VACUUM MICROBALANCE TECHNIQUES
Volume 2 Washington,D.C., Conference-1961
Volume 5 Princeton Conference-1965 Edited by Klaus H. Behrndt
Volume 6 Newport Beach Conference-1966
Edited by A. W. Czanderna
Volume 7 Eindhoven Conference-1968
Edited by C. H. Massen and H. J . van Beckum
Volume 8 Wakefield Conference-1969 Edited by A. W. Czanderna
VACUUM MICROBALANCE TECHNIQUES VOLUME 8
Proceedings of the Wakefield Conference June 12-13. 1969
Edited by A. W.Czanderna
<:f? PLENUM PRESS • NEW YORK-LONDON • 1971
Library of Congress Catalog Card Number 61-8595
ISBN 978-1-4757-0135-7 ISBN 978-1-4757-0133-3 (eBook) DOl 10.1007/978-1-4757-0133-3
© 1971 Plenum Press, New York Soft cover reprint of the hardcover 1st edition 1971
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United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Corporation, Ltd.
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No part of this publication may be reproduced in any form without written permission from the publisher.
Introduction
This volume contains the proceedings of the Eighth Conference on Vacuum Microbalance Techniques held at Wakefield, Massachusetts on June 12 and 13, 1969. The tenth anniversary of the first confer­ ence will be registered as this volume passes through the typeset­ ting and proofreading stages. The eight volumes that have spawned from this continuing series of conferences now contain a total of 125 papers. Thus, these volumes serve as a major repository of the world's literature on vacuum microbalance techniques. The Ninth and Tenth Conferences will be held in West Germany in June 1970 and in Texas in 1971.
Each of the eight meetings has served as a forum where new developments in this rapidly advancing fie ld can be presented and discussed constructively within a conference atmosphere of cordial informality. The interaction of the participants at the conferences has led to the first treatise on ultra mlcrogravtmetry;' edited by S. P. Wolsky and E. J. Zdanuk, with most of the fourteen chapters written by steady contributors to the volumes on Vacuum Micro­ balance Techniques. The number of research investigations and published works in which a vacuum microbalance is utilized con­ tinues to expand r apldly.f This is a direct result of several types of automatic recording balances that are now available commercial­ ly.3
The Eighth Conference was held to bring together again re­ search scientists and engineers who exploit the measurement of mass as a means of studying physical and chemical phenomena.
IS. P. Wolsky and E. J. Zda nuk, Ultra Mic ro Weight Determi nat ion in Controlled En­ vironments. Intersci ence, New York, 1969.
2 A. W. Czanderna, "Utramicrobalance Review. " in: Wolsky and Zdanuk , op. cit••p. 7.
3 D. Fox and M. Katz. "The Availability of Commerci a l Microbalances and Quar tz Crystal Oscillators, " in: Wolsky and Zdanuk , op. cit• •p. 465.
v
vi INTRODUCTION
Support for the conference was provided by the Army Research Of­ fice - Durham.! Clarkson College of Technology, P, R. Mallory and Co., Inc., and the Cahn Division of Ventron Instruments. Over 1500 users of microbalances were contacted by mail announcing the con­ ference. In addition, the meeting was announced in the Journal of Vacuum Science and Technology.! Chemical and Engineering News,6 and Research/Development. 7
There were forty-six participants at the conference represent­ ing Germany, Great Britain, and all regions of the United States. Roughly, two-thirds of the attendees from the United States came from the northeast, while the four scientists from Western Europe provided an international character to the meeting. The attendees were welcomed by the Conference Chairman, A. W. Czanderna, who provided a brief historical sketch of the conferences and indicated some of the benefits derived by the participants of previous confer­ ences. In the technical program which followed, J. W. Whalen, Th, Gast, E. J. Zdanuk, and Pat Gaskins served successively as moder­ ators for the four sessions. The first session was opened with an invited paper by E. A. Gulbransen and was followed by two contri­ buted papers pertaining to oxidation. An invited paper was presented in the second session by E. Robens on the genera] problem of the mass defect produced by thermal gradients. In the third session, W. H. King presented an invited paper on applications of the crys­ tal oscillator microbalance. Of the nineteen papers presented, seventeen are included in the proceedings and an eighteenth was accepted for publication after the conference because of its rele­ vance to the other papers in the volume. Discussion questions and answers that followed each presentation are incorporated at the end of each paper. The cooperation of the participants and authors, which made it possible to document this valuable material, is grate­ fully acknowledged. The format of the volume, abbreviations, ref­ erences, etc., conform to that of previous volumes as outlined by the publisher, Plenum Press. In addition, the editor thanks all the authors for their cooperation in using the definitions developed for
4Gram DA - ARO-D-31-124- G1l57 to Clarkson Coll ege of Technology with A. VI. Czanderna as Principal Investigator.
5 Announcements, J . Vac . Sci. Tech. 6 : 277. 1969.
6Chem . Eng. News, Feb. 24. 1969, p. 96; May 19, 1969, p. 46. 7 Research /Development. May 1969. p. 46; June 1969, p. 40.
INTRODUCTION vii
microbalances 8 and the AVS standard symbols for vacuum sys­ tems.i
It is a pleasure to thank all the people who contributed to the success of the Eighth Conference. Two complete mailings of the "Call for Papers n were handled by Pat Gaskins and Colin Williams and the staff of the Cahn Division of the Ventron Instruments Com­ pany. The papers for the technical program were selected by S. P. Wolsky and A. W. Czanderna on the basis of abstracts submitted. Local arrangements for the meeting at the Colonial Statler Hilton were made by S. P. Wolsky, E. J. Zdanuk, and Mrs. M. Dor andi. The participants enjoyed hospitality provided by the Cahn, Rodder, Sartorius, and Worden Instrument Companies. Considerable typing and secretarial contributions were made by Mrs. A. Hollister from the planning stages to the publication of this volume. The painstak­ ing task of copyediting the manuscripts and proofreading the galleys fell on Mrs. A. Czanderna and her assistance is gratefully acknowl­ edged. Finally, it is my pleasure to thank Dr. H. M. Davis of the ARO-Durham, Dr . E . E . Anderson, Chairman of Physics at Clark­ son College of Technology, and Dr. S. P, Wolsky, Director of Re­ search at P, R. Mallory and Son, Inc., whose administrative deci- s ions and / or expertise led to direct financial support that made it possible to hold the E'ighth Conference on Vacuum Microbalance Techniques.
Alvin W. Czanderna Potsdam, New York November 1969
8 Czanderna , op. cit. •p. 10-11. These definitions evolved from an. original se t suggested by T. N. Rhodin and were an outgro wth of interaction by S. P. Wolsky. R. L. Schwoebel, E. 1. Zdanuk, and A. W. Czanderna. They are recommended for use by all workers in the field .
9Graphic Symbols in Vacuu m Technology AVS Standard 7.1-1 966. J. Vac. Sci. Tech. 4 : 139-142.1967.
Contents
E. A. Gulbransen
The Simultaneous Use of Mass Spectrometer and Micro­ balance Techniques for the Carbon - Oxygen System . .. . . . . . . . . . . . • . • . . . . . . . . . • . • 17
J . Graham Br own, John Dollimore , Clive M. Freedman, and Brian H. Harrison
A System for the Determination of Oxidation- Reduction Kinetics in Nonstoichiometr ic Metal Oxides . . • • . 29
I. Bransky and N. M. Ta llan
An Automated Bakeable Quartz Fiber Vacuum Ultra- microbalance .. .. . ....... ....... •.••• 43
J. Rodder
Stanley E. Fink and Robert P. Merrill
The Effect of Thermal Gas Motion on Microbalance Measur ements (Invited) ..•.........••...• 73
E. Robens
Gravimetric Adsorption Studies of Hydrogen on Granular Metal Surfaces Using a Vacuum Microbalance 97
D. A. Cadenhead and N. J. Wagner
Gravimetric Measurement of the Molecular Area of Some Adsorbed Gases .•..•.....••...•••• 111
E. Robens, G. Sandstede , and G. Walter
ix
x
CONTENTS
121
Momentum Artifacts in the Gravimetric Measurement of 131 Fast Desorption .....•..•.......•.....•
Robert P. Merrill, Charles R. Arnold, and Andrew J. Robell
On the Development of Electromagnetic Balances in Recent Years .....•..•...•.....•••.. 0 • 141
Tho Gast
Pressure of Light Used as Restoring Force on a Micro- balance .••. 0 0 0 •• 0 0 0 • 0 • 0 • 0 • 0 0 • 0 • 0 0 0 0 0 147
Karl P. Zinnow and Jens Po Dybwad
Vacuum Microbalance Apparatus for Rapid Determination of Low-Temperature Vaporization Rates . 0 • • • • • 155
J, Gordon Davy
Wireless Temperature Measurement of a Sample in Vacuum. 0 0 0 • 0 0 0 0 • 0 0 0 0 0 • 0 0 • • • • • • • • • • • 173
G. Richard Blair
Applications of the Quartz Crystal Resonator (Invited) 183 Wo H. King, Jr.
Thermal Degradation of Piperazine Copolyamides . . . . • 201 Stephen D. Bruck and Ashok Thadani
A Thermal Analysis System for Radioactive Materials. . 215 W. J. Kerrigan, J. S. Byrd, and P. Do Holloway
Thermal Degradation of an Anhydride-Cured Epoxy Resin by Laser Heating 0 0 •••••• 0 • 0 • 0 0 0 0 0 • 229
A. So Vlastaras
Laboratory P. O. Box 1663 Los Alamos, New Mexico 87544
Warren A. Anderson Sylvania Ltg. Center 100 Endicott Street Danvers, Massachusetts 01923
Klaus Behrndt Granville-Phillips Co. 5675 E. Arapahoe Street Boulder, Colorado 80302
Joseph R. Biegen Department of Physics Clarkson College of Technology Potsdam, New York 13676
G. Richard Blair Hughes Aircraft Company Electron Dynamics Division Torrance, California 90509
1. Bransky Wright-Patterson AFB ARL(ARZ) Bldg. 450 Ohio 45433
S. D. Bruck National Heart Institute National Institute of Health Bethesda, Maryland 20014
xi
D. A. Cadenhead Department of Chemistry SUNY at Buffalo Buffalo, New York 14214
Peter G. Chamy General Electric Company 6901 Elmwood Avenue Materials Laboratory - 10-779 Philadelphia, Pennsylvania 19142
Edward G. Clarke, Jr. Department of Physics Clarkson College of Technology Potsdam, New York 13676
A. W. Czanderna Department of Physics Clarkson College of Technology Potsdam, New York 13676
J. Dollimore Dept. of Pure and Applied
Physics University of Salford Salford 5, Lancashire,England
Jens Peter Dybwad Space Physics Laboratory Air Force Cambridge Research
Laboratories Bedford, Massachusetts 01730
Owen Fiet TRW Systems 1 Space Park Redondo Beach, California 90278
xii
Division 618 Glennan Building Case Western Reserve Univer-
sity Cleveland, Ohio 44106
Pat Gaskins, Consultant 11811 Marble Arch Drive Santa Ana, California 92705
Theodor R. Gast Technische Universltat of Berlin Kurfiirstendamm 195/196 1 Berlin 15, Germany
Leonard J. Gordon MIT Lincoln Laboratory Space Communications D-013 Lexington, Massachusetts 02173
George P. Gray Systems Research Laboratories 7001 Indian Ripple Road Dayton, Ohio 45440
Earl A. Gulbransen Westinghouse Research
Laboratories Pittsburgh, Pennsylvania 15235
Eugene A. Harlacher Continental Oil Company Ponca City, Oklahoma 74601
M. H. Houston Massachusetts lust. of
Technology Cambridge, Massachusetts
Donald W. Kemp American Cyanamid 1937 Main Street Stamford, Connecticut
W. J. Kerrigan Savannah River Laboratory E. 1. du Pont de Nemours and
Co. Aiken, South Carolina 29801
W. H. King, Jr. Esso Research and Engineering
Co. P. O. Box 121 Linden, New Jersey 07036
Morton Lieberman Sandia Corporation Sandia Base Albuquerque, New Mexico 87115
Thomas D. McGee Iowa State University Ames, Iowa 50010
Robert P. Merrill Dept. of Chemical Engineering University of California Berkeley, California 94720
Donald E. Meyer Texas Instruments p. O. Box 5012 MS-913 Dallas, Texas 75238
Edward B. Murphy MIT Lincoln Laboratory Box 73 Lexington, Massachusetts 02173
William Noakes Ventron Instruments Ltd. 27 Essex Road Dartford, Kent , England
CONFERE NCE PARTICI PA ~T S xii i
Ray D. Worden Worden Quartz Products 6121 Hillcroft Houston, Texas 77036
Colin J. Williams Cahn Div, - Ventron Instruments
Co. 7fiOO Jefferson Street Paramount, California 90723
James W. Whalen Department of Chemistry University of Texas at El Paso El Paso, Texas
Jerry Weil Cahn Dlv, - Ventron Instruments
Co. 7500 Jeffers on Street Paramount , California 90723
Nor man Wagner Department of Chemistry SUNY at Buffalo Buffalo, New York 14214
J. Redder Rodder Instrument Company 775 Sunshine Dr ive Los Altos , California
Walter Tripp Systems Research Laboratory 7001 Indian Ripple Road Dayton, Ohio 45440
Erich Robens Battelle-Institut e . V. 6 Frankfurt /Main - 90 Wiesbadener Strasse, Germany
Edward Zdanuk A. S. Vlastaras r . R. Mall or y and Company , General Electric Com pany Inc. 6901 Elmwood Avenue N. W. Ind. Park Philadelphia, Penns ylvania 19142 Burlington,Massachusetts 01801
Peter H. Price AC Electronics Division General Motors Corporation Wakefield, Massachusetts 01880
James S. Radawski Calm Div. - Ventron Inst, Corp. 7500 Jefferson Street Paramount, California 90723
Daniel A. Rankin General Oceanology 27 Moulton Street Cambridge, Massachusetts 02138
Karl P. Zinnow Space Physics Laboratory Air Force Cam br idge Research
Laboratories Bedford, Massachusetts 01730
Earl A. Gulbransen
ABSTRACT
The use of sensitive microbalances enclosed in vacuum and reac­ tion systems is at least 55 years old. Since World War II, use of the vacuum microbalance method has grown rapidly and extended into many new research areas. In the area of high-temperature oxidation, it is essential to use thermochemical analysis and ki­ netic theory in the planning and interpretation of microbalance studies. Studies on the oxidat ion of silicon, chromium, and molyb­ denum are discuss ed. It is concluded that detailed thermochemical analyses must be used in planning the work and in interpreting the experimental data.
INTRODUCTION
Many physical and chemical reactions occur in high-vacuum and controlled-atmosphere reaction systems at high temperature. A major problem is to minimize the extraneous reactions so the re­ action of interest can be studied. Since most materials are capable of reaction with gases in the reaction environment, a careful selec­ tion must be made of furnace tubes, specimen support systems, re­ active gases, and the preliminary treatments of the sample and reaction system. If the rate of extraneous reactions is minimized, then we can take the next step to plan the experimental program. Finally, we have the problem of interpreting the experimental re­ sults so that meaningful conclusions can be obtained.
1
2 E. A. GULBRANSEN
We have found thermochemical analysis to be a useful disci­ pline at all stages in vacuum microbalance studies. The application of thermochemical data can be simplified through the use of dia­ grams. LogPMO vs logpoz and 10gPMO vs r/r diagrams arex x very useful in high-temperature oxidation. Here PMO refers to
x the several elemental and oxide vapor species, For silicon and chromium, these include Si, Siz, Si3, SiO, SiOz, Cr, CrO, CrOz, and Cr03' These diagrams will be applied to three problems: (1) the use of silica and mullite furnace tubes and silica support wires in vacuum microbalance systems, (2) the interpretation of oxidation studies on silicon, and (3) the interpretation of oxidation studies on chromium.
Before considering these problems, we must consider the various processes which can occur in the oxidation of materials over a wide range of temperature and pressure,
TYPES OF OXIDATION PROCESSES
Kinetic studies on the oxidation of carbon,' molybdenum.! and tungsten' >! have shown that there are at least six different stages of reaction and four types of rate-controlling oxidation processes. The six stages are as follows: (1) At low temperatures, where ad­ herent oxide scale is formed, a Wagner-type diffusion of metal or oxygen through the oxide film is present. (2) At higher tempera­ tures, although a localized breakdown of the oxide occurs, a Wagner­ type diffusion of metal or oxygen through the oxide film is rate controlling. (3) At higher temperatures, where both oxide volatility and oxide film-formation occur, either a Wagner-type diffusion pro­ cess or a chemical-type oxidation process at the metal- oxide in­ terface is rate controlling, (4) At higher temperatures, where the oxide films volatilize, a chemical-type oxidation process occurs at the metal interface. (5) At high temperatures, where a dense bar­ rier layer of volatilized oxide gases or condensed oxide crystals form, a transport of oxygen gas through the barrier layer occurs. (6) At high temperatures, where break-up of metal in the solid or liquid state occurs, transport of oxygen gas through barrier layer is rate controlling.
For silicon and chromium where relatively high pressures of volatile species develop at the element- oxide interface, an addi­ tional type of oxidation process occurs, i.e., rapid transport of
HIGH-TEMPERATURE OXIDATION OF MATERIALS 3
vapor species through a porous oxide film or ruptured oxide film. If the oxide film or scale is molten, rapid transfer of oxygen oc­ curs by means of convection currents in the liquid oxide. As a fur­ ther complication, droplets of oxide can fall off the specimen.
THERMOCHEMICAL PRINCIPLES
aA + f3 B ~ yC + oD
the mass action constant K is the ratio of the activities of each mole of the reaction products to those for the reactants
(1)
(2)
For reaction (1) to occur , it must be thermochemically favorable. The change in the Gibbs' free energy function boG used to express chemical reactivity, is
boG = boH - TboS, (3)
where boH is the change in enthalpy, boS is the change in entropy, and T is the absolute temperature of the reaction. When boG < 0, a chem ical reaction is favored; at equilibrium, boG = 0; and when boG > 0, the reverse reaction is favored.
The change in free energy of the reaction is connected with the mass action constant by the equation
boG = boGo + RT InK,
where boGo is the free energy of reaction with each reactant and product species in a standard state.
At equilibrium , K = Kp' where Kp is the equilibrium con­ stant, and
The values of boGo and log Kp for a reaction are obtained fr om a
(4)
(5)
4 E. A. GULBRANSEN
summation of the corresponding values for all of the different re­ actants and products. For most purposes, it is convenient to de­ velop log Kp values. This makes the determination of equilibrium activities and pressures possible by using equation (2). The dia­ grams presented here were constructed on the basis of such calcu­ lations.
In recent years, a major stimulus has occurred in the compila­ tion of thermochemical data in the form of tables by the use of com­ puter techniques. Free energy, enthalpy, and equilibrium constant data have been collected in the form of tables for many compounds and molecular species over a wide range of temperatures, e.g., the JANAF Tables. 5
THERMOCHEMICAL DATA
Tables 1 and 2 show the thermochemical data in units of logKp over the temperature range for the several equilibria in the sili­ con- oxygen system, mullite, and the chromium- oxygen systems.f Here, (s), (l), and (g) refer to the solid, liquid, and gaseous phases. Reactions of both the condensed and volatile oxide species are in­ cluded. To simplify the interpretation of the complex equilibria and to show the relationships between the equilibrium pressures of the volatile species over the one or more condensed oxide and ele­ mental phases and the oxygen pressure, log PMO VS log Po 2 dia-x grams prepared at a series of temperatures are used. These dia- grams were first used extensively by Kellogg" and independently by Jansson and Gulbransen. 8
Plots of logP Mox vs, logPo2 at 1400 K for the Si- 0 and Cr - 0 systems are shown in Figs. 1 and 2. Similar diagrams were prepared for the other temperatures given in Tables I and II to give a complete thermochemical description of the Si - 0 and Cr - 0 sys­ tems. High equilibrium pressures of volatile species occur at the outer oxide - oxygen interface for the Cr - 0 system and at the in­ ner element - oxide interface for both the Si - 0 and Cr - 0 systems.
To summarize the thermochemical data given in log p MOx vs, logPo2 diagrams, logP Mox vs lIT diagrams are used. Here, logP MOx is the equilibrium element and oxide pressure at the ele­ ment- oxide and oxide - oxygen interface or at any oxygen pres­ sure corresponding to a given H2/H20 mixture.
T a b
C ?: J
tr t o :::: §Z > -l o Z o 'T J S; > -l
tT l i:8 ;> r­ C
/)
o: :J S; Z gj Z
HIGH-TEMPERA TURE OXIDATION OF MATERIALS 7
Log PH /PH°2 2 12 10 4 2 - 2 -4 -6 -S
5 1111 Si0 2
- 24 -
- 28
- 40 - 36 - 32 - 28 - 24 -20 - 16 -1 2 -8 -4 Log Po aim
2
Fig . 1- The rmoche mic al dia gram fo r the Si - °system, log PSiO x
vs log P O 2 '
1400 K .
Cr tq)
-16 -14 - 12 - 10 Log po2atm
Fig. 2. Thermochem ical diagram for the Cr - ° syste m, logPCrO x
vs log P0 2
M. P. Si 141ZOC
1.0 0.950.9 0.850.8
!x 103 T
Fig. 3. Plot of log PSiOx vs. liT for the volatile oxides at the Si02(s, l) - O2 interface at 1 atm.
We now consider application of the thermochemical data to the use of quartz and mullite as furnace tubes, to quartz as a spec­ imen supporting material, and to the oxidation of silicon and chro­ mium.
QUARTZ AND MULLITE AS FURNACE TUBE AND SPECIMEN SUPPORT MATERIALS
A plot of logPSiOx vs liT is shown in Fig. 3 for the equilib­ rium vapor species over Si02(s) for logP0
2 ::= O. A horizontal dashed
line is drawn at logP siO ::= -1). Our experience has shown thatx volatility becomes appreciable at this value. At 1400 K (1127 C) and logp0
2 ::= 0, logPSi0
similar diagram for logP0 2
::= -12, logp Si0 2
::= -13.15, and logPSiO ::=
-10.50. Thus, only a small loss of SiO(g) would occur in a high­ quality vacuum system at temperatures up to 1400 K.
In a hydrogen-reducing atmosphere at 1400 K having logPH/PH20 ::= 4, logPSiO ::= -u.1, and, therefore, Si02(s) would not be reduced but appreciable losses of Si and °would occur and
HIGH-TEMPERA TURE OXIDA l ION OF MATERIALS 9
the specimen would be contaminated with Si and 0. Quartz cannot be used at 1400 K if the ratio of HdH20 is high.
Mullite, 3Al20 3 . 2Si02, is often used at temperatures above 1400 K to replace quartz furnace tubes. Thermochemical data'' show mullite to be only slightly more stable than the component oxides 3Al203(s) and 2Si02(s). At 1400 K, logKp = -0.359 for the reaction
(6)
So, Si02 in mullite behaves about the same, thermochemically, as quartz. Hence, it is concluded that both quartz and mullite hang­ down tubes can cause contamination problems under vacuum and reducing conditions at 1400 K.
It is suggested that pure alumina, zirconia, hafnia, or thoria be used as furnace tubes for temperatures of 1400 K and higher. Thermochemically, hafnia and thoria appear to have best proper­ ties for high-temperature furnace tubes.
OXIDATION OF SILICON
a. Thermochemical Predictions
The diagram log p sio, VS log P02 is plotted in Fig. 1 for the Si-O system at 1400 K. Here, logP SiO = -4.2, so SiO(g) pres­ sures develop at the Si(s)-Si02(s) interface. A logpsiO and logp Si VS 1 IT diagram is shown in Fig. 4 for the Si (s) - Si02(s) interface together with values for log p Crand log PCrO at the Cr (s)­ Cr203 interface. The Si - ° system is unusual with the develop­ ment of high gas pressures at internal interfaces.
It is seen in Fig. 1 that for logPo2 = 0, logPsioz and logPsio are -13.15 and -16.50. At 1400 K, little direct volatility occurs. For log p-, = -12, 10gPSiO and logPS iO are -13.15 and -10.50.
2 z Thus, even under high-vacuum conditions, little direct volatility occurs.
High SiO(g) pressures at the element- oxide interface can lead to a rapid transfer of SiO (g) through the porous film consum­ ing Si02(s) and to a rupturing of the film when logps;o > logpoz.
10 E. A. GULBRANSEN
1.2 1.1
700 gOO 900 1000 1100 1200 1300 1S00 1700 I I II ' 1
I I M.P. cr
2148°K
Fig. 4. The logPSiO' log PSi' logpCro and log PCrOvs l iT at the element - oxide interface.
b. Experimental Studies
The oxidation behavior of high-purity silicon has been studied extensively under conditions where protective oxides are formed. Wagner'' was the first to recognize the nature of the transition from active to passive oxidation for the oxidation of silicon in inert-gas atmospheres containing low partial pressures of oxygen. Wagner's analysis assumed that oxygen diffuses through a barrier layer of volatilized SiO(g) to the silicon interface and that SiO(g) diffuses away from the surface into the surrounding oxygen gas. The maximum oxygen pressure for which a bare silicon sur­ face could exist was given by the equation
1
)2 P SiO (eq),
where PSiO (eq) is the equilibrium pressure of SiO(g) at the Si(s)­ Si02(s) interface and DSiO /D 02 is the ratio of diffusion constants for SiO(g) and 02 in the boundary layer and is assigned the value 0.64. Substituting, we have
P 02(max) = O.4PSiO (eq)
or
11
To ve To verifyWagner 's theoretical predictions, Gulbransen, Andrew and Brassartl" studied the oxidation of high-purity silicon under flow conditions and at oxygen pressures of 9 . 10-3, 4 . 10-2, and 10-1 torr. At 1100 C and 10-1 torr , a slow weight gain of 1.1 3 .1016
atoms of Si reacting per cm2-sec was obser ved. At 1200 C and 10-1 torr, a rapid weight loss of 3 .51 • 1018 atoms of Si reacting per cm2-sec was found. Rapid weight losses occurred in all of the ex­ periments at 9 . 10-3 tor r and 4 . 10-2 torr and for the 1300 C ex­ periment at 10- 1 torr. The rates of oxidation were nearly independ­ ent of temperature and were nearly a linear function of gas pres­ sure or gas flow.
In Fig. 5 there is a plot of log PS iO vs l/T for SiO(g) pres­ sures at the Si (s) - Si02(s) interface. The experimental oxidation data are plotted using logpoz as the ordinate and the values of 1/ T
Temp, ·C
~ :- 141 20C M. P. Si Is)
- 3 ,/ ':- 1109PSiO leQ )~.4)
/ Wa<j ner' < Condition
- 4 ® ®/ ® For Log PO
3' - 7
- 8 -
l. 0 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 O. 45
!x 103 T
Fig. 5. Active and passive regions for the oxidation of silicon on a plot of log PSiO vs 1IT.
12 E. A. GULBRA NSEN
as abscissa. The P and A signs indicate passive (weight gain) and active (weight loss) types of oxidation. The heavy diagonal line gives the equilibrium pressures of SiO(g) at the Si(s)-Si02(s) in­ terface. Areas of the diagram above and to the left of the line are conditions where 10gp02 > 10gPSiO (eq), and areas below and to the right of the line are conditions where log P02 < log PSiO(eq). The kinetic data show the area to the left of the line is the passive oxi­ dation region and the area to the right of the line is the active oxi­ dation region. Rapid transfer of SiO(g) occurs through the porous oxide film which is consumed by the reaction. Rupturing of the oxide film also can occur when 10gP02 < 10gPsiO (eq).
Extremely rapid oxidation occurs in the active region since the barrier layer of volatilized oxide species (according to the equilibria of Fig. 2) consists of Si02(s) smoke (crystals) and not SiO(g) gas as assumed by Wagner.9 Much higher oxidation rates can occur when the barrier layer consists of oxide crystals rather than gaseous oxides.
At 10-1 torr and 1200 C, 7100 Aof Si reacted per cm2-sec
using a flow rate of 1 . 1019 oxygen atoms/sec in the tube. At a rate of 5350 cm/sec, 36.4% of the oxygen atoms flowing over the sample reacted. For the reaction conditions, this is the highest rate of oxidation we have measured. Wagner's condition for active and passive oxidation is also shown in Fig. 5. We conclude that the condition log P02 = log PSiO (eq) is the essential condition separating active and passive oxidation of silicon.
OXIDATIONOF CHROMIUM
a. Thermochemical Predictions
It should be noted that Fig. 2 and other log PCrOx vs log P02 diagrams show volatile species are important for two reasons: First, a relatively high pressure of Cr (g) can develop at the Cr­ Cr203 interface, and second, relatively high pressures of Cr03 (g) exist over the Cr203 (s) - O2(g) interface. In Fig. 4, there is a plot of 10gPcr and 10gPcro vs l/T at the metal- oxide interface. LogPCr:= -9 for a temperature of 975 C. Relatively high tempera­ ture and low oxygen pressure must be used to observe the condi­ tion where 10gPcr > 10gpo2• Thus, at 1530 C, 10gPCr = -4. Rapid oxidation should occur for log P02 < -4.
HIGH-TEMPERATURE OXlD }\ n ON OF MA TERIA LS
Temp, °C
800 900 1000 llOO 1200 1300 1400 1500 1600 1700 1800
-4 M.P. Cr 1875°C
- 8
~ - 12
Ix 103 T
Fig. 6. Plot of the log PCrO vs 1IT for volatile species in the oxidation x
of Cr at 0.1 atm 02 pressure.
13
In Fig. 6 there is a plot of logp c-o; vs liT for an oxygen pressure of 0.1 atm. LogP Crz03 =~ for a temperature of 1000 C. At this temperature, oxide volatility should be observed. As the temperature is increased, oxide volatility increases although the temperature coefficient is small. Even at the melting point of chromium, logPc r0
3 and logP cr0
b. Experimental Studies
Unfortunately, complete oxidation studies have not been made. Both oxygen consumption and weight-change experiments must be made to evaluate the complex oxidation behavior. Two studies have been made in our laboratories on the vapor pressure of chromium, the transport of chromium vapor through oxide films, and the ki­ netics of oxidati on at temperatures up to 1100 C.11,2 A plot of the parabolic rate law constant vs. 1 IT in Fig. 7 sh ows a transforma­ tion occurs near 1000 C. This was related to the equilibrium pres­ sure of chromium at the metal- oxide interface. The transforma­ tion point, C-B in Fig. 7, corresponds to the condition at which the
14
1100
-10.5
-11.0
-11.5
! X103 T
Fig. 7. The log A vs l/T for the oxidation of Cr. From the slopes, D.H C- D =37.5 keal/mole and D.HA-B = 59.4 keal/mole.
rate of evaporation is equal to the rate of chromium metal diffusion in oxidation. Thus, the high vapor pressure of chromium short cir­ cuits the normal diffusion processes and for these conditions an in­ crease in the rate of oxidation occurs. The volatility of Cr03 should begin to exert its influence at 1000 C on the oxidation pro­ cess and on the stoichiometry of the oxide although this has not been verified experimentally.
CONCLUSlONS
Thermochemical analysis of the nature of the volatile oxide species, their equilibrium pressures , and the composition and sta­ bility of the condensed oxide phases can be used to evaluate furnace tubes and support wires for specimens, plan productive experiments, and interpret the experimental measurements.
Quartz and mullite as furnace tubes and silica as a support fiber were considered for use at 1400 K and at 02 pressures of 1 atm, 10-12 atm, and under reducing conditions. Both materials yield volatile reaction products at 10-12 atm of 02 and under reduc­ ing conditions.
HIGH-TEMPERAT URE OXIDATION OF MATERlALS 15
The active and passive regions of oxidation of silicon were considered thermochemically. Active oxidation occurs when log P02 < log P SiO (eq), and passive oxidation occurs when log P02 > log P SiO (eq). Rapid rates of oxidation are predicted and observed experimentally.
Thermochemically, chromium should show a transition to a rapid oxidation rate at 975 C where logPcr > -9. This was ob­ served experimentally. Direct volatility of Cr03 (g) also should be observed.
REFERENCES
1. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, The oxidation of graphite at temperatures of 600 to 1500 C and at pressures of 2 to 76 torr of oxygen, J. Electrochern. Soc., 110,476 (1963).
2. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, Oxida­ tion of molybdenum 550 to 1700 C, J. Electrochem. Soc., 110 , 952 (1963).
3. E. A. Gulbransen and K. F. Andrew, Kinetics of oxidation of pure tungsten from 500 to 1300 C, J. Electrochem. Soc., 107, 619 (1960).
4. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, Kinetics of oxidation of pure tungsten, 1150-1615 C, J. Electrochem. Soc., 111, 103 (1964).
5. JANAF Tables of Thermochemical Data, Dow Chemical Com­ pany, Midland, Michigan, including Supplement No. 30 dated Dec. 31, 1968.
6. C. E. Wicks and F. E. Block, Thermodynamic properties of 65 elements - their oxides, halides , carbides, and nitrides, Bur. of Mines Bulletin No. 605, Washington, U. S. Government Printing Office (1963).
7. H. H. Kellogg, Vaporization chemistry in extractive metal­ lurgy, Trans. Met. Soc. AIME, 236, 602 (1966).
8. S. A. Jansson and E. A. Gulbransen, Evaluation of Gas­ Metal Reactions by Means of Thermochemical Diagrams, Paper presented at the International Congress on Corrosion, Amsterdam , Sept. 1969.
9. C. Wagner, Passivity during the oxidation of silicon at ele­ vated temperatures, J. Appl, Phys. , 29, 1295 (1958).
16 E. A. GULBRANSEN
10. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, Oxida­ tion of silicon at high temperatures and low pressure under flow conditions and the vapor pressure of silicon, J. Electro­ chern, Soc. , 113, 834 (1966).
11. E. A. Gulbransen and K. F. Andrew, Kinetics of the oxidation of chromium, J. Electrochem, Soc., 104, 334 (1957).
DISCUSSION
D . E. Me y e r: How applicable are the techniques you describe to the oxida­ tion studies where gaseous components such as phosphorous and boron are also present?
E. A. G u I bra n sen: I see no majo r difficulties in the study of materials where gaseous compounds of phosphorus and boron are formed. The logpPOx and logpo diagram for phosphorus is one of the very interesting oxide systems we have consid~red since high pressures of volatile oxides develop at the phosphorus- oxygen interface . These pressures explain the rapid oxidation reactions of phosphorus. Some day we hope adsorption chemists will take a look at phosphorus and relate their mea­ surements to thermochemistry of the phosphorus- oxygen system.
The Simultaneous Use of Mass Spectrometer and Microbalance Techniques for the Carbon-Oxygen System
J. Graham Brown, John Dollimore, Clive M. Freedman, and Brian H. Harrison Department of Pure and Applied Physics Univer sity of Salford Salford 5, Lancashire United Kingdom
ABSTRACT
The initial degassing of a high-surface-area graphite is character­ ized using mass spectrometric and thermogravimetric weight-loss measurements. It will be indicated how far the combination of these allied techniques can be used to define the graphitic nature of the material in terms of the extent of the basal and edge planes of the graphite crystallite. The active surface area of the graphite was measured by the formation of surface oxide during low-pres­ sure oxygen chemisorption onto the clean surface of the material. By subsequent thermal desorption of surface oxide an additional value for the active surface area was obtained from the weight-loss data and the known ratios of the desorbed gaseous species CO and CO2, The utility of a mass spectrometer - microbalance system for the study of gas - surface reactions is discussed.
INTRODUCTION
Microbalance techniques have been used extensively in the study of the thermal decomposition of powdered materials. In many decom­ position reactions, the evolution of various gaseous products occurs in discrete stages, and weight-loss data are adequate to character­ ize the process.
17
18 J. G. BROWN ET AL.
In the carbon- oxygen system, it has now been established that the oxidation of various carbons and graphite proceeds from the formation of a stable surface oxide to the production of gaseous CO and CO2• Heating of this stable surface oxide results in its thermal desorption as CO and CO2• One is therefore concerned with the simultaneous evolution of CO and CO2 in both oxidation and thermal desorption studies. This is particularly the case in the temperature range 300-1000 C, so that the weight-loss data need to be supplemented with other measurements.
The graphite surface oxide has been shown by many workers to be associated with the reactive edge-plane carbon atoms of the graphite crystallttea.lf On this basis, by making the assumption that CO is the predominant gaseous product' due to thermal desorp­ tion of surface oxide, weight-loss data were used to obtain physical crystallographic data on the basal to edge plane ratio of graphite during a grinding series. This technique of determining crystallo­ graphic parameters has been improved, in the present study, by the additional information obtained from the mass spectrometer.
In the past, the mass spectrometer has been combined with thermogravimetric measurements for the purpose of qualitatively describing a process.4,5 The present work is intended to show the varying degree of participation of the mass spectrometer in a study of the thermal treatment of graphite and some of the proper­ ties and stability of its surface oxide produced by reaction with molecular oxygen. Finally, it will be demonstrated how the mass spectrometer alone may be used as a microbalance, using the broader meaning of this nomenclature.f
EXPERIMENT AL
Apparatus
The material used in this study was a ground sample of Ache­ son 's graphite with a BET specific surface of 102 m2/g when measured by nitrogen adsorption at 78 K. The grinding process reduced the crystallite size and produced extensive graphite edge planes. Since small sample masses are employed in vacuum microbalance work, this particular high-area graphite enabled the mass spectrometer - microbalance system to be matched readily based on high gas evolution quantities.
MASS SPECTROMETER AND MICROBALA NCE TECHNIQUES
RGA MS 10
Vacuum Gas
storage Cahn RG Electrobalance Twin Furnace
Fig. 1. System for simultaneous use of a Cahn RG microbalance and an AEI MS10 mass spectrometer.
19
The simultaneous TGA- MSA system is shown in Fig. 1. A Cahn RG Electrobalance® was used and the enclosure could be evacuated to 10-6 torr using two cold traps, a 3-in. oil-diffusion pump, and PTFE greaseless stopcocks. Viton O-ring seals were employed for the symmetrical hangdown tubes which together with the crucibles and suspension were made of high-purity silica. Sample temperatures were measured with a chromel- alumel thermocouple situated on the axis of the sample tube and just be­ low the sample. To prevent interaction with gaseous products the thermocouple was enclosed in a thin quartz tube sealed to the bot­ tom of the sample tube.
Gaseous products evolved from the sample were transferred, for analysis, to the mass spectrometer system by a baffled 2-in. oil-diffusion pump. The removal of gases from the microbalance enclosure prevented spurious weight changes arising from TMF effects 7 and also prevented readsorption and secondary reactions from occurring. The mass spectrometer system, described else­ where," consisted of a 5.5-liter reservoir connected to an AEI MS10 mass spectrometer via a fixed molecular leak of 10-2 torr liter / sec at atmospheric differential. This fixed leak allowed par­ tial pressures from 0.1 to 600 mtorr in the reservoir to be mea­ sured on the mass spectrometer.
20 J. G. BROWN ET AL.
This type of system can be used either to obtain a qualitative analysis of the gaseous products to supplement the weight-loss data, or by accurate calibration of the reservoir volume and the mass spectrometer senstttvtty." the mass of evolved gas can be determined from the general gas law, PV = mRT. The direct cor­ relation between the weight of gas evolved determined on both the microbalance and mass spectrometer systems allows the mass spectrometer to be used as a microbalance for chemisorption and oxidation studies in the pressure regions where the conventional microbalance is troubled by spurious weight changes.
Procedure
A 0.25-g sample of the original ground Acheson graphite was degassed at room temperature for 12 hr to remove physical­ ly adsorbed gases. The sample temperature was raised in tem­ perature increments of 100 C up to 900 C. The gaseous products were transferred to the mass spectrometer for analysis after half-hour collection times at each increment. At the end of each temperature increment, the evolved gas was removed from the reservoir by evacuation before proceeding to the next tempera­ ture run. To ensure a cleaned surface for chemisorption experi­ ments, the sample was heated at 1000 C until a pressure of 10-6
torr was achieved. The sample was then lowered to the desired reaction temperature before admission of oxygen to the required pressure. The desorption of the surface oxide, formed by oxygen chemisorption, was monitored in a manner similar to that de­ scribed above but was continuous up to a collection time of 50 min at selected temperature increments. Chemisorption and oxidation experiments were carried out using just the mass spectrometer to follow the change in the partial pressures of the gaseous compo­ nents.
RESULTS AND DISCUSSION
The initial degassing of the Acheson's graphite is shown in Fig. 2 as a cumulative weight loss curve expressed in milligrams per gram of sample. The weight of the major gaseous components detected during degassing is also shown. The specific weights of CO and CO2 evolved can be used to estimate the extent of the graph­ ite edge planes by determining the number of carbon atoms in the evolved oxides of carbon.14 On this basis, the initial degassing gives a coverage of 14.8 m2/g and 10.0 m2/g from CO and CO2,
MASS SPECTROMET ER AND MICROBALA NCE TECHNIQUES
20
21
800
Fig. 2. Cumulative weight loss showing major components on initial degassing of a ground Acheson's graphite . Total Hz = 0.106 mg/g; total HzO = 0.865 mg/g.
respectively, and a total edge-plane extent of 24.8 m2/g. Since some of the coverage may, in fact, be due to "ground in" defects, a more precise procedure of chemisorbing oxygen onto the clean graphite surface was employed. In cleaning the graphite surface by evacuation at 1000 C, the "ground in" defects are annealed out'' and the subsequent formation of surface oxide will then be confined to the crystallographic edge planes. Oxygen was chemisorbed on the sample at 250 C and 2 torr pressure for 1 hr, with less than 0.1% "burn-off" occurring. From other studies,9 it was found that this period was sufficient to obtain at least 95% of the saturation coverage at 250 C. The desorption of the surface oxide was followed using the simultaneous thermogravimetric and mass spectro­ metric weight-loss technique.
Typical isothermal weight-loss curves are illustrated in Fig. 3 for the 500, 650, and 800 C desorption runs with Fig. 4 show­ ing the breakdown of gaseous components in the 500 C run. The cumulative weight-loss data obtained from the desorption of the
22 J. G. BROWN ET AL.
0.20,----,-----,----,----,
0.05
o
Fig, 3. Typical isothermal desorption curves of 02 chemisorp­ tion at 2 torr ~nd 250 C for 1 h.
surface oxide over the whole temperature range are presented in Table I and shows the excellent agreement between calculated (MSA) and measured (TGA) weight losses. The extent of surface oxide coverage corresponded to 7.8 m2/g and 0.055 m2/ g for CO and CO2, respectively, giving a total edge-plane extent of 7.85 m 2/g.
It is pertinent at this point to compare the quantity of CO2 evolved during the initial degassing with that obtained from a con­ trolled oxygen chemisorption. The large quantity of CO2 found on the initial degassing has been tentatively associated with defects caused by the grinding process. Electron spin resonance methods '" have shown an increase in the free spin concentration on grinding and that subsequent thermal annealing at temperatures up to 1000 C greatly reduces this concentratton.i Further work has also shown the correlation between the production of CO2 and spin cen­ ters,11 and it is suggested that the large drop in CO2 evolution after the initial degassing is, in fact, associated with the anneal­ ing out of damage caused by the grinding process. Further evi­ dence for this annealing is found in the reduction of the surface
MASS SPECTROMETER AND MICRO BALANCE TECHNIQUES
0.125.------,-----..,..------,-,
23
0.100 -
Ul
Fig. 4 . Component analysis of 500 C isothermal desorption curve.
Table 1. Cumulative Weight Loss* - A Comparison of Simultane­ ous Mass Spectrometer and Microbalance Data
CO, mg . C0 20 mg .
Cumulative total: MSA, mg
Temperature range, C
400- 500- 600- 650- 700- 750- 800- 900-
500 600 650 700 750 800 900 950
0.063 0.199 0.335 0.473 0.663 0.823 1.010 1.085 0.052 0.094 0.111 0.121 0.128 0.128 0.128 0.128
0.115 0.293 0.446 0.594 0.791 0.951 1.138 1.213
0.120 0.305 0.454 0.602 0.810 0.961 1.150 1.231
• From a 0.2662-g sample .
24 J. G. BROWN ET AL.
area after heat treatment to 1000 C. The initial surface area of the sample after degassing at 300 C to remove adsorbed gases was 102 m2/ g; after heat treatment of the sample at 1000 C, the surface area decreased to 90 m2/g in a reproducible manner. This more than accounted for the surface oxide coverage associated with the CO2 evolved.
It is als o possible to obtain surface area data on powders by using the broadening of the lines on x-ray powder diffraction photo­ graphs, and, therefore, such x-ray measurements were made to provide comparative data. The photographs were obtained using a quadruple Guinier focusing camera, and the pr ofiles of the powder lines were obtained using a recording microdensitometer. The quadruple camera permitted the simultaneous exposure of three samples together with a suitable standard material for the evalua­ tion of the instrumental line width so that the observed pr ofiles could be corrected to give the pure diffraction widths. In this way,
275 ~...... ~ -.::... E ~
... 15~.5 225 :::0
'" Ox Ql Ql 0...
~ 200 :::0 10 -e '"01 '" 0
>. Ql (J
'E 20 c:: Ql 0 '0 .c .~ ...
0 :::0 Uc:r
20 40 60 Time (minutes)
Fig. 5. Formation of graphite surface oxide at 300 C and 250 mtorr of 0 2 on a cleaned surface of ground Acheson's graphite .
MASS SPECTROMETER AND MICROBALANCE TECHNIQUES 25
30
~ .~ Q)
OL4~O§0=::~§~=:;~==!==j~=~t~J
Fig. 6. Thermal decomposition of surface oxide after 1.70,10"burnoff" at 300 C.
using the (110) and (004) powder lines, values of the layer diam­ eters La and the dimensions of the crystallites perpendicular to the layers , Lc , were obtained. Surface areas could then be calcu­ lated assuming that the particles are cylinders of diameter La and height L c; the total surface area, the basal-plane area, and the edge­ plane area can all be evaluated. It is necessary to assume a value of the density of the graphite, and since the x-ray method measures the extent of the regions of perfect crystallinity, the appropriate value is the ideal x-ray density of 2.26 g/cm3• Using these methods we find for the ground Acheson's graphite a total specific surface area of about 100 m2/g and a specific edge-plane area of about 46 m 2/ g.
In the present study, the mass spectrometer was used as a sensitive microbalance during the oxidation process. Figure 5 shows the buildup of surface oxide on the clean graphite surface at an initial oxygen pressure of 250 mtorr and a temperature of 300 C. The figure also shows the production of "burn-off" products CO and CO2 and the continual depletion of oxygen during the first hour of oxidation. The total "burn-off" of carbon amounted to 1.7% w/w of sample after a 13-hr exposure to the oxygen. Figure 6 shows the cumulative weight-loss data obtained in subsequent desorption of the surface oxide up to 950 C. The total surface oxide coverage corresponded to 38.2 m2/g and consisted of 36.9 m2/g and 1.3 m2/g
of CO and CO2, respectively.
26 J. G. BROWN ET AL.
The advantage of the mass spectrometer is apparent when one considers that the conventional microbalance weight change would be a complex function of oxygen chemisorption and carbon removal as CO and CO2, Normally in microbalance studies at low oxygen pressures, the oxygen is diluted with an inert gas 12 and the oxidation process followed after the initial formation of surface oxide has been completed. This restriction allows only tentative conclusions to be drawn about the processes occurring in the ini­ tial period of oxidation.
CONCLUSION
It has been demonstrated that a mass spectrometer may be used to supplement microbalance data. Previous techniques, used to determine edge-plane extents of ground graphite samples, could be in error in the light of the present work. With ground samples, the large proportion of CO2 evolved can lead to significant error in the edge-plane extent, if weight-loss measurements are based sole­ lyon the evolution of CO. Defects caused by the grinding process appear to be associated with the majority of the evolved CO2,
In view of the good agreement for total surface area as mea­ sured by physical adsorption and x-ray line-broadening techniques, it must be concluded that not all the edge-plane surface can chemi­ sorb oxygen. This would account for the low values of edge-plane extent obtained from chemisorption studies when compared with the values from x-ray data. The use of chemisorption studies to de­ fine the edge-plane extent could therefore lead to many problems of interpretation.
It is demonstrated by the present work that even as little as 2% "burn-off" on the sample can alter by at least threefold the measured edge-plane extent. This is most likely due to "internal channeltng't'! arising from catalytic oxidation due to the 0.2% iron content introduced in the grinding process.
A clearer insight into the energetic nature of the surface oxide formed on graphite can be obtained'! from the present results by careful analysis of the isothermal desorption kinetics using an established technlque.P
ACKNOWLEDGME NTS
B. H. Harrison and C. M. Freedman would like to acknowl­ edge financial assistance from the National Gas Council (UK) and The University of Salford, respectively.
MASS SPECTROMETER AND !v!ICROBALANCE TECHNIQUES
REFERENCES
27
1. G. R. Hennig, Proceedings of the Fifth Conference on Carbon, Vol. 1, Pergamon Press, Oxford (1963), p. 143.
2. E. A. C. Follet, Carbon, .!.' 329 (1964). 3. S. J. Gregg and J. Hickman, Second Conference on Industrial
Carbon and Graphite, London, 1965 , Soc. Chern. Ind. (1966), p.424.
4. F. Zitomer , Anal. Chern., 40, 1091 (1968). 5. W. W. Wendlandt and T. M. Southern, Anal. Chim. Acta, 32,
405 (1965). 6. J. Dollimore, C. M. Freedman, and B. H. Harrison, Seven­
teenth Annual Conference on Mass Spectrometry and Allied Topic s, Dallas, 1969.
7. A. W. Czanderna, in: Vacuum Microbalance Techniques, Vol. 4, Plenum Press, New York (1965), p. 69.
8. H. Harker , J. B. Horsley, and A. Parkin, J. Nucl. Mater., 28, 202 (1968).
9. J. Dollimore , C. M. Freedman, and B. H. Harrison, unpub­ lished work.
10. S. Mrozowski and J . F. Andrew, Proceedings of the Fourth Conference on Carbon, Pergamon Press, Oxford (1960), p. 207.
11. H. Harker, J. T. Gallagher, and A. Parkin, Carbon, !' 401 (1966).
12. B. G. Tucker and l\L F. R. Mulcahy, Trans. Faraday Soc., 65, 274 (1969\.
13. G. R. Hennig, J. Inorg. Nucl. Chem., 24, 1129 (1962). 14. J. Dollimore, C. M. Freedman, and B. H. Harrison, to be
published. 15. J. Dollimore, C. M. Freedman, and B. H. Harrison, Ninth
Biennial Conference on Carbon, SP-26 (1969).
A System for the Determination of Oxidation-Reduction Kinetics in N onstoichiometric Metal Oxides
I. Bransky*
and
ABSTRACT
The chemical diffusion coefficient can be determined from measure­ ments of the kinetics of oxidation or reduction of a nonstoichiomet­ ric metal oxide. To accomplish this thermogravimetrically when the homogeneity range of the oxide is small , all disturbing influ­ ences and sources of noise, such as gas-flow irregularities and temperature gradient variations , must be minimized. A system is described which delivers high gas flows at constant pressure and flow rate to the furnace and switches rapidly from one oxygen par­ t ial pressure to another with minimum disturbance to the Cahn RG Electrobalance® us ed . The importance of linear gas velocity and furnace geometry when using CO- CO2 mixtures is discussed and a satisfactory gas preheater is described. An example of the ap­ plication of the apparatus to the reduction of Mn01+x in steps of ~x ~ 0.2% is presented.
• Visiting Senior Research Physici st at Aerospace Research Laborator ies .
29
INTRODUCTIO N
In recent years, a considerable amount of effort has been devoted to the study of the oxidation - reduction kinetics of metal oxides, with particular emphasis on the calculation of the chemical diffu­ sion coefficient from the observed reaction rates. The chemical diffusion coefficient :5 is defined as the proportionality constant in Ftck's law
J = :5(dc/dx), (1)
where, since interdiffusion in the presence of a chemical potential gradient is occurring, J is the total flux of all mobile species and c , for a nonstoichiometric compound, is the excess concentration of one of the components.
There are many practical and theoretical reasons for this in­ terest in the values of D. The chemical diffusion coefficient is im­ portant in the calculation of equilibration times for a nonstoichlo­ metric semiconductor interacting with its vapor, in diffusion-con­ trolled oxidation of metals, and in solid state reactions between oxides. Furthermore, it is sometimes possible to use values of :5 to estimate the self-diffusion coefficients of the constituents of a compound'v and to compare these with values obtained from tracer experiments. From a theoretical point of view, these diffusion co­ efficients are of interest because they are sensitive to the defect structure of the oxides under study. The role of chemical diffu­ sion in sintering may be of particular importance in ceramic tech­ nology . For example, Kuczynskl'' has suggested that the sintering rates of various oxides are controlled by the chemical diffusion co­ efficients of the oxides, rather than by the self-diffusion coeffi­ cients of their constituents.
During the reduction of a metal-deficient oxide specimen in a gaseous atmosphere, metal vacancies diffuse toward the oxide­ gas interface. Since, for a metal oxide M,Oj,
_ a [V 0] _ a [00] -----,
ax ax
Ftck's first law, given in equation (1), can often be simplified to
OXIDATION -REDUCTION KINETICS IN METAL OXIDES
J v = Doc/ax, M
is the flux of metal vacancies. This is particularly
true when the self-diffusion coefficient for oxygen vacancies is much smaller than that for metal vacancies. If the surface reac­ tions involved in the incorporation of oxygen from the gas phase in­ to the crystal lattice are sufficiently rapid, then the change in metal vacancy concentration is controlled by volume diffusion and Fick's second law can be written
(3)
Levin and wagner! presented a very convenient simplified treat­ ment of equation (3) in the analysis of their reduction experiments on wiistite. Their mathematical solution assumed (1) a constant D, and (2) that the surface of the specimen equilibrates instantly to the composition required by the chemical potential of the oxygen in the gas phase. Two integrated solutions of equation (3) were pre­ sented. The first, which is valid during the initial part of the com­ positional change , t.e ., when Dt/a2 -s 0.15, has a parabolic form
(4)
where kp = 4fj(~c)2 / 1T and ~m = m - mo; m is the sample weight at time t; mo the initial weight at t = 0; ~c the change in the cation concentration; A the area of the specimen; and a the half-thickness. The second integrated solution of equation (3) is valid for the rest of the process, when f5t/a2 :::: 0.15, and it has a logarithmic form
~m 8 1TDt log (1 - mf - m/ = log;2 - 2.3 (4a2) , (5)
where mf is the final weight at time t = 00. Both analyses are for one-dimensional diffusion only. Edge corrections for finite samples have been given by Landler and Komarek. 5 A survey of the mathematical analysis of oxidation- reduction data, experi­ mental techniques, and the recent studies of chemical diffusion co­ efficients in metal oxides has been given by J. B. Wagner.6
32 I. BRAN SKY AND N. M. TALLAN
EXPERIME NTAL
Determination of Chemical Diffusion Coefficients
To determine the chemical diffusion coefficient from oxi­ dation or reduction rates of an oxide, a specimen is equilibrated at a given oxygen pressure at some temperature and then, at some arbitrary time zero, the oxygen pressure is changed rapidly to a new value. The isothermal rate of change of some physical prop­ erty, such as electrical conductivity, 7,8,9 weight change ,4,5,10 or the density of color centers.!' that is proportional to the rate of com­ position equilibration must then be measured. It has been pointed out by Campbell, Kass, and O'Keeffe9 that the apparent :5 is sensi­ tive to the electrode configuration used in the conductivity measure­ ments. It is therefore desirable, whenever possible, to study rates of oxidation or reduction processes by a more direct method, such as weight change, which follows the vacancy concentration itself.
Design of the Thermogravimetric System
The chemical diffusion coefficient has been found to be strong­ ly dependent on defect concentration in several metal oxides4,5,10,12,13
and therefore it varies rapidly with stoichiometric deviation. It is therefore extremely important for the thermogravimetric system to have maximum sensibility to weight change to permit recording the rates of oxidation or reduction in composition steps that are suffi­ ciently small so that Dcan be considered constant. Furthermore, to meet the requirement that the change in oxygen partial pressure be as rapid as possible, the system should be capable of handling high gas flows. At the same time, the gas flow should be sufficient­ ly constant so the force exerted on the sample does not vary with time, and the switching of the gas mixtures at time zero, to change the oxygen partial pressure, should disturb the balance as little as possible.
Description of the Thermogravimetric System
A schematic diagram of the system is shown in Fig. 1. The sample 12, in the form of a thin, single crystal disc, is suspended from a Cahn RG Electrobalance®. For the study of MnG, a sap­ phire fiber was used in contact with the specimen to minimize in­ teraction. The balance was operated on the 10-mg mass range and in either the 200- or the 400-llg/mV output position. A Leeds and
OXIDATION- RE DUCTION KINE TICS IN METAL OXIDES
Gas I Gas n Gas I Gas n CO CO2 CO CO2
I,
33
CD '
16
8
Fig. 1 . A schematic diagram of the thermogravimetric system: 1) Matheson Model 70 low-pressure regulator ; 2) purifiers; 3) valve ; 4) Matheson's Floating Spheres flow­ meters ; 5) gas mixer ; 6) mercury manometer ; 7) two-way solenoid valves : 8) capil­ lary ; 9) preheater: 10) alumina cruci ble ; 11) alum ina furnace tube ; 12) sample; 13) sapphire fiber; 14) platinum or nichrome wire; 15) radiation shields ; 16) balance; 17) toggle valve: 18) Cartesian manostat No. 6; 19) vacuum pump; 20) outlet to ex­ haust.
Northrop AZAR recorder was used with I-mV full-scale input. The furnace construction has been described elsewhere.I!
Mixtures of CO2 and CO were used to obtain oxygen partial pressure in the range of 10-3 to 10-11 atm. The CO2 was purified by passing the gas over copper turnings 2, heated to about 750 C. Floating ball flow meters used to measure the flow of CO2 and CO were calibrated for the gases used by timing the rise of a soap mem­ brane in a burette. As seen in Fig. 1, two identical gas-mixing sys­ tems were used, one to provide the initial oxygen partial pressure and one to provide the oxygen pressure required for the desired step change in composition. Two solenoid valves 7 were used to switch from one mixture to the other. To conveniently maintain a constant gas flow through the furnaces, a capillary which repre­ sented the maximum restr iction in the line was used in conjunction with a manostat 18 on the furnace and a manometer 6 on the mix- ing chamber 5. Since the pressure drop across the capillary was
34 1. BRAN SKY AND N. M. TALLAN
constant, the flow through the system was essentially constant and independent of the settings of other valves in the system used to control the individual gas flow rates. While one mixture was flow­ ing through the furnaces, the other one was vented into an exhaust system. To minimize the disturbance to the balance when switch­ ing gas mixtures, identical capillaries were used at the inlets to the furnace and the exhaust system. The cartesian manostat, which was used to maintain constant pressure in the furnace, was set generally at a pressure between 150 and 200 torr to minimize thermal fluctuations of the balance beam. A toggle valve 17 was used to terminate the gas flow abruptly to permit weight measure­ ments in a static rather than a dynamic gas environment when necessary.
RESULTS
Operation of the System
A total gas flow of about 500 cc/min at atmospheric pres­ sure was selected to obtain a favorable time constant for the pro­ cess of exchanging the gas mixtures. With the 17-in.-long, 1}­ in.-diameter furnace tube used, this flow rate would give a time constant of about 6 sec if laminar flow were maintained. However, when this flow was introduced directly into the bottom of the fur­ nace during the initial trial measurements on MnO, obvious signs of difficulty were observed. At 1300 C, the COdCO ratio was changed from 90 to 50, a change which should have produced a mass loss of about 400 J1.g on the specimen used, but no mass change was detected. When the change in gas mixture involved lower COdCO ratios , i.e. , higher CO contents, asymmetric amounts of oxidation and reduction were obtained from switching back and forth between the same two gas mixtures . This behavior was suggestive of two effects associated with the possibility that the gas flowing through the furnace tube at this high flow rate might not be reaching the temperature of the furnace. First, if the gas striking the sample surface is unheated, the rate of sur­ face reaction might be slowed to a point where the oxidation and reduction kinetics are no longer controlled by volume diffusion. Second, unheated gas flowing past the sample might contain oxy­ gen present in the incoming gas stream which is not removed by reaction with the CO to produce CO2,
OXIDAnON- REDUCTION KINETICS IN METAL OXIDES 35
If we consider a furnace tube of radius R and a hot zone of length Lt> the transit time of a gas molecule through the hot zone for a flow rate F is given by 1TLtR
2IF. The diffusion time for a gas molecule from the center of the furnace tube to the wall is es­ sentially given by R2l Ug, where Dg is the interdiffusion coeffi­ cient of one gas in another. For about 93% of the gas molecules to collide with the furnace wall and thereby to reach the furnace temperature, the length of the hot zone should be at least F I 1TDg•
For a flow of 500 cc/min measured at atmospheric pressure but flowing in a furnace at 150 to 200 torr and a value of Dg of 0.3 cm2/sec for CO2 diffusing in CO at 1300 C, the hot zone should therefore be at least about 40 cm long. Since the hot zone of the furnace used was not more than 10 cm long, it is indeed quite likely that much of the gas flowing past the sample was substan­ tially colder than the indicated furnace temperature.
If the gas flow is constrained to a region near the furnace wall by the insertion of a concentric tube of radius r < R, then it can be shown that the required "constrained hot-zone" length is given by
F (R - r) 141TDg (R + r).
By inserting a l%-in.-diameter crucible below the sample in a 11/ 2-in.-diameter furnace tube, the required hot-zone length for the same gas flow rate is reduced to only about 0.4 em,
Effective heating of the gas flow was assured in the system described here by introducing the incoming gas stream through a preheater (9 in Fig. 1) which supported an alumina crucible 10 in a position immediately below the sample. The preheater was con­ structed of concentric alumina tubes heated to about 1000 C by a platinum wire heating element. The alumina crucible below the sample contributed not only to the heating of the gas, as described above, but also to the minimization of fluctuations in the weighing of the sample caused by gas turbulence and to reduction in the lift­ ing force exerted on the sample by the flowing gas. After intro­ ducing the preheater and crucible, the spurious effects noted earlier were not observed again; the oxidation and reduction mea­ surements were always found to be essentially symmetrical.
36 1. BRANSKY AND N. M. TALLA N
Ta1325'C COt/COa25IoCOlCOoI3
T=1275'C COt/COo 39 loC0z/COaI9
Fig . 2 . Recorded weight change of the reduction of Mn0 l-0054 to Mn0 l.O040 at 1275, 130 0, and 1325 C
Determination of the Chemical Diffusion Coefficient in MnO
The first step in an actual measurement was the equilibra­ tion of the sample at a given temperature with a predetermined CO2/CO mixture within the MnO phase field. 15 After an equilibri­ um weight was attained, the COdCO mixture was changed and the change in sample weight due to oxidation or reduction was record­ ed continuously. The results of reduction measurements on an MnO single crystal disc, 0.9 mm thick with ( 100) crystallographic faces 12 mm in diameter, are shown at three different tempera­ tures in Fig. 2. The reduction corresponds in each case to a
OXIDATION - REDUCTION KINETICS IN METAL OXIDES 37
3000.---------r-----.-----,------....------,
400 500
Fig . 3a. Parabolic ra te of reduction of MnO l +X at 1300 C: 1. CO zl CO = 142 .5
to codco = 81. 5; II . COz/CO = 53.6 to codco = 24.4.
MnO. 130 0 · C
0 ...J
0 20 0 300 400 500 Time(minl
Fig . 3b . Logarithmic rate of reduction of MnO!+x at 1300 C: 1. COz/ CO =142 .5 to COz/CO = 81. 5; II . COz/CO = 53.6 to COz/CO = 24.4 .
38 I. BRANSKY AND N. M. TALLAN
change in composition from MnOt.0054 to MnOt.0040' It may be noted from the recorder traces that the noise level , using all of the fil­ tering available electronically in the balance circuit, was about ±2 J.Lg. The uncertainty in the :5 values calculated from equations (4) and (5) is largely due to the uncertainties in the values of mo and mf determined from the recorder traces. It is therefore necessary to determine the initial and final weights as carefully as possible from data of the type shown in Fig. 2. It was found to be particularly difficult to determine mo when the initial reduction kinetics were very rapid. Static values of mo and mf were always used to check the reliability of the values measured in flowing gas atmospheres.
The chemical diffusion coefficient :5 was calculated from equations (4) and (5) using a computer which also plotted the mea­ sured weight change as both parabolic and logarithmic functions of the time. Values of :5 were calculated from the slope of the linear part of each plot by the method of least squares. The agree­ ment between values of :5 calculated from the initial parabolic part of the reduction rate and from the later-stage logarithmic partwas usually within experimental error, but the parabolic values were generally more consistent. Examples of the computer plots are shown in Figs. 3a and 3b, where arrows have been used to indi­ cate the end points of the linear parts from which :5 values were calculated.
Since the integrated solutions of equation ~) which are used to calculate :5 are obtained under the assumption that all surface reactions involved are much more rapid than the volume diffusion process, it is always important to determine that this condition is satisfied for the material studied and for the experimental condi­ tions used. This was accomplished for MnO by varying the flow rates of the initial and final COdCO mixtures, by varying the total pressures of the COdcO mixtures, and by diluting the COdCO mixtures with argon. The initial and final CO2I CO ratios, and therefore the step in composition, were the same in all cases. Al­ though the kinetics of the reduction were not influenced by varia­ tions in flow rate, they were significantly slowed down by either reduction in the CO2leo total pressure or increase in argon di­ lution. These effects will be discussed further in a separate pub­ lication on the kinetics of MnO reduction in CO2I CO mlxtures.J''
OXIDATION- REDUCTION KINETICS IN METAL OXIDES
10,....--:---~-----r------,
9
8
o .0 15
Fig . 4. Chemical diffusion coefficient of Mn01+x at 1300 C as a function of the deviation from stoic hiomet ry.
In Fig. 4, the chemical diffusion coefficient of Mn01+X is shown as a function of x at 1300 C. The values shown were calcu­ lated from composition steps of about Ax ~ 0.2%. It may be noted that :5 decreases with increasing stoichiometric deviation. This behavior was also found in Fe01+x by other investigators4,5,10 us­ ing gravimetric measurements in steps of about Ax = 1% and in Mn01+x by Price12 using electrical conductivity measurements.
CONCLUSIONS
The gravimetric system described here, which has been found to be sufficiently sensitive for the determination of chemical diffusion coefficients in MnO from small changes in the composi­ tion , is currently being used for additional studies of MnO and will be used for future studies of CoO and U02. The system should, in fact, prove to be valuable for similar studies in other materials where the weight change accompanying oxidation or reduction is large enough to permit gravimetric measurements to be used. A system of the same design might also be applied to studies of the initial stages of oxidation of metals.
40
REFERENCES
I. BRANSKY AND N. M. TALLAN
1. L. S. Darken, Diffusion, mobility, and their interrelation through free energy in binary metallic systems, Trans. Am. Inst. Min. Met. Engra., 175, 184 (1948).
2. C. Wagner, Uber den Zusammenhang zwischen Ionenbeweg­ Iichkeit und Dlffuslonsgeschwlndigkett in festen Salzen, Z. Physik. Chem., Bll, 139 (1930); Beitrag zur Theorie des Anlaufvorganges. II, Z. Physik. Chem., B32, 447 (1936).
3. G. C. Kuczynski, Grain boundaries and the phenomena of the diffusion in oxides, Bull. Soc. Franc. Ceram., 80, 45 (1968).
4. R. Levin and J. B. Wagner, Jr., Reduction of undoped and chromium-doped wtistite in carbon monoxide - carbon di­ oxide mixtures, Trans. AIME, 233, 159 (1965).
5. P. F. Landler and K. L. Komarek, Reduction of wtistite within the wtistite phase in H2- H20 mixtures, Trans. AIME, 236, 138 (1966).
6. J. B. Wagner, Jr., Chemical diffusion coefficients for some nonstoichlometrtc metal oxides, Mass Transport in Oxides, Natl. Bur. Stnds, Special Publication 296, P. 65 (1967), U.S. Department of Commerce.
7. J. B. Price and J. B. Wagner, Jr., Determination of the chemical diffusion coefficients in single crystal CoO and NiO, Z. Physik. Chern., 49, 257 (1966).
8. K. W. Lay, The oxygen chemical diffusion coefficient of uranium dioxide, Am. Ceramic Soc. Annual Meeting, Washington, D. C., May 1969.
9. R. H. Campbell, W. J. Kass, and M. °'Keeffe , Interdiffusion coefficients from electronic conductivity measurements ­ application to CU20, Mass Transport in Oxides, Natl, Bur. Stds, Special Publication 296, P. 173 (1967), U.S. Department of Commerce.
10. P. L. Hembree and J. B. Wagner, Jr., Kinetics of reduction of wtistite in CO2- CO mixtures at 1100"C, to be published.
11. J. Buyn, PhD Thesis, University of Notre Dame, Indiana (1967).
12. J. B. Price, Chemical and radiotracer diffusion in Mn01+x' PhD Thesis, Northwestern University, Evanston, Illinois (1968).
13. r, Bransky, M. Gvishi, and N. M. Tallan, Thermogravimetric
OXIDATION -REDUCTION KINETICS IN METAL OXIDES 41
studies of chemical diffusion in MnO!+x, Am. Ceramic Soc. Annual Meeting, Washington, D.C., May 1969.
14. W. C. Tripp, R. W. vest, and N. M. Tallan, System for measuring microgram weight changes under controlled oxy­ gen partial pressure to 1000°C, in: Vacuum Microbalance Techniques, Vol, 4 (1965), p. 141.
15. I. Bransky and N. M. Tallan, The phase field of Mn01+x in the temperature range 1000°C-1400°C, to be published.
16. I. Bransky and N. M. Tallan, Kinetics of Mn01+x reduction in COdCO mixtures, to be published.
DISCUSSION
E. A . Gu I bra n sen: What is the influence of volatile oxides of manganese on your measurements?
­
min at 1500 C and co2/co = 6.3 . The kinetic studies reported here were conducted in a range of temperatures and oxygen partial pressures where evaporation could be neglected, as is seen in Fig. 2 from the constant weight at equilibrium . This conclu­ sion was also verified many times during the course of these measurements by simply reoxidizing the specimen in the initial gas mixture and comparing its weight to the in­ itial weight before reduction.
R. M. A I ire: How did you assure yourself that you had diffusion in only one dimension, when your sample was a disc, which could have diffusion in two dimensions? Did you establish what species diffuses?
I. Bra n sky: The solutions of Fick 's laws used to determine the chemical dif­ fusion coefficient in the present work do assume one-dimensional diffusion . Corrections for edge effects have been given by Landler and Komarek. f The samples used in this study were thin enough that the corrections due to edge effects were within the experi­ mental error.
No tracer diffusion expe riments were made in the present study to evaluate the individual diffusivities of the oxygen and manganese ions. However, the relatively high chemical diffusion coefficient obtained in the single crystals studied indicates that the rate s of oxidation and reduction are determined by the manganese ion diffusiv­ ity rather than by the diffusivity of the slower oxygen ion. The self-diffusion coeffi­ cient of Mn in MnO calculated from the value of the chemical diffusion coefficient found in this study (using the Darken relation and neglecting the oxygen diffusivity) is about 10- 8 cm2/sec at 1300 C. Price12 found a value of 2.25 ' 10- 8 cm 2/sec for the tracer diffusivity of Mn54 in MnO at 1141 C in an oxygen partial pressure of 10- 7 atm .
An Automated Bakeable Quartz Fiber Vacuum Ultramicrobalance
J. Radder
ABSTRACT
An automated bakeable quartz fiber vacuum ultramicrobalance is described. A precision of 5 • 10-9 g has been obtained with a 200­ mg load yielding a load to precision ratio (LPR)1 of 4 . 107• The load sensitivity product (LSp)t,2 is 1.2 . 106• The design of the shock-resistant beam, its suspension, and its special housing are described. Automatic operation is accomplished with flags mount­ ed on the hangdown suspensions, two photocells , magnetic com­ pensation, and the appropriate electronics. Causes of instabilities encountered in high vacuum with the automatic system are dis­ cussed and the methods used to eliminate the problems are given.
INTRODUCTION
For many experiments it is necessary to measure submicrogram mass changes. The balance desired was required to meet the fol­ lowing specifications: 1) a stability of 10-8 g, 2) a ratio of capa­ city to precision greater than 10 7, 3) a bake able system to permit operation at pressures below 10- 9 torr, 4) construction from glass-type materials wherever possible, and 5) a design that makes it practical to use the instrument. Concerning 5), this means the balance must be rugged, portable, and insensitive to the usual vi­ brations found in the laboratory. One instrument which is able to meet these qualifications is the quartz fiber torsion balance. As a mechanical device , its sensitivity remains virtually unchallenged.I As a beam balance, an LPR exceeding 107 is easily attained.
43
44 J. RODDER
Bakeability and remarkable stability are assured because of the nearly ideal physical properties of fused silica. Finally, if proper­ ly designed and constructed, quartz fiber balances are surprising­ ly rugged and the disadvantages offered4 can be eliminated.
DESIGN OF THE BALANCE
Beam
Most quartz fiber balances are constructed with the torsion fibers nearly horizontal. With this design, however, the quartz fibers are sensitive to shock because they are under large stress. The explanation for this can be understood by referring to Fig. I. It is observed that the stress on the fiber is Fcsco when the fiber supports a constant load 2F. This stress increases rapidly as the fiber approaches a horizontal position, vlz.., CY - O. Thus, by in­ creasing CY from 2° to 10°, the stress on the fiber is reduced by a factor of ten.
Careful attention must be given to the design of the terminal suspension, which is used for loading the beam via hangdowns, One of the designs used frequently is a fine vertical fiber fused to a rod as shown in Fig. 2. For high sensitivity the bending mo­ ment of the fiber must be small, which requires a fiber diameter of approximately 5 u , Although a 5tJ- fiber can sustain a load of 9 g, fracture occurs readily under the forces of steady mechanical vibration or hard impact on the beam limit stops.
The torsion suspension shown in Fig. 3 is just as sensitive but more shock resistant than the fine vertical fiber. This is be­ cause the torsion suspension is strained over a much longer length
Fig. 1. The stress on a fiber.
A N A UTOMA TED ULTRA MICROBALAN CE
f ig . 2. Early beam showing fragile terminal suspension.
45
than the bending of the fine vertical fiber at a point. Hence, a larger-diameter fiber can be used without decreasing the sensi­ tivity.
The principles indicated above were used to design the beam which has been used in more than 75 commercial balances.! As illustrated in Fig. 4, the trussed beam and each terminal suspen­ sion are supported by a pair of fine fibers. To increase the sensi­ tivity without sacrificing strength, the central pair, or torsion fibers, are longer than those usually associated with this type of balance. It is worth noting that the spring, sometimes found at the end of the back torsion fiber, is absent in this design.
f ig . 3. Torsion terminal suspension.
46 J. RODDER
Fig. 5. Pic ture of a prototype microbalance .
AN AUTQI,1ATED ULTRA l>lI CROBA LAl\ CE
f ig . 6 Pic ture of microbalance after impact.
47
A prototype balance of the same beam design is shown in Fig. 5 with the top and side of the housing removed . The beam is slightly heavier on the s ide touching the beam arrest; other wise the weight of the beam is carried by the torsi on fibers . It can be see n that the beam is r athe r low with respect to the ends of the tors ion fibers. The housing, with it s sus pended beam , was lifted two inches above a wooden table and then dropped . Shor tly after impact, the picture shown in Fig. 6 was taken . The torsi on fiber is s lack, the far side of the beam has moved upward nearly an inch , and the tr iangle of the rear te rminal sus pension has moved to the r ight while r otat ing. It is evident that this sever e test provided an excess s train for the fine fibers .
The beam used In a typical vacuum bal ance weighs 175 mg and is constructed fr om fused s ilica r ods r anging in diamete r from 0.2 to 0.4 mm . With a zuo-mg sample load, the center of mass was adjus ted to give a per iod of 45 sec and a deflection se ns iti vity of 6· / "g.
48 J. RODDER
Housing
In order to accommodate the long torsion fibers, the design of the glass housing presented some special problems. The diffi­ culties were overcome as shown in Fig. 7. There are two posts inside to which the torsion fibers are fused. After the adjustments on the beam are completed and the subassemblies added, the four end caps are sealed. While some care must be exercised in the assembly, the result is a compact lightweight housing having a volume of less than 1.5 liters. If desired, the sample hangdown tube can be sealed to a vacuum flange which makes it easy to move the balance to a different location.
Electronics
A photocell was chosen as the transducer to detect beam movement for several reasons. First, it exerts no force on the beam. Second, the photocell is located outside the vacuum sys­ tem and can be removed during the bakeout, Finally, the associ­ ated electronic circuitry is relatively simple. Small mass changes are determined by using the well-known magnetic compensation method! in which the magnetic field of a coil interacts with a per­ manent magnet suspended from the beam. The beam is maintained in a null position by an electronic feedback system whose output current to the coil is a linear function of the weight change. A block diagram of the electronic system is shown in Fig. 8. The electronic circuitry is complicated by the tendency of the flexible quartz system to Vibrate. As a consequence, the electronic com­ ponents must be selected carefully.
RESULTS
The system was first tested at atmospheric pressure. The balance drifted continually after initial equilibrium was established because heat from the photocell lamp generated air currents within the housing. Subsequent pumping to 10- 2 torr reduced the drift to an acceptably small level. As a final check the system was pumped to 10-6 torr. At approximately 10-4 torr the noise level at the control system output increased abruptly. Apparently, at 10-2 torr the air was still effective in damping the mechanical system, but at 10-4 torr damping disappeared. At pressures less than 10-4 torr, the slightest vibration caused up to a 2000-fold in­ crease in the noise level of the system.
A ~ AtrTmtATED t 'LTRA\lI CROBALANCE 49
f ig. 7. Prororype vacuum balance .
50 J. RODDER
The magnitude of the vibration problem ruled out the usual brute force method of mounting the balance on a massive support. The problem can be solved if there exists a transducer which pro­ vides a signal to the amplifier only if the beam rotates. Vertical oscillations caused by vibration should contribute nothing to the signal. This transducer can be realized in practice by using two photocells as shown in Fig. 9. In this circuit the connection of the photocells eliminates the signal due to the vertical displacement of the beam. In addition to solving the vibration problem, the two photocell system provides temperature compensation and doubles the signal to the amplifier. To use the two photocell system, the beam and housing were modified according to the diagram shown in Fig. 10. The two flags interrupt the light to the photocell.
Another effect can occur as the pressure is reduced below 10-4 torr; that is, the magnet begins to swing. The oscillations are gradually amplified by the control system until the control loop becomes unstable. This problem proved a most difficult one to solve. Since the oscillations began only after air damping had been removed, magnetic damping was tried first. This proved in­ effective and also interfered with the beam magnet and coiL
Finally, it was postulated that even though the field in a cylindrically wound coil diverges, there must be one position where the field of the coil is axial to the field of the suspended magnet. At this point no lateral forces are exerted on the mag­ net. Such a relationship between the coil and magnet does exist. With a properly positioned coil the total excursion of the magnet can be decreased to less than 25 p.. Furthermore , a forced oscil­ lation of the magnet can be damped within 20 min.
PERFORMANCE
The sensibility of the balance is a function of the distance be­ tween the center of the coil and the poles of the permanent magnet. By making the distance relatively long it is poss ible to obtain a calibration that yields an output of 1 mV/0.5 p.g; thus , 5 . 10-9 g corresponds to a 1% movement on the I-mV scale. At this high sensibility, it is necessary to tare the balance to within 400 p. g of the absolute null because of the limited range of compensation by the coil. The balance is insensitive to vibration so a sturdy wood­ en table provides an adequate support. Even with the vibrations from a compressor operating nearby, the balance performed satis­ factorily. Finally, a balance of this type has been used effectively
AN AUTOMATED ULTRAMICROBALANCE 51
Fig. 9. Wheatstone bridge circuit of two-photocell system.
Fig. 10. Components of the beam and housing: 1) sample tube; 2) window; 3) flag : 4) magnet; 5) vacuum flange; 6) ring seal.
52 J. RODDER
as a tool for surface studies, which will be discussed in detail in the paper by R. Merrill.6
CONCLUSION
A beam design has been developed with features not found in other balances. First, when used as a torsion balance, the deflec­ tion sensitivity varies only a few parts per 10,000 from no load to maximum load. Second, the design of the terminal suspension pro­ vides for a nonrotatable sample. Finally, as.a torsion fiber bal­ ance, the design is unique regarding the ruggedness of the quartz system.
ACKNOWLEDGEMENT
The author is indebted to Dr. D. Clark for his help in design­ ing the electronic system.
REFERENCES
1. A. W. Czanderna, Ultramicrobalance review, in: S. P. Wolsky and E. Zdanuk (eds.) , Ultra Micro Weight Determina­ tion in Controlled Environment, Interscience, New York (1969), p. 11.
2. R. L. Schwoebel, Ultramicro