and the plate, is the only electrode which they can reach.

Those positive ions which are created in the annulus between the

grid and the plate are in an electrostatic field directed radially outward.Being positively charged, these ions are driven outward to the plate,

where they register as a positive current. Those ions which are formedin the space between the cathode and grid, however, are in a field whichaccelerates electrons (— ) outward. These ions are therefore attractedto the cathode, where they are captured and are electrically equivalentto electrons leaving the cathode. Only those positive ions reaching

Cothode

Fig. 3-23. Hot-cathode ionization

gauge. A typical electron trajec-

tory is shown. The useful region

of positive ion production is the

shaded area. [Taken with permis-

sion from J. H. Leek, Pressure

Measurement in Vacuum Systems

(Published for the Institute of

Physics and the Physical Society byChapman and Hall, Ltd., London,

1964), 2nd ed.]


the plate or collector are recorded as positive ion current and contribute

to a measurement of the density of molecules in the tube.

An alternative method of operating a triode-type vacuum tube as anionization gauge is to use the grid as the positive ion collector. In this

case the plate potential Vj, is highly positive (e.g., +200 V) and the grid

potential somewhat negative (e.g., —25 V). This arrangement of

potentials is similar to that applied to the elements of a triode used in

an electronic circuit. The electron output from the cathode is then

heavily space-charge-limited because of the retarding effect of the inter-

posed negative grid. Those electrons which do escape into the grid-

to-plate region gain energy as they travel outward and strike the plate

with their maximum kinetic energy. Ionization occurs mostly in the

region near the plate, and the positive ions are drawn into and are

collected by the grid. Electronic tubes are traditionally checked after

assembly and evacuation by measuring the grid current, which is an

excellent indication of the residual gas. This process amounts to

the use of the tube as its own ionization gauge. Because in this modeof operation the electrons do not oscillate back and forth through the

grid as they do when the grid is at positive potential, the electron paths

are much shorter and the sensitivity as an ionization gauge is poor.

In practice, ionization-gauge tubes are therefore normally used with

the grid positive and the plate negative with respect to the cathode,

as described in the previous paragraphs.

In order to produce ionization by impact with an atom or molecule

an electron must have kinetic energy at least equal to the ionization

potential, which ranges from 3.89 eV for cesium to 24.6 eV for helium.

Of more practical interest in the formation of ions is the probability of

ionization Pi, which is defined as the fraction of electrons at a given

energy producing an ionizing collision per centimeter of path and per

torr of gas pressure. In Fig. 3-24 the probability of ionization is showngraphically as a function of electron energy for several common gases

as measured by Tate and Smith, i*

Since at a pressure of 1 torr and temperature of 0°C the molecular

density is

2.69 X 10"'

760

= 3.54 X 10" cm-»

the probability of ionization

Pi = Wio-j = 3.54 X lO^cTi (3-32)

in which a^ is the cross section for an ionizing collision by an electron.

The number of ions produced by an electron per centimeter ofpath from

94 VACUUM SCIENCE AND ENGINEBEING

(3-32) and (1-16) is then

273 273

20

(3-33)

15

Pi 10

AlA^sf/^^Vl

^:- '

^—

'

"=H

Plate or ion

collector

200 400

Electron energy, eV

600

-15 IVp+P^Vgto Z^ to ^

-30 :=: +180J_

volts -^ volts ^:

Fig. 3-25.

circuit.

Simple ionization-gaugeFig. 3-24. Probability of ionization

in C^HalD, 0^(2), ^^(Z), A(4), n^(5),

Ne(6), and He(7). [Taken with per-

mission from J. H. Leek, Pressure

Measurement in Vacuum Systems

(Published for the Institute of Phys-ics and the Physical Society byChapman and Hall, Ltd., London,

1964), 2nd ed.]

in which n is the molecular density corresponding to the pressure P andtemperature T of the gas. For an electron stream of current i_

amperes (6.24 x 10^* electrons/sec = 1 A), the positive ion current i^

amperes, assuming all the ions are collected, is thus given by

273 „.(3-34)

The maxima for the Pi curves for most gases occur in the energy rangefrom 60 to 200 eV, above which p^ decreases steadily with increasing

electron energy. For the common gases for which curves are shown in

Fig. 3-24, p^ reaches maximum values of about 1.5 for helium to about17 for acetylene so that the maximum values of the cross sections for

ionization (Tj vary from about 4 xfor the gases shown in the figure.

10-" cm2 to about 5 x lO-is cm^


The use of ionization of gas molecules by electron collisions as a means

of measuring the pressure (or more exactly the molecular density) of a

gas was first described by Buckley.^'' A simplified circuit for operating

an ionization gauge is shown in Fig. 3-25. The positive ion current

i^ to the plate (or ion collector) for a given value of the grid voltage Vg

and grid (electron) current i_ is a direct indication of the molecular

density and therefore also of the pressure. The sensitivity s of an

ionization gauge is defined by the relation

or

i^ = si_P

s i_(3-35)

and in principle could be calculated from (3-34) and the geometry of

the gauge tube. However, the average length of path for the electrons

is not easily estimated for tube geometries of practical interest, and

the energy of the electrons varies from the maximum value of the grid

voltage Vg to zero in a complicated way so that direct calibration of

each tjrpe of ionization gauge against a McLeod gauge is the only

practical means of determining the sensitivity. For sufficiently low

pressure only a small fraction of the electrons which contribute to i_

produce ionizing collisions, and therefore essentially none produce two

or more collisions. Therefore at sufficiently low pressure the sensitivity

s is expected to be independent ofC However, when the pressure is

high enough that a significant fraction of the electrons produce more

than one ionizing collision, then the multiplicity will increase with the

pressure, and the sensitivity is no longer independent of i_. In Fig.

3-26 the dependence of the ion current ^+ on the electron current i_ is

shown for three different makes of ionization gauges with nitrogen gas

at a pressure of 5 x lO-^ torr.^" At this pressure of nitrogen, i+ oc i_

for all three gauges up to values of i^ from about 10"^ to 3 X 10"* Adepending upon the characteristics of the gauge tube.

Measurement of the sensitivity 5 as a function of the pressure in the

range IQ-* to 1 torr shows that s increases with increasing pressure

until a maximum is reached and then decreases^" as shown in Fig. 3-27

for nitrogen and helium. The value of the pressure at which the gauge

sensitivity reaches its maximum value for helium is seen to be about

a factor of 10 greater than that for nitrogen. Since the process is

governed by the ionization probability Pi, which is about 6 to 10 times

as large for nitrogen as for helium in the electron energy range used in

ionization gauges, the pressure difference for the maxima is to be

expected. The rise in sensitivity in the vicinity of 10"^ torr for

nitrogen is caused by multiple ion production by each electron when the

96 VACITtrM SCIENCE AND ENGINEEEING

lO'10"* 10"

Electron current,I_,amp

10'

Fig. 3-26. Ion current as a function of electron current for three different gauges

operating on the same pressure of nitrogen gas. [Taken with permission fromW. B. Nottingham and F. L. Torney, Jr., in 1960 Vacuum Symposium Transac-

tions (Pergamon Press, London, 1961).]

ionization mean free path becomes small compared with the average

electron path length because of the high molecular density. Thedecrease in sensitivity with increasing pressure beyond the maximum is

attributed by Nottingham and Torney^" to ion-electron or positive-

ion-negative-ion recombination which becomes much more probable

at high molecular density.

Since those ions which are formed in the region between the cathode

p.torr

Fig. 3-27. Gauge sensitivity at very low electron current as a function of pressurefor nitrogen and helium. [Taken with permission from W. B. Nottingham andF. L. Torney, Jr., in 1960 Vacuum, Sym,posium, Transactions (Pergamon Press,London, 1961).]

PRESSTTBE MEASUREMENT IN VACUUM SYSTEMS 97

and the grid are drawn toward andbombard the cathode, operation of

an ionization gauge at pressures

much above 10"^ torr greatly short-

ens the life of the cathode. Theupper limit of operation of com-mercial gauges is therefore usually

set at this pressure with the result

that except near the upper limit of

the pressure range, say from 6 x 10"*

to 1 X 10~* torr, the sensitivity is

essentially independent of both the

electron current and the pressure.

However, for precision measure-

ments detailed calibration of eachgauge tube against a IMcLeod gaugeover the pressure range from 10~*

to 10-* torr is essential.

Since the ionization probability

Pi varies with the electron energy

(see Fig. 3-24) the sensitivity s de-

pends upon the grid potential V^.

As shown in Fig. 3-28 for nitrogen

H.U

1 ''<''^^T^n r^

;'/fpff

2.0

t/

////it

i J\r

—

'

1.0

/ A" i

ofA/

0.5

0.25!

50 100 150 200 250

Electron accelerotinq voltage.voits

Fig. 3-28. lonization-gauge sensi-

tivity for nitrogen and neon as afunction of the grid potential. (1)

Relative sensitivity, neon/nitrogen;

(2) sensitivity, nitrogen; (3) sensi-

tivity, neon. [Taken with permissionfrom J. H. Leek, Pressure, Measure-ment in Vacuun Systems (Published

for the Institute of Physics and the

Physical Society by Chapman andHall, Ltd., London, 1964), 2nd ed.]

(2) and neon (3) the sensitivity for

a given gas increases with the pressure rapidly for low values of Vgand then much more slowly, changing very little with increasing grid

potential above 200 V. Because the ionization potential for neon(21.6 V) is much higher than that for nitrogen (14.5 V) the relative

10 20

Electron current.mA

(o)

200 400Electron occ volts

(b)

'0-1 1.0 10 100

Collector-v bios

(c)

0.5 1.0

Pressure, microns

(d)

Fig. 3-29. Characteristics of typical triode ionization gauge for nitrogen. [Takenwith permission from J. H. Leek, Pressure Measurement in Vacuum Systems(Published for the Institute of Physics and the Physical Society by Chapmanand Hall, Ltd., London, 1964), 2nd ed.]


sensitivity changes with grid potential as is shown in curve (1) in the

figure. Thus the relative sensitivities of an ionization gauge for

different gases are not fixed values but depend upon the gauge design

and the value of Vg.

The somewhat complex dependences of the positive ion current

on (a) the electron current , (6) the grid or accelerating potential F^,

(c) the plate or collector potential F,,,

and {d) the pressure are shown in the

curves in Fig. 3-29. These four ciurves

are convincing evidence that the sen-

sitivity 5 as defined in (3-35) is not a

true constant but depends upon a

number of factors.

Commercial ionization-gauge cir-

cuits are designed to maintain the

critical circuit parameters (partic-

ularly i_ and F^) constant at values for

which the sensitivity is approximately

independent of the pressure. The prob-

lem of regulating the cathode-emission

current was first solved by Ridenour

and Lampson^i by means of the circuit

shown schematically in Fig . 3-30 . The

lifetime of the cathode becomes quite

short at higher pressures because of

bombardment by positive ions formed

in the space between the cathode and

grid, so that commercial gauge circuits

are not normally made to operate

above 10-^ torr. Modern commercial

gauge circuits not only provide regu-

lation of the circuit constants for the

gauge but also means of precondition-

ing the tube by heating and outgassing

the electrodes as well as a sensitive

vacuum-tube electrometer circuit with

several ranges controlled by a selector

switch for reading the positive ion current conveniently over a wide

range on a simple panel meter. A sensitive relay in series with the

output meter is also frequently provided as a means of shutting off

the gauge circuit and performing other protective functions, such as

turning off diffusion-pump heaters and closing valves in the event that

the system pressure should exceed a safe limit.

" supply

Fig. 3-30. Circuit of Ridenour and

Lampson for regulating the emis-

sion current of an ionization gauge.

[Taken with permission from J. H.

Leek, Pressure Measurement in

Vacuum Systems (PubHshed for the

Institute of Physics and the Phys-

ical Society by Chapman and

Hall, Ltd., London, 1964), 2nd ed.]

PEESSUBE MEASUREMENT IN VACUUM SYSTEMS 99

The circuit constants and sensitivity (air) for a number of ionization-gauge tubes of different design are shown in Table 3-1. In this tablethe sensitivity is given in units of ,aA/micron/mA, that is, the positiveion current i^ in microamperes resulting from a pressure of 1 micron(10-3 torr) of air in the tube when the electron current i_ is 1 milli-ampere.

Table 3-1. Ionization-gauqe Opbbating Data"

Reference or supplier

Jaycox and Weinhart*"

Morse and Bowie*^

Bayard and Alpert**

Edwards High Vacuum IG.2Edwards High Vacuum IG.3 *

AEI. 29D.15 (miniature) . . .

AEI. 29D.2NRCNRC*CVC GIC.Oll*CVC VG.IA35 TG Eital-McCuUock"E 31 Precision Scientific Co.

1949 RCA"D 79512 Western Electric". . .

KIGT KinneyVAC-NIG, Vactronis Lab.f. .

F„, volts

-6-25

volts

-5 to -30-50 to -100-15 to -25

-25-20-40-45-25-25-25-25-25-30

+ 20 to -50

120

150

150

125

150

200

200

150

100

200

150

150

150

150

150

160

150

i_, mA

20

5

10

to 10

to 10

to 5

to 5

to 5

to 15

to 20

to 5

5

5

5

5

7

10

Sensitivity

(N^), s,

/<A/micron/mA

12.5

40

10

5

12.5

5.5

13

20

12.5

18

20

4

12

14

10

14.3

10

<• These data largely taken with permission from J. H. Leek, Pressure Measure-ment in Vacuum Systems (Published for the Institute of Physics and the PhysicalSociety by Chapman & Hall, Ltd., London, 1964), 2nd ed.

" E. K. Jaycox and H. W. Weinhart, Rev. Sci. Instr. 2, 401 (1931)." R. S. Morse and R. M. Bowie, Rev. Sci. Instr. 11, 91 (1940).'' R. T. Bayard and D. Alpert, Rev. Sci. Instr. 21, 571 (1950)." B. B. Dayton, Le Vide, p. 349 (1947).* Bayard-Alpert construction.

t Nude Bayard-Alpert constrviction.

Although the elements of the traditional ionization-gauge tube aresuperficially similar to those of an electronic tube, the function is quitedifferent and therefore also the details of the design. Since for manyapplications pressures of 10-« torr (10"^^) or lower are to be measured,the positive ion current is of the order of 10 x lO-^ x 5 ^A or5 X 10-8 A. There is no difficulty in amplifying such a current to themilliampere range for the operation of a sturdy panel meter. However,any electrical leakage in the gauge tube, in the leads, or in the power


supply chassis must be small as compared with the minimum plate

current to be measured.

The design of ionization-gauge tubes is therefore such as to minimize

internal electrical leakage to the plate. In Fig. 3-31 is shown the

construction of the RCA 1949, which is widely used. The plate

support and lead are brought into the tube envelope

through the opposite end to those for the cathode and

grid, providing a very long leakage path from the

other elements of the tube to the plate. The RCA1949 also has two spiral-wound tungsten wire cath-

odes, only one of which is required for operation of

the tube. When one filament burns out, the other

one can be put into service, thus doubling the life of

the tube. The design of Morse and Bowie^^ shown

in Fig. 3-32 has been popular in industrial applica-

tions. The innovation introduced with this gauge

tube is the use of a platinum film deposited on the

inner wall of the tube as the ion collector. Not only

in this case is the electrical leakage path to the plate

large, but also the plate can be easily heated for out-

gassing by flaming the gauge tube. Connection to

the plate is made by a wire sealed into the side wall

of the tube. The grid is in the form of a spiral fila-

ment through which a current can be passed for

heating and outgassing.

Because all glass ionization-gauge tubes must be

connected to the system by a tubulation, the con-

ductance from the gauge to the system tends to be

somewhat constricted. In studying the performance

of diffusion pumps. Blears^* connected to the test

dome a normal ionization gauge with its usual tubu-

lation and also mounted inside the test dome an identical gauge from

which the glass envelope had been removed so that the gauge elements

were exposed directly in the test volume. Striking differences were

observed, the "nude" ionization gauge always reading higher by a

factor of 10 or more when the pressure reading was mainly due to the

vapor backstreaming from the oil diffusion pump. This effect was

attributed by Blears to the adsorption of the oil vapor on the inside

surfaces of the glass tube and tubulation of the conventional gauge.

Because of the very high conductance into the electrode structure of'

the nude gauge, the pressure indicated should be very nearly correct

even if adsorption does occur to some degree on the plate and

grid. Several designs of nude ionization gauges are now available

Fig. 3-31. RCA1949 ionization-

gauge tube. [Re-

produced through

the courtesy of

Radio Corpora-

tion of America.]

PEESSURE MEASUREMENT IN VACUUM SYSTEMS 101

commercially. The gauges are built on flanges for mounting withtheir electrodes inside the region where the pressure is to be measured.

Initial operation of an ionization gauge just after the system hasbeen pumped down from atmospheric pressure results in the heatingof the electrodes and the emission of large

quantities of absorbed gases from the surfaces.

Unless the gauge elements are heated vig-

orously to drive off absorbed gases, the readingwill remain high as compared with the systempressure for a long time. The grids of severalof the commercial designs are in the form offilaments which can be electrically heated.The plate can be heated by electron bombard-ment by connecting the grid and plate to-

gether at the same positive potential. Finally,

it is sometimes necessary to heat the glass ormetal envelope of the gauge tube to the safe

limit of temperature.

After the gauge tube and elements have beenthoroughly outgassed, an opposite effect be-comes noticeable. Because the surfaces withinthe tube are all thoroughly outgassed, gasentering the tube is readily adsorbed, partic-

ularly on the tube walls. Chemical reactionsinduced by the hot filament can further en-

hance the absorption of gas by the gauge.These processes are responsible for the pump-ing action of well-outgassed ionization gaugesreported by a number of observers beginningwith Langmuir.24 Riddiford^s has measured apumping speed for oxygen of about M Hter/sec

due to chemical reaction of oxygen with thehot filament of an ionization gauge. Gaspumping, either due to adsorption or due tochemical reaction, will cause the pressure atthe gauge to be lower than that in the system.If the pumping effect includes adsorption of gas on the inside surface ofthe tubulation, the pressure recorded by a conventional gauge is some-times a factor of 10 less than that recorded inside a test dome by anude gauge. Furthermore, according to Reich^s the time necessary forpressure equilibrium to be established between the test dome and thegauge tube through the tubulation can be many hours or even days.The adsorbed layer on the inner wall of the tubulation builds up first at

Fig. 3-32. Ionization

gauge designed by-

Morse and Bowie.

[Taken with permission

from R. S. Morse andR. M. Bowie, Rev. Sci.

Instr. 11, 91 (1940).]


the end nearest to the test dome and then progressively grows along the

tabulation. Equilibrium is not estabhshed until the adsorbed layer has

grown the length of the tube. The growth rates of films for substances

of high molecular weight, such as oil vapor, are very slow so that the

equilibrium time becomes correspondingly long. Investigation of the

"Blears effect" by Haefer and Hengevoss^' confirms the original

results of Blears^* and leads to the conclusion that if diffusion-pump

oil vapor is present in a system operating in the ultrahigh vacuum

regime (P < 10-^ torr), a normal tubulated ionization gauge indicates

little more than the partial pressure of the permanent gases and does

not respond appreciably to the organic vapors present due to back-

streaming. According to these authors, "this behavior lies in the

vastly different conductance of the small connecting tube for oil vapor

and permanent gas in conjunction with the cracking of the oil molecules

by the gauge." The processes of thermal decomposition and wall

adsorption in ionization gauges are not completely understood, but

it is clear that these processes do, under some circumstances, lead to

large errors in pressure measurement which can be greatly minimized

by elimination of the tubulation and the use of the nude type of

ionization gauge.

The lower limit of pressure which can be measured with a conven-

tional ionization gauge is determined by a process not anticipated until

it was pointed out by Nottingham. ^^ He found that after all normal

leakage current was eliminated in an ionization gauge there remained

a base current to the plate even when the pressure in the system by

other indications was far too low to produce a positive ion current of

comparable magnitude. He found the residual plate current to be due

to the production of soft X-rays by the electrons striking the grid.

When electrons strike a target they produce X-ray photons of energies

up to the full kinetic energy of the electrons. These photons in turn

go in all directions from the source, in this case the grid, and release

photoelectrons from whatever surfaces they strike. Since in the con-

ventional ionization gauge most of the soft X rays produced at the grid

strike the plate, photoelectrons in significant numbers are continuously

produced at the plate. The electrostatic field at the plate is such as

to attract positive ions and therefore also to repel the photoelectrons,

the current of which is recorded by the external circuit as if it were

due to positive ions collected by the plate. Results by Nottingham

and others demonstrate that conventional ionization gauges never

give plate currents less than that corresponding to about 10~* torr even

when the pressure is of the order of IQ-i^ torr. Because of the X-ray

effect, the lower limit of reliability of the conventional ionization gauge

is found to be about 10-' torr.


3-7. The Bayard-Alpert Ionization Gauge. In order to reducethe low-pressure limit of the conventional ionization gauge due tophotoelectron emission from the plate, Bayard and Alpert^" deviseda modified ionization gauge as illustrated in Fig. 3-33. The gaugefeatures a cylindrical grid structure with a fine wire ion collector alongits axis and a cathode located just outside the grid structure to one side.

Because the plate structure of the conventional ionization gauge is

replaced by a fine wire, the total area exposed for X-ray-inducedphotoelectron emission is reduced by a factor of about 200. Thesensitivity of the Bayard-Alpert gauge proves to be comparable withthat of the conventional gauge because the electrons in oscillating fromthe external cathode back and forth through the grid structure spenda large portion of their time in the nearly field-free space (except for

the slight field due to the —20 V on the collector wire) within the gridat the kinetic energy (typically 200 eV) at which the probability ofionization 'p^ is near its maximum.The difference in performance between the Bayard-Alpert and the

conventional ionization gauge is shown graphically in Fig. 3-34 in whicha log-log plot of the collector current as a function of the grid potentialis shown for each type of gauge for various values of the pressure. Atsufficiently high pressure the collector current does not increase signifi-

cantly with grid potential above 200 V, a characteristic also illustrated

in Fig. 3-296. However, at very low pressure the positive ion currentbecomes small as compared with the photoemission current. Thecollector current then increases indefinitely with increasing grid poten-tial, being proportional to a power of the grid potential lying between1.5 and 2.0 as indicated by the slope of the log-log curve in the figure.

This characteristic can be explained on the assumption that the entire

collector current is due to photoemission. For intermediate pressuresa characteristic made up of a mixture of the ionization current andphotoemission current is obtained. The characteristic of the conven-tional ionization gauge at P < 10-^ torr is a pure power law typicalof photoemission with no vestige of any ionization current. Thecharacteristics for the Bayard-Alpert gauge, however, retain the ioniza-

tion component for values of the pressure lower by a factor of at least

100. Even at P < 5 x lO"" torr a slight departure from the purepower law provides a basis for crudely estimating the true positive ioncurrent. Gauge tubes made essentially as described by Bayard andAlpert are now commercially available from a number of sources andare frequently used on systems even when the operating pressure is

not below the limit of the conventional ionization gauge.A. van Oostrom^o describes a modified Bayard-Alpert gauge in which

the X-ray limit is reduced to lO-i^ torr or less by reducing the diameter

104 VACUUM SCIENCE ANB ENGINEERING

of the ion-collector wire to 4 /^ (1 /* = IQ-^ mm) and decreasing the

electron energy below 100 eV. The author states that by applying

a high negative voltage (-200 V or more) to the collector relative to

the grid, the sensitivity with the small-diameter collector is comparable

with that of the standard Bayard-Alpert gauge. Schuetze and Stork"

Conventional

Ion GougeNew Ion Gouge

torr

P=4xl0-'torr

100 1,000 100 1,000

Grid potentiol, volts

(a) (b)

Fig. 3-34. Ion collector current as a

function of grid potential for (a) con-

ventional ionization gauge and (6)

Bayard-Alpert gauge. [Taken with

permission from R. T. Bayard and D.

Alpert, Rev. Sci. Instr. 21, 571 (1950).]

Fig. 3-33. The Bayard-

Alpert ionization gauge.

(A) one of two alterna-

tive cathodes; {B) the

grid structure; (C) the ion

collector. [Taken with

permission from R. T.

Bayard and D. Alpert,

Rev. Sci. Instr. 21, 571

(1950).]

also report markedly reduced X-ray limit (5 x lO"" torr) by using an

ion-collector wire oflO /i diameter as compared with the usual diameter

of about 150fj.and by reducing the electron energy to 50 eV.

A further advance in the suppression of the X-ray photocurrent in

an ionization gauge is reported by Schuemann,*'' whose gauge modifi-

cation is shown schematically in Fig. 3-35. A suppressor ring electrode

located adjacent to the collector electrode is maintained at a high

negative potential ( — 300 V), imposing a strong electric field such as to

drive any photoelectrons emitted by the collector back into its surface.


_ Filament

(+50 volts)

ie-t-~^.

-Sh—Ionization grid

(+200 volts)

Shield (ground)

^

J

Between the suppressor electrode and the grid is a grounded shield,the function of which is to prevent X rays from the grid from strikingthe suppressor, causing emission of photoelectrons, which would thenbe attracted to the ion-collector plate and subtract from the ion-collector current. Schuemann states that this arrangement completelysuppresses the photocurrent and thus removes the X-ray limit entirely.Pressures as low as 2 x lO-i^ torr have been measured with the photo-current-suppressor gauge.

The Bayard-Alpert gauge displays the same tendencies either ofoutgassing or of "pumping" by gas absorption as were described forthe conventional ionization gauge.

According to Redhead,^^ the pump-ing speed of a Bayard-Alpert gauge,

operated at 8 mA electron current

and 250 eV electron energy, is about2 liters/sec for nitrogen when first

put into operation. This pumpingaction is made up of ion pumpingand chemical pumping. The ion

pumping results from ion bombard-ment of the electrodes and the glass

envelope. The chemical pumping is

due to chemisorption of gas on the

electrode and any metal films whichmay have formed, e.g., on the innersurface of the glass envelope. Red-head reports that the chemical pump-ing ceases for nitrogen after about lO^^ molecules have been pumped.The ion pumping continues at about 0.25 liter/sec until 10" moleculeshave been pumped, at which point it decreases rapidly. Chemicalchanges in gases are produced by the hot tungsten cathode normally op-erated at a temperature of about 1700°C, which is high enough to dissoci-

ate water vapor, hydrogen, and hydrocarbons. Carbon impurities in thetungsten cathode react with oxygen to form carbon monoxide anddioxide. Also at this temperature an appreciable fraction of hydrogenmolecules incident on the cathode are converted to atomic hydrogen.Since atomic hydrogen is readily absorbed at glass surfaces and reactschemically with components of the glass envelope and metal electrodesof the gauge tube to produce other gases such as carbon monoxide, anyhot-cathode gauge, such as the Bayard-Alpert, has an anomalouslyhigh pumping speed for hydrogen. Chemical changes which occur atthe surface of the hot filament result in serious errors in pressuremeasurement when hydrogen, oxygen, water vapor, or hydrocarbons

Suppressor wng (-300 volts)-' /

Collector /

Fig. 3-35. Schematic of photo-current suppressor gauge. [Re-printed with permission from TheMacmillan Company, from 1962Vacuum Symposium Transactions.

Copyright © 1962 by American Vac-uum Society.]


are present. These effects are particularly troublesome in ultrahigh-

vacuum systems in which the predominant gas is hydrogen. These

troublesome effects can be largely eliminated by the use of a rhenium

filament coated with lanthanum boride (LaB,), which emits an ample

electron current (10 mA) at a much lower temperature (1,000°C) than

that (1,700°C) required for a tungsten

filament.

The Bayard-Alpert gauge is much

more susceptible to gross error due to

the accumulation of an insulating coat-

ing on the ion collector than is the con-

ventional ionization gauge. Lauer^*

reports that this condition, which can

result in gauge readings which are too

low by a factor of 10 or more, can be

easily corrected by connecting the ion-

ncollector electrode to the grid potential

for a few minutes, thus cleaning the

collector electrode by electron bombard-

ment.

Discrepancies between gauge readings

and the true system pressure are

greatly reduced, as in the case of the

conventional ionization gauge, when the

glass envelope is removed from a

Bayard-Alpert gauge and the gauge

unit immersed in the vacuum space.

In Fig. 3-36 is shown a flange-mounted

nude Bayard-Alpert gauge constructed

of ceramic and metal parts which

allegedly will withstand baking at high temperature for thorough

outgassing. Even if the elements of such an open gauge struc-

ture absorb, desorb, or chemically react to some degree with the

gases present in the system, the very large conductance for gas inter-

change ensures that the molecular density within the gauge will be

essentially the same as that in the surrounding volume and the gauge

reading will be reasonably accurate. Santeler^^ states that a nude

Bayard-Alpert gauge cannot measure pressures less than about lO""

torr, however, unless the backing plate which supports the gauge

elements can be baked at high temperature for thorough outgassing.

Also in the nude Bayard-Alpert gauge, space- and surface-charge effects

are frequently bothersome unless the gauge element is completely

enclosed in a metal-screen cylinder connected to ground potential.

Fig. 3-36. Nude Bayard-Alpert

gauge. [Reproducedthroughthe

courtesy of Vactronic Lab.

Equipment, Inc., East North-

port, Long Island, N.Y.]

PEESSURE MEASUREMENT IN VACUUM SYSTEMS 107

In a study of the operation of Bayard-Alpert gauges, Winters, Denison,and Bills^s conclude that many of the conditions leading to no'nlinearityin response can be greatly alleviated by the simple expedient ofreducingthe filament temperature and electron emission current. Accordingto Nottingham,^' one cause of anomalous behavior in the originaldesign of the Bayard-Alpert gauge is the loss of positive ions out theends of the grid structure. He has shown that this defect can becorrected by closing both ends of the grid structure with wire mesh.The uncertainty which develops at low pressure, particularly for

P < 10-« torr, is due to the fact that the composition of the residualgas cannot, in general, be predicted. Since the gauge sensitivity is

a function of the gas composition, varying by a factor of about 5 forthe common gases, interpretation of gauge readings in terms of molec-ular density at low pressure becomes quite uncertain. Because of thisobvious difficulty, low-pressure readings taken with a Bayard-Alperttype of ionization gauge are usually quoted in terms of the equivalentair pressure based upon a calibration against a McLeod gauge using acontrolled air flow. A much more precise measurement at low pressureinvolves vacuum analysis, i.e., the measurement of the partial pressuresof the gas components present in the system, a topic which will bediscussed in a later section.

3-8. Hot-cathode Magnetron Ionization Gauge. In the orig-inal design of the Bayard-Alpert gauge the X-ray limit (i.e., the pressurecorresponding to the photoelectron current emitted by the ion collectorbecause of X rays emitted by the grid) was reduced by a factor of about200, compared with the conventional hot-cathode ionization gauge.This was done by reducing the solid angle subtended at any point ofthe grid by the ion collector, thereby reducing the probability for anX-ray photon emitted by the grid to be intercepted by the ion collector.

A further improvement in this respect has been accomplished byLafferty,38 whose hot-cathode magnetron ionization gauge is shown inFig. 3-37. According to Lafferty,

It is evident that if the gauge is modified in such a way that the electronstravel in longer paths before they are collected by the positive grid or anode,the probability of them colliding with and ionizing a gas molecule will begreatly enchanced and the sensitivity of the gauge will be improved withno increase in x-ray photoemission. One obvious way of increasing the pathlength of the electrons is to employ a magnetic field.

The Lafferty gauge has certain features in common with the mag-netron, after which it is named. The hot-cathode filament is approxi-mately on the axis of symmetry of a cylindrical electrode, which is theanode. Electrons leaving the cathode in the absence of a magnetic

108 VACXTTJM SCIENCE AND ENGINEERING

field are attracted directly to the anode. However, when an axial

magnetic field is superimposed, the electron paths are bent. Finally,

as the magnetic field is increased in intensity, with the anode-to-cathode

potential held constant^ the electron current reaching the anode

suddenly decreases to a much smaller value. The magnetic field value

at which this sudden drop occurs corresponds to the magnetron cutoff.

Ep= 300 volts

Ec= -45 volts

Es= -10 volts

V-i,lon collector

Filament

Magnet

Anode

Shield

Ion current XIOO

Fig. 3-37. Hot-cathode magne-

tron ionization gauge. [Taken

with permission from J. M.

Lafferty, in 1960 Vacuum Sym-posium Transactions (Pergamon


100 200 300 400 500 600

Magnetic tield, oersteds

Fig. 3-38. The anode electron current

and positive ion-collector current of the

magnetron gauge as a function of the

applied axial magnetic field. [Taken

with permission from J. M. Lafferty,

in 1960 Vacuum Symposium Transac-

tions (Pergamon Press, London, 1961).]

For higher values of the magnetic field, an electron emitted by the

cathode performs a cycloidal orbit which fails to reach the anode and

turns back toward the cathode. Only those electrons which are

disturbed from this orbit, either by high-frequency electrostatic fields

due to electron space-charge oscillation or by collision encounters with

gas molecules, ever reach the anode under these conditions. The

electron current curve, shown in Fig. 3-38 from Lafferty's paper,

decreases by about a factor of 10 as the magnetic field is increased from

zero to 200 oersteds.

The ion collector for the Lafferty gauge is a disk of about the same


diameter as the cylindrical anode, and is supported over one end of theanode with a sufficient gap to stand off a voltage. The lead for the ioncollector is at the end of the tube opposite that at which all the otherleads are located, to provide minimum electrical leakage. The loweror opposite end of the anode is closed by a similar disk, referred to asthe shield, which catches any positive ions leaving in that direction.The electrical potentials relative to the cathode are typically as follows

:

anode, 300 V; ion collector, -45 V; shield, -10 V. Typical magneticfield intensity is 250 oersteds, which can be maintained either by acylindrical alnico magnet or by a solenoidal coil placed around the tube.As the magnetic field is increased slightly beyond the magnetron

cutoff value, the length of the electron orbits, and thus also the numberof ions produced per electron, is increased by a large factor. The ioncurrent registered on the ion collector is also shown in Fig. 3-38 as afunction of the magnetic field intensity. It will be noted that thiscurrent is a maximum for a value of the magnetic field only slightlyabove the magnetron cutoff value. The positive ion current increasesby a factor of 10* or 10^ as the magnetic field is changed from less thanthe magnetron cutoffvalue of about 100 oersteds to about 150 oersteds,at which the ion current is a maximum. As the magnetic field is

further increased, the electrons emitted by the cathode are confinedmore closely to the vicinity of the cathode as their orbits are contracted,and thus sweep a shorter path through the gas, producing fewer ions.The maximum ratio of positive ion-collector current to electron anodecurrent is thus reached at a magnetic field value about twice as largeas the magnetron cutoff value. These are the most favorable con-ditions for operation in order that the X-ray limit be as low as possible.

In Fig. 3-39 the ion-collector current, as a function of the pressure,is plotted together with similar data taken with a Bayard-Alpert gauge.Based upon a determination of the X-ray limit of the ion magnetrongauge, which proves to be about 6 x 10"" torr, and a calibrationagainst the Bayard-Alpert gauge at higher pressures, the readings ofthe former were assumed to be a linear function of the pressure downto the lowest readings obtained. The Bayard-Alpert gauge readingsbegin to deviate noticeably from a straight line at lO-^" torr and reachan asymptotic value corresponding to an X-ray limit of about 3 x lO-^*torr, whereas the ion magnetron gauge indicates collector current aslow as that corresponding to a pressure of 4 x 10"" torr. Operatingparameters for both gauges are given in the figure. It will be notedthat for the ion magnetron gauge, /„ = 10-' A for the run, where I^ is

the emission current read on the anode when the magnetic field is zero.To produce approximately the same ion-collector current at higherpressures, the Bayard-Alpert gauge is operated with /j = 5 x 10-3 A,

no VACTJTJM SCIENCE AND ENGINEERING

indicating a greater sensitivity for the ion magnetron gauge by a factor

of 5 X 10-3/10-' = 5 X 10*.

At high pressure the secondary electrons produced by ionizing col-

lisions add to the electron space charge in the magnetron gauge, with

W-

10-'

10-'

10-'

10-'

10-'

Gauge Operating Conditions

o Magnetron gouge »Boyard-Aipert gouge

Ep= 300 volts

= -45 volts

Es= -10 volts

H = 250 oersteds

Ep= ISOvolts

Ec= -45 volts

Io= 5 mA

"I >I I I 1 1 III

I I I ' I I ml i_'

10",0-13 io-'2 IQ-" 10-'° 10-'

Pressure, torr

FlQ. 3-39. A comparison of the ion-collector current characteristics of the Bayard-

Alpert gauge and the magnetron gauge. A linear relationship between the

magnetron-gauge ion current and pressure is assumed at pressures below 10~*

torr. [Taken with permission from J. M. Lafferty, in 1960 Vacuum Symposium

Transactions (Pergamon Press, London, 1961).]

the result that the space charge becomes large enough for oscillations

to set in because of cooperative electrostatic forces. The gauge tends

to become unstable in operation, with frequent reversal of the ion-

collector current because of the ejection of high-energy electrons against

the repelling field of the collector. Because of this phenomenon, the

magnetron gauge is normally operated at low emission current of


Electron

multiplier

First dynode

Electrostatic lens

Multiplier

^/shield cylinder

Focusing

cylinder

Aperture

"--I .,

I

i-^-Alnico magnet^— Ion accelerator

w ^ M I I -Magnetron gauge

LaBfi

10-' A or less and is also normallyused only for measuring relatively

low pressures, say 10"' torr as theupper limit.

A further improvement in thehot-cathode magnetron ion gaugehas been described by Lafferty.^^*'

By drawing the ions produced in themagnetron gauge out one end byan electrostatic lens system designedto focus the ions on the first dynodeof an electron multiplier tube, as

shown in Fig. 3-40, the sensitivity

of the gauge has been increased bya large factor. The soft X raysfrom the magnetron anode wereprevented from falling on the dy-node, with the result that the X-raylevel was decreased to such a lowlevel that a pressure of 10"" ton-

should be detectable by countingindividual ions striking the first

dynode of the electron multiplier.

To prevent direct light emitted bythe thermionic cathode from pro-

ducing a response on the electron

multiplier, a lanthanum boride

(LaBg)-coated rhenium filament,

which produces electron emission at

much lower temperatures, was sub-stituted for the tungsten cathode.As shown in the figure, the low-

temperature cathode consisted of alO-mil-diameter rhenium wire, withan open helix of a 5-mil-diameterrhenium wire wound on it and then coated with lanthanum boride.The lower-temperature cathode should also contribute to a reductionin the anomalies caused by a hot cathode referred to in the previoussection.

3-9. Magnetically Collimated Electron-beam IonizationGauge. An ionization gauge in which the ions are produced by anelectron beam collimated by a carefully aligned magnetic field hasbeen described by Klopfer." As is apparent from Fig. 3-41, electrons

LJ Filament

detail

Fig. 3-40. Hot-cathode magnetronionization gauge with electrostatic

lens system to focus ions on the first

dynode of an electron multiplier tube.

Also detail of low-temperature, lan-

thanum boride (LaBg) coated cathode.

[Reprinted with permission of TheMaomillan Company from 1962 Vac-uum Sym.posium Transactions. Copy-right © 1962 by American VacuumSociety.]


are emitted from a thermionic cathode K, coUimated through a series

of apertures at various electrical potentials, traverse an isolated chamber

in which ions are produced, and finally collected by an electron-trapping

electrode T. Ions produced within the chamber between G^ and G^

are attracted to the ion-collector plate / at ground potential, which is

negative relative to the electron beam and the chamber walls. The

magnetic field of about 1,000 oersteds intensity is carefully aligned

10'

field

1,000 gauss

30 volts

Fig. 3-41. Schematic diagram of

magnetically coUimated electron-

beami ionization gauge. [Takenwith permission from A. Klopfer,

in 1961 Vacuum Symposium Trans-


10

:10'

10"

10-"

// Vk= + 30,V5= VA=+180volts

B = l,000gauss

IQ-12,0-10 10-8 10-6 10-4 ,0-:

Pressure, torr

10"

Fig. 3-42. Relative ion current vs.

nitrogen pressure for the electron-

beam ionization gauge of Fig. 3-41.

[Taken with permission from A.

Klopfer, in 1961 Vacuum Sympo-sium. Transactions (Pergamon Press,

London, 1962).]

relative to the series of apertures through the electrodes G^ through

(t4 so that at all the electrons pass through the apertures and are caught

on the electrode T. The geometry of the gauge is such that X-ray

photons emitted by the electron-trapping electrode T because of electron

impact cannot irradiate the ion-collector electrode J directly, so that

electron emission from the ion collector is minimized. The presence of

the magnetic field further reduces the X-ray effect by causing anyelectrons emitted at the electrode surface to move in circular orbits

and return to the electrode. Emission of photoelectrons due to light

from the cathode striking the ion collector is avoided partly by the

geometry of the gauge, which shields the collector from direct irradiation

by the cathode, and also by the use of a low-temperature cathode, suchas a lanthanum boride-coated rhenium filament.

The use of a low-temperature cathode also serves to reduce substan-tially the pumping effect due to chemical reactions at the cathode. As


a consequence, the pumping effect of the gauge is determined primarily

by the rate of production and collection of positive ions. For nitrogen

the pumping speed of the gauge is calculated to be about 3 x 10"^

liter/sec with an electron beam current of 1 mA. One side of the

ionization chamber is covered by an open screen providing high con-

ductance to the surrounding space, so that the gauge error due to

pumping is believed to be very small.

As is illustrated in Fig. 3-42, the response of the gauge is linear from

about 10~^ torr to at least as low as 10~i^ torr. The linear response

up to such a high pressure is apparently due to the fact that only the

electrons coming directly from the cathode and not those produced byionization along the beam are effective in producing ionization. The

electrical potentials are arranged such that the electrons traverse the

ionization chamber at an energy of 100 eV, a value at which the specific

ionization is near maximum. Electrons formed by collision processes

in the chamber, however, have very little energy and no means of

gaining energy from the electric fields present in the chamber.

3-10. Cold-cathode Ionization Gauges. The useful life of a

hot-cathode ionization gauge is determined by that of the cathode.

lOcm

Fig. 3-43. Penning cold-cathode ionization gauge. [Taken with permission

from J. H. Leek, Pressure Measurement in Vacuum Systems (Published for the

Institute of Physics and the Physical Society by Chapman and Hall, Ltd.,

London, 1964), 2nd ed.]

Particularly at relatively high pressures, approaching 10"' torr, chem-

ical attack by some gases and bombardment by positive ions limit the

useful life of hot cathodes. In 1937, Penning*^ described a cold-cathode

gauge, sometimes called the Philips ion gauge or PIG. As shown

schematically in Fig. 3-43, Penning's original gauge consisted of two

parallel plates P at cathode potential separated by a distance of about


• H

2 cm and a ring electrode R at anode potential suspended in the mid-

plane between the two plates. A magnetic field of about 500 oersteds,

with the lines of magnetic flux perpendicular to the planes of the

electrodes, was provided by a permanent magnet with a pole on either

side of the tube. When a potential difference of 2,000 V was applied

between the plates as cathodes and the ring as anode, a current was

observed to flow and was found to be

approximately proportional to the pressure

for the range 10"^ to 10"^ torr.

In the absence of the magnetic field the

electrode structure of the Penning gauge

would not result in a discharge current

except at relatively high pressure, of 10"^

torr or more. The presence of the magnetic

field changes completely the character of the

discharge because electrons emitted by the

cathodes are constrained to move in tight

helical paths along the lines of force and are

thereby prevented from going directly from

the cathode plates to the anode ring. The

electrons, instead, oscillate through the ring

between the plates and slowly drift outward

across the magnetic field toward the ring

only as a result of collisions with gas mole-

cules, which are ionized to form positive ions

and additional electrons. The positive ions

are attracted immediately to the cathodes

and, in contrast with the usual gaseous dis-

charges, account for most of the current flow

in the discharge. The additional electrons

contribute to further ionization. Because of the comparatively long

electron path, which results from the oscillatory motion, the gas breaks

down into a discharge even when the pressure is as low as 10~^ torr.

The original design of the Penning gauge, characterized by the ring

tjrpe of anode illustrated in Fig. 3-43, proved to be somewhat unsatis-

factory in that the discharge is unstable and the current as a function

of the pressure exhibits unpredictable changes of magnitude between

2 and 5 per cent. Below 10~^ torr the discharge becomes erratic andfrequently fails entirely at pressures of 10~* torr and below. These

difficulties were partly overcome in an improved form of the cold-

cathode gauge described by Penning and Nienhuis*^ and illustrated in

Fig. 3-44. The anode of the improved gauge is in the form of a cylinder

of about equal length and diameter, with flat plates as cathodes located

Fig. 3-44. Cold-cathode

ionization gauge ofPenning

and Nienhuis with cyhn-

drical anode. [Taken with

permission from F. M.Penning and K. Nienhuis,

N. V. Philips' Tech. Rev.

11, 116 (1949).]

PBESSUBE MEASUREMENT IN VACUUM SYSTEMS 115

at either end of the cylinder. The sensitivity of the gauge was in-

creased by about a factor of 10 to about 1 mA at 10"* torr for a circuit

voltage of 2 kV, the range of linear response extended down to less than10^' torr, and the amplitude of the erratic changes in the discharge

current reduced to 2 per cent or less. With a gauge of similar geometry,

but with nickel instead of zirconium cathodes, Leek and Riddoch**

obtained the calibration curves shown in Fig. 3-45, which are in goodagreement with those obtained by Penning and Nienhuis. The current

100

=1.

I 50

4kV 2ky

l^ j.-1kV

0.3

0.15

i\y

J^^ TkV

1 2 " 2.5 5

Pressure, X 10^ torr Pressure, X 10^ torr

Fig. 3-45. Penning gauge calibration curves for air obtained by Leek and

Riddoch (these characteristics are independent of the magnetic field over the

range 500 to 1,000 gauss). [Taken with permission from J. H. Leek, Pressure

Measurement in Vacuum Systems (Published for the Institute of Physics and the

Physical Society by Chapman and Hall, Ltd., London, 1964), 2nd ed.]

is proportional to the pressure over the useful range of the gauge, i.e.,

from about 10"' to 10"* torr. Also the sensitivity is proportional to the

anode-to-cathode voltage over the range 1 to 4 kV. At a pressure of

about 10-* torr the current decreases suddenly to a much lower value

so that the gauge is not considered reliable below about 10"' torr.

Since a ballast resistor must be put in series with the power supply for

protection in the event of a short circuit, the gauge is somewhat non-

linear from 10-* to 10-3 torr, above which the current increases steeply

with the pressure. The steep increase of the current with increasing

pressure above 10-^ torr can be used to protect a system against pressure

bursts. A relay in the circuit set to operate in this range can be used

to shut off gauges, close valves, and perform other protective functions

in the event of an excessive gas burst.

The Penning cold-cathode ionization gauge cannot be relied upon for

pressure measurements of high precision, even with great care in cali-

bration, because of the slightly unstable character of the discharge.

However, this type of gauge is sufficiently reliable as a pressure

indicator for many vacuum process applications and has a very long


useful life as compared with the hot-cathode ionization gauges because

of the rugged character of the cold cathodes.

A cross-sectional view of a commercial Penning discharge type of

gauge is shown in Fig. 3-46. The anode in this design is shaped to

provide a maximum area while keeping the exterior dimensions of the

gauge tube to a minimum. A shield protects the high-voltage insulator

from accumulating spluttered atoms and ions, contributing to a long

life against electrical leakage and breakdown. The gauge tube and

tubulation are of stainless steel. Because of these features the gauge

is said to provide an operating life under favorable conditions up to

Section AA

Fig. 3-46. Cross section of Kinney all-metal Penning discharge vacuum gauge.

50,000 hr. However, as with all cold-cathode gauges, excessive

exposure to hydrocarbons will result in contamination due to decom-

position products deposited on the electrodes and insulator. To remove

oil from the gauge, the manufacturer recommends washing with

trichlorethylene, rinsing with acetone, and drying by gentle heating in

air. To remove decomposition products, a cleaning solution made up

of 225 g of ferric chloride, 500 cm^ of hydrochloric acid (38 per cent HCl)

and 1,400 cm' of distilled water is recommended. The gauge tube is

placed in a beaker and filled nearly to the top with hot cleaning

solution which is maintained at the boiling point for about 15 min;

the tube is then rinsed with distilled water followed by acetone, alcohol,

or ether and finally thoroughly dried by warming in air.

Although the Penning discharge gauge described above is mechani-

cally rugged and is not damaged by exposure to atmospheric pressure

while the voltage is on, observing certain precautions will contribute

to greater operating life by avoiding contamination. The gauge tube

should not be mounted in a position where it is in a direct line with a

source of hydrocarbon vapor. It should not be operated at pressures

in excess of 10 torr nor during the pumpdown period.

A simplified circuit diagram for the Penning discharge gauge is shownin Fig. 3-47, and the pressure response curve is shown in Fig. 3-48.


Note;S -Fully CCW ; rear view of switch shown

Fig. 3-47. Circuit diagram for Kinney Penning discharge vacuum gauge.

~^ -n ^ —000

L 1 1

">///

1 1 1

50/iAatO.Ol/i^

1 1 1

/100

N./y/—1—1—1

1 1 /lu 7

//

1 /

10' 10" 10"* 10"*

Pressure, torr

10" 10" 10"'

Fig. 3-48. Calibration curve for Kinney Penning discharge gauge.


The gauge is calibrated over the pressure range from 2 x 10~' to 10 torr,

the response above about 2 x 10~* torr being much flatter than at lower

pressures as shown in the figure.

A further development of the cold-cathode ionization gauge wascarried out by Beck and Brisbane,*^ Haefer,** and Redhead*' and has

culminated in a gauge of high sensitivity and reliability. The added

ooo oo oo oo oo ooo

A xiol magnetic

field

start of electron

Fig. 3-49. Schematic of

the Haefer inverted-mag-

netron type ofcold-cathode

ionization gauge. [Takenwith permission from Hel-

mut Schwarz, Vacuum 11,

151 (1961).]

Auxiliory cathode -Anode

Cothode

Fig. 3-50. Cutaway view of inverted

-

magnetron cold-cathode ionization

gauge. [Taken with permission fromP. A. Redhead, in 1958 VacuumSymposium Transactions (PergamonPress, London, 1959).]

feature is the use of crossed electric and magnetic fields to increase bya large factor the path of the few electrons emitted by the cold cathode,

and thus also the efficiency of the electrons in producing positive ions.

A schematic representation of the Haefer inverted-magnetron gauge is

shown in Fig. 3-49. The cathode is a cylinder (actually the metal case

of the gauge tube) about 5 cm in diameter, and the anode is a small

diameter metal rod located on the axis of the cathode. A magneticfield of about 2,000 oersteds intensity parallel with the axis of the tubeis maintained by an external coil. A potential difference of several

kilovolts is applied between the anode and cathode so that a radial

electric field is superimposed upon the axial magnetic field. An electron

anywhere in the region between the anode and cathode will move on acycloidal path in the E x H (azimuthal) direction with a drift velocity

given by

v^ = lO^E/H) cm/sec

PRESSUEE MEASUREMENT IN VACUUM SYSTEMS 119

in which E is the electric field intensity in volts per centimeter and H is

the magnetic field strength in oersteds. Since the drift velocity is

everywhere perpendicular to both E and H, the electrons move in

circular cycloidal paths at a constant average radius from the center.

Only upon collision with a gas molecule is the electron disturbed from

this path because of energy loss in the collision. Each time such a

collision occurs the electron moves into a new circular cycloidal path

closer to the anode. With a proper

choice of the parameters the drift

velocity of the electrons is sufficient

to ionize gas atoms so that an

appreciable fraction of the colli-

sions results in the production of

positive ions which are attracted im-

mediately to the cathode. By this

process each electron emitted from

the cathode produces a large num-

ber ofionizing events before it finally

spirals into the center of the gauge

and is caught on the anode.

In Fig. 3-50 is shown a cutaway

view of an inverted-magnetron

gauge developed by Redhead*' in

which the cathode is surrounded byan auxiliary cathode outer shell

with cylindrical shields protruding

through the openings into the cath-

ode. The auxiliary cathode acts as

an electrostatic shield and protects

the edge of the openings through the cathode from field concentrations,

thus preventing field emission. The cathode and auxiliary cathode

are both grounded, but the current to the cathode alone is taken as

the measure of the true positive ion current. The anode rod is typically

maintained at 6 kV and the magnetic field intensity at 2,000 oersteds.

In the pressure range from 10"" to 10"* torr the positive ion current

was found to conform to the relationship

i+ = cP"

in which n varied from 1.10 to 1.15 and c was a constant. Above10-3 torr the space charge changes from negative to positive with

the result that the characteristics of the gauge change completely.

Calibration curves for several models of the inverted-magnetron

gauge are shown in Fig. 3-51, together with a similar curve for the

,0-11 ,0-9 ,0-7

Pressure, torr

Fig. 3-51. lon-current-vs. -pressure

relationship for inverted-ion-magne-

tron gauge. [Taken with permission

from P. A. Redhead, 1958 VacuumSymposium, Transactions (Pergamon



Anode

Cathode

Fig. 3-52. Cold-cathode magnetron gauge. [Taken with permission from P. A.

Redhead, 1958 Vacuum Symposium Transactions (Pergamon Press, London,

1959).]

Bayard-Alpert gauge. As in the case of the hot-cathode magnetron

gauge discussed in the previous section, the X-ray hmit of the

inverted-magnetron gauge is well below that of the Bayard-Alpert

gauge.

The type of gauge generally referred to as the Redhead gauge is aninversion of the geometry discussed above and designated the cold-

cathode magnetron gauge by Redhead.** The cathode, as shown in

Fig. 3-52, is in the form of a spool consisting of a small-diameter central

cylinder and two end disks. The anode is a cylinder with a diameter

about equal to that of the end disks

and is perforated with many holes

to ensure good conductance be-

tween the regions inside and outside

the gauge volume. An auxiliary

cathode in the form of an electro-

polished ring is placed at each endof the cylindrical anode in the gapbetween the anode and cathode to

reduce field emission currents to a

minimum. Redhead found that in

the pressure range from 10~^ to

10~* torr the cold-cathode magne-tron gauge with anode potential of

5 kV and magnetic field of 1,070

oersteds has a linear characteristic

as shown in Fig. 3-53 for nitrogen

and helium. As can be seen fromthe graph, the ion current in amperes

Pressure, torr

Fig. 3-53. lon-current-vs. -pressurerelationship for magnetron gauge inthe range 10"* to 10-9 tQj.r. [Takenwith permission from P. A. Redhead,1958 Vacuum, Symposium, Trans-actions (Pergamon Press, London,1959).]

PEESSUBE MEASUREMENT IN VACUUM SYSTEMS

Table 3-2. Cold-cathode Gauge Chaeactebistics*

121

GaugeAnodevoltage,

kV

Ion-current

pressure.

A/mm Hg

Pretreatmentof gauge

GasPumping

rate,

1/sec

Bayard-Alpert, 10 mA. . 0.1 Outgassed Argon 0.080

5.0 4.0 Baked at 400°C ArgonNitrogenOxygen

0.200

0.140

0.150

5.0 4.0 Operated for several

hotirs in oxygenArgonNitrogen

Oxygen

0.050

0.100

0.120

Reduced -size cold

5.0 4.4

Operated for several

hours in argonBaked at 400°CInduction heated to

800-900°C

Argon

ArgonArgon

0.018

0.042

0.350

Reduced-size cold

1.2 0.46

Induction heatedInduction heatedfInduction heatedf

ArgonArgonOxygen

0.110

0.330

0.340

Reduced-size cold

0.3 0.03t

* Taken with permission from T. N. Rhodin and L. H. Rovner, in 1960 Vacuum SymposiumTransactions (Pergamon Press, London, 1961), p. 228.

f Prolonged treatment with some evaporation of metal.

% Ratio of ion current to pressure is not constant.

for nitrogen is given approxi-

mately byi^ = lOP

in which the pressure is given in

torr. It was also observed that

at a pressure of about 2 x lO^^"

torr there is a break in the re-

sponse curve so that below this

value of the pressure the curve

is no longer linear but takes the

form

as shown for helium in Fig. 3-54.

Redhead reports that the cold-

cathode magnetron gauge has a

pumping speed of approximately0.15 liters/sec. Rhodin andRovner** have made extensive

measurements of the pumpingspeed of cold-cathode magnetron

10-'

eio''

10'1-12

Helium

,y

-->

• Run 1

,/59'

Magnetron gauge

operating alone

'SkVB=l,060 gauss

X Bayard-Alpert gauge

operating alone

Run 2

Run 3 J

1010 10"

Pressure, torr

Fig. 3-54. lon-current-vs.-pressure rela-

tionship for magnetron gauge in the

range 10~' to 10~l^ torr. [Taken with

permission from P. A. Redhead, in

1958 Vacuum Sym,posium Transactions



gauges similar to that of Redhead and report that the principal disad-

vantage is the high pumping speed of such gauges, leading to some

ambiguity in interpretation of the ion current reading. The results

of their measurements are summarized in Table 3-2 in which the pump-

ing speeds of the normal size (Redhead) cold-cathode magnetron gauge

and one of reduced size are compared with that of a Bayard-Alpert

type of hot-cathode ionization gauge. In spite of the high pumping

speed and its dependence upon the

Section A-A30 to 40 volts

contoined in amplifier

power supplyQutput

Housing

1 2l'Mi|i|i|

I II I

Fig. 3-55. The Alphatron gauge.

[Taken with permission from J. R.

Downing and G. Mellen, Rev. Sci.

Instr. 17, 218 (1946).]

previous history of the gauge, as

illustrated in Table 3-2, the cold-

cathode magnetron gauge is useful

in the pressure range below 10~ii

torr, a pressure well below the

range of the Bayard-Alpert gauge.

The high pumping speed is appar-

ently associated with the very high

efficiency of ionization by the elec-

trons in their circular cycloidal

orbits, which results in a high

sensitivity, i.e., high positive ion

current, as compared with that of

the Bayard-Alpert gauge operating

at the same pressure.

3-11. The Alphatron Gauge.Any process which causes ioniza-

tion of the residual gas in a tube or

chamber can, in principle, be used

as a basis for an ionization gauge.

X rays, alpha particles, beta

particles, and gamma rays are all ionizing agents, the advantages of

which may be considered as possible means of ionizing gas for the

purpose of measuring its molecular density. A practical development

of this type is the Alphatron (National Research Corporation) gauge of

Downing and Mellen'" which utilizes a small source of alpha particles,

for example, 0.5-mg piece of an alloy of gold and radium sealed in

a capsule. The gauge consists of a source holder and two grid struc-

tiires inside a small metallic ionization chamber which serves as the gauge

tube (see Fig. 3-55). A diiference in potential of 30 to 40V is maintained

between the two grid structures to sweep out the ions and electrons

formed by the ionization process. The ionization current is found to be

substantially a linear function of the pressure over a wide range, from10-* to 40 torr for the first version of the Alphatron, the current being


2 X 10-1" A for a pressure of 1 torr of dry air. An improved version of

the Alphatron described by Vacca'^ is provided with six ranges with full

scale readings of 10-^, 10"^, 10, 100, and 1,000 torr. The low range is

accomplished by an improved electrometer tube and circuit capable

of amplifying currents as low as 10-^* A. The higher ranges are

obtained by using a second ionization

chamber of very small volume. Thelinearity of the new gauge is said to

be within 2 per cent of full scale for

all ranges.

3-12. The Knudsen RadiometerGauge. The Knudsen*^ radiometer

gauge is perhaps the most widely

known and described^' of the less com-

mon vacuum gauges. The basic ele-

ment of the radiometer gauge consists

of two parallel plates, one of which is

heated, separated by a distance which

is small as compared with the dimen-

sions of the plates, as shown in

Fig. 3-56a. The unheated plate is

supported on a sensitive suspension so that a small force acting uponit can be measured. An alternative form is shown in Fig. 3-566 in which

the unheated vane is suspended between two fixed plates, one of which

is heated and the other cooled. The force per unit area on the sus-

pended vane or plate is given approximately by

Fig. 3-56. The two alternative

basic elements of the Knudsenradiometer vacuum gauge. [Takenwith permission from J. H. Leek,

Pressure Measurement in VacuumSystems (Published for the Institute

of Physios and the Physical Society

byChapman and HalI,Ltd., London,1964), 2nd ed.]

f-I ©% {^

dyne/cm^ (3-36)

for the first case in which T^ and T^ are the temperatures respectively

of the heated plate and the vane, T is the ambient temperature of the

walls of the gauge tube, and P is the gas pressure. In the second case

/2 =T,V^"

w^m dyne/cm ^ (3-37)

in which T^ and T^ are respectively the temperatures of the heated andcooled plates and T is the ambient temperature. In this latter case

the force on the vane does not depend on its temperature T^. In either

case the force depends directly upon the pressure in the strictest sense,


the force per unit area exerted by the gas, with no dependence upon the

molecular weight of the gas. In this respect the Knudsen gauge maybe considered an absolute pressure-measuring device.

A more exact treatment of the theory of the Knudsen gauge, taking

into account the accommodation coefficients for the vane surfaces and

the inside surface of the gauge tube, leads to much more complicated

expressions for the force per unit area on the vane. Differences in

accommodation coefficients at the various surfaces result in responses

which differ for various gases, with the response to helium and hydrogen

being particularly low for some gauge designs.

The linear expressions for the response of the Knudsen gauge are

valid only in the pressure region for which the molecular mean free

path is large as compared with the spacing between the vane and fixed

plate or plates. By using the smallest practical spacing and a closed

box structure about the vane system, linear response up to a pressure

of 10-» torr can be obtained. At higher pressures the response is

always less than the linearly extrapolated value and eventually begins

to decrease with increasing pressure. The useful range of the radi-

ometer gauge thus tends to be from about 10"* to 10-* torr.

In practical designs of the Knudsen gauge pressures as low as 10-^

torr are detectable. Since a sensitive suspension is required, all designs

of the Knudsen gauge thus far developed are too cumbersome and

fragile for most applications. Many special adaptations have been

made and successfully applied, however, when the unique features of

the Knudsen type of gauge are important, such as freedom from

chemical decomposition of heavy organic molecules, a process which

does occur in all types of ionization gauges.

3-13. Calibration of Vacuum Gauges. For many years the

accepted standard for calibrating other vacuum gauges in the pressure

range below that easily accessible to the simple mercury U-tube

manometer has been the McLeod gauge. The limitations of the

McLeod gauge and the precautions necessary to obtain consistent

results are discussed in Sec. 3-4. It is clear from that discussion that

the calibration of other vacuum gauges is limited to gases which obey

Boyle's law up to the maximum pressure to which it is compressed

in the operation of the McLeod gauge. Accepted practice has been to

provide a glass- or metal-walled chamber evacuated by a liquid-

nitrogen-trapped diffusion pump to which the McLeod gauge and the

gauges to be calibrated are connected each through a liquid-nitrogen-

cooled trap, somewhat as shown in Fig. 3-57. The use of liquid-

nitrogen-cooled traps is essential to protect the ionization gauges

from mercury vapor from the McLeod gauge and also to protect the

McLeod gauge from contamination by hydrocarbon vapor from the


system. A needle valve is provided so that any chosen gas can be

admitted to the system at a controlled rate to vary the pressure.

For calibrating thermocouple and Pirani gauges, usually from 10'^ to

1 torr, only a rather insensitive McLeod gauge (small bulb and large-

diameter capillary) is required, and no serious difficulties are reported.

However, for calibrating ionization gauges over a sufficient pressure range

in the region of linear response, the greatest McLeod gauge sensitivity

Gas input

through drying tube

Gauges

to be

coiibrated

Severe I

locations

around

chamber

McLeodgauge

Liquid- Liquid-

nitrogen trap nitrogen trap

ffiK^'\K.'\K<^K Liquid-nitrogen and

Iwater-cooled baffles

Diffuion

pump

Fig. 3-57. System for calibrating vacuum gauges against a McLeod gauge.

is required. Even so, the lowest pressure which can be rehably

measured with sufficient precision by means of a McLeod gauge is

about 10-5 torr. Thus ionization gauges are normally calibrated from

10-5 to 10-^ torr, in the upper portion of which range the response of

most ionization gauges is no longer linear. The range of linear

response available for calibration in this manner is therefore only about

a factor of 30 in pressure for determination of the gauge constant.

Recently, however, a much more serious objection to this method of

calibration of ionization gauges has been raised by Ishii and Nakayama,^*

who find a pronounced dependence (up to 25 per cent) of the calibration

upon the ambient temperature. They attribute this effect to the

pumping action of the mercury vapor stream from the McLeod gauge

into the liquid-nitrogen-cooled vapor trap. By cooling the McLeod


gauge at the cutoff point with dry ice before the mercury is raised,

thereby reducing substantially the vapor pressure driving mercuryvapor into the cold trap, this particular gauge error was eliminated.

The result of these observations brings into serious question the long-

accepted method of pressure measurement involving large temperaturedifferences when condensable vapor pressure dominates in some portion

of the vacuum system.

Gas

Throttle

valve

To (reference)

gougeGouge to be

calibroted

inlet

Fig. 3-58. Apparatus for calibrating vacuum gauges at low pressure by gas flowthrough apertures. [Taken with permission from J. R. Roehrig and J. C.

Simons, Jr., in 1961 Vacuum Symposium Transactions (Pergamon Press, London,1962).]

An alternative method for calibrating ionization gauges has beendeveloped by Roehrig and Simons^^ and results compared withcalibrations against a McLeod gauge. The apparatus as illustrated

in Fig. 3-58 consists of a test chamber and an adjoining pumpingchamber connected by an aperture of small conductance Cj. Thepumping chamber is evacuated by a high-speed trapped diffusion pumpthrough a second aperture of conductance C^ which is small as comparedwith the pumping speed Sj, of the trapped diffusion pump. Thepumping speed out of the pumping chamber is then, according to (2-8),

Co — GoS^

s^ Go(3-38)

which differs only slightly from G^ if Cj < S^. Thus the pumpingspeed out of the pumping chamber is relatively constant and independ-ent of small changes in S^. The pumping speed out of the test chamber


IS

S,= Gi + S2

G1S2

G, + G2(3-39)

as long as Cj < S^.

For a measured flow of gas Q the resulting change in pressure AP is

given by

Q^^ = ^-^- = ^.-C,-fC;.Q

G-fi^(3-40)

The pumping apertures are most conveniently in the form of circular

holes for which the conductance given by (2-89) is

\^rC = 2.861— 11)2 liters/sec

and is accurately determined as long as the diameter of the aperture

and the ambient temperature are known. The method also requires

an accurate measurement of the gas flow Q, alternative methods for

which are discussed in Chap. 7. This type of system may be extended

by the addition of several pumping chambers with apertures between

stages to permit calibration down to very low pressure.

Gauges to be calibrated are connected to the test chamber, and the

gauge responses are compared with a series of pressure increases AP.

The authors state that results obtained in this manner on a four-stage

system were in agreement with results obtained by calibration of the

same gauges with a McLeod gauge within 2 per cent over the pressure

range from 10"^ to 10""^ torr, with poorer agreement below 10"* torr

because of the inaccuracy of the McLeod gauge in this range. This

agreement appears to be inconsistent with the discrepancies reported by

Ishii and Nakayama^* for McLeod gauge calibration. In any case, the

aperture method is free of criticism based upon the pumping action of

a liquid-nitrogen trap associated with a McLeod gauge and is apparently

the most reliable method yet developed for ionization gauge calibration.

This method has the further advantage of being applicable, according

to Roehrig and Simons, for accurate calibration of gauges down to

10-9 torr. Precautions which seem to the author to be important are

to ensure

1. That the diameters of the apertures between the test chamber and

the pumping chamber and between the stages are very small compared

with the dimensions of the chambers


2. That the actual pumping speed of each diffusion pump is large as

compared with the conductance of the pumping apertures

3. That the base pressure P, is small as compared with the pressure

P at which calibrating measurements are made

Requirement 1 ensures that the gas in the test chamber is essentially

static so that directional pressure effects due to dynamic flow will be

negligible. Requirement 2 allows the use of the approximate expres-

sion in (3-40) involving the conductances only. Otherwise the value

of *Si given in (3-39) must be estimated and substituted for Cj in (3-40).

For precision calibration S^ should be at least of the order of lOCj.

Requirement 3 ensures the elimination of subtle questions regarding the

propriety of simply subtracting P^ from P for determining the pressure

rise P due to the gas flow Q.

3-14. General Remarks on Ambiguities of Pressure Meas-urement in Vacuum Systems. In describing the instrumentation

used in measuring the pressure in vacuum systems some of the pre-

cautions required to obtain consistent results have been mentioned.

However, the extent of the ambiguity in measurement at low pressure

(e.g., less than 10~* torr) has perhaps not been stressed sufficiently.

The processes which occur in ionization gauges and contribute to

uncertainties have been discussed in the descriptions of the various

types of gauges. These processes are

1

.

Surface adsorption (gauge pumping) and desorption

2. Chemical decomposition, dissociation, or reaction with the hot

filament

3. Electrical oscillations

4. Radiation (the Nottingham X-ray limit)

5. Electrostatic effects due to surface and space charges

Whether a vacuum gauge meets the requirements of a given appli-

cation depends not only upon its sensitivity, but also upon the extent

to which it reflects without excessive distortion the conditions wherethe pressure is to be measured. The distortions due to sorption proc-

esses are greatly minimized by making the conductance into the

sensitive portion of the gauge from the region of interest as high as

possible. The nude ionization gauge represents the logical extremein this regard. Proper electrostatic shielding, use of a low-temperaturecathode, thorough outgassing of the gauge components all contributefurther to minimizing the discrepancy between the gauge reading andthe true pressure. Specialized techniques have contributed to anextension of the range of measurement with improved assurance ofreliability down to exceedingly low values of the pressure. Redhead^*has extended the lower limit for a Bayard-Alpert type of gauge, as

PBESSUHB MEASUREMENT IN VACUUM SYSTEMS 129

determined by the X-ray effect, from lO-" to about 10-" torr bymtroducing an additional electrode and superimposing a voltagemodulation. Torney and Peaks*' have used this technique to extendthe range of comparison between the modulated Bayard-Alpert andthe cold-cathode ion magnetron gauges, confirming the results reportedby Redhead" down to 10-" torr and observing ion current readingscorresponding to a nitrogen pressure of about 3 x 10-" torr. Resultssuch as these suggest that, in spite of the difficulties listed above,reasonably reliable pressure measurements can be made even in therange below lO-" torr if the proper precautions are observed.

These processes have been discussed in relation to relatively staticsystems, i.e., systems in which the pumping speed is relatively smallso that directional effects are not important. In this case the isotropicpressure is given by the familiar P = QjS, where Q is the total gasload due to leaks and outgassing, and 8 is the pumping speed. Inorder to attain a very low pressure in such a system (as in the usualultrahigh vacuum systems), the gas load Q is reduced by eliminatingall leaks and outgassing the internal surfaces by baking the system athigh temperature.

An alternative approach to the attainment of low pressure is toprovide the highest possible pumping speed. The additional problemsarising in this instance because of directional effects have been discussedby Santeler.58 In space-simulation systems the objective is to exposea test body to an environment as nearly like that of outer space aspossible. Since such test bodies cannot generally be baked at hightemperature, the simulation must be accomplished as well as possible inthe presence of surface outgassing so that the gas load Q remains high.In outer space, molecules leaving a space vehicle fly off into space andvery few ever return. Thus true simulation of the outer space environ-ment would be accomplished by surrounding the test body withperfectly absorbing walls. If this could be done, then at low pressureat which the mean free path exceeds the dimensions of the system,gas molecules desorbed from the test body would travel on straight-linepaths to the wall of the vacuum vessel and there be absorbed, whereasno gas molecules would be received by the surface of thg test body.The pressure would then be highly directional. An ionization gaugelocated in a recess in the wall of the vacuum vessel would receive a fluxof molecules which could produce an ion current corresponding to apressure reading. An ion gauge located in a recess in the test bodyshielded from direct access by molecules from the surface of the testbody would receive nothing, as would be the case in outer space.

In practice no such perfectly absorbing surfaces exist. Liquid-nitrogen-cooled or cryogenically cooled surfaces condense some gas


molecules more or less completely, but not generally on a single bounce.

Evaporated surfaces of active metals absorb certain gas molecules very

well, but again only after several encounters. Other gases must be

pumped by diffusion pumps. If A is defined as the ratio of the total

pumping speed of the system to that which would exist if all the walls

were perfectly absorbing, then, as Santeler shows, the directional

pressure effect is given by 1/(1 - A). An ordinary ionization gauge

Liquid-nitrogen

extension

Electrical

leads

Gouge

electrodes

Perforations

Chamber wolChamber liquid-nitrogen

surface

Fig. 3-59. Gauge mounting designed to compensate for directional pressure

effect. [Taken with permission from D. V. Santeler, Rev. Sci. Instr. 33, 283

(1962).]

located in the wall of the test vessel will then receive a flux of molecules

1/(1 —A) times the flux received by the surface of the test body.

In order for a gauge located in the wall of the vacuum vessel to

produce a reading corresponding to the flux arriving at the surface of

the test body, Santeler developed the gauge arrangement illustrated in

Fig. 3-59. A Bayard-Alpert nude gauge is mounted in a cylindrical

extension from the liquid-nitrogen-cooled inner surface of the chamber.

The liquid-nitrogen-cooled surface is perforated with an array of holes

through which gas is admitted from the center of the test chamber.

The ratio of the area of the holes to the total area of the cooled surface

is made equal to the wall pumping efficiency A of the main chamber.

Because the pumping speed for permanent gas is small both for the

gauge and for the main chamber, the pressure due to permanent gas is

isotropic and essentially uniform throughout the test chamber and the

gauge recess. However, only the fraction of condensable vapor which

returns from the surrounding walls to the test object is admitted to the

gauge recess. Thus the gauge reads the full value of the permanent

gas, all of which the test object receives, but only that portion of the

nonisotropic pressure of the condensable vapors which the test object

receives.

PEESSUEE MBASUEEMENT IN VACUUM SYSTEMS 131

The extent to which the techniques described by Santeler can beused to correct for the directional pressure effect in systems of veryhigh pumping speeds is difficult to assess. However, the directionaleffect exists and results in large gauge errors which cannot be easilyevaluated unless special precautions are exercised.

1

2

3

4

5

6

7,

8,

9.

10,

11,

12.

13.

14.

15.

16.

17.

19,

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

REFERENCES

. K. C. D. Hickman, Rev. Sci. Instr. 5, 161 (1934).

.Wallace and Tiernan, Incorporated, 25 Main Street, Belleville 9, N.J.,Absolute Pressure Indicator Type FA- 160.

. H. G. East and H. J. Kuhn, J. Sci. Instr. 23, 185 (1946).

. D. C. Pressey, J. Sci. Instr. 30, 20 (1953).J. Dubrovin, Instruments, 6, 194 (1933).H. McLeod, Phil. Mag. 48, 110 (1874).M. P. Romann, J. Sci. Instr. 3, 522 (1948).E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill Book Company NewYork, 1938), pp. 162-168.

W. Voege, Physik Z. 7, 498 (1906).

T. Hasse, G. Klages, and H. Klumb, Physik Z. 37, 440 (1936).G. C. Dunlop and H. G. Trump, Rev. Sci. Instr. 8, 37 (1937).R. J. Webber and C. T. Lane, Rev. Sci. Instr. 17, 308 (1946).J. M. Benson, in 1956 Vacuum Symposium Transactions (Pergamon Press,London, 1957), p. 87.

M. Pirani, Verhandl. deut. physik. Ges. 8, 686 (1906).C. M. Schwartz and R. Lavender, Rev. Sci. Instr. 19, 814 (1948).A. R. Hamilton, Rev. Sci. Instr. 28, 693 (1957).J. A. Becker, C. B. Green, and G. L. Pearson, Trans. A.I.E.E. 65, 711 (1946);and Bell System Tech. J. 26, 170 (1947).P. T. Smith, Phys. Rev. 36, 1293 (1930); Phys. Rev. 37, 808 (1931); J. T.Tate and P. T. Smith, Phys. Rev. 39, 270 (1932).

0. E. Buckley, Proc. Natl. Acad. Sci. U.S. 2, 683 (1916).W. B. Nottingham and F. L. Torney, Jr., in 1960 Vacuum SymposiumTransactions (Pergamon Press, London, 1961), p. 117.L. N. Ridenour and C. W. Lampson, Rev. Sci. Instr. 8, 162 (1937).R. S. Morse and R. M. Bowie, Rev. Sci. Instr. 11, 91 (1940).J. Blears, Proc. Roy. Soc. (London) A188, 62 (1947).1. Langmuir, J. Am. Chem. Soc. 37, 1139 (1915).L. Riddiford, J. Sci. Instr. 28, 375 (1951).G. Reich, in 1960 Vacuum Symposium Transactions (Pergamon Press,London, 1961), p. 112.

R. A. Haefer and J. Hengevoss, in 1960 Vacuum Symposium Transactions(Pergamon Press, London, 1961), p. 67.

W. B. Nottingham, J. Appl. Phys. 8, 762 (1937).R. T. Bayard and D. Alpert, Rev. Sci. Instr. 21, 571 (1950).A. van Oostrom, in 1961 Vacuum Symposium Transactions (Pergamon Press,London, 1962), p. 443.

H. J. Schuetze and F. Stork, in 1962 Vacuum Symposium Transactions (TheMacmillan Company, New York, 1962), p. 431.


32. W. C. Sohuemann in, 1962 Vacuum Symposium Transactions (Tho Macmillan

Company, New York, 1962), p. 428.

33. P. A. Redhead, in 1960 Vacuum Symposium Transactions (Pergamon Press,

London, 1961), p. 108.

34. E. J. Lauer, Lawrence Radiation Laboratory, Livermore, private

communication

.

35. D. J. Santeler, Rev. Sci. Instr. 33, 283 (1962).

36. H. F. Winters, D. R. Denison, D. G. Bills, Rev. Sci. Instr. 33, 520 (1962).

37. W. B. Nottingham, in 1954 Vacuum Symposium Transactions (Committee

on Vacuum Techniques, Inc., Boston, 1955), p. 76.

38. J. M. Lafferty, in 1960 Vacuum Symposium Transactions (Pergamon Press,

London, 1961), p. 97.

39. J. M. Lafferty, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962), p. 460.

40. J. M. Lafferty, in 1962 Vacuum Symposium Transactions (The Macmillan


41. A. Klopfer, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962), p. 439.

42. F. M. Penning, Physica 4, 71 (1937).

43. F. M. Perming and K. Nienhuis, Phillips Tech. Rev. 11, 116 (1949).

44. J. H. Leok and A. Riddoch, Brit. J. Appl. Phys. 7, 153 (1956).

45. A. H. Beck and A. D. Brisbane, Vacuum 2, 137 (1952).

46. R. A. Haefer, Acta Phys. Austr. 7, 251 (1953); 8, 213 (1954).

47. P. A. Redhead, Can. J. Phys. 36, 255 (1958).

48. P. A. Redhead, Report on the 18th Annual Conference on Physical Elec-

tronics, MIT (1958); and in 1958 Vacuum Symposium Transactions (Per-

gamon Press, London, 1959), p. 148.

49. T. N. Rhodin and L. H. Rovner, in 1960 Vacuum Symposium Transactions

(Pergamon Press, London, 1961), p. 228.

50. J. R. Downing and G. Mellen, Rev. Sci. Instr. 17, 218 (1946).

51. R. H. Vacca, in 1956 Vacuum Symposium Transactions (Pergamon Press,

London, 1957), p. 93.

52. M. Knudsen, Ann. Phys. 31, 633 (1910).

53. J. H. Leok, Pressure Measurement in Vacuum Systems (Published for the

Institute of Physics and the Physical Society by Chapman & Hall, Ltd.,

London, 1964), 2nd ed.. Chap. 4.

54. H. Ishii and K. Nakayama, in 1961 Vacuum Symposium Transactions


55. J. R. Roehrig and J. C. Simons, Jr., in 1961 Vacuum Symposium Transactions


56. P. A. Redhead, Rev. Sci. Instr. 31, 343 (1960).

57. F. L. Tomey, Jr., and F. Feakes, Rev. Sci. Instr. 34, 1041 (1963).

58. D. J. Santeler, in 1959 Vacuum Symposium Transactions (Pergamon Press,

London, 1960), p. 129; and Rev. Sci. Instr. 33, 283 (1962).

CHAPTER 4

VACUUM ANALYZERS AND LEAK DETECTORS

Cover

cut away

The measurement of the "total" pressure as represented by the

response of an ionization or thermal-conductivity gauge is a very useful

indication of the state of a vacuum system, but is insufficient as a guide

toward further improvement.

Measurement of the partial pres-

sures (or molecular densities) of

the component gases, the com-

bined effects of which produce the

gauge reading, provides muchmore insight into the processes

which limit performance and stim-

ulates ideas for further improve-

ment. Measurement of specific

partial pressures also permits the

use of a gas not normally present

in significant quantities as a meansof detecting leaks in vacuum sys-

tems more quickly and with greatersensitivity than by other methods.

4-L Magnetic-deflectionMass Spectrometers. The first

systematic application of partial-

pressure measurement or vacuumanalysis for the purpose of under-

standing and improving vacuum-system performance, to the

author's knowledge, was that

Fig. 4-1. The mass spectrometer ana-

lyzer. [Taken with permission fromA. Guthrie and R. K. Wakerling (eds.),

Vacuum Equipment and Techniques

(McGraw-Hill Book Company, NewYork, 1949).]

carried out at the University of California Lawrence Radiation Labora-tory in connection with the development of the electromagnetic method(Calutron) for separation of uranium isotopes in 1943 and 1944. Theapparatus developed by Backus^'* was an adaptation of the simplestform of mass spectrometer due to Dempster,^ as illustrated in Fig. 4-1.


133

134 VACUUM SCIENCE AND BNGINBEEING

Ions of the various gases present in the system are produced in a Penning(PIG) type of discharge, drawn out of the discharge through a narrowsource sht by means of an electric field, and deflected through approxi-

mately 180° by a magnetic field normal to the direction of motion of the

ions. Por appropriate values of the applied voltage and magnetic field

all ions of a given charge-to-mass ratio zejm are refocused at the 180°

point of a receiver slot, through which they pass to impinge on a

collector electrode, and can be recorded. The kinetic energy of the

ions issuing from the ion source is

y^mv^ 108zeV

(4-1)

where mV

e

z

Vc

= mass of the ion

= its velocity, cm/sec

= electronic charge, esu

= number of electronic charges carried by the ion

= applied potential difference in volts

= velocity of light, cm/sec

The radius of curvature of the orbit for an ion in a magnetic field is

P =cmv

cm (4-2)

in which B is the magnetic flux density in gauss. Combining (4-1) and(4-2) yields

cm /2zeV

zeB\ mc

= 1.12 X 10

108

,,hI_Y- (4-3)

Since the mass of an atom of unit atomic weight is 1.66 x 10~^* g, the

mass of an atom of atomic weight if is m = 1.66 x 10"^* M, so that

(4-3) becomes

144.5/ifF\^

B \~ (4-4)

As an example, for a singly charged atomic oxygen ion [M = 16), anaccelerating potential of 1,560 V, and a magnetic flux density of 3,600

gauss

p{M = 16) = 6.35 cm

so that the focus is located 2p = 12.7 cm from the slit of the ion source.

With a choice of this dimension for the location of the receiving slot,

the accelerating potential necessary to record an atomic hydrogen ion

{z=l,M

VACUUM ANALYZERS AND LEAK DETECTORS

1.008) would be

135

Vh{p = 6.35 cm)16.0

1.008X 1,560 = 24,700 V

which would be somewhat impractical. Rather than attempt to applysuch high voltages, a second receiving slot was provided in the Backusanalyzer at a distance 2p = 5.7 cm from the slit of the ion source sothat ions of p = 2.85 cm were also recorded. From (4-4)

if\144.5/

so that F Gc p2 for fixed values ofM and B. Thus

/2 85\^Fo(p = 2.85 cm) = I^ 1,560

315 V

and (285\^

^24,7006.35/ '

5,000 V

A wide range of masses could thus be focused on one or the other ofthe two slots with a reasonable range of the accelerating potential.

Ionic masses from 1 to 40 could be scanned by varying the accelerating

potential from 5,000 to 625 V. By imposing the accelerating voltagehorizontally on an oscilloscope and the current received through theslots vertically, a trace showing current peaks roughly proportionalto the partial pressures of the residual gases in the chamber was dis-

played by sweeping the accelerating voltage repeatedly over the desired

range. In Fig. 4-2 is shown a schematic diagram of the mass spec-

trometer vacuum analyzer together with its circuit diagram.The resolution of the 180° magnetic-deflection mass spectrometer

can be readily determined by reference to Fig. 4-3, in which the central

orbit of the ion beam and orbits diverging by ±a radians from the

central orbit are shown. If the source is a narrow slit parallel withthe magnetic fleld, which is perpendicular to the plane of the figure, thecentral ray reaches the base line drawn through the source and the centerof curvature of the central ray at a distance x^ = 2p from the source.

Prom the figure it is apparent that both the + a and — a rays return tothis same base line at a distance x^ = 2p cos a = 2/3(1 — ol^j2) =2p — pa^ since cos a = 1 — <x.^l2, approximately, when a is a smallangle. The width of slot to accept all orbits from +a to —a is

therefore

Ax = Xg — x^ = poL^ (4-5)

136

From (4-4)

so that

and


M144.5/ V

\ 144.5/ V ^

^M Ap Aa;2— = 2—p X

(4-6)

Magnetic field

perpendicular

to paper

PIGsupply

Phase-shifting

network

Fig. 4-2. Schematic circuit diagram for the vacuum analyzer. [Taken with

permission from A. Guthrie and R. K. Wakerling (eds.), Vacuum Equipment and

Techniques (McGraw-Hill Book Company, New York, 1940).]

since x = 2p. For acceptable resolution of ion masses of interest in

vacuum analysis the slot width Ax was made to equal a half mass unit

for Jf = 16 (oxygen). Thus the slot width must be

A.=^^2 16

Po

32PoK (4-7)

VACUUM ANALYZERS AND LEAK DETECTORS 137

from (4-5) and the corresponding angular half-width of the beam is

32

or a = 0.177 radian !^ 10"

In the instrument the beam was limited by metal vanes at the 90° pointto a total angular width of 20°

( ± 10°). The receiving slot was located12.7 cm (p = 6.35 cm) from the ion source and had a width equal to6.35/32 fn 0.2 cm. Ionic masspeaks of If = 15, 16, 17 werethen completely resolved, andionic masses up to about 50 werereasonably distinct.

The gas-discharge ion source

produces a wide variety of ions

from the residual gas in a vacuumsystem. Atomic ions such as H+,C+, N+, and 0+, and molecular

ions such as H2+, N2+, O2+, CH+,CH3+, CH,+, C0+, CO2+, and B.fi+are nearly always observed. Some

Receiving

slot

Fig. 4-3. Quality of focus for 180°

magnetic -deflection mass spectrometer.

of the ions result from dissociation and ionization of atmospheric gasespresent because of small leaks in the system. Water is usually presentand produces not only the H2O+ ion but also H+, H2+, and 0+ ions.

Decomposition of hydrocarbon diffusion-pump fluid and of oil left oninner surfaces of the vacuum system results in C+, CH+, CH2+, andCH4+ ions as well as additional H+ and H2+ ions. The relativemagnitude of the peaks corresponding to these ions on the oscilloscope

trace changes as the pressure in the vacuum system decreases andthe internal surfaces outgas. The if = 18 (II2O+) peak usually domi-nates for some time after the system has been pumped down fromatmospheric pressure. Later, if the system is pumped by trapped oil

diffusion pumps, the hydrogen, carbon, hydrocarbon, C0+, and CO2+peaks become predominant and the water peak decreases and finally

disappears. If the M = 16 and M = U peaks remain high, there is astrong possibility of a leak admitting air into the system. If thisshould be the case the mass spectrometer vacuum analyzer can beused very effectively for locating the leak by directing a jet of gas otherthan air in turn over the flanges and other parts of the system vulnerableto developing leaks. When the jet falls on the leak, the air leakinginto the system is mixed with probe gas, and ion peaks appropriate tothe probe gas appear or increase on the oscilloscope trace. Because


there is normally no if = 4 peak on the oscilloscope trace, helium

makes an ideal choice as a probe or leak-hunting gas since the ilf = 4

peak rises from the zero line very quickly when the helium jet strikes

the leak.

The use of helium gas in leak hunting was found to be so effective

that a simplified version of the mass spectrometer analyzer, as shown in

Fig. 4-4, was developed by Loevinger^ at the University of California

To pumps

Cathode

Tank

Removable

faceplate

Kovor seal

Fig. 4-4. The mass spectrometer helium leak detector. [Taken with permission

from A. Guthrie and R. K. Wakerling (eds.), Vacuum Equipment and Techniques

(McGraw-Hill Book Company, New York, 1949).]

Lawrence Radiation Laboratory. The ion source used was a PIG

similar to that in the Backus vacuum analyzer, but only one receiving

slot was provided, and the angular width of the beam was reduced to

increase the sharpness of focus. Since the leak detector was intended

to respond only to the If = 4 beam due to helium, the amplitude of the

a-c sweep applied to the accelerating potential was only large enough

to cover the full width for Jlf = 4 on the oscilloscope. The pulsating

current to the ion collector was amplified and applied to the vertical

plates of an oscilloscope and also to a meter through a tuned amplifier.

The design of the apparatus, with a self-contained vacuum system all

mounted in a compact cabinet on casters, made the helium leak

detector a convenient and effective instrument for vacuum-system

diagnostics.


Electron torget

Electrons

Accelerator

^^\m% of mass^

^^12 or greoter

Plate PMognetic

field

Since the pioneering use of the

magnetic-deflection mass spec-

trometer in vacuum analysis andleak detection, many improve-

ments have been made and a

number of excellent units of far

greater mass resolution and sensi-

tivity are now available com-mercially. Thomas, Williams, andHippie* substituted a hot-filament

type of ion source for the PIG andgenerally refined the electronic cir-

cuits, with resulting improvementin resolution, sensitivity, and sta-

bility. In Fig. 4-5 is shown a per-

spective drawing of the ion source,

beam focusing, and collector

arrangement used by Charpentier^ in a simplified mass spectrometertype of helium leak detector. The author states that the sensitivity

of his improved instrument for relatively rapid detection of leaks is

Hydrogen

Helium target j Filament

Helium ions

Fig. 4-5. Ion source, beam focusing,

and collector for 180° magnetic-deflec-

tion helium mass spectrometer. [Takenwith permission from D. E. Charpentier,

1956 Vacuum, Sym'posium, Transactions


/

t

A

Magnetic field

Filament

Section A-A

ollector

Baffle'-

Collector slit-

Suppressor^

100,000 megohms^

Fig. 4-6. 60° deflection mass spectrometer designed for helium leak detection.[Taken with permission from Saul Dushman, Scientific Foundations of VacuumTechnique (John Wiley and Sons, Inc., New York, 1949).]


10-8 atm cm^/sec or 7.6 x lO-" torr liter/sec, and about an order of

magnitude lower for detectability over background when care in the

use of the instrument is exercised.

For the accurate measurement of the masses of the isotopes of the

Hght elements a 60° magnetic-deflection mass spectrometer was de-

veloped by Nier^ several years before initiation of the Manhattan

Project work reported above. Subsequently a vacuum analyzer and

helium leak detector of high resolution was developed for the Manhattan

Project operations at Oak Ridge under contract with the University

of Minnesota by Hustrulid and Nier' and was later perfected for com-

mercial manufacture in the form described by Nier, Stevens, Hustrulid,

and Abbott.8 An instrument of the Nier type, designed specifically as

a helium leak detector by Worcester and Doughty,^ is illustrated in

Fig. 4-6. In this design the Jf = 4 peak is focused on the collector slot

Fig. 4-7. Sensitive 90° magnetic-deflection mass spectrometer for ultrahigh-

vacuum applications. [Taken with permission from W. D. Davis and T. AVanderslice, in 1960 Vacuum Symposium Transactions (Pergamon Press, London,

1961).]


when the accelerating voltage is set at about 270V and the magnetic field

at 900 oersteds. The preamplifier tube for the ion current to the collec-

tor is mounted inside the spectrometer tube to ensure high resistance

and to minimize leakage currents. The vacuum system for the massspectrometer tube consists of an oil difi"usion pump and dry-ice-cooled

vapor trap with a resultant pumping speed of about 30 liters/sec. Theauthors claim a sensitivity of about 1.5 x 10~^ torr liter/sec of helium.

A 90° magnetic-defiection mass spectrometer especially designed for

ultrahigh-vacuum applications has been developed by Davis andVanderslice. 1" The instrument is of unusually compact design, con-

sisting of an electron-bombardment type of ion source and an electron-

multiplier tube connected by a 90° elbow of welded stainless steel as

shown in Fig. 4-7. After bakeout is completed, a magnet is put in

place with poles on either side of the 90° elbow to bend the ion beaminto the detector. The ion detector is a 10-stage commercial photo-

multiplier tube with the glass envelope removed and the unit remounted

in a stainless steel housing. For ions incident upon the first dynode

of the electron multiplier the gain is 10^ at 300 V/stage before bakeout

and becomes about 10' after bakeout at 425°C. Slit dimensions andalignment in the ion source are so chosen that the mass peak width

is just equal to the separation due to one mass unit at an ion mass of

140. Partial pressures of the order of 10-^* torr can be measured with

the instrument. Fast electronic sweeping of the ion-accelerating

voltage, using a sawtooth sweep generator, provides a continuous

oscilloscope trace of the gas components present.

A double-focusing magnetic-deflection mass spectrometer, the beam-

focusing scheme for which is illustrated in Fig. 4-8, is described byPeters. ^^ The ion beam passes through a 90° deflection magnet and is

focused on the interstage slit, which becomes the source 8^ for an

identical second-stage deflection magnet which refocuses the beam on

the collector slot. The author states that by the double-focusing

technique the signal-to-background ratio is improved relative to the

typical single-focusing apparatus by about a factor of 100. The back-

ground signal in the normal mass spectrometer consists mainly of ions,

other than that for which the instrument is focused, entering the

collector slot either because the normal breadth of the focus overlaps

the mass separation or because ions which are well separated initially

are scattered and enter the receiving slot. In the double-focusing

instrument the intensity of the Jf = 4 beam is not changed significantly,

but the background due to random ions other than ilf = 4 is reduced

by a large factor. The author claims a sensitivity to helium of 10-^*

cm^/sec of helium at atmospheric pressure, or slightly less than 10-^^

torr liter/sec.


-i-s,l'°"

Median energy

1 St anolyzer

pole piece

Interstage

slit

2nd anolyzer

pole piece

Fig. 4-8. Ion beam trajectories

for double -focusing mass spectrom-

eter. [Taken with permission

from J. L. Peters, in 19S9 VacuumSymposium Transactions (PergamonPress, London, I960).]

Fig. 4-9. Ion trajectories in a cycloi-

dally focused mass spectrometer.

[Taken with permission from G. D.

Perkins and D. E. Charpentier, in

1957 Vacuum, Sym,posium Trans-

actions (Pergamon Press, London,

1958).]

Robinson and Hall^^ describe a cycloidally focused mass spectrometer,

the operating principles of which are illustrated in Fig. 4-9 and Fig.

4-10. The structure of the instrument consists of three parallel,

equally spaced plates. An electric field is maintained between the

plates by application of voltage across the outside positive and negative

field plates, and a magnetic field is applied parallel with the plate

structure. The region between the field plates is thus one of crossed

electric and magnetic fields. The center plate has a source slit, an

ion-resolving slit, and a collector slit, all running parallel to the magnetic

field. Ions are formed by an electron beam and projected through

the source slit by application of a substantial voltage to a repeller

electrode. The resulting beam of

ions is roughly focused on an4

passes through the resolving slit

and is then brought to a good focus

at the ion-collecting slit. Thecycloidal focusing is such that ions

of a given charge-to-mass ratio all

come to a sharp focus at the collec-

tor slit, even though the spread in

energy gained from the repeller is

large. The advantages of the de-

sign are (1) high resolving power

due to the double-focusing feature

resulting from the use of the re-

solving and collector slots, (2) high

ion efficiency because the focus is

Positive field plate

Ion

collector

resolving^slit

lectron

node

Negot

field

Fig. 4-10. Cutaway view of ion sourceand beam-focusing scheme for cyc-

loidally focused mass spectrometer.[Taken with permission from G. D.Perkins and D. E. Charpentier, in

1957 Vacuum Symposium, Transactions(Pergamon Press, London, 1958).]

VACUUM ANALYZERS AND LEAK. DETECTOBS 143

Moss spectrum of propane (C3Hg

H H H

Fig. 4-11. Complete mass spectrum of propane obtained with cycloidally focused

mass spectrometer. [Taken with permission from G. D. Perkins and D. E.

Charpentier, in 1957 Vacuum Symposium Trnasactions (Pergamon Press, London,

1958).]

Path of ions

at resonance

Signal

generotor

independent of the ion energy, and (3) unusually compact structure

compared with other magnetic-deflection mass spectrometers. Thecomplete ion mass spectrum obtained with a similar instrument devel-

oped by Perkins and Charpentier^* is shown in Fig. 4-11 and demon-

strates the resolution of individual

mass units in the range 16 to 44.

The sensitivity of the instrument

is reported to be about 1.7 x 10"^

torr partial pressure of nitrogen.

Sensitivity to other gases depends

upon the ionizing probability andvaries from about one-tenth to

twice the nitrogen sensitivity.

The spectrum is maintained on an

oscilloscope of medium persistence

by sweeping the voltage at the

rate of about 5 sweeps/sec, provid-

ing an almost continuous record of

the gas components in the system.

4-2. The Omegatron Mass Spectrometer. Sommer, Thomas,

and Hippie^* reported a precision determination of the charge-to-mass

ratio of the proton by measurement ofthe cyclotron resonance frequency

in a device illustrated in Fig. 4-12, which has since been referred to as an

omegatron. A singly charged ion moving in a direction perpendicular

End view

Ion collector h-

Side view

VTrapping

voltage

Fig. 4-12. The omegatron of Sommer,

Thomas, and Hippie. [Taken with

permission from H. Sommer, H. A.

Thomas, and J. A. Hippie, Phys. Rev.

82, 697 (1951).]

144 VACTJUM SCIENCE AND ENGINEERING

to a uniform magnetic field moves in a circular orbit of radius R, such

that

Bev mv^

and the radius of the orbit in centimeters is

J?mcv

(4-8)

(4-9)

where m = mass of the particle

c = velocity of light, cm/sec

V = velocity of the particle, cm/sec

B = flux density of the magnetic field, gauss

e = unit atomic charge, esu

The period of rotation is

277i? mc= 27Be

sec

so that the rotational frequency is

/ = - = cycles/sec' T 2TTCm •'

'

Substituting the numerical values e = 4.80 x IQ-i" esu, c = 3 x lO^"

cm/sec, and m = 1.66 x 10-^* M, in which M is the mass number of the

ion in question, this expression becomes

/ = 1.53 X 10=5M cycles/sec (4-10)

which depends only upon the flux density of the magnetic field and the.

charge-to-mass ratio of the ion. If the kinetic energy of an ion in a

uniform magnetic field increases, the radius of its circular path increases

according to (4-9), but the frequency of the motion remains constant.

The cyclotron type of particle accelerator is based upon this principle;

thus the term cyclotron frequency is used to refer to the rotational

frequency given in (4-10).

The omegatron is somewhat similar to the cyclotron in that ions are

produced at the center of the device and spiral outward as shown in

Fig. 4-13 under the influence of a high-frequency field which is perpen-

dicular to the steady magnetic field. The body of an omegatron is in

the form of a metal box, along the axis of which and parallel with the

magnetic field a beam of electrons is directed as shown in Fig. 4-14.

The electrons are drawn from a hot filament by an accelerating potential

,

pass through holes in opposite sides,of the box, and are collected on an

VAOUtrM ANALYZERS AND LEAK DETECTORS 145

Lost ion

VCollected ions

\ P,

i

.

>tt\ /

15 / / V2>C:n^

/ / /oc^ ^^^ *\ \

\'

''/^

\\^ ^v—ix^ J/

15 x^ _

, Ro=10 .>

'

< 3 -^-— 13——

Fig. 4-13. Spiral orbits of ions in an omegatron. [Taken with permission from

D. Charles and R. J. Wamecke, Jr., in 1959 Vacuum Symposium Transactions

(Pergamon Press, London, I960).]

Ion collector R-f electrode

Electron beam

Slit

Box (trapping voltage) >Ion-collector shield r-f,

d-c and electrometer

ground point

RN

L->-To electrometer

Electron-source

filament

Fig. 4-14. Electrode arrangement of an omegatron. [Taken with permission

from W. R. Watson, R. A. Wallace, and J. Lech, in 1960 Vacuum SymposiumTransactions (Pergamon Press, London, 1961).]

146 VACUUM SCIENCE AND ENGINEEEING

electrode on the far side of the box. Ions produced by ionization of

the residual gas molecules in the metal box are extracted from the

electron stream by an applied high-frequency electric field. If the

frequency of the applied field is equal to the cyclotron frequency for a

particular type of ion formed in the electron column, ions of this type

R-f ^^supply

Filament

supply

1,0 volts 221/2

dic volts d-c

Electrometer Recorder

to 2 cmp

Oto 2 volts o-c

10" 'to 10'^ amp

Fig. 4-15. Electrical circuit for the omegatron. [Taken with permission fromW. R. Watson, R. A. Wallace, and J. Lech, in 1960 Vacuum Symposium Trans-

actions (Pergamon Press, London, 1961).]

gain transverse energy and spiral outward until they strike the ion-

collector electrode at the side of the box. Ifthe frequency ofthe applied

'

field is not equal to the ion cyclotron frequency, ions spiral out from the

electron beam a short distance and then spiral back in again, oscillating

in radius but never getting out to the ion collector. Such ions are

lost along the lines of force to the end plates of the box. At high gas

pressure nonresonant ions tend to accumulate and produce an excessive

space charge near the electron column and reduce the effectiveness of

the applied high-frequency field in extracting ions. At very lowpressure insufficient positive ions are formed to neutralize the space-

charge potential of the electron beam with the result that resonantions must be extracted from a potential well by the alternating field.

To counteract these effects a weak positive d-c trapping voltage is

applied to four sides of the box relative to the two sides across which thealternating voltage is applied. A schematic diagram of the circuit


of the omegatron as developed by Watson, Wallace, and Lech" is

shown in Fig. 4-15.

As the frequency of the applied field is varied, the ion-collector

current varies from some low background value to peak values occur-ring whenever the oscillator frequency corresponds to the cyclotron

'^/iA

Variation of

magnitude of peak

44 OS a function of

the amplitude Eq

of the electric field

for various values

of the ionizing

current

+015volt

-0.48volt

—•-With B = 2,820gauss

P = 4»10"^torr

90 volts

1.5 20 2.5

Eo, volts/cm

Fig. 4-16. Influence of the amplitude of the alternating field on the magnitudeof the peaks for an omegatron. [Taken with permission from D. Charles and R.J. Warnecke, Jr., in 1959 Vacuum Symposium Transactions (Pergamon Press,

London, I960).]

frequency of some type of ion present. The height of the current peakfor a given partial pressure is a measure of the sensitivity of the

instrument and has been examined by Charles and Warnecke. i® In

Fig. 4-16 are shown their results on the influence of the amplitude of the

alternating electric field on the magnitude of the current peak for M =44 (CO2+). When the alternating-field amplitude is very small, ex-

traction of ions from the negative space charge of the electron beam is

inefficient, and furthermore the spiral path for ions to reach the collector

is long as compared with the collision mean path. As a result, ions

are lost to the walls of the box by scattering along the magnetic field

before they reach the collector and the collector current is low. As the

alternating field is increased from about 0.5 to 1.0 V/cm, the magnitudeof the peak current increases rapidly as the spiral path to the collector

becomes progressively shorter. However, beyond 2.0 V/cm the mag-nitude of the peak current is observed to decrease again, and the authors


250-

200

150

100

50

Variation of the magnitude of the

peak 44 as function of the intensity

Ic of the ionizing current

|U--f(Ic)|

for different volues of the

amplitude Eq of the electric field E

Vpi=t0.15volt

Vp2 = -0.48volt

with B = 2,820 gau

P = 4xlO'Sn

Vo = Vo =90 V

Eo = 2.I98volts/cm

En = 1.884 vol ts/ci

l.57volts/cm

Eo=1.256volts

= 0.942 volt/cm

\Eo = 0.628 volt/cm

Eo= 0.314 volt/cm

0123456789Fig. 4-17. Influence of the electron-beam current on the magnitude of the

positive ion peaks for an omegatron. [Taken with permission from D. Charles

and R. J. Warnecke, Jr., in 7959 Vacuum Symposium Transactions (PergamonPress, London, I960).]

state that the ion-ciirrent-versus-frequency peaks become distorted

and broadened. This latter condition develops when the increase in

radius per turn in the spiral path is so large that some of the resonant

ions take the outer orbit shown in Fig. 4-13 and miss the collector

entirely. Thus an optimum alternating-field amplitude was found to

be about 2 V/cm, at which the collector current was maximum and the

current peaks (as a function of frequency) were sharp and undistorted.

The influence of the electron-beam current on the magnitude of ,the

ion peaks as measured by Charles and Warnecke is shown in Fig. 4-17

for various values of the amplitude of the alternating field. For analternating-field amplitude of about 1 V/cm or more the ion-collector

current is approximately proportional to the electron-beam current as is

expected. At lower values of the alternating-field amplitude the curvesare badly distorted, probably because of failure of the small alternating

field to extract ions from the negative space charge of the electron beam.Finally, Fig. 4-18 shows the results of Charles and Warnecke for the


dependence of the peak ion current for ilf = 44 on the partial pressure

of CO2 for various values of the electron-beam current. It is noted that

the peak current is proportional to the partial pressure up to about4 X 10-* torr for small electron-beam currents (1 to 3 //A) and up to

about 2 X 10-* for an electron-beam current of 5 /lA. These authors

report that under favorable circumstances and with an electron-beam

current of 10 /lA a partial pressure of the order of 5 X lO-^^ torr

can be detected. The corresponding ion-collector current is about

5 X lO-is A.

Charles and Warnecke also report that the sensitivity of a similar

omegatron designed specifically as a leak detector using argon as the

probe gas is 2 x lO-^^ torr liter/sec in a dynamic system and as low as

2 X 10-1* torr liter/sec in a well-baked system using an accumulation

process. The authors state that for the omegatron leak detector, argon,

because of its relatively high ionization probability, is preferable to

helium as a probe gas.

In a detailed discussion of the potentialities of an omegatron as a

leak detector Nicollian^' reports results in agreement with those of

Charles and Warnecke,1* using argon as the probe gas. However, he

finds that the alternating-field gradient can be increased tenfold whenusing helium as the probe gas without causing broadening and splitting

60

.50

,40

30

20

10

Relotion between amplitude of peak 44

and the corresponding partial pressure Pp

n7^(p

for different values of the

ionizing current Iq

Vp|= 0.17 volt

Vp2=-0.48volt

B =2,820 gauss

E =0.94volt/cm

Vo = Vo =90 volts.

/

^.

/

la) ......lc = l/iA

0' 5 10 15 20 25 30

P« 10'^ torr

35 40

Fig. 4-18. Dependence of the peak ion current for M = 44 on the partial

pressure of COj for various values of the electron-beam current for an omegatron.

[Taken with permission from D. Charles and R. J. Warnecke, Jr., in 1959 VacuumSymposium Transactions (Pergamon Press, London, I960).]


of the M = i peak. By taking advantage of this effect NicolHanobtains about the same leak-detection sensitivity with hehum as withargon. In either case a Hmiting partial-pressure sensitivity of about10-12 torr and an ultimate leak-rate sensitivity of about 10-" torrliter/sec are reported.

Hydrocarbon

fractions

12 13 14 15 1617 1819 202122 26 27 28 29 30 3132 4041424344

Mass number

Fig. 4-19. Mass spectrum during bakeout of reflex klystron, (a) Just before'development of an air leak; (6) just after development of a small air leak. Tem-perature 320°C, total pressure 5 x 10-^ to 1 x lO-^ torr by ionization gauge.[Taken with permission from D. Lichtman and A. Hebling, in 1960 VacuumSymposium Transactions (Pergamon Press, London, 1961).]

The use of an omegatron in the analysis of the residual gases dilring

the processing of ultrahigh-vacuum power tubes is discussed byLichtman and Hebling." In Fig. 4-19 are shown the residual gasspectra obtained (a) during the advanced stage of bakeout of a reflexklystron and (b) just after the development of an air leak. In (a)

the residual gas is made up mainly of hydrogen (H2+), water vapor,methane, and hydrocarbon fractions. When the leak develops in (&),the carbon dioxide, argon, oxygen (O2+ and 0+), nitrogen (N2+ and N+),and neon peaks become dominant.

VACUUM ANALYZEKS AND LEAK DETECTOES 151

Omegatron mass spectrometers have generally been operated with

magnetic-field flux densities in the range of 2,500 gauss. In order to

cover the ion mass range from M = 2to M = 50, using this strength of

magnetic field, the range of alternating-field frequency required, accord-

ing to (4-10), is from 1,915 kilocycles/sec down to 87 kilocycles/sec.

Since the ionization cross section for the formation of H2+ ions in

hydrogen gas is 30 to 50 times greater than for H+, the M = 1 peak is

frequently not seen on vacuum-analyzer traces.

Table 4-1. Pressures and Sensitivities of Omegatron to Methane andNeon*

Omegatron sensitivities calculated from ionization-gauge "pressure" readings

and the heights of the principal peaks of the respective gases, that is, ikf = 16

for methane and M = 20 for neon.

Methane

Pressvire, torr

Sensitivity, div/torr. . . .

Sensitivity, {*+/»'_)/-? • • •

1.15 X 10-«

5.8 X 10'

5.8

2.7 X 10-'

5.7 X 109

5.7

6.5 X 10-8

6.2 X 10"

6.2

ICeon

Pressure, torr

Sensitivity, div/torr ....

Sensitivity, (i_,_/'J_)/P . . •

2.4 X 10-5

6.1 X 109

6.1

3.9 X 10-'

8.1 X 109

8.1

* Taken with permission from W. R. Watson, R. A. Wallace, and J. Lech, in

1960 Vacuum, Symposium Transactions (Pergamon Press, London, 1961), p. 421.

Watson, Wallace, and Lech^^ have investigated the sensitivity in

terms of (i^/O/P,,, in which i^ is the peak current for a given ion, i__

the electron-beam current, and P^, the partial pressure of the gas from

which the ion current is produced. Table 4-1 gives some typical values

for the sensitivity obtained by Watson, Wallace, and Lech. The gases

used for these measurements were neon and methane. The "pressures"

quoted are the nominal readings ofan ionization gauge calibrated against

nitrogen. Since the sensitivity of ionization gauges, i.e., the ratio

{i+liJ)P, is about four times greater for nitrogen than for neon, the

actual pressure of neon present was greater by about a factor of 4 than

that indicated in the table. The conversion factor for methane (CH*)

is not known to the author. The decrease in sensitivity for neon at

2.45 X 10^5 torr partial pressure is consistent with the general obser-

vation that the sensitivity of the omegatron decreases noticeably for

pressures in excess of lO^^ torr. This trend is illustrated most clearly

in Fig. 4-20 from the paper of Watson, Wallace, and Lech, in which the

response to carbon monoxide is plotted as a function of pressure, giving a


low-pressure sensitivity of about 9.5 x 10^ div/torr for the Jf = 28

peak and dropping off rapidly with increasing pressure beginning at

about 10~^ torr.

Considering that the omegatron element is a small metal box of only

about one inch on a side, the sensitivity and mass resolution achievable

10-7

Omegatron

Carbon monoxide calibration

o

o

^ SensitivityOiv.mass28 ^^q-9Torr pressure

,_ô„9.*o% oo- /„:„o?ô„„ô

oo

° oo

(feo

o o

o

cP

oo

o

•.-•,.• rf • t^ «

-(Pattern coefficient, m/e = 12) = (100 x

-D1V12

OiV28

11

i

10"6 10-5

Pressure, torr

10"

FiG. 4-20. Sensitivity of omegatron as a function of partial pressure of CO as

indicated by current in the M = 28 peak. The pattern coefficient ratio betweenM = 12 (C+) and the M = 28 (CO+) ion currents remains nearly constant as

the sensitivity decreases at pressures above 1 x 10~^ torr. [Taken with per-

mission from W. R. Watson, R. A. Wallace, and J. Lech, in 1960 VacuumSymposium Transactions (Pergamon Press, London, 1961).]

are remarkably high. A problem which has not to the author's

knowledge been satisfactorily resolved arises from the fact that the

omegatron element is almost completely closed and has an enormousratio of surface to volume. Both absorption and desorption effects

must be present so that pronounced differences in the partial pressures

of component gases must generally exist between the system being

tested and the interior of the omegatron.4-3. Linear High-frequency Mass Spectrometers. Linear

resonant systems which depend upon the selective processes familiar in

high-frequency linear accelerator design or upon the differences in timeof flight for ions of different mass have been utilized effectively for

VACUUM ANALYZERS AND LEAK DETECTOBS 153

jywvA*—o+Resolution

adjustment

Ion

chamber

Kinetic-energy

selector

atomic mass discrimination. One advantage of these systems is that a

magnetic field is not required to effect mass separation.

The linear accelerator scheme was adopted by Moody^' in the design

of a mass spectrometer helium leak detector and vacuum analyzer.

The arrangement of ion source, r-f accelerator, and ion detector is

illustrated schematically in Fig. 4-21. Ions are produced in a chamberby a beam of electrons which are emitted from a filament outside the

chamber, pass through small colli-

mating holes in the walls, pass

completely through the chamber,

and are stopped by an electrode

outside the chamber on the far

side. Positive ions formed by the

electron beam are drawn out of the

column by an extracting voltage

between the ionization chamberand the focusing electrode. Theextracted ions are focused on a

collector through apertures in a

series of plates which serve as

electrodes for applying a high-

frequency accelerating field. Alter-

nate elements of the high-fre-

quency electrode system are driven 180° out of phase by an oscillator.

Actually, one set of alternate plates is grounded and the other is

driven by the oscillator.

The electric field in the gaps between any two adjacent plates varies

as (EgjG) sin 2TTft, during the positive half-cycle of which ions comingfrom the source will experience an accelerating pulse. During the

negative half-cycle, ions will be decelerated. Thus, if the ions pass

through the series of high-frequency gaps in random phase, the net gain

or loss in energy will be very small. However, if the spacings G^

between the electrodes increase in the proper sequence, ions of a partic-

ular ejm ratio and initial velocity entering the first gap in the proper

phase will arrive at each succeeding gap at the proper time to receive

an accelerating pulse at each gap. Such ions gain energy about

proportional to the number of high-frequency gaps and attain consider-

ably higher energy than those ions which are not so synchronized. Bychanging the applied frequency, ions of other e/m ratios can also be

accelerated. Sweeping the frequency of the oscillating voltage througha sufficient range brings different ions into synchronism in succession.

The ion beam leaving the high-frequency section is electrostatically

deflected. Those ions which are not in synchronism, and thus have

R-f

analyzer

Fig. 4-21. Schematic of linear massanalyzer. [Taken with permission

from R. E. Moody, in 1956 VacuumSymposium Transactions (PergamonPress, London, 1957).!


not gained much energy, are bent sharply by the deflecting field, whereas

those which are in synchronism and do gain maximum energy are only

slightly deflected and enter the ion collector. In order to discriminate

between the true ion current and the background current, the ion beam

is modulated by imposing a 15 cycle/sec voltage to an electrode between

the ion source and the accelerating electrode and detecting only the a-c

component of the collector current through a tuned amplifier. A block

diagram of the complete circuit for the helium leak detector version of

1

Ion

gouge

(21

-^ -^ 1 InFilament

regulator

(2)

+ 375 volts

powersupply

(4)

1—^ i_ |U

—

—

^^-i15-

modulotor

(2)

R-f

oscillator

(4)

- 250 volts

power

supply

(4)

,..,.„, .'., 1-

// z'

"a + \

Preomplifie

(2)

A-c

amplifier-^

(2)

Fig. 4-22. Block circuit diagram for linear r-f helium leak detector. [Taken

with permission from R. E. Moody, in 7956 Vacuum Symposium Transactions


the device is shown in Fig. 4-22. In the vacuum analyzer version the

applied high frequency is swept over the range necessary to bring into

synchronism ion masses from M = 2 to M = 100. In Fig. 4-23 is

shown the electrode structure for the r-f vacuum analyzer.

An alternative form of linear r-f mass spectrometer featuring an

array of equally spaced grids as an e/m filter, illustrated in Fig. 4-24,

was originally proposed by Redhead^" for use as a vacuum analyzer.

Ehlbeck et al.î have discussed the theory of this type of mass spec-

trometer and given results of measurements on the resolving power and

sensitivity as a function of operating parameters. Ions are produced

by electron bombardment in the ion source, accelerated through an r-f

filter consisting of {2N + 1) precision-made grids, decelerated by a

retarding grid, and finally selectively recorded on the partial-collector

electrode, provided a particular type of ion has gained sufficient energy

to surmount the potential applied to the retarding grid. Between the

ion-retarding grid and the collector is an additional grid at high negative

potential to prevent any electrons from reaching the collector. Asshown in the d-c potential plot in Fig. 4-24, the filament and partial

ion collector are at ground potential, the ion chamber at a positive


potential f/j^, and the r-f grid structure at negative d-c potential.

Between the ion source and the r-f filter is a grid at high negative

potential so that ions are drawn out of the source by a high accelerating

electric field then decelerated somewhat to

attain an energy eUg (as indicated on the

diagram) on entering the r-f filter. Onlythose ions which gain an energy AW >e?7j(,t ill passing through the r-f filter will

reach the partial collector and be recorded

as a partial pressure. The highly negative

grid between the ion source and the r-f filter

is designated the total collector since it inter-

cepts a uniform fraction of ions of all masses

and thus provides a current indication

which is proportional to the total pressure

as read by an ionization gauge.

The grids of the r-f filter are equally

spaced, and are alternately connected to

the opposite polarities of a variable-fre-

quency r-f oscillator so that successive grids

are driven 180° out of phase. Each group

of three adjacent grids constitutes a sorting

structure of the Bennett type.^^ In passing

through the sorting structure, ions, in

general, experience a succession of acceler-

ating and decelerating impulses and on the

average gain or lose kinetic energy. Thechange in energy AlFy for an ion depends

upon the number N of Bennett stages in

the structure, the entering accelerating

potential ?7o, the amplitude U of the r-f

potential, the phase cp of the r-f at the in-

stant the ion enters the first stage, and the

transit angle oc where

Fig. 4-23. Linear r-f massspectrometer vacuum-ana-lyzer electrode structure.

[Taken with permission fromR. E. Moody, in 1956 Vac-

uum Symposium, Transac-

tions (Pergamon Press,

London, 1957), and through

the courtesy of BeckmanInstruments, Inc.Fullerton,

CaUf.]

The transit angle is the phase interval of the

applied r-f which a particle would spend in traversing the distance dbetween two adjacent grids of the ion sorter at the velocity v„ =[2(e/m)f7„] at which it enters the sorting structure. The entering phaseinterval A 99 over which the change in energy AW^- after N stages is

positive and the fractional gain in energy AWÎÛ^ are both critical

2nfd\2-U„m


functions of the ion e/m ratio when the remaining parameters (d, U„, U, f)

are held constant. Alternatively, if all other parameters are held con-

stant and the radio frequency varied, then ions of different e/m ratios

receive the maximum energy gain at discrete values of the frequency.

Pump

Fig. 4-24. Schematic drawing of electrode arrangement and d-c potential distri-

bution for r-f mass spectrometer according to Redhead. [Taken with permission

from H. W. Ehlbeck, K. H. Loecherer, J. Ruf, and H. J. Schuetze, in 1960

Vacuum Symposium Transactions (Pergamon Press, London, 1961).]

In the instrument developed by EhllDeck et al.^i using five stages as

shown in Fig. 4-24, the resolving power is defined as

R = /m

X(f2-A)= 100

in which /max is the radio frequency for a given e/m value at which the

collector current is maximum and f^ and /a the frequency values below'

and above /max at which the collector current reaches half the maximumvalue. The operating parameters of the instrument are given in Table

4-2 . The authors emphasize that the transparency of the grid structure

is a critical feature in determining the resolving power. They found

that a grid structure in which each grid was a square mesh of 5 X 10"*

cm diameter molybdenum wire with a spacing of 0.05 cm transmits only

7 per cent of the incident ions, whereas a structure in which each grid

consists of parallel wires precisely aligned transmits 35 per cent.


Table 4-2. Operating Parameters for R-F Mass Spectrometer VacuumAnalyzer*

Total yield of ion source at 4 mA electron current. . . 1 x 10~^ A/torr

Half width of energy distribution of ions 4.5 eVTotal current sensitivity (signal to total ion collector) 8 x 10"^ A/torr

Partial current sensitivity at U (r-f amplitude) =140 volts 2 X 10-" A/torr

Resolving power at U = 140 volts 100

Upper limit of pressure at which the partial current

is proportional to the partial pressure 5 x 10—* torr, approx

* Taken with permission from H. W. Ehlbeck, K. H. Loecherer, J. Ruf, and

H. J. Schuetze, in 1960 Vacuum Symposium Transactions (Pergamon Press,

London, 1961), p. 407.

Resolving power of 100 could only be attained by using such a high-

precision grid structure. A mass spectrogram obtained with the

instrument at a total pressure of 1 X 10"^ torr and resolving power of

about 100 is shown in Fig. 4-25.

Assuming that a partial-collector cur-

rent of 10-1* A can be detected above

background, the minimum partial

pressure detectable with the sensi-

tivity of 2 X 10-« A/torr is 5 X 10-»

torr. By sacrificing resolving power

this limit of detectable partial pressure

can probably be reduced somewhat,

at least for the lower range of mass

values.

A compact and relatively simple

type of r-f mass spectrometer, called

the Farvitron, has been described by

Reich. 23 The electrode system for

the Farvitron is shown schematically

in Fig. 4-26 together with the axial

potential distribution. Because of

the geometry of the electrodes and the

d-c voltages applied, the axial poten-

tial distribution is approximately a

parabola, that is, 99 = F — kx^, in which V is

between the two end electrodes and the central

3.10""amp

oLLuIIL JL10 12 14 16 18 22 2822

M

Fig. 4-25. Mass spectrogram at

total pressure of 1 x 10^^ torr

and resolution of i? = 100 from

r-f sorter type of r-f spectrometer

of Ehlbeck et al. [Taken with

permission from H. W. Ehlbeck,

K. H. Loecherer, J. Ruf, and H.

J. Schuetze, in 1960 Vacuum Sym-posium Transactions (Pergamon


the voltage applied

ring electrode. An

ion of charge-to-mass ratio e/m injected into such a field experiences an

axial oscillation of frequencj^

f = C!\- V

V


where C = 4/7rL and L is the distance between the end electrodes at

which the electrical potential g9 = 0. If an alternating potential of

frequency / is superimposed upon the d-c potential, an ion of e/m

satisfying the above frequency relation will resonate and gain sufficient

energy to escape from the potential pocket.

W A S

J r-'r-i-ii

r I"-!-"! :

D-c supply

Tube

I i^i'-r-'.3

R-f

amplifier

1

Wobbler

50cps

R-f generator

0,l3-l8Mc

Demodulator

D Oscilloscope

Fig. 4-26. Schematic diagram

of the electrodes and of the

axial potential distribution

of the Farvitron mass spec-

trometer. [Taken with per-

mission from G. Reich, in 1960

Vacuum Symposium Trans-

actions (Pergamon Press,

London, 1961).]

Fig. 4-27. Circuit diagram for the

Farvitron mass spectrometer. [Takenwith permission from G. Reich, in

1960 Vacuum, Symposium, Trans-

actious (Pergamon Press, London,

1961).]

In the Farvitron the ions are produced by accelerating a regulated

current of electrons from a tungsten filament axially into the electrode

on the left, the end of which is a wire mesh. The electrons start froma cathode potential of —100 V, as shown in the schematic circuit

diagram in Fig. 4-27, and will therefore penetrate the parabolic field

to a depth of —100 V, producing positive ions by collisions with anymolecules present. These ions oscillate in the parabolic field, most of

them not having sufficient energy to reach the cup-shaped electrode onthe far end. However, when an r-f voltage is applied to the electrode

on the left, ions of the e/m corresponding to the above frequencyrelation gain in amplitude of their motion and escape to the collector

electrode on the right. The r-f current to the collector electrode is

amplified and then rectified to produce a d-c voltage which is appliedto the vertical deflection electrodes of an oscilloscope. The radio


frequency is varied periodically by a 50 cycles/sec wobbler signal over

the range of 0.13 to 1.8 megacylces/sec. For the dimensions and d-c

voltages chosen by Reich the resonant frequencies are given by

/ = 2AM- megacycles/sec

LflMfiiJ

whereM is the molecular weight of the atomic or molecular ion involved.

The frequency swing imposed by the wobbler can be varied in breadth

anywhere over the available frequency range so that either the full

mass range from ilf = 2 to ilf = 250 can be displayed, or a muchnarrower mass range can be chosen and expanded to the full width of

the oscilloscope trace.

The Farvitron is a relatively simple and compact form of r-f mass

spectrometer which can be conveniently constructed for baking out at

high temperature. The sensitivity is apparently limited, at least in

the form described by Reich, to partial pressures not less than about

10~^ torr. The high scanning rate

of 50 cycles/sec makes the Farvitron

particularly useful in following rapid-

ly changing conditions in a vacuumsystem.

4-4. Halogen Leak Detector.

A discussion of leak detectors

would not be complete without

mention of the halogen leak detector

based upon the enhanced positive

ion output of a halogen-sensitive

diode. Langmuir and Kingdon^*'^^

had demonstrated the production

of positive ions by ionization of gas

molecules coming into contact with

a hot surface provided the therm-

ionic work function of the surface

is greater than the ionization potential of the gas molecule. White

and Hiokey^" utilized the greatly enhanced production of positive ions

which occurs when a gas containing any one of the halogens (fluorine,

chlorine, bromine, and iodine) comes in contact with a hot (^^900°C)

platinum surface as the basis for a leak detector. Their detector

consists of a platinum cylinder mounted on a ceramic-clad heating

element placed centrally within a larger platinum cylinder, as shown

schematically in Fig. 4-28. The heated inner cylinder is made positive

(100 to 500 V) relative to the outer cylinder, and the ion current is

read on a microammeter, as shown in the diagram, or by means of an

Air flow-

FiG. 4-28. Schematic diagram of

halogen leak detector. [Taken with

permission from W. H. White and

J. S. Hickey, Electronics 21, 100

(1948).]


amplifier. The halogen detector is most effectively used as a leak

detector by placing it inside the vacuum system and probing the

system with a fine jet of Freon-12 or other halogen-containing gas.

Torney^' has made a study of the optimum conditions for operating a

halogen detector to ensure stability and sensitivity. The platinum

diode produces a background current of positive ions even when no

halogens are present. The background current due to this effect varies

with the gas pressure and the tem-

perature of the inner element.

The signal due to the enhanced

ionization in the presence of a

halogen-containing gas also de-

pends upon the gas pressure (of

air). The dependence of the re-

sidual ionization current for two

different values of the heater cur-

rent and of the signal in detecting

a calibrated leak of 10~^ cm^/sec

on the pressure in the system is

shown graphically in Fig. 4-29.

The operating range (70 to 200 fi)

crosshatched in the figure is so

chosen that the background cur-

rent is relatively independent of

the pressure in the system andthe ratio of signal to background

is relatively large, resulting in anoptimum ratio of signal to background.

Torney also observed that the background positive ion current

changes slowly with time provided that the pressure and circuit param-eters are steady, whereas the signal due to the introduction of a halo-

gen gas rises much more rapidly. Utilizing this difference in response,

Torney developed a circuit which facilitates discrimination betweenbackground fluctuations and signals due to a leak. The circuit, a block

diagram of which is shown in Fig. 4-30, contains a network between the

detector and the amplifier which constitutes a bandpass filter which by-

passes through C2 the high-frequency noise generated in the detector, is

unresponsive to the very low frequencies associated with changes in

the background ion current, but transmits an intermediate band of

frequencies typical of changes in the signal due to detection of a leakby use of a halogen gas. Subsequent amplification of the signal beyondthe bandpass filter then permits the sensitive detection of the enhancedpositive ion current due to the application of a halogen gas to a leak even

20 40 100 200 400 ipOO

Pressure,;!

Fig. 4-29. Halogen leak detector back-

groand positive ion current for 1.60-A

and 1.75-A heater current and signal

current for standard leak of 10~*

cm^/sec as a function of the pressure in

the system. [Taken with permission

from F. L. Torney, Jr., in 1957 VacuumSymposium Transactions (PergamonPress, London, 1958).]


Sensing

element

Loudspeaker

^C; Amplifier

relaxation

oscillator

ond

power

supply

Sensing head

From system

under test

From regulated source of

clean uncontaminoted air

RequlotedO ,. O 1

voltages

Fig. 4-30. Block diagram of circuit for halogen leak detector. [Taken withpermission from F. L. Torney, Jr., in 1957 Vacuum Symposium Transactions(Pergamon Press, London, 1958).]

though this change is small as compared with typical changes in the

background ion current.

One feature of halogen leak detectors which can cause difficulty is

the relatively long "memory" of the detector once it has been exposedto a surge of halogen gas. To re-

duce the memory period, Torney^'

devised a mounting for the detec-

tor which provides for the purging

of the detector by the introduction

of gas free of halogen contamination,

as shown in Fig. 4-31. The unit

is either connected in series in the

forevacuum line of the system as

shown in Fig. 4-31a or connected

in parallel as shown in Fig. 4-316.

The principal disadvantage of the

series arrangement is the resulting

low conductance for gas flow. Theparallel arrangement in Fig. 4-316

may be permanently installed in asystem without impairing pumpingperformance.

According to Torney, 2' leak rates

of 2 X 10~* atm cm^/sec will pro-

duce a full-scale deflection on his

version of the halogen leak detector,

and leak rates as small as 2 x 10"^

atm cm^/sec can be detected when proper precautions are observed.4-5. Leak-detection Techniques. Leakage through flange seals,

welded or soldered joints, and flaws such as cracks and porous sectionsof metal is an important cause of vacuum-system failure. The degree

To vacuum pump

Coble to

control unit

To vacuumpump

From system

under test

Fig. 4-31. Methods of connecting

halogen leak detector into a vacuumsystem. [Taken with permission

from F. L. Torney, Jr., in 1957Vacuum. Symposium Transactions



BurnerHole to view flame

Copper plote

to which leakage must be eliminated in vacuum systems is far greater

than that required for pressure and most other vessels in common

engineering experience. Because of the importance of eliminating

leakage, methods of detecting and localizing leaks constitute an impor-

tant element in vacuum practice.

Larger leaks in vacuum systems may be detected by any of several

relatively crude methods. The system may be pressurized slightly by

closing the valve to the pump and

connecting a tank of nitrogen to

the system through a regulating

valve set at a gauge pressure of a

few pounds per square inch, care-

fully avoiding the risk of applying

an unsafe overpressure. Gas will

then flow out through the leaks,

the larger of which can then be

located by painting suspicious

areas with soap solution and look-

ing for bubbles. A very large leak

can be detected most easily if the

gauge pressure is kept very low.

Alternatively, the system may be

pressurized with a halogen-con-

taining gas such as Preon-12 and

a sniffing method used to detect the halogen gas coming out through

the leaks. A hahde torch such as that illustrated in Fig. 4-32 is

convenient for this purpose and reasonably sensitive. The air-intake

hose shown in the figure is used to explore the system for leaks.

When the inlet end of the hose sniffs the halogen gas, the flame in the

torch turns green. Small components of a vacuum system can be

separately sealed, connected to a compressed-air supply, and immersed

in water. A trail of bubbles indicates the location ofa leak. According

to Guthrie and Wakerling,^* the pressurizing methods are limited in

sensitivity to a leak rate of the order of 10^^ atm cm'/sec, which is

entirely adequate for locating the larger leaks that would prevent

pumping a system down to the region of ionization-gauge operation.

When the leak rate in a vacuum system is low enough that the

diffusion pumps can be put into operation and a pressure less than 10~^

torr attained, more sensitive methods are required to locate the remain-

ing small leaks. In this case ionization gauges may be operated in the

fine vacuum portion of the system and heat-conductivity gauges in the

forevacuum section. The behavior of a vacuum in this condition has

been described by Briggs, Jones, and Roberts^^ in terms of the pressure

flir-intoke tube used

to hunt for leaks

Fig. 4-32. Halide torch and auxiliary

equipment. [Taken with permission

from A. Guthrie and R. K. Wakerhng(eds.), Vacuum Equipment and Tech-

niques (McGraw-Hill Book Company,Now York, 1949).]

VACUUM ANALYZEBS AND LEAK DETECTORS 163

as a function of the time, as shown in Fig. 4-33. The system assumedfor this example has a liquid-nitrogen-cooled baffle over the diffusionpump. When the pressure has reached a nearly steady value duringpumpdown, the trap is cooled by liquid nitrogen removing the condens-able vapor, after which a base pressure is reached depending upon theoutgassing and leak rates. The valve between the diffusion pump andthe liquid-nitrogen-cooled trap is then closed and the pressure rise

eokoge rote

Punnping

storted

ILiquid nitrogen

introduced

into trap

Pumpvolved off

from system

Time >Fig. 4-33. Pressure vs. time for a vacuum system with a significant leak present.[Taken with permission from W. F. Briggs, A. C. Jones, and ,T. A. Roberts, in

195S Vacuum. Symposium Transactions (Pergamon Press, London, 1959).]

followed in time. Since the outgassing rate diminishes with time, thepressure-rise curve typically has a decreasing slope as long as the curveis dominated by outgassing. However, if the curve becomes a straightline after some time, the pressure rise may be assumed to be dominatedby a leak, the value of which \s Q = V dPjdt, where V is the volume ofthe system.

When it has been determined that a leak is present, the next step is

to localize the source. The procedures which may be used are many,but only some of the most efficacious will be mentioned. Briggs et

al.29 describe the use of a null method in the circuit of a cold-cathode(PIG) type of ionization gauge as shown in Fig. 4-34 to detect with highsensitivity any change in the system pressure. Usually when a definite

leak is present, the system pressure remains fairly steady at a valuedetermined by the leak rate and the pumping speed of the system.Under these conditions the steady reading due to the system pressurecan be balanced out as shown schematically in the figure and anychanges in pressure, up or down, detected with increased sensitivity.


D-cpower

supplyI—

I

Ionization

gouge d^

SrTo

vacuum system

ShuntoNull indicotor

If the leak rate can now be

changed by squirting water or

other liquid on suspicious parts of

the system to cause a momentary

decrease in the leak rate or by

using some gas other than air,

such as Freon, COj, or helium, to

cause a change in the gauge re-

sponse, the balance in the gauge

circuit will be disturbed and the

location of a leak indicated.

Methods such as these are gener-

ally capable of detecting leak

rates of the order of lO"" atmcm'/sec.

The next order of sensitivity is

the halogen leak detector described

in the previous section. As was

already stated, this device is in-

stalled in the forevacuum line of

the vacuum system and has a

sensitivity of about 2 X lO"** atmcm*/sec.

By far the most sensitive and versatile of the leak detectors is the

mass spectrometer helium leak detector, several types of which are

described earlier in this chapter. In application the helium leak

detector, which has its own complete vacuum system, is connected into

the forevacuum of the system being

tested through a control valve as

illustrated in Figs. 4-35 and 4-36.

In Fig. 4-35 the system to be leak

tested is enclosed in a hood into

which helium is injected so that the

system is surrounded by a mixture

of air and helium. This method is

particularly effective if the problem

is to determine whether a vacuumdevice has a leak greater than somespecified value, but it does not

help to locate the leak. On verylarge systems the hood method canbe applied to sections of the systemby enclosing portions of the system

Reference J.

voltage

P"iG. 4-34. Null method for detecting

changes in system pressure during

leak hunting. [Taken with per-

mission from W. F. Briggs, A. C.

Jones, and J. A. Roberts, in 195S



Equipment

under test\

Envelope containing

helium-air mixture

Fig. 4-35. Hood method of applying

helium leak detector. [Taken with

permission from W. F. Briggs, A. C.

Jones, and .T. A. Roberts, in 1958

Vacuum Si/mposium Transactions



in hoods of plastic foil, thus roughly localizing any leaks present. Thegas probe method illustrated in Fig. 4-36 is very widely applied since

it facilitates localizing the leak within a small area. A tank of helium

with a regulator valve and a hose terminated by a small nozzle is used

to explore the vacuum system in detail. When the probing gas jet hits

the leak, the helium leak detector responds in a time depending uponthe capacity of the system and the size of the leak. Most leak detectors

produce an audible signal, the sensitivity of which can be set for

detection of small or large leaks. The sensitivity of a helium leak

detector is defined in terms of the

smallest air leak rate to which the

instrument will respond when air

is replaced by pure helium at at-

mospheric pressure. In the earlier

sections of this chapter the sensi-

tivities of several helium leak de-

tectors are given on this samebasis. However, in searching for

leaks in vacuum systems con-

ditions are much less favorable

than those under which the sensi-

' C3 a ^

S7 /?=^—® wrn y

Equipment

Leak

detecto

Roughing

pump

under test ^^|,^^

Fig. 4-36. Gas probe method of apply-

ing helium leak detector. [Taken with

permission from W. F. Briggs, A. C.

Jones, and J. A. Roberts, in 1958

Vacuum Symposium Transactions (Per-

gamon Press, London, 1959).]

tivity is measured. In any case, detection of leaks of 10"^ atm cm^/sec

is usually relatively straightforward, and detection of leaks as small as

10^1" atm cm^/sec is entirely possible under good conditions.

No matter what probe gas is used in leak detection, precautions must

be taken to avoid excessive flooding of the system and its surroundings

with probe gas. The objective is to determine the precise location of

the leak, not simply to determine whether one is present. If there is an

excessive amount of probe gas about the system, the leak detector will

continue to respond for some time, whether or not the gas probe is

directed at a leak, so that time is lost in localizing a leak. A fine gas

jet which is turned on only for brief intervals and then turned off again

is best. The leak detector can then be kept operating at high sensitivity

and will respond when the leak is struck by the gas probe with whatever

delay is characteristic of the system.

In Chap. 9 the operation of getter-ion pumps is discussed in somedetail. Ackley et al.^" describe how the current drawn by a Vac-Ion

type of pump may be used as a sensitive indicator for leak detection.

One property of this type of pump is that for a given type of gas the

current drawn by the pump is proportional to the throughput. Thusfor gas of type a

Qa = S,xPa (4-11)

and similarly for each component gas in the system, where 7„ is the


current drawn for a given throughput Q^, P„ the resulting partial

pressure of the gas component in question, and S^ the pumping speed

of the getter-ion pump for that same component. Consider the case

of a system with a leak present. The getter-ion pump current is

I =h

SPh '

(4-12)

where Qg represents the internal outgassing load and Q^ is the leakage

throughput of gas of type 1. If, now, at time t = 0, gas of type 1 is

replaced by gas of type 2, then after a time t the change in the getter-ion

pump current is

Mit)

(4-13)

since presumably Qg, the internal outgassing, remains constant. The

detailed form of the current change with time depends critically on the

relative pumping speeds and leak rates for the two gases. After a

sufficient time the exponential factors approach zero and the fractional

change in the current is

lit) -

1

(^b' 1 -exp(^^^)_

(^h. 1 --exp(-^<)_

CO)[IIP). S, Q,

(IIP), S, Q,1 (4-14)

The data for the parameters (IjP)2l{IIP)i, S^jS^, and Q^jQi and the

observed values for A/// are given in Table 4-3 for several gases and

conditions. It is noteworthy that values of A7/7 ~ +1 are observed

in response to the substitution of one gas for another, providing an

excellent sensitivity for leak detection. The value of IjSP for air was

measured and found to be about 20. Using the data from Table 4-3

and the above parameter for air, one finds from (4-14) that by substi-

tuting helium for air at a leak in the system, the change in current drawn

by the getter-ion pump is

M = lOQair

in which A/ is in amperes when Qair is the leak rate for air in torr

liters per second. Ackley et al. claim that since a simple electrometer

circuit can easily measure currents of lO^^^ A, the corresponding

minimum detectable leak rate is about 10^^' torr liter/sec, and that

even smaller leak rates may be detected by using a more sensitive


electrometer circuit. Since the measurement depends upon the change

in the value of the current resulting from the substitution of the gas at

the leak, the limit of sensitivity for leak detection by this methoddepends upon how small the fluctuations in the getter-ion pump current

may be before making the substitution. The authors state that bytaking proper precautions the fractional change in the getter-ion pumpcurrent can be of the order of 1/2,000. The smaller the equilibrium

value of the getter-ion pump current determined by Qg, the throughput

'r.\BLE 4-3. Relative Values of Pumping Speeds, Leak Rates, and IjP

Factors Used in Determining the Change in Getter-ion Pump CurrentDue to Substitution of One Gas for Another*

Probo gas (IlnjillPh SJS, Q2IQ, Ai//t

A 1.25 0.834 0.85 + 0.5

He 0.167 0.30 2.7 -1-0.5

He (with increased pumping speed) 0.167 0.50 2.7

Ha 0.50 1.73 3.8 + 0.1

Hj (with increased pumping speed) 0.50 2.12 3.8 -0.1

Oa 1.0 1.25 0.95 -0.5

CO, -0.5

* Taken with permission from Ackley, Harrington, Francis, Jopsen, Lothrop,

and MandoH, in 1902 Vacuum Symposium Transactions (The Macmillan Company,Xcw York, 1962), p. 380.

I The vahies of A/// were experimentally determined.

due to outgassing, the smaller the minimum detectable leak rate. The

consequence is that the minimum detectable leak rate is generally in the

range from 10^" to IQ-^^ torr liter/sec, depending upon the condition of

the system. Whatever the limiting value may be, it is comparable

with that achieved using a mass spectrometer type of leak detector and

is very convenient in systems in which getter-ion pumps are used.

REFERENCES

1. R. Loevingor and A. Guthrie, in A. Guthrie and R. K. Wakcrling (eds.),

Vacuum Equipment and TccliHiques, National Nuclear Enei-gy Series

(McGraw-Hill Book Company, New York, 1949), pp. 207ff.

2. A. J. Dempster, Phys. Rev. 11, 316 (1918).

3. Locvinger and Guthrie, in op. cit., pp. 212ff.

4. H. A. Thomas, T. W. Williams, and J. A. Hippie, Rev. Sci. Instr. 17, 368

(1946).

5. D. E. Charpentier, in 195G Vacuum. Symposium, Transactions (Pergamon

Press, London, 1957), p. 114.

6. A. O. C. Nior, Rev. Sci. Instr. 11, 212 (1940).

108 VACUUM SCIEKCE AND ENGINEERING

7. A. Hustrulid and A. O. C. Nier, The Mass Spectrometer as a Leak Detector for

High Vacuum Systems, University of Minnesota Report A-578, Apr. 5, 1943.

8. A. O. C. Nier, C. M. Stevens, A. Hustrulid, and T. A. Abbott, J. Appl. Phys.

18, 30 (1947).

9. W. G. Worcester and E. G. Doughty, Trans. AIEE 65, 946 (1946).

10. W. D. Davis and T. A. Vanderslice, in 19G0 Vacuum Symposium Transactions


11. J. L. Peters, in 1959 Vacuum Symposium Transactions (Pergamon Press,

London, 1960), p. 94.

12. C. F. Robinson and L. G. Hall, Rev. Sci. Instr. 27, 504 (1956).

13. G. D. Perkins and D. E. Charpentier, in 1957 Vacuum Symposium Trans-

actions (Pergamon Press, London, 1958), p. 125.

14. H. Sommer, H. A. Thomas, and J. A. Hippie, Phys. Rev. 82, 697 (1951).

15. W. R. Watson, R. A. Wallace, and J. Lech, in 1960 Vacuum Symposium

Transactions (Pergamon Press, London, 1961), p. 421.

16. D. Charles and R. J. Warnecke, Jr., in 1959 Vacuum Symposium Trans-


17. E. H. Nicollian, in 1960 Vacuum Symposium Transactions (Pergamon Press,

London, 1961), p. 80.

18. D. Lichtman and A. Hebling, in 1960 Vacuum Symposium Transactions


19. R. E. Moody, in 7956' Vacuum Symposium Transactions (Pergamon Pr(>ss,

London, 1957), p. 119.

20. P. A. Redhead, Can. J. Phys. 30, 1 (1952).

21. H. W. Ehlbeck, K. H. Loocherer, J. Ruf, and H. J. Schuotzo, in 19G0 Vacuum

Symposium Transactions (Pergamon Press, London, 1961), p. 407.

22. W. H. Bennett, J. Appl. Phys. 21, 143 (1950).

23. G. Reich, in 1960 Vacuum Symposium Transactions (Pergamon Press,

London, 1961), p. 396.

24. I. Langmuir and K. H. Kingdon, Science 57, 58 (1923); Phys. Rev. 21, 380

(1923); Proc. Royal Soc. (London) A107, 61 (1925).

25. K. H. Kingdon, Phys. Rev. 23, 774 (1924).

26. W. H. White and J. S. Rickey, Electronics 21, 100 (1948).

27. F. L. Torney, Jr., in 1957 Vacuum Symposium Transactions (Pergamon


28. A. Guthrie and R. K. Wakerling (eds.). Vacuum Equipment and Techniques,

National Nuclear Energy Series (McGraw-Hill Book Company, New York,

1949). Chapter 5 of this book provides an excellent review of leak-detection

instruments and techniques developed by the Manhattan Project during

World War II.

29. W. F. Briggs, A. C. Jones, and J. A. Roberts, in 1958 Vacuum. Symposi^im

Transactio7is (Pergamon Press, London, 1959), p. 129.

30. J. W. Ackley, A. E. Barrington, A. B. Francis, R. L. Jepsen, C. F. Lothrop,

and H. Mandoli, in 1962 Vacuum Symposium Transactions (The Macmillan


CHAPTER 5

MECHANICAL VACUUM PUMPS

5-1. Functions of Mechanical Pumps. Mechanical vacuumpumps perform a variety of functions in vacuum systems. Tiie first

requirement is that of removing most of the atmospheric air from the

system to some acceptable operating pressure; this operation is some-times referred to as roughing out the system. The final operating level

as far as the mechanical roughing pump is concerned is in many cases

the forepressure required for safe operation of a diffusion pump. Theroughing pump must also maintain a satisfactory operating pressure

in the presence of whatever gas evolution occurs during the operation

of a system. Pumps which commonly perform these two functions are

essentially oil-sealed gas compressors in which the inlet pressure is that

of the system and the outlet pressure is that of the atmosphere. Twoother types of mechanical pumps which are effective in vacuum systems

when backed by a roughing pump as a second stage are the positive

displacement mechanical booster pump (sometimes called a blower)

and the molecular-drag pump. The function of these latter two types

of pumps is to provide high pumping speed at low pressure.

5-2. General Features of Oil-sealed Mechanical Pumps.Any mechanical pump capable of maintaining a high pressure ratio

when used as an air compressor may be used as a vacuum roughing

pump. Of the many possible types those which are most successful

are oil-sealed rotary pumps of positive displacement, i.e., pumps which

isolate at each revolution a specific volume of gas at the pressure in the

system, compress the sample, and exhaust it to atmospheric pressure.

In Fig. 5-1 is shown a cross section of a rotating plunger type of pumpin several phases of operation from suction to exhaust. Figure 5-2

illustrates one type of vane pump in which an eccentric cylinder rotates

within a hollow, cylindrical casing with a reciprocating vane mountedin the casing and maintained in contact with the eccentric rotor to

provide a seal between inlet and outlet ports. Another type of vanepump in which vanes are mounted in a balanced, rotating member is

shown in Fig. 5-3. Pumps of all these types are commercially available

169 ^


II I III I I

(a) (b)

(c)

Fig. 5-1. Cross section of a rotating-plunger oi- Kinney type of pump (a) at thebeginning of the suction stroke, (6) at an intermediate position, and (c) at theend of the exhaust stroke.


Discharge valve

Inlet port

171

Rotor

Seal

Fig. 5-2. Vane type of |3ump in which an eccentric cyhnder rotates within ahollow, cylindrical ca.sing with a reciprocating vane mounted in the casing andmaintained in contact with the eccentric rotor to provide a seal between inlet

and outlet ports.

in both single- and double-stage versions. A compound or double-stage Kinney KC pump is illustrated in Fig. 5-4.

Two important characteristics to be considered in rating mechanicalroughing pumps are the pressure ratio which the pump can maintainbetween inlet pressure and the exhaust pressure, and the pumpingspeed with which the pump removes gas while decreasing the pressurefrom atmospheric pressure down to the limiting pressure of which thepump is capable. As a mechanical pump removes air or other gas froma tight system, the pressure decreases with the time until the pressurereaches the ultimate vacuum of the pump. As long as the system is

free of leaks, the ultimate pressure is the atmospheric pressure dividedby the compression ratio capability of the pump. As compared with

Fig. 5-3. Vane type ofpump in which\-anes are mounted in a balanced,rotating member.

Fig. 5-4. Schematic drawing of a com-pound, or double-stage, Kinney KCpump.

r


ordinary air-compressor performance, the compression ratio required

of mechanical vacuum pumps is very high, typically from 10^ to 10'.

In the design of pumps to be used for vacuum service great care is

exercised to ensure that during each cycle the entire volume of gas

which is taken in during the suction stroke is exhausted at the end of the

cycle. Any small sample of gas which is not forced through the exhaust

valve will be added to the subsequent displacement volume and tend

to limit the ultimate pressure of the pump. Single-stage mechanical

vacuum pumps are typically capable of maintaining an ultimate

pressure of 5 x 10~^ torr partial pressure of air as indicated on a McLeod

gauge. This performance represents a compression ratio of over 10^

and in practice can be achieved more effectively by a rotary rather than

by a reciprocating compressor.

Because mechanical vacuum pumps must have positive clearances

between the operating parts which communicate directly between the

exhaust port and the inlet port, a sealing medium is required to prevent

leakage through the clearances and ensure the maintenance of a high

compression ratio. Because the closely mating parts require lubri-

cation, the most satisfactory sealing medium is lubricating oil of low

vapor pressure and high lubricity. In addition to sealing the pumpagainst blow-by from the exhaust into the intake, the proper flow of oil

through the pump is essential to ensure lowest attainable ultimate

vacuum. When the pressure on the inlet side of the pump is low, the

gas admitted to the pump during the early portion of the cycle is

compressed into a tiny bubble by the time it reaches the exhaust port.

If there is a sufficient flow of oil through the pump, this small bubble of

gas is carried out through the exhaust valve with the slug of oil admitted

during the cycle. Because the oil in a mechanical vacuum pump serves

these two separate functions, the rate of flow and the distribution of

oil through the pump are important features of the design. Unfortu-

nately, the processes of sealing the clearances in a rotary pump, the

entrainment of air in the oil stream, and the final ejection of the slug

of oil with entrained gas bubbles are not understood in detail so that the

design of mechanical vacuum pumps depends much more upon experi-

mental development than upon analytical procedures.

5-3. Pumping Speed of Oil-sealed Mechanical Pumps. In

Sec. 2-2 the pumping speed of a vacuum pump is defined as the volumeof gas, measured at the inlet pressure, which the pump removes fromthe system per unit of time. In the case of positive displacement

pumps the pumping speed can be defined as the product of two per-

formance factors, displacement speed and volumetric efficiency. Thedisplacement per revolution of such a pump is a purely geometrical

quantity and is the free volume exposed to the inlet port at each

'

MECHANICAL VACUUM PUMPS 173

revolution of the pump. This quantity multiplied by the rotational

speed of the pump is the displacement speed 8j). Mechanical pumpsgenerally are rated in terms of the displacement speed rather than thetrue pumping speed, which is the displacement speed multiplied by

Table 5-1. Displacement Speeds or Kinney Mechanical Vacuum Pumps

Model no. Pump rpin cfm liters/min liters/sec rc?jhr

Rotary Piston Type, Single Stage

KS-13 450 13 369 6.14 22.1

KS-27 360 27 765 12.7 45.9

KS-47 360 47 1,330 22.2 80

KD-30 530 31 880 14.6 52.7

KD-850 444 850 24,100 401 1,445

KDH-65 440 65 1,840 30.6 110.5

KDH-80 555 80 2,260 37.8 136

KDH-130 535 131 3,710 61.9 221.1

KDH-150 630 154 4,360 72.6 262

KDH-250 476 250 7,090 118 425

KT-300 880 301 8,540 142 510.2

KT-500 796 520 14,700 245 885

Rotary Piston Type, Compound

KC-2 755 2 57 0.944 3.4

KC-3 1,135 3 85 1.42 5.1

KC-5 630 5 142 2.36 8.5

KC-8 1,000 8 226 3.78 13.6

KC-15 525 15 424 7.08 25.3

KC-46 500 46 1,300 21.7 78.1

KTC-21 1,725 21.2 600 10 36

Vane Type, Compound

KCV-2 479 2.3 65.3 1.09 3.91

KCV-3 646 3.2 91 1.51 5.44

KCV-5 378 4.4 124.2 2.04 7.47

KCV-7 650 6.8 192 3.2 11.6

the volumetric efficiency, that is, Sj, = eSjj. In Table 5-1 are listed the

various models of Kinney rotary oil-sealed vacuum pumps together

with their displacement speeds at designated rotational speeds. For

convenience the theoretical displacements are given in cubic feet per

minute (cfm), liters per minute, cubic meters per hour, and liters per

second, all of which units are commonly used in designating the pumpingspeed of mechanical pumps. (See Appendix IV for conversion factors.)


The true pumping speed of mechanical vacuum pumps varies from a

value which is nearly equal to the displacement speed at atmospheric

pressure to zero at the ultimate pressure of the pump . The performance

curve of a mechanical vacuum pump consists of a graph showing the

actual pumping speed as a function of the pressure from atmospheric

pressure down to the ultimate pressure of the pump. Such curves can

be obtained only by detailed measurement of the pumping speed over

many decades in the pressure by methods such as those described in

detail in Chap. 7. Air is bled through a needle valve at a constant rate

into a small, vacuum-tight vessel connected to the inlet of the pumpand the equilibrium pressure read on a McLeod gauge. The flow rate

of air at atmospheric pressure is measured by any of several methods,

depending upon the magnitude of the flow at each point. The flow

rate is then

760 vol of atmospheric air in ft' .

Q =: r^— torr cimtime in mm

760 vol of atmospheric air in liters

time in sectorr liters/sec (5-1)

when atmospheric pressure is 760 torr.

The reasons for the particular choice of the McLeod gauge (see Chap.

3) for these measurements are of some interest. One reason is that the

McLeod gauge is an absolute gauge for permanent gases, which obey

the general gas law PV = RT, and can therefore be calibrated bystraightforward measurement of gauge dimensions. The other reason

is that the McLeod gauge measures only the permanent gas pressure

and does not respond significantly to condensable vapor pressure unless

the vapor pressure is much higher than occurs under the conditions here

described. The permanent gas pressure rather than the total pressure

(permanent gas plus vapor) is also the only logical pressure to use in the

method described above. The gas flow which is measured and enters

the pump is that of the permanent gas, such as atmospheric air.

Therefore the equilibrium partial pressure of the permanent gas deter-

mined by this flow is the pressure which should be measured to deter-

mine the pumping speed. The vapor pressure present during these

measurements is mostly that of the sealing oil used in the pump and has

nothing directly to do with the mechanical pumping action being

measured. Moreover, the vapor pressure can be varied over a wide

range, depending upon whether the oil is vacuum-processed or ordinary

lubricating oil, without noticeably affecting the pumping speed of the

pump for permanent gas. The vapor pressure is thus not an indication


of the pumping speed of the pump but is only an indication of what is

put into the pump as a sealing medium.The pumping speed of Kinney oil-sealed mechanical pumps depends

upon the inlet pressure in a manner indicated by the graphs in Figs.

5-5 and 5-6, in which the pumping speed is plotted as a function of the

permanent gas pressure. It will be noted that, whereas the pumpingspeed of the single-stage pump falls to practically zero just below 10"^

torr, the pumping speed of the compound pump is greater than 50 per

19,824

16,992

0.001 0.005 0.010 0.050 0.100 0.500 1

Pressure, torr

500 1,000

Fig. 5-5. Pumping speed of Kinney single-stage oil-sealed mechanical pumps as

a function of inlet pressure.

cent of the theoretical displacement at 10~' torr and does not fall to

zero until the pressure reaches the range of 1 to 2 x 10^* torr McLeodgauge reading or about 10~* torr on a liquid-nitrogen-trapped ionization

gauge.

Equation (2-1) defines the gas flow through a pump as Q = P-m^j,^

which is equivalent to Eq. (2-18) in which the gas flow is defined as the

volume flow dVjdt multiplied by the pressure. This quantity is some-

times called the throughput and is the same at all points in a system

consisting of pumps and conductances, as long as there are no leaks.

The throughput of a pump as a function of the pressure is a useful

representation of pump performance for the design of vacuum systems.

I

KCV-7

Displocement;/ cfm (198 liters/mm)

ot 650 rpm

KCV-5

Displacement : 5 cfm (142 liters/min)

at 378 rpm I

KCV-3 ^Displacement: 3.2 cfm (91 liters/min)

at 646 rpm

KCV-2'Displocement; 2.3 cfm (65 liters/mini

ot 479 rpm

226,4

169.8

113.2

56.2

10

0.0001 00005 0.001 0.005 0.010 0.050 0.100 0500 1

Pressure, torr

(a)

5 10 50 100

2832

2264

169.8

113.2

56.6

0.0001 0.0005 OOOl O005 QOlO 0.050 0.10 0.500 1 5 10 50 100

Pressure, torr

(6)

Fig. 5-6. Pumping speed of Kinney compound oil-sealed mechanical vacuumpumps as a function of inlet pressure. (Continued on next page.)

176


0.0001 0.0005 0.001 0.005 QOlO 50 1000.050 0.100 0.500

Pressure, torr

(c)

Fig. 5-6 (continued). Pumping speed of Kinney compound oil-sealed mechanical

vacuum pumps as a function of inlet pressure.

In Fig. 5-7 the throughput for typical single- and double-stage mechan-

ical roughing pumps is shown as a function of the pressure from

"blank-off" to atmospheric pressure. The use of throughput curves

in vacuum-system design is discussed in Chap. 8.

5-4. The Effect of Condensable Vapor upon Mechanical

Pump Performance. After the pressure has been reduced to the

operating level, a mechanical vacuum pump removes the gas from a

vacuum system at a very low pressure and compresses it by a large

factor to somewhat above atmospheric pressure during ejection through

the exhaust valve. For permanent gases this process entails no serious

complications. However, condensable vapors are frequently present.

These materials tend to condense during compression and seriously

impair pumping efficiency.

The condensable materials of concern in the operation of mechanical

vacuum pumps are those which have a vapor pressure which at

moderate temperatures is high as compared with, or at least comparable

to, the desired total pressure in the system being evacuated, but low

as compared with atmospheric pressure. Such a material enters the


vacuum pump as a vapor but condenses inside the pump during com-

pression. Performance of the pump is adversely affected in two ways:

(1) That portion of the condensed material which is not ejected through

the exhaust valve with the slug of sealing oil is added to the gas in the

subsequent displacement volume and reexpands, thereby reducing the

capacity of the pump for the subsequent stroke; (2) that portion which

is carried out in the ejected slug contaminates the sealing oil in the

10^

10^

10'

£ 10

10'

10"

10-2

10-3

10"

^^^

_^^^ ^ ''

^,^^y

f^^pump

...,.,_^y.

"

y"/ — 47-cfm single-stage pump^ h^ /^ :/

>^ f/1-4

10-3 10" 10"

110^ lO""

Inlet pressure, torr

Fig. 5-7. Throughput for typical single- and double-stage mechanical roughing

pumps as a function of the pressure.

reservoir. The contaminated oil eventually reenters the vacuum pumpand further impairs pumping efficiency. In some cases the contam-

inant also causes sludge formation in the reservoir with the result that

the oil does not flow properly and is no longer an effective sealant. In

any case, once the oil is excessively contaminated by a condensable

material there is no very effective cleanup action in the standard

operation of the pump, and the contaminated oil must be replaced byfresh oil to restore good pumping efficiency.

An important factor contributing to poor performance of a vacuumsystem, in which an appreciable quantity of water or other condensable

material is present, is the fact that the condensed material expands bya very large factor in evaporating and thus occupies a disproportion-

ately large pump capacity. As an example, water at 72°F expands bya factor of 50,000 in changing from the liquid to the vapor phase, so

that 1 lb of water becomes about 800 ft^ of vapor, provided the tem-perature of the source of vapor is maintained at the initial value. Inpractice, because of the high latent heat ofvaporization, the temperatureof the source of vapor drops significantly, the equilibrium vapor


pressure decreases correspondingly, and the pump capacity occupied

by the vapor is even larger. Thus, aside from questions of contami-

nation of the pump sealant, the pumping of condensables such as water

in a vacuum system is disadvantageous because of the extremely low

density of the material as it passes through the pump as compared with

its much higher density as a liquid or solid in the system.

Whereas the condensable material which most persistently causes

trouble in mechanical vacuum-pump applications is water, other

materials, such as the Freons encountered in the reconditioning of

refrigerator units and the various solvents encountered in vacuum

processing of many materials, also cause difficulties. Because of the

wide range of contaminants encountered in vacuum processes and the

wide range of requirements as to desired operating pressure, no one

solution to the problem of contamination of vacuum-pump sealing oil

has been found, but a variety of remedies applicable to specific situ-

ations have been developed.

In connection with the problem of contamination of vacuum-pump

sealing oil by condensable materials a word of caution is needed on the

installation of an exhaust pipeline to carry away the discharge. Such

lines, unless steam or electrically heated, normally provide very large

condensing surfaces. If the pump discharge contains water vapor or

other condensable material, condensation will occur in the exhaust

line. This line should not, therefore, run directly upward from the

outlet of the vacuum-pump separator tank because the condensate

formed in the line would then drop back into the oil reservoir and

recontaminate the sealing oil. An appropriate "drop-out" tank or

trap with a drain should be installed beside the separator tank and the

exhaust line taken up from the drop-out tank. Any condensate from

the line is then caught where it can be drained periodically without

getting back into the pump reservoir. The interconnection between

the separator tank and the drop-out tank should preferably be heated

to eliminate condensation at a point where flow back into the reservoir

would be possible. This precaution should be taken on any installation

involving an exhaust line, no matter which of the several methods for

dealing with condensable contaminants is adopted.

5-5. Gas Ballast. The term gas ballast was applied by Gaede^-*

to a method of preventing condensation in mechanical vacuum pumpsinvented by him and first applied to pumps manufactured by E.

Leybold's Nachfolger of Cologne, Germany.The principle of gas ballast is to admit sufficient air into the cylinder

during the compression stroke to prevent condensation of any vapor


chapter.


being pumped. In the adaptation of Kinney pumps for gas ballast a

hole is drilled through the head at the end of the cylinder in such a

position relative to the eccentric cam that the hole is uncovered only

during a portion of the compression stroke when the body of air being

compressed in preparation for ejection is sealed off from the intake by

the position of the piston. A valve is provided, which controls the

Outlet

Gas-bollast

line needle-

odjustment

valve

Gas-ballast

air inlet

180° 360° 540°

Amount ot rotation »-

Functional Piston Performancevs

Amount of Rotation

720°

Admission of gas ballast

Compression

harge to atmosphere

Fig. 5-8. Gas ballast arrangement is shown schematically.

flow of atmospheric air entering the pump through the hole from zero

up to about 10 per cent of the displacement of the pump. The arrange-

ment is shown schematically in Fig. 5-8.

Under conditions of gas-ballast flow the exhaust temperature, taken

conveniently as the temperature of the sealing oil in the vicinity of the

exhaust valve, may, for example, be 140°F (60°C), at which temperature

the vapor pressure of water is 150 torr. Thus in order to prevent

condensation when pumping water at a vapor pressure of 10 torr, the

body of vapor cannot be compressed in volume by more than a factor

of about 15/1 without causing condensation. Sufficient air must bebled into the cylinder during the compression stroke to prevent thevolume of gas mixture during e:khaust from being less than 1/15 that ofthe displacement. 2 The exhaust pressure is about 900 torr, determinedby atmospheric pressure plus the load of the valve spring. If the


temperature of the vacuum system is 68°F (20°C), the exhaust temper-ature is 140°F (60°C) and dry air is admitted as gas ballast at a flowrate equal to a fraction / of the displacement speed >S^, then from thegeneral gas law (1-9)

where T^ = 273

T^ = 273

F.,

20 = 293° abs

60 = 333° abs

fSi, X 760 _ Fex X 900

293 ~ 333

= 333^93 X 76^00 XfSjj = 0.96 /<S^

(5-2)

(5-3)

For the above example the exhaust volume V^^ must be no less than(l/15)»Sjr„ where Sj) is the initial volume per unit of time of the body of

vapor being pumped. Thus

Fex=^'S^ = 0.96/^^ (5-4)

so that /1

(15)(0.96)0.069 (5-5)

This means that for the assumptions in the above example the gas-

ballast dry air flow must be about 6.9 per cent of the displacement of

the pump in order to prevent condensation when water vapor at 10 torr

vapor pressure is being pumped.The ultimate pressure of a single-stage mechanical vacuum pump is

impaired by the introduction of gas-ballast air because the average gaspressure across the seals between intake and exhaust is greatly in-

creased with a corresponding increase in internal leakage past the seals.

The curve shown in Fig. 5-9 illustrates the performance of a gas-

ballasted Kinney KDH-130 vacuum pump. From these tests it

appears that a single-stage, duplex Kinney pump will blank off" at

approximately 1.0 torr with a full gas-ballast flow and 5 x 10-=* torr

with gas ballast turned off".

Gas ballast is even more attractive for two-stage mechanical vacuumpumps. To prevent condensation in the sealing oil, only the second or

backing stage requires gas ballasting. In the case of the older modelsof Kinney compound pumps the two stages are of equal displacement,so that there is no danger of condensation in the interstage volume.The newer models of Kinney compound pumps, however, have a 3 :

1

displacement ratio so that during full gas-ballast operation of the second


120

.^ ^ .*-' /100

80

6 sb alia St off

7V

//

t

/

/

f-

1

/

^60/ L

40

/ 1

1z% ^" t

gas ballast / 5%gc s bollos

20

/-f

1. r0,001 0.01 0.1 1 10 100

Pressure, tcrr

Fig. 5-9. Performance curves for a gas-ballasted Kinney KDH-130 vacuum

pump with zero, 2 per cent, and 5 per cent gas-ballast flow.

stage, some interstage condensation is possible during the early phase

of pumping down a system which has been exposed to humid atmos-

pheric pressure. Since the ultimate pressure at the intake of such a

pump is not sensitively dependent upon the interstage pressure, the

interstage pressure can be raised considerably by gas-ballast air

injection into the second stage without seriously impairing the ultimate

pressure at the intake. A typical gas-ballasted Kinney KC-15 pump

blanks off at 2 x lO^^ torr with the gas-ballast valve open. In Fig.

5-10 are shown the performance curves for a KC-15 Kinney vacuum

pump with zero and full gas-ballast flow (10 per cent of the displacement

speed).

16

14

e 12

10

~1

Gas ballast off\^--'

X

s—^ "/?*

//

/ (/[

//

/

'

J

t

_} ?7 / -/gas ballast / -10% gas ballast

/ 1

0.0001 0.00) 0.01

Pressure, torr

0.1

Fig. 5-10. Performance curves for a KC-15 Kinney vacuum pump with zero,

2 per cent, and 10 per cent gas-ballast flow.


A problem of some concern in the application of gas ballast is the

water content of the injected air. Although dry air is obviously

preferred, in most cases it is inconvenient or impractical to use anythingbut regular atmospheric air.

Consider a gas-ballast flow of 10 per cent displacement with air at

78°F and 80 per cent relative humidity. Since saturation water vaporpressure at 78°F is 24 torr, the water vapor partial pressure is about20 torr in the gas-ballast air. The water vapor injected into the pumpwith 10 per cent gas-ballast flow of humid air is thus equal to that

which would be pumped at an inlet vapor pressure of about 2 torr.

Since a dry air gas-ballast flow of 10 per cent would normally permit

pumping water vapor at 10 torr, the use of air at 78°F and 80 per cent

relative humidity would limit satisfactory operation to 8 torr water

vapor pressure, about a 20 per cent reduction in the amount of water

vapor which the pump can handle without condensation in the sealing

oil. For the worst conditions of temperature and humidity likely

to be encountered, the capacity of a gas-ballasted pump for water vaporshould not be decreased to less than about 3^ of its capacity with dry

gas-ballast air. A single-stage mechanical pump with adequate gas-

ballast flow performs with good pumping efficiency with water vaporinlet pressure in the range 5 to 20 torr. However, the pumping effi-

ciency of a single-stage pump with adequate gas-ballast flow is poor at

pressures below 5 torr. For operation with gas ballast in the range

0.02 to 5 torr a compound pump is required for satisfactory pumpingefficiency.

All mechanical vacuum pumps make somewhat more noise when the

pressure is near the ultimate attainable by the pump. The hydraulic

noise due to action of the exhaust valves can be eliminated by opening

the gas-ballast valve slightly without impairing the inlet pressure to the

pump significantly.

5-6. Other Methods of Preventing Contamination by Con-densables. Although gas ballasting is a satisfactory method of

preventing contamination of vacuum-pump sealing oil by conden-

sables in many applications, other methods are more effective in someapplications. One disadvantage of gas ballast is the impairment in

pump performance, especially in the case of single-stage vacuum

'

pumps. Furthermore, gas ballast is particularly applicable to batchoperations in which condensables are pumped for only a brief period

followed by a period of relatively vapor-free operation during which the

pump can rid itself of contamination. However, for continuous pump-ing of saturated vapor, such as water, and in very large installations

other methods, some of which are briefly described below, are moreeffective.

184 VACUUM SCIENCE AND ENGINBEKING

Hot Pump. One of the most obvious methods of preventing con-

densation of a condensable material in any system is to maintain

throughout the system a temperature so high that the saturation vapor

pressure is in excess of the maximum gas pressure. Since the pressure

at the discharge of a mechanical vacuum pump is typically about

900 torr, a temperature throughout the pump and separator tank of

230°F (110°C) is normally sufficient to prevent condensation of water

vapor. At this temperature water vapor should pass through the

pump as if it were a permanent gas.

Kinney has developed a hot-pump installation and has applied it

successfully in a number of large installations. The hot pump is

particularly applicable to large installations involving very long running

periods and saturated water vapor, such as large freeze-drying and

vacuum-cooling installations and water deaeration, and for maintaining

vacuum in power-plant condensers.

The hot-pump installation should consist of a lagged pump and

separator tank with thermostatic control at 230 to 235°F connected to

a drop-out tank, as previously described. An oil of higher viscosity

must be used in place of the standard sealing oil so that the viscosity at

the elevated running temperature will be in the correct range to seal the

pump effectively.

Knox Method of Air Stripping. In some installations a method

consisting of blowing dry air into the discharge pipe between the

exhaust valve and the separator tank has proved to be effective in

preventing contamination. This method was devised by F. A. Knox'

at Oak Ridge during World War II and applied to large Kinney pumps

in the Y-12 plant. The method has been independently discovered by

others, particularly for application to small single-stage pumps where

the Freons are troublesome sealing-oil contaminants. One advantage

of the Knox method over gas ballast is that gas is not introduced into

the pump interior so that the ultimate pressure capability of the pumpis not impaired. For optimum effectiveness the air stream should be

injected just above the exhaust valve assembly.

Oil Purifier Systems. In many large installations involving several

large mechanical vacuum pumps, such as cable vacuum impregnation

'

plants, the use of oil circulating and purification systems has proved to

be advantageous. Oil from the discharge of all the pumps is pumpedthrough a purification system and thence into a reservoir for purified

oil. The sealing oil for all the pumps is supplied directly from this

reservoir, rather than from the separator tanks on the pumps.

Condensers and Vapor Traps. In some installations, particularly

for high-vacuum systems, it is preferable to prevent condensable

materials from passing through the mechanical vacuum pumps. In


Chap. 8 the use of refrigerated traps in this connection is discussed in

some detail. When systems of very large volume must occasionally

be let down to atmospheric pressure, the vapor load on condensers andtraps can frequently be greatly reduced by drying the air bled into

the system. Such a precaution can in some installations save hours of

outgassing time in restoring the system to operating pressure after

each letdown to atmospheric pressure.

5-7. Mechanical Booster Pumps. As can be seen from Fig. 5-6,

compound vacuum pumps consisting of two conventional, oil-sealed

pumping units connected in series are generally capable of maintaining

good pumping efficiencies down to pressures of the order of 10"^' torr

and of maintaining limiting pressures of 10~^ torr or lower. However,

in such a two-stage vacuum pump the compression ratio maintained bythe first or high-vacuum stage is very low. Thus the useful work done

by the first-stage unit in pumping the low-pressure gas is very small

indeed, whereas the power required for operation is large because of

the viscous drag of the sealing oil. In spite of doing little useful work,

a conventional, mechanical oil-sealed pump as a high-vacuum stage is

limited to operating at low rotational speeds in part because of the

viscous drag of the sealing oil and in part because of mechanical

limitations.

The net pumping action of a mechanical pump may be considered as

the theoretical pumping speed or displacement speed minus the rate at

which gas migrates back through the pump because of internal leakage

or other causes. If the forward pumping speed is large as compared

with the reverse migration, then the volumetric efficiency will be high

even with a high pressure ratio between outlet and inlet, and the

compression ratio which the pump can maintain at zero fiow (no fiow

into the inlet) will be large.

For operation at or near atmospheric pressure positive displacement

gas compressors of a variety of different types are used successfully

without the use of a sealing oil. Such pumps are built with well-

balanced interleaving rotors and definite clearances between the moving

parts so that operation at high rotational speeds is common practice.

Thus compressors or blowers of this type have high displacement

speed for relatively modest dimensions. In normal use, however, the

pressure ratio against which compressors of this type are required to

pump is small. The loss in pumping speed with increasing pressure

ratio, moreover, is very rapid even in the case of axial flow compressors,

which are designed specifically to extend the range of operation into

the region of higher compression ratios.

To adopt an unsealed, positive displacement compressor for use as a

vacuum pump would seem at first thought unpromising since good


pumping efficiency with a high pressure ratio is a normal requirement

for vacuum service. However, the hmitation on the attainable com-

pression ratio for positive displacement blowers is the reverse flow

called slip due to the pressure difference maintained by the pump.

This reverse-flow rate is given by the pressure difference across the

pump multiplied by the average conductance of the clearance slots

between the internal parts of the blower. As we have seen, gas con-

ductance is proportional to the pressure in the viscous-flow range and

at reduced pressure finally reaches the comparatively low value char-

acteristic of molecular flow. The effectiveness of the positive dis-

placement type of blower in terms of maintaining a high compression

ratio should therefore improve as the outlet pressure is decreased until

the transition pressure range, discussed in Sec. 2-6, is reached. Below

the transition pressure the conductance through the clearance slots

in the pump is constant, and the compression ratio of the pump should

therefore be expected to remain high. As the first-stage unit of a two-

stage vacuum pumping system, a positive displacement blower does

therefore have considerable potentiality.

5-8. Analysis of Mechanical Booster-pump Performance.

The pumping speed of a typical single-stage, oil-sealed vacuum pump

begins to decrease appreciably as the inlet pressure falls below 1 torr.

At this pressure the mean free path for air [see Eq. (2-57)] is

5 X 10~3 cm = 2 X 10-3 j^. Thus for mechanical clearances of several

thousandths of an inch, which are tjrpically maintained in positive

displacement blowers, the maxi-

mum compression ratio is attained

^^^ Pi ^^^ ^.gll within the range for good per-

formance of a single-stage backing

pump.An example of the type of pump

which can be designed and con-

structed to meet these requirements

is that commonly referred to as a

Roots blower, as illustrated in Fig.

5-11. Because of the high rota-

tional speed at which pumps of this

type can be operated, very large dis-

placement speeds can be obtained

in relatively small dimensions.

The operation of such a pump has

been analyzed in some detail by

Van Atta and Sylvester,* Van Atta,^

Ziock,'' and Winzenburger.'

Fig. 5-11. Schematic cross section of

a mechanical booster pump. [Takenwith permission from C. M. Van Atta,

in 1956 Vacuum Symposium Trans-actions (Pergamon Press, London,1957).]


In any multistage vacuum pumping system the throughput deter-

mines the pressure at the inlet of each successive stage in accordance

with the continuity equation (2-1) of Chap. 2, which for our present

purpose we shall write as

Q ^nPn const (5-6)

where Q = gas throughput

S^ = pumping speed of any of several stages of pumps arranged

in series

P„ = resulting inlet pressure

This is, in general, true for permanent gas flow as long as the gas which

enters the first-stage unit goes through all stages in series and noadditional gas is admitted, as for example by a leak, between the

stages. Then, in a two-stage pumping system the compression ratio

which the first-stage pump sustains is

Pi S9.(5-7)

Thus, if the first-stage pump is capable of sustaining a high compres-

sion ratio, the second-stage pump may have a correspondingly small

pumping speed, resulting in an overall economy in the size and cost

of the two-stage system.

The net forward pumping speed of a positive displacement booster

pump may be stated as

QOj = Si S,-

Pi(5-8)

where Sj) = displacement speed

Q = flow of gas into the pump at inlet pressure P^

S^ = loss in pumping speed due to internal leakage backward

through the pumpWhen there is no flow into the pump inlet, i.e., when Q = 0, the

inlet pressure reaches the limiting value determined by the internal

leakage parameter and the interstage pressure, i.e., the pressure Pj

maintained at the discharge by a backing pump. Under these con-

ditions of zero net flow the forward pumping capacity of the pumpSjj is completely balanced

Sr S,- (5-9)

by the internal leakage, which is due to two causes

:

1. The flow back through the clearances of the pump due to the

pressure difference (P2 — Pi) maintained by the pumping action. This


may properly be referred to as the pump slippage, as a result of which

an amount of gas

Q, = (P, - Po)C, (5-10)

leaks back into the inlet side of the pump from the discharge side

through the clearances. Here P^ respresents the inlet pressure under

conditions of zero flow and C^ is the conductance through the clearances

in the pump mechanism.

2. The reverse pumping action due to the existence in the pumpmechanism of small pockets of gas which get trapped and carried back

from the discharge port to the inlet port. If S^ is the volume per unit

of time of gas at discharge pressure which is thus carried back, the

amount of gas due to this cause which must be again pumped out is

Qr Pj'S'r (5-11)

The combined effect of these two mechanisms accounts for the entire

loss of pumping speed. Thus the quantity of gas which flows back

from the discharge to the inlet because of these two internal processes

is

Qi ^Qs + Qr (5-12)

From Eqs. (5-9) through (5-12) the loss in pumping speed due to this

internal leakage is

o o Qi Qs+Qr^i = ^D =-B- = 5

-^ -^

p — p p

-^0 *

(5-13)

so that the compression ratio K maintained under conditions of zero

flow is

K = Sj) + C,

Po C', + S^(5-14)

In order for the compression ratio to be high, the two quantities in the

denominator must be small, i.e., both the gas conductance C^ through

the clearances of the pump and the reverse pumping speed S^ must besmall.

The above discussion applies to the compressive action of the pumpagainst the forepresssure when no net gas flows into the intake. Nowconsider the result of admitting a gas flow Q, as in Eq. (5-8), whichby reference to Eq. (5-13) becomes

S,Px

a Qi(5-15)


since now the inlet pressure is Pj instead of Pj. By combining this

result with Eq. (5-6) we have

Q = P^S, = P.Sr, - Q, = P,S, (5-16)

where S2 is the speed of the backing pump which maintains the fore-

pressure Pj. Since P^ is now the inlet pressure, by analogy withEq. (6-13) we have

Qi __°2 "1

r JL. ^ V

so that (5-16) becomes

PiSn - {P2 - Pi)Os - PA = P,S,

, s, + c, + s^from which P,

The pumping speed at pressure P^ is then

S,

(5-17)

(5-18)

(5-19)

(5-20)

from which it appears that the pumping speed of the mechanical booster

pump is a magnification of that of the backing pump. Moreover,

since from Eqs. (5-14) and (5-19)

Pi (So

Sj, + C, ' K (5-21)

the pumping speed of the first-stage pump is related to its zero-flow

compression ratio in accordance with

S^ Sj, + c.

1

(5-22)

obtained from Eqs. (5-20) and (5-21). Thus if K, the zero-flow com-pression ratio, is very large and therefore both 0^ and S^ are very small,

the pumping speed S-^ is nearly equal to the displacement speed Sj).

By a similar analysis Winzenburger' arrives at an expression slightly

different from (5-21) for the pressure ratio, namely

Pi S.

= T^ +SD Kby considering the reverse flow through the clearances to be of the

nature of gas flow through a nozzle in which the pressure ratio exceeds


the critical value. For this case the mass flow is given by

cAP,w

PiS,

T^^ RT^

This assumption appears to be valid for P^ > Pc defined in (5-30), i.e.,

in the region of viscous flow, in which (5-21) reduces to a simflar ex-

pression to that given by Winzenburger. However, for P^ < P^ the

flow through the clearance slots is molecular, and an expression of the

form given in (5-21) is then valid.

In the foregoing discussion the conductance through the clearances

of the pump G, and the reverse pumping speed 8^ due to imperfections

in the rotor contours have been tacitly treated as constants independent

of the pressure. This is true only for limited ranges of the pressure.

In Sec. 2-6, the Knudsen formula for the conductance of a tube of

circular cross section in the transition pressure region is discussed.

By analogy with Eq. (2-39) the conductance of a slot of long, narrow

cross section in the transition pressure region is of the form

C = C„&lPa

KP:C,P^ (5-23)

2-* av

in which Pav is the average pressure through the slot, Co is the low

pressure or molecular-flow conductance of the slot similar to that

given in (2- 102), 6^ and 62 are constants similar to k^ and Ajj used in (2-39),

and Ci is a constant which replaces the constant TrD*ll28rjL of (2-39)

in the case of a slot. The clearance slot, the conductance of which we

wish to represent in general form, is one for which the width is a

minimum at the line of near contact between the rotors or between

rotor and cylinder and increases with the contour of the parts on either

side of this minimum clearance. This slot can be represented by one

of a uniform width equal to the minimum clearance and of a length in

the direction of flow, which depends on the details of the geometry.

The conductance is in any case given by an expression of the general

form of (5-23), although the exact values of the constants Cq and C^

which depend upon the geometry must be determined empirically.

Note that for very small values of the pressure Eq. (5-23) reduces to

1 1

C = Co Pav "< T ' -^av "^ 7~ (5-24)

and that for large values of the pressure (5-23) reduces to the approxi-

mate expression

C — Co T h CjPa61 62

(5-25)


in which the first term becomes negligible as compared with the second

when Pav is sufficiently large. Since 61/62 is a quantity somewhat less

than unity as has been shown for the case of a tube in (2-37) and (2-38),

Eq. (5-25) can be written in the form

where

C - Co + C,(^P.. -^)

„ 62 — 61 Co

p-1 av ^ —^

4

62 Ci

(5-26)

(5-27)

in which the constant 4 is arbitrary so far as the consistency in this

step is concerned but is chosen to conform with the definition of the

transition pressure P^ discussed in Sec. 2-6. An approximation to the

conductance of a tube to replace the more exact expression given in

(2-43) leads to an expression like (5-26) in which the transition pressure

is that given in (2-55). Equation (5-26) approximates the true

conductance (5-23), which has the same general form as Eq. (2-43),

shown graphically in Fig. 2-3 by two straight lines, a horizontal

straight line given by (5-24) for Pav < Pt/4 extending the molecular-

fiow value up to the transition pressure and a straight line proportional

to the pressure for the viscous-flow region for Pav > P«/4.

Since by definition the average pressure through the clearance slot

is

Pav = ^^^ (5-28)

then if the operating conditions are such that Pj is very small as com-

pared with P2 the former may be neglected in (5-28) so that

P — —-t av — ^r^ approx

and Eq. (5-26) becomes

C. ~r -^ (P2 p.>4'

(5-29)

(5-30)

in which P^ = Pj/2 will be called the critical pressure.

Several rather gross approximations are made in the transition from

the exact expression (5-23) for the conductance through a slot to the

combination of Eq. (5-24) for Pg < P(/2 and Eq. (5-30) for P2 > Pf/2.

For an analysis of the performance of a mechanical booster type of

vacuum pump, however, these approximations lead to a sufficiently

accurate representation of the conductance through the clearances


since in practice Pj (the interstage pressure) is 10 or more times P^

(the inlet pressure) over most of the pressure range of interest.

The low-pressure conductance of a long, narrow slot for air at low

pressure is given by Eq. (2-102) of Chap. 2. For our present purposes

we write this equation in the following form

C, = k— (5-31)

in which the constant k depends upon the units used. The clearance

between the rotors of a Roots type of compressor, however, is not of

uniform width for a clearly defined depth z, but is defined by curved

surfaces. Nevertheless it can be seen that the low-pressure conductance

of such slots will have the form

Co = k^d^ (5-32)

where d is the root mean square of the mechanical clearance between the

rotors or between each rotor and the cylinder wall, and fcj is in part

a geometrical constant averaged over all orientations of the rotors.

What is of main significance is that the low-pressure conductance

varies as the square of the radial clearance d.

As can be seen from Eq. (5-30), for sufficiently high values of the

pressure the conductance through a slot is proportional to the pressure.

Also in the case of a slot the conductance at high pressure is proportional

to the cube of the slot width. Thus it is clear that in Eq. (5-30) as

applied to the conductance through the radial clearances of the pump,Cj must be of the form

Ci = fc^rf* (5-33)

in which k^ is in part a geometrical constant.

Note that in the above discussion no mention is made of conductance

through the clearances at the ends of the rotors. The reason for this

omission is that the flow path \z in Eq. (5-31)] for the end clearances

is very long between flat surfaces. Thus for very adequate endclearances this conductance is negligible as compared with that through

the radial clearances.

The transition pressure Pj has been related to the mean free path arid

diameter in the case of gas flowing through a tube. In Eq. (2-56) it is

seen that at the transition pressure the diameter of the tube D is about11 times the mean free path 1< of the gas molecules. Approximatelythis same factor applies to a slot in which case the width of the slot dat the transition pressure is

d = 12L approx (5-34)

The sharp knee in the approximate conductance curve in (5-30) occurs


when the interstage pressure Pg = P(/2 = P^, at which pressure themean free path is twice as long as it is at the pressure P^. Thus at

the value of the pressure Pa at which the sharp break appears in

the approximate conductance curve

d = 62, ^2 = Y = Pc (5-35)

For air at 20°C we have from (2-57) for the mean free path

A = -'(5-36)

where /Ij = 5 x 10-^ cm = 2 x 10~^ in. is the mean free path at P = 1

torr. Thus at the critical pressure P^ the width of the clearance slot

is related to the corresponding mean free path as follows

:

or P =d

(5-37)

in which d is the average rotor clearance.

From the above discussion of the conductance of gas through slots

it can be seen that the conductance through the mechanical clearances

of a positive displacement type of compressor used as a vacuum booster

pump may be represented with reasonable approximation by the fol-

lowing expressions, each applied to its proper pressure range

:

6Ai

TC, k^d^ for P, < (5-38)

and C^ = k^d^ + k^d^(--^) for P, > '-^d

(5-39)

The general form of the pumping speed 8^ of the mechanical booster

pump as a function of the pressure can now be seen from Eq. (5-20).

The fact that C^ is independent of the pressure until the interstage

pressure reaches the transition value and then increases linearly with

the pressure above this value, as given in Eqs. (5-38) and (5-39), is of

fundamental importance. When the gas flow Q is zero and the inter-

stage pressure is at the limiting pressure of the backing pump, that is,

82 = 0, the pumping speed 8-^ of the booster pump will also be zero.

At this point the limiting value Pq of the inlet pressure will be deter-

mined by the zero-flow compression ratio as in Eq. (5-14). Thepumping speed will then rise rapidly as the gas flow and pressure in-

crease, primarily because the pumping speed of the backing pump is

increasing. When the pumping speed of the backing pump reaches its

normal plateau value at an interstage pressure of about 0.1 torr, the

pumping speed of the booster pump will also reach a plateau value.

T194 VACUUM SCIENCE AND ENGINEERING

As the pressure is further increased this plateau value of the pumping

speed will then be maintained until the interstage pressure reaches the

critical value P^, which in practical cases may be in the range 1 to 5'

torr. Above this point the pumping speed is expected to decrease with

increasing pressure, primarily because C„ the internal leakage through

the clearances, is increasing rapidly with the pressure. Thus one

expects a very broad pumping-speed curve which rises from zero at

the ultimate pressure to a flat plateau value and then decreases as the

interstage pressure is increased beyond the critical pressure. If the

zero-flow compression ratio given in Eq. (5-14) is high as compared with

the staging ratio between the displacement of the booster and its backing

pump, the plateau pumping speed should be very nearly equal to the

pumping speed of the backing pump multiplied by the staging ratio.

5-9. Computed Performance Curves for Mechanical Booster

Pumps. By; choosing reasonable values for the parameters C^ and

8^ and knowing the pumping speed of the backing pump as a function

of the pressure, the performance curve of a positive displacement

compressor used as a mechanical booster pump can be computed point

by point from Eq. (5-20). The performance of the first experimental

mechanical booster pump was predicted in this manner and was later

confirmed in its general features by pumping speed measurements.

However, for a more accurate test of the theory and a better

understanding of mechanical booster-pump performance subsequent

calculations of pumping-speed curves have utilized the results of

two preliminary tests designed to measure directly the parameters C,

and K:

1. With the pump rotors at rest but set in turn at equally spaced

positions throughout a complete revolution, the conductance through

the clearances of the pump was determined by admitting a measured

flow of air into the inlet with the forepump in operation and measuring

the pressure at the inlet P^ and that at the interstage P^. By appli-

cation of the conductance formula

Q = C,{P, - P,)

to these observations for a small gas-flow rate and averaging these

results, the low-pressure value Co of the conductance C, through the

clearances was determined.

2. With the booster pump in operation but without any flow into the

inlet the forepressure was varied from the limiting pressure of the

backing pump up to several torr, and the pressures at the inlet and

interstage were measured. The ratio of these pressure readings, K =P2IP1, is the zero-flow compression ratio, which combined with C^ from


the preceding test and Eq. (5-14) amounts to a determination of the

parameter S^. In addition, the value of the interstage pressure at

which K begins to decrease as the pressure increases is identified as

the critical pressure P^.

f 14

I 12

^"110

h-i .,

--- --/r" ._.. ._..

J Hj /[ . 1.J

Average = 8.0 cfm

45 90 135 180 225 270 315 360

Angular position of rotors, deg

Fig. 5-12. Curve for obtaining experi-

mental value of conductance through

pump clearances. [Taken with per-

mission from C. M. Van Atta, in 19S6



o .

70

^~60Q_

B 50

i''°

^ 30<L>

I 20O" 10

10"' 10"^ 10"' 1 10 100

Interstage pressure, torr

Fig. 5-13. Compression -ratio curve

for a mechanical booster pump.[Taken with permission from C. M.Van Atta, in 19S6 Vacuum, Sym,-

posium Transactions (PergamonPress, London, 1957).]

The significant dimensions of the positive displacement type of

mechanical booster pump, on which extensive calculations and tests

were carried out, were as follows

:

Cylinder length: 16 in.

Cylinder bore : 9-M in.

Radial clearances, d : 0.008 in. average

Displacement speed at 1,740 rpm, Sj^: 1,230 cfm

Displacement speed of backing pump: 130 cfm

The results of the measurements on the conductance through the

clearances as described in the first of the two preliminary tests outlined

above are given in Fig. 5-12. From these measurements the average

value of Co = 8 cfm. The dependence of the compression ratio on the

interstage pressure is shown in Fig. 5-13. Although these latter results

show an unanticipated droop in the compression ratio at the lower limit

of the pressure range, an average value for the low-pressure range is

taken to be ii' = 50. These values of Co and K substituted into Eq.

(5-14) yield S^ = 16.8 cfm.

The results of the second test also yield a value for the critical

pressure. Since K begins to decrease sharply at an interstage pres-

sure of 1.5 torr, P^ = 1.5 torr, consistent with a rotor clearance of

0.008 in.


The remaining undetermined constant is C^ appearing in Eq. (5-30).

The value of this constant has been arrived at by trial-and-error

fitting of the high-pressure end of the experimental performance curve.

The value chosen by this procedure is Ci = 2.8 cfm/torr.

From these results we have for Eq. (5-30)

C, = 8.0 + 1.4(P2 - 1.5) cfm

1,200

1,000

e 800O

I 600

I 400Q.

200

Mechanical booster pumf own

\,'i"

r \

'

\ \ \ \;;'K

I

\\

\ I V

\I \

>/ \' \

L I\

\

\

/.\ \

\

> \

\ \ \

1 \

V \ ^°

f:\

\ \

\

\V

\ 1

\^ \ \

\ V\

\ \\ i I \

\\1

* \

PI

1>

\

\I

\\

/•

\ \

\ \» \

V 1 .

S \ ^

\

\ V -^\

',Ji

1 k _i..l

s.;^

^^ ^^Backing pump

10" 10-" 10" 10" 10-1 10 100

McLeod gauge pressure, torr

Fig. 5-14. Pumping-speed curve for a mechanical booster pump. [Taken with

permission from C. M. Van Atta, in 1956 Vacuum Symposium Transactions


With the numerical values of the above constants measured or

assumed and the pumping speed 8^ of the backing pump as a function

of the interstage pressure Pg known from previous measurements, the

pumping speed S^ of the booster pump as a function of the inlet pressure

Pj can be calculated using Eq. (5-20). Thus we have

8i = -;;; —TT^ S, for Pj < 1.5 torr

1,238 + 1.4(P2 - 1.5)

8^ + 24.8

8,.

8^ + 24.8 + 1.4(P2 - 1.5)

The corresponding value of the inlet pressure is

^2 n

for P, > 1.5 torr

Pi8,

The calculated performance curve for the standard combination of

parameters given above is shown in Fig. 5-14 together with a typical


experimental performance curve of the 130-cfm backing pump used.Dotted lines connect points on the booster-pump performance curvewith those on the backing-pump curve from which they were computed.The staging ratio for the standard combination is 1,230 to 130, or

very nearly 10 to 1. The curve plotted in Fig. 5-15 as Case I is arepetition of the computed performance curve shown in Fig. 5-14.

Pressure (McLeod

Fig. 5-15. Pumping-speed curves showing dependence of mechanical booster-pump performance upon the displacement of the backing pump. [Taken withpermission from C. M. Van Atta, in 1956 Vacuum Symposium Transactions(Pergamon Press, London, 1957).]

Case II of Fig. 5-15 is a similarly calculated performance curve illus-

trating the expected effect on booster-pump performance of doublingthe staging ratio, i.e., decreasing the displacement of the backing pumpby a factor of 2 from 130 to 65 cfm. For simplicity it is assumed thatthe pumping speed of the smaller backing pump would be just half thatof the measured value for the standard backing pump at each value of

the pressure.

Conversely, the performance curve shown as Case III in Fig. 5-15

illustrates the expected effect on the booster-pump performance of

decreasing the staging ratio by a factor of 2, that is, by increasing the

displacement of the backing pump from 130 to 260 cfm.

Figure 5-16 illustrates the effect of radial clearances on the perform-ance of the mechanical booster pump. The calculated performance


1,000

800

600

400

200

.,, .. CoseE"*

cy' •"

\ ^^/:^ ,„. s

^s

1 // •

' Case I

/ / \, \//

1Cose Rotor s \

// ( 0.008 in.

J 0.004 in.

[ 0.01 6 in.

cking-pump displacement = 1

oster-pumpdisplocement = 1

'''

Case!

I\,

1 i Ro 30cfI ±'.Bo 230cfm

n \

10"^ 10"' 10"-' 10"^ 10

Pressure (Mc Leodl,

100

torr

Fig. 5-16. Pumping-speed curves showing the effect of radial clearances on the

performance of the mechanical booster pump. [Taken with permission from

C. M. Van Atta, in 195(i Vacuum Symposium Transactions (Pergamon Press,

London, 1957).]

curve for Case I with standard clearances of 0.008 in. is shown for

comparison with similar curves calculated for radial clearances of 0.004

in. (Case IV) and of 0.016 in. (Case V). Note that for this latter case

the plateau has disappeared and the pumping-speed curve falls off

rapidly for values of the pressure above and below that at the peak.

The throughput curve for a typical combination consisting of a

10°

,10'

^ 10*

jio^

§•10'

,-<<^'i^^^--'-^ T

,^ Backing pump-KOH-130^y^

///

10° so

10* %

10^

0.001 0.001 0.010 0.100 1.0 10 15 100 1,000


Fig. 5-17. Throughput curve for a typical combination consisting of a mechan-ical booster pump of 1,234 cfm displacement speed backed by a roughing pumpof 130 cfm displacement.


I

mechanical booster pump of 1,234-cfm displacement speed backed by aroughing pump of 130-cfm displacement speed is shown in Fig. 5-17.

The shaded area where the two curves join represents the changeoverfrom the booster-pump operation to the booster bypass.

5-10. Measured Performance Curves for Mechanical BoosterPumps. The pumping speed at any point in a multistage systemmay be defined in accordance with Eq. (5-6) as

Q_

P.*s«

in which Q is the throughput admitted as a steady flow at the inlet to

the system, and P„ is the resulting pressure at the point of interest.

However, if this definition of pumping speed is to bear any relation-

ship to the analysis of the pumping action given in the previous

sections, the significant pressure at each point in the system where

the pumping speed is to be measured is that due to the gas admitted at

the inlet. Under the usual conditions of test, the pressure of permanent

gas in the system is due to air and the remaining pressure is due to

condensable materials originating, for example, in the backing pump.Since a McLeod gauge measures the pressure due to the permanent gas

and is very little affected by the vapor pressure present under these

circumstances, the pressures used for pumping speed measurements are

McLeod gauge readings. The role of condensable materials back-

streaming from the backing pump is a separate matter and will be

discussed later.

Experimental results for the pumping speed of a 1 ,230-cfm mechanical

booster pump backed by a 130-cfm forepump are shown in circles in

Fig. 5-14. These results compare favorably with the calculated

pumping-speed curve for which the basic parameters are in good

agreement.

Experimental pumping-speed results are also shown as circles in

Fig. 5-15 for the 1,230-cfm booster pump backed by a 220-cfm fore-

pump. These results should correspond fairly closely with the calcu-

lated curve designated as Case III of Fig. 5-15, although the backing

speed is not quite as high as that assumed for the calculated curve.

Comparison between the experimental and calculated pumping speeds

shown in Fig. 5-15 indicates that the theory developed for the

operation of a positive displacement rotary compressor as a vacuumbooster pump is approximately correct. However, examination of the

experimental results reveals minor deviations in behavior from that

predicted.

The greatest and most fundamental deviation from expected perform-

ance is exhibited by the zero-flow compression ratio. From Eq. (5-14)


'

it is apparent that the compression ratio should be independent

of the pressure from the lowest attainable pressure up to the point

where the interstage pressure equals the critical value. Above this

point the slippage conductance G^ through the rotor clearance is no

longer constant, but increases linearly with the pressure. Measure-

ments, as shown in Fig. 5-13, show that the compression ratio decreases

as expected as the pressure is increased above the critical value.

However, as the pressure is decreased from the critical value, the com-

pression ratio, instead of remaining constant at its maximum value as

expected, drops off appreciably.

Tests carried out by Dobrowolski^ show a pronounced dependence of

the zero-flow compression ratio of a mechanical booster pump on the

mechanical clearances and surface finish of the rotors. Three booster

pumps of 1,300-cfm displacement speed but with different rotor

clearances and surface finish were tested, all with a 220-cfm backing

pump. The rotor svirface finish in two of the booster pumps was the

standard machined surface whereas the surface in the case of the third

pump was polished (64-microinch finish). The clearances and rotor

surfaces of the three pumps were as follows

:

PumpAverage rotor

clearance, in.

Slippage

conductance (Cg), cfmRotor finish

ABC

0.012

0.008

0.0115

18.2

8.35

16.8

MachinedMachined64-microinch polished

In Fig. 5-18 the measured zero-flow compression ratio is shown as a

function of the interstage pressure for the three pumps. The curves

show the anticipated marked increase in compression ratio with de-

creasing clearances in the high-pressure region above the maximumcompression point. However, for pressures less than that for the

maximum, the compression ratio falls off rapidly with decreasing

pressure for pumps A and B, but much less rapidly for pump C. The

ratio of low pressure to maximum compression ratios is 0.27 for pumpA, 0.21 for B, and 0.67 for C. The very marked improvement in low-'

pressure compression ratio due to improved surface finish largely

explains the discrepancy between the theoretically predicted perform-

ance curves and the measured curves. The zero-flow compression

ratio at low pressure is theoretically expected to be independent of the

pressure. When the rotor surfaces are rough they may be expected to

carry gas back from the high-pressure outlet side of the pump to the low-

pressure inlet side in the form of adsorbed gas. The dependence of this

effect upon pressure cannot be predicted except that outgassing effects


generally are known to be steep functions of the pressure and to be muchmore pronounced for rough than for polished surfaces. Since pump Cin the above tests had large rotor clearances, the zero-flow compression

ratio at high pressure is poor. Even so, its compression ratio at low

pressure is much better owing to the polished surfaces than either pumpA, with about equal clearances, or pump B, with smaller clearances

but with the standard rough machined rotor surfaces.

80

60

40

^ 20

ys ee Fig. 5 -13-^

/ \\

=^i^ F^ s.

\^^>'^A

^^^—10" 10' 10" 10" 10 10'

Interstage pressure, torr

Fig. 5-18. Zero-flow compression ratio as a function of rotor clearances and

surface finish.

The pumping-speed curves also show a minor deviation from the

expected shape. The predicted pumping-speed curve rises very

sharply from zero for values of the pressure slightly in excess of the

ultimate value for zero flow. Although accurate measurements on the

steep part of the performance curve are difficult, the results indicate that

the rise in pumping speed with increasing pressure above the ultimate

value is not as steep as predicted. Furthermore, the experimental

results shown as circles in Fig. 5-14 are not quite as good a confirmation

of the predicted performance as first appears. The effect of the drop

in compression ratio in the low-pressure range on the pumping speed

was partly compensated by the fact that the performance of the

particular 130-cfm backing pump used in the tests was somewhat

better at low pressures than had been assumed for the calculations.

The minor differences between the observed and predicted perform-

ance noted above can best be explained by assuming that the reverse

pumping parameter, by which some gas at outlet pressure is carried

back to the inlet side of the pump, is not a constant but increases as

the inlet pressure decreases. Experimental study of this effect has

demonstrated that the reverse pumping action is partly due to an

outgassing process, that of alternating absorption and reemission of gas


by the inner surfaces of the pump, which are alternately exposed to the

interstage and to the inlet pressure.

5-11. Overheating of Mechanical Booster-pump Rotors.

Compression of a gas in the process of pumping, as occurs in all me-

chanical vacuum pumps, involves doing work on the gas. Unless there

is some process by which heat can flow easily from the gas to a heat

sink, the temperature of the gas increases. In the case of mechanical

roughing pumps, oil is circulated with the gas stream and the exhaust

gas bubbles through oil in the reservoir. The result is that heat is

removed from the gas and rather efficiently distributed throughout the

pump. Because of this process, cooling the pump as a whole dissipates

the heat satisfactorily. Thus small roughing pumps are cooled by air

convection and large roughing pumps by water circulated through

portions of the pump housing. However, in the case of mechanical

booster pumps there is no oil present for distributing the heat generated

throughout the pump structure. Furthermore, the rotors are not in

immediate contact (except indirectly out through the shafts to the

bearings) with the pump housing and therefore tend to overheat when

the pressure difference across the pump is too great. As is pointed out

by Noller^ the power required for pumping the gas is

W = SniP, - Pi) (5-40)

in which Sjy is the displacement speed of the booster pump. From the

continuity equation (5-6)

PA = €P,S„ = PA (5-41)

where S-^ and S2 are the pumping speeds respectively of the booster

pump and its backing pump, and e = S^ISj^ is the volumetric efficiency

of the booster pump. Combining these two equations yields

W = S'^'ik~^)

(5-42)

From this equation there are obviously two ways of limiting the power

requirements of the booster pump: (1) The upper value of the inlet

pressure P^ during operation can be limited to some maximum value riot

to be exceeded in operation ; or (2) the pumping speed S^ of the backing

pump may be increased as needed to tolerate a larger value of the

pressure. In practice either remedy is applied, depending upon the

requirements of the system.

In the pressure range below 1 torr the power requirements of mechan-ical booster pumps is determined almost entirely by the frictional

characteristics (shaft seals, bearings, gears, etc.). However, at 10 torr

the power required for pumping has become significant. For example.


in the case of the pump, the test results of which are given in detail in

Sec. 5-9, the pumping power as computed from (5-42) with Sjj = 1,230

cfm. Si = 690 cfm, S2 = HO cfm at an inlet pressure P^ = 10 torr

turns out to be IT = 4,080 watts = 5.47 hp, which is in good agreement

with the measured power input. For this pump operating at an inlet

pressure of 10 torr, about 4 kW is therefore put into the gas fiow. Aportion of this power is dissipated in the pump rotors which heat up

and expand. If the pump is operated at inlet pressure above 10 torr

for an extended period, the expansion of the rotors exceeds the available

end clearances and the pump will

seize.

Two remedies have been applied

to extend the range of operation

of mechanical booster pumps to

higher pressure. Thees^" describes

a design of booster pump in

which the rotors are cooled by oil

circulated through hollow shafts.

He also describes the use of an

interstage cooler at the outlet of

the mechanical booster pump to

cool the exhaust gas and therefore

indirectly the rotors. Figure 5-19

illustrates the arrangement of an

exhaust cooler used in systems for vacuum melting of steel and similar

installations in which the operating pressure is high.

Because of the limit on pressure differential imposed by the expan-

sion of the rotors due to overheating, mechanical booster-pump

installations frequently include a pressure-sensitive switch set to operate

at 10 to 50 torr, depending upon the characteristics of the particular

booster and backing-pump combination. At pressures greater than the

set value the pressure switch holds a valve in a bypass connection open

so that the gas flows directly into the backing pump from the system

and the booster-pump power is turned off. When the pressure becomes

less than the set value, the pressure switch closes the bypass valve and

starts the booster pump. A system so equipped, when started from

atmospheric pressure, will pump down initially through the bypass

with only the backing pump in operation and will then switch over to

pump as a two-stage system as soon as the pressure passes through the

selected switch-over value. Figure 5-20 illustrates such a two-stage

system with the bypass connection around the mechanical booster

pump. Manual operation of the bypass valve is an obvious alternative

which is entirely suitable for some installations.

Fig. 5-19. Exhaust gas cooler in-

stalled at discharge port of mechanical

booster pump. [Taken with per-

mission from R. Thees, Vacuum V, 25

(1955).]


Fig. 5-20. Mechanical booster pump, backing pump, and bypass connection.

5-12. Vapor Compressor Action of a Mechanical BoosterPump. As was emphasized in the discussion of the pumping-speedcurves, the pressure measured and referred to throughout in this

connection is the partial pressure of the permanent gas which is admittedin controlled and measured amounts at the inlet of the pump. This

procedure is justified on the grounds that only in terms of the pressures

at various points in the system of the gas admitted as a measured flow

at the inlet can one hope to understand the performance of a multistage

system. The condensable vapors present are generally progressing

backward through the system and therefore have nothing directly to

do with the processes by which the permanent gases are pumped.The behavior of condensable vapors originating from the sealing oil

used in the backing pump, however, is determined directly by the zero-

flow compression ratio. Since the mechanical booster pump itself canbe clean and free of sources of volatile materials, the condensablevapors of concern are those incident on the interstage side of the boosterpump. Therefore the vapor pressure on the high-vacuum side of thebooster pump will be that in the interstage region due to backstreamingfrom the forepump divided by the zero-flow compression ratio of thebooster pump.


Observations made on the performance of a mechanical booster

pump are consistent with this expectation. lonization-gauge readings

at the inlet of the two-stage system consisting of a 1,230-cfm booster

pump backed by a 130-cfm single-stage backing pump show limiting

plate currents corresponding to a pressure of 5 x 10"* torr on an air

calibration. A very small two-stage mechanical booster pump of only

30-cfm displacement backed by a conventional compound forepump

produced McLeod gauge readings of 1 X IQ-" torr or lower and un-

trapped ionization-gauge readings corresponding to 8 x 10~^ torr. Since

the true calibration of the ionization gauge for the vapor concerned is

not known, it can only be concluded that the true total pressure is

considerably below the latter value.

Another observation of interest is that the limiting pressure indicated

by an ionization gauge in a system evacuated by a mechanical booster

pump is not changed by putting dry ice in a trap situated between the

booster pump and the gauge tube. However, substituting liquid

nitrogen for dry ice in the trap results in the ionization-gauge reading

dropping to the pressure indicated by a McLeod gauge. This obser-

vation demonstrates that the vapor compression action of the mechan-

ical booster pump is such as to decrease the vapor pressure in the system

due to backstreaming from the forepump below that corresponding to

the equilibrium at dry ice temperature. Noller' confirms that the

vapor pressure "is 1 or 2 powers often lower behind the blower than it is

in front of it."

5-13. Molecular-drag Pumps. In 1912 Gaede^^ introduced a

type of mechanical pump which does not operate on the positive

displacement principle but upon the principle of im-

parting momentum to gas molecules preferentially

in the direction of the desired flow. In the molec-

ular-drag pump there is an open passage from the

inlet to the outlet, between which a pressure difl'er-

ential is maintained by the high-velocity motion of

one side of the passage relative to the housing of

the pump in which the inlet and outlet are located.

In Fig. 5-21 the principle of the molecular-drag

pump is illustrated. A cylindrical member rotates

within a casing with a radial clearance h between

them. At the top of the cylinder the clearance space

is blocked by a projection of the cylinder wall which reduces the clearance

locally to essentially zero. At either side of the projection the clearance

passage opens into a closed volume. If there are no leaks in the system

the total amount of gas in the system remains constant, but some gas is

shifted by the motion of the rotor with a reduction of the pressure Pj

Fig. 5-21. Prin-

ciple of the molec-

ular-drag pump.


y//////////////A^7>my//.

and increase in the pressure P^. The equiUbrium relationship between

P^ and Pa depends upon the rotational velocity of the rotor and upon

the pressure regime in which the pump is operating, i.e., whether

viscous or molecular flow is involved in the process.

If the average pressure Pav = (Pi + P-Sl"^ is large enough so that

the mean free path of the gas molecules A < A, then the process is

dominated by viscous behavior. Assuming that the layer of gas at

each surface is at rest with or moving with the surface, then the gas in

contact with the outer cylinder is at rest and that in contact with the

rotor is moving with the peripheral speed rw, in which r is the radius

and w is the rotational speed in

radians per second. If A < r, the

curvature of the annular space can

be ignored and the problem re-

duced to that oftwo plane surfaces

separated by a distance A, with

the upper surface moving with

respect to the lower surface with

velocity v = rio, as illustrated in

Fig. 5-22. The peripheral dis-

tance between the inlet and outlet in Fig. 5-21 is L, which is the length

ofthelower or stationary plate in Fig. 5-22 in the plane case.

Following a procedure analogous to that in Sec. 2-3, the gas contained

in a thin layer of thickness by at height y above the stationary plate,

and of length bx in the direction of the motion, experiences a force

opposite to the direction of motion of the upper plate given by the cross-

sectional area w by, where w is the width of the plates perpendicular

to the plane of the figure, multiplied by the pressure difference bP

which occurs in the distance bx, so that

Fig. 5-22. Plane representation of the

molecular-drag pump.

F =wbP by (5-43)

At equilibrium this force is balanced by the difference between the

viscous forces from the gas above and below the thin layer under

consideration. The component of viscous force from the gas below

the layer can be written by reference to the definition of viscosity given

in (1-54) as

F, = -.,^s'^=-yjwbx[^^^ (5-44)dy

in which u is the velocity of the gas in the sample layer, since the area

S = w bx. The negative sign arises since the gas below the sample

layer is moving more slowly and therefore retards its motion. The


viscous force from the gas above the sample layer is

F

207

(du\TjW 0X1—-I

\dy/y+dy

= rjW bx-—\udu

dy ^y) (5-45)

Equilibrium will occur when the force due to the pressure difference

given in (5-43) balances the sum of the viscous forces in (5-44) and(5-45), so that

IV bP by^F, + F,

which yields

riw bx —— bydy^

d^v __ 1 bP

dy^ 7} dx

the solution of which is of the form

u = Ay^ + By + C

(5-46)

(5-47)

(5-48)

By differentiating (5-48) twice and comparing the result with (5-47),

one finds that

2rj bx(5-49)

Since the gas in contact with the lower plate is at rest, m = at y == 0,

so that the constant C = 0. Also, since the gas in contact with the

upper plate moves with its velocity v, u = v at y == Ji. Putting these

conditions into (5-48), the result is

1 bP

2,7] bxh^ Bh

so that BV 1 ^-P,

h 2rj bx

(5-50)

(5-51)

Substituting the above values for A, B, and C into (5-48) gives for the

velocity distribution

1 ^P /v I bPir^y h 2r] bx

h y (5-52)2r] bx

which is a parabolic form.

The net volume flow of gas from the region at the pressure Pi to

that at Pj is given by integrating the flow from y = to y = h. Since


the volume flow in the layer of thickness by at the level y is wii by, the

total flow is

dV'dt v=o

wu by

Jy=0= W

Jy=i

wvh~^ Ur] bx

1 bP ^

y.2rj bx

w bP

\h 2ri bx / .

dy

h^ (5-53)

Under equilibrium conditions the pressure difference (Pj - -Pi) has

such a value that the net flow is zero. Thus from (5-53)

wvh w bP~2~ ~

12r] bx

so that bPQrjV bx

h^

(5-54)

(5-55)

If the length of the channel is L, then by integrating (5-55) one obtains

the pressure difference

f^^ 6-nv f

^

QrjvL

bx

h^

(5-56)

since the viscosity is independent of the pressure. The molecular-drag

pump operating in the regime of viscous flow is thus expected to

maintain a pressure difference between inlet and outlet under conditions

of zero flow which is directly proportional to the peripheral velocity and

the length of channel between inlet and outlet and inversely propor-

tional to the square of the channel depth. In order for this pressure

difference to give rise to a large compression ratio P2IP1, it is necessary

that P2 not be much larger than the pressure difference (P^ - Pi)-

Consider a pump in which the clearance between the outer and

inner cylinders is h = 0.2 in. = 0.5 cm, r = 4 in. = 10 cm; the

rotational speed is 10,000 rpm, so that w = 1.04 x 10^ radians/sec

and V = rm = 1.04 x 10^ cm/sec. Since for air at 20°C rj = 1.83 x 10"*

poise, the expected pressure difference is

^1 =X 1.83 X 10-* X 1.04 X 10* X 50

0.25

2.28 X 103 X 750 X 10-«

= 2.28 X 10^ /xbar

1.71 torr

assuming a distance of 50 cm between inlet and outlet ports m the


cylinder. The compression ratio P2IP1 for the pump described above

would not become large, therefore, unless the outlet pressure were only

slightly greater than 1.71 torr. The simple molecular-drag pump here

described is therefore effective only as the first stage of a two-stage

system in which the interstage pressure is fairly low. By decreasing

the depth of the pumping channel h, the pressure difference maintained

by the pump in the viscous-flow regime, and therefore also the backing

pressure required for a large compression ratio, can be substantially

increased since the pressure diff'erence depends inversely on h^.

If the molecular-drag pump is backed by a pump which maintains

the interstage pressure P^ at such a low value that the mean free path

of the gas molecules is long compared with the dimension h of the

pumping channel, viscosity no longer plays a role and the relationship

(5-56) between the inlet and outlet pressures no longer holds. In this

regime the gas molecules collide alternately with the stationary and

moving surface. Consider the flow across an element of length bx

of the channel. 12 Each molecule which strikes the moving surface of

area w bx receives drift velocity equal to v, the velocity of that surface.

Each molecule which strikes a stationary surface, either opposite to

the moving surface or at the two sides of the channel, receives a

zero-drift velocity. The resulting average drift velocity is the velocity

of the moving surface times the ratio of the area of this surface to the

total surface of the channel element of length bx,

wv" 2(w + h)

The flow due to this drift motion is

(5-57)

Qa ^^-^^^^

= 5X 10-«P-

IV%V

2{w + h)

w%vh

torr cm^/s^c

torr liters/sec (5-58)

If a pressure difference bP is produced by the above pumping action,

a flow will occur in the opposite direction because of this pressure

difference through the conductance of the channel. The counterflow

is given by

34.4/ T\'^ w%2 ^p

2{w + h) bx

9 71 — torr liters/ sec (5-o9)

\M/ w + h bx


by reference to (2-79) and (2-80). Under equilibrium conditions with

no flow into the system Q^ = Q^, so that

9-^1 hr7 7— = 5\MJ w + h dx

10* Pw%vw

ordP _5x lO-^i^V

~P~~

9.71 \t} hdx (5-60)

Integrating this expression from P = P^ to P = P^ and x = to

X = L, the result is

InP,vL

\nP^=k—h

or

where

PP

kT~\t)

5 X 10-

(5-61)

(5-62)

Thus if the pressure P^, is sufficiently low that the flow is molecular,

the compression ratio maintained by the simple molecular pumpdescribed above is independent of the pressure and depends exponen-tially on the quantity vLjh, which is made up of the parameters of the

pump.For air at 20°C the constant (T/Jf)'^ = 3.181

kio-« 1

9.71

so that (5-61) then becomes

P

(3.181)1,62 X 10-5

Y =exp(l.62 X 10-s^j

(5-63)

(5-64)

Taking as an example the same values for v, L, and h as before for the

parameters of a pump,

vL _ 1.04 X 10* X 50

T ^(15

1.04 X 10"

so that the compression ratio for air should be

P2/P1 == exp (1.62 X 10-5 X 1.04 x lO")

= exp (16.8) = lO'-^"

which is surprisingly large.


From the foregoing calculation the zero-flow compression ratio for

a simple molecular-drag pump is predicted to be so very large whenoperating in the molecular-flow regime that the limitation in a real

pump is due to factors not specifically considered. In the simple

pump described, leakage from the outlet region back into the inlet

through the clearances at the ends of the rotor and the imperfect

sealing between the rotor and cylin-

der, where the radial clearance is

assumed to be zero, would prevent

the attainment of the theoretically

predicted compression ratio. Even

so, Gaede reports and Dushman^^

confirms compression ratios of the

order of 10^ attained by a multistage

molecular pump based upon the prin-

ciple of the simple design described

above.

A number of alternative designs

for molecular-drag pumps have been

devised with two considerations in

mind. The first is to ensure a low

conductance leakage path from out-

let to inlet through the running clear-

ances of the pump. The second is

to vary the depth of the pumping

channel to provide a decreasing

channel depth as the gas is com-

pressed so that the cross section of

the channel at the inlet of the pumpwill be as large as possible to ensure

good pumping speed, but still to

ensure that this depth will be small

relative to the molecular mean free path over as much of the com-

pression range of the pump as possible. In Fig. 5-23 is shown a cross

section of a design due to S. Siegbahn^* in which pumping channels

in the form of Archimedes' spirals are cut in the two flat sides of the

housing, within which a disk rotates at high rotational velocity. The

clearance between the disk surface and the flat section of the end

plate between the adjacent spirals is made as small as practicable for

free rotation. The inlet is at the periphery of the disk and the dis-

charge at the hub. In the unit shown, three spiral grooves are cut

in parallel, starting 120° apart, providing three times the pumping

speed of a single channel.

Fig. 5-23. Cross section of molecu-

lar-drag pump design due to S.

Siegbahn with pumping channels in

the form of Archimedes' spirals cut

in the two flat sides. [Taken with

permission from S. Von Friesen,

Rev. Sci. Instr. 11, 362 (1940).]


Fig. 5-24. Molecular pump of Williams and Beams. Rotor is suspended magnet-ically and driven by induction. [Taken with permission from C. E. Williams andJ. W. Beams, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962).]

Because the computed compression ratio for a pump of this descrip-

tion is tremendous when the internal leakage is ignored, the pump acts

as though it has a forward pumping speed which is independent of the

pressure shunted at intervals of pressure between Pj and Pj t>y leakage

conductances. Examination of this model leads to the conclusion that

the zero-flow compression ratio should have the form

- = exp ^'iri (5-65)

in which w is the rotational velocity, A; is a constant for the particular

pump design, and a is the clearance between the rotating disk and the

end plates through which the internal leakage flows. In comparingthis expression with (5-64) it must be realized that a in this expression

represents the internal leakage clearance, whereas the h in (5-64)

corresponds to the depth of the pumping channel.

The pumping speed of a pump of this description with disk diameterof 54 cm is reported by Eklund^^ to be as high as 80 liters/sec at 8,300rpm and to increase proportionally with the rotational speed. The inlet

pressure P^ was reported by Eklund to depend upon the forepressure


Pj according to

Pi cP,

where Pq was the lowest pressure attainable and c is a constant of the

order of 10^^.

The performance of a pump somewhat analogous to that of Siegbahn

(see Fig. 5-24) is described by Beams.^^ The rotor in this case is

suspended magnetically and driven by induction through the vacuumwall, eliminating the problems of shaft seal and material bearings.

Peripheral speeds of the order of 1.4 x 10* cm/sec, which is about

one-third Vav for air molecules at room temperature, are typical for the

preliminary model tested." Since the unit is completely sealed and is

Ijacked by an oil diffusion pump with a liquid-nitrogen-cooled trap,

the forepressure can be very low. A composite curve of the observed

compression ratio P2/P1 for various values of the forepressure Pg and

the rotational speed is shown in Fig. 5-25.1^ A theoretical curve for the

compression ratio as a function of rotational speed is shown for com-

parison. It is evident that P2/P1 departs further from the theoretically

predicted value as the forepressure Pg is decreased, indicating the

influence of outgassing from surfaces at the lower values of Pj attained

during the test. As an example, with a forepressure of 4 x 10"' torr

the untrapped ionization-gauge reading at the inlet was 2 X 10"* torr,

yielding a compression ratio of only 200 compared with the predicted

value of nearly 3,000 for 01/277 equal to 225 rps. Results of these tests,

10-^

10

P310-

olxlO'^torr / ,--©'

A 6x10"^ / ,-'-' 1.2x10

-''

s 4x10-^

X6xl0"^

y:° ,-'-^9'xio>^Theoretical

mass 30 y^'^^'\,''^''^^^^y^<''5<'^^ 4«10-'"

X^?-: ^^^^

- jk:> Theoretical moss 8

/^'^y^

/•1 1 . 1 . 1 1

100 200 300 400

27r

Fig. 5-25. Composite curve of observed compression ratio for various values of

the forepressure and the rotational speed. [Taken with permission from C. E.

Williams and J. W. Beams, in ld6l Vacuum Symposium, Transactions (PergamonPress, London, 1962).]


including variation of the rotational speed and of the forepressure,

indicate that the zero-flow compression ratio is only in very rough

agreement with (5-65), although the deviations may be due entirely to

outgassing.

Some advantages claimed for the molecular-drag pump are freedom

from contamination by condensable vapors, high compression ratios,

and short startup time. One additional feature which is useful in someapplications is a higher pumping speed for gases of high molecular

weight, which is the inverse of the performance of diffusion pumps.One obvious disadvantage is the low pumping speed, considering the

size and complexity of the device. There is also a very real hazard

associated with rotational speeds of 10^ rpm and more, which are

required to ensure good performance. Although molecular-drag pumpshave proved to be effective in certain special applications, particularly

in Europe, they have not been widely used in the United States, either

for industrial or for scientific applications.

5-14. Axial-flow Molecular Turbine Pump. Brief mention

must be made of a type of molecular pump introduced in 1958 byA. Pfeiffer, GmbH, of Wetzlar, German Federal Republic, which maybe described as an axial-flow molecular turbine pump.^' Figure 5-26

shows the general arrangement of

the pump, and Fig. 5-27 illustrates

the details of the design. Rotating

disks all mounted on the central

shaft are disposed alternately with

stationary plates mounted in the

housing. The disks and plates are

cut with slots set at an angle so

that gas molecules caught in the

slots of the moving disk are pro-

jected preferentially in the direc-

tion of the slots in the stationary

plates. The running clearances be-

tween the rotating and stationary

plates generally are of the order of

1 mm, which is an order of magnitude greater than the permissible

clearances in a conventional type of molecular pump. The rotational

speed for a pump having a rotor diameter of about 17 cm is 16,000

rpm, giving a peripheral speed of 1.56 x 10* cm/sec, about one-third

Wav for air molecules at room temperature.

The observed dependence of the inlet pressure P^ on the outlet

pressure P^ is shown graphically in Fig. 5-28 for hydrogen, air, and therefrigerant Freon-12. A compression ratio P2/P1 of the order of 10'

Fig. 5-26. General arrangement of

the axial-flow molecular turbine

pump. [Taken with permission fromWilli Becker, Vakuum-Technik 7, 149

(1958).]


is obtained for air when Pj is equal to 0.1 torr, but the value drops off

rapidly with increasing pressure to about 10 when Pj is equal to 1 torr.

The compression ratio for hydrogen is significantly smaller for the sameoutlet pressure.

Fig. 5-27. De-

tails of the rotor

and stator plates

of the molecular

turbine pump.[Taken with per-

mission fromWilli Becker,

Vakuum-Technik7, 149 (1958).]

io''i 1 nil 1 nil 1III

1 nil: = : 1

10-2:=: = = .1 J = =

'-'-'- ==^ ?=::::10"' - 3 -

-^H ;=:|-:10-^::=

-J =4 =:--^^--

'---izl:Kf'-^' : = -. == :== =

--

° 10-' = -: :--: -. 1— - = :

- = = :: = = :=:;:= = ::

10-'::;;:=: .!_.-- '--

l-\zz-.10-8=-:: = -= t-.: -=-.

' hxi 1 •eoi-2]

io-'::;i:Z:;;|=;;:=:

^,o~~V" ::::::r'° A .1

10-' 10'^ I0-' 1 10

P2,torr

Fig. 5-28. Observed de-

pendence of inlet pres-

sure on outlet pressure

for hydrogen, air, andthe refrigerant Freon-12

for the molecular tur-

bine pump. [Taken

with permission fromWilli Becker, Vakuum-Technik 7, 149 (1958).]

The pumping speed of the molecular turbine pump as a function of

the inlet pressure P^ is shown in Fig. 5-29 for the same three gases.

The pumping speed characteristic of the forepump used in these tests is

not given in the paper so that the relationship between the curves in

these two graphs is not clear.

The pumping characteristics of an axial-flow, bladed turbine pumphave been investigated theoretically and experimentally by Kruger^"

and by Kruger and Shapiro. ^^ A portion of the vane structure of a

rotor of the type used in the high-vacuum turbine pump is shown in

Fig. 5-30, illustrating the probability of transmission of molecules


700

600

500

400

300

200

100

Ha

Au.

Freon-12

I10-' 10"^ 10"' IQ-" 10"^

P,, torr

10"^ 10- 10-

FiG. 5-29. Pumping speed of the molecular turbine pump as a function of the

inlet pressure for hydrogen, air, and Freon-12. [Taken with permission from

Willi Becker, Vakuum-Technik 7, 149 (1958).]

through the rotor blade for the case in which the blade speed is large as

compared with molecular speed (a) when the molecules are incident

from upstream (side 1), and (6) when they are incident from downstream

(side 2). The difference between these probabilities, S12 and S21.

determines the net pumping speed. If we designate by H (the Hocoefficient) the ratio of the net molecular flow through the rotor to the

^Molecules incident

from side (T)

Fig. 5-30. Probability of transmission of molecules through the rotor blade of anaxial-flow turbine pump for the case in which the blade speed is large as comparedwith molecular speed, {a) Molecules incident from upstream; (b) molecules

incident from downstream. [Taken with permission from C. H. Krugor and A.

H. Shapiro, in 1960 Vacuum Symposium Transactions (Pergamon Press, London,1961).]


molecular flux v^ incident on the area A of the rotor blade from up-

stream, then the net flow in molecules per second is

Q = HAvy = Avj:^^ - J-VaSai

where v^ is the molecular flux incident from downstream,

the temperature is the same on both sides of the rotor,

"1 «i ^1

(5-66)

However, if

(5-67)

from Eqs. (1-31) and (1-16), where n^ and n^ are the molecular densities

and Pi and Pj the pressures respectively upstream and downstream.

Then from (5-66) and (5-67), the compression ratio is given by

^1 ^21(5-68)

and the zero-When the flow through the pump is zero then Hv^

flow compression ratio is

J) =^ (5-69)vPi/e=o 2.21

It is also evident that the compression ratio across the rotor blade

should decrease linearly as the flow Hv^ is increased. This prediction

has been confirmed experimentally by Kruger and Shapiro. ^^ Also

from (5-68) it appears that for no pressure rise across the blade, Pj = Pi,

the net flow through the rotor blade is

Qi (S12 — ^2\)A (5-70)

In order for the compression ratio to be high it is important that Sia

be large compared with Hji. However, for the pumping speed

[8 = QjP) to be large it is necessary for S12 to be large in an absolute

sense.

According to Kruger and Shapiro, ^^ in the design of a multistage

pump of the axial-flow turbine type it is possible to design the blades

of the first few rotors for large pumping speed and low compression

ratio and later stages increasingly for high compression ratio and low

pumping speed. The increase in pressure toward later stages permits a

lower pumping speed to accommodate the flow. By carrying out a series

of Monte Carlo calculations of the motion of individual molecules

through rotor blades, Kruger20 has determined the compression ratio

and pumping speed for rotors with various values of the pitch angle,

spacing, and length of the blades. To be effective the velocity of the

rotor blades must be two or three times the quantity (27^T)'^, but

increasing the blade velocity beyond this value does not result in a


significant gain in performance. Although variation of the pitch

angle varies the zero-flow compression ratio and pumping speed, a

pitch angle of 20° appears to be a good compromise for many applica-

tions. Since a compression ratio per stage of about 5 can be achieved,

a pump having 9 stages should maintain a zero-flow compression ratio

of the order of 5" <=« 2 x 10''. The pumping speed of a well-designed

axial-flow turbine pump is comparable with that of a diffusion pumpof the same diameter but has the advantage of being free of hydro-

carbon vapors. The disadvantages of the axial-flow turbine pump are

(1) the hazard of very high rotational speeds, (2) the comparatively

great weight for the pumping speed, and (3) the very high cost in terms

of dollars per liter per second.

REFERENCES

1. W. Gaede, Z. Naturforsch. 2A, 233 (1947).

2. B. D. Power and R. A. Kenna, Vacuum V, 35 (1955).

3. F. A. Knox, U.S. Patent No. 2,551,541, May 1, 1951. NSA 5, No. 3578.

4. C. M. Van Atta and R. L. Sylvester, in Proceedings of the Vacuum MetallurgySymposium of the Electrochemical Society, Boston, Mass. (Electrochemical

Society, Inc., 1955), p. 86.

5. C. M. Van Atta, in 1956 Vacuum, Symposiwm Transactions (Pergamon Press,

London, 1957), pp. 62-70.

6. K. Ziock, Vakuum-Technick (Rudolph A. Long Verlag, Berlin, 1957).

7. E. A. Winzenburger, in 1957 Vacuum Symposium Transactions (PergamonPress, London, 1958), pp. 1-5.

8. Z. C. Dobrowolski, Lab. Rep. No. 2290, Kinney Vacuum Division, The NewYork Air Brake Company, Dec. 20, 1961.

9. H. G. Noller, in 1956 Vacuum Symposium Transactions (Pergamon Press,

London, 1957), pp. 57-61.

10. R. Thees, Vacuum V, 25 (1955).

11. W. Gaede, Ann. Physik 41, 337 (1913).

12. Robert B. Jacobs, J. Appl. Phys. 22, 217 (1951).

13. Saul Dushman, Phys. Rev. 5, 224 (1915).

14. S. Von Friesen, Rev. Sci. Instr. 11, 362 (1940).15. S. Eklund, Arch. Math. Astron. Phys. (Roy. Swed. Acad.) 27A, No. 21 (1940),

and 29A, No. 4 (1942).

16. J. W. Beams, Science 130, 1406 (1959).

17. C. E. Williams and J. W. Beams, Bull. Am. Phys. Soc. Ser. II 5, 286 (1960)'.

18. C. E. Williams and J. W. Beams, in 1961 Vacuum Symposium Transactions(Pergamon Press, London, 1962), pp. 295-299.

19. Willi Becker, Vakuum-Technik 7, 149 (1958).20. Charles H. Kruger, "The Axial-flow Compressor in the Free-molecular

Range," Ph.D. Thesis, Department of Mechanical Engineering, MassachusettsInstitute of Technology, Cambridge, Mass., 1960.

21. Charles H. Kruger and Asoher H. Shapiro, in 1960 Vacuum SymposiumTransactions (Pergamon Press, London, 1961), p. 6.

CHAPTER 6

VAPOR-JET VACUUM PUMPS

6-1. The Steam Ejector. Since the effectiveness of the steam-jet

ejector in evacuating large volumes down to pressures of the order of

about 1 torr was first demonstrated by M. Leblanc,i* steam ejectors

have been used successfully in a wide variety of rough vacuum appli-

cations. A typical steam ejector is illustrated in Fig. 6-1 and consists

of (a) a steam chest in which the pressure and temperature are main-

tained at the proper values, (6) the nozzle through which the steam

flows to form a jet, (c) the mixing chamber through which the steam

jet passes and entrains gas admitted to the chamber through {d) the

inlet port, and (e) the diffuser through which the jet carries the

entrained gas to (/) the discharge. Under normal operating conditions

the pressure in the mixing chamber is very low as compared with that

in the steam chest and at the discharge port so that the steam is

expanded in passing through the nozzle by a large factor and then

compressed in passing through the diffuser. Since the cross-sectional

area of the steam chest is large as compared with that of the nozzle,

the directed or drift velocity in the steam chest is small as compared

with that through the nozzle. The random energy of thermal motion

of the steam is therefore converted in passing through the nozzle into

directed kinetic energy with the formation of a supersonic jet, i.e.,

one in which the directed velocity of flow is large as compared with the

average random velocity of the molecules determined by the tempera-

ture.

The flow of steam from the steam chest, through the nozzle and

mixing chamber, and out through the diffuser is a special case of the

flow of a compressible fluid through a tube of varying cross section.

Thermodynamic analysis of the flow through a converging-diverging

nozzle, assuming isentropic behavior (no heat exchange with the walls,

that is, PV^^ = Pjpi = const), leads to two specific results. If Pj is

the pressure upstream from the nozzle, P^ the pressure at the throat

* References indicated by sviperscript numbers are listed at the end of the

chapter.

219 '^


of the nozzle (the point of minimum cross section), and P^ the pressure

downstream from the nozzle,

1. The flow through the nozzle increases with decreasing pressure

P3 beyond the nozzle until a critical value P^ is reached beyond whichthe flow is independent of P3 and P^ = P^-

2. The flow velocity at the throat of the nozzle is Mach 1, that is,

is equal to the local sound velocity,

when P3 < Pj.

Steam inlet

Mixing

chamber

The calculation shows that

\r + 1/

v/(,-l)

Discharge

Fig. 6-1. Cross section of typical

steam ejector. [Taken with per-

mission from V. V. Fondrk, in 1957Vacuum Symposium Transactions


1^1/ ^1 (^-^)\y + 1/

for the pressure at the throat as long

as P3 < Pj. If the gas flowing

through the nozzle is a perfect dia-

tomic gas for which y = 1.40 (see

Table 1-4), the result is P, =O.535P1. However, for steam y =1.32 and thus for steam sufficiently

superheated so that condensation

does not occur in the throat, P^. =O.545P1. For steam not sufficiently

superheated, however, condensation

does occur and the effective value of

y is such that P^ == 0.575Pi, approxi-

mately.

Associated with the critical flow

pressure P^ is the flow velocity v^

at the throat of the nozzle. This

velocity is given by

2y P,

y Pi

-©'(i-i)/y-l

•(6-2),

where p^ is the density of the gas

upstream from the nozzle (e.g., of the steam in the steam chest). Byreference to (6-1) the stream velocity at the critical pressure is given by

2y Pj 2yPiFi (6-3)

y + I Pi y + I

where V^ = l/p^ is the specific volume in cubic centimeters per gram.

VAPOE-JBT VACUUM PUMPS 221

According to (1-28) the velocity of sound in the gas at the nozzle

throat under critical flow conditions is given by

y—Pc

2y Pi

r + 1 Pi

Thus v^lVgj = 1 and the flow at the throat is Mach 1.

Since the flow is isentropic,

'pU/y / 9 \l/(y-l)

(6-4)

/PX'' I 2 V'' '

again by use of (6-1).

The mass flow rate through the nozzle is

dW = cp.v^A^dt

-cp,v,D^^ g/sec

(6-5)

(6-6)

where D^ is the diameter of the nozzle at the throat in centimeters andc is the nozzle coefficient, which is a number generally in the range of

0.95 to 1.0, depending upon the geometry of the nozzle and the flow

conditions (particularly the Reynolds number). By substituting (6-3)

and (6-5) into (6-6) the critical flow rate is

~dt

Since for steam the average value of y = 1.30, the mass flow for steam

through a converging-diverging nozzle is

d.W,

"df0.524c

(9P'g/sec (6-8)

when Pi is measured in /^bars (dynes per square centimeter), V^ in

cubic centimeters per gram, and Z>2 in centimeters. If the pressure

Pi is measured in torr, this expression becomes

dW^

dt19.14c Elf

vjD, g/sec (6-8a)

Finally, if as in most engineering applications Pi is in pounds per

square inch, V^ in cubic feet per pound, and D^ in inches, the expression

becomes

dW, /PiV^

dt892.6cm Ib/hr (6-86)

From the steam conditions upstream from the nozzle the mass-flow

rate may be calculated approximately from (6-8a or 6-86) by assuming

that c = 1. Engineering steam tables give values for the specific


volume Vi as a function of temperature and pressure, which is all that

is needed to carry out the approximate calculation. A more precise

determination of steam-flow rate can he made by using the procedure

outlined in Standards for Steam Jet Ejectors published by the HeatExchange Institute, pp. 18-34. In Fig. 6-2 is a graph taken from this

publication showing the steam flow

through a 1-sq-in. nozzle throat

area for a nozzle coefficient c = 1

and a range of steam conditions.

Additional curves of this type as

well as the procedure for determin-

ing the value of the nozzle coefficient

are given in the reference.

As an example, for the steam

conditions given as

Pj = 4 atm = 58.8 psia

Ti = 508°K = 454.6°F

the steam tables give

Fi = 9.06 ft3/lb

13

12

11

10

9

8

7

6

5

4

3

2

1

n

oSaturation w^

T~4

3tal

00°remperature-

"~i¥

s ~ h1

/ f^V'

50frv^^'^

600° F-4^^O — ^f ^700°

F

^ 800° F

s s Am ho 0°F

E A^ lUU U''F

/^fr

20 40 60 80 100 120 140 160 180

Pressure, psig

Fig. 6-2. The critical mass-flow rate

for steam through a convefging-

diverging nozzle of 1 sq in. throat

area assuming a nozzle coefficient of

1.00 for the pressure range to 620

psi gauge pressure (14.7 to 634.7

psia) for steam temperatures up to

1000°F. [Reprinted from the Stan-

dards for Steam Jet Ejectors, 3rd ed.

Copyright 1956 by the Heat Ex-

change Institute, 122 East 42nd

Street, New York, X.Y. 10017.]

SO that according to (6-86) the flow

rate through a nozzle of 1 sq in.

throat area for which

£>, =^. in.

IS

dW,

~df2,900c Ib/hr

in which c is a number slightly less

than 1.

Beyond the throat the ejector

nozzle must diverge sufficiently to

allow for the expansion of the steam in its free expansion from the

pressure P^ = P„ at the throat to the design value for the pressure in

the mixing chamber where gas at pressure Pg is to be mixed with the

steam jet and pumped out through the diffuser. The external pressure

on the steam jet as it traverses the mixing chamber is P^, the inlet gas

pressure, which at the design point for the system is just balanced by

the transverse pressure in the steam jet because of the random thermal

molecular motion. Since in practice the design inlet pressure is quite

low, the intrinsic pressure in the steam jet is also low, corresponding

to a low temperature frequently well below the freezing point. The

VAPOB-JET VACUUM PUMPS 223

large random molecular energy of the steam in the steam chest is

converted by the converging-diverging nozzle into very low randomenergy plus a high directed energy. Since the drift velocity is then

large as compared with the random molecular velocity, the jet stream

in the mixing chamber has a high Mach number, typically in the range

2 to 4. Because the temperature of the steam jet is low in the mixing

chamber, the vapor pressure is also very low as compared with that at

room temperature, so that the water vapor pressure seen at the gas

inlet port is correspondingly low.

When the steam jet enters the difii'user, a process of isentropic

compression occurs. The steam together with the entrained gas being

pumped through the inlet port is compressed from the low pressure in

the mixing chamber to the exhaust pressure. The maximum exhaust

pressure attainable is that for which the flow velocity of the steam

jet is completely converted to random velocity. The design of the

diffuser and the imposed steam conditions must be such that this

minimum requirement is met. Otherwise the jet will be unable to

sustain the pressure differential and will break down, allowing exhaust

gas to flow back through the system.

The pumping speed of a steam ejector is a sensitive function of the

design of the nozzle and diffuser. The design of the nozzle is based

upon sound thermodynamic principles and can be specified with

considerable precision for a given set of requirements. The design of

the diffuser is much more empirical, for which experience in a great

variety of industrial vacuum applications provides a sound basis for

predicting performance. The pumping capacity of a steam ejector

is generally given in terms of the number of pounds of dry air removed

in one hour (lb air/hr). Since

Pair (760 torr and 20°C) = 1.205 x IQ-^ g/cm^

= 7.52 X 10-2 ib/ft3

1 lb dry air (68°F = 20°C) = 13.31 ft^ at 760 torr

and 1 lb dry air (68°C)/hr = 168.5 torr cfm

= 79.5 torr liters/sec

The capacity of a typical single-stage steam ejector as a function of

the inlet pressure is shown in Fig. 6-3, and the corresponding pumping

speed in Fig. 6-4.

^

For high-vacuum pumping, steam ejectors are used in multiple

combinations, such as the three-stage system illustrated in Fig. 6-5.

^

A water-cooled condenser is placed between the second and third

stages to decrease vapor load on the final stage. In such a system the

first two stages are referred to as booster stages, in which the steam

conditions are such that very low temperatures are reached by the


50 100 200 500 1,000


Fig. 6-3. Capacity of a typical single-

stage steam ejector as a function of

inlet pressure. [Taken with per-

mission from V. V. Fondrk, in 1957



120

100 / ^80 / s

/ *•>,

60 /f

40 )

1

201

/

^

20 50 100 200 500


1,000

Fig. 6-4. Pumping speed of a typical

single-stage steam ejector as a func-

tion of inlet pressure. [Taken with

permission from V. V. Fondrk, in

i957 Vacuum Sym,posium, Transac-

tions (Pergamon Press, London,

1958).]

Suction chomber

Steom inlet

Third stage

Discharge

Intercondenser

Water dischorqe

Fig. 6-5. Layout of three-stage steam ejector system. [Taken with permissionfrom V. V. Fondrk, in 1957 Vacuum Symposium Transactions (Pergamon Press,

London, 1958).]

VAPOR-JET VACUUM PUMPS 225

steam-water or steam-ice jet as it leaves the nozzle so that the vaporpressure of water from the jet is correspondingly very low. Theultimate vacuum attainable with steam ejector systems is consequently

surprisingly low as compared with the vapor pressure of water at roomtemperature (17.5 torr at 20°C). Multistage steam ejector systems

may consist of as many as seven stages with interstage condensers

after the first two or three stages. With such systems base pressures

as low as 10^^ torr are attainable with capacity of the order of 6 Ib/hr

of dry air or pumping speed of 100,000 cfm at 10~^ torr.

4-stage steam ejector

system tor hondling

gases at I torr

evolved from pour at

4-tons/min

Common surtace

condenser (C) servmg

4 2-stage units (8, ,82)

2-stage steam

ejector evocuatinq

common surface

condenser (C)

4 2-staqe steam ejectors

'B|, Bj) parallel for

reducing pressure to

I torr and handling goses

of pouring rote 4 tons/min

of I torr

v4 t2-in diophragm volves(V|l

hogging steam

ejectors (A)

62N62 range

30 to V2 torr

in 2 min

6-ia diophragm

volve (Vj'

Fig. 6-6. Schematic arrangement of four-stage, series-parallel steam ejector

system.


For economy and flexibility in operation, steam ejector systems mayconsist of several booster ejectors in parallel, backed up by one or two

final stages. In the system illustrated in Fig. 6-6 there are four two-

stage boosters in parallel, backed by two final stages with interstage

Table 6-1. Perfobmance of Four-stage Steam Ejector System Shown in

Fig. 6-6

InletCapacity,

lb air/hr

Throughput Pumping speed

torr torr cfm torr Hters/soc cfm liters/sec

0.140

0.280

0.500 (design)

0.580

0.775

1.000

1.0

2.5

3.0

4.0

5.0

169

421

505

674

843

80

199

238

318

397

604

842

871

870

843

286

398

411

410

397

condensers. The performance of this four-stage multiple ejector

system is shown in Table 6-1 and shown graphically in Fig. 6-7 and

Fig. 6-8. The inlet pressure for which the system was designed was

0.500 torr as indicated in the table.

900

800

g 700yy

/y "-600

cu

S.500

//

,|'400

// §300

D-

200

// 100

5.0

4,0

3.0

2.0

1,0

01 0.2 03 04 Q5 06 0.7 0.8 09 1.0

Inlet pressure.torr

Fig. 6-7. Capacity of four-stage

steam ejector system shown in Fig.

6-6.

423

400

350 „

300"^

250:|

200 S

150 g'

100 IQ_

50

o'or 02 03 0.4 05 0.6 07 0.8 0.9 1.0

Inlet pressure.torr

Fig. 6-8. Pumping speed of four-stage

steam ejector system shown in Fig. 6-6.

^1 —•—r-'

//

J/

1

/

LL ;1401 1

As the inlet pressure is raised, the throughput of a steam ejector

system increases and the discharge pressure at each stage is correspond-

ingly increased. A limit is reached when the discharge pressure in oneof the interstage regions equals the maximum which the steam canattain in the diffuser during compression. If the flow is increased


beyond this critical value, the jet collapses in one of the stages with the

result that discharge gas and steam flow back through the system into

the vacuum vessel. The steam conditions and load must be regulated

in such a manner as to avoid this type of blowback since the conse-

quences in most cases would be serious.

The problem of backstreaming of water vapor into the vacuum vessel

does not present a serious problem unless the flow of gas from the

vacuum vessel to the mixing chamber falls off to a value which is

considerably less than the design point for the system. However, at

zero throughput serious backstreaming will occur. It is sometimes

necessary to provide means for introducing air, steam, or other gas

at a controlled rate into the system between the steam ejector inlet

and the vacuum vessel through a needle valve to prevent the inlet

pressure from dropping to the point where backstreaming would

become serious.

Steam ejectors operate generally in the pressure range of single-stage

mechanical vacuum pumps. However, for processes involving the

evolution of large amounts of water vapor (as vacuum cooling or

dehydrating), steam ejectors usually have a distinct advantage in spite

of a high rate of consumption of steam. For processes in which

corrosive gases must be pumped, ejector systems lined throughout with

graphite or other corrosion-resisting material are used. The nozzle

and diffuser parts can be made of any material which can be machined

or ground with precision.

6-2. Diffusion Pumps. The term diffusion pump is normally

applied to jet pumps which utilize the vapor of liquids of comparatively

low vapor pressure at room temperature and which provide base

pressures significantly lower than those easily attainable with oil-sealed

mechanical vacuum pumps. The development of the modern diffusion

pump has a complicated history which is too involved to trace in

detail. Those interested should refer to Dushman's book^ for the

contributions of Gaede and Langmuir to the invention respectively of

the diffusion pump and the vapor-condensation pump, from which

beginnings the modern diffusion pump descended.

The cross section of a typical diffusion pump is shown in Fig. 6-9.

Such a pump normally consists of a cylindrical housing within which

is a jet assembly and at the bottom of which is a boiler for the work-

ing fluid. The nozzles which form the jets are generally annular and

arranged so that the vapor streams from them are directed downwardand outward. The housing, particularly in the region where the vapor

jets impinge, is cooled to ensure condensation. The vapor from the

boiler passes up through the chimney formed by the jet assembly and

out through the annular slits, which act as nozzles for directing the

228 VACUUM SCIENCE AND ENgAbEBING

vapor streams. Gas entering the pump at the inlet is given momentumdownward by the vapor streams and forced out the discharge, where

an appropriate forepressure is maintained by a backing pump, usually in

the form of an oil-sealed mechanical vacuum pump. The annular space

between the jet assembly and the housing must be completely sealed

by vapor at sufficiently high pressure so that the back pressure from the

discharge cannot break through the jets and flow backward through

the pump inlet. For any design of diffusion pump there is a fairly

critical forepressure below which the pump is effective and above which

the pump fails because of breakdown of the jets.

Typical diffusion-pump jet assemblies consist of three or four annular

nozzles, as shown in Fig. 6-9, or three annular nozzles and an ejector

type of nozzle located in the discharge port, as shown in Fig. 6-10.

The downwardly directed vapor stream from each annular nozzle

entrains gas molecules incident from above and gives them momentumdownward toward the discharge port. Each annular jet is capable

of maintaining performance against a specific forepressure, which is

relatively low for the first jet, for which the radial clearance is large,

Fig. 6-9. Cross section of typical diffusion pump with four annular jets.


Pump inlet (low pressure) — = Pump fluid

^— ' = Gas molecules

Jet assembly

Fractionating

boiler

Electric heoter

y-. )-<-Foreline

(Pump outlet)

Foreiine c"'•

High forepressure

baffle ^;-;3

:i'u.<---::-

3

3

Fourth compression stoge

(Ejector type)

Pump fluid

Fig. 6-10. Cross section of typical diffusion pump with three annular and oneejector jet.

and relatively high for the final jet, for which the radial clearance is

small. In a pump of optimum design, the forepressure limits for the

successive jets are in regular progression. Although a great deal of

work has gone into the study of diffusion-pump design and performance,

an exact understanding of the mechanisms of jet formation, gas

entrainment, and pumping has not yet been attained.

Consider the enlarged view in Fig. 6-11 of the vapor jet issuing from

the nozzle, directed downward and radially across the annular space

between the jet assembly and the housing, and condensing on the wall.

The vapor stream cannot be regarded as a well-defined jet with a sharp

boundary, particularly if the surrounding gas pressure is very low.

The vapor stream in leaving the nozzle will tend to expand, causing

some molecules of the working fluid to acquire net upward velocities

opposite to the desired direction of flow, with the result that twoundesirable effects are introduced. The backward-directed vapor

molecules in colliding with gas molecules impart momentum in the

wrong direction so that some of the gas molecules are expelled from the

jet region and thus fail to be pumped out of the system. Also someof the backward-directed vapor molecules continue their contrary

flight upward and out through the inlet, resulting in backstreaming

of working vapor, which constitutes a major source of contamination

in vacuum systems. During the past few years significant steps have

been taken to decrease the backstreaming and improve the pumping


efficiency of diffusion-pump jets with resulting increase in pumping

speed and decrease in the rate of contamination of the system by the

working fluid.

Serious attempts have been made*"* to understand in detail the

physical processes involved in vapor-jet vacuum pumping with the

conviction that optimum design can only be realized on this basis.

There are two principal performance characteristics of vapor-jet pumps

which need to be explained. These are (1) the compression ratio P2/-P1

which the pump can maintain under conditions of zero flow and (2) the

pumping speed under conditions of steady gas flow into the inlet.

Vapor

flow

wwwwwwGas

flow

,,j||||

Fig. 6-11. Enlarged cross section of

jet issuing from diffusion-pump

nozzle. [Taken with permission from

B. D. Power and D. J. Crawley,

Vacuum IV, 415 (1954).]

Exhoust

Fig. 6-12. Cross

section of simpli-

fied jet pump.

6-3. Theoretical Compression Ratio for a Vapor-jet Pump.Based upon the original work of Gaede,* Jaekel/" and Noller' the

following derivation of the compression ratio for a single-stage jet pumpis provided. Figure 6-12 is an idealized version of a vapor-jet

pump in which everywhere below the surface a-b the cross section of the

pump barrel will be assumed to be uniformly filled with vapor movingwith a velocity U downward to the surface c-d, where the vapor is

condensed and removed. Above the surface a-b the permanent gas


pressure is Pj and the molecular density t^^ cm"". Below the surfacec-d the permanent gas pressure is Pg and the molecular density ?^2 cm-^.All gas molecules which become entrained in the vapor stream quicklyacquire the drift velocity U of the vapor. If the density of gas mole-cules entrained in the vapor is n^ cm-^, the number of gas moleculesper second and per square centimeter swept downward is n U. How-ever, since P^ is greater than P^ as a result of the pumping action,there is diffusion of gas molecules in the reverse direction given byD{dnjdy), where D is the diffusion coefficient of gas molecules in thevapor. Under conditions of zero flow these two quantities must beequal, so that

When, as in this case, the density rig of the gas molecules is very smallas compared with the density n„ of vapor molecules, then the diffusion

coefficient is inversely proportional to the vapor density and can bewritten as

D = ^ (6-10)

so thatDo drig

n^ dy

ordP~P

nJJ_

D„dy (6-11)

Integration of this expression yields

W2£1 exp(f4 (6-12)

where L is the distance from the surface a-b to the surface c-d.

Since the value of Z>„ is given approximately by the expression^

8\2/ 77(1, + |j4(6-13)

in which ^^ and |„ are respectively the diameters of the gas and vapormolecules, M^ and M^ are the molecular weights respectively of the gas

and vapor, Rj^ = 8.315 x 10' ergs/°C mole, and T^ is the temperature(°K) of the vapor stream.

As an example let us consider the case of air pumped by mercuryvapor for which the temperature in the jet may typically be about


100°C. The constants for Eq. (6-13) are then

T^ = 373°K

ig = 3.72 X 10-8 cm

1^ = 4.26 X 10-8 cm

M, = 28.96 g

M, = 200.6 g


D.4 X 10" 229.56

(8.315 X 10')(373)8 X (27t)'^ (7.98)2 L(28.96)(200.6)

= 3.32 X 10"

Since the pressure in the core of a mercury vapor jet is of the order

0.05 torr = 67 /ibar(dynes/cm2)

P, = n^kT, = 67 fih&T

in which k is the Boltzmann constant (1-14), so that

67n = = 1.3 X 10^^ molecules/cm*

" (1.38 X 10-i« X 373)

The vapor stream issuing from the nozzle, as in the case of the steam

ejector jet, is typically about Mach 1, so the velocity of the vapor would

be as given in (1-28)

in which, for mercury, y = 1.66 and

n„M„ 1-3 X 10" X 200.6

Pv = w„m^ =

giving

6.023 X 1023

U --

6.023 X 1023

/ 1.66 X 67 \^

\1.67 X 10-V

= 2.6 X 10* cm/sec

1.67 X 10-' g/cm^

Substituting the above approximate values of n^, U, and Dg into (6-12)

and taking for the length of the vapor column L = 10 cm, the exponent

in (6-12) becomes

n„U

so that

L = 1.3 X 1015 X 2.6 X 10*

3.32 X 10"

,102 _ ]^Q(102)(0.434) ^_ lO**-^

X 10 = 102

In the above crude calculation almost any reasonable set of numbersfor vapor density, pressure, and temperature in the vapor stream

results in a very large theoretically predicted compression ratio. The

calculation as presented tacitly assumes in Eq. (6-9) that the velocity

of the vapor stream U is small compared with the velocity of the gas

motectiles tiiffusing bacK through the vapor. If this were not the case,

the rate of back diffusion would be appreciably diminished by the flow

of the vapor stream and the compression ratio would be even greater

than that calculated above.

N

(c) (d)

Fig. 6-13. Configuration of a vapor jet for various values of forepressure. Oper-

ation of the vapor pump. {A) Pumping aperture; (B) nozzle; (C) nozzle aperture;

(D) vapor inlet; (E) gas inlet; (F) vapor jet; (G) pump casing; (H) water or air

cooling; (L )forepressure outlet; (M) to forepump; (JV) shock wave, (a) Fore-

pressure about 0.001 torr; (6) forepressure about 0.02 torr; (c) forepressure about

0.04 torr; (d) forepressure about 0.1 torr. [Taken with permission from N. A.

Florescu, Vacuum 10, 250 (I960).]

Florescu* approaches the analysis of vapor-jet pumping from a

somewhat different point of view from that given above. The be-

havior of a vapor jet for various values of the forepressure is illustrated

in Fig. 6-13 from Florescu's paper. When the forepressure is very low,

the jet spreads on leaving the nozzle, as shown in Fig. 6- 13a, and

completely fills the body of the pump from the pumping aperture Adown to the forepressure outlet L. The full length of the pump is

sealed against backward flow of gas which enters at E and is ejected

at L.

As the forepressure is increased (Fig. 6-136), a point is reached such

that the vapor stream no longer persists for the full length of the pumpbarrel but is terminated in a shock front as indicated at N by the

dashed line. With further increase in the forepressure the shock front

moves up close to the pumping aperture, as shown in Fig. 6-13c.

Beyond the shock front the vapor and gas densities are appreciably

greater than in the vapor stream. The molecules in the jet stream

above the shock front have net directed velocity downward, whereas

those below the shock front are randomly directed.


Further increase in the forepressure results in a change in form of

the jet stream. Since the shock front would tend to retreat further,

the result is that the vapor stream can no longer reach the walls of the

pump barrel and effect a complete seal between inlet and outlet. The

jet stream then becomes narrow, as shown in Fig. Q-I3d, and gas from

the forevacuum region can then flow freely backward past the jet

through the inlet.

Florescu then considers the case corresponding to that shown in

Fig. 6-136, in which the forepres-

sure is low enough that an appreci-

able length of the pump barrel

is filled and sealed by the vapor

stream. The vapor stream, con-

sisting of vapor molecules with

velocities directed downward in

the pump barrel, subjects the gas

molecules present in this region to

a series of impacts, driving them

downward. This action estab-

lishes and maintains a gradient

of gas concentration increasing

toward the forevacuum outlet.

Also, gas molecules entering

through the pumping aperture are

continually captured and driven

toward the forevacuum outlet by

the downwardly directed vapor

molecules. Near the pumping

aperture where the gas molecules

first encounter impacts from

vapor molecules the gas mole-

nrPressure, torr

Fig. 6-14. Density distribution of

permanent gas along a diffusion-pump

barrel from inlet to exhaust pressure

due to the pumping action of the jet.

{A) Gas inlet; (B) vapor inlet; (C) fore-

pressure outlet. [Taken with per-

mission from N. A. Florescu, Vacuum10, 250 (I960).]

cules are given a high velocity in the direction of the vapor stream.

By this action the density of gas molecules should decrease sharply just

below the pumping aperture and then increase because of the pressure

gradient maintained by the vapor stream toward the forevacuum. In

Fig. 6-14 is shown the jet pump configuration and the pressure (or

density) of the permanent gas being pumped as deduced by Florescu

from measurements made by Alexander.^"

The gas pressure throughout the pump barrel can be visualized in

terms of a series of isobaric surfaces, which for convenience may be

assumed to be plane surfaces perpendicular to the axis of the barrel.

Between two successive isobars separated by a distance dy at a distance

y from the nozzle the pressure increase dP^ results from momentum

rVAPOR-JET VACUUM PUMPS 235

transferred during collisions from vapor molecules to the gas mole-

cules.

Since the gas pressure below the nozzle is everywhere, according to

(1-12),

P, = }4n^m,v^^ (6-14)

where v^ is the root-mean-square velocity of the gas molecules, andsince the density of the gas molecules increases with the distance below

the nozzle, the pressure difference between two isobars separated by the

distance dy is

dPg = }/3mgV^^ drig (6-15)

The number of vapor molecules in the volume between the isobars

within a unit area (1 cm^) is n^dy. Since n^ decreases with distance

below the nozzle as the vapor stream spreads, assume as a convenient

model that

n„ N(-1) (6-16)

such that n^ = Bit y = L, the length of the vapor stream.

For gas molecules of most probable thermal velocity Vj, passing

through the vapor of average thermal velocity Wav, the probability for

a given gas molecule to have one collision per second with the vapor

molecules is®

= n„aua,v

(D(x)

where

2

2

1 (f. + f.)

r+^;jo^"dz

(6-17)

and ^{x) = er^ + 2x-).rxl Jo

' dz

Since the average time between collisions is then t = 1/0, the mean

free path for the gas molecules between collisions with vapor molecules

is

v„V^r

V(6-18)

In an infinitesimal thickness dy the probability of a given gas molecule

suffering a collision with a vapor molecule is dy]!^. The number of gas


molecules crossing a unit area of thickness dy in one second is WgWav so

that the number which suffer collisions with vapor molecules in this

infinitesimal volume per second is

n^v^y— = -^-- O a; dy

UgNaunv(l -|)(D(x)%

since from (1-23) Wav/«» = S/tt'-^. If the velocity of the vapor jet is U,

the momentum transfer per collision is mÛ and the rate of change of

momentum per square centimeter over the layer in question, which is

equal to the change in pressure over the distance dy, is

dP^=^Û^^\l-l)^(.)dy (6-19)

But this pressure difference is the same as that given in (6-15) so that

^'^"?-^(l-|)0(.)<Z,}/3 m^v^ dtig = mJJ

anddP,

P„

ZNaniMun

tt'^ m„t; 2^j<^{x)dy (6-20)

Integrating (6-20) from P = P^ to P = P2 and from y = to y = I

gives for the compression ratio

Piexp

'3NaM„Uue.

M„v^^{x)L (6-21)

in which the ratio of the molecular weights MJM^ is substituted for the

ratio of the atomic masses m^jm^.

If the same conditions are assumed in evaluating this expression as

were assumed in evaluating (6-12), we note that

M^ (for mercury) = 200.6 g/mole

Mg (for air) = 28.96 g/mole

iV^ (for mercury) = 1.3 x 10" molecules/cm^

(I, + |,)2 = - (4.26 + 3.72)2 X 10-

= 5.01 X 10-15 cm^

[/ = 2.6 X 10* cm/sec


assumed to be Mach 1 at 373°K for mercury vapor. Correspondingly,

u^ = (2/y)'-^C/ = 2.86 X 10* cm/sec

and ttav = (2/77'-^)Wj, = 3.24 x 10* cm/sec

from (1-30) and (1-23).

If we assume the temperature of the gas being pumped is 300°K,then from (1-15)

/3A;TV-^ /3 X 1.38 x 10"" x SOOV-^v^ = = r-î 777^^ = 5.1 x 10* cm/sec

\ nig / \ 4.81 x 10-23 /

/2kT\î 12^-Vj, = I I = I- 1 «r = 4.16 X 10* cm/secand

from (1-22). The parameter x appearing in (6-17) is

77'^ Mav

2 4.151.45

tt'-^ 3.24/•1-45

from which cl)(l.45) = e-^" + (2.90 + 0.69) e-^'dzJo

f* _ -

The integral \ e ' dz cannot be evaluated analytically but is relatedJo

to the probability integral

2 r^n(x) = -r2 e-''dz

77-^ Jo

numerical values of which can be found in tables. ^^ The result is that

so that

and

ri-i

Jo

n(1.45) = 0.960

'A

e- dz = '"—0(1.45) = — (0.960) = 0.848

Â

2--'--'

2

(D(1.45) = 0.122 + (3.59)(0.848) = 3.16

Substituting this value of together with the other parameters given

above into (6-21) gives for the compression ratio

p^=exp/3 X 1.3 X 1 015 X 5.01 X 10-16

277'/^

200.6 X 2.6 X 10* X 3.2x10* „_ ,\

X -— — -— X3.16 X 1028.96 X26.1 X 108

= exp (392) = 10(392)(0.434) = 10170

which again is a very high compression ratio, even higher than that

obtained for the same example by the method of Jaekel and Noller. ^m.


A simple approach to the problem of the compression ratio for a jet

pump is to assume that the velocity of the gas molecules is high com-

pared with that of the vapor jet, which can then be considered essen-

tially at rest. Gas molecules penetrate the jet from the forevacuum

side, where the density is Wj and the pressure Pj. If we assume that

those gas molecules which experience a collision with a vapor molecule

are entrapped in the jet stream and are carried to the forevacuum

region, then only those gas molecules which pass completely through

the jet from the forevacuum region without collision with vapor

molecules penetrate to the high vacuum side of the vapor jet. If

^ =J

(f. + ^.r (6-22)

is the collision cross section for gas molecules on vapor molecules, then

the mean free path for the gas molecules between collisions with vapor

molecules is

X=— (6-23)W„(T

The number of gas molecules incident per square centimeter on the

vapor jet on the forevacuum side is, from (1-31),

- Xm%0z,v (6-24)

where n,^ is the density of gas molecules in the forevacuum region and

«av is their average thermal velocity. The number of these which

will penetrate a distance L through the vapor jet and thus reach the

high-vacuum region beyond is

dn dn

dt dt

2 g_i/AHn^Vs.^e-^"' (6-25)

If there are no other gas molecules entering the system on the high-

vacuum side of the vapor jet, then when a steady state is reached just

this same number of gas molecules (per second and per square centi-

meter) is being pumped by the jet from the high-vacuum region. Therate at which molecules strike each square centimeter of the exposed

area of the jet from the high-vacuum side is WiWav/4, according to

(1-31). However, because of the turbulent properties of the boundaryof the jet, with some vapor molecules moving in the opposite direction

of that desired, not all these gas molecules will become entrained in the

vapor jet. If we assume that about one-half this number are actually


captured and carried to the forevacuum by the jet, then the numberpumped is

dn

dt(6-26)

Since at equilibrium this rate is the same as that given in (6-25), then

so that

Hn2Va,ye-^'^ = y%niVa.v

Pi ^1(6-27)

Using the previously selected values for the parameters, i = 10 cm,cr = 5.01 X 10-15 cm2, and ?i„ = 1.3 x 10" molecules/cm^, the value of

and

1.3 X 1015 X 5.01 X 10-15 6.52

L- = 10 X 6.52 = 65.2

cm

The compression ratio on this simplified model is thus

Pi ^ I, ,

: = _ g65.2 _ _ ]^()(6S.2)(0.434)

Pi 2 2

1= - 1028.3 = IQii2

again a very large number.Thus for the simplified model of a vapor jet which has been adopted

at the outset of this discussion any reasonable theoretical treatmentleads to a very high compression ratio P2/P1 against the forevacuumgas when the gas flow into the inlet is zero. However, the expression

for the compression ratio in each case is of the form

in which the quantity /S is different for each method of derivation.

The predicted compression ratio is thus in each case critically dependenton the average value of the vapor density n^ in the jet length L overwhich this density persists. In the typical diffusion pump the annularnozzles produce vapor jets in the form of conical sheets. The vertical

thickness through the dense part of such a jet may only be of the orderof 1 cm instead of 10 cm taken for the simple model with purely axial

flow. Furthermore, the first-stage jet in modern diffusion pumps, par-

ticularly those using organic fluids rather than mercury, is generally

found to be undersupplied with vapor so that n^ may be less than the-


values assumed above by a factor of 10 or more. Finally, since a depends

upon the molecular diameter of the gas being pumped, a pronounced

difference between gases is to be expected. Since helium and hydrogen

have particularly small molecular diameters, the compression ratio for

these gases may be expected to be lower than for air. It is found in

practice that some commercial diffusion pumps are so marginal in

vapor density for the first-stage jet that the compression ratio for air

is quite adequate, but that for helium and hydrogen is poor. In some

cases the performance indicates that for pumping light gases the

first-stage jet is so ineffective that the pumping speed is determined

entirely by the subsequent jets. This deficiency comes about in an

effort to obtain high pumping speed for air while avoiding excessive

backstreaming of diffusion-pump fluid from the first-stage jet back-

ward out through the pump inlet.

6-4. Working Fluids for Diffusion Pumps. In the above

theoretical discussion of the compression ratio at zero gas flow for

vapor-jet pumps, mercury has been assumed to be the working fluid

because it is the only chemical element widely used for this purpose.

Since it is an element, mercury is not subject to decomposition. How-ever, because of its relatively high vapor pressure (about a micron at

room temperature) mercury can be used successfully as a working

fluid for many applications only if a vapor trap, usually in the form of a

baffle system maintained at low temperature, is installed between the

diffusion pump and the vessel being evacuated. In this case the

pressure for permanent gases is determined by the effective pumping

speed of the pump through the trap, whereas the pressure of conden-

sable vapors, including that of mercury, throughout the system is

determined by the efficiency and temperature of the trap. Thus, if

the pumping speed of a pump (normally quoted for air at room tempera-

ture) is 8 J, and the conductance of the vapor trap is C^, then the

effective pumping speed 8^ of the combination for air as given by (2-8)

is given by1 1 1

^ = ^ + 7T (6-28)

^e ^v ^t -,

In order to maintain a sufficiently low vapor pressure of mercury

beyond the baffle system and at the same time not cause rapid accum-

ulation of all the mercury from the diffusion-pump boiler on the

baffle system, the trap design becomes rather elaborate and the

resultant conductance lower than one would like. It is generally

difficult to design an effective trap within an acceptable volume which

has a conductance greater than the pumping speed of the diffusion

pump. Thus even with good trap design, typically 8^ ?« 8^,12 for


,£lO-

pumping permanent gases. There is a bonus, however, in that for the

pumping of condensable vapors the effective pumping speed due to

condensation on the baffle surfaces

may be considerably greater than

that of the diffusion pump.During the past 25 years or more

the fluids most commonly used in

diffusion pumps are vacuum-dis-

tilled hydrocarbon oils and a variety

of synthetic liquids, all of which

have much lower vapor pressures

than mercury at room temperature.

The usual advantage of these fluids

is that the base pressure attainable

without the use of low-temperature

vapor traps is acceptable for manyapplications. Generally, systems

using the better grades of diffusion-

pump oils can be operated downto pressures of the order of 10~^

torr, and sometimes as low as 10~*

torr, using only water-cooled baffles

to impede the backstreaming of

working fluid vapor into the evacu-

ated vessel.

Latham, Power, and Dennis^^

have given the results shown graph-

ically in Fig. 6-15, in which the

vapor pressures of a number of

diffusion-pump oils are plotted as

a function of the pressure. Thecurve for mercury is shown for

comparison.

From the discussion in the pre-

vious section one might assume that

the ultimate pressure attainable in

terms of the partial pressure of the

permanent gas being pumped wouldbe so low that the observed base

pressures would be independent of the working fluid. This is, in fact,

essentially true, as long as the design ofthe diffusion pump is competent.

However, what is normally observed is not the base pressure due to the

permanent gas being pumped, but the total background pressure due to

10 15 20 25 30 35 40 45 50 55

Temperature ,°C

Fig. 6-15. Vapor pressure as a func-

tion of temperature of various diffu-

sion-pump oils and mercury. Temper-

ature-pressure curves for : ( 1 ) Mercury

;

(2) Arochlor 1254; (3) Narcoil 10; (4)

Edwards 8A Rotary Pump Oil; (5)

G.A.B. Pump Oil 6; (6) Apiezon G;

(7) Silicone 702; (8) Apiezon B; (9)

Apiezon BW; (10) Silicone 703; (11)

tri-TO-cresyl phosphate; (12) di-2-

ethyl hexyl sebacate; (13) Octoil S;

(14) tri-xylene phosphate; (15) Apie-

zon C. [Taken with permission from

D. Latham, B. D. Power, and N. T.

M. Dennis, Vacuum II, 33 (1957)].


all causes existing on the high-vacuum side of the diffusion pump. Asdiffusion pumps are normally operated with oil as the working fluid, the

oil decomposes because of local regions of high temperature in the

boiler and the catalytic effect of the metal parts of the boiler chamber.

Some products of decomposition are of lower vapor pressure than the

original fluid and tend to remain in the boiler without evaporating.

Accumulation of tarlike, low-vapor-pressure decomposition products

will eventually clog the jet system. Other products of decomposition

are of high vapor pressure, so much so that they evaporate from the

jet region of the pump and escape condensation on water-cooled baffles.

The base pressure measured under these conditions represents the

equilibrium density of decomposition products on the high-vacuumside of the pump rather than the partial pressure of the gas being

pumped.Most measurements made on the base pressure of oil diffusion pumps

consist ofionization-gauge readings near the inlet of the pump when the

gas flow has been reduced to zero. Since ionization gauges are normally

calibrated for dry air and the readings being recorded in such measure-

ments are due to the ionization of heavy and complex organic molecules

from oil decomposition, no knowledge of the true pressures or molecular

densities corresponding to the ionization-gauge readings is obtained.

However, measurements taken in this manner with different workingfluids, or on different diffusion pumps, are still significant since anionization-gauge reading measures a property of the high-vacuumregion which is related to the electrical breakdown and is of primaryimportance in electronic and electronuclear applications.

Blears^* has investigated the base pressure attainable using various

commonly available diffusion-pump fluids. The measurements weremade in a metal test dome having a diameter about three times that of

the diffusion pump with a set of water-cooled baffles over the pumpinlet to prevent direct backstreaming of hot vapor from the jet region

into the test volume. A standard ionization gauge with the usual

long tubulation was connected to the test volume and a high-speed

or nude ionization gauge, consisting of a standard ionization gauge withthe glass envelope removed, was mounted inside the chamber. Theultimate pressure recorded by the nude gauge was always higher thanthat recorded by the standard gauge by about a factor of 10. Blears

used both a, fractionating and a nonfractionating version of the diffusion

pump and compared the base pressures obtained with various pumpingfluids with those previously published. He attributes the much lower

base pressures reported by others to the adsorption effects within the

standard gauges. His results are given in Table 6-2.

To this list of pump fluids must be added Silicone No. 704 and


Silicone 705 (Dow-Corning Chemical Co.) and OS-124 high-temperature

functional fluid and lubricant (Monsanto Chemical Co.). The use of

the latter as a diffusion-pump fluid was first suggested by Hickman, i*

Silicone 704 and OS-124 have been tested by Batzer'^ in a multistage

Table 6-2. Ultimate Pressure Produced by a Diffusion Pump withVarious Oils*

Expressed in Terms of Equivalent Nitrogen Pressure at 20°C; P in 10"* torr

Oil

Measured valuesValues quoted in

Nonfractionating Fractionatingthe literature

Octoil-S 6.4

14.0

17.0

45.0

225

310

2.9

6.6

9.2

19.0

260

0.01-1.0

1.0

0.1-5.0

Aniezon A. 10.0

Dibutylphthalate . . .

Aroohlor 1254

100

100

* Taken with permission from J. Blears, Proc. Roy. Soc. (London) A188, 62

(1946).

diffusion pump with housing diameter of about five inches. In these

tests a 90° elbow served as a one-bounce baffle which could be main-

tained at about 20°C by passing water through a cooling coil, or at a

much lower temperature using liquid nitrogen. The pressure was

measured by a Bayard-Alpert type of ionization gauge connected to

Table 6-3. Ultimate Pressure Produced Using Silicone 704 and OS-124*

Expressed in Terms of Equivalent Air Pressure at 20°C

OilElbow

cooled byUltimate pressure,

torr

Silicone 704. .. .

OS-124WaterWaterLiquid nitrogen

0.5 X 10-8

1-2 X 10-9

OS-124 0.5-1 X 10-9

* Taken with permission from T. H. Batzer, in 1961 Vacuum SymposiumTransactions (Pergamon Press, London, 1962), pp. 315-319.

the end of the elbow furthest from the diffusion-pump inlet. The

ultimate pressures shown in Table 6-3 were observed. In order to

obtain optimum performance with OS-124 it was necessary to increase

the power input into the pump boiler by nearly a factor of 2 over the

rated power input and to allow the lower end of the pump barrel to

operate at a temperature of 90 to 100°C. The fact that the ultimate


pressure decreased by only about 1 x 10-» torr when the elbow was

cooled with liquid nitrogen indicates a very low rate of production of

condensable vapor from the fluid. Whether the results quoted in

Table 6-3 are directly comparable with those in Table 6-2 is doubtful

because of the many differences between the conditions of measure-

ment.

Hickman" has also discussed- the use of the polyphenyl ethers as

diffusion-pump fluids. The chemical structure of these compounds

consists of a number of phenyls linked together by oxygen. BL-10

is a refined mixture of 5-ring polyphenyl ethers made available com-

mercially for use as a diffusion-pump fluid. The vapor pressure at

25°C is reported by Hickman as (1.3 ± 0.3) x IQ-^ torr, but later

samples were predicted to have substantially lower vapor pressure.

Hickman reports attainment of base pressures of 2 to 3 x 10"^ torr

using BL-10 in commercially available diffusion pumps with a room-

temperature baffle. He recommends the combination of two baffles

in series, one at slightly above ambient temperature and the other

cooled by chilled water for the attainment of partial pressure due to

backstreaming vapor of less than lO"" torr. The advantages of the

polyphenyl ethers are claimed to be due to the very high bond energies,

which are among the strongest in organic chemistry.

Latham, Power, and Dennis^'' tested the ruggedness of a number of

commonly used diffusion-pump oils by repeatedly pumping down a

system of a few liters volume and then letting in air with the diffusion

pump still hot but the heater turned off. The sequence was repeated

until the oil decomposed to the extent that the diffusion pump failed.

The fluids are given in Table 6-4 in the order of increasing ruggedness.

The choice between mercury and oil as the working fluid for a

diffusion pump is generally not difficult to make. However, the choice

between the vacuum-distflled hydrocarbons and the many synthetic

fluids is not so easily made. Mercury may be used for practically any

application for which diffusion pumps are required, provided only that

vapor baffles at sufficiently low temperature are used to condense the

mercury vapor which would otherwise be present at the room-tem-

perature vapor pressure of about 2 x 10-^ torr throughout the high-

vacuum region of the system.

For long periods of pumping, the vapor baffles must be designed to

avoid accumulation of frozen mercury in such quantities that the

contents of the boiler eventually are condensed on the baffles and the

pump fails for lack of working- fluid. The difficulty can be avoided bydividing the baffle into two sections, the section nearest the diffusion

pump operating at a temperature just above the melting point of

mercury (— 38.87°C) and arranged so that the condensed mercury


runs back into the pump, and the second baffle at a much lower tem-

perature (such as that of liquid nitrogen), depending upon the accept-

able mercury vapor pressure in the system.

The performance of large mercury diffusion pumps has been in-

vestigated by Power, Dennis, and Crawley." The pumps were of mild

Table 6-4. Fluids Arranged in Ascending Obdeb op Ruggedness*

Fluids

Number of cycles

1st run 2nd run

160

279-307

230

323-359

368-430

530

574-582

491-504

205

376-395

302

566-583

516-583

670-714

Pumps failed because of

decomposition of the

Octoil S* residual oil.

Di-2-ethyl hexyl sebacate

Tri-xylene phosphate ....

G.A.B. Pump Oil 6t

Tri-m-cresyl phosphate . .

tC"areoil 10+ *.. 964-980

1,100

Pumps failed because of

Dow-Corning 703 § total loss of oil to the

backing pump.

Dow-Corning 702 § 500 1,51611 Test discontinued before

failure.

* Taken with permission from D. Latham, B. D. Power, and N. T. M. Dennis

Vacuum II, 33 (1952).

t Vacuum-distilled hydrocarbon oil.

J Di-2-ethyl hexyl sebacate.

§ Methyl polysiloxanes (silicones)

If In the case of Dow-Corning 702 the fluid never broke down, but the tests

were discontinued when half the original charge had been lost into the

forevacuum.

or stainless steel construction of conventional multijet design and of

2M to 24-in. barrel diameter. Since the vapor pressure of mercury

is considerably higher than that of most diffusion-pump oils, the density

of vapor backstreaming from the first jet is much greater than for oil.

In order for gas molecules entering the inlet to reach the first jet, they

must diffuse through this cloud of mercury vapor, the molecular

density of which is generally much greater than that of the gas being

pumped. In the absence of a vapor trap the pumping speed is found

to decrease with the distance above the mouth ofthe pump, as shown in

Fig. 6-16. These curves were taken for three different temperatures

of the condensing surface (25, 19, and 5°C), i.e., the upper portion of the


pump barrel. By mildly refrigerating the condensing surface the

mercury vapor pressure throughout the region above the jet is reduced,

thereby reducing also the resistance to gas flow into the pump. The

pumping speed is increased by a factor of 3 or more by cooling the

condensing surface from 25 to 5°C. Power et al. take advantage of

the dependence of pumping speed on the distance above the inlet

Condensing wall temperature [I] 25°C,[2] I9°C,[3] 5%

Measured pumping speed,liters/sec

4,000 8,000 12,000 16,000

Fig. 6-16. Variation of air-pumping speed with distance above inlet flange for

three different cooling-wall temperatures. Curves plotted to scale for pump of

60 cm diameter. [Taken with permission from B. D. Power, N. T. M. Dennis, and

D. J. Crawley, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962).]

by placing the combination of a refrigerated (.~— 30°C) and a liquid-

nitrogen trap above the umbrella nozzle with as little vertical clearance

as possible without seriously obstructing the pump inlet.

Performance of mercury diffusion pumps has been found by many in-

vestigators to depend critically upon the cleanliness of the condensing

wall and of the pump housing generally. Mercury condensation is

seriously impeded by wall contamination, resulting in poor or even negli-

gible pumping speed and a higher than normal mercury vapor pressure

above the jet. Table 6-5 gives some data by Power et al. showing the

mercury back-migration rate and pumping speed for clean, slightly


Table 6-5. Effect of Contaminated Condensing Wall on Back-migbationRate and Pumping Speed*

Wall Temperature 14°C

Wall conditionBack-migration rate,

cm^/hr (liquid)

Pumping speed,

liters/sec

Clean

Slight contamination

Heavy contamination. . . .

1.05

4.3

12.4

800-850750-800

150-200

* Taken with permission from B. D. Power, N. T. M. Dennis, and D. J.

Crawley, in 1961 Vacuum Sym,posium Transactions (Pergamon Press, London,

1962), p. 1218.

4.5

4.0

jf 3.5

13.06

or 2.5

2.0

f 1.5

1.0

contaminated, and heavily contaminated walls; all taken at a wall

temperature of 14°C, using a 9-in. diffusion pump. Back-migration

rate was measured as a function of wall temperature with and without

a water-cooled copper cover with a long skirt reaching down to intersect

a portion of the jet stream, as described by Vekshinsky, Menshikov,

and Rabinovich.^* The results of these measurements are shown in

Fig. 6-17. Power et al. recommendstainless steel for the pump barrel,

cleaned by vapor phase degreasing

or by electropolishing. The effect

of contaminants on the condensing

walls was also observed by Chupp^'

during the development of 24- and32-in. diameter mercury diffusion

pumps made of mild steel. Chuppobserved that thoroughly cleaned

pumps sometimes fail to exhibit

any appreciable pumping speed,

but after a day or two of opera-

tion become "conditioned" so that

mercury is efficiently condensed andthe performance finally comes upto standard. Once conditioned, the

pump operates at a high perform-

ance level indefinitely. An alter-

native precaution found by Chuppto be effective is to copper plate

the inner surface of the pump barrel

where the mercury vapor should

condense. Apparently the slight

0.5

-5 5 10 15 20 25 30

Condensing woll temperoture,°C

Fig. 6-17. Variation of mercury back

-

migration rate with temperature of

the pump condensing wall. [Taken

with permission from B. D. Power,

N. T. M. Dennis, and D. J. Crawley,



1962).]


amalgamating affinity between mercury and the copper surface en-

hances the condensing efficiency.

However, the choice of mercury usually means a significantly lower

pumping speed for a given size of diffusion pump. Whether this

disadvantage is due to an inherently lower Ho coefficient (see Sec. 6-5)

for mercury jets, or whether it is merely a reflection of the greater

effort expended in developing oil diffusion pumps is not clear. Even

with this disadvantage there are applications for which mercury is the

preferred diffusion-pump fluid

:

1. In the vacuum deposition of certain materials which are inordi-

nately sensitive to the presence of hydrocarbons, such as rhodium and

semiconducting films.

2. In the evacuation of vessels in which high electric-field gradients

must be maintained. At the University of California Lawrence

Radiation Laboratory large (32-in.-diameter) mercury diffusion pumps

are used on many particle accelerators and certain other electronuclear

machines in preference to oil diffusion pumps. Surface contamination

by oil films results in deterioration of the attainable voltage gradient,

probably because of the decomposition products remaining on the

surfaces after repeated vacuum sparking.

3. In systems in which a very high forepressure is an advantage,

either because of unusually large throughput or because of the choice

of the backing pump, e.g., a steam ejector.

4. For pumping highly reactive chemical vapors which might

decompose diffusion-pump oils. Mercury, being an element, is the

most rugged of the diffusion-pump fluids in the sense that it cannot be

decomposed by overheating or by chemical action.

5. For evacuation of mercury vapor electron tubes, such as rectifiers,

ignitrons, and thyratrons. For these applications a vapor trap is not

required since the finished tubes contain pools of mercury to be partly

vaporized during operation.

Oil diffusion pumps have the distinct advantage of simplicity for

the many applications in which the desired operating pressure caiT.be

maintained with a simple water-cooled baffle and no refrigerated trap.

Operating pressures down to 10"^ torr can easily be attained in this

manner, and with care in selection of the fiuid down to about 10~^

torr. Below 10"^ torr a refrigerated trap in addition to the water-

cooled baffle must usually be provided. The baffle arrangement

sometimes used is similar to that described for mercury, the baffle

nearest the pump maintained at a temperature of —30 to —40°C

by a refrigerator, and the second baffle at a much lower temperature.


e.g. that of liquid nitrogen. In any case there are many applications

for which oil is the preferred diffusion-pump fluid

:

1. In general-purpose vacuum-pumping systems for laboratory andsmall production applications.

2. For the evacuation of most types of transmitting electron tubes,

klystrons, and magnetrons.

3. For the evacuation of particle accelerators in those cases in which

the voltage gradient requirement is not too severe. Most cyclotrons,

betatrons, and electron and proton synchrotons are oil-pumped, but

with the addition of liquid-nitrogen-cooled vapor baffles.

4. In vacuum coating and sputtering systems.

5. In vacuum molecular stills and fractionating columns.

6. In the vacuum purification of metals, as in vacuum melting and

casting, electron beam melting, and vacuum zone refining.

6-5. Pumping Speed of Diffusion Pumps. In the normal

operating pressure range the action ofa diffusion pump can be compared

with that of a somewhat imperfect hole into a region of zero pressure.

This behavior can be understood in terms of the incidence of gas

molecules on the surface of the vapor jet and the process by which

some fraction of them are trapped by the jet and carried into the

forevacuum region. Each gas molecule that approaches the vapor-jet

surface experiences collisions with heavy vapor molecules. If the

pressure at the inlet of the pump is low as compared with the vapor

pressure of the jet because of its local temperature, the jet will expand on

leaving the nozzle. The boundary layer of the jet consists in part of

vapor molecules which diverge outward and upward from the main

body of the jet and impede penetration of the jet by gas molecules.

However, some fraction H of the gas molecules incident on the jet

surface penetrate the boundary layer and are captured by the jet.

The value of H depends upon the detailed structure of the boundary

layer. If A is the pumping aperture (i.e., the surface area through

which gas molecules enter the vapor jet from the inlet) then the rate

of incidence of gas molecules on this surface is, according to (1-31),

vA = Hn.VavA (6-29)

The rate at which gas molecules are trapped and pumped by the jet is

thus

q = HvA = HHn^v^vA (6-30)

The pumping speed is defined as the volume of gas at inlet pressure

pumped per unit of time. If Q denotes the gas-flow rate as defined in

(2-18), then the pumping speed is obtained by dividing the molecular


flow given in (6-30) by the molecular density, so that

(6-31)

in which Pj represents the partial pressure at the inlet of the gas being

admitted at the flow rate Q. The existence of other gas components

which contribute additional background pressure at the pump inlet,

such as backstreaming vapor from the jet and outgassing from the

walls of the vacuum chamber, has nothing directly to do with the

pumping process and should, therefore, be ignored in the determination

of the pumping speed. By substituting the value of Wav from (1-23)

into (6-31) one obtains for the pumping speed

ITV= 3.64 X \0^H[— \ A cm^/sec

liters/sec= 'Mm) ^

which for air at room temperature (20°C) becomes

8^ = \\.%EA liters/sec

(6-32)

(6-33)

when the pumping aperture A is measured in square centimeters.

Because the surface of the vapor jet is diffuse and its area therefore

difficult to define, the cross section of the annulus between the nozzle

and the pump housing is normally taken as the pumping aperture A.

The coefficient R appearing in the above equations is a measure of the

efficiency of the pump and is referred to as the Ho coefficient. ^^ As-

suming that the Ho coefficient is independent of the molecular weight

of the gas being pumped, Eq. (6-32) implies that the pumping speed

of a diffusion pump should be inversely proportional to the squall

root of the molecular weight of the gas. This proves to be approxi-

mately true for some pump designs, but is by no means consistently

the case, particularly for multistage pumps with closely spaced jets.

For example, results reported by Noller, Reich, and Bachler^i obtained

for the pumping speed of a multistage diffusion pump, with a liquid-

nitrogen-cooled vapor trap, for hydrogen and air yield a ratio of 2.25

instead of 3.8. Stevenson^^ reports a factor of only 1.2 between the

pumping speed for hydrogen and that for air.

Equation (6-32) also implies that the pumping speed of a diffusion

pump is independent of the pressure. This is indeed very nearly the


case when the pressure substituted into (6-31) is the partial pressure

of the gas admitted at the measured flow rate Q. The performanceof a typical four-stage diff'usion pump of modern design when pumpingair is shown graphically in Fig. 6-18. The solid curve represents thetrue pumping speed for air as a function of the pressure ; each pointon the curve was obtained by substituting the measured flow Q of air andthe corresponding pressure Pj in the

equation

Q„ „ (6-34)S„

^ 1.600

i. 1,200

800

400

r

^'-

^/

1

/ V\

/

\/

F^,

10" 10'" 10'' 10'^ 10'^ 10'


where Pj is the inlet pressure

measured with either a McLeodgauge or an ionization gauge whenthe flow rate is Q, and Pq is the base

pressure of the pump when the flow

rate is zero. The base pressure Pg is

made up of backstreaming diffusion-

pump vapor, products of decomposi-

tion of the oil vapor, and permanentgas arising from outgassing of surfaces

on the inlet side of the pump. The difference between Pj and Pq is

due to the flow of air admitted at the inlet and is therefore equivalent

to Pi in (6-31).

The dotted curve in Fig. 6-18 is obtained by deflning the apparent

pumping speed as

Q

Fig. 6-18. Pumping speed as a

function of inlet pressure for a

typical 6 -in. oil diffusion pump.

W„ = (6-36)

which has generally been used in commercial practice, instead of the

true pumping speed. The apparent pumping speed given by (6-35)

becomes zero at the base pressure Pq. However, the true pumpingspeed obtained by using Eq. (6-34) is found to be independent of the

pressure for as small a value of the leak for which the pressure diff"erence

Pj — Pj can be reliably measured.

The validity of Eq. (6-34) in giving the true pumping speed is

emphasized by the measurement of the pumping speed through a

liquid-nitrogen-cooled vapor trap installed at the inlet of the pump.Figure 6-19 shows the conflguration of the trap and Fig. 6-20 the

resulting performance curve. The base pressure of the pump is nowreduced by a large factor by the condensation of the condensable

vapors from the pump oil. It is therefore possible to carry the

measurement of the pumping speed of the pump plus the vapor trap

252 VACUITM SCIENCE AND ENGINEERING

to much lower values of the leak rate. The expected pumpingspeed for air is that of the untrapped pump combined with the con-

ductance of the trap

or

1

8

S =

1 1

8p C,

8^ C,(6-36)

in accordance with (2-8). Note

that the measured pumping speed

for the combined diffusion pumpand cold trap as shown in Fig.

6-20 reaches a peak value at about10~^ torr and then decreases with

decreasing pressure to a value

which is then independent of the

pressure to values of the pressure

substantially less than the base

pressure of the pump without the

trap.* This would not be the

case if the true pumping speed for

air were zero at the base pressure

for the untrapped pump. Consis-

tent with the theoretical results

discussed in Sec. 6-3, indicating

that a very high zero-flow com-

pression ratio for the gas being

pumped by a jet pump is to be

expected, the true base pressure

in terms of the partial pressure of air due to migration back through

the jet is apparently always low as compared with the background

pressure due to outgassing and other factors. This being the case, the

true pumping speed should be essentially independent of the pressure

for many decades in pressure. Noller, Reich, and Bachler^^ have meas-

ured the pumping speed for air and hydrogen of a multistage diffusion

pump with a liquid-nitrogen-cooled trap over the range from 10~^ to 10~"

torr and observed a decrease in pumping speed of only about 20 per

* The peak in the curve at relatively high pressure arises from the fact thatthe annular clearances in the vapor trap are of the order of 2 in., which is com-parable with the mean free path at a pressure of 10~* torr. As the pressureincreases in this range, the conductance for the trap is no longer that for truemolecular flow but increases with the pressure as expected (see Chap. 2) in thetransition range.

Fig. 6-19. Cross section of vapor trap

mounted on 6-in. diffusion pump.

VAPOE-JET VACUUM PUMPS 253

600

,200/ I

800 ^y \\

400 \

^ _j10"' 10"^ 10"=' 10'" 10"^

Inlet pressure.torr

10"'

cent. Whether the observed slight decrease with decreasing pressure

is real or instrumental is a valid question in view of the difficulty of the

measurement at pressures as low as 10~* torr.

The principal difference between the measured pumping speeds of

diffusion pumps and that implied by (6-32) is that the pumping speed

is not necessarily inversely proportional to the square root of the

molecular weight of the gas. The pumping speed for hydrogen should

be greater than that for air by a factor of 3.8, but for most multistage

diffusion pumps the factor is consider-

ably smaller. One may conclude that

the Ho coefficient // is a function of

the molecular weight of the gas and

more specifically that H decreases

with molecular weight. There is someevidence that the difficulty arises be-

cause of an insufficient quantity of

vapor flowing through the flrst-stage

nozzle. Since for hydrogen the molec-

ular velocity is greater and the colli-

sional cross section smaller than for

air, the effectiveness of the first-stage

jet may be good for air and poor for

hydrogen as is implied by the remarks

at the end of Sec. 6-3. In this case the pumping speed for hydrogen

would be primarily determined by the second-stage jet for which the

aperture is smaller. Since commercial diffusion pumps are usually

rated on the basis of maximum pumping speed for air with minimumbackstreaming of oil vapor, the optimum jet design tends toward

minimum effective vapor flow through the first-stage nozzle compatible

with high pumping speed for air. This criterion may automatically

ensure insufficient vapor flow for pumping gases of low molecular

weight, such as hydrogen and helium. Results reported by Normand^^

on the pumping speed of a commercial diffusion pump show a normal,

smooth performance curve for air with a pumping speed of about 320

liters/sec over the range from 5 x 10"^ to 2 x lO"' torr, but an erratic

behavior when pumping hydrogen. The pressure fluctuations were

such that the pumping speed varied rapidly over the range from about

320 to 480 liters/sec.

The Ho coefficient is not necessarily the best figure of merit for

diffusion pumps, as has been pointed out by Stevenson. ^^ The area

A referred to in (6-32) is the cross-sectional area of the annular space

between the first-stage nozzle and the pump housing. A design which

requires a large diameter nozzle may have a high Ho coefficient in —

Fig. 6-20. Pumping speed as a

function of inlet pressure for

diffusion pump (Fig. 6-18) with

vapor trap (Fig. 6-19).


terms of the small pumping aperture which remains but a small

pumping speed for the diameter of the pump. Stevenson suggests

that a better criterion is the speed factor defined in terms of the

pumping speed for air as

S^ M'^

3.64J„ T

U.6A,for air at 20°C (6-37)

similar to the definition of the Ho coefficient H in (6-32) and (6-33)

except that A^ is the cross-sectional area of the pump housing rather

than the annulus. This definition is consistent with the Knudsen andClausing conductance factors discussed in Chap. 2. For the particular

pump developed by Stevenson the Ho coefficient was found to be 0.51

and the speed factor as defined by (6-37) was 0.45.

6-6. Limiting Forepressure for Diffusion Pumps. In Fig.

6-13 the behavior of a vapor jet as a function of the forepressure is

illustrated. When the forepressure is sufficiently high, the shock

front, which is the boundary between the jet composed of directed

vapor molecules and the randomized region of forevacuum vapor andgas, contracts to the point where the jet fails to bridge the pumpingaperture. When this condition is reached, there is direct communi-cation between the forevacuum and high-vacuum sides of the jet andeffective pumping ceases.

The forepressure limit of a diffusion pump may be explored either byincreasing the flow rate Q through the pump or by increasing the fore-

pressure (e.g., by admitting an increasing flow of gas into the forevac-

uum region) with a constant or zero flow of gas into the diffusion-pump

inlet. In the former method the pumping speed of the pump is found

to be independent of the pressure until the forepressure limit is ap-

proached. The pumping speed then decreases rapidly with increasing'

flow and finally reaches the pumping speed of the forepump. Thecurve in Fig. 6-18 shows the decrease in pumping speed as the fore-

pressure reaches the limiting value. This effect can be presented moredramatically by plotting for a constant throughput Q, the inlet pressure

as a function of the forepressure controlled by admitting air into the

forevacuum region, as is done in Fig. 6-21. In this latter method the

inlet pressure is found to be independent of the forepressure over a

wide range and then to increase rapidly as the forepressure is increased

beyond a critical value. The value of the forepressure at which theinlet pressure has increased above its normal value by 10 per cent canbe used as an arbitrary definition of the limiting forepressure. Thelimiting forepressure as a function of the flow rate or throughput


(Q = PSJ,)

is shown graphically in

Fig. 6-22 for the pump used in

obtaining the performance curves

shown in Figs. 6-18, 6-20, and 6-21.

The zero-flow limiting forepressure

is independent of the pumping

speed of the forepump and is there-

fore a useful standard for comparing

diffusion pumps.

The limiting forepressure of a

diffusion pump depends upon a

number of factors of which the

following may be listed

:

1. Clearances between the nozzle

and housing, particularly of the

final stage; the smaller clearance

generally giving the higher limiting

forepressure

2. Vapor pressure of the work-

ing fluid ; the higher vapor pressure

giving the higher limiting fore-

pressure

3. Power input into the boiler;

the greater power input giving the

higher limiting forepressure

10"

10"

^ 10"

- 10'

10"

10'

0,100 0.200 0.300 0.400 0.500

Forepressure, torr

Fig. 6-21. Inlet pressure as a function

of forepressure with a constant value

of throughput for a 6-in. diffusion

pump.

/

= 1,440 torr iters/sec

Q = 144 tor liters/sec/

Q = 14.4 torr liters/sec /

Q= torr liters /sec/

Optimum design and operating conditions for a multistage diffusion

pump are a compromise between these factors and others, such as the

rates of decomposition and backstreaming of the working fluid. In

Fig. 6-23 are curves of inlet pressiu-e

as a function of forepressure with

constant throughput for various

values of the power input. It will

be noted that for power input

appreciably above that recom-

mended for normal operation the

pumping speed for low gas flow

decreases as the power input and

limiting forepressure increase.

Increase in the power input,

and therefore the temperature and

density of the vapor in the first-

stage jet, causes greater expansion

lo.6

5 0.5

|o.4>£ 0.3

B 0.2

lo.i

^s

_Iff

,-2 2 3 5 7 ]Q-I 2 3 5 71 10

Throughput, torr liters/sec

Fig. 6-22. Limiting forepressure as a

function of throughput for 6-in.

diffusion pump.

256 VACtrUM SCIENCE AND ENGINEERING

of the jet in leaving the nozzle and therefore more vapor molecules

adversely directed on the surface of the jet exposed to the high vacuum.

The result is a greater proportion of gas molecules knocked away from

the jet by backward-moving vapor molecules before penetrating to the

core of the jet where they can be

propelled toward the forevacuum.

The first-stage jet must withstand

not only the back pressure due to

the gas being pumped, but also

the higher vapor pressure from

the subsequent jets. The result

is a change in the jet form which

contributes to the condition men-

tioned above. Also, in the case of

organic fluids, as contrasted with

mercury for producing the work-

ing vapor, the diecomposition rate

increases rapidly with tempera-

ture. Some of the components of

the decomposition are permanent

gases in the sense that they do not

condense at any convenient trap

temperature, and others are of

comparatively high vapor pres-

sure. These contaminants con-

tribute further to the decrease in

the net pumping speed as the

boiler temperature is increased.

A high limiting forepressure is

important but not because of any

difficulty in attaining sufficiently

low pressure with mechanical

backing pumps to meet the re-

quirements at low gas flow. A high limiting forepressure permits

the continued operation of a vacuum system at the full pumping speed

of the diffusion pump for a high gas flow or throughput with a backing

pump of modest capacity. Since the throughput is Q = PS^,, thenat the limiting forepressure for the diffusion pump the forepump speedmust be

10"

10"

o 10"*

^10

10"'

10"

0,100 Q200 0.300 0.400 0.500

Forepressure, torr

Fig. 6-23. Inlet pressure as a function

of forepressure for various values of

power input for a 6-in. diffusion

pump.

o or<S

O

o

ooro

1

—CO T3- o

0\J

- o —

§- o,

—

oo o

* * *o o o

J J J

Q.torr liters/sec

OOo_

;

- o c

o o o 5

o o o £O _0 C\J ^

7 77 ?Q,torr liters/sec

^ I

(6-38)

m order to maintain operation in which P, is the limiting forepressure.


The larger Pj is, the smaller need 8^, be to meet this requirement.In Fig. 6-23 on the left is the throughput as a function of inlet

pressure, showing the maximum reached at that value of the inlet

pressure for which the forepressure is equal to its limiting value. Fromthis characteristic of the diffusion-pump performance and a knowledgeof the maximum throughput to be expected the required capacity

of the forepump can be determined from (6-38). Alternatively, in abatch-processing system in which a short roughing-down time is

important, the high limiting forepressure permits transfer from the

relatively low pumping speed of the mechanical pump to the high

speed of the diffusion pump at an earlier point in time. For systems

of high throughput or of frequent pumpdown a high limiting fore-

pressure contributes to economy and efficiency.

In order to increase further the maximum throughput without

increasing the size of the mechanical backing pump, an additional

vapor-jet pump may be inserted at the exhaust of a diffusion pump.Two types of vapor-jet pumps using working fluids of higher vapor

pressure than those normally used in diffusion pumps have been

developed for this purpose, the booster diffusion pump and the oil-

vapor ejector pump. The former is similar in design to a diffusion pumpexcept that the jet clearances are smaller and the number of stages

is usually only two. The latter resembles the steam ejectors described

at the beginning of this chapter, having a converging-diverging nozzle

and a diflfuser. The designs of booster diffusion and oil ejector pumpsare optimized for fluids such as butyl phthalate, butyl sebacate, high-

vapor-pressure hydrocarbons, chlorinated hydrocarbons, and ethyl

or propyl phthalate. Limiting backing pressures are typically of the

order of 0.5 torr for booster diffusion pumps and several torr for oil-

vapor ejector pumps. In addition to their usefulness in backing

diffusion pumps, boosters and ejectors are effective in rough vacuumapplications such as vacuum distillation of organic materials and

vacuum degassing of metals.

6-7. Factors Contributing to tlie Ultimate Pressure of a

Diffusion Pump. The ultimate pressure of a diffusion pump is the

inlet pressure which the pump maintains with zero gas flow. This

definition is incomplete because the conditions of measurement are

not defined. The use of low-vapor-pressure oil instead of mercury

as a working fluid makes it possible under many circumstances to use

water-cooled baffles without a refrigerated trap for obtaining a suf-

ficiently low base pressure for many applications. Because of the

convenience of this type of operation it has become customary to define

the ultimate pressure of an oil diffusion pump as the ionization-gauge

reading obtained in a test dome protected from the direct backstreaming


vapor from the pump by a simple water-cooled baffle. For such

measurements the air calibration of the ionization gauge is normally

used, even though the residual gas remaining in the test dome is not air

but is a mixture of gaseous and vaporous products of decomposition

from the diffusion-pump fluid, as was briefly mentioned in Sec. 6-4.

Some of the factors which in-

fluence the ultimate pressure as

defined above are

:

1. Backstreaming of vaporized

working fluid from the diffu-

sion pump.

2. Decomposition of the working

fluid with the evolution of com-

ponents which in part consist

of condensable vapors of high

vapor pressure and of perma-

nent gases.

3. Release in the vapor jet of

forevacuum gases dissolved in

the working fluid after conden-

sation and carried into the

boiler by the circulating fluid.

4. Outgassing of surfaces on the

high-vacuum side of the pump.

Some aspects of the back-

streaming of diffusion-pump

fluid from the jet region have

already been briefly discussed

in Sec. 6-4. The results of a

comprehensive study of the

backstreaming problem have

been published by Power arid

Crawley.2* They report that for a diffusion pump of typical design

at the time of their investigation the sources of backstreaming

vapor could be identified as indicated in Fig. 6-24 as

a. The leakage of vapor around the nut with which the "umbrella"

for the first jet was secured to the center post.

6. The wetting of the umbrella of the first jet by condensation of

vapor on the lip followed by evaporation.

c. The scattering of some oil molecules upward toward the inlet

of the pump by collision processes in the first-stage jet.

d. The evaporation of oil vapor and spitting of oil droplets up

Fig. 6-24. Sources of vapor back-

streaming in a diffusion pump.[Taken with permission from B. D.

Power and D. J. Crawley, VacuumIV, 415 (1954).]


Copper supporting arm

through the annular space between the nozzle structure and the

pump housing from the free surface of oil in the reservoir.

e. The evaporation of oil vapor from the region of the pumphousing where the first-stage jet impinges and is intended to

condense.

The leakage of vapor from source (a) was easily eliminated by providing

an unperforated cap and attaching it to the center post from below.

Wetting of the lip of the umbrella

of the first-stage jet (6) was found

to result from condensation of the

working fluid on the bottom sur-

face of the nozzle cap due to the

continual loss of heat by radiation.

Heating the umbrella cap was found

to eliminate "wet running" and

reduce the backstreaming substan-

tially. They found that evapora-

tion and spitting from the region

of the oil reservoir {d) could be

eliminated by proper design of the

boiler. The remaining sources of

backstreaming (c) and (e) from the

region of the flrst jet and the region

of its impingement on the condens-

ing wall were found to be substan-

tial. Working on the hypothesis

that the boundary layer of the jet

adjacent to the nozzle surface consists largely of vapor molecules some-

what randomized in direction because of collisions with the nozzle sur-

face, as illustrated in Fig. 6-11, they devised a water-cooled guard ring,

one form of which is shown in Fig. 6-25, to intercept and condense the

randomly directed vapor molecules originating in the boundary layer.

When the bottom rim of the cap extends sufficiently below the lip of

the nozzle to intercept a significant portion of the jet, the back-

streaming is found to be reduced by a factor of 10 to 30, depending

upon the design of the pump tested. Except in pumps of small bore,

the pumping speed is not reduced by addition of the cooled guard ring.

Vekshinsky, Menshikov, and Rabinovichi* described the use of a

water-cooled cap with a long skirt placed over the first-stage nozzle

and reaching down far enough to intercept the boundary layer of the

jet to reduce the backstreaming, as illustrated in Fig. 6-26. The func-

tion of the cap is identical with that of the guard ring described by

Power and Crawley.

Fig. 6-25. Water-cooled guard ring

to repress backstreaming from diffu-

sion-pump jet. [Taken with per-

mission from B. D. Power and D. J.

Crawley, Vacuum IV, 415 (1954).]


The thermodynamic principles involved in the performance of a

diffusion-pump boiler and nozzle system in producing vapor jets were

examined theoretically and experimentally by Smith. ^^ Observation

of the temperature of the oil in the boiler and that at various locations

on the vapor stack and nozzle system showed that the stream issuing

from the nozzles in a typical commercial oil diffusion pump is a mixture

of vapor and condensed fluid due to contact with relatively cold surfaces

in the stack and nozzle assembly. The "wet running" referred to by

Power and Crawley above was therefore attributed to condensation on

these cold surfaces.

Fig. 6-26. Water-cooled cap

over diffusion-pump nozzle to

repress backstreaming. [Taken

with permission from S. A.

Vekshinsky, M. I. Menshikov,

and I. S. Rabinovich, Vacuum 9,

201 (1959).]

Enthalpy

Fig. 6-27. Curve of enthalpy as a

function of temperature for diffu-

sion-pump fluid. [Taken with per-

mission from H. R. Smith, in 1959



Smith points out that a minimum requirement for the formation of a

well-defined supersonic jet is for the oil vapor to be everywhere abovfe

the vapor-mixture line on the enthalpy diagram as represented by

point 3 in Fig. 6-27, corresponding to superheated vapor. The amount

of superheating desired is such that in expanding through the nozzle

the vapor temperature does not drop below that corresponding to

point 1 in Fig. 6-27 on the vapor-mixture line. Cooling to a lower

temperature corresponding to point 2, which is in the mixture zone,

during expansion through the nozzle will result in some condensation

with the formation of droplets of oil in the jet stream and a deposit

of a film of liquid oil on the nozzle surfaces.

Another requirement discussed by Smith is the generation of sufficient

VAPOE-JET VACUUM PUMPS 261

vapor in the boiler to maintain the pressure required by the nozzles

of the diffusion pump. It is noted that the boiler temperature for the

particular diffusion pump tested increased more than it should for agiven increase in power input if the Clausius-Clapeyron equation for

change of state and the Langmuir equation for the rate of vaporization

both apply to the fluid. The conclusion reached as a consequence of

these tests was that the pump boiler did not provide adequate surfaces

of proper geometry to promote the generation of vapor at a rate highenough to supply the jets at the normal rate of evaporation. In-

creasing power input instead of increasing the rate of evaporation by asigniflcant factor raised the temperature of the oil by more than the

appropriate amount.

By providing a tubular radiant heater down through the center of

the jet assembly above the level of the oil and a separate heater

attached to the top umbrella, the nozzle assembly could be kept

at higher temperature than the oil in the boiler and the vaporthus superheated. As a consequence of these changes Smith found

that the peak pumping speed of the pump was about one-third greater

and the base pressure typically reduced by a factor of 2.5 as comparedwith the performance of the pump without the axial superheater andtop nozzle heater in operation.

Another approach to the problem of jet formation is that described

by Florescu,* who has developed a special coaxial nozzle illustrated

in Fig. 6-28. The nozzle consists of a central cylindrical section which,

because of the lack of any expansion, produces a dense, low-velocity jet

core and an outer de Laval type of expanding nozzle which produces a

supersonic jet of low density. According to the author, the coaxial

nozzle reduces backstreaming substantially but at the same time

provides the high-density core necessary for effective pumping against

a high forepressure. The coaxial nozzle had not been incorporated

in any commercial diffusion-pump design of which the author wasfamiliar at the time of writing this section.

In two excellent papers Hablanian and his colleagues^*'^' have

reported results on the backstreaming rates and the sources of back-

streaming vapor for diffusion pumps of improved design. Theymeasured the backstreaming rate for a 6-in. diffusion pump with the

apparatus shown in Fig. 6-29. The backstreaming oil vapor wascaught on the walls of a chamber mounted on the pump with a flange

cut conically at the top to admit all oil molecules leaving the rim of the

top nozzle and flying directly out of the pump inlet. The oil ac-

cumulation drained into the calibrated collector was measured period-

ically during each run. With the flrst-stage nozzle, as illustrated in

Fig. 6-29, the backstreaming rates shown in Fig. 6-30 were obtained.


Fio. 6-28. Coaxial diffu-

sion-pump nozzle. [Takenwith permission from N.A. Florescu, Vacuum 10,

250 (I960).]

Ion gouge

Collector'

Fig. 6-29. Apparatus for backstream-

ing measurements. [Taken with per-

mission from M. H. Hablanian andH. A. Steinherz, in 1961 VacuumSymposium Transactions (PergamonPress, London, 1962).]

.0.04

;0,02

V

Dry dome /50

Time.hr

100

Fig. 6-30. Backstreaming rates

measured by two different tech-niques showing eventual agreementbetween the methods after sufR-ciently long running time. [Takenwith permission from M. H. Hab-lanian and H. A. Steinherz, in 1961Vacuum Symposium Transactions(Pergamon Press, London, 1963).]

1

Speed

\" \- \

\Bockst——•—reoming

05

D 2D

Distance from pump inlet

Fig. 6-31. Effect of length of

connecting pipe on backstreamingrate. [Taken with permission fromM. H. Hablanian and H. A. Stein-

herz, in 7967 Vacuum Sym,posiumTransactions (Pergamon Press,

London, 1962).]


IT

IT

Bockstreoming

foctor

1

05 to 03

When the chamber was thoroughly cleaned before the run, the curvelabeled dry dome was obtained; whereas when the inner surfaces of thechamber were dehberately wetted in advance with diffusion pumpoil, the curve labeled wet dome resulted. It may be seen that aboutforty hours of operation were required to reach a steady rate with thewet dome, but nearly twice that long was required with the dry dome.The authors emphasize the need for long periods

of operation to reach equilibrium rates in experi-

ments of this type.

By inserting lengths of pipe between the collect-

ing chamber and the pump, the dependence of the

backstreaming rate on the length of connecting

pipe was measured, with results shown in Fig.

6-31. The decrease in pumping speed due to the

added lengths of connecting pipe is also shown.The insertion of a length of pipe equal to 1.5

diameters of the pump reduces backstreaming to

only about 2.5 per cent of the original value,

whereas the pumping speed is reduced to about63 per cent. Thus for the simple,uncovered first-

stage nozzle used in these tests the backstreamingrate could be reduced by a large factor by in-

sertion of a length of connecting tubing withoutexcessive loss in the resulting pumping speed.

The effect of various cold-cap shapes added to

the original simple first-stage nozzle is shown in

Fig. 6-32. For the type of water-cooled capadopted as standard the reduction in backstream-ing rate was a factor of 0.02 to 0.01. Applyingthis factor to the asymptotic results shown in Fig. 6-30, one obtained0.024 to 0.012 mg/cm^ hr as the backstreaming rate for the pumpwith optimized cold cap, which is said not to impair pumping speed.

This backstreaming rate is of the same order as, but slightly smaller

than, that reported by Hickman^" for a pump of similar improveddesign.

Hablanian and Steinherz^" have also reported results on the back-streaming rate as a function of inlet pressure which show a rapid

increase with pressure as the pressure exceeds lO^^* torr. The results

are shown in Fig. 6-33, in this case using a 32-in. diffusion pump and adifferent tjrpe of collecting system. The change in backstreamingrate is negligible with increasing pressure until the inlet pressure

reaches 10-^ torr; then the rate increases by more than a factor of

1,000 as the inlet pressure increases from 10^^ to 10-^ torr. In systems

0.5 to I

02 to 015

O02to0.01

Fig. 6-32. Effect of

cold-cap configura-

tion on backstream-

ing. [Taken with per-

mission from M. H.Hablanian and H. A.

Steinherz, in 7967

Vacuum Symposium,Transactions (Perga-

mon Press, London,1962).]


requiring contaminant-free operation the need for avoiding high-

pressure operation of the diffusion pumps is emphasized by these

results, which are more quantitative but entirely consistent vi^ith

previous results, such as those of Power and Crawley.^*

In a study of the remaining sources of backstreaming in a diffusion

pump with a water-cooled cap over the first-stage nozzle, Hablanian

1,000

100

10 r

0.1

*

/:

/

/

=

//

/

/

" •—

-

/

//

10"^ 10"^ 10"^ 10"' 10"2 10"'


Fig. 6-33. Backstreaming rate vs.

inlet pressure for a 32-in. diffusion

pump (fluid: Narcoil 40). [Taken

with permission from M. H. Hab-lanian and H. A. Steinherz, in 19C)1

Vacuum Symposium TransacHofis


-6-in, diffusion pump (HS-6-1500)

Fig. 6-34. Experimental arrangement

for detection of backstreaming source.

[Reprinted with permission from TheMacmillan Company from M. H. Hab-lanian, in 1962 Vacuum Sym,posium

Transactions. Copyright © 1962 byAmerican Vacuum Society.]

uses a pinhole camera technique, as illustrated in Fig. 6-34. His

conclusion is that the remaining major source of backstreaming is

the region of the jet around the edge of the cold cap.

Decomposition of the working fluid in an oil diffusion pump always

occurs at operating temperature, the decomposition rate depending

upon a number of factors. In Sec. 6-4 various fluids are rated in

terms of their relative ruggedness. In all cases, as one should expect,

the decomposition rate increases rapidly with the boiler temperature.

The heat transfer area in contact with the oil is an important design

parameter which has recently received critical study. Several ob-

servers have noted the occurrence of eruptive boiling resulting froman insufficient heat-transfer area. The heat of vaporization for the


Glass tape I «O.OI4in

vapor flow required by the jets determines the power input necessary

for effective pumping. The power density must be relatively low in

order to avoid local hot spots resulting in a high decomposition rate

and eruptive boiling. Erratic pressure surges, excessive backstream-ing, and poor average base pressure are observed in the performanceof most of the older types of oil diffusion pump. Stevenson^^ describes

a major advance in boiler design, in which the heat-transfer area is not

only large as compared with that of

previous designs but is in the form

of hot baffles which extend up above

the fluid level, providing flash heat-

ing of droplets thrown up from the

fluid and superheating of the vapor.

Stevenson reports a much lower

rate of decomposition, broader

pumping-speed curve, higher peakpumping speed, and higher limiting

forepressure than were obtained

with heater systems previously

used. A further advance in heater

design for diffusion pumps is re-

ported by Milleron and Levenson.^*

Their heater consists of a corru-

gated strip of Nichrome woundinto a spiral with a strip of glass

tape to provide insulation between

adjacent turns. The heater, as shown in Fig. 6-35, is operated only

partially submerged at the surface of the oil. Even with a high rate

of evaporation from the surface, the oil below the heater remains

relatively cool.

Stevenson^' has demonstrated a pronounced effect of the shape of the

first-stage nozzle upon the backstreaming rate of a diffusion pump.Backstreaming from the first-stage vapor jet may be thought of either

as a random scattering of some of the oil molecules toward the pumpinlet or as the directed expansion of a coherent supersonic vapor jet

into a region of relatively low surrounding gas pressure, both of which

processes are illustrated schematically in Fig. 6-36 from Stevenson's

paper. The distribution of backstreaming vapor from the jet wasmeasured by catching the condensed vapor as it drained down the wall

of the extended pump casing into a series of gutters arranged at several

heights above the pump nozzle, the first gutter being located at the

same height as the lip of the pump nozzle, as shown in Fig. 6-37.

The apparatus also provided means of draining off the oil vapor

Nichrome 1 xO.OOl in.

Fig. 6-35. Diffusion-pump heater of

Milleron and Levenson. [Taken with

permission from X. Milleron and L.

L. Levenson, in 1961 Vacuum Sym-posium Transactions (PergamonPress, London, 1962).]


o

c

o

o

o

Directional scottering from this

portion of the coherent vopor jet

Random scattering

o

D

Fig. 6-36. Nature of backstreaming.

[Reprinted with permission from TheMacmillan Company, from D. L.

Stevenson, in 1963 Vacuum Sym-posium Transactions. Copyright ©1963 by American Vacuum Society.]

Return line to boiler

Fig. 6-37. Schematic diagram of test

apparatus for measuring amount anddistribution of backstreaming. [Re-

printed with permission from TheMacmillan Company, from D. L.

Stevenson, in 1963 Vacuum Sym,posium,

Transactions. Copyright © 1963 byAmerican Vacuum Society.]

condensed on the top of the test chamber. The oil flow from each of

the collecting surfaces was conveyed by a tube to a separate buret

so that the accumulation during a specified period of time could bemeasured. The backstreaming total rate was measured as a function

of the angle of the lower member of the nozzle, as shown in Fig. 6-38.

The angle of the conical surface of the lower member of the nozzle

was varied from +15° (protruding) to —45° (receding) relative to the^

vertical. Curve A was obtained with normal heater power input andcurve B with heater input reduced about 18 per cent. The dotted

curves are corrections to curves A and B due to a measurement of

the backstreaming contributed by the lower jets of the pump. It is

apparent from these results that the total backstreaming rate is reducedby a factor of about 5 by changing the angle in question from + 15° to

— 45°. The distribution of relative rates of backstreaming as deter-

mined by readings on the separate collection burets is shown in Fig.

6-39. The rapid decrease in backstreaming rate as a function of theaverage angle above the plane of the nozzle lip is evident from the


curves shown for the various nozzle configurations tested. The dotted

curve shows the correction to the —45° curve due to subtraction of

backstreaming from the lower jets. From these results Stevenson

concludes that the rate of backstreaming of oil diffusion pumps can besubstantially reduced by improving the configuration of the nozzle.

The paper does not give any data, however, on the effect on pumpingspeed of various gases such as nitrogen and hydrogen caused by chang-

ing the nozzle configuration in the manner described. If the improve-

ment in backstreaming results in a decrease in vapor-jet density, it mayalso result in a poorer ratio of pumping speed for hydrogen relative to

that for air, which would be a distinct disadvantage for some applica-

tions.

The rate of decomposition of diffusion-pump fluids is greatly

increased by the catalytic effect of some materials of construction and

is self-catalytic in the sense that the carbon deposits resulting from the

1.0 p

5 1.0

- '1

'1

'1

11 _

r- 1

1

>. *I5° -15°

1 :-30°

1-

\\ °1

I NX. z

~Correction ^ ^

_ bosed on effect of

installation of a baffle

under the first stoge

.1,1,1

A I

B -

, 1

+ 15° 0° -15° -30° -45°

Angle of inner wall of nozzle

Fig. 6-38. Relative rates of total

backstreaming for various nozzle

configurations. [Reprinted with per-

mission from The Macmillan Com-pany, from D. L. Stevenson, in 1963

Vacuum Symposium Transactions.

Copyright © 1963 by AmericanVacuum Society.]

20 40 60

Angle, deg

Fig. 6-39. Distribution of relative

rates of backstreaming as a function

of the angle above the plane of the

diffusion-pump nozzle. [Reprinted

with permission from The INIacmillan

Company, from D. L. Stevenson, in


actions. Copyright © 1963 byAmerican Vacuum Society.]


decomposition act as a catalyst. Insufficient quantitative work on the

role of materials in catalyzing the decomposition of diffusion-pump

fluids has been reported to permit a detailed discussion of the subject.

However, the decomposition rate in glass pumps is apparently sig-

nificantly less than in comparable metal pumps. Hot aluminum in

contact with the working fluid is regarded as undesirable. However,

individual differences in chemical properties of the fluids used are so

great that generalizations are not valid.

The products of decomposition of diffusion-pump fluids consist of

materials of both higher and lower vapor pressure than the original

fluid. Those of sufficiently high vapor pressure act as permanent

gases in the sense that their vapor pressures are so large that they are

not condensed on liquid-nitrogen-cooled baffles. Other products are

heavy liquids and solids of very low vapor pressure which accumulate

in the boiler and eventually clog the nozzle system with a dark deposit.

Because an appreciable decomposition rate is typical of diffusion-pump

operation, the ultimate pressure, even with good liquid-nitrogen-cooled

baffles, is limited by the rate of decomposition and production of high-

vapor-pressure products which migrate into the high-vacuum system

beyond the baffles and must then be pumped out again. Best results

in terms of very low ultimate pressure are obtained when a diffusion

pump is run with low power input and with a fluid of greater than

normal stability.

6-8. Fractionation and Purging. From the time high-boiling-

point fluids were first introduced by Burch^" in 1928 for use instead of

mercury in diffusion pumps, the need for continual purification to

eliminate high-vapor-pressure components initially present in the oil,

or produced during operation by decomposition, was realized. Hick-

man'i and his collaborators were largely responsible for the systematic

study of decomposition and contamination of diffusion-pump fluids

and the development of specific mechanisms for purging the pump-boiler of undesirable constituents and separating the remaining

constituents in the proper order. Figure 6-40 shows a two-stagb

glass diffusion pump with boiler compartments to separate the fluid

roughly according to the vapor pressure of the constituents and

catchment lobes on the exhaust arm of the pump for elimination of

high-vapor-pressure components into the backing pump. Large

horizontal pumps of metal construction based upon the glass fraction-

ating designs were developed but have not proved to be as convenient

in practice as pumps of vertical design.

The principles of fractionation have been incorporated into the

design of metal vertical pumps. One of many such designs is illus-

trated in Fig. 6-41. Fluid returning from the jets to the boiler flows


radially inward toward the center of the reservoir. If this flow is

impeded by barriers with small openings, the fluid is heated substan-

tially while it is still near the outer portion of the reservoir so that

high-vapor-pressure constituents are boiled off near the outside.

As the fluid flows toward the center it is further heated and lower-

vapor-pressure components are vaporized. The nozzle stack is con-

structed of concentric tubes arranged such that each nozzle receives

Fig. 6-40. Two-stage fractionating glass diffusion pump. [Reproduced throughthe courtesy of ConsoHdated Vacuum Corp., Rochester, N.Y.]

vapor from only a specific annular region of the boiler. The backing

or flnal jet receives vapor from the outer portion of the boiler where the

vapor pressure is highest, and the first jet receives vapor from the

central section where the vapor pressure of the fluid is the lowest.

One advantage claimed for the mechanism of fractionation is that the

high-vacuum jet is supplied only by the relatively low-vapor-pressure

constituents of the working fluid, contributing to a lower backstreamingrate and vapor pressure at the inlet of the pump. Another advantageclaimed is a higher forepressure tolerance because of the relatively

high vapor pressure of the constituents forming the backing or final jet.

However, these advantages have not been as clearly demonstratedin commercial diffusion pumps of metal construction as in glass pumpsof the type fllustrated in Fig. 6-40, at least in part because of the

process of reverse fractionation discussed by Hickman. ^^'^^


Fig. 6-41. Three-stage fractionating oil diffusion pump of metal construction.

Effective fractionation can only be obtained by careful separation of the respec-

tive boiler zones. This is obtained by shaping the component resting on the

pump base plate as shown (shaded). The lower jet cap is at the same height as-

the lower end of the cooling jacket. As a result, the oil flowing down the walls is

warmed, facilitating degassing. [Taken with permission from H. G. Nollei-,

Vacuum V, 59 (1955).]

The partial condensation of the vapor on the inner walls of the tubes

supplying vapor to the nozzles in fractionating pumps, such as that

shown in Fig. 6-41, is held to be responsible for a reversal of the desired

direction of fractionation. Furthermore, the separation of the fluid into

constituents according to vapor pressure is not as well controlled or

efficient in the commercial metal pumps as in the glass fractionating

pump, such as that shown in Fig. 6-40, since the concentrically dividedboiler of the vertical metal pump is not the equivalent of the separatedboiler compartments of the horizontal glass pump. Another serious


disadvantage in the construction of a metal fractionating pump is the

low conductance for vapor flow to the nozzles inherent in the concentric

tube design for the nozzle stack. Because of the relatively small gain

in ultimate vacuum actually achieved by the introduction of fractiona-

tion in metal diffusion pumps and the limitations imposed by the

presence of the concentric tubes against significant improvements to the

boiler and jet system, the design trend has been away from fractionation

to gain some of the features described in the previous section. All

recent commercial pump designs, such as those illustrated in Figs. 6-9

and 6-10, as of the date of this writing (1964), achieve better perform-

ance without the fractionating feature than earlier designs of either

fractionating or nonfractionating pumps.Distinct from the question of fractionation of the diffusion-pump

fluid into components according to vapor pressure is the problem of

purging the pump fluid of high-vapor-pressure components by ejection

into the forevacuum. Hickman^^ and Latham, Power, and Dennis^^

have demonstrated that complete ejection of the more volatile con-

stituents of the working fluid from the pump is more effective than

fractionation. The rate of ejection of volatiles in a design such as that

shown in Fig. 6-9 is influenced by the vertical spacing from the bottom

nozzle to the liquid level in the reservoir and the temperature of the

pump housing on which the oil condenses. The temperature of the

pump housing near the top must be cool to ensure efficient condensation

of the fluid from the first jet. In some applications the top few turns

of tubing are separated from the rest of the cooling coil and either

cooled by chilled water just above the freezing point or by a mechanical

refrigerator to reduce further the vapor pressure at the inlet of the

pump. However, the wall temperature should preferably increase

from the region of condensation of the first jet to a considerably higher

temperature below the bottom jet so that higher-vapor-pressure

components which are condensed near the top are evaporated as the

fluid drains down the housing wall toward the backing jet and pumpedout with the permanent gas into the forevacuum.

The forevacuum section of the diffusion pump must also be allowed

to run warm so that the more volatile constituents of the effluent will

not be condensed and permitted to flow back into the boiler. Theoptimum temperature distribution is a compromise which allows a

sufficiently high rate of ejection of volatiles from the pump without

permitting an excessive rate of loss of pump fluid into the forevacuum.

For a given pump design the stability and vapor pressure of the fluid

are factors which determine the optimum temperature distribution

along the pump housing and forevacuum connection. An extreme

example mentioned in Sec. 6-4 is OS- 124 (Monsanto Chemical Company)


for which best performance was obtained by Batzer" when the lower

end of the pump housing was allowed to run at 90 to 100°C.

6-9. Resume of Diffusion-pump Performance. Although his-

torically the original development of diffusion pumps was based upon

mercury as the working fluid, since about 1930 the far greater eff'ort

has been devoted to understanding and improving "oil" diffusion

pumps. With a few important exceptions listed in Sec. 6-4, oil

diffusion pumps instead of mercury diffusion pumps are used on nearly

all industrial and electronuclear systems. In spite of certain inherent

advantages of mercury, such as chemical stability, the speed factor

(6-37) for oil diffusion pumps is significantly greater than for mercury

diffusion pumps.

Organic fluids, usually referred to as oils, now available for use

in diffusion pumps range in vapor pressure from that about equal to

mercury down to such low values that the room-temperature vapor

pressure can only be estimated by extrapolation from high-temperature

measurements. Narrow cuts of petroleum oils, chlorinated hydro-

carbons, and a wide variety of synthetic organic fluids have been

successfully used. In the development of synthetic fluids of high

molecular stability and low vapor pressure there would appear to be an

opportunity for continued improvement in the future. Highly stable

fluids with a wide range of vapor pressures are needed to meet an

extreme range in performance from high pumping speed at low ultimate

pressure to high throughput at high backing pressure.

The performance of diffusion pumps can be judged in terms of the

base pressure, backstreaming rate, speed factor, and limiting fore-

pressure. Several industrial vacuum firms have demonstrated dif-

fusion pump designs for which

:

1. The base pressure for baflftes at 20°C is of the order of lO^' torr

using Silicone 705 or OS- 124 fluid.

2. The backstreaming rate is of the order of lO"" g/cm^ min.

3. The speed factor as defined in Eq. (6-37) is of the order of 0.5.

4. The limiting forepressure is 0.3 torr or higher.

System designs should be based upon the assumption that diffusion

pumps meeting approximately the above performance specifications

can be obtained.

REFERENCES

1. M. LeBlanc, in L. Dunoyer, Vacuum Practice, trans, by J. H. Smith (D. Van

Nostrand Company, Inc., New York, 1962), pp. 41-42.

2. V. V. Fondrk, in 19S7 Vacuum Symposium Transactions (Porgamon Press,

London, 1958), p. 88.


3; Saul Dushman, Scientific Foundations of Vacuum Technique (John Wiley &§ons, Inc., New York, 1949).

4. W. Gaede, Ann. Physik 46, 357 (1915); Z. Tech. Physik 4, 337 (1923).

5. R. Jaekel, in Proceedings First International Congress on Vacuum Technology,

1958 (Pergamon Press, London, 1960), p. 21.

6. R. Jaekel, Kleinste Drucke (Springer-Verlag, 1950), pp. 140-197.

7. H. G. Noller, Vacuum V, 59 (1955).

8. N. A. Floresou, Vacuum 10, 250 (1960).

9. E. H. Kennard, Kinetic Theory of Oases (McGraw-Hill Book Company, NewYork, 1938), p. 108, p. 194.

10. P. Alexander, J. Sci. Instr. 23, 11 (1946).

11. Smithsonian Physical Tables, 9th rev. ed. 1954, p. 40.

12. D. Latham, B. D. Power, and N. T. M. Dennis, Vacuum II, 33 (1952).

13. J. Blears, Nature 154, 20 (1944); Proc. Roy. Soc. (London) A 188, 62 (1946).

14. K. C. D. Hickman, Nature 187, 405 (1960).

15. T. H. Batzer, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962), p. 315.

16. K. C. D. Hickman, in 1961 Vacuum Symposium Transactions (Pergamon


17. B. D. Power, N. T. M. Dennis, and D. J. Crawley, in 1961 Vacuum Sym-

posium Transactions (Pergamon Press, London, 1962), p. 1218.

18. S. A. Vekshinsky, M. I. Menshikov, and I. S. Rabinovich, Vacuum 9, 201

(1959).

19. Warren W. Chupp, Lawrence Radiation Laboratory, Berkeley, Calif., private

communication

.

20. T. L. Ho, Physics 2, 386 (1932).

21. H. G. Noller, G. Reich, and W. Bachler, in 1959 Vacuum Symposium Trans-


22. D. L. Stevenson, in 1959 Vacuum Symposium Transactions (Pergamon Press,

London, 1960), p. 134.

23. C. E. Normand, Oak Ridge National Laboratory, private communication.

24. B. D. Power and D. J. Crawley, Vacuum IV, 415 (1954).

25. H. R. Smith, in 1959 Vacuum Symposium Transactions (Pergamon Press,

London, 1960), p. 140.

26. M. H. Hablanian and H. A. Steinherz, in 1961 Vacuum Symposium Trans-


27. M. H. Hablanian, in 1962 Vacuum Symposium Transactions (The Macmillan


28. Norman Milleron and L. L. Levenson, in 1961 Vacuum Symposium Trans-


29. D. L. Stevenson, in 1963 Vacuum Symposium Transactions (The Macmillan


30. R. C. Burch, Nature 122, 729 (1928).

31. K. C. D. Hickman, J. Franklin Inst. 221, 215 and 383 (1936).

32. K. C. D. Hickman and J. J. Kinsella, in 1956 Vacuum Symposium Trans-


33. K. C. D. Hickman, Rev. Sci. Instr. 22, 141 (1951).

CHAPTER 7

THE MEASUREMENT OF PUMPING SPEED

7-1. Alternative Definitions of Pumping Speed. The basic

equation for the pressure in a vacuum system is

dPPS V

dtQ + Qo (7-1)

in which P is the pressure measured at some particular point in the

system, S is the pumping speed at that same point, V is the volume of

the system for which S is the effective pumping speed, Q is the through-

put (e.g., in torr liters/sec) of gas flowing into the system, and Qgis the gas flow due to interior surface outgassing. Thus, in general,

the pumping speed is

VdP Q Qo

^^-P^ P PIn order to measure the pumping speed, conditions are imposed on

the system so that a simplified form of Eq. (7-2) is applicable. Forexample, if the outgassing rate is negligible {Qq = 0) and the systemis operated at constant pressure with a steady flow of gas {Q = const)

entering the system, then dPjdt = and from what remains of (7-2)

-I (7-3)

as given in (2-1). This expression is sometimes used as the definition

of pumping speed and is a valid basis for measuring the pumping speedin the pressure range of most oil-sealed mechanical pumps, provided

'

the pressure measured actually corresponds to the gas admitted to the

system, as discussed in Sec. 5-3. If air is admitted to the system at a

measured flow rate Q and the pressure measured with a McLeod gauge,then because of the compression effect of the McLeod gauge, as de-

scribed in Sec. 3-4, the pressure reading will be just the partial pressureof the permanent gas (in this case air) admitted to the system at themeasured flow rate Q. Also, in the pressure regime of oil-sealed

mechanical pumps the sorption processes (adsorption and desorption)

274

THE MEASUREMENT OF PUMPING SPEED 275

of surfaces reach a balance in a relatively short time, particularly for

permanent gases, so that if Q (the admitted flow) is kept constant,

Qf, (the outgassing rate) rapidly approaches zero and the pressure

reaches the value given in (7-3) rather quickly.

Also, in the case of mechanical vacuum pumps, the pumping speed

varies considerably with the inlet pressure, decreasing rapidly with

decreasing pressure near the ultimate pressure Pq of the pump. Thusthe ultimate pressure is determined not so much by the outgassing

in the system as it is by the decreasing pumping speed approaching

zero at the ultimate pressure.

Whether the outgassing rate Qg is important (or whether there is an

excessive leak in the system) can be ascertained by closing off a valve at

the pump so that S = 0. Then with the flow Q = 0, Eq. (7-1) becomes

dP'dt

or

Qo

V

p -u9if ;7-4)

Observation of the pressure several times during the pressure rise

yields a linear curve, the slope of which is Qo/ V. By putting the result-

ing value of Qo into (7-1) with Q = and dPjdt = 0, the pumping

speed at the ultimate pressure can then be determined from

a ^0On = -;^ (7-5)

If the system is free of accidental leaks then, for mechanical pumps,

Sf, is generally very small as compared with the value of S at higher

pressures and can be neglected.

In the case of diffusion pumps, however, the situation is quite

different. As discussed in Sec. 6-5, the pumping speed of a diffusion

pump is essentially independent of the pressure over the range in which

measurements are normally carried out. The ultimate pressure is then

not the result of the pumping speed approaching zero but of a limitation

on the attainable pressure due to the outgassing rate Q^. The situation

is frequently such that a base pressure is soon reached which then

changes only very slowly with the time because the outgassing rate

becomes nearly constant.

Returning to (7-1) for the case in which the system is operated at

constant pressure, we have

PS = Q + Qo

and (7-6)


SO that instead of (7-3) we have the equivalent of (6-34)

(7-7)

which is unambiguous only if the pumping speed is essentially inde-

pendent of the pressure. In this case it also follows that

S = P2-P1(7-8)

Thus if the equilibrium pressure P is measured for each of several values

of the gas flow Q, in sequence, and Q is plotted against the resulting P,

then the slope of the curve is the pumping speed S, as illustrated in

Fig. 7-1.

Still another way in which the pumping speed can, in principle, be

determined is by observing the pressure as a function of the time as the

system is pumped down. If the

gas flow Q = and the outgassing

rate Q^, is negligible, then from (7-1)

SdtdP

(7-9)

so that by integrating and re-

arranging we have

V P,S = 2.30 login^

(7-10)

Unfortunately, there are very few

real situations to which this ideal

pumpdown equation applies. In

the regime of mechanical roughing

pumps, the pressure usually changes

so rapidly during the pumpdown,

operation that the outgassing rate is not negligible and is changingwith time. Only if the volume of the system is very large as comparedwith the displacement speed of the pump, so that the pressure changesslowly during pumpdown, will observations based upon Eq. (7-10)

check approximately with the known pumping speed of a mechanicalvacuum pump. In this case the walls remain nearly in equilibriumwith the pressure in the system and outgassing does not play an im-portant role.

Pressure, P

Fig. 7-1. Graph of throughputagainst resulting pressure for deter-

mination of the pumping speed.


In the pressure regime of diffusion-pump operation (7-9) and (7-10)

do not generally apply because the outgassing rate is an important

factor near the base pressure. However, in this case the outgassing

rate rather soon reaches a nearly constant value, changing slowly

enough that it may be regarded a constant during the period required

for a pumpdown test. In this case Eq. (7-1) can be written

dP_

dtPS + Q, (7-11)

Since the pumping speed of a diffusion pump is independent of the

pressure and since for periods of interest the outgassing rate Q„ may

be regarded as constant, the value of Q^ can be substituted from (7-6)

so thatdP

F^ = -S(P - Po)at

the base pressure. Rearranging terms and integratingwhere P,, is

yields

so that

Jp, P-Po ~ V k

In

PP

dt

Po 8

Pi~Po= - T7 (*2 - ^1)

V

and S = 2.30V

H ^1

logiP1--P0

(7-12)

When the assumptions leading to Eq. (7-11) are vahd, then Eq. (7-12)

provides a basis for pumping-speed measurement which has certain

distinct advantages. Measurement of the gas flow is not required, and

the gauge constant cancels out, provided that the gauge is linear over

the pressure range of the measurement. The volume of a system can

generally be determined with fair precision from external dimensions.

The procedure is simply to pump down the system to a steady base

pressure, then let in enough air (preferably through a drying tube)

to bring the pressure back up by a factor of 10 or more, and flnally

to read the pressure at several specific values of the time as the system

pumps down again. This procedure works well on large systems,

particularly when the rate of change of pressure during pumpdown

is not so rapid as to make pressure readings difficult.

7-2. Measurement of Gas Flow. Pumping-speed measurements

for determining vacuum-pump performance are predominantly carried

out under conditions of constant flow. The full range over which gas

flow must be controlled and measured for the routine measurement of

pumping speeds of commercial vacuum pumps extends from about 10"


to about 10-5 torr liters/sec. Gas is normally admitted through a

control valve or standard orifice into an appropriate test dome mounted

on the pump and the flow rate controlled to a value at which the desired

pressure is maintained. The gas flow must be measured in such a waythat the volume per second and the pressure are both known, so that

the throughput Q = P{dVjdt) is determined. In those cases in which

no significant pressure drop occurs in the flow-measuring device, the

pressure of interest is the barometric pressure when the test is in

progress. In those cases in which there is a pressure drop, the value of

the pressure at which the flow dVjdt is measured must be determined.

Some of the devices commonly used for throughput determination in

various flow ranges will be briefly described.

Calibrated Orifice. For large flow rates a calibrated orifice

connected to the test dome through a gate valve is convenient and

reliable. The surrounding air at atmospheric pressure or any desired

gas maintained at a controlled pressure in a tank upstream from the

orifice flows into the system at a rate determined by the diameter of the

oriflce and the temperature, average molecular weight, and pressure of

the gas upstream of the orifice. The flow rate is independent of the

pressure downstream from the oriflce, provided that the pressure is less

than the critical pressure given in Eq. (6-1), as in the case of the flow

of steam through an ejector nozzle. For the common diatomic gases

y = 1.40, so that the critical pressure from (6-1) is

P, = 0.535Pi (7-13)

where P^ is the pressure upstream from the orifice.

The critical mass flow through an oriflce under these conditions is

given by Eq. (6-7), which for a diatomic gas becomes

dMHI

= 0.538c(Pipy^'D^ g/sec (7-14)

when the pressure is measured in /ibars (dynes per square centimeter)

and D, the diameter at the throat of the orifice, is in centimeters

ordW-^ = 19.64c(Pip)'^^Z»2dt

g/sec

when the pressure is measured in torr. Finally,

dW11

915c(Pi/Fi)'^i)^ Ib/hr

(7-14a)

'

(7-146)

in the usual engineering form in which D is in inches, the pressure is in

pounds per square inch, and F^ = 1/p is the specific volume in cubic


feet per pound. The parameter c is the nozzle coefficient and generally

has a value close to unity. Since from Eq. (1-8) the gas density is

W MPV R,T

the critical volume flow through the orifice is

dt p dt

= 4904c|— Z)2 cm^/secMl

(7-15)

by substituting R^ = 62,364 from Table 1-2.

For air, for which M = 28.98, at a normal room temperature of

20°C

dY— = 15.6 X 103cZ)2 cm^/secdt

= 15.60c7)2 liters/sec

when D is measured in centimeters, or

dVdt= 213.3cZ'2 cfm

(7-16)

(7- 16a)

when D is measured in inches.

For example, the approximate critical flow of atmospheric air through

an orifice of 1 in. throat diameter under the above conditions is 100.6

liters/sec or 213.3 cfm, obtained by setting c = 1 in the above equation.

If atmospheric pressure is 760 torr, then the throughput for air through

a 1-in. -diameter orifice is

Q = P— = 760 X 100.6 = 7.65 X 10* torr liters/secdt

= 760 X 213.3 = 1.62 x 10^ torr cfm

In practice the values of the temperature and pressure at the time of

the measurement must be substituted in (7-15).

The exact value of the nozzle coefficient depends upon the flow

conditions and the detailed shape of the orifice. For testing the

"capacity" or pumping speed of steam ejectors, the Heat Exchange

Institute! * has developed a standardized long radius orifice, the design

of which is shown in Fig. 7-2. The arrangement prescribed by the

institute for the mounting of the standard orifices in pumping-speed


chapter.


measurements is shown in Fig. 7-3. The above reference also gives

tables and graphs of flow rates in pounds of air per hour for a sequence

of standard nozzles ranging in throat diameter from 0.0625 in. to 1.0 in.

Table 7-1 contains a sample of the data given in one section of the

above reference with the flow rates

in pounds per hour as in the

original, and also for convenience

with the flow rates converted to

torr cubic feet per minute and

to torr liters per second. These

values differ very little in general

from those calculated from (7-15)

by assuming that c = 1, indicat-

ing that for flow in the range of

interest for vacuum applications

the nozzle coefficient c for the

HEI standard orifice shape is very

nearly equal to 1. The tables

and curves permit accurate deter-

mination of the critical flow rates

for a wide range of atmospheric

pressure and temperature for the

full set of standardized orifices

listed in Table 7-1.

Also in Ref. 1 a detailed method

is given for computing the nozzle

coefficient for an orifice of any

throat diameter, but of the HEIstandard shape. The flow values

given in Table 7-1 are extended to orifices of larger dimensions than

those of the HEI series.

In using standard HEI orifices for controlling and determining flow

rates it is most important to note whether the pressure in the system

just downstream from the orifice satisfies

P3 < P^ = 0.535Pi

from (7-13), where

P, (^ 400 torr for P^ = 760 torr

If this condition is not fulfilled, then the flow is subcritical and

depends on the pressure difference across the orifice instead of simply

the upstream pressure. The expression for subcritical flow is

dW— = 19.64c(Pi - P^y-^'p^'^D^ g/sec (7-17)

Fig. 7-2. Proportions of standard

long-radius flow nozzle recommendedby the Heat Exchange Institute for

gas-flow determination. [Reprinted

from the Standards for Steam Jet

Ejectors, 3rd ed. Copyright 1956 bythe Heat Exchange Institute, 122 East

42nd Street, New Yorli, N.Y. 10017.]


-Manometer

ly^^^ Downstream pressure tap

To ejector suction —*-

Control volves

Fig. 7-3. Arrangement of standard orifice for critical air-flow tests. [Reprinted

from the Standards for Steam Jet Ejectors, 3rd ed. Copyright 1956 by the HeatExchange Institute, 122 East 42nd Street, Xew Yorlc, N.Y. 10017.]

Table 7-1. Critical Flow Rates fob Heat Exchange Institute StandardOrifices *t

Dry Air at 70°F and Barometer Pressure of 30.0 in. Hg = 762 torr

Density = 0.07510 Ib/ft^ = 1.203 g/liter

Orifice Volume flow Mass Throi] ghputHEI flow

no. diameter, in. cfm liters/sec Ib/hr torr cfm torr liters/sec

1 0.063 0.810 0.382 3.65 6.17 X 102 2.91 X 102

2 0.094 1.82 0.857 8.18 1.38 X 103 6.53 X 102

3 0.125 3.24 1.53 14.6 2.47 X 103 1.17 X 103

4 0.188 7.35 3.45 33.1 5.60 X 103 2.64 X 103

5 0.250 13.0 6.16 58.8 9.94 X 103 4.69 X 103

6 0.313 20.5 9.68 92.4 1.56 X 10* 7.37 X 103

7 0.375 29.5 13.9 133 2.25 X 10* 1.06 X 10*

8 0.500 52.6 24.8 237 4.01 X 10* 1.89 X 10*

9 0.750 119 56.0 535 9.05 X 10* 4.27 X 10*

10 1.000 212 100.1 956 1.62 X 105 7.63 X 10*

1.250 332 156 1497 2.53 X 105 1.19 X 105

1.500 476 224 21.50 3.63 X 105 1.71 X 105

* Reprinted from the Standards for Steam Jet Ejectors, 3rd ed. Copyright

1956 by the Heat Exchange Institute, 122 East 42nd Street, New York, N.Y.10017.

t Mass flow data for HEI standard orifices Xos. 1 through 10 given in ibid.

Pig. 20, p. 23.


when D is in centimeters, the density in grams per cubic centimeter,

and the pressure in torr. This expression becomes

915cP,

V,D^ Ib/hr (7-17a)

when the pressure is measured in pounds per square inch, V^ = l/p

is the specific volume in cubic feet per pound, and D is measured in

inches.

1.0 [- n ~1~11 nn —:= __

,

—0.99 -

Nozzle dio^^S5^:—

:

;

—

——= =0.98 -

.--'^^=—

!

Z.0.5003£^

;:: ::::"""=— ^"

t-°-5^

^

FT^=^^.._ .

—

—— ^S 0.96 r ^& —

'

".— — — ,

.—— —° 0.95

-

/yP rz-^^^---^ ,^ ..^

-^ U.94-

'/,0^ <^

y' ^-^ —> 0^ .f /

^c->

/'

o^-

.^—

^ 0.91- -f-

/OJ / /S 0.89

^

oJ^ 0.88

-

/0.87

nflfi"""100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300

Flow, pounds per hour per square inch of nozzle throat area

Fig. 7-4. Nozzle coefficients for standard orifices. Dry air at 70°F. [Reprinted

from the Standards for Steam Jet Ejectors, 3rd ed. Copyrigiit 1956 by the Heat

Exchange Institute, 122 East 42nd Street, New York, N.Y. 10017.]

The expressions for critical and subcritical flow are correct as long

as the diameter of the pipe immediately downstream from the orifice

is at least four times the throat diameter of the orifice.

Values of the nozzle coefficient c have been determined for the

standard orifices by a series of tests conducted by the Heat Exch3,nge

Institute. Some results of these tests are shown graphically in Fig.

7-4. Inspection of this set of curves and comparison with the flow

rates shown in Table 7-1 for critical flow will reveal that the range

of values of the nozzle coefficient of interest for most vacuum work is

from 0.94 for the smallest orifice {D = 0.0625 in.) to 0.99 for the

largest shown on the graph (D = 1.00 in.).

Rotameter. The rotameter (see Fig. 7-5), which is a variable

orifice device, is a vertically mounted tube of tapered precision bore


i

with a rotating float inside. The height of the float is determined by the

gas-flow rate upward through the tube. Rotameters are calibrated bythe manufacturer and can be obtained in a wide range of sizes. Thethroughput range from about 150 torr liters/sec to about 1 x 10*

torr liters/sec can be covered conveniently with overlapping ranges

with a set of four units. Care must be exercised

to ensure that the rotameter is accurately vertical

or the float will rub on the side of the tube, pro-

ducing erratic readings.

Inverted Buret. This term is used here to

designate any of several versions of a simple de-

vice which in its original form consisted of an

inverted buret thrust into a beaker of diffusion-

pump liquid, as shown in Fig. 7-6. The outlet at

the top of the buret may be connected to a T in a

tube leading to the needle valve, the other leg of

the T opening to atmosphere through a stopcock,

so that when the stopcock is closed the gas flow

sucks oil up into the tube. To a first approxi-

mation the rate of rise of the oil level in the tube

multiplied by the cross-sectional area of the tube

is a direct measure of the flow rate. However, in

this simple arrangement the pressure on the gas

above the oil level is continually decreased by the

difference in head of oil in the buret and in the

beaker, so that for precise results a correction

must be made.

Since the density of a light oil is only about Ksthat of mercury, the reduction in pressure of the

gas entering the pump when the oil level in the

buret is 30 cm above that in the reservoir is only

about 20 torr in a normal atmospheric pressure

of 760 torr, or a pressure reduction of about 2.6

per cent. The pressure of the gas entering the

pump can be kept constant by using as a reservoir

a tall cylinder which is moved up around the

buret as the oil level rises. Timing the rise in level between two marks

and manipulating the oil reservoir to keep the levels inside and outside

the buret the same is somewhat inconvenient, but can be managed. If

this is not done, then the pressure of the entrapped gas decreases as

the oil level rises^ such that

poil

Fig. 7-5. The rotam-

eter gas flowmeter.

[Reprinted through

the courtesy of

Fischer and Porter

Co., Warminster, Pa.]

png(7-18)


where P„ = atmospheric pressure

h = difference in height of the oil levels

pjjg = density of mercury

poii = density of the oil in the buret

If V represents the volume of gas at atmospheric pressure initially

trapped above the oil level at the instant the bypass valve is closed,

then when the oil level has risen h cm, the volume is

V =Vo-hA (7-19)

in which A is the cross-sectional area of the buret. The total quantity

of gas in the apparatus above the oil level is the product of (7-18) and

(7-19), which is

pollTo needle valve

on system

PV PaVo P„AhPag

Light

(Voh -h^A)

(7-20)

The average flow of gas through the needle

valve for the time interval A< is then

e=^(P„F„ PV)

i*: iisi;

I WM

P„APoll

PHg{V,-hA)

(7-21)

If h is measured in centimeters, A in square

centimeters, t in seconds, and P in torr, the

Fig. 7-6. The inverted-resulting flow is given in torr cubic centi-

buret type of flowmeter, meters per second.

If the volume hA displaced by the ofl is

nearly equal to V^, the correction term in (7-21) becomes very small

so that

Q (7-22)

This is the case when the diameter of the buret is large, the oil level

is raised essentially to the top, and the volume of the connecting tubing

over to the needle valve is small. However, if hA < Fo,

Q AAPA +^ F,

PHg .)(7-23)

In this case, which is more usual, the correction term may be quite large


and use of the simple expression (7-22) will lead to a large systematic

error in the measurement of the flow rate.

In the use of the inverted-buret flowmeter the bypass valve is opened

after each measurement and the oil level in the measuring tube drops

back down to that of the reservoir. Before closing the valve and

starting another measurement it is essential to wait long enough for

the oil to drain down from the wall of the tube. Since the surface film

initially left behind on the tube wall can, in effect, reduce the cross-

sectional area of the tube significantly, large errors in the flow measure-

ments can result from this effect, particularly when the diameter of the

measuring tube is small. This type of error can be reduced consider-

ably by using a liquid of low viscosity. Since air cannot have a larger

content than that corresponding to 100 per cent relative humidity

(Ph o ^ 18 torr at room temperature or ~2.4 per cent of atmospheric

pressure), water is for some purposes a better choice than oil. With

a 0.2-cm3 buret tube calibrated in units of lO-^^ cm^ a throughput as

low as 10"* torr liter/sec can be measured with acceptable accuracy.

The importance of variations in room temperature in measuring small

flow rates by the inverted-buret method is emphasized by Dayton.

»

A change of temperature of 3°C results in a 1 per cent change in volume

of a body of gas at constant pressure. During the measurement of a

small throughput the rise in the oil level may be completely masked

by a change in volume of the gas entrapped between the oil level and

the needle valve. An example given by Dayton is quoted below

:

For example, a 50-cc buret is a convenient size for testing 4-inch pumps

having peak speeds of about 200 liters per second at pressures from 10"^ to

10-2 mm. But in the range from 10"* to the ultimate vacuum of about

3 X 10"* mm the leak rate drops below 1 cc in 10 minutes. While the oil

might normally rise from to the 1-cc mark in 10 minutes, if the room

temperature increases by 3°C and about 50 cc of air are trapped above the

oil, the expansion wiU force the oil back down the tube by 0.5 cc. The

measured leak rate is thus 0.55 cc in 10 minutes, which is just one-half the

true leak rate. A rise of only 0.3°C in 10 minutes will cause an error of

about 5% in this case. Of course, the ambient temperature of the buret

could be held constant by a water jacket, but the author has found it more

convenient to hang a thermometer near the buret and note the temperature

at the times of starting and stopping the stop watch. Usually the room

temperature can be adjusted so that the final temperature is within O.TC of

the initial temperature.

The Pipe Organ. The pipe organ is a compact multiple-tube

arrangement, based upon the principle of the inverted buret, designed

and built at the Kinney vacuum laboratory for measuring gas flow

over a wide range.* The apparatus shown in Fig. 7-7 consists of two


Ven1 valve

Selector volve

(typical)

To pump under

test

Sight glass

Calibrated

measuring

cylinder (typical)

Oil or other low-

vapor -pressure

fluid

Drain plug

Section A-A

Fig. 7-7. The pipe organ flowmeter of J. F. Cleveland.

groups of concentric, vertical metal tubes with several valves at the

top so that the volume of each central tube and each of the several

annular spaces between the tubes can be separately, or in combination,

connected to the manifold at the top. A large rectangular reservoir

at the base provides an ample volume of the fluid.

Two glass sight tubes are mounted on the front of the instrument.

One runs from the reservoir in the base to the manifold at the top and is

connected in parallel with whatever combination of tubes is being used

for measuring the flow rate. The liquid from the reservoir rises in this

tube as well as in the measuring volume and provides a means of

observing the liquid level. The other transparent tube protrudes into

the liquid in the reservoir at the bottom and is open at the top. Bymeans of a two-way valve, which is normally open to the atmosphere,

the volume above the liquid surface in the reservoir can be connected

to a compressed-air supply and the pressure raised as necessary to

maintain the liquid level in the open sight tube the same as that in the

measuring volume.

When all measuring volumes are connected into the manifold, the

total volume displaced is about 2.3 liters, which enables the operator

to measure throughput up to about 200 torr liters/sec. By using only

the liquid-level indicating tube as a measuring volume, flow rates as

low as 0.1 torr liter/sec can be measured.

THE MEASUREMENT OP PUMPING SPEED 28/

The volume of the connecting manifold is small so that the liquid-

level compensation makes a perceptible difference only when the smaller

measuring volumes are being used. By applying a correction of the

type given in (7-23) to these smaller measuring volumes, the com-

pensation system can be eliminated entirely, thus simplifying somewhatthe operating procedure.

Constant-pressure Gas Flowmeters. In Fig. 7-8 is shown a sketch

of a constant-pressure flowmeter described by Stevenson'* in which a

group of five calibrated tubes of widely differing volumes are used for

measuring the flow rate. The novel feature of this instrument is the

upper reservoir and overflow arrangement by which the tube in use

is filled by oil flowing in near the top instead of by suction from below.

The level in the upper reservoir is maintained by pumping oil from the

lower to the upper reservoir, from which it returns to the lower reservoir

by way of an overflow. The spout for supplying oil requires the oil

level to rise only a limited amount to spill over into the measuring

tubes.

The static head corresponds to no more than 0.2 torr for the smallest

to 2.0 torr for the largest buret. Maximum correction throughout

in the measured flow due to pressure difference does not exceed 0.5

per cent on any of the burets. The practical range of throughput

measurement is from about 50 to about 3 x 10-^ torr liter/sec. As in

the simple inverted buret, an oil film remaining on the inner surface

of a measuring tube due to a previous operation can cause significant

error, especially in the use of the smaller-diameter tubes. Sufficient

Overflow

column

Fig. 7-8. Constant -pressure gas flowmeter. [Taken with permission from D. L.

Stevenson, in 1961 Vacuum Symposium Transactions (Pergamon Press, London,

1962).]


time for the oil to drain back into the reservoir must be allowed be-

tween measurements. Also reasonably constant room temperature is

essential to avoid error due to expansion.

Another form of a constant-pressure flowmeter, which is particularly

effective for the measurement of small flow rates, is shown in Fig. 7-9.

This instrument* consists of a glass capillary tube of 0.1 to 0.3 cm bore

in an approximately horizontal position with a drop of mercury

inserted at one end. If a small

Needle volve

Baffle,

Test dome

McLeodgouge

Colibroted

copillory

Air ond

mercury inlef

Mercury pellet

Mercury trop

MonometerVacuum pump

Fig. 7-9. Gas flowmeter consisting of a

calibrated glass capillary with a travel-

ing mercury pellet. [Taken with per-

mission from C. E. Rufer, in 1956

Vacuum Symposium, Transactions


gas flow has previously been estab-

lished through the tube, the mer-

cury drop moves along the tube

at the flow rate of the gas with

very little frictional drag. Thecapillary is expanded into a

funnel at one end into which a

drop of mercury can be inserted

with an eye dropper whenever a

measurement is to be made. Theother end of the capillary is ex-

panded into a normal-diameter

tubing for connecting to the needle

valve and also for connecting a

small reservoir on a T, in which to

accumulate the mercury droplets which come through the tube. Al-

though the pressure difference required to move the mercury drop

in the capillary is small, the true pressure of the gas entering the system

can easily be measured by means of a manometer connected to the

connecting T near the mercury trap, as shown in Fig. 7-9. The cross-

sectional area of the capillary can be checked for uniformity by noting

any variation in length of a mercury drop in passing along the tube

and can be measured by weighing several mercury fillings of a markedlength. Flow rates as low as about 3 x 10~* torr liter/sec can be

measured with acceptable accuracy.

Calibrated Capillary Leaks. The trick of preparing very fine

capillaries is known to many familiar with glassblowing techniques.

A short length of glass tubing is softened in a flame and allowed to

thicken and contract. When the central part of the tube is nearly

a solid rod, the bore having contracted to a fine line, the tube is removedfrom the flame and quickly stretched out at arm's length. Thewhisker of glass connecting the two ends of the tubing will then be a

capillary of small diameter and microscopic bore. The fine capillary

can be broken off at one end but left attached at the other end of the

normal-diameter tubing from which it was drawn to be used for


connecting to the vacuum system. When the system is pumped downagainst the air leakage through the capillary from atmosphere, the leak

rate can be adjusted by breaking off sections of the capillary until the

desired equilibrium pressure or flow rate is achieved. The system musthave a valve at the inlet to the vacuum pump, and the volume isolated

from the pump by the valve must be known. Then by closing the

valve and noting the rate of pres-

Controlled leok

1^ Liquid

Hz

Pz

|_Jlon gauge

4- in.

pump

Metering

tube

To forepump

D = 1.27cm

L= 30.5 cm

i-2-in.pump

To forepump

D,= )0.5cm

D2=5.3 cm

sure rise, the leakage rate of the

capillary can be determined. Aset of capillaries can be adjusted

and calibrated on a laboratory

vacuum system and then used

for pumping-speed measurements.

By this technique capillaries of

leak rates as low as 10~^ torr

liter/sec can be prepared. Theprincipal drawback in the use of

calibrated capillaries is their ten-

dency to become partially clogged

by dust particles. By enclosing

each capillary in a rugged glass

sleeve plugged by a filter of glass

wool, the tendency to clog up is

reduced and the capillary is pro-

tected against breakage. Evenwith the best protection, however,

the leakage rate of a capillary

can change because of clogging

so that a periodic check of the leakage rate is essential to ensure

reliability.

Pressure Drop through a Known Conductance. The measurementof very small flow rates can frequently be most effectively accomplished

by measurement of the pressure difference across a known conductance

in the form of a tube or aperture.''* The gas entering the test dome of

a vacuum pump flows through a tube or aperture of known dimensions

from an auxiliary chamber, as in Fig. 7-10. A needle valve for ad-

mitting the test gas and a separate diffusion pump are connected to the

auxiliary chamber so that the pressure Pi can be adjusted to any

desired value. If the pressure is sufficiently low that the molecular meanfree path is not too small compared with the diameter, the gas flow

through the interconnecting tube into the test chamber is then, ac-

cording to (2-4),

Q = C{P, - P,)

Fig. 7-10. Arrangement for deter-

mining gas flow by measuring the

pressure drop across a known con-

ductance. [Taken with permission

from A. A. Landfors and M. H. Hab-lanian, in 1958 Vacuum Symposium,Transactions (Pergamon Press, Lon-

don, 1959).]


in which, according to (2-96),

C ^ 3.810yZ)3

hters/secL + %D

when the diameter D and the length L of the tube are measured in

centimeters. If, instead of a tube, the conductance is in the form of an

aperture, according to (2-93),

MlC 3.641 ^J A Hters/sec

in which A is the area of the aperture in square centimeters.

The conductance of the metering tube or aperture is accurately

known from dimensions which can be measured with great precision.

The principal error in determining the throughput by this means is in

the determination of Pj, the pressure in the auxiliary chamber, since

generally Pg < Pi for cases of interest. The uncertainty can be

reduced substantially if the parameters are so chosen that P^ is in any

case greater than 10"* torr so that an accurate determination using a

McLeod gauge is possible. However, in order to maintain the ad-

vantage of using the simple conductance formulas given above, the

parameters must be chosen to ensure that the maximum value of P^

does not exceed the lower limit Pj of the transition pressure range,

as discussed in Sec. 2-7, for which values for air at room temperature

are given in Table 2-1. This requirement is approximately equivalent

to the requirement that the molecular mean free path not be less than

the diameter of the metering tube.

Thus, for example, the metering tube diameter should not exceed 0.5

cm if the pressure Pj is to be as high as lO-^ torr. If the length of the

tube is 30 cm and its diameter is 0.5 cm, then from (2-97) the conduct-

ance C = 4.94 X 10-2 liter/sec for air at room temperature. The

highest pressure for which this conductance value is valid is lO^^ torr,

so that the maximum flow rate measurable is Qmax = 4.94 x 10~* torr

liter/sec, provided Pj < Pj. The lowest flow measurable with

accuracy using a McLeod gauge (Pj = 10"* torr) is then about 5x10-"torr liter/sec using this same metering tube.

By using ionization gauges instead of a McLeod gauge much lower

flow rates have been measured by this method, as described in Refs. 5

and 6. Although reliance upon ionization gauges for absolute measure-

ments is open to criticism due to the difficulties described in Chap. 3,

the measurement of the throughput, described above as applied to

pumping-speed determination, is a relative measurement, Pj relative

to Pj in a sequence of observations. Since in such a system the base

pressure for zero flow is nearly the same for both gauges, the error in the


pressure difference (P^ — Pg) is less than the error in either pressure

reading alone. At very low values of the pressure, such as lO"" torr

as observed in Ref. 6, however, significant gauge errors, even for the

pressure differences, are to be expected. Errors of this type dueprimarily to sorption and decomposition effects in the gauges can be

significantly reduced by using the noble gases such as helium, neon, andargon, for which these effects are far less bothersome than for the

chemically active gases.

7-3. Mechanical Pump Speed Measurements. Over most of

the operating pressure range of mechanical vacuum pumps the molec-

ular mean free path is short as compared with the diameter of the

Leak valve

Q. To flowmeter2 min

10 D max

Vacuum gauge I

I« min

L_i_:Pump

"TtMini D

I min

-~. To flowmeter

-©Vacuum gouge

(a)

Pump

(b)

Fig. 7-11. Arrangements for measuring the pumping speed of oil-sealed

mechanical vacuum pumps, (a) For inlet larger than 2 in. inside diameter;

(6) for inlet smaller than 2 in. inside diameter.

pump inlet. Gas flow is therefore viscous and the conductance into the

pump large as compared with the molecular-flow value. The con-

ductance of any reasonably proportioned test dome connected to the

pump inlet for the purpose of making pumping-speed measurementswill therefore be very large over most of the pressure range of interest

and will not seriously affect the results. However, some precautions

are necessary to ensure consistent results.

Typical arrangements for measuring the pumping speed of a mechani-cal vacuum pump with constant gas flow are illustrated in Fig. 7-11.

The system consists of a test dome of the same diameter D as the pumpinlet and of height equal to at least 1.5Z). The connection for at-

taching a McLeod gauge should be perpendicular to the wall of the test

dome at a distance of 1 in. or 0.25i), whichever is larger, above the

pump inlet. The gas flow should preferably be admitted at a distance

at least equal to 1.257) above the pump inlet near the closed end of the

test dome furthest from the pump inlet through a small tube bent so

that the air flow is directed toward the closed end of the dome. This

precaution is necessary only when the pressure is less than 1 torr to


avoid the possible formation of a supersonic gas jet directed into the

pump inlet, the occurrence of which may result in fictitiously high values

of the pumping speed. For pressures above 1 torr this precaution is

not necessary However, the gas inlet should not be oriented directly

toward the gauge inlet.

Oil-sealed mechanical pumps all tend to splash or spit some oil out

the inlet into the test dome. In some cases this condition can be so

troublesome that the gauge connection becomes clogged and the gauge

Table 7-2. Pkbssube Gauges Recommended fob Use in Determination of

Pumping Speeds op Oil-sealed Mechanical Vacuum Pumps

Pressure range, torr

1 X 10-*-0.5

10-2-5.0

0.1-100

1.0-760

Type oj gauge

Fine McLeod gauge

Coarse McLeod gauge

Precision mercury manometerMercury manometer

contaminated with sealing oil. It is frequently necessary to introduce

some baffling in the test dome or some manifolding of larger diameter

between the pump inlet and the test dome to prevent oil accumulation

from interfering with pressure measurements.

Pressure measurements should preferably be made with closed

mercury U-tube manometers and McLeod gauges connected directly

to the test dome without a low-temperature vapor trap. The ranges

of the pressure gauges should overlap and have full scale readings no

greater than the upper range of the pressure limits given in Table 7-2.

As has been discussed in Sec. 5-3, the objective of the pressure measure-

ment is to determine the partial pressure of the gas admitted as the

measured throughput Q, unaffected by the vapor pressure of the sealing

oil in the pump. Total pressure gauges, such as a precision U-tube

manometer, should not be used for pressures below about 1 torr, since

the pressure of a poor quality or contaminated oil can easily be as great

as 0.05 torr without affecting the pumping speed of a mechanical

pump significantly. The McLeod gauge (see Chap. 3) has the distinct

advantage of responding perceptibly only to the permanent gas under

these conditions and should therefore be used for all values of the

pressure less than 1 torr.

For all but the largest flow rates, air should be admitted to the system

through a properly chosen needle valve after passing through the

flowmeter. When calibrated orifices are used, a gate valve should be

installed between the test dome and the orifice mounting to facilitate

changing orifices without shutting down the pump being tested.

Approximate ranges for various flow-measuring devices are given in

THE measurement OF PUMPING SPEED 293

Table 7-3. Instruments should be chosen to provide some overlap

in ranges to minimize errors in transition from one instrument to the

next as the throughput is changed.

In testing mechanical pumps by the constant-flow method it is foundthat consistent results are most readily obtained by first pumping downthe test system to an acceptable base pressure and then increasing

the throughput from zero upward, taking pumping-speed readings at

Table 7-3. Flow-measuring Means Recommended for Use in Determi-nation OF Pumping Speeds of Oil-sealed Mechanical Vacuum Pumps*

Flow range QFlow-measuring device

scfm torr cfm

0-0.2

0.1-100

20 and up

0-150

76-7.6 X 10*

15,200 and up

Inverted buret

Rotameters (1% accuracy) of

overlapping ranges

ASME standard, long-radius

orifices

* Orifices should preferably be used in the critical flow range (i.e., P < 400

torr). If they are used in the subcritical flow range (i.e., P > 400 torr) the flow

rate should be computed as outlined in Ref. 1.

successively higher values of the pressure. By this procedure the base

pressure is checked to see whether it is reasonable and the system is

tested for excessive leaks. Also, by the time the preliminary pump-down is completed the outgassing rate will have dropped to a low

enough value not to affect the results measurably.

A typical set of data of this type is shown in Table 7-4 and showngraphically in Fig. 7-12. A smooth curve is drawn through the data

points as representative of pump performance. The combined un-

certainty in the measurement of the gas throughput and the attending

pressure result in errors of the order of 5 per cent in pumping-speed de-

termination, when all reasonable precautions are taken.

7-4. Measurement of the Pumping Speed of Diffusion Pumps.As can be seen from the pumping-speed curves shown in Sec. 6-5, the

pressure range of interest for diffusion-pump operation is generally less

than 10-* torr, the pressure range in which the molecular mean free

path is of the order of, or greater than, the diameter of the pump barrel.

In this pressure range the geometry and dimensions leading into the

pump inlet affect the resulting pumping speed critically. For example,

adding a tubular extension of the same diameter as the pump barrel

and of length equal to three times its diameter to the inlet of a diffusion

pump will reduce the net pumping speed to about half that measured


Table 7-4. Typical Set of Data for Determining Pumping Speed as a

Function of Inlet Pressure for a Single-stage Mechanical VacuumPump

Inlet Throughput P umping speed

pressure,

torr torr cfm torr liters/sec cfm liters/sec m^/hr

0.007

0.010 0.149 0.0703 15.0 7.08 25.5

0.021 0.821 0.389 39.2 18.5 66.6

0.030 2.01 0.95 67.0 31.2 114

0.050 4.18 1.97 83.5 39.4 142

0.070 6.50 3.07 93.0 43.9 158

0.10 9.66 4.56 96.6 45.6 164

0.20 21.9 10.3 109.5 51.8 186

0.50 55.3 26.2 111 52.2 189

1.0 117.3 55.35 117.3 55.35 199

3.0 375 177 125 59.0 212

5.0 690 325 138 65.0 234

7.0 924 436 132 62.2 224

10 1,280 604 128 60.4 217

20 2,640 1,244 132 62.2 224

30 3,960 1,866 132 62.2 224

50 6,295 2,967 126 59.5 214

80 10,400 4,910 130 61.3 221

100 12,800 6,040 128 60.4 217

200 26,200 12,500 131 61.8 222

300 39,000 18,390 130 61.3 221

10"' 10"' 10° 10' 10^


Fig. 7-12. Plot of typical data(Table 7-4) of pumping-speedmeasurements on an oil-sealed

mechanical vacuum pump.

Air inlet

Diffusion punnp

Fig. 7-13. Incorrect method of

measuring pumping speed.

[Taken with permission from B. B.

Dayton, Ind. and Eng. Chem. 40,

795 (1948).]

THE MEASTJBEMBNT OF PUMPING SPEED 295

directly at the pump inlet. The configuration of the test dome con-

nected to the pump inlet, the location and orientation of the gas inlet

into the test dome all influence the measured value of the pumpingspeed more or less critically.

In a significant paper Dayton^ has discussed directional effects in

pumping-speed measurements. An extreme example of incorrect

method criticized by Dayton is illustrated in Fig. 7-13. In this

80° 70°

Fig. 7-14. Entrance and exit flow patterns for gas flowing through a circular

hole for which L = 5D (solid curves) compared with a cosine pattern (dotted

curve). [Taken with permission from B. B. Dayton, in 195G Vacuum, SymposiumTransactions (Pergamon Press, London, 1957).]

arrangement there is no test dome, but simply a flat plate bolted to the

inlet flange of the pump with connections for vacuum gauges and the

gas inlet. Gas molecules flowing from the inlet tube form a molecular

beam in which the molecular velocities are far from randomly oriented.

The angular distribution of molecular velocities resulting from gas

flow through a tube of length equal to five times its diameter, as

calculated by Dayton,^ is illustrated in Fig. 7-14, which must be

compared with the normal cosine distribution (dotted curve) char-

acteristic of random molecular motion. The angular distribution is

even more forwardly directed if the length of the inlet tube is manytimes its diameter. The gas molecules preferentially directed into the

pump jet are more effectively removed from the system than are

randomly directed molecules. The result is that the pseudo pumpingspeed measured by this incorrect method is invariably much greater

(such as a factor of 2) than that obtained by recommended methods


't^'T^'t:^150 liters/sec 280 liters/sec

or

230 liters/sec

1 "^180 liters/sec 240 lifers/sec

Fig. 7-15. Effect of position and

orientation of the gauge opening on

the measured pumping speed of a

diffusion pump. [Taken with per-

mission from B. B. Dayton, Ind.

and Eng. Chem. 40, 795 (1948).]

which do not involve beaming of the gas flow into the pump inlet.

As Dayton^ has also pointed out, pumping-speed measurements can

easily be in error pessimistically if

the gas inlet is so oriented that a gas

jet is directed into the gauge opening.

The position and orientation of the

gauge opening also has a striking

effect upon the measured pumping

speed as illustrated in Fig. 7-15 from

Dayton's paper.^ This striking effect

arises because the flux of molecules

(i.e., the number per second per

square centimeter) through a small

opening placed above the inlet to the

pump is not independent of the

orientation of the opening. The distribution of the molecules is not

isotropic because they are coming generally from above, where they are

admitted, and disappearing below, where many of them are removed

by the diffusion-pump jet. Par-

ticularly in the pressure range be-

low 10-* torr, where the molecular

mean free path is very long, this

effect is pronounced. Since the

pressure measured by the gauge

is proportional to the flux of mole-

cules entering the gauge opening,

the gauge reading reflects the

nonisotropic distribution, giving a

higher reading if the end of the

gauge tube is turned upward to-

ward the top of the test dome and

a lower reading if it is turned

downward toward the pumping

inlet.

As a result of his investigation

of pumping-speed measurements

Dayton^ recommended the test

dome arrangement shown in Fig.

7-16 for testing diffusion pumps.The gas flow was admitted at the

top of the test dome through a series of circular baffles so placed as to

break up the molecular beam from the inlet tube and distribute the

flow randomly. The question arose whether the gauge connection

Fig. 7-16. Test dome arrangement for

measuring diffusion-pump speeds.

[Taken with permission from B. B.

Dayton, Ind. and Eng. Chem. 40, 795

(1948).]


shown at A or that at B in the figure would be more appropriate. Thegauge connection at A, with its opening oriented directly away from thepump inlet, will receive the same flux of molecules as does the pumpitself and will therefore produce a pressure reading equivalent to thatreceived by the pump. However, the question is not so much thepressure incident on the pump inlet, but the pressure associated withthe random motion of the molecules just above the pump inlet, unin-fluenced by the added increment of flux due to the downward flow.

Dayton reasoned that the gauge connection at B, with the plane of its

open end parallel with the direction of flow, would receive no additionalflux (positive or negative) due to the gas flow, but only that due to therandom thermal motion of the molecules, and would therefore receive

just the correct flux to produce a reading properly characterizing thepressure above the pump inlet. In addition, a nude gauge C of the typerecommended by Blears (see Sec. 6-4) was also included in the test domeas an alternative means of pressure measurement. The signiflcant

differences between nude and tubulated ionization gauges are dis-

cussed in some detail in Chap. 3.

Because of the critical dependence of the measured pumping speedof a diffusion pump on the arrangement of the test dome and its

accessories, adoption of a standardized test dome and procedure is

needed so that the performance of different models of diffusion pumpscan be specified unambiguously. A preliminary step toward meetingthis need was taken by the Committee on Standards and Nomenclatureof the American Vacuum Society." The committee recommendedthat the test dome to be used for this purpose have

:

1. Inner diameter D equal to that of the pump barrel.

2. Height (face of diffusion-pump flange to the closed end of thedome) of at least 1.5Z).

3. Exit of gas-inlet tube located on the axis of the test dome 1.0Z>

above the face of the pump flange and oriented directly toward thetop of the dome.

4. Gauge-connection tube oriented so that the plane of the open endis parallel with the axis of the test dome and located so that the openend is just above the top surface of the pump and protruding inwardfrom the wall of the test dome about 0.25 in. to avoid fouling by dif-

fusion-pump fluid condensed on the wall. Such a test dome is illus-

trated in Fig. 7-17.

The committee also recommended that the gauge not be connectedthrough a low-temperature vapor trap and that the gauge be cali-

brated before and after each series of measurements by inserting a


and the test dome and

Sloped top

Gas-inlet line

Leak vol«e

Input meter

Optional cooling coils

Test dome

Vacuum gauge

Diffusion pump

standard conductance between the pumpobserving the resulting change in pressure.

The principal difference between the recommendations of the

committee" and those made earlier by Dayton^ is in the choice of the

diameter of the test dome. By choosing the diameter equal to that

of the pump barrel the problem of

the entrance conductance (equiva-

lent to the end effect in the case of

the conductance of a tube, as dis-

cussed in Sec. 2-11) is avoided

since the test dome becomes a

uniform extension of the pumpbarrel. If the test dome is con-

siderably larger in diameter than

the pump barrel, as illustrated in

Fig. 7-16, then the flow pattern

for gas entering the diffusion

pump would be somewhat similar

to the entrance flow pattern illus-

trated in Fig. 7-14, showing that

some of the molecules are reflected

back from the entrance, resulting

in an impedance to the flow.

Because no entrance conductance

is involved in the use of a test

dome of a diameter equal to that

of the pump barrel, the pumping

speed measured by the procedure

recommended in the committee's

report will be somewhat greater than that which would be obtained by

using a test dome of larger diameter.

In estimating the net speed of a diffusion pump when installed on a

system this effect must be taken into account by combining the

specified pumping speed with the appropriate entrance conductance

if the pump is to be installed on a valve body, manifold, or vapor

trap of expanded diameter. An effort to be more precise on this point

is hardly justified, however, since the geometry of a diffusion pumptogether with its associated components is such that only rather rough

calculations of the net pumping speed can be made using the simple

formulas given in Chap. 2. In most cases the net pumping speed can

be calculated accurately only by the Monte Carlo method described

in Sec. 2-12. This method has been applied by Pinson and Peck"to a number of practical combinations of vacuum components.

Fig. 7-17. Test dome and accessories

for measuring the pumping speed of a

diffusion pump consistent with the

recommendations of the Committee on

Standards and Nomenclature of Amer-ican Vacuum Society.


Although the recommendations contained in the committee's reporthave not been officially adopted by the American Vacuum Society,the testing of diffusion pumps in commercial practice generally followsthe recommended procedure with respect to the four items listed

above. Choice of gauge, use of refrigerated traps, method of flowmeasurement, and the like are still questions left to individual choice.

However, the procedure as practiced at the Kinney Vacuum Laboratorymay be considered as an example and is illustrated in some detail inFig. 7-17.

Pressure Measurement. There are two gauge-connection tubesin the test dome, both installed as prescribed in item 4 above. Forpressure greater than 10"* torr a McLeod gauge is used, connected to

the test dome through a liquid-nitrogen-cooled vapor trap. The useof the vapor trap with the McLeod gauge is essential to prevent mercuryvapor from the gauge from contaminating the test dome and to preventbackstreaming oil vapor from the diffusion pump from contaminatingthe gauge. The McLeod gauge in any case responds only to permanentgas, which is appropriate for the measurement of the true pumpingspeed as defined in (6-34).

For pressure less than 10"* torr two ionization gauges are used, oneconnected directly and the other connected through a liquid-nitrogen-

cooled vapor trap. The pressure read by the trapped ionization gaugeis the partial pressure of permanent gas only and is again appropriate

for substitution into (6-34) for the true pumping speed. The untrappedionization gauge provides a reading dependent upon the "total pres-

sure," including condensable vapor, which can be used for determination

of the apparent pumping speed according to (6-35).

Gas Flow. The gas flow into the test dome passes through a

flowmeter and needle valve. Since the throughput must be constant

for appreciable periods of time in order to establish equilibrium pressure

in the test dome for each reading, the needle valve must be of suitable

design to ensure steady and controllable flow at the low flow rates usedfor diffusion-pump tests (typically from about 10"^ to about 10*

cm^/min at atmospheric pressure). All routine pumping-speed tests

are made with air, although measurements for other gases, such as

hydrogen, helium, and argon, are also made for the purpose of under-

standing pump performance.

Various types of flowmeters suitable for measuring the throughputare described in Sec. 7-2. In the diffusion-pump range some form of the

inverted buret, such as the pipe organ shown in Fig. 7-7 or the con-

stant-pressure version shown in Fig. 7-8, is most convenient in use andis relatively free of systematic error when used with proper pre-

cautions.


The pumping-speed curve shown in Fig. 6-18 was obtained sub-

stantially as described above. As will be apparent from the deviations

of the experimental points from the smooth curve, the probable error

in individual determinations of pumping speed is about 5 per cent

because of uncertainty in the measurement of the pressure and through-

put. Provided that systematic errors due to vacuum-gauge calibration

and flowmeter reading are avoided,

results of this quality are satis-

factory for most applications.

With increasing interest in

pumping speeds at very low pres-

sure, the methods described above

are frequently found to be inade-

quate since they depend upon the

integrity of a vacuum gauge.

The problems of calibration of

ionization gauges and the errors

inherent in the use of a McLeodgauge have been sufficiently em-

phasized in Chap. 3 to raise

doubts concerning the validity of

a pumping-speed measurement

based upon a presumably pre-

cision reading of a vacuum gauge.

With this problem in mind,

Oatleyi^ has developed a method

of measuring pumping speeds

which is independent of the accuracy of vacuum-gauge calibration.

The method consists essentially of comparing the pumping speed

of a diffusion pump with the conductances of a series of apertures

placed in series with the pump. The experimental arrangement as

shown in Fig. 7-18 consists of a short tube A of diameter large as

compared with that of the pump barrel to which is connected the test

dome B. The opening between B and A is obstructed by a thin plate

D, in which there is a series of apertures C of various diameters, aijy

one of which can be brought in line with the opening into A by rotating

the plate. The plate D is mounted snugly on the base plate F so

that leakage of gas from the test dome around the selected aperture

into the region A is negligible. Gas enters the system through the

capillaries L and K between which there is a small chamber M main-

tained at a chosen value of the pressure by means of a mechanical

vacuum pump and throttling valve. The leak rate through K can

by this means be set and maintained at any desired value. With a

Fig. 7-18. (o) General arrangement

of Oatley's apparatus for measuring

pumping speeds; (6) arrangement of

apertures in plate D. [Taken with

permission from C. W. Oatley, Brit.

J. Appl. Phys. 5, 358 (1954).]


fixed value of the leak rate Q, the pressure in the chamber is read on the

ionization gauge B with each of the apertures C set in position over the

central hole. The conductance C through any of the apertures fromEq. (2-93) is known accurately from its diameter. From Eqs. (2-5)

and (2-7) the total pumping speed of the diffusion pump and the

aperture is given by1 P 1 1

S Q S^ C(7-24)

The pressure in the test dome (provided only that it is in the region of

linear response of the gauge) is

P = ki+ (7-25)

where ^+ is the positive ion current reading of the ionization gauge.

Thus

1j-

k \o„ C(7-26)

so that the gauge reading is a linear function of the quantity 1/C and

the intercept of the curve at 1/C = is reciprocal of the pumpingspeed Sj, of the pump alone. The pumping speed of the pump is thus

determined without measuring the gas throughput Q or the calibration

constant k of the ionization gauge.

The procedure of Oatley described above contains the elements of

what is needed to meet the final recommendation of the Committee on

Standards of the American Vacuum Society, i" that of calibrating the

gauge by inserting a standard conductance between the pump and the

test dome. By measuring the gas flow Q in the above procedure and

inserting its value in (7-26), the gauge constant k is also determined

from the slope of the line.

The accuracy of the method described above depends upon the

constancy of the flow rate Q throughout a series of readings for all

values of the conductance C. The selection of aperture diameters must

also be chosen so that the conductances are in reasonable proportion

to the pumping speed to be measured.

A pumpdown method of measuring the pumping speed at very low

pressure in a situation in which Eq. (7-10) is applicable is described

by Milleron.i^ Equation (7-10) is valid when the base pressure Pq

of the system is small as compared with Pj and Pg. The method

described by Milleron consists of baking the system and pumping downto a low base pressure P,,, increasing the pressure by admitting helium

or neon gas, and then observing the pressure as a function of the time

from Pj to Pj, where P^ > lOOP^ and P^ > lOPo- Since neither

helium nor neon is adsorbed appreciably, the pumping speed with

302 VACUUM SCIENCE AKD ENGINEERING

these gases can be determined without appreciable error due to sorption

or outgassing effects. Since only the ratio of the pressures PijP^

enters the calculation of the pumping speed, the gauge calibration

cancels out. If the measured pumping speeds for helium and neon are

accurately proportional to the square roots of the molecular weights,

then this law can be assumed to hold in general and the pumpingspeed for air and other gases computed accordingly. However, if

the pumping speeds measured for these two gases do not follow this

relationship, it is not clear how to extrapolate these results to other

gases. In that event a similar measurement using dry nitrogen would

probably yield reasonably accurate results in spite of the somewhatgreater problem due to sorption processes.

REFERENCES

1. Standards for Steam Jet Ejectors, 3rd ed. (Heat Exchange Institute, NewYork, 1956).

2. J. H. Leek, Pressure Measurement in Vacuum, Systems, 2nd ed. (Published

for the Institute of Physics and the Physical Society by Chapman and Hall,

Ltd., London, 1964), pp. 173ff.

3. B. B. Dayton, Ind. and Eng. Chem. 40, 795 (1948).

4. J. F. Cleveland, Kinney Vacuum Division, The Xew York Air Brake Com-pany, private communication, Sept. 19, 1949.

5. D. L. Stevenson, in 1961 Vacuum, Symposium Transactions (PergamonPress, London, 1962), p. 555.

6. C. E. Rufer, in 7956' Vacuum Symposium Transactions (Pergamon Press,

London, 1957), p. 74.

7. A. A. Landfors and M. H. Hablanian, in 1958 Vacuum Symposium Trans-


8. H. G. Noller, G. Reich, and W. Bachler, in 1959 Vacuum Symposium Trans-


9. B. B. Dayton, in 195G Vacuum Symposium Transactions (Pergamon Press,

London, 1957), p. 5.

"Report of Committee on Standards and Nomenclature" (Chairman, B. B.

Dayton), in 1955 Vacuum Symposium Transactions (Committee on VacuumTechniques, Boston, 1956), p. 91.

J. D. Pinson and A. W. Peck, in 1962 Vacuum Symposium Transactions

(The Macmillan Company, New York, 1962), p. 406.

C. W. Oatley, Brit. J. of Appl. Phys. 5, 358 (1954).

Norman Milleron, in 1958 Vacuum Symposium Transactions (PergamonPress, London, 1959), p. 140.

10.

11

12

13

CHAPTER 8

THE DESIGN OF VACUUM SYSTEMS

A vacuum system consists of a vessel to be evacuated together withthe vacuum gauges, vapor jet and mechanical pumps, vapor traps,valves, connecting manifolds, and pipes. The vacuum vessel may bea processing tank, a space simulator, the chamber of a particle acceler-ator, or any enclosure within which the gas pressure must be reducedto a value substantially less than atmospheric. Designing the systemconsists of deciding upon the features of the vessel, selecting specific

commercial vacuum components, and arranging these componentstogether with interconnecting piping and accessories to achieve thespecified vacuum conditions in the vessel.

8-1. The Vacuum Vessel. Vacuum vessels are built to meetsuch a wide variety of requirements that a detailed description appli-cable to all circumstances is not feasible. However, a design philosophycan be suggested, and certain generally desirable features and fabri-

cating methods will be described.

Since a vacuum vessel is subjected to external atmospheric pressure,the usual precautions for the design of tanks subject to externalpressure should be taken to ensure that the vessel can safely withstandan external pressure of somewhat more than 1 ton/ft^. Aside from thepossible danger of buckling or collapsing, the walls of a vacuum vesselwill deflect during evacuation and return to normal when air is re-

admitted. Such deflections must be evaluated and any excessivedeflections corrected by increasing the wall thickness or by providingstructure to aid in sustaining the load imposed by the atmosphere.The materials of construction of vacuum vessels are predominantly

mild steel, stainless steel, and aluminum, although brass and copperare also fairly common. Castings are generally troublesome owing toporosity and are to be avoided whenever possible. Sections of glassm the form of plates or of tubes are frequently used for viewing portsor for electrical insulation. High-quality ceramics are frequentlyused as insulators for high-voltage leads. The vacuum vessels of large

proton synchrotrons are probably the most complex in design and303


exotic in the choice of materials because of the unusual combination

of electrical and mechanical properties required. Certain of the epoxy

resins were first used extensively in this application and have since

been used to advantage in other vacuum applications involving unusual

electrical, magnetic, and mechanical requirements.

Table 8-1. Some Properties op Commonly Used Solvents*

VaporBoiling Flash Toxicity, •

Solvent Formulapressure

at 20°C,point, point. M.A.C.

torr°C °C in ppm

Chlorinated hydrocarbons:

Trichloroethylene (_/ {j-HOlq 60 87 None 200

Carbon tetrachloride CCI4 88 77 None 25

Chloroform CHCI3 180 61 None 100

Aromatic hydrocarbons:

Benzene t_/rt_tle 80 80 -11 25

Toluene C,Hg 23

5

110

140

5

30

200

200XylenePetroleum hydrocarbons:

Stoddard solvent 25 155 40 500

Ethers:

Ethyl ether C,H,„0 440 35 -30 400

Ketones

:

^4^^10^

Acetone C,H„0 180 56 -20 1,000

Methyl ethyl ketone C.HgO 71 80 ^2 250

Alcohols

:

Methyl (wood) alcohol CH4O 98 65 15 200

Ethyl (grain) alcohol C2H5O 46 78 18 1,000

Isopropyl alcohol CoHoO 38 82 15 400

Fluorinated hydrocarbons:3 8

Trichloromonofluoromethane

Freon-MF(CCl3F) 700 24 None 1,000

Trichl orotrifluoroethane

Freon-TF(CCl2FCClF2) .... 284 48 None 1,000

Tetrachlorodifluoroethane

Froon-BF(CCl2FCCl2F) . . . 57 93 None 1,000

* From Bulletin FS-6, Solvent Properties Chart, issued by E. I. du Pont deNemours & Company, Inc., by permission.

The interior of a vacuum vessel should be as smooth and free of

crevices as possible. After fabrication the interior surfaces should becleaned by vapor-phase degreasing or by the use of a highly volatile

solvent to remove oil and other contaminants which would otherwise

maintain a high organic vapor pressure long after the vessel is evacuated.A list of useful solvents and their properties is given in Table 8-1.

THE DESIGN OF VACUUM SYSTEMS 305

The cleaning of a very large vacuum vessel can be a rather difficult

undertaking since health hazards and the danger of an explosion areserious factors. The use of detergents with water is not recommendedsince detergents leave a thin, highly tenacious film. In the case of anaccelerator cavity 9 ft in diameter and 90 ft in length the most satis-

factory answer to the problem of cleaning has been to scour the surfacewith fine emery and then wash with distilled water using carefully

selected cloths.

The quality of welding required for the fabrication of vacuum vessels

is such that only gas-shielded arc welding is recommended. Atomichydrogen welding produces excellent results and was for several years

the best commercially available process. The molten metal at the

weld is protected by a blanket of atomic hydrogen, reducing any oxides

present and preventing further oxidizing of the metal. More recently,

arc welding with helium or argon has become generally available,

helium being more common and inexpensive in the United States andargon in Europe. Using these methods a skillful welder can produce

leak-proof welds with far greater dependability than by oxyacetylene

or by ordinary electric arc welding in air. These latter methodsrequire the use of flux, which frequently results in occlusions whichcan cause leaks to develop after a weld has been tested and found to be

free of leaks.

In order to present a smooth interior surface free of crevices the welds

in a vacuum vessel should either be prepared for welding from inside

or, if to be done from outside the vessel, should be prepared for full

penetration. In either case no crack or crevice remains on the interior

surface. The exposed weld metal can then be machined or ground to a

smooth finish if desired.

A vacuum vessel must generally have a number of access and viewing

ports, flanged connections for the attachment of pumps, motion seals,

and other features required for the process to be carried out. Eachsuch feature requires cutting through the wall of the vacuum vessel

and welding in a tube or a flange and should be planned with care to

facilitate the welding operation and thereby minimize the probability

of a leak. Figure 8-1 illustrates acceptable designs for (A) a tube in the

side of a cylindrical tank, {B) a flange at the end of a tube, (C) a side

seam in a cylindrical tank and (D) the joining of an end bell onto the

cylindrical section of a tank. If internal welded joints need reenforce-

ment by additional welding on the outside, as illustrated in (B) above,

the outside weld should not be continuous, but should consist of a

series of segments with gaps between. If the outside as well as the

inside weld were continuous, then a volume of gas would be trapped

between the two welds. A small hole in the inner weld would slowly


leak gas into the chamber but could not be located by a helium leakdetector or any other method. Such leaks are referred to as virtual

leaks and can arise whenever pockets of trapped gas are formed duringfabrication. The very anomalous symptoms of a vacuum system witha virtual leak are so difficult to diagnose that the designer shouldconscientiously avoid any possibility of pockets of trapped gas.

'Bell

^^—Tcnk

(D) Bell-to-tonk Weld

rK'Tank

S /, Tube

^Tank

(Where inside

welding possible

Tube

1

Where only

outside welding

possible

A) Tube-to-tank Weld

Outside

W^WVxVM ^th>TankVocuum side

Where inside ( Where only outside'

welding possible) welding possible

(C) Seam Weld

Flange

B) Flange-to-tube Weld

Fig. 8-1. Details of welds for vacuum vessels and compononts. {A) Tube intothe side of a cylindrical tank; (_B) flange on the end of a tube; (C) side seam in acylindrical tank; (£») end bell on a cylindrical tank.

Of major importance in the design of a vacuum vessel is the areaallocated to the pumping port. In the pressure range below 10"* torrthe flow is molecular so that the conductance at room temperaturethrough an aperture in a thin wall is that given by Eq. (2-93),

c

which for air at room temperature is

G = 11.6^ liters/s

where A is the area of the hole in square centimeters. Levenson,Milleron, and Davis^* have shown that the transmission probabilityachievable in the design of the combined vapor baffle and valve for adiff"usion pump is about 0.35; that is, the conductance of the baffleand valve can be as great as 0.35 that of the aperture alone. Com-bining this result with an assumed Ho coefficient (see Sec. 6-5) of 0.5,


THE DESIGN OF VACUUM SYSTEMS

the pumping speed for air achievable with good design is

S = 0.2C = 2.3^ liters/sec

307

(8-1)

Thus the pumping speed for air realizable through a 6-in. pumpingport is about 400 liters/sec. In the weighing of priorities for wall space

in a vacuum vessel, the importance of providing an adequately pro-

portional pumping port should not be neglected if the system is to

perform in accordance with requirements.

The final step in the fabrication of a vacuum vessel should be a

thorough job of leak hunting using a mass-spectrometer type of leak

detector. All the openings in the vessel should be blanked off with

gasketed cover plates, and the vessel evacuated by means of a mechan-

ical roughing pump with the leak-detector unit in the pumping line.

All welded joints should be inspected for leaks using a fine jet of probe

gas in brief, carefully directed bursts in order to facilitate localizing

any leak which may be present. With the superior leak-detection

(see Chap. 4) and welding methods now available it is no longer neces-

sary to accept as unavoidable a leakage rate which is great enough to

constitute a serious limitation on the performance of a vacuum system.

8-2. Demountable Seals. In the assembling, operating, and

servicing of vacuum systems demountable seals are convenient if not

absolutely essential. The major components of a vacuum system are

generally assembled using demountable seals to facilitate subsequent

disassembly for servicing or modification. Access port covers, viewing

windows, gauges, and other accessories are typically connected to the

vacuum vessel with demountable seals. Many types of seals have been

used for this purpose, but with the development during World War II of

rings for seals in aircraft hydraulic systems, the adoption of various

flange configurations sealed by rings has become an almost universal

practice.

An ring is a molded, ring-shaped gasket with circular cross section

made in a wide range of dimensions and of any of several elastomers,

depending upon its intended use. For vacuum service the material

should have a Shore hardness of about 60. Buna N is commonly used

because it does not deteriorate when exposed to oil and has excellent

mechanical properties for room-temperature seals. Figure 8-2 illus-

trates a number of typical 0-ring seals. For sealing flanges an O ring

is inserted in a groove cut in one member of the mating flanges, the

other member having a smooth, flat surface. Several shapes of

grooves, some of which are illustrated in Fig. 8-2a, have proved to be

useful. However, whatever the shape of the groove, its depth should

not exceed two-thirds the cord diameter of the O ring, and the area


of its cross section should exceed that of the ring. When the

mating flanges are then forced together metal-to-metal, as shown in

Fig. 8-26, the ring is sufficiently distorted to provide a good seal

but does not fill completely the volume available in the groove. This

latter provision ensures that the elastomer of the O ring is not over-

stressed. If the volume of the groove does not exceed that of the

aAJ:ij

A= ~ 13/16 X O-ring diameter

B = ~ 1 1/2 xO-ring diameter

A=~ 49/64x0-ring diameter

B = ~ 7/8 X O-ring diameter

(c)

Body

Gland nut

^Glond

^''<'!<-/M/A

O-ring

Bell jar

Fig. 8-2. O-ring demountable seals, (a) Types of O-ring grooves; (6) flangewith single O ring; (c) flange with double O ring and guard ring; {d) O-ringcouplings; (e) double O-ring seal for a metal bell jar.

ring, the ring will lose its elasticity and may fail to maintain aleak-proof seal. In any case, an overstressed ring cannot be reusedand may have to be scraped out of its groove. For some vacuunlcryogenic applications it has been found necessary to compress the

ring to as little as one-third its original thickness to ensure a leak-proof seal at low temperature. The rule of providing sufficient volumefor the ring to expand laterally still applies even when the grooveis as shallow as that required for this type of application. The groovedesign for an O-ring seal assumes that the bolting or clamping means is

adequate to bring the faces of the mating flanges into contact (metal-to-metal). In most cases the need for rigidity of the system ensures thatthe bolts or clamps provide much greater total compressional forcethan is needed to achieve metal-to-metal contact, and the groove


dimensions are such as to ensure that the O rings are not overstressed.

Another advantage of the metal-to-metal contact is that the conduct-

ance from the O ring to the vacuum space is then very small so that

outgassing of the elastomer is somewhat inhibited. rings are

commercially available over a wide range of sizes, from about aneighth of an inch in major diameter to about eighteen inches. More-

over, much larger rings can be made from extruded buna N cord

cut to the desired length and vulcanized, preferably with a 45° splice.

The use of a double O-ring seal with a guard-ring groove between

the rings is illustrated in Fig. 8-2c. The guard ring is normally vented

to atmosphere through a small fitting. Leakage at the flange can be

checked by evacuating the guard ring, which reduces the pressure on

the inner ring substantially and therefore also the leakage rate if a

leak is present. Alternatively, a probe gas may be introduced into the

guard ring to provide a very sensitive test for leaks through the inner

O-ring seal. The guard ring can also be filled with a low-vapor-

pressure liquid, such as diff'usion-pump oil, as a means of decreasing

the leak rate. Farkass and Barry ^ report that by circulating cold

(6°C) water through the guard ring of such a seal "significant reductions

can be made in the total gas load of the system by lowering the tem-

perature of the sealant material." For seals which are to be opened

and closed frequently, as in the case of the seal at the base of a metal

bell jar (see Fig. 8-2e), the use of a double O ring with the guard ring

routinely pumped out by an auxiliary vacuum pump reduces sub-

stantially the leakage problem.

rings can be used in convenient couplings for connecting lengths

of pipe together or for connecting a glass tubing to a metal tubing.

A typical coupling of this type is shown in Fig. S-2d and is merely

illustrative of many such couplings now available. Vacuum couplings

of this type are also convenient for attaching gauges and other acces-

sories to vacuum systems and for improvising temporary vacuum

systems for bench use.

Guthrie and Wakerling^ have described the use of square-cross-section

synthetic rubber (buna N) gaskets for the purposes for which rings

are now commonly used. Because of the greater convenience and

availability of rings the square-cross-section gasket material is now

seldom used. However, the double grooveless gasket described by

Guthrie and WakerUng (see Fig. 8-3a) also developed during the Man-

hatten Project period is now available commercially to fit several sizes

of standard flanges. The grooveless gasket assembly consists of two

rings of rubber vulcanized to both sides of a metal ring on which are

mounted an array of metal spacers to limit the spacing between the

flanges as they are bolted together to prevent overstressing the rubber


gaskets. The space between the two rubber rings may be used as aguard ring by drilling a hole through one flange and installing a fitting.

Since no grooves are required, all flanges are ground flat. This type of

gasket is particularly convenient and eff^ective for assembling fore-

vacuum pipe lines. The Gask-0-Seal (Parker Seal Company) illus-

trated in Fig. 8-36 is a commercially available example of a grooveless

A^

Gaskets

Spocers

Spacers spot-welded

to each face

(a)Section A-A

(6)

Fig. 8-3. (a) Grooveless gasket for use on standard pipe flanges. [Taken withpermission from A. Guthrie and R. K. Wakorling (ods.), Vacuum Equipmentand Techniques (McGraw-Hill Book Company, New York, 1949).] (6) ParkerGask-0-Soal. [Taken with permission from the Parker Seal Company, Hayward,-Calif.]

gasket suitable for sealing between two flat flanges. A metal ringhas grooves cut in both sides and filled with molded elastomer gasketswhich have protruding ridges. The shape of the gasket material is

such that when the mating flanges are pulled metal-to-metal againstboth sides of the metal ring, there remains some free volume when thetwo ridges on each gasket are fully compressed. Thus the elastomeris never overstressed. The figure shows the gaskets before and aftercompression by the flanges.


Atmospheric

pressure

Ultrahigh

vacuum

Farkass and Barry^ have carried out tests on the base pressure

attainable in a vacuum chamber using rings made of various elas-

tomers. The O ring under test

was placed in the inner groove of a

double seal, between the grooves

of which was a guard-ring channel,

as shown in Fig. 8-4. In these tests

the guard-ring channel was used

to control the temperature of the

ring and flanges. The results

obtained with flange temperatures

of 6°C and -25°C are shown in

Table 8-2. In another set of tests

the base pressure of the empty

chamber was observed at room

temperature with inner rings of

either butyl or neoprene. Then

a 143^-in.-diameter ring of the

material to be tested was placed

loosely in the chamber and the base

pressure again observed. The in-

crease in base pressure multiplied

by the known pumping speed of

the system was taken as a measure

of the room-temperature outgassing rate. In Table 8-3 the results

of these tests are shown together with the measured outgassing rates

in micron liters per second per square centimeter of 0-ring surface area.

Fig. 8-4. Double O-ring seal with

guard ring cooling channel. (1)

Inner O ring; (2) cooling channel;

(3) outer O ring. [Taken with per-

mission from I. Farkass and K. J.

Barry, in 1960 Vacuum Symposium

Transactions (Pergamon Press,

London, 1961).]

Table 8-2. Base Pressures with O Rings Made of Various Elastomers

WITH Flange Temperature Maintained at 6°C and at — 25°C*

Flange temperature 6°C Flange temperature — 25°C

ElastomoterLowestpressure

attained,

torr

Numberof runs

Ranges of

values,

torr

Lowestpressure

attained,

torr

Numberof runs

Ranges of

values,

torr

ButylNatural rubberNeopreneBuna NSilicone (red). .

Silicone (green)

Viton ATeflon

1.0 X 10-"

4.5 X 10-"

2.1 X 10-"

3.8 X 10-"

2.2 X 10-'

3.2 X 10-'

1.3 X 10-"

4.2 X 10-"

5

2

6

4

2

2

3

4

0.8-1.2 X 10-"

4.0-5.0 X 10-"

2.0-2.4 X 10-"

3.6-4.0 X 10-"

2.1-2.3 X 10-'

2.4-4.0 X 10-'

1.2-1.4 X 10-"

4.0-4.4 X 10-"

1.75 X 10-"

1.2 X 10-"

2.1 X 10-"

4.8 X 10-"

5.6 X 10-"

1.0 X 10-"

2

2

2

2

2

2

1.5-2.0 X 10-"

1.0-1.4 X 10-"

2.0-2.2 X 10-1"

4.6-5.0 X 10-"

5.5-5.7 X 10-"

0.9-1.1 X 10-"

, „ , .,, . . „ T T7 I . „„,! V T Rnrrv in 1960 Vacuum Symposium Trans-* Taken with permission from I. Farkass and h,. J. uarry, ni jjt>i/ a i-



As an example of one of the tests performed, the authors state that

when the flange and 0-ring seal were at room temperature, the base

pressure attained was 2 x 10~^ torr. However, when the temperature

of the flange and O ring was raised to 40°C, the pressure increased

to 1.5 X 10~*torr; and when the temperature was —25°C, the pressure

decreased to 1.5 x 10^^" torr. These tests indicate that butyl is a

preferred 0-ring material for room temperature or below, having both

Table 8-3. Material Outgassing Rates of Rubber O RingsAll Tests Conducted at Room Temperature*

Material of

vacuumsystemO ring

Pressure with Pressure with Outgassing rate

empty chamberafter 24 hr

pumping,

Material of

tost ring

test O ring in

chamber after

24 hr pumping,

of test O ring

with entire

surface exposed,

torr torr ^fl/sec cm^

Butyl 1.0 X 10-" Neoprene 4.6 X 10-8 6.40 X 10-5

Neoprene . . . 2.0 X 10-» silicone (red) 5.8 X 10-" 0.44 X 10-5

Nooprone . . . 2,0 X lO-" Silicone (green) 5.8 X 10-" 0.44 X 10-5

Butyl 1.0 X io-» Teflon 2.2 X 10-8 2.32 X 10-5

Butyl 1.0 X io-i> Butyl 1.0 X 10-8 1.08 X 10-5

Butyl 1.0 X 10-" Viton A 1.8 X 10-8 2.04 X 10-5

Neoprene . . . 2.0 X 10-» Natural rubber 2.0 X 10-8 2.16 X 10-5

* Taken with permission from I. Farkass and E. J. Barry, in 1960 Vacuum Symposium Trans-actions (Pergamon Press, London, 1961), p. 35.

a low outgassing rate and low base pressure so that its gas permeability

must also be low. Neoprene and Viton A also rate very close to butyl

according to these tests. It is to be noted that although the silicones

tested have the lowest outgassing rates, the base pressure at 6°C is veryhigh, indicating a high gas permeability.

Addis, Pensak, and Scott* have compared Viton A and B with buna NO rings using a mass spectrometer and a vacuum chamber which could

be baked out at temperatures up to about 300°C. After some prelimin-

ary tests it was established

1

.

That the gases given off by Viton as it is baked out to tempera-

tures up to about 300°C is predominantly water vapor, CO, and CO2',

and no detectable hydrocarbons, whereas buna N rubber gives off

water vapor and a whole series of hydrocarbons from C2H3 to C^Hjg

and presumably beyond2. That Viton does not decompose until the temperature exceeds

300°C, whereas buna N cannot safely be baked at temperatures in

excess of about 150°C

3. That prebaking the Viton rings in vacuum at 200°C for several

days and then storing them in a desiccator greatly reduces the evolutionof water, CO, and COj when they are finally put into use

The lowest pressure attainable in the vacuum chamber using buna N


rings was about 10"' torr. When the buna N was replaced by Viton

rings, a base pressure of 3 x 10-^ was attained. The mass spectrom-

eter trace of residual gases in the chamber with buna N and with

Viton rings shows that, aside from the total gas present being muchless with the Viton than with the buna N O rings, hydrocarbons are

essentially absent with Viton, whereas the entire series of hydrocarbons

are present with buna N rings. The authors recommend the use of

Viton A or B O rings with baking the system at a temperature of

about 250°C for several hours whenever low base pressure and absence

of hydrocarbons are important.

For many years various forms of metal gaskets have been developed

to avoid the use of elastomers as gaskets. Because metal gaskets play

an important role in ultrahigh-vacuum technology, this topic is reserved

for Chap. 9. Two distinct advantages may be gained by the use of metal

gaskets: (1) the hydrocarbons and other gases associated with elas-

tomers are eliminated from the system, and (2) metal gaskets permit

baking the system to much higher temperatures than can be tolerated

by elastomers, permitting a more thorough outgassing of the metal

parts of the system.

8-3. Motion Seals. Manipulation of objects inside a vacuumchamber while the system is at high vacuum is a common requirement.

In some cases the motion can be accomplished by mounting a soft steel

member on a shaft inside the vacuum chamber and a rotatable per-

manent magnet just outside the chamber wall. The shaft then responds

to the motion of the magnet as long as the torque required is not too

great. Continuous rotation can be achieved by mounting the rotor

of a small induction motor on a shaft inside the vacuum chamber and

the stator outside with a thin metal casing between to provide the

vacuum barrier. The rotating magnetic field from the stator penetrates

through the thin wall of the casing and drives the rotor in the usual way.

The molecular-drag pump of Beams and Williams described in Sec. 5-13

is driven in this manner.

Both rotational and translational shaft motion is made possible by

the Wilson'^ seal, the construction of which is shown in Fig. 8-5a. The

seal is built into a cylindrical fitting with a smoothly machined opening,

the base of which has a conical contour around the shaft hole. Twoelastomer washers, two metal spacers, and a packing nut make up the

seal. The outside diameter of the elastomer washers is cut to fit the

inside diameter of the casing closely, and the central hole diameter is

about two-thirds that of the shaft. The first metal spacer has a

central conical portion which matches the conical shape at the base

of the casing. The second spacer is a plain circular collar which

transmits pressure from the compression nut to the outer rim of the two


gaskets, causing them to seal against the outer wall of the casing. Theconical sections support the gaskets at the proper angle and prevent

them from being pushed inward by the external pressure. In order

to seal properly, the elastomer gaskets must be cut smoothly andlubricated with a low-vapor-pressure grease or with diffusion-pump oil.

The elastomer material should have a Shore hardness of 50 to 60.

The region between the two washers may be pumped out to reduce

Pumpouf connection

Pumpout port

Fig. 8-5. (a) The Wilson seal. (1) Body; (2) seal washer; (3) pumpout ring;

(4) compression ring; (5) compression nut; (6) shaft.

(6) Chevron seal. (1) Body; (2) seat ring; (3) gasket; (4) pressure andpumpout ring; (5) pressure ring; (6) compression spring; (7) compression nut;

(8) shaft. [Talien with permission from Lawrence Radiation Report UCRL-7830,Apr. 15, 1964, by T. H. Batzer.]

leakage through the inner seal, may be filled with a low-vapor-pressure

oil, or may be used for testing the leakage through the inner seal.

When properly assembled, the leakage rate for a Wilson seal for a

M-in. shaft is, according to Dawton,* not more than 10~' torr liter/sec,

most of which is condensable at liquid nitrogen temperature. Theleakage rate during rotation of the shaft is about three times the

stationary leak and that due to translational motion inward is consider-

ably greater. For repeated in-and-out motion the shaft must be kept

lubricated. The surface of the shaft must be very smooth and, free

of scratches in order for the washers to seal properly. Since atmos-pheric pressure tends to push the shaft into the vacuum chamber,provision should be made to limit the motion of the shaft, particularly

for shaft diameters in excess of 2 in. Very similar to the Wilson seal

is the chevron seal illustrated in Fig. 8-56. The chevron seal permitsgreater range of adjustment of the compressional loading with the

result that materials such as Teflon may be used for the washers.A number of commercial seals similar to the Wilson seal have


To mechonicol pump

t

Silicone rubber

Gorlock Klozures

become available. In Fig. 8-6 is shown the rotating vacuum seal

described by Roberts,' which utilizes two Garlock Klozures (the

Garlock Packing Company, Palmyra, New York) of silicone elastomer

lubricated with Dow-Corning 704 Silicone diffusion-pump liquid.

Silicone rings are used to seal against leakage between the Garlock

Klozure units and the wall of the seal housing. The shaft is supported

on two ball bearings, one of which

is on the vacuum side of the seals,

presenting the problem of lubrica-

tion at high vacuum. Although

this problem can be solved by the

use of low-vapor-pressure grease or

a dry lubricant such as molybdenumdisulfide, a better solution for some

applications would be to locate both

bearings outside the double seal.

As used by Roberts, the space be-

tween the two seals is evacuated to

a pressure of about 10"* torr by

a mechanical pump. With a shaft

diameter of 0.406 in. he reports a

base pressure of 1 X 10"' torr with

the shaft stationary and 7 x 10"'

torr with the shaft rotating at 1,000

rpm. The system was pumped by

a 300-liter/sec diffusion pump with

a liquid-nitrogen-cooled trap.

Very simple shaft seals can be made using rings as shown in Fig.

8-7. In Fig. 8-7a is shown a seal in which two 0-ring grooves have

been machined in the wall of the clearance hole for the shaft. A third

groove placed between the 0-ring grooves is connected by a small

drilled hole to a pump-out fitting. In assembling this type of seal

the rings are well lubricated with vacuum grease and placed in the

grooves. The shaft with its leading end tapered is then thrust down

through the seal.

In Fig. 8-76 the shaft hole is drilled oversize down to the depth of

the seal, the total diameter being about equal to the shaft diameter

plus 1.5 times the cord diameter of the ring, so that the 0-ring

circular section will be compressed to about three-quarters of its initial

diameter. A metal collar serves as a spacer between the rings, and a

nut permits adjustment of the pressure on the rings. The region

between the rings may be filled with low-vapor-pressure oil or may

be used as a vacuum guard ring.

Scale

Fig. 8-6. Rotary vacuum seal con-

struction. [Taken with permission

from R. W. Roberts, Rev. Sci. Instr.

32, 750 (1961).]


A type of shaft seal frequently used in mechanical booster-pump

construction is shown in Fig. 8-8. The heart of the seal consists of a

highly polished graphite surface which is held in contact with a similarly

Compression

nut

Vacuum chamber

wall Vacuum chamber

wall

Fig. 8-7. O-ring shaft seals.

highly polished steel surface by means of a spring. Elastomer O rings

and gaskets are used to prevent leakage between one seal member and

the shaft as well as between the

other seal member and the wall

of the housing. Ordinary lubricat-

ing oil or a low-vapor-pressure oil

such as diffusion-pump fluid maybe used for lubricating the rotary

seal, depending upon requirements.

The principal advantage of this

type of seal is the high rotational

speed—1,200-3,600 rpm and more

—of which it is capable. When the

seal is properly assembled, the leak-

age rate for permanent gas can Hbe

very small, the principal difficulty

being the tendency to weep lubri-

cant along the shaft into the vacuumregion.

For many years metal bellows

have been used as schematically

illustrated in Fig. 8-9 to transmit translational motion of a shaft into a

vacuum chamber. Bellows of bronze and stainless steel are mostgenerally useful for this purpose, the bronze bellows normally being

soldered and the stainless steel bellows generally being arc-welded for

Fig. 8-8. Mechanical rotary shaft

seal. (1) Sealing washer; (2) floating

seat; (3) bellows; (4) retainer shell;

(5) driving band; (6) disk; (7) spring;

(8) spring holder; (9) seat sealing

ring.


sealing the ends. Metal bellows seals of this type have the great

advantage over Wilson and similar seals in that they can be completely

free of leakage. Their disadvantage is the relatively more difficult

job of effecting a repair in case of failure. The stroke permitted by a

bellows seal is limited so that the designer must be strictly guided by

the recommendations provided by the bellows manufacturer. Even

Welded or brazed closures

Air

Welded or brazed closures

Vacuum ^

Fig. 8-9. Metal bellows seal for linear

motion. (1) Guide bushing; (2) stop

collar; (3) bellows; (4) shaft. [Taken

with permission from Lawrence Radia-

tion Lab. Rep. UCRL-7830, Apr. 15,

1964, by T. H. Batzer.]

Fig. 8-10. Metal bellows seal for trans-

mitting rotary motion. (1) Guide

bushing; (2) collar; (3) drive shaft;

(4) bellows; (5) drive rotor; (6) driven

rotor; (7) bushing; (8) driven shaft;

(9) housing. [Taken with permission

from Lawrence Radiation Lab. Rep.

UCRL-7830, Apr. 15, 1964, by T. H.Batzer.]

then, metal bellows crack, usually near one of the end welds. By far

the greatest use of bellows seals is in the construction of vacuum valves,

some examples of which are given in the next section.

Metal bellows can also be used for transmitting rotary motion into a

vacuum vessel. An example of one of the many designs for this pur-

pose is shown schematically in Fig. 8-10. Although several designs

of rotary bellows seals have been developed, they are not used ex-

tensively, probably because of frequent failure and the complexity

of construction. In all such devices some torque is imposed on the

bellows during rotation of the shaft. Whenever bearings in which the

shaft should turn freely tend to seize or gall, the bellows receives a

twist which can cause it to buckle and crack.

A unique design of dual-motion feedthrough has been described by

Gerber .8 The construction of this device is shown in Fig. 8- 1 1 ;a detail

of the weld joint at one end of the type 316 stainless steel bellows

is shown in Fig. 8-12. All joints are Heliaro welded and are designed

so that relatively thin mating edges can be fused without the use of any

filling material. For a travel of 2 in. the bellows used has an extended

length of 3M in. and an outside diameter of iKe in. The rotary


Leod -screw key

Wheel -retoining

ring

Bellows-seoling

flonge

Heliarc weld

Bellows

motion is accomplished by means of an inner and an outer magnetassembly of which the inner is supported on the linear motion rod by

means of a ball bearing. If the

unit is required to tolerate high-

temperature bakeout, the inner

magnet is replaced by a Kovarblock machined in a quadrupoleconfiguration and the outer mag-net assembly is removable during

baking. For situations not per-

mitting the use of a lubricant, the

moving stainless steel parts maybe treated by a nitriding process

which produces a relatively abra-

sion-free surface.

8-4. Vacuum Valves. Theconvenience in operation of avacuum system depends greatly

upon the choice and location of

valves for isolating various por-

tions of the system. Very early

in the development of all-metal

vacuum systems it was discoveredthat valves which are entirely

satisfactory for use on steam andcompressed-air systems are un-satisfactory for vacuum apphca-

Heliarc weld

Ball-bearing

mounting screw

Outer

magnets^'

Magnetic

locoting pin

Heliarc weld

Handwheel

Wheel bearingplate

Lead screw

Mounting bracket

Linear motion

activating rod

Moin assembly

body

Boll-bearing

retaining tlonge

Ball beoring

Inner magnets

'nner magnet

capsule

Vacuum spoce Gasket groove

Fig. 8-11. Sectional view of

motion feedthrough. [Takenpermission from J. F. Gerber,

Sci. Instr. 34, 1111 (1963).]

dual

with

Rev.

tions because of excessive leakage through the packing around thevalve stem and at the joint between the bonnet, which carries the stempacking, and the valve body. Many different methods for modify-ing standard steam globe valves to re-

duce or eliminate leakage may be foundin the literature. Steam valves in

which the bonnet is remachined to

accommodate a Wilson or chevron seal

and an adequate gasket, such as anring at the joint between the bonnetand valve body, are satisfactory for

many rough vacuum applications.

However, there are so many different

varieties of diaphragm and metallic bellows-sealed valves designed spe-cifically for vacuum application now available commercially that impro-vising adaptations of steam valves is no longer necessary or expedient.

Fusion weld

Welding relief

Fig. 8-12. Typical Heliarc weldjoint. [Taken with permissionfrom J. F. Gerber, Rev. Sci.

Instr. 34, 1111 (1963).]


\^'Vacuum

chamber ^4

5

Diffusion

pump

Liguid-nitrogen

^^<1- baffle

y^

Vacuumreservoir

y^1

The major locations and functions of valves in vacuum systems are

(see Fig. 8-13):

1

.

Near the inlet of the mechanical roughing pump to permit checking

the performance of the mechanical pump isolated from the system

and to permit bringing the mechanical pump up to operating speed

before opening the valve for roughing down the system.

2. A small side valve and gauge

connection in the short length of

pipe between the main valve and

the pump inlet facilitates the check-

ing of mechanical pump perform-

ance.

3. At the outlet of the diffusion

pump to be used in conjunction

with item 4 to isolate the diffu-

sion pump from the system when

the pressure exceeds the stalling

limit, as during the pumpdownperiod. A forevacuum reservoir be-

tween this valve and the diffusion-

pump outlet will provide the

capability of a period of diffusion-

pump operation before the pressure will exceed the stalling point.

4. At the inlet to the diffusion pump, a large conductance valve to

permit isolation of the diffusion pump from the system for testing

purposes and protection.

5. A small side valve and gauge connection between item 4 and the

inlet to the diffusion pump to facilitate performance tests on the

diffusion pump when isolated from the system with valve 4 closed.

6. At the vacuum vessel to provide a connection for a bypass

roughing line to permit pumping down the system from atmospheric

pressure with valves 3 and 4 closed. The roughing bypass permits

batch operation of the system without subjecting the diffusion pump

to high-pressure gas, so that the diffusion pump may be kept operating

continuously—isolated from the system when the pressure is too high.

This arrangement proves to be a convenience in most large systems and

is particularly advantageous in systems operating on a repetitive batch

process involving frequent reloading of the vacuum chamber.

7. On the vacuum vessel, a small valve and gauge connection for use

in testing the performance of the system as a whole. Actually, on

most systems several such connections to the vacuum vessel will be

needed.

Mechanical

vacuum pump

Fig. 8-13. Locations of valves in a

typical vacuum system.


The valves listed above are generally of three fairly distinct types.

Valves 1,3, and 6 may be referred to as forevacuum or roughing valves

for which the conductance need not be very large. For this type of

(a) (&)

Fig. 8-14. Diaphragm-sealed valves, (a) Manual operation; (6) pneumaticoperation.

service, steam globe valves with modifications described above are

suitable as are certain diaphragm-sealed valves. In Fig. 8-14 is

illustrated the Kinney diaphragm-sealed valve which is available in

sizes from 1 to 6 in. and for either

manual or pneumatic operation. Across-sectional view of the manually

operated diaphragm valve is shown in

Fig. 8-15. Bronze bellows-sealed valves

derived from modified steam valves are

shown in Fig. 8-16, the cross-sectional

view showing the metal bellows seal be-

tween the bonnet and the valve disk andthe vacuum-tight gasket joint between

the bonnet and the valve body. Out-

line drawings show the threaded andflange connections as well as the 90° and45° stem configurations. An impro^^ed

version of bronze bellows-sealed globe

valve for high-vacuum applications is

shown in Fig. 8- 17a and h in manuallyand pneumatically operated forms and in cross section in Fig. 8-18.

In this design the bellows assembly, cover plate, stem, and valve disk

can all be conveniently removed in one assembly from the valve body.This feature facilitates soldering or brazing the valve body into thepiping system. Because of the amalgamation with mercury, bronze

Fig. 8-15. Cross section

diaphragm-sealed valve.

of


K-pipe tap

inlet

2- and 3- in. valves

90° stem

D Closed

Flanged bodies have standard

150-lb ASA flonges

K-pipe

tap inlet

K-pipe tap

outlet

C Open

D^CIosed1K-pipe tap

outlet

1- and 1 l/2-in valves

45° stem

Fig. 8-16. Bronze bellows-sealed valves.

(a) (6)

Fig. 8-17. High-vacuum bronze bellows-sealed globe valves, (a) Manuallyoperated valvo; (b) pneumatically operated valve.


DISC SEAL BOTTOM"O" RING (BUNA-N)

STEM

"O" RING (BUNA-N)

SCREW

DISC ADAPTER(BRASS)

DISC SEAL TOP"O" RING (BUNA-N)

PIN

COVER (BRONZE)'

tf.THRUST WASHER^ 5.

BODY (BRONZE)-

BELLOWS (BRASS)

NUT (BRASS)-

-WASHER (BRASS) DISC (BUNA-N)

Fig. 8-18. Cross section of high-vacuum bronze bellows-sealed globe valve.

Fig. 8-19. Fabricated steel valve with cover and bellows assembly removed.


valves should not be used in systems in which mercury may be aproblem.

A fabricated steel bellows-sealed valve is shown with its cover andbellows assembly removed in Fig. 8-19 and in cross-sectional view inFig. 8-20. Since silicone rubber gaskets and valve disk are used thevalve can be operated over the temperature range from about —90to -fl75°C. The stainless steel

bellows, made of a series of thin

washers welded alternately onthe inner and outer edges, pro-

vides greater flexibility and longer

life than the usual corrugated

bellows. This type of valve is

available in 1-, ij^-, 2-, 3-, and4-in. sizes.

Bellows-sealed globe valves are

convenient and relatively inex-

pensive for a limited range of sizes.

However, even for the 4-in. valve

the globe design is unduly heavyand cumbersome. The passage

through a globe valve moreoveris rather tortuous with the result

that the conductance at high

vacuum is small. Use of the

globe valve should therefore belimited to the pressure range

above about 10-^ torr in whichthe conductance is high compared with its value at high vacuum, or

to auxiliary applications in which its relatively low conductance is

not of serious concern.

For many years gate valves of the type generally used in watersystems have been used with modifications similar to those appliedto steam valves to reduce leakage sufficiently for vacuum applicationas is illustrated in Fig. 8-21.9 ^^g advantages of the gate valve are the

straight-through gas flow and the relatively short flange-to-flange

dimension. The gate valve also provides a convenient basis for avacuum lock through which items may be inserted into and withdrawnfrom a vacuum chamber without letting a significant amount of air

into the chamber. The main difficulty encountered in attempting a

completely satisfactory vacuum conversion of the conventional gate

valve is the long travel of the stem from the closed to the fully openposition. Although compound bellows designs may be found in the

Fig. 8-20. Cross section of fabricated

stool valve.


literature, a bellows seal for the stem of a conventional gate valve is

much more complicated than that for a globe valve.

The modern vacuum gate valve seems to have descended from a

design by Wahl, Forbes, Nyer, and Little"

shown in Fig. 8-22. The sliding-plate type of

gate valve has appeared in a variety of com-

mercial designs adapted for hand wheel, toggle,

or pneumatic operation as illustrated in Fig.

8-23. Valves of this description are available

over a wide range of sizes (2 to 32 in.). The

flange-to-fiange dimension is much smaller than

for any other type of valve yet devised, and the

conductance is correspondingly high. In most

commercial valves of this type buna N rings

are used for sealing, in which case the temper-

ature range is limited. However, with Viton

O rings the sliding-plate type of valve can be

baked to temperatures of about 300°C. The

interior surfaces of a valve of this type can be

thoroughly cleaned so that outgassing problems

are a minimum and are determined primarily

by the type of rings used in the assembly.

Because of the wide range of sizes and high

conductance of the sliding-plate gate valve, it

is suitable not only for use in forevacuum lines

but also on the high-vacuum side of diffusion

pumps. This type of valve has in fact become

in recent years the most generally useful be-

cause of its compact design, straight-through

opening, high conductance, and relatively low

cost.

Another type of valve which has distinct

advantages for some installations is the butter-

fly valve, one type of which is illustrated in

Fig. 8-24. The butterfly valve is somewhat

similar to a damper of the type used in stove

pipes. It consists of a relatively thin, ringhke

valve bod}^ the inner surface of which is

machined to conform to a spherical shape and

a flat disk mounted on a shaft across its

diameter. The disk is thick enough to accommodate an 0-ring groove

which runs completely around the edge of the disk. An ring mounted

in the groove makes an excellent seal when the disk is turned to a

Fig. 8-21. A commer-

cial gate valve modified

for vacuum application.

The gate seats (A) are

machined to a blunt

edge, and rubber an-

nulae {B) are inserted

into the gates. Thejimction between the

body and the bonnet is

made vacuum tight bysetting a gasket (C) into

a groove cut in the

body. The stem is

sealed with a Wilson

seal {D). [Taken with

permission fromF.^v . D.

Kurie, Rev. Sci. Instr.

19, 485 (1948).]


=o

position such that it lies in the median plane of the valve body. Whenthe disk is turned 90° from the closed position the valve has relativelygood conductance, although not quite as good as a gate or sliding-platevalve of the same aperture. One end of the shaft on which the diskis mounted passes through an 0-ring seal on one side of the valve bodyand is fitted with a handle for setting the valve position. The butterflyvalve has two distinct advantagesover the gate and sliding-plate

types of valves. One is that there

is much less surface exposed to the

vacuum space so that there is less

difficulty with contaminants. Theother advantage is that the butter-

fly valve is more compact in every

dimension for a given aperture.

As is clear from Fig. 8-24 the

flange-to-flange dimension is evenless than that of the sliding-plate

type of valve, which is also rather

good in this respect.

A class of valves generally re-

ferred to as disk valves are par-

ticularly suitable for use in the

low-pressure range in which high

conductance is of primary concern.

The features of a disk valve are

illustrated in Fig. 8-25. The valve

disk covers a large opening equal in

diameter to the diffusion pump to

which it is to be connected. The vertical travel of the disk in openingis chosen to be sufficient that the open conductance of the valve

imposes a minimum restriction on the resultant pumping speed. Disk

valves are most conveniently built as right-angle valves such as the

commercial models shown in Fig. 8-25 in the manually and pneumati-

cally operated forms. Valves of this type are commercially available

in sizes ranging from 2 to 32 in. in aperture diameter, corresponding to

the range of diffusion-pump diameters. Modern versions of the disk

valve utilize O rings for sealing between the disk and the seal face, as

illustrated in the figure.

Both for testing vacuum-pump performance and for carrying out

tests on vacuum systems a means of admitting air or other gases at a

controllable, steady rate is needed. For many situations an ordinary

gas needle valve is satisfactory. However, for control of a small gas

Fig.

plate

J. S.

Xyor,

8-22. Gate valve with sliding

[Taken with permission fromWahl, S. G. Forbes, W. E.

and R. N. Little, Rev. Sci.

Instr. 23, 379 (1952).]


'^i>r<^Fig. 8-23. Commercial sliding plate gate valves, (a) Pneumatic operation;

(6) toggle operation; (c) hand wheel operation.

2.250",

pump side

Fig. 8-24. Cross section of butterfly type of vacuum valve.


o

a

-3

o

>>>> n J >>>/!?> /7-r

^Wyj^j^^/zf ////// ///r9n^

mur>|oo

"

scS


flow with reasonably steady throughput at a given setting, a needle

valve of special design is required. An early but quite successful type

of needle valve is that described by Bush" and illustrated in Fig. 8-26.

The principal feature of the design is the slowly tapering needle fitting

snugly into a carefully reamed conical seat. For some applications

a bellows seal may be substituted for the packing shown in the figure.

Such valves are now commercially available. As Bush" mentions,

-Coated lightly with glyptol

'^^^^^fp^^^^"J0<;'M fe».-^^~^'^^^^^^^^p^'H {y|^j64^^^y::^^s:^^^^|^l

Material Brass, except

where noted otherwise

String packing soaked in

Lubriseal grease

Fig. 8-26. Vacuum needle valve. [Taken with permission from A. Guthrie

and R. K. Wakerling (eds.), Vacuum Equipment and Techniques (McGraw-Hill

Book Company, New York, 1949).]

very fine adjustment of the gas flow can be obtained by the use of two

valves in series with a small volume in between. The first valve is

adjusted to take most of the pressure drop and the second valve used

for fine adjustment of the flow rate. Johnson and Good^^ also describe

a double needle valve for small gas-flow rates (2 to 3 cm^/hr) using this

same principle.

8-5. Vapor Baffles and Traps. The term vapor trap is applied

to a device which may have either of two functions in a vacuumsystem : (a) to prevent the back migration of the vaporized pump fluid

from a vacuum pump into the vacuum chamber and (6) to condense

from the volume of the vacuum chamber any condensable vapor which

may be present. In many cases a refrigerated vapor trap placed

between a diffusion pump and the vacuum chamber performs both

these functions. However, depending upon circumstances, one

function may be much more important than the other, in which case

the choice of type and location of the refrigerated trap should be madewith its principal function in mind. Cryogenic pumps which are

discussed in Chap. 9 are, in fact, vapor traps of category (b) operated

at such a low temperature that many gases which are normally regarded

as permanent gases condense on the cryogenically cooled surface.


Fig. 8-27.

baiHe unit.

Water- or Freon-cooled

Vapor traps are most widely known in their use at the inlets ofdiffusion pumps primarily to condense vaporized pump fluid andproducts of decomposition of the pump fluid. The backstreaming ofdiff'usion pumps is discussed in some detail in Chap. 6, and the use ofwater-cooled baffles and refrigerated traps is also briefly described.The direct blast of vapor back-

streaming from the inlet to a

diff'usion pump is so great that

without some precautions to con-

dense and return the vaporized

fluid to the diffusion-pump boiler

the entire charge of working fluid

would be lost and the pump wouldfail after a few days of continuous

operation. Placing a water-cooled

cap over the first-stage nozzle andcooling the upper portion of the

pump barrel or using a set of

water-cooled baffles, such as that

shown in Fig. 8-27, at the inlet

of the pump suffice to eliminate

the more virulent components of

backstreaming vapor. These measures also greatly reduce the rateof loss of pump fluid so that the operating lifetime of a boiler filling

is not determined by loss of fluid by backstreaming but by eventualdeterioration due to decomposition (except in the special case ofmercury as the working fluid). To make these measures even moreeffective, the water cooling may be replaced by the use of refrigerationby which the baffles and other cooled surfaces are cooled to the lowesttemperature at which the condensed fluid will still flow back into thediffusion pump. Both for mercury and for many of the organic pumpfluids a temperature of about — 35°C is optimum for this purpose,although this temperature is too low for those pump fluids which havehigher pour points. For many applications of off diffusion pumps thewater-cooled baffle system is sufficient to maintain the base pressureand surface cleanliness required. lonization-gauge readings of theorder of 10-" torr are typically maintained in systems so equipped.Refrigerating the baffle at -35°C will generally result in a reductionof the base pressure to about 10"' torr.

The backstreaming that still persists after elimination of the direct

blast of high-temperature vapor from the hot jet region is the volumemigration of vapor at the approximate temperature of the condensingsurfaces. In the case of organic pump fluids which wet metal sur-

faces, the surface film of the fluid spreads out from the area of direct


Thin-wosfainless-steel

tubing

Chomber wa

Liquid nitrogen

or dry ice in

low -freezing-

point liquid

Well-

polished

surface

Fig. 8-28. Thimble trap.

condensation and by surface migration may also spread into the region

beyond the baffle structure. The volume and surface migration

results in the contamination of the high-vacuum chamber with approxi-

mately the room-temperature vapor pressure of the pumping fluid

and its decomposition products. In a system

evacuated by an oil diffusion pump protect-

ed only by water or Freon-cooled baffles a

base pressure reading on an ionization gauge

less than IQ-® torr (air calibration) can

seldom be realized for an extended period of

time. To realize base pressures significantly

less than this value requires the use of re-

frigerated traps at lower temperature and

of special design.

The most common type of refrigerated

vapor trap for many years has been the

thimble trap, as shown in Fig. 8-28, cooled

either by dry ice (solid CO2) at -78.5°C in

a low-freezing-point liquid such as trichlor-

ethylene to provide good thermal contact or by liquid nitrogen at

about — 195°C. A trap of this type has frequently been installed

in the manifold between the disk valve at the inlet of the diffusion

pump and the vacuum chamber. If the manifold has large enough

dimensions, the conductance for flow of gas into the diffusion pump

is not seriously impaired and the thimble trap is in a strategic position

to condense backstreaming vapor from the diffusion pump and also

to pump by condensation any water or other condensable vapors which

may be present in the chamber. If the temperature of a thimble trap

is very low as compared with that at which the vapor in the system

would be at saturation, then the sticking probability for condensation

is very high and the trap acts like a nearly perfect pump for the con-

densable vapors. The trap in the position indicated thus not only

reduces significantly the pressure due to backstreaming from the

diffusion pump, but also in most cases provides a much higher pumping

speed for water vapor and other condensables from the vacuum chamber

than the diffusion pump alone would provide. If the area of the cold

section of the thimble trap is B cm2, then by reference to Eq. (2-93)

the condensing speed of the trap for vapor is

MISr 3.64^—J B (liters/sec) (8-2)

For the case of water vapor at room temperature (293°K) the result is

Sr = 14:.1B liters/sec (8-3)


If the conductance for water vapor of the manifold up to the locationof the trap is large as compared with the condensing speed given in(8-3), then the pumping speed of the trap for water vapor can easilyexceed that of the diffusion pump by a large factor. A thimble trap2 in. in diameter and with a cold length of 4 in. will have a condensingspeed of nearly 5,000 liters/sec for water vapor. Since the trap will

Table 8-4. Vapor Pressure op Various Substances as a Function orTemperature *

Temperature Vapor pressure, torr

°C °K Water NH3 CO2 Hg

100

50

-40

~78.5t-120-150-195.81

373.1

423.1

273.1

233.1

194.6

153.1

123.1

77.3

760

93

4.6

0.1

5 X 10-4

10-7

10-14

~ 10-24

3,220

540

42

0.2

6 X 10-4

10-11

760

10

6 X 10-2

10-8

2.7 X 10-1

1.3 X 10-2

2 X 10-4

1 X 10-6

3 X 10-9

10-13

* Source: Handbook of Phijsics and Chemistry (Chemical Rubber PublishingCompany, Cleveland, Ohio).

t Sublimation temperature of dry ice at pressure of 760 torr.

I Boiling point of liquid nitrogen at pressure of 760 torr.

accumulate a surface layer of condensate, the temperature must below enough so that the equilibrium vapor pressure is low as comparedwith the base pressure required in the vacuum chamber. In Table8-4 are given the values of the vapor pressure of water, NII3, COj, andmercury at a few significant values of the temperature. Note that for

a base pressure of 10-^ torr the temperature of dry ice is not low enoughfor water vapor, so that the next convenient temperature is that of

liquid nitrogen, for which the extrapolated value of the vapor pressure

is negligible for most practical purposes. Whether anything approxi-

mating the equilibrium vapor pressure corresponding to the tempera-ture of the trap is realized in practice depends upon the amount of

material co^^densed on the trap. In the case of water vapor, the

accumulation of ice, which has a very low thermal conductivity, maycause the surface exposed to the vacuum space to attain a temperature

well above that of the metal or glass surface of the trap with the result

that the limiting vapor pressure may be considerably above that

expected. This particular difficulty applies to a thimble trap, the cold

surfaces of which are usually exposed to surrounding walls of the system


at room temperature, but not so critically to some other types of vapor

traps the cold surfaces of which are not so exposed.

Because thimble traps do provide very high pumping speed for

condensing vapor under favorable circumstances, they are frequently

installed directly in the vacuum chamber independently of the dilFusion-

pump manifold to ensure essentially infinite conductance for vapor

in reaching the condensing surface. A vacuum chamber thus equipped

is normally pumped down to the pressure at which the diffusion pumps

can be put into operation (e.g., by closing the bypass roughing valve

and opening the forevacuum and disk valves) and the thimble trap

then immediately filled with liquid nitrogen to ensure very rapid

reduction of the pressure. In the case of large accelerators, which are

usually evacuated for long periods after each pumpdown cycle, the

thimble traps may later be allowed slowly to run out of liquid nitrogen

and warm up to room temperature. The slowly evaporating vapors

from the thimble trap in this case are pumped out of the system by

the diffusion pumps over a period of m.any hours. The thimble trap

thus provides for a rapid reduction of total pressure to an acceptable

operating level and may save several hours of machine time. In

systems involving frequent recycling from atmospheric pressure to

high vacuum, a thimble trap may decrease by a large factor the time

for each cycle. In this type of application the thimble trap should be

removed and cleaned each time the system is brought to atmospheric

pressure to ensure reasonable efficiency.

The thimble trap placed in the diffusion-pump manifold is quite

effective in systems using mercury as a working fluid. Mercury does

not wet surfaces and migrate along surfaces to any significant degree,

nor does mercury decompose into products of widely differing vapor

pressures. Any mercury molecules which happen to escape the

condensing surface and enter the vacuum chamber will eventually

return to the trap and be condensed. If the diffusion pump is prevented

from blasting a hot stream of vapor back into the chamber by an

effective combination of Freon-cooled baffles or jet cap and cooled

pump barrel, the partial pressure of mercury in the system with a

properly proportioned thimble trap at liquid-nitrogen temperature

will normally be negligible as compared with that of the other elements

present.

When organic pump fluids are used, however, the thimble trap is

much less effective. As discussed by Milleron^^ and illustrated in

Fig. 8-29, the working fluid from the diffusion pump may invade the

high-vacuum space either by volume migration or by surface migration.

Volume migration can be prevented by arranging refrigerated surfaces

in the vapor trap so that an oil molecule must have at least one


encounter with a cold surface before it can enter the high-vacuumspace. Surface migration is greatly inhibited and essentially stoppedby so designing the trap that oil films migrating along surfaces will

encounter a cold barrier before entering the high-vacuum space.Figure 8-30 illustrates a refrigerated trap of the chevron type with anoil creep barrier together with a water-cooled baffle to prevent anexcessive backstreaming load on the liquid-nitrogen-cooled baffle

Clean vacuum

Cleon vacuum

Volume Surface

migration migration

Oil -creep

barrier Heat shield continuous

roll of polished stainless

three layers thick

Air vent"Diffusion

pump

_A_Conductance I

-100I iters /sec

Liquid nitrogen

in

Fig. 8-29. Schematic illus-

tration of the migration of

pump fluid. [Taken with

permission from KormanMilleron, in 1958 VacuumSymposium Transactions

(Pergamon Press, London,1959).]

Strips first cooled

by HjO then by

radiotion loss to

liquid nitrogen

Fig. 8-30. Schematic drawing of

chevron type of vapor trap withsurface creep barrier. [Taken withpermission from Norman Milleron,

in 1958 Vacuum Sym,posium, Trans-actions (Pergamon Press, London,19,59).]

system. Another form of trap with these same features is that illus-

trated in Fig. 8-31 and attributed by Ullman " to R. F. Post. Liquid-

nitrogen-cooled vapor traps with surface creep barriers such as those

illustrated in Fig. 8-30 and Fig. 8-31 have proved to be effective in

reducing by a very large factor the backstreaming of condensable

materials from the diffusion pump back into the high-vacuum space.

Traps of this tj^e, combined with other techniques to be described

in Chap. 9, have in many systems contributed to the attainment of

operating pressures below 10"^ torr in the region referred to as ultrahigh

vacuum.

A disadvantage of vapor traps such as those shown in Figs. 8-30 and8-31 is that the conductance is so low that the resulting pumping speed

for permanent gases is impaired. This is a serious handicap since the

operating pressure of systems using liquid-nitrogen-cooled traps is very


low SO that the highest possible pumping speed is needed to accommodate

any appreciable throughput. The problem is to achieve the blocking

effect of a well-designed vapor trap without introducing such a low

conductance for the pumping of permanent gases. A commercial

Liquid-nitrogen

trap

Water-cooled

baffle

Fig. 8-31. Water-cooled baffle andliquid-nitrogen-cooled trap with sur-

face creep barrier. [Taken with

permission from J. R. Ullman, in



1958).]

r^^ W/D

2 001.33

1,00

P

Expenmentol

0.44

0.39

0.32v^ii QBulged elbo* t***)

GBulged elbow with

9jet cop

2,00

1.33

33

0.30

GBulged elbow on d ffusic n pufnp

2001 33

32

27

Bulged elbow with

A/B-5

chev on

2001.66

1 33

0.38

0.35

0.31

Fig. 8-32. Several bulged-elbow vapor-

trap designs together with the experi-

mentally determined value of the

transmission probability p. [Taken

with permission from L. L. Levenson,

N. Milleron, and D. H. Davis, in

1960 Vacuum, Symposium, Transactions

(Pergamon Press, London, 1961).] ,

vapor trap meeting these objectives is that shown in Fig. 6-19. Thepumping speed of the 6-in. diffusion pump alone, as indicated by the

performance curve in Fig. 6-18, is about 1,400 liters /sec. The combinedpumping speed with the vapor trap is about 600 liters/sec, as shown in

Fig. 6-20, so that the diffusion pump and vapor trap combination

delivers about 43 per cent of the pumping speed of the pump alone.

The optimization of the vapor trap and diffusion pump for maximum


transmission probability for molecules leaving the chamber is discussedby Levenson, Milleron, and Davis.i'^ Among vapor-trap configurationsrecommended by these authors is the "bulged-elbow" model, severalversions of which are shown schematically in Fig. 8-32, together withmeasured values of the transmission probability p, defined as

conductance of the trap configuration

conductance of an aperture of diameter Dwhere D is the diameter of the opening into the trap from the vacuumchamber and also of the opening out of the trap into the diffusion pump.p is thus a measure of transmission efficiency of the trap comparedwith that of a simple aperture utilizing the same wall area of thevacuum chamber. Figure 8-33 is a cutaway drawing of a commercialadaptation of the bulged-elbow trap with a chevron baffle combined

Cooling-medium inlet

and outlet connections"

Lifting lugs

Chevron-valve-baffle seal

Stoiniess-steel

coolant tubing

Copper chevron

CValve-plate actuator

KVB-32

Cooling -woter

connections

Volve-plate gasket

Valve plate

Oil drain valve

Vocuum-chombermating flonge

Heaters

Fig. 8-33. Bulged-elbow trap with chevron baffle combined with disk valvmounted on 32-in. diffusion pump.


with a disk valve as used on a 32-in. diffusion pump. The "pumping

speed" at the inlet of the 32-in. diffusion pump as a function of the

inlet pressure and also the pumping speed of the pump and trap

combination are shown graphically in Fig. 8-34. From the perform-

ance curves the pumping speed at the pump flange is S„ = 30,400

~~'

35,000

70P00

V 30P00^E 60P00o Un

1

)alt

1

ed //

/

I — 25,000

"S 50POO —

1

/

/

\ 20,000

iping

'

Vol

1—

1

ve-t off ed ^y] \ 15,000

5 30300Q-

(

\V- 10,000

2Q0O0/ \

^ 'i.nonlOPOO

1

0-' 0-^1(

Pr

)-5

;ssu re, to

1(

rr

,-4 10-' ic-^

Fig. 8-34. Typical puraping-speed curve of Kinney Model KDP-32 diffusion

pump with and without bulged-elbow chevron baffle.

liters/sec and the resultant pumping speed at the inlet to the bulged

elbow is S, = 15,000 liters/sec. From Eq. (6-28)

and the measured values of S^ and S,, the conductance of the trap is

(15,100)(30,400)Ct

= 30,350 liters/sec

30,400 - 15,100

The cross-sectional area of a 32-in.-diameter aperture is about 5,190

cm^, so that the conductance of the aperture is

G^ = 11.6^4 = 60,200 liters/sec

Thus for this case the transmission probability is p = C,lC„'!v 0.50,

which is somewhat higher than the values reported by Levenson,

Miheron, and Davis for a similar trap. Overall efficiericy of the pump

trap combination may be stated as

S, 15,1000.25

C„ 60,200

which is about as high as the overall pumping efficiency ever is in

practice.


The pumping-speed curve for the baffled 32-in. diffusion pumpshown in Fig. 8-34 and that for the baffled 6-in. diffusion pump shownin Fig. 6-20 both show a peak in pumping speed in the pressure range

from about 10^* torr to about 10"^ torr. In this pressure range the

molecular mean free path is equal to or less than the openings throughthe baffle so that in this pressure range the conductance of the baffle

system is greater than its value at lower pressure. The performance

curve finally falls off with increasing pressure even though the con-

ductance of the baffle system continues to increase because the pumpingspeed of the pump is falling rapidly. In this pressure region the char-

acter of flow through the baffle system is becoming viscous in character

so that molecules no longer are assured of colliding with surfaces but

may experience significant collisions with other molecules. Thus

molecules which should condense on baffle surfaces can pass entirely

through the trap without encountering the cold surfaces. In systems

which use trapped oil diffusion pumps, but which must be kept free of

organic contaminants, this awkward pressure region must be avoided

as much as possible by arranging to pass through the pressure range

from 10~3 to 10~^ torr as quickly as possible.

When a liquid-nitrogen-cooled trap is filled periodically, the liquid

level falls significantly between fillings, resulting in a portion of the

trap surface warming up slightly. The result is a sequence of abrupt

drops and slow increases in the pressure recorded on an ionization

gauge. There are a number of systems commercially available, such

as that illustrated in Fig. 8-35, to maintain the Kquid level in the trap

G B WSolenoid cord

SL-l-308

Rubber stopper

Fig. 8-35. Liquid-nitrogen automatic-level control, {a) General arrangement;

(6) controller circuit.


nearly constant, so that only an occasional change of the large liquid-

nitrogen dewar is necessary to keep the trap continuously filled.

Another solution to the problem of automatic liquid-nitrogen supply

and also an alternative effective form of vapor baffle with a surface

migration barrier are described byTaylor^^ and illustrated in Fig.

8-36. In the reference is shown a

schematic diagram for the auto-

matic control of the liquid-nitrogen

flow through the cooling coil. Theliquid-nitrogen-cooled baffle is

shielded from the direct blast of

vapor from the pump by the 45°

shield built into the water-cooled

elbow. The baffle is a simple

array with a minimum of twobounces for molecules to penetrate

the trap. The pressures attain-

able with this trap proved to be

about 3x10-' torr without bake-

out and about 1.5 x lO-^" ton-

after baking the system at 250°Cfor 12 hours. The design of the

trap is such that it can be installed

either in the horizontal position as

shown in the figure or in the ver-

tical position. The high-conduc-

tance water-cooled elbow with the45° shield eliminates the need for

other water-cooled baffling over

the oil diffusion pump, increasing

somewhat the transmission prob-

ability for the combination. Thecalculated conductance for a 4-in.

baffle is 800 liters/sec and for a 6-in. baffle is 4,000 liters/sec. Themeasured pumping speed of the 4-in. pumping system was 367 liters/sec

for air at 7 x 10"' torr and 1,024 liters/sec for hydrogen at 8.5 x 10"'

torr.

Vapor traps in large systems are sometimes preferably cooled bylow-temperature mechanical refrigerators rather than by dry ice or

liquid nitrogen. From the data in Table 8-4 it is evident that for manypurposes a temperature intermediate between that of dry ice and liquid

nitrogen would be entirely satisfactory from the point of view of the

Fig. 8-36. Liquid-nitrogen circulating

vapor baffle. (1) Baffle structure

(tough pitch copper); (2) liquid-

nitrogen coil, inlet, and outlet (copper)

;

(3) oil-migration barrier (stainless

steel); (4) heat shields; (5) water-cooled elbow; (6) line-of-sight heatshield with drain hole; (7) dam to

stop oil condensed on the elbow fromdraining into the baffle housing; (8)

baffle housing with low heat con-

ductance inlet and outlet tubes.

[Taken with permission from A. R.Taylor, in 1961 Vacuum, SymposiumTransactions (Pergamon Press,

London, 1962).]


indicated vapor pressures. This is, for example, true in the case of amercury-pumped system if the traps over the diffusion pumps areprimarily intended to maintain a sufficiently low vapor pressure ofmercury in the chamber. Liquid-nitrogen-cooled thimble traps maybe used for rapid pumping of water vapor and other high-vaporpressure materials. Mechanical refrigerators of cascade or compound

Water

fWrr

Boffle

Receiver

Fig. 8-37. Schematic drawing of a double-cascade refrigeration system for

cooling chevron type of baffle system on a mercury diffusion pump. [Takenwith permission from H. R. Smith and P. B. Kennedy, in 1959 Vacuum Sym-posium, Transactions (Pergamon Press, London, I960).]

designs are capable of maintaining temperatures in the range —100to — 150°C with an adequate heat capacity for most vapor-trap

applications. A number of such systems are discussed by Smith andKennedy, 1' among them the double-cascade system illustrated in Fig.

8-37. The installation and operating costs of several types of low-

temperature refrigerators are compared with those of liquid nitrogen

in Table 8-5 from the paper of Smith and Kennedy. The binary

system mentioned in the table was developed for the heavy-ion linear

accelerator at Berkeley and is still in service after many years of

operation. Whereas the savings in liquid-nitrogen costs have beenvery large, the refrigerator units have been a major source of downtime on the accelerator because of excessive servicing requirements.

Experience to date is that the specialized servicing required and the

frequency of failure largely negate the savings on liquid nitrogen byloss of operating time.


The working fluid of a diffxision pump can be lost from the boiler bymigration into the forevacuum portion of the system as well as bybackstreaming into the high-vacuum region. Also the working fluid

of a diffusion pump can be contaminated by oil vapor from the backing

pump. These two problems can be partially solved by the use of

forevacuum condensers or traps the design of which is rather different

Table 8-5. Cost Comparison between Refrigebated and Liquid-nitrogbn-

cooLED Traps*

CostCompoundcascade

Cascade BinaryLiquid

nitrogen

Operating:

Maintenance . . .

Refrigerant ....

WaterPower

Initial installation.

Total, first year . . .

Yearly^

$330

315«

270<*

6,800«

7,715

1,595

$330

315-^

270*

6,050'^

6,965

1,520

$330

315<^

270*

7,300'^

8,215

1,645

$ 1,200"

6,100*

500^

7,800

7,350

* Taken with permission from H. R. Smith and P. B. Kennedy, in 1959

Vacuum Symposium Transactions (Pergamon Press, London, 1960), p. 271.« Servicing trap or baffle. <* % 0.0085 kW/hr." $ 0.107/liter 25% loss. " Does not include baffle.

" $ 0.0003/gal. f Operating cost + 10% depreciation.

from that of the high-vacuum vapor trap. The pressure in the fore-

vacuum line is usually in the range of viscous flow, well above the

region of molecular flow, so that molecular encounters with the walls

of the forevacuum system are normally rather rare events. In order

to ensure reasonable efficiency of condensing vapor is it is necessary to

provide a fairly long and tortuous flow path through a maze of con-

densing surfaces so arranged that the condensate will flow in the desired

direction. Many commercial diffusion pumps include a vapor con-

denser at the outlet with provisions for cooling either by water or bya refrigerator unit. The need for an effective exhaust baffle systemis particularly vital when mercury is used as the working fluid. Therefrigerator coil used for cooling the inlet baffle and the top of the

diffusion-pump barrel can conveniently be extended to cool the exhaust

baffle as well. To prevent excessive backstreaming of mechanical

pump oil into the diffusion pump, a rather large trap similar to a thimble

trap built into an expanded section of the forevacuum line or a U bendcooled by a slush of dry ice in trichlorethylene as shown in the sketches

in Fig. 8-38 is fairly effective. Such a trap should be placed far enough


from the inlet to the mechanical pump and preferably upstream from a

bend in the pipe to avoid accumulation of oil due to the direct spitting

of oil droplets into the pumping line which most mechanical pumpsexhibit to some degree. Eliminating completely the back migration

of mechanical pump sealing oil into the high-vacuum portion of the

system and the consequent hydrocarbon contamination from this source

by the precautions described above is probably not feasible. However,

Thin-wGll —stainless-steel

tubing

Quick-disconnect couplings

Flow

Liquid-nitrogen

Dry-ice "slush"

Dewar'

flosk

Copper tubing

Fig. 8-38. Two types of forevacuum traps which may be cooled by dry ice in

trichlorethylene or by liquid nitrogen.

for the great majority of applications the measures described above

are entirely adequate and in some cases even superfluous. A more

effective method of preventing back migration of oil vapor is the use

of an absorption trap utilizing artificial zeolite or alumina as an ab-

sorbing medium as described in the following section.

A system incorporating the features of liquid-nitrogen-cooled high-

vacuum trap, water-cooled inlet, and exhaust baffle for the diffusion

pump and a thimble trap near the inlet to the mechanical pump is

illustrated in Fig. 8-39. The valve and manifold arrangement together

with the forevacuum ballast tank permits rapid cycling of the system

without shutting down the diffusion pump.8-6. Absorption Traps. In the vacuum lore of hand-assembled

glass vacuum systems the practice of using a bulb partly filled with

phosphorous pentoxide for absorbing water vapor from atmospheric

air periodically admitted to the system and an absorption tube loosely

filled with charcoal placed in the forevacuum line to prevent back-

streaming of mechanical pump oil into the high-vacuum system was

well known." Chemical and physical absorption have been used in

many forms in vacuum practice. In recent years further significant


advances have been made in absorption traps, both for forevacuumand high-vacuum apphcations. A few examples will suffice to give animpression of what can now be done with absorbing traps and whatcomponents can be obtained commercially.The development of modern absorption traps appears to have

started with the report by Alpert" of the results observed when he

Flexible

connector

Main vocuum

isolation valve

Baffle

lonizotion-

gauge tube

Haas Thermocouple-

chamber gauge tube

Roughing and

ocking pump

Fig. 8-39. Diffusion-pump system incorporating traps and baffles to preventoil migration both in th© high-vacuum and forevacuum portions of the system.

added a roll of corrugated copper foil to a glass liquid-nitrogen-cooledvapor trap to reduce fluctuations in the gas pressure due to change in

the liquid-nitrogen level on the outside wall of the trap, as shown in

Fig. 8-40. The procedure had been to bake out the trap with its spiral

of copper foil and then cool it down to liquid-nitrogen temperature tomake observations at very low pressure. During the course of theexperiments, however, it was found that after high-temperature bake-out the copper-foil trap became fully effective at room temperatureand did not have to be cooled down to low temperature.

Carmichael and Lange^" have conducted a series of tests to determine


the period of time a room-temperature copper-foil trap remains effective

after bakeout. In a small, glass vacuum system using a two- or

three-stage glass diffusion pump with Octoil-S as the working fluid

a copper-foil trap 6 in. in length and 2 in. in diameter was installed

between the diffusion pump and the test chamber. The base pressure

attainable after bakeout was typically in the range lO-i" torr. The

graph in Fig. 8-41 shows the history of the pressure recorded by the

ionization gauge on the test chamber over a period of several days.

For a period of nearly twenty days

the pressure rose slowly but re-

mained below 10-9 ^orr. However,

at about twenty days after initiation

of the test the pressure then rose

rapidly to about 10^' torr. Mass

spectrometer analysis of the gases

after saturation was reached in-

dicated that carbon monoxide was

by far the major gas present.

Carmichael and Lange then madeup a number of combinations of

small (2-in. -diameter) copper-foil

traps and measured the "stay-down

time" for each combination, as

shown in Fig. 8-42. Additional

experiments were carried out vary-

ing the conductance between the

oil diffusion pump and the copper-

foil trap with the result that the

smaller the conductance the longer the stay-down time of the trap

became. This very simple type of trap is useful on small systems in

which performance of a week or less is all that is required. However,

efforts to make a high-conductance trap of the copper-foil type for use

on large systems have thus far not been successful because of the very

short stay-down time or period of effectiveness which results.

A much more promising type of absorption trap is that described by

Biondi^i utilizing artificial zeolite* or activated aluminaf pellets. Asmall glass trap of this type and the arrangement for testing is shown mFig. 8-43. Either with 3^-in.-diameter pellets of zeolite or with 8-14

mesh chips of alumina in the trap the system after bakeout of 8 hr

* A porous alkaU metal aluminosilicate, type 13X, manufactured by Linde

division of Union Carbide Corp.

t A highly porous material provided for these tests in the form of 8-14 mesh

chips by Aluminum Company of America.

Fig. 8-40. Copper-foil trap. [Taken

with permission from D. Alport, Rev.

Sci. Instr. 24, 1004 (1953).]

344

10-^


Diffusion Copper X~IO-8[_ pump trap ,„„ g^^^^

T 1

Vacuum system

Experiment Type of trap Stay down time

1~2 days

-*^\"\^

2k2"^

~ 6 days

3 ~ 6 days' fc—^ ^= ^^ i"k2"*^ 1" k-

4

U-2"-*l

~15days

Fig. 8-42. Stay-down times for

various copper-foil trap arrangements.

[Taken with permission from J. H.Carmichael and W. J. Lange, in 1958



10 15 20

Time, days

Fig. 8-41. Typical pressure depend-

ence with time over a period of

several days for a small system in

which a room-temperature copper-

foil trap 6 in. in length is used betweenthe oil diffusion pump and the test

chamber. [Taken with permission

from J. H. Carmichael and W. J.

Lange, in 1958 Vacuum Sym-posium Transactions (PergamonPress, London, 1959).]

at 450°C remained in the lO-^" torr range for about three months. Thediffusion-pump fluid used for these tests was Octoil-S.

Biondi^i also describes the performance of the large room-tempera-

ture zeolite trap illustrated in Fig. 8-44. The trap provides a series of

trays in which artificial zeolite pellets are placed. The trays are so

arranged that molecules in passing through the trap must encounter

zeolite several times. Before each test the trap and test chamberwere baked out and the system typically reached an ionization-gauge

reading of slightly over lO"!" torr after cooling to room temperature.

Using Octoil-S in the diffusion pump resulted in a stay-down time

(below 10^^ torr) of only about twenty days. However, when Con-

voil-20 was substituted for the Octoil-S the base pressure remained at

1 X 10~"i" for more than one-hundred days without any evidence of

rising. The results of these tests are given in Fig. 8-45 showing three

different tests with Octoil-S and one test run with Convoil-20. Thestriking difference in performance of the room-temperature zeolite

trap depending upon the choice of fluid used in the diffusion pump is

apparently not understood. Room-temperature traps with zeolite

or alumina apparently provide no protection whatever against mercurybackstreaming.


The principal disadvantage encountered in the use of zeolite andalumina in vapor traps is the enormous amount of gas and vaporgiven off by the material in the bakeout period. Milleron and Leven-son22 measured an output of 28 g of water from 250 g of zeolite pellets

baked at 450°C for 48 hr. This measurement was made in the courseof developing a high-conductance room-temperature trap as illustrated

in Fig. 8-46. The trap was made by lining a right-angle elbow withabout two layers of zeolite pellets, the pellets being about K in. in

diameter and length. A No. 10 mesh stainless steel screen was usedto retain the zeolite pellets as shown in the figure. After bakeout thepressure history observed was similar to that reported by Biondi,^!

but in this case the test was continued for a much longer period. Thepressure after bakeout was 3 x lO"!" torr initially but rose to 1 x 10"^

torr where it remained for a period of about one year. Biondi^i

To ultrahigh

vocuum system

Bokeout oven

(b)

Fig. 8-43. (a) .Scale drawing ofglass trap utilizing artificial zeolite

or activated alumina; (h) diagramof arrangement used for testingthe effectiveness of the trap.

[Taken with permission from M.A. Biondi, in 1960 Vacuum Sym-posium Transactions (PergamonPress, London, 1961).]

Flow poth Flow path]

1 r I

Scale- in.

Fig. 8-44. Scale drawing of an 8-in.-

diameter nonrefrigerated trap for use

with a metal oil diffusion pump. The

central trays are supported by tabs

attached to the ajiter walls. [Taken

with permission from M. A. Biondi,


actions (Pergamon Press, ^London,

1961).]

346 VACUUM SCIENCE AND BNGINEEEING

"O 5 10 15 20 25 30 35 40 45 50

Timej days

Fig. 8-45. History of ionization

gauge reading in test chamberprotected from oil diffusion pumpby zeolite room-temperature trap

over a period of many days with

Ootoil-S and Convoil 20 as working

fluids. [Taken with permission from

M. A. Biondi, in 1960 VacuumSymposium Transactions (PergamonPress, London, 1961).]

reports that repeated exposure of

the zeolite to gases such as nitro-

gen, carbon monoxide, hydrogen,

hehum, and argon at pressures as

high as 10^^ torr does not impair

the effectiveness of the zeolite in

trapping hydrocarbons. After such

exposures for extended periods of

time the system remained free of

hydrocarbons. Levenson and Mil-

leron^^ also studied the adsorption

of various gases by zeolite at roomtemperature and found no evidence

of absorption of hydrogen, helium,

nitrogen, argon, carbon monoxide,

and methane, but did observe some

absorption for carbon dioxide and

n-butane. In the tests performed

by Milleron and Levenson, power

failures occurred and in one in-

stance the forevacuum valve was closed and the power to the diffusion-

pump heater turned off. Recovery to nearly the original pressure

Ion gauge

'Water-cooled baffle

-MCF 300 diffusion pump

Fig. 8-46. High conductance, nonrefrigerated isolation trap using artificial

zeolite. [Taken with permission from N. Milleron and L. L. Levenson, in 1960

Vacuum Symposium Transactions (Pergamon Press, London, 1961).]


occurred within about a half hour after the diffusion pump was put backinto operation. In a subsequent experiment Levenson and Milleron^*

determined that the evaporation of less than 1 cm^ of Convoil-20 into

a room-temperature trap containing about 436 g of zeolite resulted in

the eifective saturation of the zeolite. Also in these tests the stainless

steel housing of the zeolite trap wascooled with liquid nitrogen with the

result that the pressure typically

dropped from 2 x 10~* torr at

room temperature to 6 X lO^^" torr

reached in about one hour after

application of liquid-nitrogen cool-

ing. The role of the zeolite versus

that of the more effectively cooled

stainless steel walls in lowering the

pressure on application of liquid-

nitrogen cooling is not entirely clear

from these experiments, but the

authors conclude that the effect is

mainly due to the walls.

The use of liquid-nitrogen-cooled

zeolite adsorbing units instead of

pumps has recently become commonin two distinctly different types of

service. In Fig. 8-47 is illustrated

an ultrahigh-vacuum adsorbing

pump developed by Batzer and

McFarland^* to provide a hydro-

carbon free vacuum for electron

beam excitation and ionization experiments. The base pressure in-

dicated on a Bayard-Alpert gauge is typically of the order of 10~* torr.

The second application of liquid-nitrogen-cooled zeolite is in the

adsorption pumping of a clean vacuum system from atmospheric

pressure down to a pressure of about 10"^ torr, at which point getter-ion

pumps can take over. The obvious advantage of this combination of

roughing by adsorption pumping and finishing by getter-ion pumping

is the complete elimination of hydrocarbon comtaminants. In this

application the zeolite pumping unit is first outgassed by baking at a

temperature of about 200°C with a valve open to the atmosphere so

that water vapor and other adsorbed gases can escape. The vent valve

is then closed and the unit allowed to cool down with both valves, the

vent valve and the valve to the system, closed. The unit is then

immersed in liquid nitrogen and the valve to the system opened. By

Fig. 8-47. Liquid-nitrogen-cooled

ultrahigh-vacuum adsorption pump.

(1) Zeolite; (2) copper wool; (3)

copper retaining screen; (4) stainless

steel heat shield; (5) liquid-nitrogen

reservoir; (6) bakable pressure

release; (7) copper pinch gasket.

[Taken with permission from T. H.Batzer and R. H. McFarland, Rev.

Sci. Instr. 36, 328 (1965).]

348 VACUUM SCIENCE AND BNGINEBBING

having a number of units of this type connected to a manifold, large

vacuum chambers can be quickly pumped down from atmospheric

pressure to the point where a getter-ion pump can be put into operation.

This topic will be discussed further in Chap. 9.

8-7. The Pumpdown Time. The simplest situation one can

imagine for computing the pumpdown time of a vacuum system is one

in which there is no leakage from the outside, no outgassing from the

walls, and the pumping speed is independent of the pressure. In-

tegration of Eq. (7-9) then yields the pressure as a function of the time

P^ = Pie-<-^"'>* (8-4)

where P^ = initial pressure

P, = pressure after pumping for the time t

S = pumping speed

V = volume of the system

Thus the pumpdown time for such a simple case is

V

.

Pit = 2.30-log,„^ (8-5)

In the operating pressure range of mechanical roughing pumps the

assumptions made above are frequently all nearly valid except that the

pumping speed decreases with the pressure, as shown in the performance

curves of Figs. 5-5 and 5-6. However, even in this case one can apply

Eq. (8-5) to successive intervals of the pressure and obtain a set of time

intervals as follows

:

<i.2 = 2.30^^1ogio^

2.30

'S'1,2

Flogio

2,3

F

P.

P.,2.30 -—logio-^ etc. (8-6)

in which S^^^ S^^s, S^^, etc., are the average values of the pumpingspeed in the pressure intervals Pj to Pj, P2 to P3, P3 to P4, etc. Thenthe total pumpdown time is

tl.2 +

2.30F/lo^

<3,4 4

PilP:

Si.

etc.

^

logioP,/P3

So n S3 ,

etc. (8-7)

The quantity within the brackets of the above equation can be obtained

directly from the performance curve of the pump in question. If, as in

Sec. 5-3, we designate Sjj the theoretical displacement speed of the


pump and e the volumetric efficiency, then the pumping speed is

S = eS^ and (8-7) becomes

^ ^ 2 3, Z(l^gilZl/^ + i^gi^Zi^ + l^iliZi/£f + etcSd\ Cj 2 ^2,3 ^3,4

) (8-8)

Experience at the Kinney Vacuum Laboratory has shown that the

volumetric efficiencies of pumps of different displacement speeds but

of the same general design are very nearly the same at various values

of the pressure. Thus for such a series of pumps one may write

F = 2.30 P"g-^-^^- + '°g- ^-^^- + '''- ^-^"^^

+ etc.) (8-9)\ ^1,2 ^2,3 ^3,4 '

which is very nearly the same for all pumps of the series regardless of

size.

The pumpdown time then becomes

t

_F

Sr^1\'P, (8-10)

where P, is the last pressure value in the series in Eq. (8-9) and is the

pressure for which the pumpdown time is to be determined. Generally

in calculations of interest P^ = 760 torr, but the F curve may be used

in calculating the pumpdown time from any other initial value of the

pressure as desired.

The quantity F is referred to as the pumpdown factor for the

particular type of pump and is calculated from the measured per-

formance curves. In Fig. 8-48 is shown the pumpdown factor P as a

function of the pressure for single-stage and compound Kinney mech-

anical pumps as a function of the pressure. Obviously F is just the

time required for a pump to reach the pressure P( from atmospheric

pressure when evacuating a chamber of volume equal to the displace-

ment speed; i.e., when F = Sj).

The pumpdown factor of a combination consisting of a mechanical

roughing pump backing a mechanical booster pump can be computed

from the performance curves such as those shown in Fig. 5-14 and that

in Fig. 5-5, choosing an appropriate pressure for the changeover from

bypassing to pumping through the mechanical booster pump. Such a

pumpdown factor P as a function of the pressure is shown in Fig. 8-49

for the combination of a 1,200-cfm mechanical booster pump (KMB-

1200) and a 130-cfm backing pump (KDH-130).

From the curves of the type shown in Figs. 8-48 and 8-49 the pump-

down time from atmospheric to any desired pressure can be calculated

by multiplying the value of F on the graph by the ratio F/;S^ for the

iU

\ 1

^^i

T 1

—1-

\1

14

22 \]

1—t-

\ \

1

1

20

\ \ 1

18

16

14

-^

\,

—

A

\II III

.Kinney single -stage pumps

1

1

\ \ // H 1

\tmosphere -

11^

1

-t-

^ ^,\ /

12

10

8

6

/I \<s

1

1" Kinney compound pumps

'

1 1 1 1

^^ 1

VV. ^^

1

1

'^

^ 1

—1-

2

0(

-^ 1

> 1

1

)00 001 0.01 00

Pr 'ssure ,tor

1

r

100 1,0

Fig. 8-48. Pumpdown factor F as a function of the pressure for Kinney .single-

stage and compound mechanical vacuum pumps.

30

28

26

24

22

20

t 18O

i 14o

i" 12

^ 10

\

\V \\s \

\ 1 \KMBl?On s KDH 130

1-

^^F I\s l/ \ 1/

/ t ansition pressure

<J^,< T

n KMB1200i

^"v

\,1

r

^ ^^..^^

^v-4.^^ "'^

\N ^_0.0001 0.001 0.01 0.1 1.0

Pressure, torr

10 15 100 1,000

Fig. 8-49. Pumpdown factor F for the combination of a mechanical booster

and a single-stage mechanical backing pump (KMB-1200 and KDH-130).

350

THE DESIGK OF VACUUM SYSTEMS 351

system, provided only that there is no significant leakage or outgassing.

With the leak-hunting and welding techniques available today actual

leaks of any significance need not be tolerated so that it is reasonable

to insist upon a sound system in which the throughput Q = 0. Out-

gassing, however, is another matter. By avoiding porosity and

crevices inside the vacuum system and by thorough cleaning, the

Table 8-6. Observed Pumpdown Compared with That Computed byPumpdown Factor F

Volume of System: V = 11,800 ft^

Displacement Speed of Roughing Pump: So = 500 cfm

Computed Pumpdown Time: t = ' F = 23.6 i*' min

P, torrF, t computed, t observed,

System factormin mm

760 1.0

200 1.5 35.4 34 0.96

100 2.2 52.0 52 1.00

50 2.9 68.7 70 1.02

20 3.9 92 94 1.02

10 4.6 106 112 1.06

5 5.2 125 130 1.04

3 5.9 139 144 1.04

2 6.2 146 156 1.06

1 7.1 168 178 1.06

0.5 8.1 182 203 1.11

0.3 8.8 208 270 1.30

0.14 10.0 236 865 3.66

pressure at which outgassing becomes important can be made quite

low. In Table 8-6 is shown the pressure at various times during the

evacuation from atmospheric pressure of a vacuum tank of volume

11,800 ft^ by a Kinney single-stage pump of displacement speed equal

to 500 cfm. The pumpdown curve is plotted in Fig. 8-50. The

errors between the computed and observed pumpdown times are not

large until the system pressure becomes less than about 1 torr. For

pressure values below 1 torr experience indicates an increasmg dis-

crepancy between the calculated and observed pumpdown times.

This discrepancy is due to outgassing effects mostly associated with the

presence of water vapor on the walls of the vacuum chamber. When

a svstem which has been under vacuum is "let down" to atmospheric

pressure by admitting dry nitrogen, then on subsequent evacuation

the pumpdown curve follows that computed from the pumpdown factor

down to much lower values of the pressure.


The discrepancy between the actual pumpdown curve and that

computed by use of the pumpdown factor (provided that the pumpis in good condition) is due to the extent to which the surfaces of the

vacuum system evolve adsorbed gases. This discrepancy is therefore

not an indication of the failure of the pump to do its job, but is anindication of the extent to which the internal surfaces of the system

1,000

100

a 10

10

s.

\\\

V

\\\

1 —

\\ / Observed

rompu ^pH -J<\.

N Otor35 m

~^

:>\ at 81

n —30 60 90 120 150 210 240 270 300 330

Min.

Fig. 8-50. Pumpdown curve compared with that computed by use of the pump-down factor F. Data of Table 8-6.

are contaminated by oil films, adsorbed water, and possibly other

condensable materials. The ratio between the observed and calcu-

lated pumpdown times may conveniently be called the system factor,

values of which for the pumpdown data in Table 8-6 are given in the

last column. Because of minor errors in pressure readings, changes in

temperature during the period of the pumpdown, minor discrepahcy

in the actual as compared with the assumed rotational speed of the

pump, etc., a system factor in the range 0.95 to 1.05 may be considered

not to be significantly different from 1.00. It will be noted, however,that the computed system factor in this case rapidly exceeds 1.05 whenthe pressure drops below 1 torr. The very large increase in the systemfactor for pumpdown to 0.14 torr is not typical and was most probablycaused by the presence of a leak of the order of 40 torr cfm. Thepump is capable of reaching an ultimate pressure of the order of


0.005 to 0.010 torr on a tight, dry system, but it seems doubtful whethera continuation of the pumpdown test illustrated would ever reach apressure less than 0.1 torr.

In the above discussion the conductance of the connecting pipinghas not been taken into account. However, the criterion used forselecting the pipe size for connecting a roughing pump is such that theimpedance offered by the piping is not likely to be a measurable factorin determining the pumpdown time. As discussed in Sec. 2-4, thepipe size is selected to ensure an acceptably small pressure drop whenthe system has reached its normal operating range (i.e., the lowestpressure of practical interest). The criterion frequently applied is thatthe pressure drop in the line (up to the inlet of the mechanical pumps)should not exceed 10 per cent of the pressure. However, duringpumpdown from atmospheric pressure this pressure drop is negligibleas compared with the pressure itself. The conductance of the con-necting piping is proportional to the pressure in this pressure range sothat over most of the pumpdown cycle the conductance is very largeindeed as compared with the pumping speed of the pump and is there-fore not normally a significant factor in determining the pumpdowntime within the range of mechanical pump operation.

Many pumpdown experiments have been carried out under bothfavorable and unfavorable conditions. When there are sizable leakspresent in the system or when puddles of water have accumulated atsome low point in the plumbing, then the pumpdown process becomesstalled and the system factor approaches infinity. However, whenthere are no leaks present, when the interior of the system has beencleaned section by section before assembly, and when no unforeseenevent has created puddles of water somewhere in the system, thenexperience shows that rather definite values of the system factor applyto the pumpdown time, depending upon the pressure limit involved,such that

^(actual) = (system factor)^ (calc)

V(system factor) -— i^^^^^ (8-11)

The recommended system factor makes allowances for the normaloutgassing of surfaces exposed to atmospheric air and provides a basisfor judging whether the system is pumping down normally or whethersome problem exists which must be corrected. On the basis of ex-perience, therefore, recommended system factors are given in Table8-7 not only for single-stage mechanical pumps, but also for compoundpumps and mechanical booster pumps. It should be emphasized thatby special care, such as letting down the system to atmospheric

354 VACXJUM SCIENCE AKD ENGINEBBING

pressure by admitting only dry nitrogen, shorter pumpdown times than

those computed using the recommended system factors can be reahzed.

Naundorf25 has attempted a rather complete and systematic ap-

proach to the determination of the pumpdown time extending into the

lange of diffusion-pump operation. His approach leads to a solution

based upon the graphical representation of two quantities which typify

Table 8-7. Recommended System Factors

Pressure range,

torr

System factor

Single-stage

mechanical pumpCompound

mechanical pumpMechanical booster

pump*

760-2020-1

1-0.5

0.5-0.1

0.1-0.02

0.02-0.001

1.0

1.1

1.25

1.5

1.0

1.1

1.25

1.25

1.25

1.15

1.15

1.35

1.35

2.0

* Based upon bypass operation until the booster pump is put into operation.

Larger system factors apply if rough pumping flow must pass through the

idling mechanical booster. Any time needed for operating valves and gettmg

the mechanical booster pump up to speed must also be added.

the system: (1) the throughput as a function of the pressure as repre-

sented in Fig. 8-51 and (2) the gas load as a function of the time as

represented in Fig. 8-52. At every instant of time, in order for the

pressure to be the observed value P, the throughput of the system Qmust equal the gas load L existing at the time of the observation.

Unless there is a dominating leak in the system, the gas load will

decrease with the time more or less as illustrated in Fig. 8-52. There

is no difficulty about determining the form of the throughput as a

function of the pressure. This curve can be quite accurately predicted

from the pumping speeds of the pumps used and the conductances of

traps and other components introduced. At each value of the pressure

the throughput Q = PS, where S is the resultant pumping speed of the

combined system. The gas load L as a function of the time is some-

what more difficult to construct.

In order to predict the form of the gas-load curve as a function of the

time one must know a great deal in detail about the processes of

adsorption, chemisorption, diffusion of gases through materials, and the

solubilities of gases in materials of construction. These topics are

discussed at length by Dayton^" in a paper in which tables of data are

given for all these processes for many metals, plastics, elastomers,


and ceramics. The difficulty is that a calculation of the gas load as afunction of the time for most practical situations would be a formidabletask. However, in the case of the relatively simple case of a stainlesssteel chamber 4 ft in diameter and 6 ft in length, evacuated by a 32-indiffusion pump, Naundorf was able to demonstrate good agreementbetween the predicted and actual pumpdown schedule. The out-gassing rate was determined experimentally by closing the valve into

£ 10 -

10 .

10'

10"

Qi•

-

/f Net pumping

capacity

/

/

/

- Pz P,,

10"^ 10"^ 10"

Pressure P.torr

10"

Fig. 8-51. Throughput of a diffusion-

pump system as a function of thepressure. [Taken with permissionfrom C. H. Naundorf, in 19(i0

Vacuum Symposium Transactions(Pergamon Press, London, 1961).]

10"'

10^Oi

V

\

I

(J V

"> 3S 10

-

\5-0^ -

\^^Gos load

o

^10' Q2

,0°T, T2

1 '

^^^1

10"' 10" 10'

Time t,hr

10^

Fig. 8-52. Gas load as a functionof the time. [Taken with permis-sion from C. H. Naundorf, in 1960Vacuum Si/m,posium, Transactions


the diffusion pump once each hour and measuring the rate of pressurerise, which multiplied by the volume of the tank gave the gas load dueto outgassing. The data thus obtained were plotted as shown in Fig.

8-53, and prove to be in excellent agreement with the data on outgas-sing of stainless steel contained in Dayton's paper. The result of

combining the gas-load curve with the throughput-capacity curve of

the pumping system is shown in Fig. 8-54. A horizontal line drawnthrough any value of the throughput and gas load intersects the

throughput-vs. -pressure curve and the load-vs. -time curve. Droppingvertical lines down from each intersection yields the pumpdown timefor a particular value of the pressure.

This procedure is alleged to provide an excellent prediction of the

pumpdown time provided the pressure in question is not seriously

limited by some other process than outgassing, such as leakage andpermeation. In the event that these other processes are important.


Gas load

(by rate-of-rise method)

f-Throughput vs. pressure

\ for mcf-15,000 system

\. used

Predicted ».

gas lood vs.

time ^y* \\

f 10°

I 10''

^ 10"'

.''Key:

« Pressure read at

valve inlet

• Measured values

Note: Untrapped ion

and McLeod gauge

data

Log time.hr

Fig. 8-53. Experimental gas load

as a function of the time for a

stainless steel tank of total surface

area of 165 sq ft. [Taken with

permission from C. H. Naundorf,

in 1960 VacuumSymposium Trans-


1961).]

10"' 10° 10' 10^ Time,hr

10"^ 10"' 10"^ 10"' Pressure,

torr

Fig. 8-54. Gas load as a function of the

time combined with throughput as a

function of the pressure. A vertical

line drawn at any value of the pressure

to the throughput curve, then a horizon-

tal line drawn to the intersection with

the gas-load-vs.-time curve, and finally a

vertical line drawn down from this inter-

section gives the pumpdown time for

the chosen value of the pressure. [Taken

with permission from C. H. Naundorf,


actions (Pergamon Press, London, 1961).]

the gas-load curve must be corrected and in general will have the form

shown in Fig. 8-55.

Further understanding of the problem of predicting pumpdown times

is provided in a paper by Kraus" in which it is stated that for a metal

apparatus the pressure as a function of the time is expressed by the

following differential equation

:

dt

d{P - P^;)-S = const (8-12)

P is the pressure attained after pumping for the time t, P^ is the ulti-

mate pressure attainable after pumping for a long time, and S is the

pumping speed of the system. The prediction of this equation is that

the quantity (P - P^)"! is a linear function of the pumping time

provided that the pumping speed *S is a constant. That this is indeed

true in cases of interest is shown by the graph in Fig. 8-56. The two

curves in the figure were obtained from the same system, the steeper

curve after the system had been exposed to atmosphere for only 2 mmand the less steep curve after an exposure to atmosphere of 2 hr. The

value of the constant a in the above equation depends upon the initial

THE design of VACUUM SYSTEMS

state as well as dimensions and pumping speed of the system,gration of (8-12) is shown to lead to the expression

V

S P + C

357

Inte-

(8-13)

for the pumpdown time, provided P^ > P > Pj^. Here P^ is a param-eter of the system being defined as P^ = aj V, where a is the sameas that in Eq. (8-12) and V is the volume of the system. The widerange over which the above pumpdown time relationship holds in

practice is demonstrated in Fig. 8-57. When organic materials suchas elastomers and plastics dominate the outgassing properties of a

system, however, the pumpdown relationship is more complicated.

In this case (P — Pe)~^ is more nearly a linear function of the pump-down time, and the equation cannot be integrated to anything approxi-

mating Eq. (8-13).

From this discussion of pumpdown time in the range of diffusion-

pump operation it is evident that firm predictions are much moredifficult to make than in the pressure range for mechanical pumps.Factors not taken into consideration are the use of refrigerated traps

and the application of mild heating to the vacuum chamber. Thereferences cited in the above discussion will assist the vacuum designer

to make reasonable choices in pump sizes to make possible the attain-

ment of the desired pressures in the specified time. However, the

precautions taken during preparation and operation of the system will

Sio^

10'

Adsorbed

and absorbed S^ Total gas loadgas load vsJimeX^

vs. time

Inleakage and

permeation

10" 10°

Time.hr

10' 10^

Fig. 8-55. Gas load as a function

of the time corrected for the

presence of significant leakage andpermeation. [Taken with permis-

sion from C. H. Naundorf, in 1960Vacuum Symposium Transactions


MO"'

2'10"'

5-10"

1

// y

//

1

,'VA

,;> ^t4 6

Min

10

Fig. 8-56. Relationship between

1/(P = P^) and the pumpingtime t. [Taken with permission

from Th. Kraus, in 1968 VacuumSymposium, Transactions (Perga-

mon Press, London, 1959).]


10"

10"

i 10'-3

10"

\,\>•

/y' Switchover to

• diffusion pump

^:)

\\V

Log(P-PE) \t \V

^-Log(t-K1

1 10 100

Min

Fig. 8-57. Pressure-time curve for

a vacuum annealing furnace demon-strating the wide pressure range

over which Eq. (8-13) is applicable.

[Taken with permission from Th.

Kraus, in 195& Vacuum Sympo-sium Transactions (Pergamon Press,

London, 1959).]

in many cases affect the perform-

ance much more than minor changes

in the original choice of design

parameters.

8-8. Selection of Vacuum Com-ponents. The conventional vacuum

system consists of mechanical pumps,

diffusion pumps, valves, vapor traps,

vacuum gauges, and interconnecting

plumbing all assembled for the pur-

pose of attaining and maintaining the

specified environment in a vacuum

chamber. Because the vacuum de-

signer is faced with several alterna-

tive combinations of components

which will meet the specified per-

formance, the final choice involves

judgment regarding the most con-

venient and economical combination

of components which will serve the

purpose. In this section the func-

tions of each of the components in

meeting the operating requirements

of the system will be discussed

briefly and some criteria will be

given for specifying the combina-

tions and capacities of components needed.

Mechanical Pumps. The mechanical pumps of a conventional

high-vacuum system have two rather separate functions: (1) to pumpdown the system to the level necessary for the diffusion pumps to be

put into operation and (2) to maintain the backing pressure during

regular operation at an acceptable pressure for optimum operation

of the diffusion pumps. These two requirements frequently lead to

very different values of the capacity for the mechanical pumps.

In many large systems the time for roughing down the system is

much longer than that required to reach operating pressure once the

diffusion pumps and refrigerated traps can be put into operation, after

which the mechanical-pump capacity required to maintain the needed

backing pressure is very small. In such systems, as illustrated in

Fig. 8-58, it is economical and convenient to install a battery of large-

capacity mechanical pumps connected directly to the vacuum vessel

by means of a bypass line to rough out the system to a pressure below

that at which the diffusion pumps can operate. The capacity of the


roughing pumps required for this function can be computed with verylittle uncertainty from Eq. (8-11) using the system factors given in

Table 8-7. Whether this battery of roughing pumps consists ofsingle-stage pumps alone or mechanical booster pumps backed bysingle-stage pumps is an economic question which can only be answered

Nude ion Ion gouge Cold trapGote valve

Interconnecting

valve

Roughing

,0 wjvolve

-—@)-^14

^Thermocouple

Diffusion-pump^

foreline trapFreon^

compressorRoughing pump

Fig. 8-58. Representative conventional high-vacuum system. (1) Vacuumchamber; (2) internal liquid-nitrogen thimble trap; (3) liquid-nitrogon-cpoled

diffusion pump baffle; (4) gate valve (in optimum design the connecting pipe

would be as short as possible; (5) Freon-cooled baffle; (6) diffusion pump with

Freon-cooled exhaust condenser; (7) forevacuum oil vapor trap; (8) forevacuum

valve; (9) backing pump; (10) roughing pipe and valve with oil vapor trap;

(II) roughing pump; (12) interconnection between roughing and backing lines

with close-off valve; (13) ionization gauges—nude and tubulated—in vacuumchamber; (14) thermocouple gauges in roughing and backing lines.

by computing the pumpdown time for various combinations of pumps

and their associated plumbing and then comparing the resulting

performance with the cost of each combination.

In principle the determination of the capacity of the backing pumpis a simple matter. If the throughput Q of the system during normal

operation is known, then the pumping speed for backing is Sj, = QjPi,,

where Q is the throughput and P^ is the backing pressure required

during operation. This determination is generally much more difficult

to judge in advance than the pumpdown capacity required because of

the uncertainty in the value of Q due to gas flow, outgassing, and


permeation. The system should furthermore have some excess

capacity to override minor leaks sufficiently to get the diffusion pumps

into operation and expedite leak hunting. An interconnection between

the backing and roughing pumps as shown in Fig. 8-58 can be invaluable

during periods of difficulty. However, even with this added flexibility

ill the system, a factor of 2 in capacity of the backing pump above the

minimum calculated from the anticipated throughput is recommended.

Because of uncertainty in the knowledge of the value of the throughput,

an even larger margin in capacity may be required. Even with a

fairly generous factor applied to the throughput for determining the

capacity of the backing pump, however, in most cases that capacity

is very much smaller than that required for the roughing pump.

Operation of a system thus usually consists of pumping the system

down through the bypass and roughing pumps to a pressure of perhaps

0.1 or 0.2 torr, then closing the bypass valve and opening the gate valve

into the diffusion pump. The diffusion pump has presumably already

been in operation with the gate valve closed and backed by the backing

pump. The next step is then to cool down the liquid-nitrogen-cooled

baffle over the diffusion pump and also to fill the thimble trap with

liquid nitrogen (assuming a thimble trap is used). Meanwhile the

large capacity mechanical pumps used for roughing the system down

from atmospheric pressure can be stopped.

Diffusion Pumps. The pumping speed required for the diffusion

pump and associated baffles and gate valves must also be considered

from the point of view both of pumpdown time and of the required

operating pressure. The pumpdown time can best be approached by

the method ofNaundorf^^ outlined in the previous section. For

various combinations of diffusion pumps, gate valves, and baffles one

can estimate the throughput capacity of the system as a function

of the pressure. From the outgassing data supplied in the paper by

Dayton^' and the exposed areas of various materials one can construct

a gas-load curve as a function of the time. By combining these curves

as in Fig. 8-54 the pumpdown time as a function of the pressure can

be roughly predicted for any particular combination of diffusion pump,

baffle system, and gate valve for which the overall pumping speed is

known. The choice from this point of view must then be compared

with the pumping speed required to maintain the desired operating

pressure for the predicted gas load by applying S = QjPo, where P„

is the operating pressure. The choice of diffusion-pump, baffle, and

gate-valve pumping speed is usually determined by this latter con-

sideration. Although additional construction cost always results from

oversizing the system by providing excess pumping speed to override


accidental leakage or a larger gas flow for whatever process is involved,this additional construction cost will in most cases be at least partlycompensated for by the reduced pumping and processing time whichusually result from excess pumping capacity. A vacuum system withpumping capacity which is too small to do the allotted job is much less

economically sound than one which has a moderate excess capacity.Loss of time during operation can be very expensive and in a short timedissipate the initial savings one might make by installing insufficientpumping capacity.

Accessories. The accessories which are useful to include in a con-ventional vacuum system such as that illustrated in Fig. 8-58, asidefrom those specifically shown in the drawing, are

:

1. Multiplicity of ionization gauges. In many large systems it is

convenient to install ionization gauges in pairs, one with and one with-out a glass liquid-nitrogen trap. The discrepancy between the gaugesis due primarily to condensables (mostly water vapor) so that anexperienced operator can readily ascertain the condition of the systemand diagnose many troubles.

2. Thermocouple or Pirani gauges are indicated in Fig. 8-58, butthe advantage of a multiplicity of such gauges in the roughing andbacking sections of the system should be emphasized.

3. Although vacuum valves are expensive, the flexibility introducedinto the system by the inclusion of valves at strategic points is well

worth the cost. Aside from the gate valve for isolating the diffusion

pump from the vacuum chamber, valves should be installed at thefollowing positions : (a) at the vacuum chamber end of the roughingline, (b) in the forevacuum line near the outlet of each diffusion pump,(c) at the inlet of each mechanical pump, either roughing or forevacuum,and (d) in a line interconnecting the forevacuum and roughing lines.

Also recommended are small, normally closed valves installed betweeneach shutoff valve and its mechanical pump for testing and diagnosing

the source of trouble in the system, and a small, normally closed valve

on the vacuum chamber for letting down the chamber to atmospheric

pressure. Provision should be made to admit commercial dry nitrogen

or dry air through a drying unit.

Conventional vacuum systems of the type described above should

give excellent service with base pressure (untrapped ionization-gauge

reading) of 10^' torr and should perform well in the range of 10-^

torr. When operation at significantly lower pressure is desired, the

techniques of ultrahigh vacuum are required. This is the topic of the

next chapter.


REFERENCES

1. L. L. Levenson, Xorman Milleron, and D. H. Davis, in 1960 Vacuum Sym-


2. I. Farkass and E. J. Barry, in 1960 Vacuum Symposium Transactions


3. A. Guthrie and R. K. Wakerling (eds.). Vacuum Equipment and Techniques

(McGraw-Hill Book Company, New York, 1949), pp. 148-158.

4. R. R. Addis, Jr., L. Pensak, and Nancy J. Scott, in 1960 Vacuum Symposium

Transactions (Pergamon Press, London, 1961), p. 39.

5. R. R. Wilson, Rev. Sci. Instr. 12, 91 (1941).

6. R. H. V. M. Dawton, Brit. J. Appl. Phys. 8, 414 (1957).

7. R. W. Roberts, Rev. Sci. Instr. 32, 750 (1961).

8. J. F. Gerber, Rev. Sci. Instr. 34, 1111 (1963).

9. F. N. D. Kurie, Rev. Sci. Instr. 19, 485 (1948).

10. J. S. Wahl, S. G. Forbes, W. E. Nyer, and R. N. Little, Rev. Sci. Instr. 23,

379 (1952).

11. William E. Bush, A. Guthrie, and R. K. Wakerling (eds.). Vacuum Equip-

ment and Techniques (McGraw-Hill Book Company, New York, 1949),

Chap. 4, p. 179.

12. J. W. Johnson and W. M. Good, Rev. Sci. Instr. 32, 219 (1961).

13. Norman Milleron, in 1958 Vacuum Symposium Transactions (Pergamon


14. J. R. Ullman, in 1957 Vacuum Symposium Transactions (Pergamon Press,

London, 1958), p. 95.

15. L. L. Levenson, Norman Milleron, and D. H. Davis, in 1960 Vacuum Sym-


16. A. R. Taylor, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962), p. 1328.

17. H. R. Smith and P. B. Kennedy, in 1959 Vacuum Symposium Transactions


18. John Strong in collaboration with H. Victor Neher, Albert E. Whitford,

C. Hawloy Cartwright, and Roger Hayward, Procedures in Experimental

Physics (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1938), pp. 105, 124.

19. D. Alpert, Rev. Sci. Instr. 24, 1004 (1953).

20. J. H. Carmichael and W. J. Lange, in 1958 Vacuum Symposium Transactions


21. M. A. Biondi, in 1960 Vacuum Symposium Transactions (Pergamon PreSs,

London, 1961), p. 24.

22. N. Milleron and L. L. Levenson, in 1960 Vacuum Symposium Transactions


23. L. L. Levenson and N. Milleron, in 1961 Vacuum Symposium Transactions


24. T. H. Batzer and R. H. McFarland, Rev. Sci. Instr. 36, 328 (1965).

25. C. H. Naundorf, in 1960 Vacuum Symposium Transactions (Pergamon Press,

London, 1961), p. 60.

26. B. B. Dayton, in 1959 Vacuum Symposium Transactions (Pergamon Press,

London, 1960), p. 101.

27. T. Kraus, in 1958 Vacuum Symposium Transactions (Pergamon Press, London,

1959), p. 38.

CHAPTER 9

ULTRAHIGH VACUUM

The term ultrahigh vacuum has come into use in recent years todesignate the range of pressure below about IQ-' torr which cannoteasily be attained by the conventional methods and techniques de-scribed in the previous chapter. In order to reach significantly lowerpressure, additional or alternative techniques must be applied. Thetechniques thus far found to be useful in attaining operating pressuresin the range IQ-s to lO"" torr or lower will be briefly described in thischapter.

9-1. The Dominance of Surface Phenomena. From the papersof Daytoni-3* on the outgassing of "clean" metal surfaces at roomtemperature it is evident that after exposure to normal atmosphericair for several hours the amount of gas readily available for desorptionfrom the surface at room temperature amounts to many molecularlayers. As an example, Dayton's tables^ show that after 10 hr ofvacuum pumping the outgassing rate for a stainless steel surface is

about 2 X 10-5 torr liter/sec ft^ and is decreasing very slowly. There-fore to maintain a base pressure of IQ-s torr in the presence of such anoutgassing rate requires a pumping speed of at least 20 liters/sec foreach square foot of internally exposed surface. Most large vacuumchambers consist of outer walls and a complex inner structure, thetotal surface area of which must be considered. Also the wall areaavailable for vacuum pumping is usually limited by the many otherdemands of the system for access ports, high voltgage insulators, and avariety of accessories essential to the vacuum process. The result is

that a design figure of 20 liters/sec for each square foot of internalsurface can generally be realized or even somewhat exceeded in practiceso that the base pressure is limited to about lO"" torr even after manyhours or days of pumping.

In the previous chapter mention was made of speeding up theprocess of outgassing by increasing the temperature of the vacuum

References indicated by superscript numbers are listed at the end of thechapter.

363

364 VACUUM SCIENCE AND ENGINEEBmo

chamber, and this practice has been followed for many years. How-

ever, the gain in the ultimate pressure attainable by a system is not

improved by a mild baking (say to 100°C) by a large factor. The

principal advantage is that the time required to reach the typical

limit of the system may be greatly reduced. To reduce significantly

the attainable operating pressure requires baking at temperatures

much greater than 100°C. This requirement introduces a number of

complications into the design which are not encountered in conventional

vacuum-system design.

Experience has shown that outgassing from metal surfaces in vacuum

is predominantly due to water vapor. The character of the surface

deposition of water on metal surfaces is discussed by many investi-

gators: Kraus,* Hayashi,^ Lichtman and Hebling,« Mongodin and

Prevot,' and Flecken and Noller.* Because the surfaces of metals

generally used in vacuum-chamber construction consist of somewhat

porous oxides, the problem of defining the exact physical state of the

water and other contaminants on the surface of the metal is complicated.

As Dushman* has explained, there are three mechanisms by which a

gas can be taken up by a solid material, all generally included under the

general term sorption.

1. Chemisorption refers to the formation of a chemical compound

by interaction of a gas with the wall material, as in the case of the

formation of an oxide film.

2. Adsorption refers to the surface condensation of a gas on a metal

surface. This process is generally believed to result in a film of only

a very few molecular layers of gas.

3. Absorption refers to a process by which the gas molecules penetrate

into the interior of the wall material and in a sense the gas is dissolved

in the solid.

The outgassing history is expected on theoretical grounds to depend

critically upon which of these three mechanisms of sorption are in-

volved. Research on this question, which has been very extensive, is

complicated by the definition of the effective surface area. The

roughness factor (i.e., the effective microscopic surface area compared

with the gross, or macroscopic, surface area) inferred by various

investigators ranges from about 20 to 100 depending upon the details

of outgassing experiments and the assumptions of the theory applied

to the situation. Because of the complexity of the theory and the lack

of sufficient detailed knowledge of the microscopic character of the

surfaces, an empirical approach to the problem based upon experi-

mental outgassing results at various temperatures seems to be the only

practical course to follow at the present time . Dayton^ has summarized

ULTRAHIGH VACUUM 365

experimental data of this type in the curves shown in Fig. 9-1 for steel

and in Fig. 9-2 for aluminum. Based upon the macroscopic surface area,the total amount of gas given off by metal surfaces at room temperatureover a period of 10 to 50 hr of vacuum pumping ranges from 20 to 100molecular layers. What is perhaps more to the point is that untreated

Fig. 9-1. Outgassing rate versus

time for steel at room temperature.

Curves for rusty steel, sandblasted

steel, and stainless steel (curve 1)

from the data of Blears et al.^"

Stainless steel curve 2 from thedata of Gellor,!' and curve 3 fromthat of Basalaova'^ on untreated

stainless steel. [Taken with per-

mission from B. B. Dayton, in 1961Vacuum Symposium Transactions


5 10-7

J'iG. 9-2. Outgassing rate versustime at room temperature. Curve 1,

untreated duraluminum, and curve 3,

duraluminum scoured and washedwith benzol and acetone, are basedon the data of Basalaeva.i^ Curve 2,

duraluminum, is based on the dataof Geller.ii Curve 4, aluminumbright-rolled and cleaned in Stergene,

and curve 5, anodized aluminum, are

based on the data of Blears et al.^"

[Taken with permission from B. B.Dayton, in 1961 Vacuum Stjmpo-

sium Transactions (Pergamon Press,

London, 1962).]

metal samples outgas at the rate of about I0-' torr liter/sec cm^ after

1 hr of vacuum pumping at room temperature, and this rate of out-

gassing is about inversely proportional to the pumping time. Thesestatements have to do with room-temperature outgassing for whichwater vapor is by far the dominating substance. At high temperatureother factors, such as diffusion of absorbed gases through the metal,

become important so that high-temperature outgassing cannot beinferred simply by integrating the room-temperature curves andcompressing the resulting output over a shorter period of time.

9-2. High-tetnperature Bakeout. In the previous section it

was stated that operating pressures much less than about 10^* torr

366 VACUUM SCIENCE AND ENGHSTEEEING

cannot easily be attained because of the long-persisting outgassing of

internally exposed surfaces at room temperature. The total amount

of gas available on metal surfaces is so great that even with the inverse

dependence upon the pumping time of the outgassing rate the base

pressure attainable is seldom as low as lO"' unless some action is taken

to change drastically the source of gas available for desorption. The

10-^

10'* -

:

10"

Mc

on

Base pre

before

bokeout

V

X system te

first bake

ssure /Sp

//I

/ /'

/Max/ temp

/ bake

1 Time '

mp = 400°C

\ \\ \^

system N. Cut heat

on 2nd \^ 1st bake System= 200°C \ -^ cooling 1

\ \ ^ ^>\< Cut heot \| 1

\ X Air 1

\ 1\l f°"s

1

\ \ 1

^^ Pressure pips occurred wherA. 1^

\ liquid-nitrogen trap filled \^^^

>C^y-K A^i aK1 1

1 1

1 1 1 1 1 1 1

Pressure rose

w

be

1x10-'

en creep

rrier out

8hr

1 to heot

1

1 muffle 1

-5x10"'°

1

Bokeout

2 3 4 5 6 7 8

Time,lir

—>|~2weeks

10"

started

Fig. 9-3. Plot of the pressure versus the time for two typical bakoout cycles of

a chamber evacuated by an oil diffusion pump through a liquid-nitrogen trap

with and without anticreep barrier. [Taken with permission from N. Milleron,

in 1958 Vacuum Symposium Transactions (Pergamon Press, London, 1959).]

most effective means of affecting such a drastic change is to bake the

entire vacuum chamber up to and including the liquid-nitrogen-cooled

baffle system at a high temperature for an extended period of time.

The supply of gas sorbed in the metal is desorbed rapidly and pumped

at a much higher pressure during the period the chamber is maintained

at high temperature, so that the total throughput of desorbed gas is

increased during this period by a large factor. When the system is

then allowed to cool back down to room temperature, the great quan-

tities of easily desorbed gas have been removed from the surfaces, the

outgassing rate is decreased by many factors of 10, and the resulting

base pressure is correspondingly decreased.

The results of two typical bakeout cycles reported by Milleron"

are shown graphically in Fig. 9-3. The system was evacuated by a


conventional stainless steel diffusion pump using Octoil-S as the work-ing fluid. The liquid-nitrogen-cooled vapor trap was that illustratedin Fig. 8-30, featuring an oil-creep barrier and a water- or radiation-cooled baffle to take the blast of hot oil vapor from the diffusion-pumpjet. The volume of the vacuum chamber was 70 liters and wasequipped with metal gaskets to permit bakeout temperatures up to450°C. The vacuum chamber had been used for many previousultrahigh-vacuum experiments so that the stainless steel walls werefar cleaner than those of a newly constructed chamber. As indicatedin Fig. 9-3 the base pressure attained with the chamber at roomtemperature was about 2 x 10"' torr. During bakeout the tempera-ture reached the value of 400°C in about 1 hr and was maintained at

that temperature for about 5 hr, the heater power having been on for

6 hr. The pressure in the chamber reached a maximum of 10~* torr

at about the same time the temperature reached 400°C and thenslowly decreased until it had declined to a value of about 2 x 10"' torr

after 6 hr of baking when the heater was turned off. A crude in-

tegration of the area under the outgassing curve yields a total gas

output of about 30 torr liters during the bakeout, since the measuredpumping speed of the system was about 40 liters/sec. The projected

area of the interior walls of the vacuum chamber was about 7,500 cm^.

Since the number of molecules in 1 torr liter of gas is 4.5 x 10", the

gas removed during bakeout was equivalent to 30 x 4.5 x 10"/7,500 =2 X 10" molecules/cm^ of projected area. If one assumes a roughnessfactor of 50, which may be somewhat generous, the gas extracted fromthe metal during bakeout was equivalent to about 40 molecular layers.

At the pressure existing before bakeout the time required to removethis quantity of gas would be about 100 hr. However, at the end of

the bakeout when the chamber reached room temperature the pressure

had dropped to 5 x lO"" torr, where it remained for the period of the

test with no indication of rising.

A similar test run without the oil-creep barrier in place reached a

base pressure of about 1 x lO"" torr after a shorter bakeout period

(about two hours) but then began to rise rapidly after about two weeksoperation and in a period of one day rose back up to a value of 1 X 10~'

torr, where it then remained. For the conditions of this test, therefore,

the surface migration time for the oil film to bypass the liquid-nitrogen-

cooled trap along the approximately room-temperature surface of the

housing surrounding the vapor trap was apparently about two weeks.

From this result one may conclude that the oil-creep barrier is not a

necessity for the attainment of ultrahigh vacuum with an oil diffusion

pump as long as the period of interest is less than about two weeks,

but for longer periods the barrier is an absolute necessity.


Ion gouge

±

wR-f moss spectrometer

Go-ln-Sn seol

To oil

ditfusion

pump

Furncce

Thermocouple

Fig. 9-4. Gas analytical apparatus for analysis and quantitative moasuromentof gases given out during bakeout. [Taken with permission from P. F. Varadi,

in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961).]

Outgassing experiments of the type just described are very in-

formative from an empirical point of view and lead to concrete in-

dications of the ultrahigh-vacuum capabilities of oil diffusion pumpscoupled with appropriately designed vapor traps. However, the

outgassing in the case just discussed was measured with an ionization

gauge so that the details of the outgassing process in terms of the

gases being evolved as a function of time were not determined. This

point is covered by Varadi^* in a cleverly executed experiment in which

the throughput of the evolved gases are analyzed and measured

quantitatively during the bakeout cycle. Varadi's apparatus is

illustrated in Fig. 9-4 and incorporates a known conductance and r-f

mass spectrometer to identify and measure the quantity of each com-

ponent of gas evolved as a function of time as the sample is put through

the bakeout cycle. In Fig. 9-5 are shown graphically the quantitative

results of outgassing a nickel cathode sample at a temperature of 850°C

for a period of several minutes. The data shown in the figure are taken

from three separate samples prepared in the same way, showing the

excellent reproducibility of the results. The predominance of hydro-

gen during the early phase of the outgassing period and its subsequent

rapid decrease to a minor constituent is an interesting feature of the

process. Since the materials being tested in Varadi's experiment are

cathodes already prepared for use in vacuum tubes, the material had

been treated for an hour in a hydrogen atmosphere at 1150°C. The


results are therefore not indicative of the gas content of raw nickel

generally, but illustrate a method of quantitative analysis whichshould be of considerable help in disentangling the contributions ofadsorption, absorption, chemisorption, and diffusion to the process ofoutgassing.

Even though processes involved in sorption and outgassing are notyet understood quantitatively in the detail desired, experience hasshown that a well-designed diffusion-pump and vapor-trap systemaugmented by baking the vacuum chamber at temperatures from 250to 450°C can attain base pressures of 10^" torr or less. Experiencefurther indicates that a newly fabricated and carefully cleaned systemmust generally be subjected to a baking temperature of at least 300°Cfor about 24 hours in order to reach the lO"!" torr range. Subsequentbakeout temperatures can be at lower temperatures and for shorter

periods of time, depending upon the character of the gas exposure

Fig. 9-5. Graphical presentation of the thermal degassing properties of a cathode

nickel material. [Taken with permission from P. V. Varadi, in 1960 Vacuum

Symposium Transactions (Pergamon Press, London, 1961).]


Flange Cylinder

wall

during the intervening period. Best results are obtained by admitting

nitrogen from evaporating liquid nitrogen to the system and maintaining

a flow of dry nitrogen while the system is open so that a pressure slightly

in excess of atmospheric pressure is maintained in the system. Bythis procedure water vapor can be almost completely excluded from

the system for the subsequent pumpdown cycle.

The necessity of baking the vacuum chamber and all its accessories

at high temperature introduces a number of

design problems not encountered in conven-

tional high-vacuum systems. Since elas-

tomers are restricted to a relatively limited

temperature range, the sealing of flanges and

valve seats presents serious problems to

which reasonably satisfactory solutions have

been found.

9-3. Metal Gaskets. The fact that

rubber and elastomers generally are not

entirely suitable for use as gaskets in vacuumsystems because of outgassing and permea-

tion has been recognized for many years.

In Chap. 8 the properties of a number of

elastomers are discussed and the advantage

particularly of Viton A and B for use in

systems with bakeout temperatures up to

300°C is mentioned. Another technique

discussed is that of circulating a coolant

through a guard ring between two rings

with the result that the outgassing and per-

meation of the 0-ring material is substantially reduced. Alternatively,

a copper tubing for circulating the coolant may be installed in the

guard ring thus avoiding a rather messy situation when the flange is

disassembled. These alternatives are available, and in those instances

in which the resulting base pressure is satisfactory for the process in

hand more exotic solutions to the problem may not be justified.

The fact that the best of elastomers, even with the improved tech-

niques for their use, are not satisfactory for many applications still

remains. The use of various softer metals such as gold, indium, and

lead fuse wire has been mentioned in the vacuum literature for manyyears. In Procedures in Experimental Physics by Strong^^ a design

of metal gasketed flanges, as shown in Fig. 9-6, is described. It is

emphasized that lead wire gaskets joined by butt welding to form a

ring can be used to high bakeout temperature and that aluminum wire

remains vacuum tight for even higher bakeout temperatures. The

Fig. 9-6. Metal gasketed

flange design described

by John Strong. [Taken

with permission fromJohn Strong, Procedures

of Experimental Physics

(Prentice-Hall, EnglowoodCHffs, N.J., 1938).]


lOmils

20mils

temperatures used for baking out the system are not stated. Con-sidering that these techniques were in use in the mid-thirties emphasizesthat the eff'ort to develop satisfactory metal gaskets has a long history.

The most extensive early use of lead wire gaskets in the author'sexperience" was in the design and construction of the accelerating

tube for the 2.5-million-volt Van de Graaff generator built at MIT in

1937. The vacuum system wasevacuated by mercury diffusion

pumps and was constructed of

porcelain and steel with fuse-wire

gaskets at all metal-to-porcelain

joints and at all demountable

flanges. The disadvantages of the

use of fuse wire are that the bake-

out temperature is limited to

about 250°C and that the fuse

wire cold-flows even at room tem-

perature. If the mechanical de-

sign of the flange is such that the

compressional loading is main-

tained as the fuse-wire material

creeps, the gasket eventually be-

comes very thin and usually de-

velops a leak. In spite of this

feature fuse-wire gaskets have been used to advantage in a great manysituations in which the available elastomer gaskets could not be used.

Another metal wire material which has proved to be useful is an

indium- tin alloy which is, however, limited to bakeout temperatures of

about 100°C. This material has the advantage that fusing joints is not

necessary. The wire can be overlapped at the joint and will seal

tightly when the flange surfaces are pulled up snugly compressing the

gasket joint. On large or irregularly shaped flanges this feature of the

indium-tin wire may be a distinct advantage.

In recent years with the greater demand for ultrahigh-vacuum

systems requiring high-temperature (450°C) bakeout there has been

a greatly enhanced effort on the development of metal gaskets.

Copper gaskets have been developed in a number of different forms

and have been used with some degree of success. In Fig. 9-7 is illus-

trated the copper shear gasket" developed for the Atomic Energy

Commission by the Westinghouse Research Laboratories. The mating

flanges are designed with an interleaving step form so that when the

two flanges are forced together under loading from the bolt circle,

the flat copper gasket 0.045 to 0.050 in. thick is sheared to a depth of

20 mils

Fig. 9-7. Copper shear gasket. [Taken

with permission from Lawrence Radia-

tion Lab. Eng. Note EXA-122, Mar.

16, 1961, by T. H. Batzer and J. R.

Ullman.]


0.005 in.

+0.002_i_

<- 0.015 in. + 0.005

t

r-

.

A>'/i6 in. B>V32 in. C = V8 in.

about one-half its thickness. Annealed OPHC copper sheet material

was at first recommended for this purpose until cold-flow difficulties

developed during high-temperature bakeout. Details of the flange

and gasket design were developed in some detail by Batzer and

Ullman," who found that annealed cupronickel is a much more satis-

factory material than copper for

this type of seal. As developed

by Batzer and Ullman the shear

gasket is very reliable for use

with stainless steel flanges and

bakeout temperatures up to 450°C.

The proper machining of the

flanges requires adherence to close

tolerances, and the resulting prod-

uct is easily subject to damage.

The sheet stock selected for

making gaskets must be free of

scratches. If properly made, shear

gasket joints are consistently re-

liable and can be opened and

closed several times before the

gasket must be replaced. Theprincipal disadvantage is the rela-

tively high cost as compared particularly with the aluminum-foil

gaskets to be discussed later.

Milleron^^ describes a form of gasket which he calls the copper bead

gasket, the cross section of which is shown in Fig. 9-8. The gasket as

shown in the flgure is placed between polished flanges with plane sur-

faces and is compressed by a symmetric tightening of the bolts on the

bolt circle. The total area of the protruding beads is small with the

result that the concentrated loading of the flanges flattens the beads

until the steel flange surfaces come into contact with the much larger

area of the main body of the gasket. Further tightening of the bolts

results in no signiflcant further compression of the gasket but a stretch-

ing of the bolts, the stress due to which keeps the seal tight during the

bakeout and cooling cycle. This gasket configuration proved to be

much superior to copper or aluminum wire gaskets, which do not have

the feature of the greatly increased eff'ective area and therefore develop

leaks due to creep of the metal. Since the flanges are flat, there are no

difficult tolerances to hold or expensive operations to carry out in the

fabrication of the flanges. Making satisfactory copper bead gaskets,

however, has proved to be somewhat more difficult, but the problem

has been solved by the use of chemical milling using concentrated

nitric acid.

Fig. 9-8. Cross section of the soft

copper bead gasket before compression

between steel flanges with plane faces.

[Taken with permission from N.

Milleron, in 195S Vacuum SymposiumTransactions (Pergamon Press, London,

1959).]


A somewhat similar type of copper ridge seal is described by Goerzi"

for use on the Stanford 2-mi electron accelerator. As shown in Fig.

9-9, the rather thick (3/16-in.) copper gasket has a narrow ridge of

height equal to about 0.010 in. and width at its base of 0.018 in. Whenthe gasket is compressed between the flanges, the ridges are distorted as

shown in the figure. The complete assembly of the waveguide flange

joint is shown in Fig. 9-10. This case is interesting in that the wave-

2A

±16

Clomping bar

Before seolinq After seoling

Ridge Detoil

Fig. 9-9. Cross section of ridged

copper gasket before and after com-pression. [Taken with permission

from D. J. Goerz, Jr., in 1960

Vacuum Sym,posium Transactions


Fig. 9-10. Waveguide flange assem-

bly utilizing ridged copper gasket of

Fig. 9-9. [Taken with permission

from D. J. Goerz, Jr., in 1960

Vacuum Symposium, Transactions


guide, and therefore also the copper gasket, is rectangular but appar-

ently seals very well. It is reported that klystrons using these seals

have not shown an increase in pressure over a period of several months,

the pressure being in the 10~* torr range.

There have been a number of designs of knife-edge seals reported, one

example of which is that reported by Lichtman and Hebling^' and

illustrated in Fig. 9-11. The rather thick OFHC copper gasket is

silver-plated. Both stainless steel flanges have machined on them

circular ridges, referred to as knife edges, which deform the copper

gaskets as the flanges are drawn together. The mechanical process

involved would appear to be somewhat similar to that of the copper

ridge gasket. In any case the authors report excellent reliability at

bakeout temperatures up to 600°C with a system utilizing many such

seals up to a flange diameter of 12 in.


Knife edges

O.OIOR

ULTBAHIGH VACUUM 375

A-7o°-A

stainless steel

Stoinless-steel

Stainless -steel

^>«^swivel flange

Silver-plated

oxygen -free

copper washer

Fig. 9-11. All-metal knife-edge seal. [Taken with permission from D. Lichtmanand A. Hebling, in 1960 Vacuum Symposium Transactions (Pergamon Press,London, 1961).]

Lichtman and Hebling^" also report on an all-metal flare seal shownin Fig. 9-12 which provides a compact and reliable means of connectinga small-diameter copper tubing to a fitting on a manifold or chamber.The authors state that the seal is assembled by slipping the coppertubing through the stainless steel flange and then flaring the tubingwith a standard tool. The seal is said to be reliable even after severalcycles of disassembling and reassembling and to withstand the highbakeout temperatures required.

Gold wire has been used to seal vacuum flanges in a variety ofdiff'erent designs. The design shown in Fig. 9-13 is used on the

Three No. 10-32 bolts

Fitting

Copper tubing

Compression

Braze seal

^Manifoldtubing

Fig. 9-12. All-metal flare seal. [Takenwith permission from D. Lichtman andA. Hebling, in 1960 VacuumSymposiumTransactions (Pergamon Press, London,1961).]

0.020 diam gold wire

Fig. 9-13. Simple gold seal. [Takenwith permission from D. J. Grove,

in 1958 Vacuum' Symposium Trans-


Stellarator devices at Princeton and is described by Grove. ^^ Groveattributes the origin of this type of seal to Hickam,^^ but the idea

seems to have occurred independently to others as well. According to

Grove the important factors in the design are a radial clearance of

0.001 or 0.002 in. between the inner and outer members of flanges

which slide together, a surface finish of 16 microin. and a snug fit for the

gold ring in the corner of the flange. The material is 24-karat gold.

The initial diameter of the wire is 0.020 in., and it is compressed to

0.010 in. when the flanges are pulled tightly together closing the

crevice between them on the inner surface. These seals have repeatedly

withstood bakeout to 450°C without failure, and were in use in sizes

from K in. to 8 in. diameter at the time the report was written.

Power and Robson^^ summarize a series of experiences using wire

gaskets between flat stainless steel flanges. One difficulty encountered

during their tests, and indeed also encountered by others, is the tend-

ency of an aluminum-5 per cent silicon wire gasket to form a strong

bond to the surface of the flange, resulting in tearing the gasket and

leaving portions thereof tightly stuck to the flange. Their practice

was to compress the 0.040-in.-diameter wire to 0.011 in. between the

flanges, controlling the limit of compression by using shims placed

between the flange faces. The adherence of the gasket material to the

flange is a major nuisance since cleaning up the flange for subsequent

use is then a tedious chore. Power and Robson report that this

difficulty is completely eliminated by applying a surface coating of

indium to the aluminum wire gasket. An unexpected advantage is

that the compressive force required is reduced by a factor of 2 or 3

when the indium coating is applied. The authors report that the

difficulties in making successful seals in the manner described increase

with the dimensions of the flange, and that they have not been con-

sistently successful in sealing flanges for 400°C bakeout for diameters

of 12 in. or greater.

A metal gasket development of particular promise is that of Batzer

and Ryan, 2* who have devised a bakable aluminum gasketed flange

which appears to be more reliable than any previously described up to

large diameters and is far less expensive than most other designs. The

aluminum-foil flange is illustrated in Fig. 9-14. The mating flanges,

which may be either stainless steel or aluminum, are machined with

mating faces which are slightly conical at the angle Q relative to the plane

of the flange. A gasket is cut from commercial aluminum foil 0.015 in.

thick (using tin snips, for example) and placed between the flanges,

which are then bolted together. Contact will initially occur at the inner

diameter of the contacting conical surfaces, but the point of contact wifl

move to larger and larger radii as the bolts are tightened and the flanges >


Pipe 0D + 2t

0.0015 Alfoil

type 1145-0

respond with a rotational deflection. The figure includes the formulafor the rotational deflection as a function of the modulus of elasticity

of the flange material, the dimensions, and the applied loading.

The aluminum-foil seal is loaded at 2,000 to 3,000 Ib/lin in. of gasket.

The strain energy stored in the

distorted flanges ensures that the

gasket is under compression for a

wide range of temperature. Ther-

mal cycling of aluminum-foil seals

between liquid-nitrogen tempera-

ture and 450°C has been carried

out repeatedly without damage or

development of detectable leaks.

Aluminum-foil seals with gaskets

cut from single widths of foil

material have been tested andused successfully with diameters

ranging from l}4. to 22 in. It has

been privately reported to the

author by Batzer that a 48-in.-

diameter flange, the gasket for

which was made up of several

sections of aluminum foil over-

lapped at their ends, was tested

successfully. The additional com-pressional loading at the points of

overlap was apparently sufficient

to eliminate the gaps which wouldnormally be expected to be formed

at the edges of the overlapping

sections. From this experience

flanges of larger diameters will be

attempted using the aluminutti-foil

technique with overlapping sec-

tions in order to meet an, actual

need in the controlled-fusion pro-

gram. Presumably because of the relatively low local pressures de-

veloped between the flanges and the foil gasket no serious difficulty of

bonding of the gasket material to the flanges has been experienced.From the performance to date the aluminum-foil seal appears to bethe most economical and successful demountable, bakable all-metal

seal for ultrahigh-vacuum application.

Another form of aluminum-foil seal which has been found to be

7/16diam(approx, 2.00"

spacing)

Fig. 9-14. The aluminum-foil vacuumflange. Maximum stress in flange:

cr(max) = MRjZ. Rotational deflec-

tion in flange: = MR^jEI. M =moment due to bolt load and gasketreaction. R = radius of bolt circle.

Z = hd^jQ, flange section modulus./ = 6d^/12, moment of inertia of flange

section. E = modulus of elasticity ofthe flange. [Reprinted with permis-sion from The Macmillan Co., fromT. H. Batzer and J. F. Ryan, in 1963Vacuum Symposium Transactions.

Copyright © 1963 by The AmericanVacuum Society, Inc.]


thoroughly reliable is that illustrated in Fig. 9-15. This seal has been

used extensively in ultrahigh-vacuum applications by the Compagnie

General de Telegraphic sans Fil. The flanges are stainless steel and

are machined with a ridge on one flange and a mating groove on the

other. Since the half-angle of the ridge is 30° and that of the groove

is 45°, the aluminum foil, which is compressed into the groove by the

ridge, is under a tapering compressional load. The flange distortion

and stretching of the bolts provides the stored energy necessary to

ensure that a compressional load will be sustained at all times during

the bakeout.

All dimensions in mm

*nnii»

iJliil

ntO.l0*0

r+u.i'.-to

rto.l

p tO.2

r^r^

-0.3mm

Aluminum-

foil gasket

Fig. 9-15. Aluminum-foil gasket with wedge seal flange of the Compagnie

Generale de Telographie sans Fil. The circular gasket is cut from 99.95 per

cent pure aluminum foil of 0.3 mm thickness. [Taken with permission from

Societe de Reoherches Techniques et Industrielles, HI, rue la Boetie, Pans.]


A method of sealing flanges which avoids entirely the necessity of a

gasket of any kind has been described by Farkass and Vanderschmidt.^^

The method as illustrated in Fig. 9-16 consists of welding onto each

flange a thin, stainless steel skirt which protrudes out beyond the

flange. The machining of the flange to provide a thin lip of metal

onto which to weld the skirt is a typical ex-

ample of the proper preparation for a Heliarc

weld of a thin section of metal to a heavy

member. The two flanges are mounted in

position with the outer peripheries of the skirts

in contact, and the edge is then welded shut all

the way around. The resulting joint is then

completely sealed by welding . When the flange

is to be disassembled, the weld around the edge

is ground off. Such a seal can be rewelded

several times before the old skirtings must be

replaced. The advantage of absolute welded

tightness is obvious. In many situations, how-

ever, the frequency with which the weld would

have to be ground off and the seal rewelded

might become a major handicap.

9-4. Bakable Valves. In the previous

chapter, vacuum valves of several varieties

were described and illustrated. Many of the

designs discussed have metal bellows to trans-

mit the motion for opening and closing the

valve port. However, in all the examples given

the sealing of the valve port is accomplished by

some type of elastomer, so that the maximumtemperature for bakeout is limited by the choice

of seal material. The steel-fabricated valve

shown in Fig. 8-19 and Fig. 8-20 is capable of

bakeout to 175°C when supplied with silicone valve disk and gaskets.

The same valve could be supplied for somewhat higher-temperature

bakeout with Viton A or B for these parts. For many ultrahigh-

vacuum applications the bakeout temperature must be much higher

than any available elastomer will tolerate.

The first major step toward the solution to the bakable valve

problem is that reported by Alpert^' and illustrated in Fig. 9-17. The

valve consists of two main components: (1) a vacuum-tight capsule

with a heavy OFHC copper base sealed over one side by a corrugated

Kovar diaphragm which carries a Kovar plunger which can be driven

snugly into one of two 0.25-in. holes drilled through the base and

Fig. 9-16. Reweldable

seal connection between

two heavy flanges, upto 30 in. in diameter.


from I. Farkass and G.

F. Vanderschmidt, in

1959 Vacuum Sympo-sium Transactions (Per-

gamon Press, London,

I960).]


(2) a driver assembly with a differential screw thread by which theplunger is driven into or withdrawn from the sealing hole. Kovartubes are soldered into the two holes in the

copper base plate and are connected to the

system either by glass or metal tubing.

The Kovar plunger has a 60° tapered tip

and forms its own seat by deforming the

copper about the entrance to the sealing

hole. The conductance of the valve whenclosed is reported to be in the range 10"" to

10-11 liter/sec which is almost beyond the

detectable limit. Valves of the Alpert type

are available commercially and permit opera-

tion in the pressure range IQ-i" torr or less.

The virtue of this type of valve is that it

may be thoroughly outgassed by high-tem-

perature bakeout either in the open or closed

position. Its principal disadvantage is its

relatively low conductance even when fully

open.

A considerably larger valve having manyof the features of that just described is that

reported by Grove^^ and shown in cross sec-

tion in Fig. 9-18. The open conductance of

the valve shown is 80 liters/sec and the closed

conductance is typically 10"^ liter/sec. In

this design the nose piece with the 45° face

is of copper and the seat is stainless steel

with a 1%-in. opening. A stainless steel

bellows allows adequate motion to provide

the open conductance stated above. Valves

of this design have been used extensively in

the construction of Stellarators and have

been baked at 450°C in the closed position

repeatedly without deterioration in their

ability to seal properly. The differential

screw method of applying final loading on

the valve is provided by a separate assembly

which is removed when the valve is baked.

A new design principle has been introduced in the gasketless valve

described by Wishart and Bancroft." When a conical spring washer

is flattened by compression between two flat surfaces, the washer

increases in diameter. The objective was to utilize this effect to seal

U'-'-l--i Y'l

Fig. 9-17. All-metal bak-

able vacuum valve. Thevalve body consists of

(1) a 1^ -in.-diameter

copper cup with l/4-in.-

diameter holes for the

valve seat and openings,

(2) a flexible Kovar dia-

phragm brazed to the

copper cup and to (3) a

Kovar member with a

highly polished conical sur-

face. The driver mecha-

nism consists of (1) an

outside screw and stainless

steel housing, (2) a silicon-

bronze differential screw,

(3) a drive screw, (4) a

backing plate to withstand

the large forces exerted

upon the valve body.


from D. Alpert, Rev. Sci.

Instr. 22, 536 (1951).]

Fig. 9-18. Large-aperture bakable

valve. [Taken with permission fromD. J. Grove, in 1958 Vacuum Sym-posium Transactions (PergamonPress, London, 1959).]

Flattened position Relaxed position

m

Fig. 9-19. Sealing principle for a

gasketless metal valve. [Taken with

permission from J. Wishart and

G. H. Bancroft, in 1960 VacuumSymposium, Transactions (PergamonPress, London, 1961).]

Fig. 9-20. One-half inch bakable

valve utilizing the sealing principle

illustrated in Fig. 9-19. (1) Pressure

ring; (2) expanding disk; (3) valve

body; (4) shoulder to limit travel of

valve-disk assembly; (5) end piece of

valve body; (6) operating nut for

opening and closing valve; (7) pinnedcolor for retracting valve-disk assem-

bly; (8) disk carrying assembly.[Taken with permission from J.

Wishart and G. H. Bancroft, in 1960Vacuum, Sym,posium Transactions(Pergamon Press, London, 1961).]

Kinematical alignment

of gate

Pressure

chamber

OFHC copper

gate

Stpinless

knife edge

Fig. 9-21. Schematic drawing of 4-in.

bakable gate valve. [Taken with

permission from R. J. Conner, R. S.

Buritz, and T. von Zwock, in 1961



380

ULTEAHIGH VACUUM 381

the aiaerture of a valve in the manner illustrated in Fig. 9-19. A H-in.

valve utilizing this principle is shown in cross section in Fig. 9-20.

The clearance between the disk and the bore within which it travels

is only a few thousandths of an inch, so that as the disk is thrust

against the circular stop, the disk expands radially and seals against the

cylindrical wall. It is found that in applying this principle of sealing

it is not necessary to use a soft metal such as copper. The disk is

made of a spring steel material and the body of type 304 stainless steel.

The difference in hardness between these two materials is sufficient

to ensure a tight seal. The seating principle involved in this design has

been tested for disks from % to 10 in. in diameter with no indication of

difficulty in obtaining satisfactory sealing. Valves of the 2-in. size

have been baked out repeatedly to 250°C without impairment in opera-

tion, although it would appear from the lack of mention of successful

bakeout at high temperature that 250°C may be the practical limit of

the design as presently developed. A 3^-in. valve was tested to more

than 1,000 openings and closings, and a 2-in. valve to 300 without any

evidence of significant leakage rate through the closed seat.

A bakable gate valve as described by Conner et al.^^ utilizes a

stainless steel knife-edge seal against an OFHC copper disk and pneu-

matic pressure between a pair of concentric metal bellows to provide

the necessary seal loading. A schematic drawing of a 4-in. valve of

this design is shown in Fig. 9-21. The copper valve disk is raised and

lowered by a toggle mechanism sealed by a stainless steel bellows. The

valve has been tested in repeated opening and closing operations,

is bakable to 450°C, and is reported to have a closed leakage rate less

than 10-12 liter/sec atmospheric pressure. No leakage was detected

by a mass spectrometer with helium at atmospheric pressure maintained

on one side of the valve for 3^ hr. The authors state that the design

is not limited to the simple circular aperture but has been successfully

applied to a rectangular aperture of 2 by 11 in.

A large bakable gate valve has been described by Batzer^^ and is

illustrated in Fig. 9-22. The valve incorporates an inflatable metal

bladder the expansion of which under the pressure applied by hydraulic

fluid affects the seal. The valve disk is put into position by a rotary

motion seal with a metallic bellows and an internal mechanical linkage

while the disk is under no load, so that the disk slides into place and

is raised to a position of close contact with the bladder seal. Hydraulic

fluid in the bladder chamber is then pressurized as shown most clearly

in Fig. 9-22a. The design shown utilizes copper shear gasket joints

for assembly of the demountable parts. The bladder consists of an

annular diaphragm 0.032 in. thick clamped vacuum tight between

flanges utilizing the shear seal technique. The hydraulic pressure

required for sealing is typically 6,000 psi.


(a)

(6)

Fig. 9-22. (a) Valve seat and gate for bakable gate valve. [Taken with per-

mission from T. H. Batzer, in 1959 Vacuum Symposium Transactions (PergamonPress, London, I960).] (6) Cross-sectional view of bakablo gate valve. [Takenwith permission from T. H. Batzer, in 1959 Vacuum Symposium Transactions


9-5. Two-region Vacuum Systems. An approach to the design

of an ultrahigh-vacuum system which in some cases greatly simphfies

the problems of motion seals and demountable joints is that of sur-

rounding the ultrahigh-vacuum chamber by a conventional vacuumchamber so that the pressure difference determining the leakage into

the inner chamber is of the order of 10~^ torr instead of atmospheric

pressure.

A commercial vacuum system designed on the two-region principle is

shown schematically in Fig. 9-23 from a paper by Rivera and Le

ULTRAHIGH VACUUM - 383

Riche.^" The outer vacuum region is evacuated by means of a con-

ventional system utilizing a 4-in. oil diffusion pump. The inner

chamber is evacuated by a 6-in. diffusion pump through a liquid-

nitrogen-cooled chevron baffle. The 6-in. diffusion pump is backedby a 2-in. diffusion pump and a compound mechanical vacuum pumpwith a cold trap (usually dry-ice-cooled) between the 2-in. diffusion

pump and the mechanical pump.The inner chamber is a stainless steel bell jar, the bottom seal for

which is a 13-in.-diameter flat flange on a plane face plate with asimple copper wire gasket. The flange loading is provided by 12 drop-

forged C clamps. Two 3-in. sight ports are mounted on the inner

chamber wall, secured by flanges with metal wire seals.

The outer chamber is fitted with heater elements on the inner surface

and water-cooling coils on the outer surface. The system is normally

pumped down with the outer chamber removed. After leak checks

are completed, the outer chamber reaches a peak temperature of about

490°C. The inner chamber pressure as a function of the time during

bakeout and subsequent cooling to room temperature is shown graph-

ically in Fig. 9-24. At the end of the baking cycle compressed air is

first blown through the cooling coils on the inner chamber to facilitate

rapid cooling to room temperature. Liquid nitrogen is then circulated

Sight ports

Representative

power feed-throughs

ar)d rotary motion

High-vacuum valve

Radiation shielding

Inner bell jar

Outer bell jar

, Outer bel l-|ar water cooling

Heater windings

Gouge

Chevron trap

High -vacuum valve

Roughing valve

5-cfm

mechanical

pump

Fig. 9-23. Two-region ultrahigh-vacuum system. [Taken with permission from

M. Rivera and R. LeRiche, in 1959 Vacuum Symposium Transactions (Pergamon

Press, London, I960).]


t: 10"

X - Average curve -L 31Pressure of inner chamber (P,)osa function

!i of time^

Bakeout begon_

P,=f(t)

+ - C0(

Bakeout terminated.

cooling initiated —iguid-nitrogen —

through the trap and the pressure

drops rapidly, usually into the 10~i*

torr range. The complete bakeout

and cooling cycle typically requires

about fifteen hours.

A somewhat similar two-region

vacuum system described by Ehlers

and Molpi is illustrated schemati-

cally in Fig. 9-25. The inner

chamber is thin-walled and is bak-

able to a temperature of 450°C bypassing an electrical current through

the thin metal wall material. Be-

cause of the low heat capacity the

heating period is very short and the

total bakeout period at 400 to

450°C is about iH hr. The inner

chamber and an internal coil are then cooled by circulating compressedair, and finally liquid-nitrogen cooling is applied not only to thediffusion-pump trap but also the internal cooling coil. The result is arelatively short bakeout and cool-down cycle with a total about 6 hr to

operating pressures in the range 3 x ID"' to 5 x lO"" torr as read ona Bayard-Alpert gauge, depending upon the detailed features of thesystem and the operating cycle.

3 6 9 12 15 18 21

Time.hr

Fig. 9-24. Pressure vs. time for theinner chamber of a two-region ultra-

high-vacuum system. [Taken withpermission from M. Rivera and R.LeRiche, in 1959 Vacuum Sympo-sium Transactions (Pergamon Press,

London, I960).]

Window system

Ttiin-wall bakoble

contoiner

(Heated by higti o-c

Alpert gauge o

Cooling -water boffle

Oil diffusion pump

Rotary pump

High vacuum 10"* to 10"* torr

\^^ ^/ Ultrahigh vacuum

(\>'^~y'^0-' to 10"'° torr

5r^ ^,Alpert gouge b

(j)!^ Simple metal gosket

„('i Liguid -air trap

= °=>^'^~\ Bokable tube

pfT~^ \ Liquid -air baffle

-Cooling -water baffle

I

^Oil diffusion pump

Quick cooling

Fig. 9-25. Two-region ultrahigh-vacuum system with thin-wall inner chamber.[Taken with permission from H. Ehlers and J. Moll, in 1959 Vacuum SymposiumTransactions (Pergamon Press, London, I960).]


Radiation shields

Another example of a two-region system is described by Metcalfeand Trabert^^ ^^d illustrated schematically in Fig. 9-26. The outervacuum chamber is 48 in. in diameter and is evacuated by a conven-tional diffusion-pump system consisting of a 12-in. diffusion pump witha water-cooled baffle typically producing a pressure of 2 x 10-* torrafter the bakeout cycle is completed. The inner chamber is 32 in.in diameter and is fabricated of Inconel, H in. thick, the total workingvolume of which is 16 ft^. The inner chamber is evacuated through a20-in.-diameter pumping manifoldwithin which there are two chev-

ron baffles separated from eachother in the manifold and isolated

thermally by ring- and disk-radia-

tion baffles. The inner chamberand the portion of the manifoldcontaining the innermost chevronbaffle are heated by radiation

heaters in one zone of the outer

vacuum space, and the portion of

the manifold containing the outer-

most chevron baffle is similarly

heated by heaters in the secondzone of the outer vacuum space.

The elbow leading from the pumping manifold to the diffusion pump is

separately heated by heater elements on its outer surface. There is athird chevron baffle just over the diffusion pump. According to theauthors the net pumping speed out of the inner chamber is calculatedto be 750 liters/sec.

After bakeout of the inner chevron trap and the inner chamber to400°C for 6 to 8 hr, cooling for several hours, and finally cooling theinner chevron trap with liquid nitrogen, Bayard-Alpert gauge readings"corrected for X-ray limit" reached base pressures in the range 2 to3 X 10-" torr. The pressure-versus-time curve for the bakeout andpumpdown is shown in Fig. 9-27. An interesting feature of the curveis the series of ionization-gauge peaks which are observed as the liquid-nitrogen supply to the chevron baffles is shut off and the baffles slowlywarm up. These peaks are interpreted as being due to the fractionaldistillation of the condensed gases off the baffle surfaces.

9-6. Getter-ion Pumping. Thus far in this chapter we haveconsidered various ways in which the performance of the conventionaldiffusion pump and vapor-trap combination, together with variousmodifications in the methods of sealing and the technique of bakingto high temperature, could be improved for the purpose of attaining

Heaters

'

Fig. 9-26. Schematic drawing oftwo-region ultrahigh-vacuum system.[Taken with permission from R. A.Metcalfe and F. W. Trabert, in 1961Vacuum Symposium Transactions(Pergamon Press, London, 1962).]


much lower pressures than are typically obtained in conventional

vacuum systems. The diffusion pump and its mechanical backing

pump are sources of contaminants

which must be prevented from

backstreaming into the high-

vacuum portion of the system and

limiting the base pressure to some

much higher pressure than that

desired. Rather than combat this

problem of backstreaming, engi-

neers in recent years have madean intensified effort to exploit

methods of pumping which do not

generate hydrocarbon contami-

nants and give promise of provid-

ing "clean" vacuum spaces with

relatively simple combinations of

equipment. One approach to this

problem which has had some

degree of success was discussed

toward the end of Chap. 5, where

recent progress in the development

of molecular pumps and axial-flow

molecular turbine pumps was de-

scribed. We shall devote the re-

mainder of this chapter to other

methods of pumping, some of

which have already been demon-

strated to provide important capabilities in the ultrahigh-vacuum

pressure range.

It is well known that gas discharges have the ability to pump to some

degree. This is particularly true of discharges in magnetic fields, since

30 40-

Time.hr

Fig. 9-27. Typical bakeout and pump-down cycle of the two-region vacuumsystem shown in Fig. 9-26. [Taken

with permission from R. A. Metcalfe

and F. W. Trabert, in 1961 VacuumSymposium Transactions (Pergamon


Exit-gas leakPressure ~10'^ torr

Side magnet

Pressure ~5)(10" torr

"To forevocuumAnode constriction'

Hollow cold

ttiode

-300volts

Pressure~5xlO"'' torr

End view

Fig. 9-28. An ion pump based upon the pumping action of an intense discharge in

a magnetic field. [Taken with permission from .J. S. Foster, Jr., E. O. Lawrence,

and E. J. Lofgren, Rev. Sci. Instr. 24, 388 (1953).]


the ions and electrons formed by ionization are constrained to move inmore or less tight spirals along the lines of force. A neutral moleculewhich wanders into a discharge column in a magnetic field quicklybecomes ionized, trapped in a spiral path in the magnetic field, andforced to leave the region where it entered the discharge by spir'alingalong the magnetic field. The pumping action of discharges in mag-netic fields has therefore been well known for a long time. However,the first serious attempt to develop a vacuum pump utilizing thiseff'ect appears to be that of Foster, Lawrence, and Lofgren. ^s Thedevice took the form shown in Fig. 9-28, which illustrates a dischargeion pump capable of pumping at the rate of about 5,000 liters/sec.

The axial magnetic field was produced by an array of coils mounted onthe long, cylindrical body of the pump, except for the central regionwhere the pump housing is enlarged to provide high entrance conduct-ance. Across this enlarged section of the pump the coil was in the formof a rather open spiral conductor carrying a large current to maintainthe magnetic field strength and still permit gas molecules to diffusefreely into the discharge. The distribution of currents in the coils

determines the shape of the magnetic field which is optimum when thelines of force bulge slightly in the central section of the pump andconverge somewhat symmetrically toward both ends.The discharge is a large PIG discharge first investigated by Penning. »«

There are two cathodes, one on each end of the device. Experiencewith a variety of hot- and cold-cathode designs resulted in the final

selection of a hot, hollow cathode on one end and a cold, hollow cathodeon the other, as shown in the figure. The anode for the dischargeis the long cylindrical pump body reaching from the enlarged pump-inlet section to the anode constriction on each end. The dischargecolumn is limited in diameter by the anode constrictions. The shapeof the magnetic field and the diameter of the cylindrical anode from theconstriction to the pumping section of the device are sensitive param-eters. In order to maintain the proper discharge conditions in thecentral region of the pump it was found to be necessary to maintain aneutral gas density in the cathode chambers not less than about5 X 10-* torr, which is the forevacuum against which the ion pumpworks. The gas from the cathode chambers fiows in from both endsof the pump, is ionized, and as positive ions is carried back to thecathodes, where the ions are neutralized. Molecules fiowing into thedischarge column in the central section are ionized and also are carriedout the ends as ions and are neutralized at the cathodes. Many of theions striking the cathodes interact chemically. This process proceedsat such a rate that the forevacuum valves at the two ends of thepump could frequently be closed and even then gas had to be bled

388 VACUtTM SCIENCE AND ENGINEERING

into the cathode chambers in order to maintain the minimum operating

pressure of 5 x 10"* torr required to maintain the discharge.

The operating characteristics of the pump are shown in Table 9-1.

From these characteristics it is evident that the ion pump of Foster,

Lawrence, and Lofgren cannot be classed as an ultrahigh-vacuum

pump since the typical base pressure was about 1 X 10"* torr. How-

ever, the pump did have the specific advantage of not producing

hydrocarbon impurities. The feature of continuing to pump even

Table 9-1. Opekating Pabametbes of the Ion Pump Shown in Fig. 9-28*

Pumping speed 3,000-7,000 liters/sec

Base pressure 0.8-5 x 10"* torr

Arc voltage 400-300 VArc current 20-10 ACathode Radiantly heated tungsten cathode

Heating power, 4.5 kWMagnet power Side magnets, 20 kW

Center helix, 12 kW

* Reproduced by permission from J. S. Foster, Jr., E. O. Lawrence, and E. J.

Lofgren, Rev. Sci. Instr. 24, 388 (1953).

when the forevacuum valves were closed contributed further to the

cleanliness of the system relative to hydrocarbon contaminants.

Unfortunately, the pressure in the cathode region had to be maintained

at least at 5 x 10~* torr, and the compression ratio which the pumpcould maintain against the pressure in the cathode chambers was never

better than about 10^, so that pumping at pressures much lower than

10~* torr with this particular type of ion pump does not appear to be

promising.

During studies of the performance of closed-off systems with a

Bayard-Alpert gauge in operation Bayard and Alpert^^ observed a very

definite pumping action of the gauge involving chemisorption and ion

burial in metal coatings in the gauge tube. Herb and his collafcora-

^Qj.g36,37 have reported on the operation of a large device designed

specifically to exploit these mechanisms for vacuum pumping. ' The

device, known as the Evapor-ion pump, is illustrated schematically in

Fig. 9-29, and involves two principal features: (1) A feed mechanism

by which titanium wire is fed in a sequence of discrete steps from an

internal spool down a guide so that the tip of the wire periodically

touches a post of tantalum-tungsten alloy which is heated by electron

bombardment to such a high temperature that a short length of the

wire is evaporated each time the tip of the wire touches the post. The

evaporated titanium coats the walls of the pump housing, which is

ultrahigh vacuum 389

Filament F

Inner grid G|

Outer grid Gj

about 12 in. in diameter. (2) An electron-emitting filament and doublegrid system which accelerates electrons radially outward, ionizes residualgas molecules, and drives the ions with energies up to 1,000 eV intothe walls of the pump body which are coated with the evaporatedtitanium.

Freshly evaporated titanium is very active in the chemisorption ofmost of the common gases except the noble gases. These latter gasesare ion pumped in the Evapor-ionpump, driven into the wall coat-

ing, and covered up by subse-

quent layers of evaporated metal.

Pumping speeds measured for

various gases by Swartz^* were as

given in Table 9-2 when the rate

of titanium evaporation was 5.3

mg/min.

The most extensive use of the

Evapor-ion type of pump is onthe 30 X lOi'-eV AGS proton syn-

chroton at Brookhaven, whereover 50 units have been in use for

several years. Gould^^ reported

briefly on experiences and diffi-

culties encountered in the early

use of these pumps in such great

multiplicity. The method of evap-oration of titanium has beenchanged to one of sublimationfrom a heated titanium rod as de-

scribed by Gould and Mandel*"and also by Herb, Pauly, Welton,and Fisher.*! The Evapor-ionpumps which have been changedover to the new continuous subli-

mation technique are operated as

described by Gould and Mandel"under the control of an automaticpressure detector in the pressure range 2 x 10"' to 2 x 10"* torr. Theultimate pressure thus far attainable using the new technique is 2 x 10^'

torr, which the authors believe is determined by the impurities presentin the commercial (non-vacuum-processed) titanium which is used.The pumps equipped with three sections of titanium rod for sublimationdeposit, as shown in the photograph in Fig. 9-30, are expected to

Bleeder system

Fig. 9-29. The Evapor-ion[Taken with permission fromDavis and A. S. Divatia,

Instr. 25, 1193 (1954).]

pump.R. H.

Rev. Sci.

390 VACUUM SCIENCE AND ENGINBEBING

Table 9-2. Pumping Speeds for Various Gases for the Evapor-ionPump*

Gas Partial pressure,

torr

Pumping speed,

liters/sec

Air

OxygenNitrogen

HydrogenCarbon monoxide . . .

MethaneArgon

1 X 10-5

1 X 10-5

3 X 10-6

1.7 X 10-6

5 X 10-6

1 X 10-5

5 X 10-5

370

1,000

2,000

3,300

1,000

20

5

* Reproduced by permission from J. C. Swartz, in 1955 Vacuum SymposiumTransactions (Committee on Vacuum Techniques, Boston, 1956), p. 38.

Fig. 9-30. Inner structure of Evapor-ion pump with three sections of titanivim

for sublimation coating. [Reprinted with permission from The Macmillan Co.,

from C. L. Gould and P. Mandel, in 1962 Vacuum, Symposium, Transactions.Copyright © 1962 by The American Vacuum Society, Inc.]


Penning

gaugePenning

gauge

operate satisfactorily for a period of about two years before replace-ment of the titanium rods will be required.

Although as used on the Brookhaven AGS the operating pressure is

not very low, it is an acceptable range for the present needs. What is

important is that the system appears to be essentially free of hydro-carbon contaminants. The system is initially pumped down to apressure of about 10-* torr by a group of compound mechanical boosterpumps backed by single-stage mechanical roughing pumps. Thesystem is then isolated from the mechanical pumps and the Evapor-ionpumps are put into operation.

The relative simplicity of the

system in other respects seems to

have fully justified the consider-

able expenditure of effort in per-

fecting the Evapor-ion pump to

the point of high reliability.

A getter-ion pump in which the

ionization and gettering processes

are more completely separated

than in the Evapor-ion pump has

been described by Gale.*^ Thepumping unit together with the

test reservoir for admitting various

gases under controlled conditions

is shown in Fig. 9-31. The pump-ing unit consists of two chambers

;

within one titanium metal is evaporated from heated tungsten filaments

wound with titanium wire, and within the other is a Penning type of

ionization gauge. One interesting feature of this arrangement is that

ions formed in the Penning discharge unit cannot strike directly the walls

on which the titanium metal is deposited. Even so, there is a markeddifference in the pumping characteristics, depending upon whether the

Penning discharge is in operation . Particularly in the pumping of argonand helium the pumping speed is greatly enhanced. To determine the

pumping effectiveness of the combined unit, the procedure followed wasfirst to pump out the entire system with a diffusion pump and outgasthe pump and structure by heating the tungsten filaments below the

evaporating temperature. The valve to the diffusion pump was thenclosed and the filaments were raised arbitrarily to a temperature at

which titanium was evaporated onto the walls of the chamber and thenthe filament current was turned off. The valve between the reservoir

and the getter-ion pump was then closed and gas admitted to the reser-

voir to a predetermined pressure. The gas sample was shared with the

Tungsten filaments

overwound with titonium

Fig. 9-31. Getter-ion pump of Gale*^

together with test reservoir for

admitting various gases under con-

trolled conditions. [Taken with per-

mission from A. J. Gale, in 1956Vacuum Symposium Transactions



pump chamber by opening the interconnecting valve, and finally

the pressure in the reservoir was observed as a function of time. Since

the volume of the reservoir, which was about 700 cm', was about equal

to that of the pumping unit including the Penning discharge chamber,

the operation of opening the valve to the reservoir and sharing the gas

sample between the two volumes accounted for an immediate drop in

pressure to one-half that initially

in the reservoir. Thereafter, the

fall in pressure with time provided

a measurement of the pumping

speed. In the test runs reported,

the initial pressure in the reservoir

was 7 X 10^2 torr or 3.5 x lO-^

torr after sharing with the getter-

ion pump. The results of nine

runs in sequence are shown graphi-

cally in Fig. 9-32. Three regions

of performance can be distinguish-

ed: (1) the pressure range from

3.5 X 10-2 cio^n to about 3 x 10-*

torr in which the slope of the pump-down curves, and therefore the

pumping speed, is generally less

than that for the next lower pres-

sure range, and furthermore de-

creases from run to run as the

getter surface appears to become

saturated; (2) the pressure range

from 3 X 10-* to about 5 x 10-«

torr, over which the pumping

S 10"

Absorption choVocteristic of

getter-ion pump for dry oir

5 10 15 20 25 30 35 40 45 50 55 60

Elapsed time.min

Fig. 9-32. Pressure-vs.-time curves

from which the performance of the

getter-ion pump shown in Fig. 9-31

was determined for dry air. [Takenwith permission from A. J. Gale, in

1956 VacuumSymposium Transactions


speed is the same from run to run

for a large number of cycles, indicating that the pumping speed in

this pressure range is relativelj' insensitive to the amount of gas already

absorbed by the getter surface; (3) the pressure range from about

5 X 10-* to 6 or 7 X 10-' torr, over which the pumping speed decreases

toward zero at an ultimate pressure at which the absorption and

desorption rates of the getter surface appear to reach equilibrium.

The pumping speed in the pressure region (2), in which it is constant

and insensitive to the gas absorbed by the getter surface, is shown in

Table 9-3 for several gases. According to Gale*^ the pumping speed

for hydrogen is much greater than that for other gases, with the result

that the slopes of the curves were too steep to permit a measurementof its value. The most interesting feature of the performance of the


Table 9-3. Pumping Speed op the Getter-ion System of Fig. 9-31 fobVarious Gases*

^'^ Pum,ping speed, cmfijsec

Air 16Oxygen 28Nitrogen igCarbon dioxide 24Helium 9

* Reproduced by permission from A. J. Gale, in 1956 Vacuum SymposiumTransactions (Pergamon Press, London, 1957), p. 12.

pumping unit is the anomalously high pumping speed for helium andargon.

When an evaporated metal coating has reached saturation and losesits pumping efficiency, the surface can be restored to its original

t3

^Fig. 9-33. Schematic drawing of theVac Ion pump. [Taken with per-mission from L. D. Hall, in 1958Vacuum Symposium Transactions(Pergamon Press, London, 1959).]

00 60s molecule

o6as atom

>Gos ion

• Titoniumatom

• Electron

Anode

Cathode

Fig. 9-34. Assumed pumping mech-anism of the Vac Ion getter-ion pump.[Taken with permission from L. D. Hall,

in 1958 Vacuum, Symposium Transac-tions (Pergamon Press, London, 1959).]

performance by heating the filaments for a few minutes and depositinga new coating of evaporated titanium. This process can be repeateduntil the titanium wound on the tungsten filaments has been essentiallycompletely consumed by evaporation.A major advance in the development of getter-ion pumping was

initiated by Hall« in the development of the Vac Ion pump, which is

illustrated in Fig. 9-33. The device consists of a rectangular box withinwhich is mounted an electrically insulated "egg crate" electrode made


of thin metal plates (usually titanium) arranged to produce an array

of cells with square cross section. On each of the inner flat surfaces of

the boxlike stainless steel casing a plate of titanium or other active

metal is secured with a small clearance between the surface of the two

fiat electrodes and the insulated cell structure. The rather flat

assembly is put between the poles of a magnet so that the field lines

pass through the square cells of the insulated electrode and are per-

pendicular to the surfaces of the two titanium plates on either side.

When a positive electric potential is applied to the insulated electrode,

each cell of the device acts like a separate PIG or Penning discharge.

Because of the large cathode area involved the pressure at which the

discharge will start and continue to pass current is very low when a

potential difference of the order of 5,000 V is applied to the central

electrode.

The mechanism of pumping by the Vac Ion pump as visualized by

Hall" is illustrated in Fig. 9-34. As in any PIG discharge any electrons

which are present oscillate in the electric field between the cathodes and

are restricted from moving to the side and striking an anode plate by

the magnetic field. The electrons are thus very efficiently used for

producing ionization, i.e., not only is a positive ion produced and drawn

by the electric field into the surface of the cathode but in addition in

each ionizing event another electron is produced which carries on the

process of producing more ions. The ions are propelled into the cathode

plate with energies of several kiloelectron volts and sputter cathode

material (such as titanium), some of which settles on the surfaces of the

anode plate structure. The freshly deposited active metal has strong

chemical affinity for most gases with the result that gas atoms are

accumulated and held by chemisorption on the anode plates. The

cathode plates are slowly eroded by the sputtering process. Figure

9-35 is a photograph of a cathode plate after long service showing

the deep holes eroded opposite each cell of the anode.

Hall" reports that hydrocarbon contamination of the Vac Ion type

ofpump can easily prevent the pump from starting to operate. Several

hours of exposure to the pumping action of a mechanical vacuum pump

will make the Vac Ion pump difficult to start. Baking the Vac Ion

pump to 400°C for 2 hr in air may restore the pump to normal operation.

However, repeated contamination by hydrocarbons eventually results

in the pump no longer responding to air baking and the cathodes must

be replaced to put the pump back into operation.

The gas which is absorbed on the anode surfaces is partly very

tenaciously held and is partly rather weakly bound. A pump will

therefore both pump and release gas during operation, and the question

is what limit of base pressure can one hope to realize when the balance

ULTRAHIGH VACUUM395

of these two processes is reached. In a test of this point a small VacIon pump was heated to 400°C while it was in its magnet with thevoltgage applied to the anode. The pump continued to operate at thistemperature and reduced the pressure at this temperature to about2 X 10-* torr at the end of a 3-hr bakeout. After the system wasallowed to cool down to room temperature, the pressure reading was5 X 10-10 torr.

^ diQ^: I >

2i ' i '3'

Fig. 9-35. Cathode plate of Vac Ion pump after long service showing patternof erosion due to sputtering. [Taken with permission from L. D. Hall, in 1958Vacuum Symposium Transactions (Pergamon Press, London, 1959), and throughthe courtesy of Varian Associates, Palo Alto, Calif.]

The earliest pumps of the Vac Ion type were quite small and typically

had pumping speeds for air of the order of 5 liters/sec. Zaphiropoulosand Lloyd*^ have discussed some of the design considerations whicharise in scaling up the Vac Ion tjrpe of pump to much larger sizes.

Figure 9-36 shows schematically a quadrupole and an octupole con-

figuration for very large pumps of this type. Figure 9-37 is a photo-graph of a 5,000-liters/sec Vac Ion pump, showing one example of asatisfactory scaling up of the Vac Ion concept. For the 5,000-liters/sec

396 VACUUM SCIENCE AND ENGINBEBING

Cathode -anode

sections

Inner bore

W=W

L' = 2L

pump the applied voltage is 6 kV and the current is 65 mA at a pressure

of 10-« torr, which is about 400 watts. Since the current is pro-

portional to the pressure for this type of pump, the power would

become excessive at a pressure of IQ-^ torr. To alleviate this problem

the power supply is current-limited beyond a specified value and the

potential drops to about 500 V. In some applications of large pumps,

the sections are brought into opera-

tion one at a time in order to avoid

excessive power drain, and all units

are turned on only when the pres-

sure has decreased to 10"^ torr or

less.

A problem in the operation of

the Vac Ion type of pump is an

instability in the pumping of

argon. Surprisingly, helium, for

which normal sorption by any

material is insignificant, is pumpedquite well, apparently by being

rather deeply buried in the cath-

ode material. With argon the

situation is quite different, and

the problem is discussed in some

detail by Jepsen et al.*« A typical

pattern of the pressure versus time

for a getter-ion pump exhibiting

argon instability is shown in Fig.

9-38. The periodic jumps in pres-

sure by a factor of 10 or more are characteristic of this difficulty. One

solution to this problem which was proposed by Brubaker*' is to incor-

porate a third electrode in the form of a grid between the anode and the

outer plate electrode, such that the new grid becomes the true cathode

and the side plates become auxihary electrodes as illustrated in Fig. 9-39.

This arrangement is referred to as the triode getter-ion pump. By a suit-

able choice of design and operating parameters for the triode pump

Brubaker was able to show a generally improved pumping speed for the

noble gases and completely stable pumping of argon and air. However,

there are several disadvantages to the triode design, the principal one of

which seems to be the very much shortened life of the cathodes.

In order to avoid the complexities and loss of cathode lifetime

resulting from the triode getter-ion pump design, Jepsen et al.*

investigated the effect of slotting the cathodes of the diode type of

pump in the manner shown in Fig. 9-40. The result of the slotted

Fig. 9-36. Illustration of configuration

for large Vac Ion pump designs

(magnets not shown). [Taken with

permission from R. Zaphiropoulos and

W. A. Lloyd, in 1959 Vacuum Sympo-

sium Transactions (Pergamon Press,

London, I960).]

ULTEAHIGH VACUUM397

Fig. 9-37. Photograph of 5,000 liters/sec Vac Ion pump. [Taken with permissionfrom R. Zaphiropoulos and W. A. Lloyd, in 1959 Vacuum Symposium Trans-actions (Pergamon Press, London, I960).]

cathodes appears to be to provide an optimum solution. (1) Pumpingfor air is completely stable, and the pumping speed slightly higher than

with the plane cathodes. (2) The pumping speed for argon is about

10 per cent of that for air and is stable for all values of the pressure

below 10-^ torr. (3) The cathode life does not seem to have been

XlO"''

MO"'

xlO"^

xlO"''

Time

Fig. 9-38. Typical pattern of pressure vs. time for a getter-ion pump exhibiting

the argon instability. [Taken with permission from R. L. Jepsen, A. B. Francis,

S. L. Rutherford, and B. E. Kietzmann, in 1960 Vacuum Symposium Transactions .



impaired by the slotting nor do the benefits of the slotting disappear

with aging of the cathode.

Aside from the problem of rather extreme sensitivity to hydrocarbon

contamination of the cathodes, the getter-ion pump of the Vac Ion type

has undergone steady improvement and certainly must be regarded as

one of the most effective available means for ultrahigh-vacuum pump-ing. The question of hydrocarbon contamination can be completely

V=V|

Auxiliary

electrode"-*^^^^^^^^^^'-^^^^^^^^^^^^^^v^^^'^

Cathode

^=°~-Hl D D D D D ID D r^—-j^Clouds of tropped

v=o-

V=V,

Positive

Slotted

cathode

Sputtered

atoms of A^xx^xxs!

of cathodematerial

Fig. 9-39. Cross section of the triode

getter-ion pump showing the opencathode structure and the side plate

as an auxihary electrode. [Taken with

permission from R. L. Jepsen, A. B.

Francis, S. L. Rutherford, and B. E.

Kietzmann, in 1960 Vacuum Sympo-sium Transactions (Pergamon Press,

London, 1961).]

Fig. 9-40. Cross section of slotted

cathode configuration of the diode

getter-ion pump. [Taken with per-

mission from R. L. Jepsen, A. B.

Francis, S. L. Rutherford, and B. E.

Kietzmann, in 1960 Vacuum Sym,po-

sium, Transactions (Pergamon Press,

London, 1961).]

avoided in systems in which the roughing-down operation is carried

out by a mechanical pump with an artificial zeolite trap in the pumpingline or by the use of absorption pumping starting from atmospheric

pressure.

9-7. Absorption Pumping. Artificial zeolite* as a vapor-trap

material has already been discussed at length in Sec. 8-6. The recent

practice of utilizing one or more zeolite absorption pumps for roughing

out vacuum systems of large volume in order to avoid the possibility

of hydrocarbon contamination from the sealing oil of a mechanical

roughing pump is of considerable practical interest.

* 13X Zeolite is an alkali methal aluminosilicate of unusually porous structure

manufactured by the Linde Division of the Union Carbide Cornpany.


4 5 6

L(760mmHg)

lOOg zeolite

(b)

Fig. 9-41. (a) Pumping speed of a molecular sieve pump at 0.1 torr as a functionof amount of gas already pumped. (6) Final base pressure as a function of theamount of gas pumped. [Taken with permission from P. F. Varadi and K. Ettre,in 1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961).]

Varadi and Ettre''* have carried out a series of tests on a 13X Zeolite

type of "molecular sieve" absorption pump to determine (1) the pump-ing speed of the absorption pump for various gases as a function of the

amount already absorbed, and (2) the final pressure attainable as afunction of the amount of each gas absorbed. The pumping-speedmeasurements were all made at a pressure of 0.1 torr. The results of

these two types of tests are shown graphically in Fig. 9-41. Theabsorption pump contained 100 g of 13X Zeolite which was cooled byliquid nitrogen.


The rather large variation of pumping speeds for different species of

gas is very striking. As will be noted by the very small line near the

origin of the figure, the ability of 13X Zeolite to absorb hydrogen is

almost nil. Another interesting feature of the tests is the apparent

fatigue effect due to repeated absorption and expulsion of air. It will

be noted that there are two curves for air in the figure: (1) for the first

run on a new sample of zeolite and (2) for zeolite which had been

recycled several times through the absorption and degassing routine.

800 liters/sec

Main chamber \Bellows valve

Auxiliary

ion-getter

pump.

Liquid helium

trap

Liquid

helium trap

Omegatron

8 liters/sec

Bellows

Pironi

gouge

Work spoce

Support

lonizotion

gouge5W

Main

ion -getter

pump

25

I iters /sec

Front View

Sorption

pump

Fig. 9-42. Schematic diagram of ultrahigh-vaouum system incorporating sorp-

tion, ion-getter, and liquid helium cryogenic pumping. [Taken with permission

from R. H. Honig, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962).]

From these quantitative figures it should be possible to design zeolite

traps with fair assurance as to the capacity and pumping speed based

upon the amount of zeolite contained.

The use of a sorption pump under conditions in which avoidance of

hydrocarbon contaminants is necessary is represented in the system

shown in Fig. 9-42, which illustrates the arrangement developed byHonig.*' The system is one of fairly small volume and is roughed

out to 10~^ torr by a sorption pump cooled to liquid-nitrogen tempera-

ture. The system is then further pumped by the getter-ion pumpand finally liquid nitrogen is introduced to cool thoroughly the sur-

roundings of the liquid-helium thimble trap before introducing the

liquid helium. When the pumpdown cycle was preceded by a bakeout

at 350°C for 15 hr, the base pressure realized in this system was judged

to be less than IQ-i" torr on the most favorable run. Typical pressure

readings were between 10""' and 10"!" torr. This system represents

most of the more advanced techniques of fully bakable systems with

freedom from hydrocarbon contamination and the introduction of

I


liquid-helium cryogenic pumping to obtain the lowest possible basepressure.

9-8. Evaporative Deposition of Reactive Metals. Getter-ion

pumps utilize the evaporation or sputtering of active metals, usually

titanium, together with ionization of the gas by electron collisions

to enhance the gettering effectiveness of the newly deposited reactive

metal. This combination provides very satisfactory vacuum pumpingand freedom from hydrocarbon contaminants. However, for manyapplications the evaporative deposition of an active metal without

ionization of the residual gas has also been found to be useful andeffective. For many years barium particularly has been used as getter

material in the manufacture of electronic tubes. In the mass pro-

duction of receiving tubes, vacuum pumping is normally accomplished

by mechanical pumps arranged in groups on a rotating and indexing

machine having a large number of ports to which the tubes being

evacuated are connected. As the machine rotates, each tube is

connected in turn to a rough pumping section followed by stages

operating at lower pressures. Simultaneously the tube is subjected to

induction heating of the internal metallic parts and oven heating of the

glass envelope to ensure thorough outgassing. The tubulation is then

sealed off and a getter capsule is flashed dispensing barium metal as a

getter material to clean up by chemisorption the residual gas remaining

in the tube after the rather rough vacuum pumping provided in the

process. The use of a getter for completing the evacuation process

reduces by a large factor the cost of initial evacuation of electronic

tubes and in addition provides a means of continued chemisorption of

any gases which might be produced during the operation of the tube

in service.

In recent years there has been an intensive investigation of the

effectiveness of evaporated coatings of reactive metals, particularly

titanium and molybdenum, deposited on surfaces within a vacuum

chamber in pumping out residual gas by chemisorption. This tech-

nique has proved to be effective in two specific situations: (1) as a

separate pumping unit acting as a getter pump which can be attached

to a vacuum chamber, the evaporated metal being confined in this case

to the inner walls of the getter pump itself, and (2) within the vacuum

chamber itself, in which case the evaporated metal is deposited directly

on the walls of the vacuum chamber. In case ( 1 ) the getter pump must

be connected to the vacuum chamber and is therefore limited in pump-

ing speed by the conductance of the connecting tube or manifold.

In case (2) the walls of the vacuum chamber itself become absorbing

with the result that a much larger effective pumping speed can be

achieved.

402 VACUUM SCIENCE AND ENGINEERING ULTRAHIGH VACUUM 403

Negatively biased

cylindrical grid

5'

5-10 kv/^"0.030-1

0.1 amp

High

vacuum

0.030 tungsten wire

electron emitter

Nickel supports

-Molten ball

'^ Capillary tube

surrounded by

water

2

Feeder rolls

through liquid

metol vacuumseals

In contrast with the performance of a getter-ion pump (see Sec. 9-6)

which is capable of pumping the noble gases to some degree, a getter

device without ionization has no such capability. Only those gaseswhich interact chemically with the evaporated metal are effectively

pumped. Getter pumps are therefore usually supplemented by the

pumping action of a well-baffled

diffusion pump. Since the noble

gases make up a small fraction

(about 1 per cent) of atmospheric

air at sea level, active metal pump-ing of high pumping speed for re-

active gases supplemented by a

trapped diffusion pump of rela-

tively small pumping speed is aneffective combination for manyapplications. Such a getter pumpmay, for example, consist of achamber with one or more units

for evaporating a reactive metal

on the interior surfaces connected

to a well-baffled diffusion pumpbacked by a mechanical vacuumpump.

Several methods of evaporating

metals such as titanium, zirconium,

and molybdenum, all of which

have been used as getter materials,

have been developed. Milleron^"

has described a method of evap-

oration from the end of a wire, the

tip of which was heated by elec-

tron bombardment in the device

illustrated in Fig. 9-43. The wire

is stored on a reel in an auxiliary vacuum chamber, where it is outgassed

by being heated to as high a temperature as the material will stand by anelectric current. The wire is then fed by a system of rolls through a

water-cooled copper capillary tube into the evaporation chamber.

The small conductance around the wire through the capillary tube

prevents any appreciable flow of gas desorbed by the wire from entering

the evaporation chamber. The end of the wire protruding from the

capillary tube is bombarded and heated by electrons from a circular

filament at 5 to 10 kV negative potential relative to the wire. Theend of the wire is heated beyond the melting point, resulting in the

Wire degassed

byl^R heating

. Etficient

_liquid-nitrogen-

,trapped 4 in.

oil diffusion

pump

Insulated

Fig. 9-43. Device for evaporatingactive metals by electron bombard-ment. [Taken with permission fromN. Milleron, in 1957 VacuumSymposiumTransactions (Pergamon Press, London,1958).]

formation of a molten drop of metal, which is supported on the tip of thewire by surface tension forces. For metals such as titanium and molyb-denum there is no serious problem in controlling the electron bombard-ment heating so that the molten ball at the end of the wire is stable

and the rate of evaporation steady. Typical evaporating rates are

given as 0.05 g/min, which could be maintained for several hours byfeeding the wire at the proper rate from the reel in through the capillary

channel.

Using the above method of evaporating molybdenum, Milleron andPopp^i have measured the pumping of hydrogen gas admitted to the

chamber in pulses. The conditions of the test were as follows

:

Volume of chamber—70 liters

Projected area of coated wall—7,500 cm^

Microscopic area as measured by low-temperature adsorption of argon

on molybdenum surface—more than 20 times the projected area

Base pressure—less than 10~i° torr

Quantity of hydrogen per pulse—10~^ torr liter

Time duration of gas pulse—less than 1 sec

Maximum pressure rise per gas pulse with newly coated walls— 1 x 10~'

torr

Equivalent pumping speed—greater than 10* liters/sec

Quantity of hydrogen to saturate coating and raise pressure to 10~^

torr—approximately 1 torr liter

Molybdenum, zirconium, and titanium are all effective in the above

type of gettering device, but molybdenum is found to be more effective

in pumping hydrogen (the gas of major concern in the Milleron and

Popp development) in the pressure range below 10"^ torr, whereas

titanium was found to be capable of absorbing more hydrogen gas.

The reason for this difference would appear to be that molybdenummay be heated to a higher temperature without the danger of melting

than titanium or zirconium, resulting in a more thorough outgassing

of the metal before it is evaporated into the pump chamber, whereas

the latter two metals have a greater total capacity for reacting with

hydrogen.

Other methods of evaporating the most commonly used reactive

metals, titanium and molybdenum, than that described above are

mentioned in Sec. 9-6, particularly as an adjunct to the Evapor-ion

pump. The simplest and most convenient method thus far developed

is similar to that described by Gale,*^ in which a wire of the metal to be

evaporated is wound on a somewhat larger-diameter tungsten wire,

which acts as a heater element. In one of the large thermonuclear

research machines at the University of California Lawrence Radiation


Laboratory (Livermore) known as ALICE, both titanium and molyb-

denum units are used in a beam tube in which the pressure must be

reduced from about 10~^ torr of hydrogen and water vapor at one end

to an operating pressure of about 10~' torr over a distance of about ten

feet. Titanium evaporation combined with well-baffled diffusion pumpsis used in pumping units as shown schematically in Fig. 9-44 in portions

of the system in which the pressure

is comparatively high and the mainrequirement is that of relatively

high throughput. In the mainvacuum chamber where the pres-

sure must be maintained at 10~' or

less with the beam on, molybdenumis evaporated directly on a liquid-

nitrogen-cooled stainless steel liner

which covers a large fraction of the

chamber wall. The evaporator

units in each case consist of a 0.060-

diameter tungsten filament

Flap valve

Metollic

evaporotor

Liquid-nitrogen

cooled liner

" " n nn

Liquid -nitrogen-

cooled trap

Diffusion pump in

Fig. 9-44. Pumping unit consisting of

a titanium evaporator unit backed byan oil diffusion pump with a liquid-

nitrogen-cooled baffle. [This drawing

was kindly provided by Mr. William

S. Neef, Jr., Lawrence Radiation

Laboratory, Livermore, California.]

wound with a 0.020-in.-diameter

titanium or molybdenum wire.

The heating current for the tita-

nium evaporators is about 125 A,

whereas that for the molybdenumis about 190 A, consistent with the

high-temperature characteristics of

the molybdenum. Herb et al.*^ quote the data given in Table 9-4 from

the RCA Review ofJune 1957, from which it is evident that vapor pres-

sures for titanium of the order of 10~' torr are attainable for sublima-

tion, i.e., before the melting point is reached. Herb et al. estimate that

at a temperature of 1715°K sublimation from a titanium surface of 10

cm^ should produce a pumping speed for active diatomic gases of about

1,000 liters/sec when the pressure is 10~^ torr, or should absorb a

throughput of 10"^ torr liter/sec at whatever equilibrium pressure

results. This capacity or pumping speed is increased by a factor of 10

if the temperature of the titanium is raised to 1850°K. Whetherperformance of this order is realized in practice will depend greatly

upon the extent to which the titanium metal is outgassed before

evaporation. The process of evaporative deposition of active metals

for getter pumping includes a preliminary baking of the system and

thorough outgassing of the getter metal at a temperature which is high

enough not to evaporate any significant portion of the metal but high

enough to drive out absorbed gases. In some cases the baking and


outgassing may require many hours before the system can be cooled

down and the evaporative deposition process started under conditions

which will ensure effective pumping at pressures less than 10"* torr.

The practice of coating a liquid-nitrogen-cooled inner liner of the

vacuum chamber has become accepted for certain classes of controlled-

fusion research devices. One of the most famous such installation

is the Ogra machine of the Kurchatov Institute for Atomic Energy in

Moscow. The central chamber of the machine is 1.6 m in diameter

and 19 m in length, so that the volume is about 38,500 liters. The

Table 9-4. The Vapob Pressure of Titanium at Various Temperatures*

Temperature, °K Ti vapor pressure,'\ torr

1330 1 X 10-8

1415 1 X 10-'

1500 1 X 10-6

1600 1 X 10-^5

1715 1 X 10-«

1850 1 X 10-3

1945 (melting point) 4 x IQ-^

2000 1 X 10-2

* Quoted with permission from the RCA Review, June, 1957.

t These values of vapor pressure are considerably lower than those quoted in

the Smithsonian Physical Tables (Smithsonian Institution, 1954) from the results

of Brewer, The Thermodynamic and Physical Properties of the Elements, Report

for the Manhattan Project, 1946. This suggests that many of the older data on

vapor pressures of metals are suspect.

steel vacuum chamber has been equipped with a thin-walled stainless

steel liner on which titanium is evaporated periodically from several

evaporating units placed along the length of the chamber. An electron

beam of current up to 1 A at 3 keV bombards the end of a 2-cm-

diameter titanium rod on each evaporator, resulting in a maximumevaporation rate of about 50 g/hr of titanium. According to Simonov,

Kleimenov, Mileshkin, and Kochnev^^ the combination of the active

metal coating on the cooled liner backed by an array of well-baffled

mercury diffusion pumps provides a pumping speed for hydrogen of

2 X 10" liters/sec, a base pressure of 1 x lO-i" torr, and an operating

pressure during injection of a powerful molecular ion beam of about

5 X 10-" torr. Effective pumping speeds of millions of liters per

second could not possibly be achieved unless the walls of the chamber

themselves are highly absorbing. Only limited portions of the chamber

walls, primarily the ends, are available for openings into pumping

manifolds, so that no matter how high the pumping speed of the pumps

connected to these manifolds the net pumping speed limited by the

conductance of the openings alone would not exceed 100,000 liters/sec. (


If in addition one allows for the conductance of the chamber itself

toward both ends from the middle, the net conductance from the medianplane (where most of the gas originates in this machine) to both ends,

assuming that both ends of the tank are completely open, is only about

50,000 liters/sec. From this it is clear than the only possibility of

achieving pumping speeds of several

million liters per second in such a

machine is to make the walls as

completely absorbing as possible.

Simonov et al.^^ investigated the

sorption of hydrogen gas by renew-

able surfaces of chemically active

metals as a function of the tem-

perature of the surface using the

apparatus shown schematically in

Fig. 9-45. The metal to be investi-

gated was evaporated either con-

tinuously or periodically andcondensed upon a substrate, the

temperature of which could be con-

trolled and measured over the range

-195 to +100°C. Two time-of-

flight mass spectrometers were

used, one for determining the com-

position of the gas desorbed by the

specimen under test and the other

for determining the composition of

the gas generally throughout the

chamber.

The authors state that one of the

most important characteristics of

the sorption of hydrogen by a reac-

tive metal is that the sorbed hydro-

gen molecules are dissociated into atoms which migrate over the surface

of the metal and readily react with other sorbed atoms producing vola-

tile compounds which may be desorbed. This process at least partly

defeats the purpose of the original sorption process, resulting in a

portion of the sorbed hydrogen and other gases being reemitted from

the surface in a form which is no longer effectively sorbed by the surface

but must be pumped out through the diffusion pumps or otherwise

disposed of. Gases whose presence greatly affects the rate of per-

manent sorption of hydrogen are oxygen and nitrogen. For a typical

freshly deposited surface of titanium exposed only to pure hydrogen

Fig. 9-45. Apparatus for the inves-

tigation of the sorption of gases at

low pressures on renewable surfaces

of reactive metals and surfaces of

structural materials. (1) Vacuumchamber; (2) surface for condensa-

tion of metal; (3) evaporator of

metal under study; (4) sample of

structural material under investiga-

tion; (5) mass spectrometer for

analysis of the gas desorbed from the

surface of the specimen; (6) massspectrometer for analysis of the gas

in the chamber; (7) mercury vapor

pump with liquid-nitrogen-cooled

baffles; (8) getter-ion pump.


(a)

Dz

/

fH2

/<

i- HD

-200 -100

TemperQture,°C

100

the probability of absorption per surface encounter is stated to beabout 0.1 ; that is, about 10 collisions with the coated wall are necessary

on the average for a hydrogen mole-

cule to stick under the conditions

of the experiments. As gases are

sorbed by the surface, the probability

of absorption of hydrogen decreases

markedly. The process of dissoci-

ative chemisorption of pure hydro-

gen on a pure metal surface is said

by the authors to be independent of

the temperature over a wide range.

The unfavorable aspects of chemi-

sorption of hydrogen are due to the

development of catalytic reactions

resulting in the formation of products

which are weakly bound to the metal

and are thus desorbed.

The authors have shown, how-

ever, that when the absorbing sur-

face is cooled to a sufficiently low

temperature, the mechanism of

chemisorption of hydrogen changes

drastically, leading to a pronounced

increase in the specific rate of sorp-

tion, a suppression of the catalytic

reactions which lead to the forma-

tion of volatile products, and a re-

duction in the rate of desorption of

gas from the surface. In Fig. 9-46

are shown experimental curves of the

partial pressure of hydrogen (Hg),

deuterium (D^), deuterium-hydrogen

(HD), methane and deuterio-meth-

ane [IiC(H, 0)4] resulting from the

admission of a constant flow of a

mixture of hydrogen and deuterium

into the vacuum chamber in which

the active metal surface was con-

tinuously renewed by evaporation

onto a substrate, the temperature of which was varied,

and nickel were studied in this manner.

-100 +100

Temperature, °C

Fig. 9-46. Dependence of the rate of

sorption of hydrogen, the rate of

deuterium exchange, and the rate

of methane production on the

temperature of the active metal

surface continually renewed by

evaporation as indicated by the

ambient pressures of these gases in

the chamber. The evaporated

metals are {a) nickel and (6)

titanium. The rates of admission

of hydrogen-deuterium mixture

wore (a) 0.0,5 /d/sec and (6) 0.06 filj

sec. The conductance of the input

pipe was 4,000 liters/sec.

Titanium

It is evident from the curves

that the sticking coefficient remained unchanged from 100 to — 170°C


for nickel (a) and from 100 to — 130°C for titanium (b) and the catalytic

reactions of hydrogen-deuterium exchange and the formation of

methane do not decrease significantly with the temperature over these

temperature ranges. Further cooling below — 170°C for nickel and— 130°C for titanium results in a marked increase in the sticking

coefficient for hydrogen and a very marked decrease in the rate of

catalytic reactions. Thus the major problem in the use of evaporated

metal coatings for gettering hydrogen which arises from the catalytic

processes which occur at a high rate at high temperatures appears to be

completely solved by cooling the surface below a critical temperature,

depending upon the metal being evaporated, such as — 170°C for nickel

and — 130°C for titanium.

The sorption of oxygen, nitrogen, water vapor, carbon monoxide,

and carbon dioxide by evaporated metal surfaces at low temperatures

was also investigated by Simonov et al.^^ somewhat less quantitatively.

However, they report that all these gases are sorbed with considerable

effectiveness. Argon is also sorbed but with rather poor sticking

probability on titanium at temperatures from —170 to — 195°C.

Lower temperatures were not investigated. For practical applications

Simonov et al. recommend titanium as the best metal for evaporative

coating of surfaces as a gettering agent because of its relatively wide

temperature range for nondissociative sorption, ease of evaporation,

and availability in sufficiently pure form.

The findings of Simonov et al.*^ are generally consistent with those

of Milleron and Popp.^^ However, as a practical matter both titanium

and molybdenum are found to be useful in ultrahigh-vacuum pumpingin the ALICE machine, with molybdenum being the most effective

in the region of pressure below about 10"^* torr as was previously

mentioned.

Evaporative deposition of active metals on low-temperature surfaces

is particularly effective for providing very high pumping speeds for

short periods of time, e.g., for periods of a few minutes. For long

periods of continuous operation the accumulated deposit of evaporated

metal flakes off the cold surface. If a fairly large throughput is to be

pumped in this manner, the rate of evaporation of the active jnetal

must also be large so that the problem of supplying metal at the high

rate for a long period of continuous pumping is not easy to solve in a

convenient manner.

9-9. Cryogenic Pumping. The process of cryogenic pumpingconsists of exposing surfaces maintained at low temperature to the

gases in a vacuum chamber so that the gases condense on the cooled

surfaces as long as the partial pressures of the component gases are

above the equilibrium vapor pressure at the temperature of the


condensing surfaces. Liquid nitrogen and refrigerated traps generally

may, for example, be regarded as cryogenic pumps for the hmitednumber of gases, such as water vapor, for which the resulting vaporpressure is sufficiently low for the purpose at hand. Cryogenic pump-ing utilizing condensing temperatures well below that of liquid nitrogen

is not a new concept. However, with the need for high pumping speeds

at low pressure both in controlled fusion research and more recently

in space research the development of large-scale cryopumping systems

has undergone a considerable acceleration. This acceleration has beengreatly aided by the spectacular growth of the cryogenics industry to

meet the needs of the missile program for huge quantities of liquid

oxygen, nitrogen, hydrogen, and helium.

As is well known, the vapor pressure of a solidified gas as a function

of the absolute temperature can conveniently be represented by an

equation of the formB

logio P = A (9-1)

Thus for any gas, a plot of the logarithm of the vapor pressure as a

function of the reciprocal of the absolute temperature ( 1/T) is a straight

line. Such a graph is shown in Fig. 9-47 for several of the commongases. From these curves it is evident that neon and especially hy-

drogen stand out as gases which may present special difficulties because

of their relatively high vapor pressures at low temperatures. Helium

is not even shown on the graph. Since the vapor pressure of helium

is equal to atmospheric pressure at a temperature of only 4.2°K,

cryogenic pumping of helium is not feasible at temperatures which are

at present of practical interest. For all other gases the vapor pressure

is well into the ultrahigh-vacuum range at a temperature of 20.4°K,

the highest vapor pressure of these then being about 5 x lO'^" torr

due to nitrogen. The vapor pressure of hydrogen is much higher so

that even at liquid-helium temperature (4.2°K) it is about 3 x 10"'

torr and rising very rapidly with the temperature. Neon, however,

can be satisfactorily cryopumped in the ultrahigh-vacuum range by

surfaces maintained at 6°K, at which temperature the vapor pressure

of neon is about 10~ii torr.

Temperatures which can be conveniently maintained and are

frequently used in cryogenic pumping are those corresponding to the

boiling points of common gases at normal atmospheric pressure. These

temperatures are for helium, 4.2°K; for hydrogen, 20.4°K; for neon,

27.3°K; and for nitrogen, 77.4°K. In practice Hquid helium and

liquid hydrogen are widely used for maintaining surfaces at the desired

condensing temperature, and liquid nitrogen is used extensively to


provide an intermediate temperature for a protective shield betweenthe cryogenic pumping surface and the room-temperature walls of the

chamber to reduce the evaporation-loss rate of the liquid helium or

hydrogen by radiative heat transfer.

In the description above, emphasis has been placed upon cryo-

pumping in the ultrahigh-vacuum range. Bailey and Chuan^^ haveapplied cryopumping on a large scale to a low-density wind-tunnel

+3

+2

+ 1

-1

-2

t -3

O

5-5

-6

-7

-10

v

\ \ —\

s

s\>s

\\.

V\\

s

V\ H 2

N2

CO

\ \s.^ \ ^ ^e NS

'\\\^f s \s.

IkA

\ \N

1 \ \NKw \,

\S

CO\m \

V

\,N

1 \\,

°m\\\:^

0.02 0.04 Q06 008 O.IO 0.12 0.14 0.16 018 O20 0.22 Q24 l/Temperature

I, J 1,1 I II i_ I I 1^

100 50 3025 20 15 12 10 i-_L

Tennperature,°K

Fig. 9-47. The logarithm of the vapor pressure plotted as a function of thereciprocal of the absolute temperature of a number of the common gases.

installation to provide very high pumping speeds in the relatively high

pressure range from about 1 torr down to about lO"* torr. A limitation

in the cryopumping of atmospheric air arises from the mixture of

component gases present, as listed in Table 9-5. The components neon,

helium, and hydrogen add up to a total of 23.8 x 10-4 per cent of the

total atmosphere or a total pressure of about 1.84 x 10-^ torr. If a

chamber were to be evacuated simply by condensing all the air from

atmospheric pressure on surfaces at a temperature of 20°K these three

gases would not be condensed by the cooled surface, but would continue

to make collisions with the outer wall of the chamber at room tempera-

ture and maintain a pressure of the order of 2 x 10-^ torr in the

chamber. To operate a large condensing surface at lower temperature

to reduce this base pressure significantly under conditions of large

ulteahigh vacuum 411

Table 9-5. Nobmal Composition of Dry Air* near Ground Level

GasMolecular

weight

Per cent byvolume

Partial pressure,

torr

Nitrogen (Ng)

Oxveen fOoi

28.01

32.00

39.95

44.01

20.18

4.003

16.04

83.80

2.016

131.3

78.08

20.95

0.934

0.03

18 X 10-4

5.3 X 10-4

2 X 10-4

1.1 X 10-4

0.5 X 10-4

0.08 X 10-4

593

159Argon (Ar)

Carbon dioxide (COj) . .

7.2

0.24

1.4 X 10-2

Helium (He) 4.0 X 10-3

Methane (CH4)

Krypton (Kr)

Hydrogen (Hg)

Xenon (Xe)

1.5 X 10-3

8.4 X 10-4

3.8 X 10-4

6.1 X 10-B

cryopump

* See U.S. Standard Atmosphere, 1962 (National Aeronautics and Space

Administration, U.S. Air Force and U.S. Weather Bureau, Washington, D.C.,

December, 1962), table I. 2.7, p. 9.

gas throughput would be prohibitively expensive. Bailey and Chuan

therefore adopted a combination of a mechanical vacuum pump and a

cryopump, reducing the pressure to

about 1 torr by use of mechanical

roughing pumps and then applying

cryopumping at a total pressure

such that the remaining pressure

due to the uncondensed gases is

reduced to a value of about 2.4 x10-5 torr. Bailey and Chuanillustrate the pumpdown from at-

mospheric pressure of a 200-ft3

chamber for four different pumpingcombinations: (1) a 40-hp cryo-

pump alone, (2) a 4-hp mechanical

vacuum pump alone, (3) a 40-hp

mechanical vacuum pump alone,

and (4) the combination of the

40-hp mechanical vacuum pumproughing the chamber down to a

pressure of 1 torr and then a cryo-

pump of low horsepower condens-

ing the remaining gas for a rapid reduction of the pressure to a value

well below 10-* torr. The results of these four pumpdown methods

are illustrated in Fig. 9-48, the dotted line indicating the pressure

decrease when cryopumping is applied at a pressure of 1 torr in the

0.1 500 ipOO0.5 1.0 5.0 10 50 100

Pumping time,min

Fig. 9-48. Pumpdown of a 200-ft3

chamber by mechanical pumps andcryopump and by a combination

system (dotted line) applying cryo-

pumping after pumping down to

1 torr by mechanical pumps.[Taken with permission from B. M.Bailey and R. L. Chuan, in 19S8

Vacuum Sym,posium Transactions



combined system. In the combination system the heat load of con-

densing the gas is mostly eliminated so that a cryopump of "nominal"

horsepower is all that is required to obtain very rapid pumpdownfrom 1 torr on down.

For dynamic pumping of gas in a low-density wind tunnel, Bailey

and Chuan developed a gas-cycle helium refrigerator with power input

of 37.5 kW and space requirement of 105 ft^ of floor space. In Table

9-6 the performance of this cryopump is compared in terms of power

Table 9-6. Dynamic Pumping Speeds of Cryopump op 37.5 kW PowerInput and 300 Watts Capacity at 20°K with Floor-area Requirementsor 105 ft^ Compared with Power and Floor-area Requirements for

Conventional Pumping Equipment of Comparable Performance*

Pumpingspeed,

liters/sec

Floor area and power requirements for

conventional pumping equipment

Pressure,

torr

Diffusion

pumpsMechanical

pumpsTotals

Space,

ft2

Power,

kWSpace,

ft2

Power,

kWSpace,

ft2

Power,

kW

6.5 X 10-«

6 X 10-3

0.1

1.0

4.8 X lO^t

9.9 X 10«t6.5 X 103

8.4 X 10-2

360

360

300

300

286

352

308

44

145

180

156

22

646

712

308

44

445

480

156

22

* Taken with permission from B. M. Bailey and R. L. Chuan, in 1958 VacuumSymposium Transactions (Pergamon Press, London, 1959), p. 262.

f These pumping speeds based upon data obtained at one-third full capacity

(100-watt refrigeration) and multiplied by 3 to make a direct comparison with:

the other figures.

requirements and floor area needed with conventional pumping systems

consisting of diffusion and mechanical pumps or mechanical pumps

alone, depending upon the operating pressure. According to the

authors these results show that the cryopumping system provides »

clear advantage over the conventional system for all values of the

operating pressure less than about 1 torr. At higher pressures the

conventional system of mechanical vacuum pumps obviously is

preferable.

Cryopumping in the molecular-flow regime has been investigated

theoretically and experimentally by Moore. 5* The cryopumping

process is analyzed in some detail for a simple model consisting of an

infinite plane source of gas separated by a distance L from an infinite


plane surface condenser as shown in Fig. 9-49.

are:

The assumptions made

Source •^ Condenser

1. The molecular mean free path is large as compared with the

distance L between the surfaces.

2. The condensing surface is maintained at temperature T^ and has

a deposit of condensed solid formed from gas from the source surface.

3. Of the mass flow rate w-^ of

molecules from the source surface

that strike the condensing surface,

the fraction / stick and the rest

are diffusely reflected.

4. The reflected molecules leaving

the condenser constitute a mass

flow of (1 — /)Wi and have a ve-

locity distribution corresponding to

the temperature T^ of the condens-

ing surface, i.e., the accommodation

coefficient is unity.

5. The solid deposit also emits

molecules by evaporation at the

temperature Tj ^t ^^e same rate

(IF^a) ^-s if it were in equilibrium

with a gas at temperature T^.

6. The mass flow from the source

(Wj) consists of molecules emitted

by the source (Tfj) and diffusely

reflected molecules {w^ which strike

the source surface, all leaving the source surface with a velocity dis-

tribution corresponding to the temperature T^.

7. The velocity distributions of all molecular streams are Maxwellian.

The gas flow between the source and condensing surfaces consists of

two oppositely directed streams : w-^ flowing from the source toward the

condensing surface with a velocity distribution corresponding to a

temperature of Tj, and w^ flowing from the condensing surface toward

the source with a velocity distribution corresponding to a temperature

of T^. On the basis of the infinite plane model adopted and the

assumptions listed above, Moore^* finds that the mass flows for these

two opposing streams are given by

Fig. 9-49. Model for analysis of

cryopumping between infinite parallel

planes. [Taken with permission from

R. W. Moore, Jr., in 7.967 Vacuum.

Symposium Transactions (Pergamon


W, = w^ + w.

f(9-2)

414 VACUUM SCIENCE AND ENGINEERING ULTRAHIGH VACUUM 415

and w.W,{\ -/) + W,,

f(9-3)

The flow densities associated with each of these gas streams may be

obtained by reference to Eqs. (1-31) and (1-32) and are

o ©Cose A

Pp="ikT,VT^V [j

Case B

41-

Pp = fn,kT, M^.^T./I

Case C

Wi mnA ^

W2 mn2V2. (mkT\^= W, I—:—

I

\ 27

(9-4)

(9-5)

Pp-"2kVl£

Fig. 9-50. Pressure determined byopen-ended probes variously orien-

ted in a region between infinite

plane source and condensing sur-

faces. [Taken with permission

from R. W. Moore, Jr., in 1961



where 7^1A = mass flux through a

unit area

m = molecular mass of the

gas component under

consideration

V = average molecular ve-

locity given by Eq.

(1-23)

The molecular densities of the two

streams can then be determined from

the preceding four equations.

_ / 277 V^ W,*' ~ [mkTj

Tf.

/

_ / 27r f W.il -/)

[mkTj f

(9-6)

(9-7) i

Whereas the total molecular density between the source and con-

denser surfaces is the average of the above two expressions, the dis-

tribution in general is not isotropic. Thus the "pressure" in the usual

sense of an isotropic pressure does not exist. If one were to measure

the pressure in the region between the two surfaces with a probe device,

the reading would depend upon the orientation of the opening to the

probe and upon the temperature of the probe, as illustrated in Fig.

9-50. Assuming that the pressure sensed by the probe oriented in

either of the three directions shown in the figure will be determined by

the molecular density in the probe space at which the influx of molecules

is just equal to the efflux and by the probe temperature, Moore arrived

at the probe pressures Pj, given in Fig. 9-50. These probe pressures

may be expressed in terms of the symbols W^ and W^^ by use of Eqs.

(9-6) and (9-7) as follows:

Case A :

Case B:

Case C:

^ /2nkTX\ m /

^ /2nkTX\ m j

/27TkT:'

W^i(2 -/) 2 If.

m

2Af

W,{1 -/) 4 W^

Af

(9-8)

(9-9)

(9-10)

where T^ is the temperature of the pressure probe.

One important conclusion is that the contribution to the probe

pressure indication, by the mass flow rate due to evaporation from the

condenser deposit W^^, is always the same and equal to

^277fcT.,V-^W^

Af

On the basis of assumption 5 of this derivation

A

^ l2jrkTX'

\ m /

)f this deri^

(9-11)

(9-12)

where P^a is the vapor pressure of the condensed gas at the temperature

T2 of the condenser.

Thus the contribution due to reevaporation from the condensing

surface to the probe pressure indication is always

~ ^"^ [tJ(9-13)

that is, the vapor pressure of the deposition on the condenser corrected

for the diff'erence in temperature between the pressure probe and the

condenser. This quantity is thus independent of the sticking co-

efficient /.

The contribution to the pressure probe indication by the molecular

flow into the system from the source W^ is, however, dependent upon

the value of the sticking coefficient /, as illustrated in Table 9-7, in

which the probe pressures are listed on the assumption that the con-

tribution due to reevaporation from the condensing surface P^^. =for extreme values of the sticking coefficient / < 1 and / = 1. Ob-

viously, since / < 1 results in no appreciable cryopumping by the

condensing surface, the pressure is independent of the orientation of

the probe, i.e., the pressure is isotropic. However, whenever there is

significant cyropumping, the pressure is nonisotropic, as shown in the

right-hand column of the table.


Moore^* proceeds from the above analysis to offer two alternative

definitions for the pumping speed of a cryogenic system such as that

shown in Fig. 9-49. Because the pressure in the region between the

source and the condensing surfaces is not isotropic, it is not immediately

evident what value of pressure to use in an equation such a,s S = QjPfor the pumping speed. For some purposes a pumping speed per unit

of area Sg^jA based upon the molecular density %i sensed by the source

of gas is most significant, e.g., in the case of space simulation. A

Table 9-7. Probe Pressure Indications for Various Orientations of theProbe and Extreme Values of the Sticking Coefficient / when Re-evaporation trom the condensing surface is unimportant {wg2 =0)*

Case f< 1 / = 1

A

B

\ m j Af

(2nkTj^^ W^

\ m j Af

\ m J A

c

\ m J 2A

\ m J Af

* Reproduced by permission from R. W. Moore, Jr., in 1961 Vacuum Sym-posium Transactions (Pergamon Press, London, 1962), p. 426.

cavity in the source surface would receive the same molecular flux

as the pressure probe in Case C of Fig. 9-50 and the corresponding

pressure would be that for Case C with T^ substituted for T^. Thusfrom (9-10) and (9-13)

SI P,(T, = T,) =l 27TkT^Y\ m / Af m

so that since-^ SI

kT,

the pumping speed per unit area is given by

SSIA

Q,SI W, fAP. Amric

K

(9-14)

(9-15)

SI ^""'si ^ — / 4

As long as the vapor pressure Pâ ^^ the condenser temperature T^ is

very small as compared with the pressure Pî sensed by the gas source

(P„2 ^ -Psi); then the pumping speed apparent to the gas source is

independent of the pressure and the temperature of the condenser and

has the value ,

/ Vl

1-/4

Psi\T2


As Pgi approaches the value P^îTiJT^f'^, the value of the pumpingspeed apparent to the source approaches zero. From this analysis

it is clear that in order to ensure maximum pumping speed at the source,

the temperature of the condensing surface Tg must be low enoughsuch that Pj,2 < Ps\\ then the pumping speed sensed per unit area

of the source is

8 SI f1-/4

which is such that when / < 1

and when / = 1

A ~'-' 4

S.SI00

(9-17)

(9-18)

(9-19)

because in this latter case the gas flux returning to the source is essenti-

ally zero, as one would like to achieve in simulating the space environ-

ment.

An alternative definition of pumping speed 8^, for the cryopumping

system which is also useful is based upon the mass flow input W^ and

the pressure sensed by a probe in the position corresponding to Case

B of Fig. 9-50. This definition corresponds more directly to that

normally used for diff"usion pumps. In this case the pumping speed

per unit of area is

A Amrij, AmPj,(9-20)

From Eqs. (9-9) and (9-12) this expression becomes

8^ 2/

/ 1

P ITm /kj\f\277m/

(9-21)

in

(9-22)

As before, maximum pumping speed is realized when P^j

which case

8,^ 2/ /kT,f_ 2/ v^

A 2-f\27rm} 2-/4and the pumping speed is independent of the pressure as long as the

pressure due to reevaporation from the condenser is sufficiently small.

The significant temperature is that of the pressure probe, which in

conventional pumping systems does not normally present a problem

since the temperatures of all components of the system (with minor

exceptions) are ambient. However, in a cryogenic system high-

temperature gradients exist and the pressure probe temperature may


not be the ambient value, and this effect must then be taken into

account. From Eq. (9-22) it follows that for/ < 1 the pumping speed

per unit area becomes „

Zlr-.f'Hl (9-23)

and when / 1

A

2(9-24)

Of these two results (9-23) is similar to that given in (9-18), but (9-24)

differs markedly from that given in (9-19) because the pressure probe

Surface Temperature Emissivity

Chevrons

Condenser

Bock shield

Tank wall

77°-100°K

20° K

77°-100°K300° K

0.90

0.50

0.20

0.50Vacuum

,,,,,,-,,,,,,,,/,,,,,/,/,/,,/,/,,,,/,,//////chamberwoll

Back shield: condenser

>>>>>>>>>>>>>>>>>ChevronsInlet Heat

r?'^"^rodiotion y^, /r

fExperiment]

Fig. 9-51. Portion of a cryogenic

pumping array. [Taken with per-

mission from R. W. Moore, Jr., in

1961 VacuumSymposium Transactions


0.2 0.4 0.6 0.8 1.0

Condenser sticking coefficient f

Fig. 9-52. Dependence of the overall

capture probability of a cryogenic

pumping array on the sticking

coefficient at the condensing surface.

[Taken with permission from B. W.Moore, Jr., in 1961 Vacuum Sympo-

sium, Transactions (Pergamdn Press,

London, 1962).]

in the orientation of Case B still receives some molecular flux even

when the sticking coefficient at the condensing surface/ = 1.

Cryopumping surfaces cannot generally be exposed directly to^ a

source of gas at normal room temperature because the heat load due to

radiation would then exceed by far that due to the condensation of gas

molecules. Therefore, the cryogenic surface is usually protected on the

side facing the gas source by an optically opaque baffle system at an

intermediate temperature to act as a radiation shield. Gas from the

source must penetrate the baffle to be condensed on the cold surface,

but is impeded by the limited conductance of the baffle system. The

sticking coefficient / of the cryogenic surface is then not the only factor

^ULTEAHIGH VACUUM 419

determining the pumping speed of the device, because a fraction of themolecules incident on the radiation baffle is reflected back toward thesource and fails to reach the condensing surface. For such an arrayMoore^* introduces an overall capture probability G, which is the frac-tion of the total number of molecules incident upon the baffle systemwhich is finally captured on the cryogenic surface. The impedance togas flow interposed between the source and the condensing surface is

not quite as disadvantageous as would first appear because that sameimpedance ensures that those molecules which do penetrate the bafflebut are not condensed on the first encounter with the cryogenic surface,do not necessarily escape back toward the source. This same im-pedance results in many such molecules being reflected back towardthe cryogenic surface for a second opportunity to be condensed.

In Fig. 9-51 is shown schematically a typical cryogenic pumpingarray. In addition to the condensing surface and the front shieldconsisting of a chevron baffle system there is a back shield at an inter-

mediate temperature to reduce radiation loss to the wall of the vacuumchamber, which is normally maintained near the normal room tempera-ture. The temperatures and emissivities of the various surfaces typical

of such an array are also given in the figure. The condensing surface,

as shown in the figure, generally consists of an array of shields withgaps between so that some of the molecules which penetrate thechevron baffle will pass through one of these gaps, be refiected from theback shield, and have a second chance to condense on the back side ofthe condensing panels. The pumping effectiveness of the entire arrayis analyzed in terms of the overall capture probability G for gases whichwill be cryopumped on a surface maintained at 20°K.

HQs is the probability that a molecule wiU pass through the chevronbaffle, / is the sticking coefficient for molecules which strike the con-

denser surface, and g^ is the probability that a molecule incident on the

plane of the condenser will pass through one of the gaps (equal to the

fractional open area) then Moore shows that the overall capture

probability is given by

G =1 - 2(1 - sr,)(l -/) + (1 - yJ2(i ^fY „ g,

1 -(1 -g,){l -f){2~g,) +(1 -grj[(l -g^)^l - ff ~ g,^]

(9-25)

Assuming that for the chevron shield gr, = 0.23 and that for pene-

tration through the gaps of the condenser surface g^ = 0.25, Moorehas computed the value of the capture probability (? as a function of

the sticking coefficient / on the condenser. The results of this calcula-

tion are shown graphically in Fig. 9-52. The pumping speed of such


an array, as defined by a pressure probe in the orientation of Case Bof Fig. 9-50, is the same as that given in Eq. (9-22) with / replaced

by G, so that

S^ ^ ^^'"_E (9-26)

^ 2 -G4

From the curve in Fig. 9-52 it is evident that the overall capture

probability is not a sensitive function of the sticking coefficient /provided that / is greater than about 0.4. This feature arises from the

NoiicondensobleJT]_flow

Black

J,

Sapphire

window

Liquid-nitrogen

back shields (77

Liquid-nitrogen-cooled

outer shields (77°K)

Fig. 9-53. Cross section of cryogenic pumping system and vacuum chamber.

[Taken with permission from R. W. Moore, Jr., in 1961 Vacuum Symposium

Transactions (Pergamon Press, London, 1962).]

fact previously mentioned that once a molecule penetrates the chevron

baffle it is to some degree trapped between the baffle and the condenser

and has considerably more than a single encounter with the condensing

surface.

The chevron baffle at a temperature of 77 to 100°K serves an addi-

tional role as an unshielded cryopump for gases such as water vapor,

the vapor pressure of which at the chevron temperature is sufficiently

low. Because molecules incident upon a chevron baffle system bounce

several times on the average against the baffle surfaces, the capture

probability of such an array as a cryopump exceeds the sticking

coefficient / by a large factor. The advantages in a system involving

the pumping of appreciable quantities of water vapor would be an


abnormally high pumping speed for water vapor and other gases of

relatively low vapor pressure and a reduction in the heat load on the

low-temperature cryogenic surface by eliminating the heat of con-

densation of these gases.

Moore^* has determined experimentally the pumping speed of the

cryogenic pumping system shown in Fig. 9-53 incorporating the

features discussed above. The results of these measurements are

600

500

p400

r300

200

100

» Run 1,6/6/61 05D0FC,P4' Run 1,6/6/61 FP-J16-G5' Run2,6/6/6l 05D0FC,P4 with N? deposit» Run 1,6/7/61 05D OFC, P4s Run 1,6/7/61 oil man's

Run 2,6/7/61 05D OFC ,P4 with Njdeposit

Run 2,6/7/61 oil man's

4/17/61 oil man's

f=0,7

-t = 0,4

10-' 10" I0-' lO' 10-" 10"^

P,,torr

Fig. 9-54. Pumping speed as a function of pressure for the cryogenic pumpingsystem shown in Fig. 9-53. [Taken with permission from R. W. Moore, Jr., in

1961 Vacuum Symposium, Transactions (Pergamon Press, London, 1962).]

shown in Fig. 9-54 in which the pumping speed for nitrogen as defined

in (9-26) is measured as a function of the pressure in the vacuumchamber. Note that the units of pumping speed are cubic feet per

second (cfs). An interesting feature of the pumping-speed curve is the

increase in pumping speed with increasing pressure for values of the

pressure in excess of about 10~^ torr. By comparison of the results

below 10~5 torr with the theory, Moore concludes that the value of the

sticking coefficient/ for nitrogen is between 0.4 and 0.7, the value of the

overall capture probability is between 0.177 and 0.209, and the pumpingspeed per unit area of the array for nitrogen is between 71.4 and 84.9

cfs/ft2.

The large-scale cryopumping of hydrogen at modest temperatures

with the aid of a catalytic surface has been demonstrated by Grobman.^^

As has been previously pointed out, the cryopumping of hydrogen

by a pure condensation process requires that the condensing surface


be maintained at a temperature which is much lower than is practical

for most apphcations. Grobman introduces a catalytic surface

consisting of palladium-coated alumina pellets to convert hydrogen

gas to water vapor, which is then readily condensed at liquid-nitrogen

(77°K) or lower temperatures. Two arrangements of catalytic beds

were tested in a chamber as shown in Fig. 9-55a and b. A 6-in. dif-

fusion pump with a cold trap and a 15-cfm mechanical pump evacuated

^Hydrogen -««^n / r**»-

Stainless-Steel

cover plote

Instrument port /

Oxygen /

Instrument port

Hydrogen -««i-| / H-x-Oxygen

Cotolyst bed—Gloss cylinder

Spiral cold trop

(| copper tubing)

Stoinless- steel ;.

manitold^^.

Nichrome wire heater

50-mesh screen/ l"

f*—I2"0D^

-I7JID

I

Instrument ports

2"

J.

Radiation

heater

Annular

cotolyst

bed

qi" 21

Instrument port

lO 6 pipe JUl(b)

Fig. 9-55. Schematic drawings of test chamber with catalytic bed arrangementsfor converting hydrogen to water vapor and condensing the water vapor on acryogenic surface, (a) Flat cyhndrical arrangement of the catalytic bed (con-

figuration A); (b) annular arrangement of the catalytic bed (configuration B).

[Taken with permission from Jack Grobman, in 1961 Vacuum SymposiumTransactions (Pergamon Press, London, 1962).]

the chamber. An instrument port and means of introducing 9on-

trolled flows of hydrogen and oxygen were provided at the top of the

chamber. The performance of configuration A was tested with 3.1

and 5.8 lb of catalyst and that of configuration B with 6.5 lb of catalyst.

In each case performance was measured (1) with the oil diffusion pumpin operation and backed by the mechanical pump and (2) with the

diffusion-pump heater off and only the mechanical pump in operation.

The temperature of the catalyst bed was varied from to 600°F. Thetest chamber was outgassed for a period of 24 hr with the catalyst


maintained at the intended operating temperature before each series ofmeasurements. A representative set of data is shown graphically inFig. 9-56 for which the diffusion-pump heaters were turned off Amarked decrease is observed for the chamber pressure when the oxveenflow is turned on and set at an optimum value depending upon thehydrogen flow. The optimum setting for the oxygen flow proved not

1,400

-So 1,200

I'S 1,000

^ S 800£ -?

S ^ 600

I 400

^ 200

Without oxygen

oddition

With oxygen^

odditionJ

.--ti-nn'

I 10 100

Pressure upstream of cotolyst bed,

microns Hg

Fig. 9-56. Variation in tost chamberpressure as a function of total

hydrogen throughput with and with-

out oxygen addition for configuration

A of Fig. 9-55 with 3.1 lb of catalyst.

Diffusion-pump heaters turned off.

[Taken with permission from JackGrobman, in 1961 Vacuum Sym,po-

sium, Transactions (Pergamon Press,

London, 1962).]

Config-

uration

Cotolyst,

lb

Diffusion

pumps

6,000

5,000

a

b

c

d

e

- f

A

A

A

A

B

B

3.1

3.1

5.8

5.8

6.5

6.5

Oft

On

Off

On

Off

On1

4,000 -

/3,000 -

/2,000 - /•

1,000-

i // /n 1 1 LJ^Ill /_fc—1-3TtTlll

Pressure upstreom of cotolyst bed,

microns Hg

Fig. 9-57. Variation in the net

hydrogen throughput of each of the

configurations shown in Fig. 9-55

with test chamber pressure for

various quantities of catalyst in the

bed. [Taken with permission fromJack Grobman, in 1961 VacuumSymposium Transactions (PergamonPress, London, 1962).]

to be particularly sensitive but in any case was ±30 per cent of the

stoichiometric value.

The performance of the catalytic-cryogenic pumping system wasstudied as a function of the temperature of the catalytic bed and found

not to depend noticeably on the temperature. Heaters are essential,

however, to outgas the catalytic bed before each period of use. Theperformance of each of the two configurations was measured for differ-

ent quantities of catalyst as shown in Fig. 9-57. The net hydrogen

throughput in this figure represents the additional hydrogen throughput


resulting from turning on and optimizing the oxygen flow. Although

the demonstration of the cryopumping of hydrogen by catalysis as

described by Grobman^^ was carried out at relatively high temperatures

and pressures, the results are suggestive of a method which might be

extended to low condensing temperatures and pressures by a careful

study of various catalysts and alternative geometries.

Of much greater promise for ultrahigh-vacuum systems is the

process of cryotrapping, which has been investigated by Brackman

3 4 5 6

M, grams of HjO

Fig. 9-58. Quantity of nitrogen andargon required to saturate an ice

coating deposited by condensation

as a function of the accumvilated

mass ofcondensate . (Temperature

:

77°K.) [Reprinted with permission

from The Macmillan Co., fromF. W. Schmidlin, L. O. Hefiinger,

and E. L. Garwin, in 1962 VacuumSymposium Transactions. Copy-right © 1962 by American VacuuinSociety.]

/^^/Theory:

col fit:

/".Qt. ^P

/Emperi

R m fiP

/3=3.3 forr"'w= 8x10-'

-ii 10"

10'

•5 S. 10"

^ 10"* 10"' 10"2 10"'

Pressure p.torr

Fig. 9-59. Number of molecules of

nitrogen trapped per molecule of

water condensed on a surface at 77°Kas a function of the partial pressure

of nitrogen. [Reprinted with permis-

sion from The Macmillan Co., fromF. W. Schmidlin, L. O. Hefiinger,

and E. L. Garwin, in 1962 VacuumSymposium, Transactions. Copy-right © 1962 by American VacuumSociety.]

and Fite,^' Degras,^' SchmidHn, Heflinger, and Garwin,^^ and Henge-voss and Trendelenburg.^' Brackman and Fite reported that gases

are trapped on cooled surfaces on which water vapor has been con-

densed with the result that the partial pressures attainable for a numberof the common gases using cryopumping techniques may be sig-

nificantly lower than the equilibrium vapor pressures at the temperature

of the cooled surface. This process is referred to as cryotrapping andoffers the possibility of cryopumping of gases such as nitrogen, hydrogen,

and argon much more effectively in the presence of a "contaminating"

agent such as water vapor than in a system from which all such agents

have been carefully removed and subsequently excluded.


Schmidlin et al.ss have studied the trapping of normally nonconden-sible gases, nitrogen and argon, by condensed water vapor depositedon a stainless steel surface maintained at about 77°K by liquid-nitrogen cooling. From combined measurements of adsorption andtrapping the authors conclude that water vapor condensed at 77°Kforms a porous deposit with aneffective area of about six hundredsquare meters per gram of water.

The quantity of nitrogen and argonrequired to saturate the surface

deposit of water is proportional to

the quantity of water deposited,

as is shown in Fig. 9-58. Thenumber of molecules of nitrogen

trapped per molecule of water con-

densed on the surface is showngraphically in Fig. 9-59. This

number appears to have the con-

stant value ofabout 10-2 for partial

pressures of nitrogen above about0.1 torr and then decreases with

decreasing partial pressure to a

value of about 5 X 10"^ at 10^^

torr.

Hengevoss and Trendelenburg^'

have investigated the cryotrap-

ping of hydrogen and helium bycondensed argon at a temperatureof 4.2°K in a pressure range of

much greater interest for ultra-

high-vacuum application. Theapparatus used in these measure-

ments is shown in Fig. 9-60. Theentire vacuum chamber was ini-

tially baked at a temperature of 450°C and was evacuated by two oil

diffusion pumps in series through a low-conductance tube. The pump-ing speed of the evacuating system is largely determined by the conduct-ance of the connecting tube and was carefully calibrated for the gases

used in the experiments. After bakeout the pressure in the vacuumchamber before refrigeration was less than 10-' torr (nitrogen equivalent)as read on a Bayard-Alpert gauge. The conductance of the gaugeconnection tubing for hydrogen was 19 liters/sec, which by preliminary

tests was proved to be adequate to prevent the measured pumping speed

Liquid he!

Slit width

0.3 mm

Cryosurface ^A PTh Surface at(Ag 8cmM \-^\ W M liquid-air

temperature

(900 cmM

Fig. 9-60. Cryostatic vacuum systemused for measuring the cryotrappingof hydrogen and helium by a deposit

of condensed argon on a silver surface

at 4.2°K. [Reprinted with permis-

sion from The Macmillan Co., fromJ. Hengevoss and E. A. Trendelenburg,

in 1963 Vacuum, Sym^posium Trans-actions. Copyright © 1963 byAmerican Vacuum Society.]

426 VACUUM SCIENCE AND ENGINEEBING ULTEAHIGH VACUUM 427

of the gauge from falsifying the pressure reading by the gauge or the

mass spectrometer also connected to the same tubing for measurement

of partial pressures. Since the ionization gauge and mass spectrom-

eter were both at room temperature (300°K), whereas the gas in the

chamber was 83°K, the readings were multiplied by (83/300)'-^ to

determine the correct value of the pressure.

Liquid helium was used to cool the isolated inner cylinder to 4.2°K.

At the bottom of this cylinder a section of silver protrudes through

an aperture between the upper and lower sections of the vacuum

chamber and exposes a surface area of 8 cm^ to the lower section of the

chamber. The conductance between the upper and lower sections of

the chamber through the clearance around this protruding surface is

very small so that the cryostatic pumping speed exposed to the lower

chamber was that due to the protruding surface only and not to any

significant degree due to flow through the annular clearance.

With the chamber immersed in liquid nitrogen and with liquid

helium in the inner cylinder, pure hydrogen was first admitted at a

steady flow rate and the pressure resulting from the dynamic balance

between the throughput and pumping action of the system was

measured. At small flow rates for which the hydrogen pressure was

below the saturated value corresponding to the temperature of 4.2°K

the pumping speed was entirely due to the diffusion-pump arrangement.

At sufficiently high flow rates such that the resulting hydrogen pressure

exceeded the saturated value the pumping action was the sum of the

pumping speed of the diffusion-pump arrangement and the condensing

speed of the cryogenic surface. Under the conditions of the experiment

corresponding to the chamber temperature of 83°K the saturation

hydrogen pressure was 1.3 x 10^« torr. The next step consisted of

adding argon initially at a very small flow rate and then progressively

increasing the argon-flow rate with the hydrogen flow held constant.

As is evident from Fig. 9-47, the saturation vapor pressure of argon

at 4.2°K is unmeasurably small so that even a very small addition

of argon results in condensation on the cryogenic surface, for which

process a sticking probability of 0.7 was measured in preliminary

experiments. The partial pressures of hydrogen and argon were then

measured for various values of the argon-flow rate holding the hydrogen-

flow rate constant. This procedure was repeated for several different

values of the hydrogen-flow rate. The results are shown graphically

in Fig. 9-61, in which the hydrogen partial pressure is plotted against

the argon partial pressure for three different values of the hydrogen-

flow rate.

For the curves (a) and (b) the hydrogen-flow rates are both so low

that the equilibrium pressure is below that for saturation at 4.2°K so

-«

Impinging flrgon, atoms/cm^ sec

10'° lo" 10'2 lo" in'" '"'5

I I I III I I III II I I il

10'

ml-r

S 10

°-io

10

~ ~~

N

— H T-'>,u... V /

i

PotO withnnf 1

> AX .

argo n addit ion Jw ."y V11-2= U.I

' •

/V A

A10' 10"' n-9

10 ' 10 ° 10 ' lO'" IlO6-

10"

Iio'Ve

that no condensation occurs and the pumping action is only that of thediffusion pumps. In each of these cases, when the argon partialpressure reaches about 0.1 that of the hydrogen, the hydrogen partialpressure drops suddenly by a factor of 10 or more and then remainsat this lower value as the argon-flow rate and partial pressure areincreased further. The decrease in hydrogen partial pressure is due toadditional pumping resulting from the trapping of hydrogen by thecondensed argon. From the trap-

ping rates and the area of the cryo-

static surface the sticking coefficient

for hydrogen on the argon deposit

was determined to be 0.4, so that 4

out of 10 hydrogen molecules strik-

ing the surface are trapped. Astraight line is drawn at 45° in the

figure and is found to pass throughthe lower inflection points of curves

(a) and (6). Auxiliary scales show-ing flow rates in terms of molecules

per square centimeter per secondare included. The 45° line corre-

sponds to the case in which one hy-

drogen molecule is trapped by one

condensed argon molecule.

Curve (c) is taken at a hydrogen-flow rate which is great enough that

the hydrogen partial pressure ex-

ceeds the saturated value at 4.2°Kso that condensation on the cryostatic surface occurs even in the absenceof any argon. Thus in curve (c) both condensation and trapping occurat the same time so that the break in the curve corresponding to theonset of cryotrapping by argon occurs at an appreciably lower argon-flow rate than that corresponding to the intercept with the 45° line

drawn through the inflection points of (a) and (6), indicating that about10 times as many hydrogen molecules are deposited by the combinationof condensation and trapping as are argon molecules.

In a subsequent experiment the connection to the diffusion pumpwas sealed off and a large amount of hydrogen admitted to the chamber.After cutting off the hydrogen flow an equilibrium hydrogen pressureof 1.3 X 10-', corresponding to the saturation value at 4.2°K, wasreached. A continuous flow of argon resulting in an argon partial

pressure of 4 x 10~' torr was then introduced, and the partial pressure

of hydrogen slowly fell to 2 x 10^* torr. The argon flow was then

Argon partial pressure, lorr

Fig. 9-61. Hydrogen cryotrappingby argon for different values ofhydrogen and argon flow rates.

[Reprinted with permission from TheMaomillan Co., from J. Hengevossand E. A. Trendelenburg, in 2.963


Copyright © 1963 by AmericanVacuum Society.]


turned off and the partial pressure of the argon fell to an unmeasurable

value, whereas the partial pressure of hydrogen remained at 2 x 10~*

torr, indicating that the hydrogen was permanently trapped by the

condensed argon deposit.

Similar experiments were carried out to determine whether helium

could also be cryotrapped by condensing argon. The results showed

that the sticking probability of helium on the argon deposit is about

Fig. 9-62. Model of liquid-hydrogen-

cooled charcoal adsorption pumpwith liquid-nitrogen-cooled shield

having an adsorbing section up-

stream from the liquid-hydrogen-

cooled section and of the samediameter. [Taken with permission

from the American Institute of

Physics, from B. G. Lazarev andM. F. Fedorova, Soviet Phys.-Tech.

Phys. 6, 624 (1962).]

Fig. 9-63. Model of liquid-hydrogen-

cooled charcoal adsorption pumpwith liquid-nitrogen-cooled shield

having an adsorbing layer completely

surrounding a similar liquid-hydro-

gen-cooled adsorbing unit except for

the pumping aperture. [Taken with

permission from the American Insti-

tute of Physics, from B. G. Lazarev

and M. F. Fedorova, Soviet Phys.-

Tech. Phys. 6, 624 (1962)[.]

0.03 and that about 30 argon molecules are required to trap one mole-

cule of helium.

Although the process of cryotrapping has been only partially investi-

gated and the mechanism of the process is not understood, the results

described above are most encouraging for the enhancement of the

normal cryopumping process by the trapping of otherwise noncon-

densable gases on low-temperature surfaces.

The process of adsorption pumping discussed in Sees. 8-6 and 9-7

has been extended into the cryogenic region by Lazarev and Fedorova*"

particularly for the purpose of pumping hydrogen with high pumping

speeds at low pressure. Several designs of liquid-hydrogen-cooled

adsorption pumps were developed, two of which are illustrated in


Figs. 9-62 and 9-63. Because hydrogen cannot be condensed atliquid-hydrogen temperature, there is great advantage in addingmaterials which are effective in adsorbing hydrogen, particularly in

situations in which hydrogen is the major gas component present, as in

controlled-fusion research. The two adsorption pumps illustrated aretypical of a series of such devices developed by Lazerev and Fedorovaprimarily for the purpose of meeting the needs of the Soviet controlled-

fusion research program. As is evident from Figs. 9-62 and 9-63

together with their captions, the cryogenic adsorption pumps consist

of a central, double-walled cylinder, open at one end as the pumpingaperture and lined with small chunks of graphite held in place by a wiremesh. The liquid-nitrogen-cooled shield is designated as component1 and not only serves to reduce the radiation heat load on the inner

liquid-hydrogen-cooled component 2, but also acts as an auxiliary

adsorption pump for nitrogen, oxygen, and argon. This feature is said

to be important because it permits evacuation of the system to 10~*

torr or less of other common gases before pouring in the liquid hydrogenand cooling the central component 2 to 20.4°K. The inner adsorbing

surface is thus preserved for pumping hydrogen without appreciable

contamination due to the adsorption of the other more easily adsorbedgases.

Each adsorption pump is equipped with a valve (4) for connecting it

to the vessel to be evacuated and a valve (5) for connecting it to a

mechanical vacuum pump for roughing out the system. The sequence

of operation is first to rough out the system with both valves open to a

pressure of about 10"^ torr, then close valve 5. Liquid nitrogen is then

poured into the reservoir of component 1 after which the pressure in

the system quickly drops to a value of 10~^ or 10^* torr. Liquid

hydrogen is then introduced into the reservoir of component 2 and the

adsorption pump is then ready to pump hydrogen, which can then be

admitted to the vacuum chamber as needed. The pumping speed of

the adsorption pump illustrated in Fig. 9-62 is shown as a function

of the pressure (on a logu scale) in Fig. 9-64, in which the pressure

indicated is that measured at the inlet to the pump. Over the pressure

range tested, the pumping speed for hydrogen increased from about

400 liters/sec at 8 x 10~* torr to about 900 liters/sec at 10~^ torr.

From the dimensions of the inlet it is clear that even at the higher

pressure the pump is not choked by the conductance of the inlet,

which for hydrogen must be at least a factor of 5 greater than the

measured pumping speeds. The lower curve 2 is the pumping speed

as a function of inlet pressure which would normally be realized in

the second step of the evacuating procedure when the valve 5 is turned

off and component 1 of the pump is cooled with liquid nitrogen. Curve


1,000

800

600

400

200

10 10'" 10"'

Pressure, torr

10

3 is similar to curve 2 except that both component 1 and component

2 were cooled with liquid nitrogen. Substitution of liquid-hydrogen

cooling (20.4°K) for liquid-nitrogen cooling (77°K) appears to increase

the pumping speed of the adsorption

pump for hydrogen by a factor of 3 or

more and reduces the attainable base

pressure by nearly a factor of 10. Ifis worth noting that the liquid-nitro-

gen filling lasts for a period of 20 to

40 hr and that of liquid hydrogen for

24 hr or more depending on the

details of design.

Preliminary tests have been madeon a similar design of adsorption

pump by Lazarev and Fedorova using

liquid-helium (4.2°K) cooling on the

inner component for the cryogenic

pumping of helium in the pressure

range 10~^ to 10~* torr.

Bachler, Klipping, and Mascher*^

have made a study of cryopumping

in the temperature range from 4.2 to

2.5°K by controlling the pressure

over liquid helium. Because of the

very steep dependence of the equilib-

rium vapor pressure of hydrogen on

temperature in this range, this pro-

cedure provides a possible solution to

the cryogenic pumping of hydrogen

by condensation. The pumping and

pressure control system by which the

liquid helium in the cooling coil is

maintained at any desired tempera-

ture, either higher or lower than

4.2°K, is shown in Fig. 9-65. Valve

7 is throttled to obtain the required flow of refrigerant, and valve 6 is

adjusted to provide the needed pumping speed to attain any desired

temperature in the condenser. Bachler et al. report that control of the

temperature to within 0.01°K is achievable by this system.

In Fig. 9-66 is shown a schematic drawing of a condenser unit to be

operated at temperatures below 4.2°K. The low-temperature coil is

shielded above and below by chevron brffles which are cooled by the

cold exhaust gas evaporated from the low-temperature coil. These

Fig. 9-64. Porformance of the

adsorption pump illustrated in Fig.

9-62. Curve 1: Pumping speed

for hydrogen as a function of the

pressure, liquid-hydrogen cooled.

Curve 2: Pumping speed of the

adsorption pump with liquid-

nitrogen cooling in component 1

only as a function of the pressure.

Curve 3: Pumping speed of the

adsorption pump with liquid-

nitrogen cooling in both compo-nent 1 and component 2. [Taken

with permission from the AmericanInstitute of Physics, from B. G.

Lazarev and M. F. Fedorova,

Soviet Phys.-Tech. Phys. 6, 624

(1962).]


baffles not only serve as heat shields but also condense gases such asnitrogen with very high effective pumping speed. The pumping speedfor hydrogen achieved was about 2,000 liters/sec and that for nitrogenwas about 3,000 liters/sec. The consumption rate of helium was about0.5 liter/hr. According to measurements of Bachler et al. and thoseof Borovik, Grishin, and Grishina,^^ the equilibrium vapor pressureof hydrogen is approximately lO-^ torr at about 3.3°K, so that at 2.5°K

Pressure gauge

Vacuum chamber

Auxiliary pump

Liquefied gas

reservair

1 2

Fig. 9-65. Arrangement for controlling pressure of cryogenic gas and thereforethe temperature of the condenser. By this system temperatures as low as2.5°K are achieved in condensing hydrogen. [Reprinted with permission fromThe Macmillan Co., from W. Bachler, G. Klipping, and W. Mascher, in 1963Vacuum Symposium Transactions. Copyright © 1963 by American VacuumSociety.]

the vapor pressure of hydrogen should be well below IQ-i" torr, ensuringthat the sticking coefficient and pumping speed for hydrogen due tocondensation on a surface maintained at 2.5°K will be independent ofthe pressure well into the ultrahigh-vacuum range. Bachler et al.

note that whereas in their device nitrogen is pumped with about themaximum speed anticipated from theoretical calculations, hydrogenis pumped with about half the theoretical rate. However, since for

hydrogen the theoretical rate is nearly four times that of nitrogen, theresult is still very favorable for pumping hydrogen.The use of a liquid-helium-cooled condensing surface under conditions

in which the heat load from the process going on within the vacuumchamber (in this case a controlled-fusion plasma) may be a problem


has been investigated by Borovik, Busol, and Kovalenko."' In a series

of experiments with trapping surfaces of various geometries Borovik

et al. determined the maximum thermal load tolerable for the proper

maintenance of the temperature near the value 4.2°K typical of liquid

helium at normal atmospheric

/

UooooocoooppociooooocB

Fig. 9-66. Condenser unit with pro-

tective chevron radiation baffles

cooled by the exhaust gas from the

low-temperature condenser. These

baffles serve to condense gases such

as nitrogen, and the low-temperature

condenser condenses hydrogen. [Re-

printed with permission from The

Macmillan Co., from W. Bachler,

G. Klipping, and W. Mascher, in 1963


Copyright © 1963 by American

Vacuum Society.]

pressure. Since the heat of evap-

oration of liquid helium is small

(about twenty calories per mole)

the conditions of heat transfer be-

come characterized by eruptive

boiling at the metal surface if the

heat load g (watts per square

centimeter) reaches some critical

value g,r- The experiments were

generally such as to determine the

temperature of the condensing

surface as a function of the heat

load. From these experiments it

was observed that the tempera-

ture of the surface was relatively

independent of the heat load (in-

creasing very slowly with the heat

load) until a critical value sr„ was

reached in the range 3 to 5 x

10^* watt/cm^ above which value

the surface temperature increased

abruptly due to the onset of erup-

tive boiling.

In order to screen the liquid-

helium-cooled surface from the

source of radiation and still per-

mit fairly effective condensation

of gas on the surface, Borovik et

al.** devised the condensation

pump illustrated in Figs. 9-67

and 9-68. The liquid-helium-cooled, double-walled cylindrical surface

(3) is protected from the chamber wall by a liquid nitrogen-cooled

cylinder with skirts above and below the condenser unit connected

to the reservoir for a set of liquid-nitrogen-cooled louver-type baffles.

Concentric with and within this assembly is another cylindrical

arrangement of louver-type baffles, in this case water-cooled. The

outer surface of the liquid-nitrogen-cooled outer shield was brightly

polished (copper), whereas the inner liquid-nitrogen- and water-cooled


surfaces were blackened. The liquid-helium-cooled condenser wasmade of sheet copper, 2 mm thick, and was also highly polished.These precautions ensured minimum radiation heat load on the liquid-helium-cooled condenser, preserving as much of the heat capacity as

^^www;^

i=LJ#^^^^^^^Fig. 9-67. Vertical cross-sectional

view of liquid-helium-cooled lou-

vers as radiation shields. (1)

Chamber outer wall; (2) liquid-

nitrogen-cooled .shield; (3) liquid-

helium-cooled condensing surface;

(4) liquid-nitrogen-cooled louver;

(5) water-cooled baffle. [Takenwith permission from the AmericanInstitute of Physics, from E. S.

Borovik, F. I. Busol, and V. A.Kovalenko, Soviet Phys.-Tech.Phys. 8, 68 (1963).]

Fig. 9-68. Horizontal cross-

sectional view of the liquid-

helium-cooled condensationpumpshown in Fig. 9 -67 . The numbersdesignate the same componentslisted in Fig. 9-67. [Taken withpermission from the AmericanInstitute of Physics, from E. S.

Borovik, F. I. Busol, and V. A.Kovalenko, Soviet Phys.-Tech.

Phys. 8, 68 (1963).]

possible for the heat of condensation of gas in cryogenic pumping.Borovik et al."* report that:

1. With a heater of 10.5 kW output inside the inner shield the rateof evaporation of liquid helium due to the heat input was only 0.04

liter/hr, corresponding to a thermal load on the heat transfer surface

of only 7.5 x 10^^ watt/cm^, which is about a factor of 5 below thecritical value.

2. The pumping speed of the condensation pump was found to beabout II per cent of that of a perfectly condensing surface or about 1.25

liters/sec cm^ of the inner, water-cooled louver surface. The authors


^

assume that the pumping speed for hydrogen would be 4.68 Hters/seccm^, but did not make the measurement.

Borovik et al. conclude that cryogenic pumping is an effective meansof pumping hydrogen in controlled-fusion research devices. Privatecommunication with Professor Borovik reveals that a magnetic mirrormachine utilizing liquid-helium-cooled surfaces for cryogenic pumpinghas been constructed and is now in operation.

9-10. Ultrahigh-vacuum Systems. In this chapter and tosome extent in the preceding chapter the techniques of ultrahigh vacuumhave been discussed. The problem of the vacuum engineer is to utilize

these techniques in the design of ultrahigh-vacuum systems to achievethe required performance as economically and effectively as possible.

Some of the techniques described have been applied under ratherspecialized circumstances and are not necessarily applicable to a widerange of vacuum problems. However, the most important parametersto be considered are

:

1. The gas load expected in terms of the quantities of various com-ponent gases.

2. The operating pressure desired for the process to be carried out,either in terms of total pressure or in terms of the partial pressure of aparticular component gas.

Ultrahigh-vacuum systems tjrpically utilize some combination of thetechniques discussed in this and the preceding chapters. For systemsinvolving essentially no throughput of gas other than the outgassingof the surfaces, the achievement of very low pressures can be accom-plished with low pumping speed and the thorough outgassing of thesurfaces by baking the system at temperatures up to 450°C or higher.

Oil or mercury diffusion pumps with a combination of Freon- andliquid-nitrogen-cooled baffles can provide the modest pumping speedsrequired for such systems. Indeed, as was shown by Alpert,^^ athoroughly outgassed system can be maintained in the ultrahigh-vacuum range by the pumping action of the ionization gauge alone whenclosed off from the vacuum pump by a sufficiently tight bakable valve.

Systems of this type may be regarded as static systems in whichultrahigh-vacuum conditions are attained on a small scale with essen-

tially zero throughput.

Beginning with the requirements of controlled-fusion research, static

systems could no longer be relied upon to maintain the desired lowpressure because the experimental equipment was relatively large in

volume and an appreciable gas throughput required high pumpingspeeds. This need was initially met by optimizing the diffusion pump,


valve, and trap combination to provide much higher overall system

pumping speeds at low pressure than had been previously attempted.

As the requirements of the controlled-fusion program became more

demanding, auxiliary techniques were added, such as the evaporation

of active metals, first on the walls of the vacuum chamber at roomtemperature and then on liquid-nitrogen-cooled inner liners. Elimina-

tion of hydrocarbon contaminants by the use of either room-tem-

perature or liquid-nitrogen-cooled absorption pumps combined with

getter-ion pumps provides another solution to the problem of relatively

high-speed pumping in the ultrahigh-vacuum range.

The more recent advent of space research and simulation has ex-

panded much further the demand for large ultrahigh-vacuum chambers

with extreme requirements of high pumping speed at very low pressure.

For this service the combination of very large diffusion pumps with

Freon- and liquid-nitrogen-cooled traps, augmented by the extensive

use of cryopumping at liquid-hydrogen or liquid-helium temperatures

to achieve pumping speeds in the multimillion liters per second range,

has been most commonly adopted.

Each ultrahigh-vacuum system is itself a special design problem

which must be solved by a careful appraisal of the requirements to be

met and the selection of the most effective combination of the techniques

described in the preceding sections capable of meeting the require-

ments. Because of the requirements of metal gaskets, bakable

components, and extreme freedom from leaks, and the difficulties in

pressure measurement and the like, an improper choice of techniques

to be applied can result in excessive costs of construction and operation

and seriously jeopardize the chances of achieving the required per-

formance. However, the means are now available for achieving

almost any desired base pressure and enormous pumping speeds at

low pressure. If properly applied, the methods already developed are

capable of achieving spectacular goals. What is perhaps more im-

portant, the development of new techniques proceeds at such a pace

that what seems spectacular today will most certainly be commonplace

within the near future in the rapidly expanding field of ultrahigh

vacuum.

REFERENCES


London, 1960), p. 101.


London, 1962), p. 42.

3. B. B. Dayton, in 1962 Vacuum Symposium Transactions (The Macmillan


4. T. Kraus, Vakuum-Technik 8, 39 (1959).

k

r5.


C. Hayashi, in 1957 Vacuum Symposium Transactions (Pergamon Press,London, 1958), p. 13.

D. Lichtman and A. Hebling, in 1960 Vacuum Symposium Transactions(Pergamon Press, London, 1961), p. 187.

G. Mongodin and F. Prevot, Le Vide 11, 3 (1956).

F. A. Flecken and H. G. Noller, in 1961 Vacuum Symposium Transactions(Pergamon Press, London, 1962), p. 58.

5. Dushman, Scientific Foundations oj Vacuum Technique (John Wiley &Sons, Inc., New York, 1949), pp. 387, 388.

J. Blears, E. J. Greer, and J. Nightingale, Advances in Vacuum Science andTechnology (Pergamon Press, Oxford, 1960), Vol. II, p. 473.R. Geller, Le Vide 13, 71 (1958).

N. Basalaeva, Soviet Phys.-Tech. Phys. (New York) 3, 1027 (1958).N. Milleron, in 1958 Vacuum, Symposium, Transactions (Pergamon Press,London, 1959), p. 140.

P. F. Varadi, in 1960 Vacuum Symposium Transactions (Pergamon Press,London, 1961), p. 149.

John Strong, Procedures in Experimental Physics (Prentice-Hall, Inc.,

Englewood Cliffs, N.J., 1938), p. 128.

C. M. Van Atta, R. J. Van de Graaff, and L. C. Van Atta, Phys. Rev. 51,1013(A) (1937); C. M. Van Atta, R. J. Van de Graaff, L. C. Van Atta, andD. L. Northrop, Phys. Rev. 57, 536(A) (1940); and L. C. Van Atta, D. L.Northrop, R. J. Van de Graaff, and C. M. Van Atta, Rev. Sci. Instr. 12, 534(1941).

Westinghouse Research Laboratories, Research Report 100 FF 1054-Rl,Dec. 31, 1956.

T. H. Batzer and R. Ullman, University of California, Lawrence RadiationLaboratory (Livermore) Engineering Note ENA-122, Mar. 1, 1961, rev. Oct.6, 1961.

D. J. Goerz, Jr., in 1960 Vacuum Symposium Transactions (Pergamon Press,London, 1961), p. 16.

D. Lichtman and A. Hebling, in 1960 Vacuum Symposium Transactions(Pergamon Press, London, 1961), p. 187; and D. Lichtman, J. Appl. Phys.31, 1213 (1960).

D. J. Grove, in 1958 Vacuum Symposium Transactions (Pergamon Press,London, 1959), p. 9.

W. M. Hickam, Rev. Sci. Instr. 20, 472 (1949).

B. D. Power and F. C. Robson, in 1961 Vacuum Symposium Transactions(Pergamon Press, London, 1962), p. 1175.

T. H. Batzer and J. F. Ryan, in 1963 Vacuum Symposium Transactions(The Macmillan Company, New York, 1963), p. 166.I. Farkass and G. F. Vanderschmidt, in 1959 Vacuum Symposium: Trans-actions (Pergamon Press, London, 1960), p. 42.

D. Alpert, Rev. Sci. Instr. 22, 536 (1951).J. Wishart and G. H. Bancroft, in 1960 Vacuum Symposium Transactions(Pergamon Press, London, 1961), p. 13.

R. J. Conner, R. S. Buritz, and T. von Zweck, in 1961 Vacuum SymposiumTransactions (Pergamon Press, London, 1962), p. 1151.T. H. Batzer, in 1959 Vacuum Symposium Transactions (Pergamon Press,London, 1960), p. 265.

M. Rivera and R. LeRiche, in 1959 Vacuum Symposium Transactions(Pergamon Press, London, 1960), p. 55.

ULTRAHIGH VACUUM

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

437

31. H. Ehlers and J. Moll, in 1959 Vacuum Symposium Transactions (PergamonPress, London, 1960), p. 261.

32. R. A. Metcalfe and F. W. Trabert, in 1961 Vacuum Symposium Transactions(Pergamon Press, London, 1962), p. 1211.

33. J. S. Foster, Jr., E. O. Lawrence, and E. J. Lofgren, Rev. Sci Instr 24 388(1953).

'' '

34. F. M. Penning, Physica 4, 71 (1937).

35. R. T. Bayard and D. Alpert, Rev. Sci. Instr. 21, 571 (1950).

36. R. G. Herb, R. H. Davis, A. S. Divatia, and D. Saxon, Rev. Sci. Instr. 19331 (1948).

37. R. H. Davis and A. S. Divatia, Rev. Sci. Instr. 25, 1193 (1954).

38. J. C. Swartz, in 1955 Vacuum Symposium Transactions (Committee onVacuum Techniques, Boston, 1956), p. 83.

39. C. L. Gould, in 1956 Vacuum Symposium Transactions (Pergamon Press,London, 1957), p. 39.

40. C. L. Gould and P. Mandel, in 1962 Vacuum Symposium Transactions (TheMacmillan Company, New York, 1962), p. 360.

41. R. G. Herb, T. Pauly, R. D. Welton, and K. J. Fisher, Rev. Sci. Instr. 35,573 (1964).

42. A. J. Gale, in 1956 Vacuum Symposium Transactions (Pergamon Press,

London, 1957), p. 12.

43. L. D. Hall, Rev. Sci. Instr. 29, 367 (1958).

44. L. D. Hall, in 1958 Vacuum Symposium Transactions (Pergamon Press,

London, 1959), p. 158.

45. R. Zaphiropoulos and W. A. Lloyd, in 1959 Vacuum Symposium Trans-


46. R. L. Jepsen, A. B. Francis, S. L. Rutherford, and B. E. Kietzmann, in

1960 Vacuum Symposium Transactions (Pergamon Press, London, 1961),

p. 45.

47. W. M. Brubaker, in 1959 Vacuum Symposium Transactions (PergamonPress, London, 1960), p. 302.

48. P. F. Varadi and K. Ettre, in 1960 Vacuum Symposium, Transactions


49. R. H. Honig, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962), p. 1166.

50. Norman Milleron, in 1957 Vacuum Symposium Transactions (PergamonPress, London, 1958), p. 148.

51. Norman Milleron and E. C. Popp, in 1958 Vacuum Symposium Transactions


52. V. A. Simonov, G. F. Kleimenov, A. G. Mileshkin, and V. A. Kochnev, Paper

No. 255, Conference on Plasma Physics and Controlled Nuclear Fusion

Research, Conference Proceedings, Salzburg, Sept. 4-9, 1961, AEC-tr-5589,

Book 1 (U.S. Atomic Energy Commission, Division of Technical Information,

February 1963), p. 168.

53. B. M. Bailey and R. L. Chuan, in 1958 Vacuum Symposium Transactions


54. R. W. Moore, Jr., in 1961 Vacuum Symposium Transactions (Pergamon


55. Jack Grobman, in 1961 Vacuum Symposium Transactions (Pergamon Press,

London, 1962), p. 421.

56. R. T. Brackman and W. L. Fite, J. Chem. Phys. 34, 1572 (1961).

57. D. A. Degras, Second European Vacuum Symposium, Frankfurt am Main,

438 VACUUM SCIE^ AND ENGINEERING

June 5-7, 1963 [Proceedings published for the Deutschen ArbeitsgemeinschaftVakuum by Rudolf A. Lang, Esch (Taunus), 1963], pp. 54ff.

58. F. W. Schmidlin, L. O. Heflinger, and E. L. Garwin, in 1962 Vacuum Sym-posium Transactions (The Macmillan Company, New York, 1962), p. 197.

59. J. Hengevoss and E. A. Trendelenburg, in 1963 Vacuum Symposium Trans-actions (The Macmillan Company, New York, 1963), p. 101; and A. Natur-forsch. 18a, 481 (1963).

60. B. G. Lazarev and M. F. Fedorova, Soviet Phys.-Teoh. Phys. 6, 624 (1962).

61. W. Bachler, G. Klipping, and W. Mascher, in 1963 Vacuum SymposiumTransactions (The Macmillan Company, New York, 1963), p. 216.

62. E. S. Borovik, S. F. Grishin, and E. I. Grishina, Zhur. Tech. Phys. 30, 539(1960).

63. E. S. Borovik, F. I. Busol, and V. A. Kovalenko, Soviet Phys.-Tech. Phys.8, 68 (1963).

APPENDIX I

Molecular Weights of Gases*

Gas Formula Molecular weight, g/mole

Helium HeNeArKrXe

H2N2O2CI2

HClH2SSO2NON2ONH3

COCO2CH4C2-H.2

C2H4

4.003

20.18

Argon 39.944

83.70

131.30

2.016

Nitrooren 28 02

Oxvoren 32 000

Chlorine 70.91

Air 28.98 (mean)

36.47

34.08

64.06

30.01

44.02

17.03

Hydrogen chloride . . .

Hydrogen sulfide. . . .

Sulfur dioxide

Nitric oxide

Nitrous oxide

Carbon monoxide ....

Carbon dioxide

28.01

44.01

16.04

26.04

Ethylene . 28.05

* Source: Handbook of Chemistry and Physics (Chemical Rubber Publishing

Co., Cleveland, 1963), 44th ed.

439

APPENDIX II

Critical Constants, Van der Waals' Constants, Molecular Diameters,AND Mean Free Paths Computed from the Constant 6 According to

EqS. (1-40) AND (1-38)

Gas

HeliumNeonArgonKryptonXenon

HydrogenNitrogenOxygenChlorine

Mercury

Hydrogen chloride

Water vapor ....

Hydrogen sulfide.

Sulfur dioxide . . .

Nitric oxide

Nitrous oxide. . . .

Ammonia

Carbon monoxideCarbon dioxide . .

MethaneAcetylene

EthyleneCarbon disulfide .

Formula

HeNeArKrXe

HaNaO2Clj

Hg

HClH2OHjSSO2NON2ONH3

COC02CH,CgHjC2H4cs.

— 267.9— 228.7— 122.

— 63.0

16.6

— 239.9— 147.1

— 118.8

144.0

>1500

51.4

374.0

100.4

157.2

— 94.0

36.5

132.4

— 139.0

31.1

>155036.0

9.7

273.0

P*atm

2.26

25.9

48.0

54.0

58.2

12.8

33.5

49.7

76.1

>200

81.6

217.72

88.9

77.7

65.0

71.7

111.5

35.0

73.0

>20062.0

50.9

76.0

A*(cm^/mole)'

atmX io-«

0.03412

0.2107

1.345

2.318

4.194

0.245

1.390

1.360

6.493

8.093

3.667

5.464

4.431

6.714

1.340

3.782

4.170

1.485

3.592

2.253

4.390

4.471

11.62

cm^/mole

23.70

17.09

32.19

39.78

51.05

26.61

39.13

31.83

56.22

17.0

40.81

30.49

42.87

56.36

27.89

44.15

37.07

39.9

42.67

42.78

51.4

57.14

76.9

cmX 10-

2.62

2.38

2.94

3.«(6

3.43

2.76

3.14

2.93

3.55

2,38

3.19

2.89

3.24

3.55

2.81

3.27

3.09

3.16

3.22

3.24

3.44

3.56

3.94

X cmP = 1 torr

T = O^C

X 10-3

9.26

10.3

7.34

6.38

5.40

8.33

6.44

7.40

5.08

11.2

6.27

7.61

6.07

5.05

8.08

5.96

6.68

6.36

6.13

6.07

5.38

5.01

4.11

* Sources: AmericMn Institute of Physics Handbook (McGraw-Hill Book Company, New^York,1963), 2nd ed.; Handbook of Physics and Chemistry (Chemical Rubber Publishing Co., Cleveland,1963), 44th ed.

APPENDIX III

Viscosity op Gases at 0°C and 760 Torr together with Computed ValuesOP Molecular Diameters and Mean Free Paths in Accordance with

Eqs. (1-62) and (1-38)

Gas FormulaViscosity, fi*

micropoises

1

cmX 10-8

A cmP = 1 torr

T = 0°CX 10-3

Helium HeNeArKrXe

H2N2O2CI2

HClHjSSO2NON2ONHg

COCO2CH4C2H2C2H4

186.9

312.4

208.8

224.9

216.5

84.7

166.6

191.0

124.0

171.2

132.5

117.5

117

179.0

136.1

88.9

165.8

137.6

103.2

93.5

93.6

2.20

2.55

3.69

4.27

4.87

2.68

3.78

3.65

5.51

3.76

4.53

4.73

5.55

3.71

4.69

4.57

3.79

4.66

4.18

4.96

5.05

13.2

Neon 9.82

4.67

3.49

2.68

Hvdrosren 8.83

4.45

4.77

Chlorine 7.61

Air 4.49

Hydrogen chloride. .

Hydrogen sulfide . . .

Sulfur dioxide

Nitric oxide

Nitrous oxide

3.10

2.84

2.07

4.62

2.90

3.05

Carbon monoxide . . .

Carbon dioxide

4.42

2.93

3.64

2.59

Ethylene 2.50

* Source: Handbook of Chemistry and Physics (Chemical Rubber Publishing

Co., Cleveland, 1963), 44th ed.

440 441

APPENDIX IV 443

1 cubic foot per minute (cfm)

APPENDIX IV

Units and Convebsion Factoes of Use in Vacuum Technology*

Pressure

1 standard atmosphere (atm) = 760 mm Hg of density 13.595 g/cm^where g = 980.665 cm/sec^ = 760 torr

= 1.0133 X 10«dynes/cm2= 14.696 psi = 2,116.2 Ib/ft^

= 29.921 in. Hg at 32°F= 33.899 ft of water at 39.1 °F

1 bar = 10* dynes/cm^ = 10*/ibar

= 750.06 mm Hg of density 13.595 g/cm^where g = 980.665 cm/sec^ = 750.06 torr

= 0.98692 atm= 14.504 psi

1 torr = 1 mm Hg of density 13.595 g/cm^where g = 980.665 cm/sec^

= 1,333 fih&T (dynes/cm^)

1 micron {/i) = 10^^ torr = 1 millitorr

= 1.333 /^bar (dynes/cm^)

Pumping Speed and Conductance

1 cubic centimeter per second (cm^/sec) = 10-^ liter/sec = 6 x 10^^ liter/min

= 3.6 liters/hr = 10~' m^/sec

= 6 X lO-^mS/min = 3.6 x lO-^m^/hr= 3.531 X 10-5 cfs ^ 2.119 x 10-3 cfm

1 liter per second (liter/sec) =10^ cm'/sec =6x10* cm^/min= 3.6 X 106cm3/hr = IQ-Sm^/sec= 6 X 10-2ni3/jnin = 3.6 m^/hr= 3.532 X 10-2 cfs = 2.119 cfm

1 liter per hour (liter/hr) = 2.778 x 10"* liter/sec

= 1.667 X 10-2 liter/min = IQ-^m^/hr= lO^cm^/hr = 1.667 x lO-Sm^/min'= 16.67 cmS/min = 5.886 x 10-* ofm= 9.72 X lO-Scfs

1 cubic meter per hour (m^/hr) = 2.778 x 10-* m^/sec= 1.667 x 10-2m3/min = 10^ Hters/hr

= 10* cm3/hr = 0.2778 liter/sec

= 277.8 cm3/sec = 0.583 cfm= 9.72 X 10-3 gfg

* Source: Handbook of Chemistry and Physics (Chemical Rubber PublishingCo., Cleveland, 1963), 44th ed.

442

1.667 X 10-2 cfs

= 471.95 cm3/sec = 0.47195 liter/sec

= 28.32 liters/min = 1,699 liters/hr= 1.699 mS/hr = 0.0283 m^/min

Throughput or Oas Flow1 torr cm^/sec = \ fx liter/sec (fi l/sec)

= 10-3 torr liter/sec

= 2.119 X 10-3 torr cfm= 2.119 /« cfm

1.316 X 10-3 atm cm3/sec1,000 n liters/sec (fi I/sec)

= 1,000 torr cm3/sec= 2.119 torr cfm= 2,119 /< ofm

1.316 atm om3/sec10-3 ^Qj.j. liter^ggQ

= 1 torr cm3/sec= 2.119 /< cfm= 2.119 X 10-3 torr cfm

= 1.316 X 10-3 atm cm3/soc= 760 torr cm3/sec: 760 ^ liter/sec

- 0.760 torr liter/sec

- 1.610 torr ofm1,610 n ofm

- 1,000 /< cfm- 0.4719 torr hter/sec

- 471.9 torr cm^/sec

: 471.9 /< liters/sec

0.6210 atm cm3/sec10-3 ^QJ.J. pfjj^

0.4719 /« Hter/sec

= 0.4719 torr cm3/sec= 4.719 X 10-* torr hter/sec

= 6.210 X 10-* atm cm3/sec

Length

0.01 m = 10 mm= 0.3937 in.

= 3.281 X 10-2 ft

= 100 cm = 1,000 mm= 39.37 in.

= 3.281 ft

0.08333 ft

2.540 cm = 25.40 mm12 in.

30.48 cm = 304.8 mm

1 torr liter/sec

1 fi hter/sec {fi 1/seo)

1 atm cm3/sec

1 torr cfm

1 /i cfm

1 contimetor (cm)

1 meter (m)

1 inch (in.)

1 foot (ft)

Area

1 square centimeter (cm2) = 10-* m2 = 100 mm2= 0.1550 in.2

= 1.0764 X 10-3 ft2


1 square meter (m^) =10* cm^ =10' mm^= 1,550.0 in.2

= 10.764 ft2

1 square inch (in.^) = 6.944 x lO-^ ft^

= 6.452 cm2 = 645.2 mm^= 6.452 X 10-* m2

1 square foot (ft^) = 144 in.^

= 929.0 cm2 = 9.29 x 10* mm^= 9.290 X 10-2 m2

Volume

1 cubic centimeter (cm^) = 0.99997 x 10-' liter = lO^^m' = 10' mm'= 6.1023 x 10-2 in.s

= 3.531 X 10-5 ft3

1 liter = 1,000.027 cm' = 1.000027 x 10-' m'

We use hereafter the approximation1 liter = 10' cm' = 10-' m' = 10* mm'

= 3.531 X 10-2 ft' = 61.025 in.'

1 cubic meter (m') = 10' liters = 10* cm' = 10^ mm'= 6.1023 X 10* in.' = 35.31 ft'

1 cubic inch (in.') = 1.639 x 10-2 liter ^ i6.39 cm' = 1.639 x 10* mm'= 5.787 X 10-* ft'

1 cubic foot (ft') = 28.316 liters

= 2.8317 X 10* cm' = 2.8317 x 10' mm'= 1,728 in.'

Temperature

Kelvin to centigrade °K = °C + 273.16

Rankine to Fahrenheit "R = °F + 459.69

Fahrenheit to centigrade °F = 32 + 1.8°C

Rankine to centigrade °R = 1.8°C

APPENDIX V

Values op Some Physical Constants*

Symbol Name Value

Losohmidt's number (molecular density of a

gas at 760 ton- and 0°C) 2.687 X lO'Vcm'

Avogadro's number (number of molecules in

1 g mole) 6.023 X 1023/g mole

V Volume of 1 g mole of gas at 760 torr and 0°C 22,415 cm'

R Gas constant 8.3143 X 10' erg/g mole "K

^ = ^oln^ol Boltzmann's constant 1.3805 X 10-" erg/°K

Atomic mass unit (chemical scale in which

O2 = 32 mi exactly) 1.660 X 10-2* g

Electronic rest mass 9.109 X 10-28 g

e Electronic charge 4.803 X 10-"> esu

= 1.602 X 10-1" coulomb

P = »mol« Faraday 2.893 X 10" esu/g mole= 9.649 X 10* coulombs/g mole

9 Acceleration due to gravity:

Approximate range over U.S.A. 979.0-980.9 cm/sec^

Assumed "standard" value 980.665 cm/sec^

* Source: Handbook 0/ Chemistry and Physics (Chemical Rubber Publishing Co,

1963), 44th ed.

,Cleveland

Item °C °K op °R

Boiling point of water* 100

-78.2-185.8-252.9-268.95-273.16

373.16

273.16

195.0

77.35

20.3

4.215

212

32

-108.7-320.5-423.2-452.10-459.69

671 69Melting point of ice*

Sublimation point of dry ice* ....

Boiling point of liquid Nj*Boiling point of liquid H2*Boiling point of liquid He*Absolute zero

491.69

351.0

139.2

36.5

7.59

At standard atmospheric pressure.

445

AUTHOR INDEX

Tho page numbers in italics are those of references at the ends of the chapters.

-^

Abbott, T. A., 140, 168

Ackley, J. W., 165-167, 1(>8

Addis, R. R., Jr., 312, 362

Alexander, P., 234, 27.3

Alpert, D., 99, 103, 104, 131, 342, 343,

362, 378, 388, 434, 436, 437

Biichler, W., 250, 252, 273, 289, 302,

430-432, 438

Backus, J., 133, 135

Bailey, B. M., 410-412, 437

Bancroft, G. H., 379, 380, 436

Barrington, A. E., 165-167, 168

Barry, E. J., 309, 311, 312, 362

Basalaeva, N., 365, 436

Batzer, T. H., 243, 272, 273, 347, 362,

371, 372, 375, 376, 381, 382, 436

Bayard, R. T., 99, 103, 104, 131, 388,

437

Beams, J. W., 212, 213, 218, 313

Beck, A. H., 118, 132

Becker, J. A., 89, 131

Becker, Wilh, 214, 215, 218

Bennett, W. H., 155, 168

Benson, J. M., 85, 86, 131

Bills, D. G., 107, 132

Biondi, M. A., 343-346, 362

Blears, J., 100, 131, 242, 273, 365, 436

Borovik, E. S., 431-434, 438

Bowie, R. M., 99-101, 131

Brackman, R. T., 424, 437

Briggs, W. F., 162-165, 168

Brisbane, A. D., 118, 132

Brubaker, W. M., 396, 437

Buckley, O. E., 95, 131

Burch, R. C, 268, 273

Buritz, R. S., 380, 381,436

Bush, William E., 328, 362

Busol, F. I., 432-434, 438

Carmichaol, J. H., 342-344, 362

Cartwright, C. Hawley, 341, 362

Chapman, S., 21, 2^

Charles, D., 145, 147-149, 168

Charpentier, D. E., 139, 142, 143, 167,

168

Chuan, R. L., 410-412, 437

Chupp, Warren W., 247, 273

Clausing, P., 51, 53, 54, 62

Cleveland, J. F. 285, 286, 302

Conner, R. J., 380, 381, 436

Crawley, D. .T., 230, 24.5-247, 258, 260,

264, 273

Davis, D. H., 52, .54-57, 61, 62, 306,

3.34, 335, 362

Davis, R. H., 388, 389, 437

Davis, W. D., 140, 141, 168

Dawton, R. H. V. M., 314, 362

Dayton, B. B., 99, 285, 294-296, 302,

354, 355, 360, 362, 363-365, 435

Degras, D. A., 424, 437

Dempster, A. J., 133, 167

Denison, D. R., 107, 132

Dennis, N. T. M., 241, 244-247, 271,

273

Divatia, A. S., 388, 389, 437

Dobrowolski, Z. C, 200, 218

Doughty, E. G., 140, 168

447

448 AUTHOR INDEX

Downing, J. R., 122, 132

Dubrovin, J., 68, 131

Dunlop, G. C, 83, 131

Dunoyer, L., 272

Dushman, Saul, 82, 83, 139, 211, 218,

227, 273, 364, 43G

East, H. G., 65, 131

Ehlbeck, H. W., 154, 156, 157, 168

Ehlers, H., 384, 437

Eklund, S., 212, 218Enskog, T>., 21, 22

Ettre, K., 399, 437

Farkass, I., 309, 311, 312, 362, 378, 436

Feaks, F., 129, 132

Fedorova, M. F., 428-430, 438

Fisher, K. J., 389, 437

Fite, W. L., 424, 437

Flecken, F. A., 364, 436

Florescu, N. A., 230, 233, 234, 261, 262,

273

Fondrk, V. V., 220, 223, 224, 272

Forbes, S. G., 324, 325, 362

Forsythe, W. E., 4

Foster, J. S., Jr., 386-388, 437

Francis, A. B., 165-167, 168, 396-398,

437

Frank, N. H., 16, 22

Gaede, W., 179, 205, 211, 218, 227, 230,

273

Gale, A. J., 391, 392, 403, 437

Garwin, E. L., 424, 438

Geller, R., 365, 436

Gerber, J. F., 317, 318, 362

Goerz, D. J., Jr., 373, 436

Good, W. M., 328, 362

Gould, C. L., 389, 390, 437

Green, C. B., 89, 131

Greer, E. J., 365, 436

Grishin, S. F., 431, 438

Grishina, E. I., 431, 438

Grobman, Jack, 421-424, 437

Grove, D. J., 374, 375, 379, 380, 436Guthrie, A., 133, 136, 138, 162, 167,

168, 309, 310, 362

Hablanian, M. H., 261-264, 273, 289,

302

Haefer, R. A., 102, 118, 131, 132

Hall, L. D., 393-395, 437

Hall, L. G., 142, 168

Hamilton, A. R., 87, 89, 131

Hasse, T., 83, 131

Hayashi, C., 364, 436

Hayward, Roger, 341, 362

Hobling, A., 150, 168, 364, 373, 374,

436

Heflinger, L. O., 424, 438

Hengevoss, J., 102, 131, 424, 425, 427,

438

Herb, R. G., 388, 389, 404, 437

Hickam, W. M., 375, 436

Hickey, J. S., 159, 168

Hickman, K. C. D., 64, 131, 243, 244,

263, 268, 269, 271, 273

Hippie, J. A., 139, 143, 167, 168

Ho, T. L., 240, 253, 273

Honig, R. H., 400, 437

Hustrulid, A., 140, 168

Ishii, H., 125, 127, 132

Jacobs, Robert B., 209, 218

Jaokel, R., 230, 237, 273

Jaycox, E. K., 99

Jepsen, R. L., 165-167, 168, 396-398,

437

Johnson, J. W., 328, 362

Jones, A. C., 162-165. 168

Kenna, R. A., 180, 218

Kennard, E. H., 78, 131, 231, 235, 273

Kennedy, P. B., 339, 340, 362

Kietzmann, B. E., 396-398, 437

Kingdon, K. H., 159, 168

Kinsella, J. J., 269, 273

Klages, G., 83, 131

Kleimenov, G. F., 405-408, 437

Klipping, G., 430-432, 438

Klopfer, A., HI, 112, 132

Klumb, H., 83, 131

Knox, F. A., 184, 218

Knudsen, M., 36, 44, 53-56, 60, 62, 62,

123, 132

AUTHOR INDEX 449

Kochnev, V. A., 405-408, 437Kovalenko, V. A., 432-434, 438Kraus, Th., 356-358, 362, 364, 435Kruger, Charles H., 215-217, 218Kuhn, H. J., 65, 131

Kurie, F. N. D., 323, 324, 362

Moll, J., 384, 437

Mongodin, G., 364, 436Moody, R. E., 153-155, 168Moore, R. W., Jr., 412-421, 437Morse, R. S., 99-101, 131

Lafferty, J. M., 107, 108, 110, 111, 132

Lampson, C. W., 98, 131

Landfors, A. A., 289, 302Lane, C. T., 83, 131

Lange, W. J., 342-344, 362Langmuir, I., 101, 131, 159, 168Latham, D., 241, 244, 271, 273Lauer, E. J., 106, 132

Lavender, R., 87, 88, 131

Lawrence, E. O., 386-388, 437

Lazarev, B. G., 428-430, 438LeBlanc, M., 219, 272Lech, J., 145-147, 151, 152, 168

Leek, J. H., vi, 67, 77, 87, 92, 94, 97-99,

113, 115, 123, 132, 283, 302LeRiche, R., 382-384, 436Levenson, L. L., 52, 54-57, 61, 62, 265,

273, 306, 334, 335, 345-347, 362Lichtman, D., 150, 168, 364, 373, 374,

436

Little, R. N., 324, 325, 362Lloyd, W. A., 395-397, 437

Loeb, L. B., 12, 14, 22

Loecherer, K. H., 154, 156, 157, 168

Loevinger, R., 138, 167

Lofgren, E. J., 386-388, 437

Lothrop, C. F., 165-167, 168

McFarland, R. H., 347, 362

McLeod, H., 69, 131

Mandel, P., 389, 390, 437

Mandoli, H., 165-167, 168

Marks, Lionel S., 4

Mascher, W., 430-432, 438

Mellen, G., 122, 132

Menshikov, M. I., 247, 259, 260, 273Metcalfe, R. A., 385, 437Mileshkin, A- G., 405-408, 437

Milleron, Norman, 52, 54-57, 61, 62,

265, 273, 301, 302, 306, 332-335,

34.5-347, 362, 366, 372, 402, 403, 408,

436, 437

Nakayama, K., 125, 127, 132Naundorf, C. H., 354-356, 360, 362Neef, W. S., Jr., 404Noher, H. Victor, 341, 362Nicollian, E. H., 149, 150, 168Nienhuis, K., 114, 132

Nier, A. O. C, 140, 167, 168Nightingale, J., 365, 436

Noeller, H. G. (see Noller, H. G.)

Nollcr, H. G., 202, 205, 218, 230, 237,

250, 252, 273, 289, 302, 364, 437

Normand, C. E., 253, 273

Northrop, D. L., 371, 436

Nottingham, W. B., 95, 96, 102, 107,

131, 132

Nyer, W. E., 324, 325, 362

Oatloy, C. W., 300, 302

Pauly, T., 389, 437

Pearson, G. L., 89, 131

Peck, A. W., 298, 302

Penning, F. M., 113-115, 132, 387, 437

Pensak, L., 312, 362

Perkins, G. D., 142, 143, 168

Peters, J. L., 141, 142, 168

Pinson, J. D., 298, 302

Pirani, M., 86, 131

Popp, E. C., 403, 408, 437

Post, R. F., 333

Power, B. D., 180, 218, 230, 241, 244-

247, 258, 259, 264, 271, 273, 375, 436

Pressey, D. C, 67, 131

Prevot, F., 364, 436

Rabinovich, I. S., 247, 259, 260, 273

Redhead, P. A., 68, 105, 118-122, 128,

129, 132, 154, 168

Reich, G., 101, 131, 157-159, 168, 250,

252, 273, 289, 302

Rhodin, T. N., 121, 132

450

Riddiford, L., 101, 131

Riddoch, A., 115, 132Ridenour, L. N., 98, 131Rivera, M., 382-384, 436Roberts, J. A., 162-165, 168Roberts, R. W., 315, 362Robinson, C. F., 142, 168Robson, F. C, 375, 436Roehrig, J. R., 126, 127, 132Romann, M. P., 77, 131Rovner, L. H., 121, 132Ruf, J., 154, 156, 157, 168Rufer, C. E., 288, 302Rutherford, S. L., 396-398, 437Ryan, J. F., 375, 376, 436

Santeler, D. J., 106, 129, 130, 132Saxon, D., 388, 437Schmidlin, F. W., 424, 438Schuemann, W. C, 104, 105, 73,2

Schuetze, H. J., 104, 131, 154, 156, 157,

168

Schwartz, C. M., 87, 88, 131Schwarz, Helmut, 118

Scott, Nancy J., 312, 362Shapiro, Ascher H., 215-217, 218Siegbahn, S., 211

Simmons, J. C, Jr., 126, 127, 132Simonov, V. A., 405-408, 437Slater, J. C, 16, 22

Smith, H. R., 260, 273, 339, 340, 362Smith, J. H., 272Smith, P. T., 93, 131

Sommer, H., 143, 168

Stoinherz, H. A., 261-263, 273Stevens, C. M., 140, 168Stevenson, D. L., 250, 253, 254, 265-

267, 273, 287, 302Stork, F., 104, 131

Strong, John, 341, 362, 370, 436Swartz, J. C, 389, 390, 437Sylvester, R. L., 186, 218

Tate, J. T., 93, 131

Taylor, A. R., 338, 362Thees, R., 203, 218Thomas, H. A., 139, 143, 167, 168

AUTHOR INDEX

Torney, F. L., Jr., 95, 96, 129, 131,

132, 160, 161, 168

Trabert, F. W., 385, 437

Trendelenburg, E. A., 424, 425, 427,

438

Trump, H. G., 83, 131

Ullman, J. R., 333, 334, 362, 371, 436

Vacca, R. H., 123, 132

Van Atta, C. M., 186, 195-198, 218,

371, 436

Van Atta, L. C, 371, 436

Van de Graaff, R. J., 371, 436Vanderschmidt, G. F., 378, 436

Vandershce, T. A., 140, 141, 168van Oostrom, A., 103, 131

Varadi, P. F., 368, 369, 399, 436, 437Vekshinsky, S. A., 247, 259, 260, 273Voego, W., 83, 131

Von Friesen, S., 211, 218von Zweck, T., 380, 381, 436

Wahl, J. S., 324, 325, 362Wakerling, R. K., 133, 136, 138, 162,

167, 168, 309, 310, 362Wallace, R. A., 145-147, 151, 152, 168Warnecke, R. J., Jr., 145, 147-149, 168Watson, W. R., 145-147, 151, 152, 168Webber, R. J., 83, 131

Weinhart, H. W., 99

Welton, R. D., 389, 437

White, W. H., 159, 168Whitford, Albert E., 341, 362Williams, C. E., 212, 213, 218, 313Williams, T. W., 139, 167Wilson, R. R., 313, 314, 362Winters, H. F., 107, 132

Winzenburger, E. A., 186, 189, 190, 218Wishart, J., 379, 380, 436

Worcester, W. G., 140, 168

Zaphiropoulos, R., 395-397, 437Ziock, K., 186, 218

SUBJECT INDEX

Absorption, definition of, 364pumping by ahimina, copper and

zeolite, 343-348, 398-400Accommodation coefficient, definition

of, 79

role, in Knudsen radiometer gauge,124

in thermal conductivity gauge,79-81

Adsorption, definition of, 364pumping by graphite at cryogenic

temperatures, 428-430Air, effective molecular weight of, 2

normal composition of, 411Alphatron gauge, 122Argon, instability in Vac Ion pumps,

396-398

normal content of air, 411Avogadro's law, 2, 4

Avogadro's number, 4

Backstreaming in diffusion pumps,257-268, 329

catalytic effect of materials of nozzle

assembly, 267dependence, on pressure, 263on shape of first-stage nozzle,

265-267effect on ultimate pressure, 257-268measurement of, 258, 261-264reduction by water-cooled cap over

first-stage nozzle, 259, 263role of jet from first-stage nozzle,

259-264Bayard-Alport ionization gauge, 103-

107

comparison, with conventional ion-

ization gauge, 103with hot cathode magnetron gauge,

109

Bayard-Alpert ionization gauge, errorsdue to accumulation of surfacecoating, 106

limits of operation, 103-105low temperature cathodes, 106nude gauge construction, 106principles of operation, 103pumping effects, 105reduced x-ray hmit, 103sensitivity, 103, 107(See also Ionization gauge, conven-

tional hot cathode type; Magnetronionization gauges; Penning dis-

charge gauge; Pressure gauges)Bellows seals (see Metal bellows)

Blears's effect, 100-102, 242, 297Boiling points of common gases, 409Boltzmann constant, 7

Booster diffusion pumps, 257Boyle's law, 1

Calibration of vacuum gauges, 124-128aperture method for ionization

gauges, 126-128McLeod gauge, as absolute standard,

124-126

error due to use of vapor trap, 72,

125, 127

Charles's and Gay-Lussac's law, 1

Chemisorption, definition, 364Collision cross section, 21

dependence, on molecular diameter,

21

on viscosity, 21

Compression ratio, for diffusion pumps,230-240

for mechanical booster (blower)

pumps, 185, 188, 199-201, 204for mechanical oil-sealed pumps, 171

for molecular drag pumps, 205-214

451

462 SUBJECT INDEX

Compression ratio, for molecular tur-

bine pumps, 217

Condensable vapors, accelerated re-

moval by high-temperature bake-out, 363-370

backstreaming, from diffusion

pumps, 258-268, 329from oil-sealed mechanical pumps,

174, 340

from steam ejectors, 227dominance of water vapor following

pumpdown, 137, 330-332effect, on performance of mechanical

oil-sealed pumps, 177-179, 351

on reading of McLeod gauge, 71

elimination from oil-sealed mechan-ical pumps, 179-185

vapor compression action of mechan-ical booster pumps, 204

vapor traps, absorption type, 341-348

refrigerated, 328-341Conductance, definition, 24, 58

general formulas, combined withpumping speed, 25, 58

conductances, in parallel, 26, 58in series, 25, 58

molecular flow pressure range,

43-51, 60-62

annulus between two concentric

tubes, 51, 62

aperture in thin wall, 47-49, 60

channel of rectangular cross

section, 50, 61

long tube of circular cross

section, 44-47

Monte Carlo calculation of, 51-

57

narrow slot with end correction,

51, 61

tube with end correction, 49,

60

summary of, 57-62transition pressure range, 15, 23,

36-43, 59

dependence on pressure, 37-43formula for long tube, 37, 41, 59limits of, 40-42

viscous flow pressure range, 26-30,

34-36, 58change in character due to

surface slip, 34

Conductance, general formulas, viscous

flow pressure range, formulafor long tube, 29, 58

pipe -size formula based onpressure drop, 30, 59

Conductance factors, Knudsen andClausing, 52-57

Cryo-adsorption, 421-424, 428-430Cryogenic pumping, 408-434

boiling points of common gases, 409combined, with catalytic process,

421-424

with mechanical pumping, 410-412

cryo-adsorption, 421-424

cryotrapping, 424-428

liquid-helium-cooled thimble trap,

400

pumping speed of cryogenic pumps,411-421

shielded liquid-helium-cooled con-

densers, 430-434theory of, 412-421

vapor pressure dependence on tem-perature, 409

Cryotrapping, 424-428

Diffusion pump working fluids, 240-249decomposition of organic, 242-245,

264mercury and organic, comparative

advantages, 244-249vapor pressures of, 240-244

Diffusion pumps, 227-272

backstreaming, 257-268, 329

Blears's effect, 100-102, 242, 297booster, 257

compression ratio, 230-240

ejector, oil vapor, 257

forepressure, limiting valvie of, 254-

257

fractionating, 268-271Ho coefficient, 248-250, 253modern types of, 227-229

principles of operation, 227-240

^ pumping speeds of, 240, 249-254,

293-302

with vapor trap, 240, 252

purging, 271

speed factor, 253, 272

ultimate pressure, 257-268working fluids, 240-249

SUBJECT INDEX 453

Displacement speed of mechanicalvacuum pumps, 172

Dubrovin gauge, 68

Elastomers, 307-316Electron volt, unit of energy, 91

Electronic charge, definition and value,

4

Emissivity, definition, 81

Evapor-ion pump, 388-391

Faraday, definition and value, 4Farvitron mass spectrometer, 157-159Forepressure limit of diffusion pumps,

254-257

dependence on design and operating

parameters, 255design compromises, 255limitation due to decomposition of

working fluid, 256process of jet breakdown, 254throughput dependence on, 256

booster diff'usion pumps, 257oil vapor ejector pumps, 257

Gas ballast, 179-183Gas flow, 14, 23-62, 277-291through a hole, 12, 47-49low pressure range, 43-57methods of measurement of, 277-291molecular flow, 14, 23, 43-57, 60Poiseuille's law, 26-30, 34-36Reynolds number, 31

transition pressure range, 15, 23,

36-43, 59

turbulent flow, 31-34viscous flow, 14, 23, 26-30, 34-36, 58

Gas law, general, 1-4

Boyle's law, 1

Charles's and Gay-Lussac's law, 1

Gases, boiling points of, 409general gas law, 1-4

ideal gas, deflnition, 2

molecular constitution of, 4molecular weights of, 2

molecules per unit volume, 5nature and behavior of, 1-22ratio of specific heats, y, 11, 220specific heats at constant pressure

and at constant volume, 11

Gases, universal gas constant, 3vapor pressures at low temperatures,

409velocity of sownd in, 11

Gaskets, elastomer, 307-316metal, 370-378O ring, 307-313, 315

Getter-ion pumps, 385-398Bayard-Alpert gauge pumping ac-

tion, 105, 388discharge in axial magnetic fleld,

386-388Evapor-ion pump, 388-391gettering and ionization processes,

391-393

leak detection application of, 165-167

pumping action of gas discharges,

386triode getter-ion pump, 396-398Vac Ion pump, 393-398

argon instability, 396hydrocarbon contamination, 394mechanism of operation, 394slotted cathode construction, 396-

398

triode getter-ion pump, 396-398Getter pumping, 401-408

deposition of reactive metals, 401-408

molybdenum, 402-404, 408nickel, 407titanium, 401-408zirconium, 402

pumping effectiveness as function of

temperature of coated surface,

406-408

Halogen leak detectors, 159-161, 162

Helium leak detectors {see Leakdetectors)

Ideal gas, deflnition, 2

Ionization of gases, 90-98

cross section for electrons, 93

ionization potential, 92

ionization probability, 93

Ionization gauge, conventional hot-

cathode type, 90-102

454 SUBJECT INDEX

Ionization gauge, conventional hot-

cathode type, alternative meth-ods of operation, 92

Blears's effect, 100-102, 242, 297cahbration of, 97, 125-128

cross section for ionization, 93

design of gauge tubes, 99-101

ionization process (see Ionization

of gases)

Nottingham x-ray limit, 102

nude gauge arrangement, 100-102outgassing of gauge elements, 101

parameters for various gaugetubes, 99

principles of operation, 90-94range of useful application, 97

regulated power supplies for, 98

sensitivity of, 95-99

simplified electrical circuit for, 94x-ray limit, 102

(See also Bayard-Alpert ionization

gauge; Magnetron ionization

gauges; Penning discharge

gauge)

Isentropic flow, 219-221, 278-282

Kelvin temperature scale, 2

Knudsen radiometer gauge, 123

accommodation coefficient, effect onsensitivity, 124

pressure range, 124


Lambert's law of molecular emission,

52

Leak detection techniques, 161-167bubbles from air pressurizing, 162halide torch technique, 162halogen leak detector, 159-161mass spectrometer leak detection

methods, 164

Vac Ion pump current, 165-167variations in pressure gauge readings,

162-164

Leak detectors, halogen sensitive, 159-161

helium (see mass spectrometer typesof, below)

mass spectrometer types of, cyoloidal

focusing, 142Dempster 180 degree magnetic

deflection, 137-140

Leak detectors, mass spectrometer typesof, double magnetic fociising, 141

linear resonance accelerators, 152-

154

Nier 60° magnetic deflection,

140

omegatron, 149

Liquid nitrogen (LN), automatic level

control, 337

coolant, for absorption traps, 342,

347, 399

for coated getter surfaces, 404-

408, 435for vapor condensation traps, 330,

332

cryotrapping on LN-cooled surfaces,

424intermediate coolant from cryo-

pumping systems, 426-430, 432-

434

McLeod gauge, 69-78

calibration methods, 72

criterion for validity, 71

effect of condensable vapor onreading, 71

error, due to connecting tube, 73-75,

125

due to liquid-nitrogen-cooled trap,

72, 125, 127

methods of controlling mercurylevel, 75-77

primary standard for pressure meas-urement, 72

response formula, 70-72

scales, linear and quadratic, 71

multiple, 77

sensitivity, 72

Magnetron ionization gauges, cold

cathode inverted magnetron, 118-

120

cold-cathode magnetron, 120-122hot-cathode magnetron, 107-111

{See also Bayard-Alpert ionization

gauge; Ionization gauge, con-

ventional hot-cathode type;

Penr'ing discharge gauge; Pres-

sure gauges)

Manometers, diaphragm, 65-68

hquid, 63-65

(iS'ee also Pressure gauges)

SUBJECT INDEX 455

Mass flow, definition, 24relation to throughput, 24of steam ejectors, 223

Mass spectrometer leak detectors (see

Leak detectors)

Mass spectrometer vacuum analyzers,

133-159

magnetic deflection types, 133-143cycloidal focusing, 142

Dempster magnetic focusing, 133-140

Nier 60 degree deflection, 140Vanderslice 90 degree deflection,

140

resonance types, Farvitron, 157-159linear accelerator, 152-157omegatron, 143-152

Maxwell-Boltzmann distribution law,8-11

average molecular velocity, 9

most probable molecular velocity, 9root-mean square velocity, 7-10

Mean free path, 5, 13-15, 21, 23Measurement, of gas flow, 277-291

of gas pressure, partial, 133-159total, 63-128

of pumping speeds, 291-302Mechanical booster pumps (vacuum

blowers), 185-205

analysis of pumping performance,186-194

compression ratio, 185, 188, 199-201,204

net pumping speed, 187-190overheating of exhaust, 202pumping speed dependence on pres-

sure, 189, 193-202reverse flow or slip, 186-188vapor compressor action, 204

Mechanical oil-sealed pumps, 169-185compression ratio, 171

condensable vapor, effect on per-

formance, 177-179

methods of elimination, 179-185air stripping (Knox method), 184drop-out tank, 179

gas ballast, 179-183hot pump, 184inlet condensers and vapor traps,

184oil purification and circulation,

184

Mechanical oil-sealed pumps, functionsin vacuum systems, 358-360

oil, lubrication and sealing, 172operating features, 169-172pumping speed, 171-177, 291-293selection of sizes, 359stages, single and double, 171throughput, 175-178types, 169

Mechanical vacuum pumps, 169-218booster pumps (blowers), 185-205functions of various types, 169molecular-drag type, 205-214molecular turbine type, 214-218oil-sealed rotary types, 169-185

Metal bellows, 316for rotary motion seals, 317-318for translational motion seals, 316for valve-stem seals, 320-323

Metal gaskets, 370-378aluminum foil, 375-377copper bead, 372copper ridge, 373copper shear, 371flare seal, 374

knife-edge seals, 373soft metal ring, 370, 374reweldable flanges, 378

Molecular drag pumps, 205-214analysis of performance, 205-210performance of various designs, 211-

214

Molecular mean free path, 5, 13-15, 21,

23

derived in terms of molecular diam-eter, 13

relationship to viscosity of a gas, 21

role in determining character of gasflow, ''2, 23

Molecular tu.bine pump, 214-218Molecular weights, 2, 10

of various common gases, 2

Molecules, diameters of, 13-21

diatomic, 11

elastic sphere model of, 5-15ionization of, by electron impact,

90-94

masses of, 10

Maxwell-Boltzmann velocity distri-

bution of, 8-11

mean free path of, 5, 13-15, 21, 23

monatomic, 11

456 SUBJECT INDEX

Molecules, polyatomic,

velocities of, 7-1

1

Motion seals, 313-318

11

Nozzles, converging-diverging type,

219

critical pressure, 220

diffusion pump, 227-230, 265-267

isontropic flow, 219-221

mass flow through, 221

velocity of gas flow through, 220

O rings, 307-313, 315

Oil ejector pumps, 257

Omegatron, 143-152

argon vs. helium leak detection

sensitivity, 149

partial pressure analyzer, 150-152


Orifices, calibrated, 278-282

critical gas flow through, 278-281

critical pressure for, 278, 280

mass gas flow through, 278,

280-282

standardized dimensions of, 280

subcritical gas flow through, 280,

282

Outgassing, bakeout procedures and

effectiveness, 365-370

effect on ionization gauge readings,

101

effect on pumpdown time, 351-358

quantity of gas released by metal

surfaces, 363-369

rate of gas evolution at roomtemperature, 365

Partial pressure gauges (see Mass

spectrometer vacuum analyzers)

Penning discharge gauge (PIG), 113-

118

erratic behavior of, 114-116

principles of operation, 113

useful pressure range, 114-118

Pipe sizes, selection of, for viscous flow,

30

Pirani pressure gauge {see Thermalconductivity pressure gauges)

Poiseuille's law, 26-30, 34-36

Pressure, gas, definition of, 1

dependence, on kinetic energy of

molecules, 5-8

on mass of gas, 2

on temperature, 1-3

on volume, 1-3

direction effects of nonisotropic

distribution, 129-131, 412-416

gauge pressure, definition, 63

kinetic theory of, 5-8

measurement, ambiguities at low

pressure, 124

partial, 63, 133, 250, 434

permanent, 18, 63

vapor pressure, 17, 71, 331, 409

Pressure drop formula for viscous flow,

30

Pressure gauges, 63-128

caUbration methods for, 124-128

Dubrovin, 68

ionization, 90-123

Alphatron, 122

cold-cathode types, 113-122

Haefer inverted magnetron,

118-120

Penning discharge, 113-118

Redhead magnetron, 120-122

hot-cathode types, 90-113

Klopfer magnetically collimated

electron beam gauge, 111-113

Lafferty hot-cathode magne-

tron, 107-111

{See also Bayard-Alpert ioniza-

tion gauge; Ionization gauge,

conventionalhot-cathode type)

Knudsen radiometer type, 123

McLeod, 69-78

manometer, diaphragm, 65-68

liquid, 63-65

partial {see Mass spectrometer vac-

uum analyzers)

thermal conductivity, 78-90

Pirani type {see Thermal con-

ductivity pressure gauges)

thermocouple type (see Thermal

conductivity pressure gauges)

Pumpdown factor for mechanical

pumDS, 349-351

Pumpdown time, 348-361

effect of outgassing, 351-358

factor F for mechanical pumps,

349-351

SUBJECT INDEX 457

Pumpdown time, formula for roughingdown system, 348-354

functional dependence at low pres-

sure, 354-358graphically determined from through-

put and load curves, 354-356system factors, 352-354

Pumping speed, deflnitions, for iso-

tropic molecular distribution,

23-25, 58, 274-277for nonisotropic molecular distri-

bution, 416-418methods of measurement, 291-302performance, adsorption pumps, 347

cryogenic pumps, 411-421diffusion pumps, 249-254Evapor-ion pumps, 390getter-ion pumps, 391-393mechanical booster (blower)

pumps, 189, 193-202mechanical oil-sealed pumps, 171-

177

molecular drag pumps, 212molecular turbine pumps, 218steam ejectors, 223-227Vac Ion pumps, 395vacuum systems, 26, 277, 360

resultant for pump combined with aconductance, 25, 58

units of, 24

Pumping speed factor for diffusion

pumps, 253

Pumps, vacuum, absorption, 398-400cryogenic, 408-434diffusion, 227-272diffusion booster, 257Evapor-ion, 388-391

getter-ion, 385-398mechanical booster (blower), 185-

205

mechanical oil-sealed rotary, 169-

185

molecular drag, 205-214

molecular turbine, 214-218oil vapor ejector, 257

steam ejector, 219-227Vac Ion, 393-398

Reynolds number, 31

Seals, elastomer, 307-318O-ring gaskets, 307-313, 315

Seals, elastomer, O-ring gaskets, coup-lings, quick connect, 309

groove designs for, 307-309guard ring with double seal, 309

properties of various elastomers,311-313

square-cross-section gaskets, 309Solvents, properties of, 304Sorption processes, absorption, 364

absorption pumping, 398-400adsorption, 364adsorption pumping, 428-430chemisorption, 364cryosorption, 421-424cryotrapping, 424-428desorption, 365-370

Specific heats of gases, 1

1

Standard conditions of temperatureand pressure, 3

Steam ejector pumps, 219-227backstreaming of water vapor, 227components of, 219

isentropic expansion and compres-sion, 219-221, 223

principles of operation, 219-223pumping speed of multistate units,

223-227stalling condition, 226steam consumption, 227

Stefan-Boltzmann law, 81

System factors for determining pump-down time, 352-354

Temperature, absolute scales, 2, 4

absolute zero of, 2

centigrade scale, 2, 4

dependence, of gas pressure on, 1-3

of vapor pressure at low tempera-ture, 409

Fahrenheit scale, 4

Kelvin scale, 2, 4

Rankine scale, 4

Thermal conductivity of gases, 78

free molecul' . conduction at low

pressure,, 78

for rarefied gases, 78

Thermal conductivity pressure gauges,

78-90

basic principles, 78-83

accommodation coefficient, 79-81

emissivity of gauge elements, 81

458 SUBJECT INDEX

Thermal conductivity pressure gauges,

basic principles, energy transfer

from heated element, 78

free molecular thermal conduction,

78

Stefan-Boltzmann law, 81

thermal conduction loss along

filament, 81-83

thermal conductivity of rarefied

gases, 78

Pirani gauge, 86-90

control circuits for, alternative, 87

pressure range of, 87

principles of operation of, 86

response curve vs. pressure, 89-91

thermistor type of, 87-91

thermocouple gauge, 83-86

compensation for ambient tem-

perature, 85

matched tubes, 84

multi-station control circuit, 85

principles of operation, 83

response curves for several gases, 83

Thermocouple gauge (see Thermalconductivity pressure gauges)

Throughput, curves for mechanical

vacuum pumps, 175-178

definition, 24, 57, 175

relation to mass flow, 24

system pumpdown time based upon,

354-356

Titanium, getter pumping by de-

position of, 401-408

vapor pressure vs. temperature, 405Transition pressure in gas flow, 39-41

Trap{s), absorption, 341-348, 398-400

absorption materials, 341-343

bakeout cycle, 342-345, 347

capacity for gases and vapors,

344-348

copper foil type, 342-344

stay-down times for, 342

effectiveness as a pump, 347,

398-400

liquid-nitrogen-cooled, 347

tray design, 344

ultimate pressure, 344-347

vapor, 328-341

automatic liquid nitrogen level

control, 337

conductance of baffle systems,

333 337

Traps, vapor, creep barrier for organic

fluids, 332, 367

exhaust baffles for diffusion pumps,340

forevacuum, 340-342

functions of, 328-330

inlet baffles for diffusion pumps,

240, 252, 329-339

mechanically refrigerated, 338-

340

performance of diffusion pumpwith, 240, 252, 335-337

surface migration of organic fluids,

332

temperatures for various applica-

tions, 244, 246, 329-331

thimble traps, 330-332

Turbulent flow, 31-34

occurrence in vacuum systems, 32-

34

Reynolds number, 31

Two-region vacuum systems, 382-385

Ultrahigh vacuum techniques, 363-435

absorption pumping, 398-400

bakeable valves, 378-382

bakeout procedures, 364-370

cryogenic pumping, 408-434

getter-ion pumps, 385-398

liquid-helium-cooled thimble trap,

400metal gaskets, 370-378

reactive metal deposition, 401—408

surface phenomena, dominance of,

363-370

system design, 434

two-region vacuum systems, 382-385

Universal gas constant, 3

value of, in various systems of units,

4

Vac Ion pump, 393-398

Vacuum components, criteria for selec-

tion, 358-361

diffusion pumps, 360

mechanical pumps, 358-360

pressure gauges, 361

valves, 361

Vacuum gauges (see Pressure gauges)

SUBJECT INDEX459

Vacuum pumps, mechanical, 169-218

vapor-jet, 219-272Vacuum vessels, 303-307

cleaning of interior surfaces, 304

external pressure requirement, 303

finish of interior surfaces, 304

leak hunting, 161-167, 307

materials of construction, 303

pumping ports, criterion for, 306

solvents, properties of, 304

virtual leaks, avoidance of, 306

welding specifications, 305

Valves, vacuum, 318-328, 378-382

bakeable, 378-382functions of, in vacuum systems,

319

gate, 323-328

butterfly type, 324-326disk typos, 325, 327

modified plumbing types, 323sliding plate typos, 324-326

globe, 318-323

bellows sealed types, 318, 320-

323

diaphragm sealed type, 320

elastomer sealed types, 318

needle type, for control of gas

flow, 325, 328

Van dor Waals' equation of state, 15-18

change of phase (liquid, vapor andgas), 17

critical pressure, temperature andvolume, 16

permanent gas, definition of, 18

triple point, 16

\'an dor Waals' constants, 17

Vapor baffles and traps, 328-341

Vapor pressure, of gases at lowtemperatures, 409

of water vs. temperature, 331

Velocities of gas molecules, 7-11average, 9, li

Maxwell-Boltzmann distribution of,

most probable, 9, 10root mean square, 7, 9, nsound velocity, relation to, 11

Viscous fiow, 14, 23, 26-30, 34-36correction to Poiseuille's law, 34-36drag, coefficient of, 35Poiseuille's law, 26-30, 34-36pressure drop formula, 30selection of pipe sizes for, 30slip, coefficient of, 34

Volumetric efficiency of mechanicalvacuum pumps, 172

Water \'apor, contamination of oil-

sealod mechanical pumps, 177-179dominant component gas following

pumpdown, 133, 330-332, 364effectiveness of thimble trap in

pumping, 330-332elimination from oil-sealed mechan-

ical pumps (see Mechanicalvacuum pumps)

steam ejectors, attainable watervapor pressure, 223-225

backstreaming in, 227

vapor pressure as function of tem-perature, 331

Zeolite, absorbent material for vaportraps, at room temperature, 343-

347

refrigerated, 347, 398-400

effectiveness in absorbing various

gases, 344-347, 399

quantity of vapor and gas evolved

during bakeout, 345

t- (continued from front flap)

Other special features include a

thorough treatment of the ultrahigh vac-

uum development, and a discussion of

methods of pumping by the use of vapor

deposition of active metals.

Here is unique, comprehensive, and

authoritative coverage of vacuum sys-

tems, their components, operation, and

design—a book which enables the reader

to solve practical problems associated

Vifith every aspect of vacuum technology.

About the AuthorSince 1935, Dr. C. M. Van Atta has

been involved with physical apparatus

requiring larger than normal vacuumsystems. Since 1937, he has acted as

consultant in vacuum technology to in-

dustrial firms and has been actively en-

gaged in the new-product development

effort of the Kinney Vacuum Division of

The NewYorkAir Brake Company.His experience includes teaching and

research at MIT; applied physics re-

search at the Naval Ordnance Labora-

tory, Washington, D.C.; research and de-

velopment on electromagnetic separa-

tion ofthe isotopes of uranium. University

of California, Lawrence Radiation Labora-

tory; Chairman of the Division of the

Physical Sciences and Mathematics and

Supervisor of Physics Research, Uni-

versity of Southern California; develop-

ment of high-current particle accelera-

tors and controlled thermonuclear

research. University of California,

Lawrence Radiation Laboratory, Berke-

ley and Livermore, California.

' A comprehensive guide to the

modern theories, instruments, and uses of

high vacuum

FUNDAMENTALS OFVACUUM SCIENCEAND TECHNOLOGY

By GERHARD LEWIN

Plasma Physics Laboratory, Princeton University

248 pages. 6x9. 104 illustrations

Designed for the man whose work requires a

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- unique reference fully explains pertinent kinetic

" theory equations . . . gas flow . . . surface effects ...

punnping processes . . .measurements . . . com-

ponents ... and design calculations.

The book critically evaluates all basic vacuum

systems — helps you select the most efficient

equipment for your specif ic purposes— and guides

you in the actual design of special equipment.

Filled with facts, figures, tables, charts, and

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McGRAWHILL BOOK COMPANY330 West 42nd street New York, New York 10036

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