PHYSICAL CHEMISTRY OF MELTS CONTAINING

COPPER, LEAD AND ARSENIC by

Anthony Richard Aldhous B.Sc

A thesis submitted for the degree of Doctor of Philosophy of the University of London and for

the Diploma of Membership of the Imperial College.

Department of Metallurgy Imperial College London

July 1982

ABSTRACT

The activity of arsenic in copper arsenic and lead copper arsenic alloys is investigated by the transpiration technique. This method is selected because of the high vapour pressure of arsenic and the relatively low vapour pressures of copper and lead. The arsenic activity is varied by altering the temperature of arsenic in an argon stream, which then equilibrates with the metal droplets.

The activity of arsenic is measured in copper arsenic alloys in the range from 900 to 1114 °C. Pure copper droplets are equilibrated with the arsenic laden argon. In the lead copper arsenic system the arsenic activity is set and high arsenic master alloys come to equilibrium by arsenic evaporation, Iso-activity lines are plotted cn ternary phase diagrams.

Arsenic forms a number of molecules in the vapour phase. It evaporates predominantly as As. molecules at temperatures up to » 4 500 °C but dissociates into As^, As^, and As^ as the vapour is heated at the same total pressure. The equilibrium constants for each of the vapour phase reactions are calculated and the standard states and experimental vapour pressures are found by a computer programme.

The activity of copper in copper arsenic alloys is calculated from the arsenic activity data. Integral and partial molar free energies of solution are derived.

The results are compared with earlier investigations after all of the data are converted to a liquid arsenic standard state.

There is close agreement with activity data from earlier investigations.

The results from the research are discussed with reference to the smelting of complex non-ferrous charges. The position of the tie-lines across the miscibility gap in the lead copper arsenic system is explained.

CONTENTS

CHAPTER 1 - INTRODUCTION 1 1.1 Smelting of Complex Non-Ferrous Materials 2 1.1.1 The Imperial Smelting Furnace 8 1.2 Vapour Pressure of Arsenic 10 1.2.1 Determinations of the Vapour Pressure of

Arsenic 12 1.3 The Copper Arsenic System 21 1.3.1 Activity Determinations 21 1.4 The Lead Arsenic System 31 1.5 The Lead-Copper-Arsenic System 34

CHAPTER .2 - EXPERIMENTAL WORK 48 2.1 Activity and Vapour Pressure Measurement

Techniques 49 2.1.1 The Knudsen Effusion Techniques 50 2.1.2 The Langmuir Method 52

2.1.3 The Isopiestic Method 52 2.1.4 The Transpiration Technique 53 2.1.4.1 Saturation and Diffusion of the Vapour 55 2.2 Apparatus 59 2.3 Experimental Technique 63

2.4 Activity Measurement in the Lead-Copper-Arsenic System 71

2.5 Knudsen Cell Mass Spectrometry 78 2.6 Chemical Analysis 81

CHAPTER 3 - RESULTS 82 3.1 The Composition of Arsenic Vapour 83

3.2 The Copper Arsenic System 101 3.2.1 Partial Molar Free Energy of Arsenic in

Copper 101 3.2.2 Integral Free Energy of Solution 101

3.3 The Lead-Copper-Arseriic System 116 3.4 Mass Spectrometry 126

CHAPTER 4 - DISCUSSION 127

4.1 Experimental Technique 128 4.2 The Copper Arsenic System 131 4.2.1 Variation of Activity Coefficient with

Composition 131 4.2.2 The Activity of Copper in Copper-Arsenic

Alloys 135 4.3 The Lead-Copper-Arsenic System 153

APPENDIX 1 161 APPENDIX 2 165 APPENDIX 3 167

REFERENCES 172

ACKNOWLEDGEMENTS 175

1

CHAPTER 1 INTRODUCTION

2

1.1 Smelting of Complex Non-Ferrous Materials

Complex smelting is a traditional process for the treatment of materials which may contain lead, copper, nickel, zinc, iron, sulphur various other semi-metallic elements and some precious metals. The process is traditionally carried out in several stages; sinter-roasting, smelting, converting and refining.

Lead is a major component in every charge and all of the elements are soluble in it at 1250 °C, a typical blast furnace smelting temperature. The solubility of copper and some of the other important metals falls as the temperature decreases. This creates the conditions in which several phases can form.

Davey (1) reported thermodynamic data for many of the binary and ternary systems related to the drossing of lead. Many of the systems are also the constituents of phases encountered in complex smelting. In an idealised complex smelting charge the only elements present would be lead, copper, sulphur and arsenic.

The solubility of copper in lead falls on cooling so that by 600 °C only around 1% by weight of copper is still in solution. The solubility of sulphur also .falls and the similar free energies of formation of the sulphides leads to the formation of of a mixed PbS-Cu S phase, a matte. The Pb-As system forms near to ideal solutions but the copper which separates from the lead contains arsenic at a far lower activity. The copper-arsenic phase which forms separately from the matte is called speiss. The three phases come to equilibrium with each other and are mutually insoluble.

3

The Fb-Cu-As-S system has been investigated experimentally by Matyar (2).

Phase relationships are important because once these are understood the quantities and qualities of the phases which are produced can be predicted and the process optimised. The importance of these relationships was recognised when the possibility of charging copper in the Imperial Smelting Furnace was investigated (3)* Several campaigns were run,with copper, around Europe (4).

The materials for charging in complex smelting are of varying composition and texture. These may vary from complex sulphide concentrates to slimes as well as recycled batteries and scrap assemblies such as electronic circuit boards. These materials may also contain cadmium, tin, cobalt and other values

(5).

One site which was developed for the treatment of complex materials is Metallurgie Hoboken (6). The plant is so diverse that almost any material may be processed. The steps in the processing are described below.

Sinter-Roasting The sinter-roasting has two purposes; 1) To desulphurise sulphide or sulphate materials 2) To agglomerate the materials for smelting

During the sintering the temperature must be carefully controlled to ensure that the high lead concentrates do not melt and that the rate of sulphur elimination is not too high for efficient gas cleaninr'.

4

Lead/Copper Blast Furnace Smelting

The Hoboken smelter is charged by means of buckets contain-

ing 1.5 tonnes of material. The smelter has a throughput of

1100 to 1200 tonnes of lead-copper concentrates per day. Typical

ranges of charge materials are;

Sinter 1 5 - 6 0 $

Return Converter Slag 15 - 20$

Lead Drosses 1 0 - 1 5 $

Various Scrap 5 - 10%

Return Smelter Slag 8 - 10%

Low Grade Matte 2 - 5%

The coke consumption varies from 10 to 14% of the total charge.

Four phases are generally produced, these are:-

1) Slag

2) Matte 5 - 15% of charge

5) Speiss 5 - 10% of charge

4) lead Bullion 15 - 25% of charge.

Zinc is collected from the fume and can be processed separately.

Although computer programmes may be produced to optimise the

distribution and recovery of the elements in the charge, much of

the information is empirical and there are many areas associated

with smelting for which there are few thermodynamic data avail-

able. As would be expected, varying the charge alters the

relative amounts of the phases which are produced, the compo-

sitions of which are related to one another by various equil-

ibrium relationships.

The Slag

The slag concentrates the elements with the highest affinity

5

for oxygen. Its main components are SiO^, CaO, AI^O^, ZnO and

FeO. Typically seventy per cent of the iron charged is

tapped as slag, the lead content of which is one or two per

cent. Tin and cobalt tend to be divided between the slag and

the reduced phases. Elements with a lower affinity for

oxygen such as copper and lead are concentrated mainly in the

reduced phases.

The Matte

The matte or sulphide rich phase consists of four main

constituents Cu^S, PbS, FeS and ZnS. The composition of the

matte is determined by the way in which the sulphur combines

with the metals, thus depending upon the stability of the

sulphides and the activities of the metals and of sulphur in

the molten phases. In complex metallurgy the matte usually

comes to equilibrium with the bullion phase. The bullion is

really a solution of speiss and lead bullion at this stage,

but their separation will not occur until the temperature

falls to around 1050°C. This will happen after the products

have left the blast furnace, tapping usually taking place at

about 1125°C.

The mattes which are produced may be represented on a

CUgS, PbS, (Fe+Zn)S ternary diagram (Fig 1). Regions are

indicated representing the predominant compositions for

various types of smelting. In the centre of the diagram

are mattes produced in the smelting of lead, with the lead

content of the slag being one or two per cent. At the

extreme left is the region of cure lead smelting, such as

6

FeS *ZnS

C u

charges

Mattes produced by smelting complex sulphides (weight %)

Figure 1

7

the primary smelling of galena concentrates with a very low

copper content. The activity of copper gradually increases

across the diagram as the amount of copper charged increases,

until the composition of black copper is reached with only

small amounts of lead present. Towards the top of the diagram

are the mattes produced with strongly reducing smelting, with

slags containing less than 0*8 per cent lead. At the bottom

of the diagram are mattes which result from the re-melting of

drosses produced during the liquation and sulphur drossing of

lead. No reduction is applied during this process, so when a

slag is produced it has a high lead content.

The Speiss

In complex metallurgy the speiss covers a large range of

compositions. It is generally an arsenide rich phase, but

most of the bismuth, antimony, and tin will be found here too.

Charges in complex metallurgy are typified by a copper content

of between 10 and 30?. in the lead, for a copper rich phase

to form its activity would have to approach unity. If there

are sufficient impurities present, the copper may combine

with the metalloids to produce an alloy where it would be

diluted to such an extent that its activity could be lowered

to 0*1 to 0«% This constitutes the primary mechanism by

which speiss is formed. This same mechanism is applicable

to iron. If the reduction is severe the iron activity may

rise to 0»2 and in these cases the iron may alloy to produce

a phase in which its activity is in the range 0*1 to 0*2.

In the Imperial Smelting Process where the iron activity

8

may rise to 0*5, this tendency to produce a ferrous speiss

is even more pronounced and this phase will have a strongly

metallic nature.

If nickel or cobalt are present in the charge, they

too will tend to enter the speiss. One of the main charac-

teristics of these products is that they are generally

insoluble in the liquid state in mattes and lead bullion.

The speisses, however, can be contaminated with both

metallic lead and matte and may contain up to 25 per

cent of each.

An area of great interest is the distribution of the i

impurities As, Sb and Sn among the phases produced. The

speiss will separate from the bullion to a greater extent

as the temperature falls until 600°C which is the typical

temperature for the solidification of speiss.

The Dust

The liquid phases which separate after tapping from the

metal pool may approach equilibrium, owing to their intimate

contact. Gaseous products are not generally in equilibrium

with the charge, so it is usually difficult to predict these.

The main components of the dust are elements which are vapour-

ised in the hot region of the shaft and escape in suspension

with the exhaust gases. Three main components are zinc, lead

and lead sulphide.

1.1.1 The Imperial Smelting Furnace

The Imperial Smelting Process was developed initially

9

as a zinc smelting process, this was soon adapted to combined lead-zinc smelting, particularly as the two tend to occur together in ores. In 1959 experiments were started on the use of copper-bearing sinter and, after successful trials were carried out on the experimental blast furnace, several campaigns were run on various Imperial Smelting Furnaces (7, 9). The trials covered a wide range of compositions and data were collected for cooper lead ratios up to 0*2 by weight. The operators noted that the only removal of arsenic from the system was in the speiss phase, however because of the low arsenic content, very little speiss was produced. Most interest was centered upon the recovery of, and the effect of the presence of, copper. It was observed that the presence of copper reduced the rate of sulphide accretion and also reduced the rate of volatilisation of arsenic which had previously been carried to the zinc condenser. The copper ultimately formed a speiss and matte and these produced a dross as the lead bullion was cooled. This was a result of the difference in composition between the bullions produced by lead refiners and those from the high copper trials. Most lead smelters yield bullion which contains sufficient arsenic and sulphur to combine with all of the copper. Normal copper Crossing techniques were applied. As was noted earlier the volatalisation of arsenic was reduced by the addition of copper and it was thought that the vapour pressure of arsenic was related to its pressure over a lead-copper-arsenic alloy.

1.2 Vapour Pressure Of Arsenic

The vapour pressure of arsenic has been investigated by several techniques. It has been known for a long time that arsenic sublimes at ambient pressure 'and the invest-igations may be divided into two categories. Firstly, experiments to discover the vapour pressure and molecular composition of the gas produced when the solid evaporates, and secondly, investigations into the high pressure equilibrium between liquid and vapour and the determination of the triple point. Techniques for vapour pressure measurements have included quartz spiral manometers, Knudsen Cell(with mass-spectrometer), weight change methods and high pressure Bourdon Guag.es.

Apparatus for Vapour Pressure Measurement The earliest work of any significance was carried out

with a silica spiral manometer. The main component of the apparatus is a hollow silica spiral which is connected to a supply of the vapour being studied. As the pressure increases the tendency is for the spiral to unwind. As only a small strain can be tolerated, the spiral is surrounded by a second silica vessel in which the pressure may be varied and measured. As the pressure in the outer vessel is increased the spiral will tend to return to its original position. In this way the apparatus can be used as a null-point detector. To increase the sensitivity of the apparatus a mirror may be fixed to the quartz spiral so that the mirror rotates around its axis and by directing a light beam on to the mirror the null-noint m3y be more precisely fjund.

11

A similar apparatus is the silica spoon guage manometer, this is based on the same principle but the spiral is replaced by a hollow, dished, silica spoon, from the end of which a fibre is drawn to act as a pointer. This may be used as a null-point detector in the same way as the silica spiral.

The Knudsen Cell is an evaporation cell which is operated in a vacuum. A small hollow inert cell is constructed and into this the material to be evaporated is placed. The lid is then fixed onto the cell, the only exit from the cell is then a minute orifice made in the side of the cell. The cell is then inserted into the evacuated apparatus and heated. The material starts to evaporate. The exit of the vapour from the cell is controlled by the orifice. For correct operation the vapour in the cell should be at equilibrium, so the rate of effusion from the cell should be the same as the rate of evaporation from the sample. Originally the cells were made to direct the vapour onto a cold surface where the vapour was conden-sed and deposited. The deposit was then weighed and chemic-ally analysed and the weight loss from the cell measured. From this data the vapour pressure of the sample could be calculated.

More recently the Knudsen Cell has been used with a mass-spectrometer such that the molecular species could be determined directly.

In order to find out rnore about the evaporation mechanism, single crystals were suspended in vacuo and the vapour analysed in a mass-spectrometer.

Investigations, into the triple-point of arsenic and,the

liquid-vapour equilibrium have been .carried out with high

pressure Bourdon Gauges

1.2.1 Determinations of the Vapour Pressure of Arsenic

The earli.est results of any significance were produced

by Preuner and Brockmuller(lO). A quartz spiral manometer .

was used to study the equilibrium of A s ^ , As2(g) ^ ^ A84(g)

which were believed to be the only vapour species. The

proportions of the various molecular species were changed by

heating the quartz spiral guage and keeping it at a different

temperature from the vapour source. They were thus able to

study the dissociation of As^ at higher temperatures. It

was shown that arsenic evaporates predominantly as As^

molecules at temperatures up to 800°C. The equilibria which

were considered were; 2

K S 2

AS4(g) = 2A82(g) > K1 = P As,

P A S „ 4

and As 2 ( g ) = 2As ( g ) ; = p 2A s

PAS2

Their reported values were K^ = 22• 5 and = 3*15 at

: (1000°C) which indicates

dissociated to a large extent.

1273K (1000°C) which indicates that the As^ molecules had

Horiba (11) carried out the nert investigation again with

a silica spiral manometer but this time with the aim of deter-mining the triple point of arsenic. A heavier gauge of quartz was used because of the high pressures involved. The arsenic used in this study was re-sublimed to increase the purity. The results which were published seemed quite acceptable with a clear discontinuity in the pressure at 822°G and at a total pressure of 36*5 atmospheres. It was also noted that the system took some time to reach its equilibrium vapour pressure.

Brewer and Kane (12) used a Knudsen cell to investigate the evaporation of arsenic. They also noted that the arsenic evaporated relatively slowly and accounted for this by refer-ence to the crystal lattice of arsenic which, they argued, had relatively few sites to provide As^ molecules. This means that for a Knudsen cell to operate under equilibrium conditions the cell orifice should be smaller than the equilibrium vapour pressure would suggest. To increase the rate of evaporation the arsenic was dissolved in thallium which catalyses the evaporation of arsenic. This gave a thirty-fold increase in the observed vapour pressure seen outside the cell. The effusate was shown to be predominantly arsenic by mass-spec trometry.

Goldfinger and Jeunehomme (13) carried out a mass-, spec-trometry study of InAs and identified all of the ionic

+ + species from As to As^ inclusive. They believed that the species evaporating into the vapour were predominantly As^ and

+ + As0 whereas the As, and As. were thought to be due to frag-mentation of the parent molecules by electron impact. A value

for the free energy of dissociation of As^^, to 2 As^gj

was calculated to be 67*3 kcal/mol. at 298 K.

Nesmeyanov (14) reviewed the available data on arsenic and also carried out some experimental determinations of the equilibrium vapour pressure over solid arsenic. The Knudsen effusion technique was used over the range 117 to 300°C. An elaborate preparation technique was used in which As O

76 was irradiated to produce the isotope As, the oxide was then hydrogen reduced. At the end of the experiment the condensate was dissolved and the arsenic precipitated as magnesium ammonium arsenate. The radioactivity of this was then measured against standards produced by the same technique. This investigation yielded rather lower vapour pressures than expected, due again to non-equilibrium conditions within the cell, because of the relatively slow evaporation rate of arsenic.

Arthur (15) carried out a mass-spectrometric study of + + + + GaAs and found As and As^ as well as As and As the latter two being supposed to be fragments caused by the isolation process, as they were always a constant multiple of the parent molecule intensity. In the course of each experiment he noted a gradual build-up of arsenic vapour within the chamber of the mass-spectrometer. To minimise this he inserted a massive cooled copper shutter between the Knudsen cell and the mass-spectometer. The immediate effect of this was to raise the As : As ratio from around unity to one hundred and fifty at 1100 K (1373°C). He argued that

other experiments were incorrect as they allowed As molecules to recombine to As^ as the vapour cooled whilst in and approa-ching the ionisation chamber.

Herrick and Feber (16) carried out an investigation into the evaporation of arsenic by free evaporation and effusion of high purity arsenic. The main impurity in the arsenic with which they were supplied was oxygen, so their purification was aimed at reducing this substantially. The arsenic powder was deoxidised with zirconium and the arsenic was distilled from the products, it was then repeatedly sublimed and distilled in order to minimise the other impurities. Some larger grained arsenic was also used and this was a higher purity than the powder. The free evaporation experiments were less informative than the effusion technique. A variety of torsion effusion cells were used with different orifice sizes, and the results were given in the form of standard thermodynamic functions in the range 298 to 1090 K for solid arsenic, and in the range 298 to 1300 K for As^ vapour.

Hudson (17) worked on electron impact on the molecules in arsenic and antimony vapour. The experiments were carried out on a Knudsen cell, mass-spectrometer combination, however it was modified in order that the energy of the impinging electr-rons could be closely controlled. By this means the dissoc-iation energies for the various molecular species were found by measuring the exact point of the discontinuity in the ionisation efficiency curves. Only small amounts of oxide were observed and these were quickly removed from the system.

In order to minimise the build-up of arsenic vapour within the apparatus, two steps were taken;

1) A pump was located directly opposite to the flow of vapour from the cell.

2) A cold trap was held at liquid nitrogen temperature in order to condense the vapour. Data was produced for the dissociation energies for various reactions and also the equilibrium vapour pressure of each of the molecular species. This technique was not subject to the problem of recombination of the molecules which Arthur had considered to be a major deficiency in other studies with Knudsen cells.

High temperature data, above the sublimation point, is important because it will be used for determination of standard states in later experimental work. Experiments were carried out by Baker (18) who determined the triple point of arsenic and also the equilibrium vapour pressure over liquid arsenic at temperatures in excess of 816°C. The experiments were carried out in a high pressure apparatus, with the pressure being measured at temperatures from 816 to 1050°C. When values of lg P (atm.) are plotted against (1/T) K the results give a very good straight line in the region 816 to 1050°C for the liquid-vapour equilibrium. A best linear fit for the data is represented by;

lg1Q P (atm.) = - 2405/T + 3-759 This meant that liquid arsenic could be used as the standard state for these studies of activity, whereas earlier studies

had used extrapolated solid-vapour equilibrium data and a

hypothetical standard state.

Rau (19) also measured the vapour pressure above

arsenic. A study was made of the saturated vapour pressure

over liquid arsenic, and also gas density measurements

were made by measuring the pressure exerted by a known

amount of arsenic in a predetermined volume. The van der

Waals constants for As^^j and As^^j were calculated.

Baker and Rau are in general agreement about the

saturated vapour pressure in the region of the triple point,

however as the temperature increases the pressure measured

by Rau tends to be lower than that measured by Baker. The

data of Baker is preferred because of the better linear fit

of the data in the form log1QP against (1/T) K (Fig 2). It

is possible to obtain a curve similar to that found by Rau,

particularly where a complex vapour is formed, the decrease

in pressure being explained by the tendency for the vapour

to form larger molecules as the temperature increases.

However in this study it will be shown that 99*7% of the

pressure is due to As^ molecules at 1100°C, so the devia-

tion from linearity can not be explained by this phenomenon.

A complete survey of the vapour pressure data for

arsenic was carried out by Hultgren et al (20) and since

no data was produced subsequently, this was used for the

analysis of the vapour. Hultgren selected the best data for

the reaction As, i As., N in the form of AGm for temper-(s) 4 4(g) I atures from 300 to 1200 K. This data was used to produce

f Log P/atm

Baker N \

1/T x 10 K

7-0 8-0 90 Figure 2 The vapour pressure above liquid arsenic after Rau and Baker

a least squares fit, so that continuous function of temper-ature was found. The data from which the relative amounts of each molecular species were calculated was also based on the assessment of Hultgren et al. which agreed very closely with the dissociation energies which were found by Hudson in his investigation.

The vapour pressures of other elements which were used in the research were not as critical as that of arsenic. The data was taken from Hultgren et al (20), the vapour pressure data for lead and copper is given in table 1 •

20

Lead

Copper

Tenroerature Temperature Vapour Pressure /K A /atm 500 227 2*2 x 10"15

6 0 0 • 6 3 2 7 - 6 5 - 3 X 1 0 " 1 2

700 427 1-11 x 10"9

800 527 6-08 x 10~8

900 627 1-35 x 10~6

1000 727 1-61 x 10"5

1100 927 6-36 x 10~4

1300 1027 2* 60 x 10~5

1000 727 1-7 x 10"11

1100 827 6-4 x 10~10

1200 927 1-3 x 10"8

1300 1027 1-68 x 10~7

1400 1127 1-43 x 10"6

1300 1227 8-60 x 10~6

Vapour Pressure of Lead and Copper Table 1

1.3 The Copper-Arsenic System

The phase diagram for copper-arsenic has been estab-

lished by a number of workers with only small discrepancies

between investigations (21, 22, 23). The phase diagram used

for reference in this investigation was itself a compilation

based on these (24) (Fig 3). Pure copper melts at 1083°C

and addition of arsenic lowers the liquidus steeply to a

eutectic at = 0-816 and 958 K. The liquidus rises to a

maximum at the composition Cu_As at 1100 K, at higher arsenic

contents the liquidus again falls. The high arsenic region

of the diagram is incomplete because arsenic exerts high

vapour pressures above these melts which makes them diffi-

cult to study.

1.3.1 Activity Determinations

The activity of arsenic in liquid copper has been

investigated by two techniques; the transpiration technique

and measurement of E.M.F. in a differential concentration

cell. Jones and Philipp (25) working with copper droplets

at 1100°C, equilibrated them with arsenic vapour in an

inert gas steam. The arsenic -vapour was produced by passing

the argon carrier gas over solid arsenic which was held at

a temperature between 270° and 390°. In order to demonstrate

that equilibrium was achieved, alloys were made from copper

and arsenic such that the droplets contained both more and

less than the final amounts of arsenic. It was shown that

these alloys reached the same composition on rising and

falling arsenic contents. Fxperiments were carried out

ARSENIC-COPPER SYSTEM

Figure 3

over a range from five to seventy hours. The analysis of the

samples was carried out by weight change and by chemical

analysis. As the two techniques agreed, within experimental

error, the former was adopted as standard. The activity of

arsenic was given as = 'but total pressure was

used instead of monotomic parial pressures. They noted that

the arsenic evaporated as As^ and that it would dissociate

at 1100°C, but to an unknown extent. (Figure 4)

Azakami and Yazawa (26) used an electrochemical method

to measure the E.M.F. of a concentration cell,

C u ^ = Cu (in alloy).

The alloys were made with a mole fraction of arsenic up to

0»305. A NaCl - KC1 salt bridge containing CuCl2 was used

to minimise the junction potentials. The E.M.F. measure-

ments of the cell yielded the activity of the copper in

the alloy and hence values for V^ . In order to calculate

the activity of the arsenic it was necessary to integrate

by means of the Gibbs-Duhem equation. The values for ^

were only obtained over a small range of compositions, so

it was not possible to integrate directly without suppl-

ementary data. The activity of arsenic had to be found

at some composition by another technique. They selected the

transpiration technique at 1000°C and produced a Cu-As alloy

with N, = 0 2 7 by eouilibration of copper with a stream of A S

argon which had passed over heated solid arsenic.

By consideration of the equilibrium for the dissociation

of A s w % to As,./ \ t.h v were able to calculate a value of 4 ( G ) 2 1 ER ;

24

Original data from Jones and Philipp

- 4 ' 0 - R

-50

-60

-7-0

-80

10 9 *As

1 0 0-9 0-8 0-7 0-6 0-5

N Cu

The activity coefficient of arsenic in copper at 1373 K

Figure 4

25

P. at 1000 °C. As. 4 In transpiration experiments, the vapour pressure of

component i, P^ is determined by,

P. = n. x P L _ I n. + n

I G where P is the total pressure, and n. and n are the number l g

of moles of compound i and the carrier gas respectively. Now

re-nalculating as if the vapour were composed of oniy the

monomer, m, of the evaporating element, P = PA + 2Pa + 4Pa x P m As As0 As. 2 4

PA + 2P. + 4 P. + P As As2 As^ g

They then considered the equilibrium between the various

vapour species ;

2 As As_ , K1 = P, / P2 g 2 g' ASg As

4 As As. ,K2 = P. / pf + g 4 g As^ As so tnat,

P = P, +2 CK1.P 2 + 4.K2.pf x P ^ m As As As

P. +2.K1.P2 + 4.K2.P, + P As As As g

As P = P. + PA + P. + P. + P As As0 As, As. g 2 3 4

Rearranging (1) leads to,

(4.P - L P ).K2.P, + (2.P - P ).K1.P2 - P.P., - P.P = 0 m As PI AS As m

so bv substituting the value of p- found exoerimentaily the M

values of P , P, , and PA were calculated. In the original As A s ' As. 2 4 report of the work ar: error was made in these calculations

which .led to -n undulv low value for a. . The results are shown As on flvnire' 5.

8 \-

6 -

4 -

0 10 0-8 06

N 2 Cu

Activity coefficient of arsenic in copper as determined by

Azakami and Yaza.va, Figure 5

27

The only other investigation was carried out by Bode,

Pawlek, and Gerlach (27) . They used an apparatus in which

an inert gas was passed over a copper - arsenic alloy. The

amount of arsenic removed from the alloy was measured by

weight change. The vapour pressures of arsenic which they

reported were very low, so that the total vapour pressure of

arsenic over the alloy was of the same order of magnitude as

the vapour pressure of copper. This makes it difficult to

attribute the weight change to the evaporation of arsenic only.

The reported values for the activity coefficient of arsenic

relative to a solid arsenic standard state had ranged from -7 -Z

5 "x 10 to 1.45 x 10 which are extremely low and divergent

values. Recent analysis of these investigations has indicated

that higher values for should have been obtained. Lynch

(28) used data which was not available to Jones and Philipp,

and also identified the numerical error in the vapour composi-

tion calculation carried out by Aza.ka.mi and Yazawa. As noted earlier Jones and Philipp determined the activity

of arsenic in copper by transpiration-with the activity of

arsenic being given by a, = P. / . Lynch was able to ° As As As

calculate the relative abur.dancies of the various vapour-

components, and was hence a.nle to recalculate the arsenic

activity as ;

= P, / P? = (pA / pA ^ = (pA / p? and As As As As» A s ' As, As, 2 2 y i

siirp la.r'Lv for As.. The value of P° was used for the standard 4 A S 4

state as this is the nredominant species when arsenic evaporates

and there was least uncertainty about the amount of As^

present at 1100 °C. In the recalculation a hypothetical

solid arsenic standard state was used as the author was

unaware of the data of Baker(18) and Rau(l9) who had both

measured the total pressure of the vapour above solid and

liquid arsenic. The revised results are given in table 2 and

figure 6.

The data of Azakami and Yazawa was also re-assessed by

Lynch, again using a solid arsenic standard state. This

revision gave the measured point at 0*27 as 2 o a. = x 10- and {iL = 0*1976, and hence a value for VA as as as

of around 3*6 at 1273 K.

29

T/K Na As ^As. 4 aAs to

543 0-174 6-01 X 10-8 2-64 X 10" -3 1-52 X 10-2

553 0-197 2-39 X 10-7 3-73 X 10" -3 1-89 X ID"2

573 0-217 2-01 X 10-6 6-35 X 10' -3 2-93 X 10-2

584 0-228 5.4O X 10-6 8-13 X 10" -3 3-57 X 10 "

609 0-250 4-36 X 10"? 1-37 X 10" -2 5-48 X 10-2

634 0-265 2-02 X 10~4 2-01 X 10" -2 7-64 X 10-2

644 ^•267 3-58 X 10"4 2-32 X 10" -2 8-69 X 10-2

654 0-270 6-01 X 10"4 2-64 X 10" -2 9-78 X -2

10

Data for Cu-As by Jones and Philipp at 110Q°C

Revised by Lynch (solid arsenic standard state)

Table 2

50

A 30 I

aA xlO As -3

20 t

1 0 + /

0 - 1 5 0-20 0-25

. N A S ^

0-30

The activity of arsenic in copper,data of Jones and Philipp

revised by Lynch . Figure 6

1.4 The Lead Arsenic System

The lead arsenic system is one of the constituent binary

systems which make up the lead copper arsenic ternary system,

which was studied after the copper arsenic system. The data on

the Pb-As system were taken from Hansen (29), the system is a

simple eutectic, with the eutectic point at 288 °C and at an

arsenic mole fraction of 0*074 ,(figure 7). The high arsenic

end of the phase diagram is not complete because of the high

vapour pressure of arsenic. The activity data for this system

are taken from the work of Predel and Fmam (30) the data are

reproduced in figure 8. In the range of most interest, the

region from to 0*1, a slight deviation from raoultian

behaviour is observed. An arsenic activity of 0*1 corresponds

to a mole fraction of 0*1 at 640 °C. The activities were

determined by equilibrating lead- arsenic alloys with bismuth-

arsenic alloys at the same temperature.

32

N — As

The lead arsenic phase diagram

Figure 7

The activity of arsenic in lead at 64O °C

Figure 8

54

1.5 The Lead - Copper - Arsenic System

The first extensive survey of the Pb - Cu - As phase diagram

was carried out by Dice, Oldbright and Brighton (31) who were

investigating drossing techniques in lead smelters. Experiments

were carried out on a total of twenty nine alloys, ten of which

were outside the miscibility gap, which extends from the lead -

copper binary towards the arsenic - rich region. The alloys

were heated and melted to produce a single phase, they were

then slowly cooled. Observations were made as the alloys were

cooled, and the temperatures noted at which the various phases

appeared and also when the solidification of the alloy was

completed. The final compositions of the alloys were found by

chemical analysis, the results are given in table 3* In order

to compare all investigations on the same basis, the compo-

sitions have been converted to mole fractions. The position of

the miscibility gap in weight per cent and the misc-

ibility gap in terms of mole fraction are shown in the figures

8 and 9 respectively.

Kleinheisterkamp (32) investigated the formation of speiss

phases including the Pb - Cu - As system, however his results

were not tabulated; the position of the miscibility gap was

represented on a ternary phase diagram. Jacobs, Maes and de

Stryker (35) studied the Pb - Cu - As system and also the Fe -

Pb - Cu - As system so that the effect of iron on the system

could be determined. Alloys of known starting composition

were melted and homogenised in a crucible covered by molten

salts to protect the melt from oxidation. A silica tube with

35

Data of Dice, Oldbright and Brighton for Fb-Cu-As system

UPPFR LAYER LOWER LAYER

Weight Weight s

Pb Cu As Pb Cu As

31-2 61*4 3*3 87*5 11 1 0*4 29-3 68*8 5*6 92*7 7 1 0*2 13*2 73-1 10*5 95*5 4 2 0*3 4-4 74*5 17*9 98«4 1 5 0-1 4*8 73*3 18*0 98-4 1 4 0-2 4*3 71*3 20*8 98-5 1 3 0-2 10*0 63*8 24*4 97*2 2 0 0*8 9*1 63*6 22*8 07*2 2 2 0*6 12-8 61 *2 24*9 95*3 2 1 2*6 13*3 50-6 24*9 92*7 2 0 4*3 13*6 59*0 24*6 92*0 2 8 3*8 15*1 57*1 25-1 90-4 3 5 6*1 15*0 57*4 24*5 92*9 2 6 4*5 18-0 55*5 24*5 90-7 3 4 5*9 23*6 49*4 24*1 85*9 4 9 7*6 24-9 49-2 23*7 87*6 5 0 7*4 28*5 44-5 23*9 84*0 5 8 8*5 30-6 43*6 24*1 81*4 6 8 10*2 33*0 42-4 24*0 80*8 7 6 10-1

Contimied overleaf

56

Data of Dice, Oldbright m d Brighton for Pb-Cu-As system

UPPER LAYER LOWER LAYER

Mole fractions Mole fractions

Pb Cu As Pb Cu As

0 130 0*832 3*8 x 10~2 0*701 2 90 8 9 X 10"5

0 108 0*835 5*8 x 10~2 0*796 0 199 4 8 x ID"5

4 7 x 10-2 0*850 0*103 0*868 0 125 7 5 x 10-5

1 5 x 10"2 0*819 0*167 0*950 4 7 x 10-2 2 7 x 10"5

1 6 x 10"2 0*814 0*169 0*951 4 4 x 10-2 5 3 x 10~5

1 5 x 10-2 0*790 0*195 0*954 4 1 X 10-2 5 4 x -3 10 J

5 5 x 10-2 0*729 0*236 0*918 6 2 x 10-2 2 1 X 10-2

5 5 x 10-2 0*742 0*225 0*917 6 8 x 10-2 1 6 x 10-2

4 6 x 10"2 0*710 0*245 0*872 6 3 x 10"2 6 6 x 10-2

4 8 x -2 10 0*703 0*249 0*810 8 6 x 10-2 0 104 5 0 x 1 0 - 2 0*702 0*248 0*824 8 2 x 10-2 9 4 x 10-2

5 6 x 10"2 0*688 0*256 0*762 9 6 x 10-2 0 142 5 6 x 10-2 0*694 0*251 0*816 7 5 x 10-2 0 109 6 8 x 10"2 0*679 0*254 0*768 9 4 x 10-2 0 138 9 4 x 10-2 0*641 0*265 0*699 n 130 0 171 9 9 x -2

10 0*640 0*261 0*704 0 131 0 165

0 119 0*606 0*276 0*664 0 150 0 186 0 128 0*594 0*278 0*618 0 168 0 214 0 139 0*582 0*279 0*605 0 186 0 209

Chemical Analyses of Alloys within the Miscibility Gap

Table 3

37

Mi scibiiity Gap in

A " / / \ Cu

N Pb

Data from Dice, Oldbright and Brighton converted to mole fractions

F i g u r e 1934

Pb

CO

a nozzle was inserted into the melt such that half of the melt

was above the nozzle. The other end of the silica tube was

connected, by means of a T-junction to a rubber bulb, the other

junction being connected to a water-filled manometer. The alloy

was then cooled. As the alloy reached the boundary of the misc-

ibility gap it separated into two layers, one lead-rich and one

copper-rich. This separation caused the density of the melt

above the nozzle to decrease and so the pressure required to

produce a bubble from the nozzle also decreased. By plotting

pressure against temperature^ the temperature at which the alloy

formed two layers was found.

Experiments were carried out on three composition lines

across the Pb - Cu - As ternary these were, Pb - (Cu + 20% As),

Pb - (Cu + 14% As) and Pb - (Cu + 26% As). The two layers

which were formed in each case were also chemically analysed.

From this data they were able to locate the miscibility gap

in the range from 800°C to 1065°C at which temperature it

is closed up completely. The data for 800°C and 950°C together

with a conversion to mole fractions are given in tables 4 and 5,

the position of the miscibility gap is given in terms of weight

per cent and mole fraction in figures 10 and 11 respectively.

Tn complex smelting the silver tends to separate between the

lead bullion and the speiss phases. Hino, Azakami and Yazawa

(34) studied the effect of silver on the Pb - Cu - As and the

Fe - Pb - As systems, and its distribution between the two

phases which were produced within the miscibility gap. Up to

three weight per cent silver was added to the bullion, and

the two phases were analysed after they had come to

As

The miscibility gap in the Pb-Cu-As system found by Jacobs, Maes and de Stryker

F i g u r e 10

4 \

The ternary miscibility gap as measured by Jacobs, Maes and de Stryker; in mole fractions

Figu re 11

Pb - Cu - As Misclbility Gap at 800L'C

Weight per cent

Pb Cu As

35 65 0

15 75 10

77 13 10

7 73 20

44 36 20

88 12 0

10 76 14

10 65 25

20 73 7

30 47 23

40 39 21

50 31 19

60 24 16

80 11 9

70 18 12

90 6 4

Table 4 •

Mole F r a c t i o n

Pb Cu As

0-142 0-858 0

0-052 0-852 0-096

0-524 0-288 0-188

0-023 0-793 0-184

0-205 0-542 0-255

0-692 0-508 0

0-034 0-856 0-150

0-054 0-728 0-257

0-072 0-858 0-070

0-121 0«621 0-258

0-178 O.565 0-258

0-245 0-497 0-258

0-529 0-429 0-242

0 • 568 0-255 0-177

0-452 0-565 0-205

0-746 0-162 0-092

Pb - Cu - As Miscibility Gap at 950°C

Weight per cent

Pb Cu As

35 65 0

19 71 10

70 20 10

13 67 20

34 46 20

88 12 0

20 58 22

30 49 21

40 42 18

50 34 16

60 27 13

80 13 7

90 7 3

Mole F r a c t i o n

Pb Cu As

0-142 0-858 0

0-068 0-832 0-099

0-423 0-401 0- 170

0-045 0-762 0- 193

0-142 0-627 0-231

0-692 0-308 0

0-074 0-701 0-225

0-121. 0-645 0-2^4

0-176 0-604 0- 219

0-244 0-541 0-216

0-326 0-479 0- 195

0-564 0-299 0- 137

0-743 0-189 0-068

Table 5

equilibrium. It was found that K. (wt.% Ag: wt.% Ag in bullion)

was 1•16 at 900°C* The presence of silver did not alter the

position of the Pb - Cu - As miscibility gap. The reported

position of the Pb - Cu - As miscibility gap differed from

other investigations. The results of the determination of

the position of the miscibility gap at 900°C without silver

are given in table 6, together with conversions to mole

fractions. The position of the miscibility gap is shown at

900°C for both weight per cent and mole fractions in figures

12 and 13 respectively.

f As

The rriiscibility gap at 900 °C, according to Hino, Azakami, and Yazawa

Figure 12

VN

t As

The rniscibility gap at 9 0 0 ° c according to Hino, Azakarni and Yazawa,

in terms of mole fraction

Figu re 13

Pb - Cu - As Miscibility Gap at ?00°C

Weight per cent

Pb Cu As

50 30 20

80 10 10

60 23 17

36 40 24

24 50 26

14 60 26

20 70 10

8 72 20

90 4 6

35 65 0

88 12 0

30 44 26

Mole F r a c t i o n

Pb Cu As

0-246 0-482 0-272

0-574 0-187 0-238

0-350 0-412 0-258

o-i6o 0-565 0-275

0-093 0-630 0-278

0-497 0-695 0-255

0-072 0-827 0-100

0-027 0-788 0-185

0-752 0-109 0-139

0-142 0-858 0

0-692 0-308 0

0-122 0-585 0-293

Table 6

CHAPTER 2

EXPERIMENTAL WORK

2.1 Activity and Vapour Pressure Measurement Techniques

Due to the very close relationship between activity and

vapour pressure of components, several techniques have been

developed to measure the vapour pressures of alloys at elevated

temperatures as a means of determining activities. Techniques

for activity determination by equilibration of condensed phases

and electromotive force measurement have also been used. The

principal activity and vapour pressure techniques will be

outlined (35,36,37).

The dewpoint method is used to measure the vapour pressure

of a volatile component of an alloy. The alloy is treated

inside an evacuated tube. When the tube is at the required

uniform temperature, the remote end of the tube is cooled,

whilst the alloy is held at a constant temperature. At some

temperature the vapour will start to condense, so the vapour

pressure of the pure component at the lower temperature is

equal to the vapour pressure over the alloy. This technique

can only be used when the vapour pressure of one component is

very different from that of the other.

The boiling point method is.based on the principle that a

liquid boils when its vapour pressure is equal to the external

pressure. Fxperimentally the pressure may be kept constant

and the temperature varied or vice versa. The boiling point

is marked by a well defined arrest temperature. It is also

possible to use weight change for finding the boiling point

as there is a sudden decrease in the weight of a substance

as it reaches its boiling point. The nroblem with this tyoe

of determination is that the discontinuity in the weight versus

temperature curve is sometimes not sharply defined. Direct

pressure measurement is only possible when the substance is

relatively volatile.

Electromotive force measurement is usually carried out in

differential concentration cells. A pure component is held in

one h-lf of the cell, and the alloy containing that component

is held in theother half at the same temperature. The two

halves of the cell are connected by a salt bridge along which

ions may travel. The electrons must then travel along an ext-

ernal conductor. When the resistance of the conductor is very

high, a value for the F..M.F. can be found and this is related

to the free energy change by the relationship,

AG 0 = - z.F.F0 where ?, is the number of electrons transferred

in the electrode reactions and F is Faradays constant. A G 9 is

also given as AG° = - R.T.ln a,. __ ^ so that the activity e (in alloy)

of the component in the alloy may be calculated.

The equilibration of condensed systems works on exactly

the same principle as the equilibration of a condensed phase

with a vapour phase, that is, at equilibrium the activity of

each component is the same in each phase. This approach is

generally adopted in consideration of equilibrium in metal/

slag or metal/matte/slag systems, where the phases are mutually

insoluble.

2.1.1 The Knudsen Fffusion Technique

The Knudsen Effusion Technique for measuring small vapour

51

pressures is important for the determination of thermodynamic

properties of vapours and condensed phases in equilibrium. In

its simplest form the sample is held in a small isothermal cell

and the vapour with which it is in equilibrium is allowed to

flow through a small thin-edged orifice into a vacuum.

Measurement of weight loss in a known period of time at a known

constant temperature and a knowledge of the relative proportions

of the molecular species in the vapour allow the partial

pressures to be calculated. Alternatively the effusate may be

condensed and weighed and, if necessary, analysed.

The molecular weight of the species effusing from the cell

must be known, and if more than one species is produced the

molecular weight of each must be known. The most powerful method

of determining the vapour species is the- mass spectrometer.

This combination allows each vapour species to be studied indiv-

idually so long as the partial pressures do not differ by several

orders of magnitude. The system must be calibrated to determine

the sensitivity for each species. The fragmentation of larger

molecules into smaller ions in the ion source is also a problem.

Direct mass-spectrometric study of the activities of alloys

involves the use of twin cells. Partial pressures of a

component in solution can be compared with the vapour pressure

of the component in the standard state, and the ratios of the

corresponding ion peaks are equal to the activities. Problems

involve the correct alignment of the molecular beam and the ion

source, and ensuring that both cells are at the same temperature.

Belton and Kruehan (38) transformed the Gibbs-Duhem equation

52

so that it could be integrated to derive activities in an alloy

with two components with approximately equal velocities from

measurements of the ratio of ion currents, thus overcoming

problems caused by changes in the sensitivity of the mass-spec-

trometer. Corresponding equations were also derived for ternary

systems and for ternary systems with one non-volatile component.

Equations were also derived which could be applied to complex

vapours where various ions are formed, the ratios of the peak

heights of the largest ion and of the second component were always

measured, thus eliminating errors arising from the fragmentation

of the complex vapour species (39*40). The limiting factors for

this technique are the vapour pressure range which is compatible

with equilibrium operation of the Knudsen cell and the sensitivity

of the mass-spectrometer.

2.1.2 The Langmuir Method

This is another technique for the measurement of vapour

pressure within a vacuum. The sample is suspended freely so that

there is no impediment to evaporation. The mass which evaporates

is often less than that in the equivalent Knudsen method, this is

because the equilibrium vapour pressure may not be reached during

a Langmuir experiment. The fraction of the mass which evaporates

compared to that found in the Knudsen experiment is called the

vapourisation coefficient.

2.1.3 The J.sopiestic Method

The technique is very similar to the dew-point method, as

applied to a binary system the vapour pressures of the two

1949

components should differ by at least three orders of magnitude.

The reaction tube is evacuated and the non-volatile component

is held at one end of the apparatus at a known temperature.

At the other extreme of the reaction tube, the volatile

component is held at a known lower temperature. The volatile

component then evaporates and travels along the tube and comes

to equilibrium in the alloy. From the vapour pressure data of

the volatile component the activity in the alloy in the

standard state is readily calculated. In order to apply this

technique to complex vapour systems, thermodynamic data,

relating the composition changes in the vapour as it is

heated , must be available. There is also the possibility of

thermal segregation of the different molecules. The amount

of information yielded by a single experiment may be greatly

increased by putting a series of samples along the temperature

gradient. Care has to be taken to ensure that the samples are

kept close to equilibrium during quenching. 0

2.1.4 The Transpiration Technique

The transpiration method may be used in two modes these

are;

1) Removal of vapour from a liquid alloy at a known

temperature in an inert gas stream, with the vapour being cond-

ensed and weighed.

2) The volatile component of an alloy is equilibrated

at a low temperature with an inert gas stream, the alloy

picks up the volatile component from the vapour and comes to

equilibrium over a period of time.

54

There is clearly a major difference between the two modes as

method 1 may not yield equilibrium data as after some time the

volatile component will be substantially removed from the alloy.

Method 2 should reach equilibrium assuming the loss of the inert

component of the alloy into the gas stream is small. If the

carrier gas and the vapour are assumed to be ideal gases, the

total pressure of the system is proportional to the number of

molecules present, and the individual partial pressures are

proportional to the number of molecules n, of each species. Thus

for an inert gas i, and vapour v, the partial pressure of v is

given by;

p = p = n = volume of v *v *v v P x x n P + p. n + n. volume of v + volume of i ^total v l

Some of the important measurements in the two cases are

different, these are;

Method 1 Method 2

Volume or flow rate of carrier gas Temperature of volatile element

Weight change of droplet Final composition of alloy

'Weight of deposited vapour Approximate flow rate

It is notable that the exact flow rate is not critical in

method 2 once the approximate flow rate for saturation of the

vapour has been found, whereas it it critical in method 1.

Problems with Entrainment Techniques

The main problems are:

1 ) Maintaining vapour saturation

2) Vapour diffusion

5) Measuring and maintaining the temperature(s)

55

4) Finding the molecular composition with complex vapours

5) Fnsuring the alloy is at equilibrium (method 2).

2.1.4.1 Saturation and Diffusion of the Vapour

At saturation the theoretical vapour pressure will be observed,

so where the inert gas is being passed over a volatile component,

whose vapour pressure is known, it is possible to find experiment-

ally the range of flow rates which are compatible with saturation.

Where the vapour pressure data is not available it is still

possible to identify the flow rates which are suitable; at satur-

ation there is a range of flow rates where the observed vapour

pressure remains constant. By plotting apparent vapour pressure

against flow rate, a plateau is observed which typically extends

over a threefold range of flow rates. At low flow rates the effects

of diffusion become important and the apparent vapour pressure

rises; with high flow rates the carrier gas is not saturated so

the apparent vapour pressure falls (Figure 14).

In most apparatus the vapour that enters the carrier gas in

the sample region is most commonly removed by condensation or by •

being taken into solution beyond the end of a capilliary which

eliminates back-diffusion.

Merten (41) showed that under these conditions the flow, along

an isothermal capilliary may be written as the sum of two terms,

the bulk flow and the diffusion term, such that.

k the mass per unit time passing a point in the tube.

V the linear velocity of the gas.

56

x the distance from the exit,

c the vapour density.

D the interdiffusion coefficient for the carrier gas and vapour.

At a steady state k is constant, so the differential equation may

be solved to give;

c = k_ + B exp VA

Vx D

Let the capilliary length be 1 and assume that the vapour

condensed at the exit then c = 0 at x = 0 and

1- exp /-Vl\ I D /

c =_k_ VA

Replacing V by volume flow rate v and assuming ideality V = v/A,

1 - exp /—lv\ V T)AJ

p = cRT = kRT M vM

p the pressure.

T the temperature.

R the gas constant.

M the molecular weight of the vapour.

k is therefore a function of v. For large values of v diffusion

effects are negligible and p = k RT and at v = 0 only diffusion v M

is observed and o = klRT. This gives a general result illustrated DAM

in figure 15.

Thermal effects are generally more important than pure

diffusion effects, mainly because problems arise with vapour

segregation 'wherever there is a thermal gradient. Gillespie (42)

showed that the relative diffusion of two gases because of a x

thermal gradient is oroportional to 1/(mean molecular weight)':

of the mixture, so r,he effect diminishes with increasing

57

/ N

APPARENT VAPOUR

PRESSURE

FLOW RATE

Variation of apparent vapour pressure with flow rate,

in a transpiration apparatus

Figure 14

r'igure 15

58

molecular weight. The general result he produced for a mixture

of two gases is;

d ln x^ = jCl-mgV^nhX^ for gas number 2 and similarly for gas

d ln T

1 to produce,

d ln (x^/x^) = m^ - m^ where nu is the square root of the

d ^ 2^>m x molecular weight of component i, i i

and x^ is the mole fraction of component i. The other general

conclusion is that increasing the temperature gradient increases

the degree of thermal segregation. Gillespie suggested that the

use of a low molecular weight carrier gas would lead to the

reduction of the thermal segregation, by reducing the molecular

weight of the mixture.

The transpiation technique was selected for the research into

arsenic containing alloys because of its relative simplicity, its

suitability for measuring activities in liquids, and the expected

range of useable vapour pressures. The variables are easily

controlled with gas flow rates, temperatures and weight changes

all measureable with a high degree of precision.

2.2 Apparatus

The apparatus consisted of a furnace, an alumina tube

assembly which was inserted into the furnace and a gas train

leading into and out of the alumina tubes. The furnace consisted

of three wire-wound elements which were independently controlled.

The furnace assembly is shown in figure 16.

The furnace elements were wired in series, the lowest

temnerature region was where the arsenic was evaporated into the

gas stream, the second region was at an intermediate temperature.

The third winding was used to achieve temperatures of between

800° and 1114°C, where the copper or copper-lead-arsenic alloys

were equilibrated with the arsenic-laden argon stream. The low

temperature region was controlled by a Eurotherm temperature

controller which was connected to a Pt/Pt 13% Rh thermocouple.

A second thermocouple was used at the low temperature end to

measure the temperature in the vicinity of the arsenic. This

was cromel-alumel, which was selected because it had a higher

output, mV/°C, than most others in the range 200° to 450°C, so

that the temperature of the arsenic source could be accurately

determined. The thermocouple was sheathed in silica as arsenic

vapour reacted with the material of thermocouple.

The second zone was kept at a constant temperature in

excess oi 65CTC in order that the arsenic vapour would be heated

as it travelled towards the hot zone, and also so that no arsenic

would condense(Arsenic sublimes at 603°C at 1 atm). The hot zone

was controlled by a separate Eurotherm controller which was

connected to a Ht/Pt 1Y Rh thermocouple. This thermocouple was

argon in

Apparatus for Transpiration Experiments

Figure 16

ON O

61

also used to monitor the hot zone temperature.

Two concentric alumina tubes were inserted into the furnace;

the outer one about 90 cm long, the other one 1 m long. The outer

tube had one closed end, this had an outside diameter of 50 mm

and the inner tube a diameter of 15 mm. These two tubes were

held concentrically by a large brass joint which was held together

by a screw thread, and was made gas tight by "0" ring seals. The

wires from the cromel-alumel thermocouple had to be brought out

from inside the gas-tight apparatus, this was done by leading

the wires down, through the brass joint and out through holes

made in the P.V.C. tubing, the holes were then sealed. Drilled

graphite plugs were inserted into the inner alumina tube to

reduce the cross-sectional area and increase the gas velocity

along the tube and hence reduce the effects of thermal segre-

gation.

The boat containing the alloy was high grade alumina (Purox,

Morganite Refractories Ltd.), this was connected by alumina

cement to a length of thermocouple sheathing which was fixed into

the small brass joint on the inner alumina tube. The smaller

brass joint was also sealed with 0 rings. The permanent

coupling between the brass joint and the boat ensured that the

boat was placed accurately in the centre of the hot zone each

time.

Argon was used as the carrier gas and was supplied by B.O.C.,

99 *999c/ purity with specified maximum levels of impurity, nitrogen

15 p.p.m., oxygen 4 p.p.m., hydrogen 1 p.p.m., hydrocarbons

1 p.p.m. with total impurities less than 20 p.n.m. Tn order to

62

ensure that the impurities, particularly oxygen and water were

kept to a minimum the argon was purified before entering the

furnace. The argon was first passed through a furnace containing

titanium granules and then through a U-tube containing phosphorous

pentoxide. The gas leaving the apparatus carried with it the

surplus arsenic vapour, for this reason the gas was cleaned

before passing into a fume extractor.

The exhaust gases were first passed through a particle filter

and then passed through a water cooled cold finger and then

bubbled through a dreschel flask containing nitric acid, a second

dreschel flask was added to ensure that there was no possibility

of a blow-back of acid into the furnace assembly. The argon flow

rate was regulated by a pressure reduction head and a pair of gas

taps in series. The flow rate was monitored continuously by a

Meterate flow meter RS1 (Scientific Supplies Ltd) which was cali-

brated by means of a "soap-bubble" meter. The entire furnace

assembly and the two gas trains were contained entirely within

a Perspex fume cupboard which was connected to an external fume

extractor. In this way the pressure within the cupboard was kept

to below the ambient pressure, so there was little possibility

of arsenic vapour escaping into the laboratory if some unforeseen

incident had occureri in the course of the experiments.

63

2.3 Experimental Technique

Calibration of Apparatus

Temperature control and measurement are very important in

thermodynamic studies, particularly in transpiration studies where

the activity of the volatile species is determined by its vapour

pressure and hence its temperature. The hot zone temperature

was set by inserting a Pt/Pt 13?' Rh into the inner alumina tube so

that it was in the centre of the hot zone. The temperature

control on the "Eurotherm" was adjusted until the desired

temperature was measured in the hot zone. This temperature was

then monitored over 30 minutes and found to be constant - 2°C.

The use of a cromel-alumel thermocouple at the "cold" end in the

vicinity of the arsenic meant that its temperature could be

monitored very accurately; the thermocouple has a very high output

in the range 200° to 450°C. The temperature of the cold zone was

found to be constant - 2°C over 30 minutes although over a longer

period there was a slight tendency for the temperature to fall,

for a given Eurotherm setting.

Equilibration

There are two stages in this transpiration technique, and

there ere two equilibria to be considered. Firstly the argon

had to be saturated by passing it over heated solid arsenic,

and the droplet of alloy then had to be equilibrated with this

vapour.

Arsenic Saturation

The argon had to be saturated with arsenic vapour in order

that the activity of the arsenic could be calculated. In order

64

to find the conditions for saturation a series of experiments

were conducted in which the loss in weight of arsenic into a

known gas volume was measured. All of the experiments were

conducted with the same volume of argon, and necessarily differing

experimental times. The arsenic was weighed and then inserted

into the apparatus. Once the arsenic had reached 380°C, a known

volume of argon was passed over it. After a suitable time

interval, the gas flow was stopped and the arsenic cooled. It

was not possible to measure directly the amount of arsenic which

was condensed as the arsenic was condensed and collected at

several points in the exhaust gas train. It was noted earlier

that arsenic evaporates predominantly as As^ molecules at

temperatures below 800°C, this assumption was used to calculate

the apparent vapour pressure of arsenic. The arsenic which

was left at the end of the experiment was weighed. Three flow

rates were used to determine the location of the plateau in the

flow rate - vapour pressure relationship, these were 50, 75, and

100 cc per minute. From the results it was apparent that all of

these flow rates were compatible with saturation of the vapour

(Table 7). The flow rate of 75 cc per minute was used as standard

for all experiments. Although there are differences between the

theoretical weight losses and the actual weight losses, these are

not significant. The results also confirmed that the thermocouples

were accurately calibrated.

Activity Measurement in the Copper-Arsenic System

As similar transpiration experiments had been carried out on

the copper-arsenic system (25), there was some indication of the

range of -ctivities which could be measured, and the range of

Flow Rate Duration Starting Weight Final Weight

cc / min /hours /grams /grams

50 2 1-685 1-456

75 3 1-743 1-525

100 4 1-892 1 -670

Arsenic Temperature 380°C

Arsenic Saturation Experiments

Table 7

Loss Theoretical

/grams Difference

0-229 0-224

0-218 0-224

0-222 0 - 2 2 4

66

arsenic vapour pressure which could be used. Before any

experiment was started, any arsenic which had been evaporated

was replaced to ensure that there was sufficient arsenic to

saturate the argon with arsenic vapour for the duration of the

experiment. The inner alumina tube was then inserted into the

outer alumina tube, the two tubes were then joined by the large

brass connector. There were several turns of copper tubing

around the brass joint and water was run through this in order

to cool the brass and the 0 ring. The water was turned on as

soon as the two tubes were put into the furnace. This cooling

was kept on for the duration of the experiment and was only

turned off when the furnace had cooled down.

VJhen the gas train was connected the argon was turned on and

the oxygen flushed from the apparatus, the flow was turned down to

75 cc per minute. The furnace containing the titanium granules

was then turned on to ensure that the argon entering the furnace

from the gas train had an extremely low oxygen content. The three

main furnace windings were then turned on, these tyoically took

forty-five minutes to come to temperature. During the heating

of the furnace, argon was flowing over the solid arsenic. This

meant that any residual oxide on the arsenic was removed before

the copper was introduced into the furnace. The copper was cut

from a rod and was cleaned in nitric acid, washed and dried with

acetone and then weighed. In early experiments two drorlets

were used, but it was found that they would tend to run together,

usually on ouenching, before they could be weighed at the end of

the experiment. The time between the preparation of the copper

and its use in the experiment was as short as possible, typically

less than five minutes. In order to insert the copper into the

furnace it was necessary to remove the end brass joint and pull

the alumina boat out. The copper was placed in the boat when it

had cooled, the boat was then slowly pushed into the furnace.

The argon flow rate was increased during this procedure to

minimise the amount of oxygen being introduced into the furnace.

The brass joint was then tightened and. made gas tight by an 0

ring seal, this meant that all of the exhaust gases were directed

through the gas train, and that the boat was placed accurately

in the centre of the hot zone. The gas flow was then readjusted

to 75 cc per minute. The temperature of the hot and cold zones

was noted when the experiment was started and at intervals

throughout the experiment. The gas flow rate was also checked

regularly, although this was not critical. At the end of the

experiment the droplets were cooled and weighed. Two methods

of cooling were tried in order to minimise the loss of arsenic

at the end of the experiment, these were cooling within the

apparatus and water quenching.

In order to minimise the loss of arsenic, the time from

removal from the arsenic rich gas stream to quenching the

droplet bad to be as short as possible. This was done by

unscrewing the end brass joint, the boat was then pulled from the

furnace and inverted directiy above a beaker of distilled water.

It was thought that this technique may not have been suitable for

high arsenic contents, so the alternative, cooling within the

apparatus was tried. Usina this technique the boat was only

remover4 from the hot zon^ so i 1, was still In the gas stream. It

68

was hoppd that i.t would cool without any change in composition.

However as the boat cooled the droplet apparently rejected

arsenic which gave some fuming at the open end of the alumina

tube. This technique was therefore not used.

In general the quenching technique was very successful, and

it worked quite satisfactorily for arsenic contents in copper in

excess of thirty atomic per cent, due mainly to the extremely

low activity of arsenic in copper. A few of the droplets

shattered on quenching but in these cases there were sufficient

fragments to carry out a chemical analysis. The alloy was washed

and dried with acetone, it was then weighed. The weight change

was attributed solely to the pick up of arsenic by the droplet

as an insignificant amount of copper would evaporate into the

gas stream. By this means it was possible to obtain approximate

compositions of the alloys before the chemical analyses were

carried out.

Equilibration of the Copper-Arsenic Alloy

The equilibration of the arsenic with the argon was discussed

earlier, the second main step in this technique was to ensure

that the copper-arsenic alloy had come to equilibrium with the

arsenic laden vapour. For all experiments high purity copper

(99.999/) was used as the starting material with a sample weigh-

ing from 0 * 1 5 to 0 * 3 grains. It was approximately calculated

how much arsenic the copper would have to pick up in order to

achieve equilibrium. It was found that the droplet would pick

up about, half of the mass of arsenic which reached it so it was

normal practise to vanourise an amount of arsenic, similar to

69

the original weight of the cooper, as a minimum. The rate of

transfer of arsenic to the alloy is roverned by the rate of

evaporation of arsenic, so to decrease the time of some of the

experiments, the arsenic was heated to over 400°C. When an

excess of arsenic had been transfered to the alloy, the

temperature of the arsenic source was reduced, and the alloy again

allowed to come to equilibrium by loss of arsenic into the gas

stream. This was found to be a very useful approach for experi-

ments where the alloy was being brought to equilibrium with argon

saturated with arsenic at below 350°C, where the transportation

times and rising As content would have been excessive. This

technique was also useful in confirming that equilibrium had

been reached, as the final composition could be approached from

alloys containing both an excess and deficit of arsenic from the

eauilibrium value.

Variation of Hot Zone Temperature

The first series of experiments were carried out with the

alloy held at 1114°C, so there was no need to take any precaution

to ensure that the alloy was liquid as the exneriment was carried

out entirely above the liauidus temperature. Subsequent

experiments were conducted at 1000 and 900°C which is below the

melting point of pure copper, so that a slightly differnt tech-

niaue was used. The copper was introduced into the furnace at

1100°C and in a stream of arsenic laden vapour. The presence of

arsenic lowered the liquidus temperature, so that after the

copper had absorbed the arsenic the hot zone temperature could

be lowered to 1000 or 900°C whilst maintaining a liquid copper

phase. The arsenic temperature was then lowered to its final

temperature allowing the droplet to rome to equilibrium before

being quenched.

71

2.4 Activity Measurement in the Lead-Copper-Arsenic System

The governing factor in transpiration experiments is the

vapour pressure of the components, in an ideal study there should

be one volatile component and the others should be relatively

inert. In the apparatus which was used for this study, equilibrium

was reached between the arsenic vapour and the copper-arsenic alloy,

later the same apparatus was used to investigate the equilibrium

lead-copper-arsenic compositions for two arsenic activities (0*1

and 0*05) relative to liquid arsenic. In order to work as close

to equilibrium conditions as possible the vapour pressure of the

lead had to be minimised; the temperature of the lead had therefore

to be kept as low as possible. To produce an iso-activity line in

the Cu-Pb-As ternary system various lead-copper ratios were needed,

and to minimise the length of the experiments, high arsenic, lead-

copper alloys were used. To find the maximum temperature, the

vapour pressures of the arsenic and lead were compared for various

experimental conditions.

The arsenic activity was always set prior to the introduction

of the lead-copper-arsenic alloys into the hot zone. In each case

the standard state was liquid arsenic at the temperature of the

alloy. The arsenic activity was set by fixing the temperature of

the arsenic. The calculation of the temperature of the arsenic

wss carried out as follows. In this example the required activity

is a As =0-05 800°C

atm

So a = 0-05 = (P /32-90) s

72

^2-90 x (0-05)4 = P A g 4

-4 2-056 x 10 atm = P A g

4

The computer program (appendix 2 ) was then used to find the

vapour pressure of arsenic which was required to produce this

vapour pressure of As^ at 800°C, and hence the temperature at

which the arsenic source had to be held. /The results for the other

required vapour pressures and temperatures are given in table 8.

It will be noted that at 800°C arsenic is not liquid at any

pressure so a supercooled liquid arsenic standard state is used.

The ratio of arsenic (As^) vapour pressure to lead vapour pressure

at 800° and 900°C are given in table 9, together with the relative

mass transport ratio for the two metals,(the ratio of the rate of

transport of arsenic in grams to the rate at which lead would be

removed, from the pure element, for each activity and temperature

combination). For this reason high arsenic alloys were used,

because the arsenic was removed much more quickly than it was

delivered, leading to short equilibration times so that the Cu/Pb

ratio changed as little as possible. The data for the vapour

pressure of Pb were taken from Hultgren (20).

The whole composition range of Pb-Cu ratios was covered, the

starting compositions are given in table 10 and are plotted on

figure 17, together with the constant Pb:Cu ratio lines along

which arsenic losses would change the compositions. The alloys

were prepared by Metallurgie Hoboken-Overpelt.

Fouilibration

The apparatus was exactly the same as that used for the

Figure 1969

Start Compositions in

Pb-Cu-As System

\ \ l *

\ \ \ R Q

.^rsenic Hot Zone

Activity Temo/ C

0-05

0 - 1 0

0 - 0 5

0 - 1 0

800

800

900 900

Required arsenic pressure

/atn As,,

2-06 x 10~4

5 - 2 9 Y 1 0 " '

5-19 x i0~4

5-1'1 x 10

Total

Pressure of arsenic

evaporating/atm

2-15 x 10

5-59 x 10"

3-26 x 10

-4

-A

5-25 x 10 - Z

Relationship between Arsenic Activity and Temperature

Table 8

Arsenic

Temp/°C

540

405

349

4 1 7

Lead Temperature Arsenic P. : Pp, Relative mass 4

/°C Activity transfer ratio

800 0.1 46.3 67.0 800 0.05 3.45 4.99 900 0.1 12.2 17.6

900 0.05 0.76 1.10

Variation of ratio of vapour pressures of lead and

arsenic with temperature and arsenic activity

Table 9

Mole Fractions

Pb Cu As Alloy Number

0-1408 0-5305 0-3286 1 0-1248 0-5409 0-3347 2 0-2031 0-4857 0-3112 3 0-279? 0-4093 0-311? 4 0-3879 0-3065 0-3056 5 0-4587 0-2605 0-2808 6 0-4962 0-2103 0-2935 7 0-5641 0-1444 0-2914 8 0-6612 0-0724 0-2665 9

Alloy Starting Compositions

Table 10

77

activity determinations in the copper-arsenic system. The entire

apparatus was heated to operating temperature before the introduc-

tion of any alloy, the arsenic temperature was also set for the

required arsenic activity. The alloy sample was then introduced

into the hot zone in the alumina boat, it was then left for ten

minutes and then removed and water quenched. The initial,

experiments to find the equilibrium times were carried out, at

800°C and an arsenic activity of 0*1, on alloy number 4. It was

found that no significant change in composition occured with

experimental times from five to nineteen minutes; a standard

equilibration time of ten minutes was adopted for all subsequent

experiments. The droplets were weighed immediately before and

after the experiment, after washing and drying in acetone.

78

2.5 Knudsen Cell Mass Spectrometry

A Bendix time-of-flight mass-spectrometer (Model 12) fitted

with a molybdenum wound furnace was used in an attempt to analyse

the effusing vapour from a silica or Graphite Knudsen cell.

Cell Preparation

Silica tube (8 mm o.d.) was sealed at its base by heating in

the flame of a natural gas/oxygen burner. At a distance of about

3 cm from this end a neck was formed by heating the silica and

pulling. The neck was not sealed and the sample was later inserted

through it. A minute hole was then machined into the silica

approximately one centimetre from the neck. The sample was then

inserted into the cell, a typical weight for the sample was 0*2

gram. The cell was then inserted into a cork, which was drilled

such that the base of the cell protruded from the bottom. The

open neck of the cell was clear of the top of the cork. The

cork was then put into a shallow water bath so that the silica

surrounding the sample was water-cooled. The top of the cell

was then sealed with a burner. Finally the machined hole was

contracted by heating, to such an extent that it was just visible

with an eyeglass. The completed cell was then placed into a steel

capsule and the orifice in the Knudsen cell aligned so that the

effusate would emerge through a relatively large port in the steel

cell. The assembly was then lowered into the furnace.

A second type of cell was used for higher temperatures, this

was machined from graphite and the Knudsen orifice was drilled

into the side of it. The base of the cell was threaded and

79

unscrewed to expose a hole into which a 4 mm diameter alumina

crucible, containing the sample, was placed. The base was then

replaced. The sample was then ready for insertion into the furnace.

Operation of the Mass Spectrometer

The mass-spectrometer differentiated between different masses

of ions by measuring the time of travel for ions after an acceler-

ating potential was applied. Doubly charged ions would experience

twice the acceleration, and would appear to have half of their

mass, but none were found in this investigation. The mass numbers

were related to the reading on a vernier dial which had to be

calibrated. There were several species within the mass-spectrometer,

despite the vacuum, which were used to calibrate the apparatus. The

standards used were CO and lb, at mass number 18, mercury from the

diffusion pump and vacuum oil mass number 186, from these the

vernier was calibrated in the range mass number 18 to 250 from

these it was possible to extrapolate to mass numbers up to 350.

The furnace was then turned on and the sample was heated to

the required temperature. When the sample was up to temperature

the effusing beam was directed into the ionising electron stream.

The mass-spectrometer could scan in a selectable range so that it

passed through the desired mass number. The peak height was

proportional to the ion current generated. The peaks were not

perfect lines at one mass number because the accelerating

potential, despite being pulsed, had a slight rise and decay time.

To verify that the correct peak was being examined the Knudsen

cell was rotated so that the effusing beam did not enter the

spectrometer, the peak height then fell, it was also useful to find

the amount o' background at that mass number. Scanning through

a range of mass numbers gave an impression of the general

background.

81

2.6 Chemical Analysis

The copper-arsenic alloys were analysed after weighing at the

end of the transpiration experiments. The technique used gave an

analysis for arsenic, the balance was assessed as copper and on

this basis the final composition was determined . The alloy

was dissolved in equal measures of concentrated nitric and

sulphuric acid with a small amount of distilled water. The solution

was then heated to near dryness, such that all of the nitric acid

decomposed. The residue was then dissolved in distilled water.

Fifty millimetres of concentrated hydrochloric acid were added,

together with five to seven grams of hydrogen bromide and one to

two grams of hydrazine sulphate. The arsenic was all then in the

form of AsCl^ which was then distilled in an all glass apparatus.

The outlet for the distillate was below the level of the distilled

water in a collection beaker. Only the fraction distilled at over

80°C was collected. The distillate was titrated with potassium

bromate in the presence of excess acid, or with iodine in potassium

iodide after neutralisation of the distillate. The results of the

chemical analyses agreed, within experimental error, with the weight

change analyses, so only in selected cases were chemical analyses

carried out.

The lead-copper-arsenic alloys were analysed for all three

elements by the analytical, laboratories of Metallurgie Hoboker-

Overpelt.

CHAPTER 3

RESULTS

1979

3.1 The Composition of Arsenic Vapour

Arsenic evaporates as As^ molecules at temperatures below

800°C; this happens when arsenic is evaporated into the argon

gas stream within the transpiration apparatus. As the vapour

is heated the molecules will dissociate but the total pressure-

within the apparatus must remain at one atmosphere. In order

to find the activity of arsenic relative to the pure liquid it

is necessary to calculate the extent of As^ dissociation. The

As^ dissociates to give As^, As^ and As^ molecules. The

equilibria for these reactions may be represented by;

As4(g) a As5(g) ' K3 = 'As 4 / 3 ( 1 )

A 54(g) = 2 A 52(g) > K 2 = PAs ' ™

PAs 4

A54(g) = 4 As(g) ' K1=Pa s 4 0 )

pAs, 4

K^, Kg and K^ have unique values at any temperature so the

extent of dissociation may be determined.

Let P ^ be the vapour pressure of As^ on evaporation, then

if it were to dissociate completely to As^ the pressures

generated would be 2 x and similarly for the other two

reactions, such that;

P4e = P4t ' * P3t + i P2t + « P1t (4)

where P ^ represents the vanour pressure of As^ at a higher

84

temperature, t, and similarly for the other molecules.

From (1) P = (K5 P^)'* (5)

From (2) P g t - (Kg P 4 t)~ (6)

From (3) P n = P ^ ) * (7)

Substitution of (5), (6) and (7) into (4) gives,

P4e = P4t + * < K3 P4t ) f + + * ( K1 V " '

Fquation (8) was solved by computer for each experimental

vapour pressure and equilibrium constant combination (Appendix 1).

The values for the equilibrium constants K^, K^ and K^ were

calculated from the data of Hultgren et al (17). The data only

covers the range 298 to 900 K so some extrapolation of the data

was necessary. This was done by computing the best straight line

through the data nut into the form, lg-jQ P^s end 1/T (K) for n

integral values of n from 1 to 4. The best straight lines can

be represented by the following;

l g i o As1 = -1-560 x 104 (1/T) + 6-9158 (9)

l g i o ASp " = -1-0950 x 104 (1/T) + 7*8179 (10)

l g10 As, 3 = -1-2980 x 104 (1/T) + 9-4567 (11)

l g10 = -7-0000 x 104 (1/T) + 7-9944 (12)

All pressures are given in atmospheres.

The temperatures of interest are 1073, 1173, 1273, 1373 and

1387 K. Values for the pressures of the individual species and

the values of the equilibrium are given in tables 11 and 12

respectively.

The total observed vapour pressure over liquid arsenic is

given by Baker (15) as lg 1 Q P = - 2405 + 3*759 (atm). A value

T/C PAs 1 PAs 2

PAs, ? A s 4

800 2.383 x 10-8 4.100 x 10"5 2.290 x 10"3 29.56

900 4.136 x 10"7 3.040 x 10~2 2.461 x 10~2 106.36

1000 4.580 x 10-6 0.1652 0.1821 313.0

1100 3.579 x 10"5 0.6961 1.007 787.1

1114 ON

Oo X 10~5 0.8374 1.248 885.7

Equilibrium vapour pressures of arsenic molecules above solid arsenic

All pressures in atmospheres

Table 11

T/C

800

900

1000

1100

1114

1.091 x 10 -32

2.750 x 10 - 2 8

1.411 x 10 -24

2.084 x 10 - 2 1

5.315 x 10 - 2 1

5.687 x 10 7

8.689 x 10"6

8.719 x 10"5

6.156 x 1 0 " 4

7.918 x 10"4

1.021 x 10 5

6.729 x 10~5

3.298 x 10

1.282 x 10 -3

1.517 x 10 -3

Values for the equilibrium constants of arsenic vapour at various temperatures

Table 12

87

for P° in the standard state is found by substituting the value

produced by Baker into equation (8). The results of this are

given in table 13. A programme (Appendix 1) was used to calcu-

late the pressures of each of the vapour species at 1073, 1173,

1273 and 1373 K ( 800, 900, 1000, 1100 and 1114°C) for an

arsenic source temperature in the range 500 to 750 K (tables 14

to 17). The results are shown in figures 18 to 21. The effect

<ar increasing the hot zone temperature for a given source

temperature may also be demonstrated, and the results are shown

in figures 22 to 25.

The vapour pressure of As^ generated when solid arsenic

evaporates is clearly important, the data, of Hultgren et al(l7)

was used to compute a continuous function of pressure against

temperature. This is given as;

RT In P = -1-75181 x 10""7 T3 + 1-51724 T2 -1-17379 x 10 T +

; 4 ^ 9-83726 x 10

Using this equation, values for P (atm) in the range 473 to A S Z

873 K (200 to 600 C)

were calculated at one degree intervals

using a programme written for use on the college computer (Appendix

2), "he programme was also used to calculate the length of time,

for p given flow rate, for 1 gram of arsenic to be transported.

T ' K P A S 4 1 0 ^ P A S 4 P A S 5 1 0 ^ P A S 3 P A S 2 1 0 ^ P A S 2 P A S 1 L 0 ^ P A S L

500 1.5 X 10~7 -6.82 1.4 X 10"9 -8.85 2.9 x 10~7 -6.54 2.0 x 10" 1 0 -9.70

550 7.0 x 10~6 -5.15 2.5 x 10"8 -7.60 2.0 x 10~6 -5.70 5-3 x 10" 1 0 -9.28

600 9.6 x 10~5 -4.02 1.8x10~7 -6.74 7-4 x 10~6 -5.13 1.0 x 10~9 -9.00

650 9.9 x 10"4 -3.00 1.0 x10" 6 -6.00 2.4 x 10"5 -4.62 1.8 x 10"9 -8.74

700 7.0 x 10~5 -2.15 4.3 x 10~6 -5.37 6.3 x 10~5 -4.20 2.9 x 10~9 -8.54

750 4.0 x 10~2 -1.40 1.6 x 10"5 -4.80 1.5 x 10"4 -3.82 4.6 x 10~9 -8.34

The vapour pressure 0f arsenic molecules at 800 °C resulting from varying source temperature

Table 14

00 00

T / R P A S , P o ® P A s . P A s , ^ A s , P A s , l o S P A s ? P A S l ^ A s , 4 4 3 3 2 2 1 1

500 3 . 3 x 1 0 " 8 -7.48 1.8 x 1 C f 9 - 8 . 7 4 5 . 3 x 10" 7 -6.28 1.7 x 10" 9 -8.77

550 4 . 7 x 10"6 -5.33 7 . 5 x 10""8 -7.12 6 . 4 x 1 ( T 6 - 5.19 6.0 x 10" 9 -8.22

600 8 . 6 x 1 0 " 5 - 4 . 0 7 6 . 6 x 10~"7 - 6 . 1 8 2 . 7 x 1 0 " 5 - 4 . 5 7 1 . 2 x 1 0 - 8 -7.92

650 9.5 x 10~ 4 -3.02 4.0 x 10" 6 -5.40 9.1 x 10""5 -4.04 2.3 x 10" 8 - 7 . 6 4

700 6.9 x 10~ 5 -2.16 1.7 x id" 5 -4.77 2.4 x 10" 4 -3.62 8.7 x 10" 8 -7.43

750 4.0 x 10" 2 -1.40 6.6 x 10" 5 -4.18 5.9 x 10" 4 -3.23 5.7 x 10" 8 -7.24

The vapour p r e s s u r e of a r s e n i c molecules a t 900 -C r e s u l t i n g from v a r y i n g source temperature

Table 15

co vo

T / K P A S 4 l0^a34 P A S J L ° G P a 3 3 P a 3 2 L ° G P a 3 2 P A S I L ° G P A S I

500 3.9 x 10"9 -8.41 1.2 x 10"9 -8.92 5.9 x 10"7 -6.23 8.6 x 10"9 -8.07

550 1 .7 x 10"6 -5.77 1.2 x 10" 7 -6.92 1.2 x 10~ 5 -4.92 4.0 x 10~ 8 -7.40

600 6.2 x 10~5 -4.21 1.7 x 1 0 " 6 -5-77 7-3 x 10" 5 -4.14 9,7 x 10" 8 -7.01

650 8.5 x 10"4 -3.07 1.2 x 10~"5 -4.92 2.7 x 10" 4 -3.57 1.9 x 10"7 -6.72

700 6.6 x 10"3 -2.18 5.7 x 10" 5 -4.24 7.6 x 10~ 4 -3.12 3.1 x 10" 7

-1 p 1 y m""4 £ft 1 ft ir _o na a a ^ Ar\"l

-6.51

750 3 . 9 x 1 0 - 1 . 4 1 2 . 1 x 10 H - 3 . 6 8 1 . 8 x 1 0 " ; - 2 . 7 4 4 . 8 x 1 0 " ' - 6 . 3 2

The vapour pressure of arsenic molecules at 1000 °C resulting from varying source temperature

Table 16

vo o

T / K t s . l o g P A s , PAs l 0 g P A S , PAs„ l o g P A s 2 PAs. l o g P A S . 4 4 3 3 2 2 1 I

500 5.5 x 10" 1 0 -9.26 7.7 x 1CT 1 0 -9.11 5.8 x 10" 7 - 6 . 2 4 3.3 x 10~8 - 7 . 4 8

550 3 . 7 x 10"7 -6.43 1.0 x 1 0 " 7 -7.00 1.5 x 10"5 -4.82 1.7 x 10~7 -6.77

600 3.0 x 10~5 -4.52 2.7 x 10~6 -5.57 1.4 x 10" 4 -3.85 5.0 x 10"7 -6.30

650 6 . 6 x 10~ 4 -3.18 2.8 x 10~5 -4.55 6 . 4 x 10" 4 -3.19 1.1 x 10~6 -5.96

700 5.9 x 10~"5 -2.23 1.4 x 10" 4 -3.85 1.9 x 10" 5 -2.72 1.9 x 10"6 -5.72

750 3.7 x 10"2 -1.43 5.7 x 10" 4 -3.24 4.8 x 10"3 -2.32 3.0 x 1Cf6 -5.52

The vapour pressure of arsenic molecules at 1100 °C resulting from varying source temperature

Table 17

vo

Total Temp Pressure P A s

4 /C /atm /atm

800* 32.95 52.90

900 51.15 51.11

1000 74.09 74.00

1114 105.9 105.6

Values for total pressure and P°g 4

for a liquid arsenic standard state

Table 13

Undercooled arsenic standard state

93

The change in partial pressure of the arsenic molecules with

changing source temperature at a constant hot zone temperature

tog P

Figure 37

94

log P

/atm

The change in partial pressure of the arsenic molecules with

changing source temperature at a constant hot zone temperature

Figure 30

95

The change in partial pressure of the arsenic molecules with

changing source temperature at a constant hot zone temperature

Figure 37

96

The change in partial pressure _of the arsenic molecules with

changing source temperature at a constant hot zone temperature

T/K

Figure 37

600 Source Temperature

The partial pressure of As^ molecules with increasing

source and hot zone temperatures

Figure 22

The partial pressure of As2 molecules with increasing

source and hot zone temperatures

Figure 22

- 3 99

Log,. P 10 As

-4

-5

- 6

- 7

- 8

- 9 500

i lOO

•1000

900'

3 0 0

The partial pressure of As, molecules with

increasing source and hot zone temperatures

600 Source Temperature

700 T/K

Figure 24

100

-1 T

- 2 -

- 3 -

Log. P a „

500 600 700 Source Temperature T / K

The partial pressure of As^ molecules with increasing

source and hot zone temperatures

Figure 37

101

3.2 The Conper-Arsenic System

Transpiration experiments were carried out on the copper-

arsenic system in the range 900°C to 1114°C. The results of.

these experiments are given in tables 18, 19 and 20. The results

are calculated on the basis of a liquid arsenic standard state,

A S4(g) v a p o u r s P e c £ e s being considered, such that

aAs = R- - R I . PAs. 4

PAs. 4

In the tables Pg represents the vapour pressure of A s ^ j on

evaporation, and P,p the pressure of As^j ^ this generates at the

droplet temperature. The results are also plotted as a A g against

N A s on figures 26, 27 and 28.

3.2.1 Partial Molar Free Energy of Arsenic in Copper

The integral free energy of formation of a solution AG^ from

components A and B may be represented by the sum of two terms

such that AGo = n. G. + n n where G. and G n are the partial I A ii d d A y molar free energies of A and B respectively. is related to

the activity of component A in the solution by the relationship

AGa = RT ln aA = 19 * 14T log.^a. . Partial molar free energies A e A ^10 As

of arsenic have been calculated for each of the experimental

temperatures and the results are given in tables 21, 22 and 23.

3.2.2 Integral Free Energy of Formation of Solution

The integral free energy of formation o.f solution may be

calculated from partial molar functions by means of the Puhem-

Margules equation (43),

T / K T / ° C N A S P E PT aAs

/atm /atm /atm

609 336 0.277 1.763 X 1 0 - 4 1.560 x 10"4 4.18 X 1 0 - 2

588 315 0.256 6.324 X 10" 5 6.117 x 10" 5 3.31 X ID"2

579 506 0.251 3.962 X 10~5 3.429 x 10"5 2.86 X 1 0 - 2

571 298 0.242 2.580 X 10-5 1.918 x 10"5 2.48 X 1 0 - 2

559 286 0.227 1.392 X 10~5 9.324 x 10" 6 2.07 X 1 0 - 2

545 272 0.210 5.848 X 10-6 3.128 x 10"° 1.57 X 10"2

Results of Transpiration Experiments at 900°C

Table 18

O ro

a x 10 - 2

As

9 0 0 C

0 - 2

N As

The activity of arsenic at 900 C

Figure 26

r/K T/°C N A S P,,

i\ P T aAs

/atm /atm /atm

541 268 0.160 4.60 x 10~6 5.06 x 10"7 9.10 X 10-5

565 292 0.194 1.86 x 10"5 5.78 x 10"6 1.67 X 1 0 - 2

581 308 0.223 4.40 x 10"5 2.05 x 10~5 2.29 X 1 0 - 2

582 309 0.217 4 . 6 4 x 10"5 2.20 x 10-5 2.34 X 1 0 - 2

609 336 0.248 1.78 x 10"4 1.22 x 10-4 3.58 X 1 0 - 2

655 382 0.288 1.35 x 10-5 1.17 x 10-5 6.31 X 1 0 - 2

687 414 0.312 4 . 6 6 x 10-5 4.20 x 10"5 8.68 X 1 0 - 2

Results of Transpiration Experiments at 1000°C

Table 19

O

A A S X L O r2

8 I

7 +

5 +

3 4-

2 I

1 +

1000 c

0 0-1 0-2

N As

The activity of arsenic in copper at 1000 Figure 27

T/K T/°C N, As P E PT aAs

/atm /atm /atm

695 420 0.285 5.796 X 10" -3 4.724 X 10~4 8.72 X 10-2

649 376 0.247 1.053 X 10" •3 6.658 X 10~4 5.01 X ID"2

650 377 0.250 1.098 X 10" •3 7.002 X 10"4 5.07 X ID"2

618 345 0.221 2.713 X 10" •4 1.143 X 10~4 3.22 X 10-2

591 318 0.195 7.367 X 10" •5 1.593 X 10-5 1.97 X ID"2

568 295 0.162 2.190 X 10" •5 1.938 X 1 0 - 6 1.16 X ID"2

563 290 0.136 1.659 X 10" •5 6.635 X 10~' 8.90 X 10~5

Results of Transpiration Experiments at 1114°C

Table 20

a, x10"2 As

1114° C

0 0-1 0-2 0-3

N As

The activity of arsenic in copper at 1114 C

Figure 22

N, aA ln aA GA As As e As As joule/mol

0.285 8.718 x 10 2 -2.440 -2.814 x 10'

0.247 5.011 x 10~ 2 -2.994 -3.453 x 10'

0.250 5.074 x 10 2 -2.981 -3.438 x 10'

0.221 ' 3.225 x 10 2 -3.434 -3.960 x 10'

0.195 1 .971 x 10 2 -3.927 -4.529 x 10'

0.162 . 1 .164 x 10 2 -4.453 -5.135- x 10'

O . 1 3 6 8.903 x 10~ 5 -4.721 -5.444 x 10z

Partial molar free energy of arsenic in copper at 1387 K

Table 21

N As As L N A A O e As °As joule/mol

0.160 9.10 x 10 -3 -4.699 -4.974 x 10'

0.194 1 . 6 7 x 1 0 - 2 -4.092 -4.331 x 10

0.217 2.34 x 10 - 2 -3.755 -3.974 x 10'

0.223 2.29 x 10 - 2 -3.777 -3.997 x 10

0.248 3.58 x 10 - 2 -3.330 -3.524 x 10

0.288 6.31 x 10 - 2 -2.763 -2.924 x 10'

0.312 8.68 x 10 - 2 -2.444 -2.587 x 10

Partial molar free energy of arsenic in copper at 1273 K

Table 22

^As aAs ^neaAs GAs joule/mol

0.277 4.180 x 10"2 -3.175 -3.10 x 104

0.256 3.308 x 10~"2 -3.409 -3.32 x 104

0.251 2.862 x 10"2 -3.553 -3.47 x 104

0.242 2.475 x 10*~2 -3.699 -3.61 x 104

0.227 2.067 x 10"2 -3.879 -3.78 x 104

0.210 1.573 x 10~2 -4.152 -4.05 x 104

Partial molar free energy of arsenic in copper at 1173 K

Table 23

111

A G F = N B AG dn

*\ A which may be applied directly to the results

n B for the copper-arsenic system at 1387 K. This integration was

carried out graphically as the relationship between AG A g and n A g

was not known in analytic form. Extrapolation of the data for 2 activity coefficient, gave a value of approximately 2*2 x 10

o

for the activity coefficient at infinite dilution. This is

approximately constant for small amounts of arsenic therefore a

value for A G A g way be calculated for a small value, so that for

" A s = 0 ' 0 1 >

-4 a. = 2*2 x 10 + and As ln a. = -8*422 e As AG A g = -9*712 x 104 joule / mol

A G A g = -9*909 x 104 joule / mol ~ 2 n n Cu

Similar calculations were carried out for all of the

experimental compositions and the results are given in table 24.

In order to evaluate the integral,AG A was plotted against n A g

2 ~ nn Cu

in figure 29, and the areas under the curve were measured.

Having measured these areas it was necessary to multiply the

values by n p to give values for the integral free energy of L-U

solution. The results are given in table 25, and are shown on

figure 30. The activity measurements did not cover a sufficiently

large range for integral free energies of solution to be calculated

with accuracv for the other experimental tenroeratures.

112

2 N N N , , , „ wAs Cu Cu As " As' Cu 2

A G A S joule joule/molf

0.285 0.715 0.5122 -2.183 x 104 -5.493 x 104

0.247 0.753 0.5670 -3.452 x 104 -6.088 x 104

0.250 0.750 0.5627 -3-438 x 104 -6.527 x 104

0.221 0.779 0.6067 -3.960 x 104 -6.527 x 104

0.195 0.805 .0.6480 -4.528 x 104 -6.988 x 104

0.162 0.838 0.7022 -5 .135 x 104 - 7 . 313 x 104

0.136 0.864 0.7465 -5.444 x 104 -7.293 x 10z

Evaluation of A G ^ / N 2 ^ at 1387 K

Table 24

N A N - Area ^ G . As Cu ^ f 2 joule/mol joule/mol

0.10 0.90 -8725 -7850

0.15 0.85 -13225 -11240

0.20 0.80 -16800 -13440

0.25 0.75 -20075 -15060

0.30 0.70 -22630 -15840

Calculation of the integral free energy of solution

for copper arsenic at 1387 K

Table 25

AGAs x TO4 cal/mol

N R Cu

1114 C

/ /

+ +/

/ / /

/ +

/ /

,• +

114

r / /

O 0-1 0-2 C-3 As

Figure 30

115

— , 1 I 0-1 0-2 0-3

N

A s

Free energy of solution of arsonic in cooper at 1114 °C

Figure 30

116

3.3 The Lead-Copper-Arsenic System

The results of the experiments on the lead-copper-arsenic

system are given in tables 26, 27, 28 and 29. The results are

expressed as final mole fractions determined by weight change

and by chemical analysis where appropriate. A programme was

written to determine the change in composition based on the weight

change of a specified alloy (Appendix 3). The results were

output in two Lines, the first assuming that all of the weight

loss was due to • rsenic loss, the second on the assumption that

the lead was acting ideally in solution in the alloy, and that

it was saturating the argon passing over it. The chemical

analyses showed extremely good agreement at 1073 K with the

weight change analyses, this was probably due to the low vapour

pressure of the lead at this temperature. The computed final

compositions were often very similar for both assumptions

detailed abo^e at 1073 K.

The results at 1173 K are based on several chemical analyses

which were carried out, with particular emphasis on the analysis

of the alloys number 7* 8 and 9 which had the highest lead contents

and hence were subject to larger lend losses.

The computer programme to calculate the final composition

was also used, and very close agreement was found between the

chemical analyses and the assumption of lead saturation. The

results of the chemical analyses where they were oarried out,

ere given in the tables. The constant activity lines are plotted

on ternary phase diagrams, figures 31 > 32 * 33 and 34 . The

activity o"»" arsenic in the binary Pb-As system is taken from the

Alloy

number

Mole Percentages

Pb Cu As

Duration

mins

1 14.7 55.3 30.0

1 14.8 55.8 29.4

2 12.9 55.7 31.4

2 12.9 56.1 31.0

3 ' 23.0 48.6 28.3

4 29.2 42.7 28.1

4 29.2 42.8 28.1

5 40.7 32.1 27.2

6 47.7 27.1 25.3

6 47.7 27.1 25.2

7 54.5 23.1 22.5

7 53.9 22.8 23.3

7 53.7 22.8 23.5

8 63.6 16.3 20.1

8 63.9 16.3 19.8

9 76.2 8.3 15.4

10

15

10

15

10

19

5

15

10

12

11

12

11

13

10

15

Final alloy compositions at 800 °C with

arsenic activity set at 0.1

Table 26

118

Alloy Mole Percentages Chemical Analysis Duration

number Pb Cu As Pb Cu As mini

1 14.9 56.0 29.2 15.2 55.8 29.2 10

2 13.3 57.6 29.0 10

2 13.3 57.6 29.1 13.2 57.7 29.1 10

3 23.6 49.8 26.6 10

3 23.5 49.6 26.9 10

5 42.5 33.6 24.0 10

5 42.5 33.6 23.9 10

6 50.0 28.4 21.6 10

7 54.8 23.2 2 1 . 9 10

8 65.2 16.7 18.1 10

8 65.1 16.7 18.2 64.9 16.7 18.4 10

9 79.5 8.7 11.8 79.6 8.8 11.6 10

Final a .lloy compositions at 800°C with

arsenic activity set at 0.05

Table 27

119

Alloy Mole percetages Chemical Analysis Duration

number Pb Cu As Pb Cu As mins

13.2 57.3 29.5 10

23.6 49.7 26.7 10

42.0 33.2 24.i 10

49.5 28.1 22.4 10

55.7 23.6 20.7 10

55.3 23.4 21 .2 55.5 23.6 21 .3 10

65.2 16.7 18.1 65.2 16.4 18.4 10

77.8 8.5 13.7 77.6 8.5 13.5 10

Final alloy compositions at 900 C with

arsenic activity set at 0.1

Table 28

120

Alloy Mole Percentages Chemical analysis Duration

number Pb Cu As Pb Cu As mins

12.5 59.0 28.5 10

24.1 50.8 25.1 24.0 50.6 25.4 10

43.0 34.0 23.0 43.1 34.1 22.8 10

50.5 28.3 21.2 10

57.1 23.9 19.0 10

67.1 17.2 15.7 10

80.5 8.5 11.0 80.4 8.7 10.9 10

Final alloy compositions at 900- C with

arsenic activity set at 0.05

Table 29

"V

t A s

The isoactivity line, a A g = 0.1 at 800 °C in the Pb-Cu-As system

Figure 31

f A s

The isoactivity line, a A g = 0 . 0 5 at 800 ° c in the Pb-Cu-As system

Figure 32

f As

The isoactivity line, a A s = 0.1 at 900 °C in the Pb-Cu-As system

Figure 33

f As

The isoactivity line, = 0.05 at 900 °C in the Pb-Cu-As system

Figure 34

125

investigation of Predel and Emam (30). No activity measurements

were carried out on the lead-arsenic binary system in this study.

Two lead-copper-arsenic alloys were prepared which had very high

copper to lead ratios, however, there was insufficient arsenic

dissolved in these alloys for equilibration to take place by

evaporation of arsenic into the gas stream. If the equilibration

had taken place it would have meant waiting for the alloy to pick

up arsenic from the vapour. This would have lead to long

experimental times and large lead losses.

126

3.4 Mass Spectrometry

The mass-specrometer was used to analyse the vapour from

three Knudsen cells, these contained pure arsenic, copper with

0*2$> by weight of arsenic and pure copper. The pure arsenic was

heated to a relatively low temperature, before the As^+ peak

was identified, around 330°C. The mass number vernier scale had

already been calibrated, using internal standards, so the other •F + + peaks As^ , As^ and As^ were easily identified. The peak

heights diminished when the molecular beam was rotated away from

the ionising source, however the background was gradually rising.

The copper-arsenic sample was heated to 1100°C but the Cu +

peak was not observed. It was thought that the vernier scale

could have been incorrectly calibrated. A pure copper sample was

next used, to ensure the maximum amount of effusate from the

graphite cell which was for high temperatures. The copper was

placed into the alumina crucible within the graphite cell. The

whole assembly was then put into the spectrometer. The cell was

then heated to 1600°C. The copper peak was not observed, nor did

any of the neighbouring peaks diminish when the cell was rotated.

The cell orifice was not blocked. It appears that the vapour

pressure of copper was too low to be detected, so the sensitivity

of the mass-spectrometer was below its optimum. As the copper

peak could not be observed no further experiments were carried out

on the mass-spectrometer.

CHAPTER 4

DISCUSSION

128

4.1 Experimental Technique

The transpiration technique is an extremely useful experi-

mental method for equilibrating a condensed phase with vapour

phase. There were two unusual complications in this work, the

fact that arsenic forms a complex vapour and the fact that lead

exerts a considerable pressure above its melting point.

The copper-arsenic system had been studied before this work was

started (18), however the previous study was of limited scope,

since one temperature only was used. The workers did not recognise

the seriousness of the problems of working with a complex vapour,

although they noted that the As^ molecules would dissociate but

to an unknown extent. Data on the thermodynamic properties of

arsenic were used to calculate the composition of arsenic vapour

in the present work, and to calculate the activities of As^ relative

to a liquid arsenic standard state. A solid state had been used

in all previous investigations.

A volatile component in the liquid phase was clearly going to

be a problem and this inevitably led to compromises in operating

temperatures for the study on the Pb-Cu-As system. Fortunately it

was found that the arsenic in -the alloy came to equilibrium with

the vapour phase very quickly. The lead losses did not become

significant, so the system was operating near equilibrium.

The technique used with this apparatus was generally successful,

one problem was designing an apparatus which would satisfy the

laboratory authorities that the equipment was safe. The apparatus

which finally used was located in an enclosure protected

129

against accidental ingress of water. The furnace used to heat the

arsenic had a low thermal capacity and could easily be removed

from the apparatus. This meant that the arsenic could be cooled

very quickly if the need arose. The cabinet containing the

furnace arrangement was operated at a slight negative pressure

and there was an extremely strong draught when one of the access

doors were opened.

The apparatus proved reliable and equilibrium of the droplet

with the vapour was rapidly attained, as was shown by some prelim-

inary experiments. The main problem was removing the droplet from

the system without losing any of the arsenic. This problem was fin-

ally overcome by removing the droplet in one swift operation and

quenching it in distilled water.

The problem of monitoring the approach to equilibrium can be

overcome by carrying out the experiments on a microbalance, the

boat with the alloy in is put on the balance and then the weight

change throughout the experiment is measured. This technique is

particularly useful as there can be no doubt about the equilibrium

arsenic concentration. The main problem is designing the remainder

of the apparatus around the microbalance. The gas flow has to be

deflected so that it has no effect on the balance. Time and

resources did not allow this technique to be explored.

The mass spectrometer was used to detect the vaoour species

from samples containing arsenic. The problem was the wide difference

of vapour pressures between copper and arsenic. The technique

had been used to great effect in the past, but in this instance

the alloys were not suitable. The mass spectrometer may have

130

been useful at very low arsenic concentrations, but to calculate

the activity of arsenic, the data would have to be an extension

of the activity-concentration data from the transpiration

experiments.

131

4.2 The Copper-Arsenic System

To compare the current work with earlier investigations, it

is necessary to convert all of the activity data to a common

standard state. With the data which is available regarding the

vapour composition of arsenic, it is possible to recalculate the

arsenic activities frora..the data of Jones and Philipp (25). It

is also possible to convert from the hypothetical solid arsenic

standard state to a liquid arsenic standard state. The data of

Jones and Philipp as revised by Lynch (28) are converted to a

liquid arsenic standard state and are given in table 30. The

resulting data are plotted in figure 35 • It is then possible to

compare directly the two series of data. The two graphs are

given together in figure 36 . The present work is the upper curve

representing experiments carried out at 1387 K (1114°C). Clearly

for a given arsenic activity, Jones and Philipp introduced more

arsenic into the alloy. The difference between the two lines de-

creases as the activity increases, no explanation of these

discrepancies has been found. In view of the experimental tech-

nique of Jones and Philipp it was expected that they would have

found a lower arsenic concentration at each arsenic activity.

Their experimental technique involved slowly cooling the droplets

in a stream of arsenic laden argon. This approach led to a

considerable loss of arsenic in earlier experiments carried out

in the present investigation.

4.2.1 Variation of Activity Coefficient with Composition

It is possible to analyse the activity data from binary

alloys 'n several different ways. One of the most common tech-

T/K NAs PAs4 aAs 4 aAs 4s M s

5 4 3 0.174 6 . 0 1 x 1 0 " 8 2.64 x 10~5 0.682 4.93 x 10"3 2.84 x 10""2 - 1 . 5 5

553 0.197 2.39 x 10""7 3.73 x 10"5 0.645 6.97 x 10~3 3-54 x 10" 2 - 1 . 4 6

573 0.217 2.01 x 10"6 6.35 x 10~5 0.613 1.19 x 1 0 " 2 5.47 x 10"2 -1.26

584 0.228 5 . 4 0 x 10"^ 8 . 1 3 X 10""5 0 . 5 9 6 1 . 5 2 X 1 0 " 2 6.66 x 10"2 -1.18

609 0.250 4.36 x 1 0 " 5 1.37 x 10"2 0.563 2.56 x 1 0 " 2 1.02 x 1 0 " 1 -0.99

634 0.263 2.02 x 10"4 2.01 x 10"2 0.543 3-76 x 10~*2 1 . 4 3 x 10"1 - 0 . 8 5

644 0.267 3-58 x 10"4 2.32 x 10~2 0.537 4.33 x 10"2 1.62 x 10~1 -0.79

654 0.270 6.01 x 10~4 2.64 x 10*"2 0.533 4.93 x 10"2 1.83 x 10"1 -0.74

Data from Lynch Data revised to liquid standard state

Data of Jones and Philipp revised to a liquid arsenic standard state

Table 30

133

dA x102 As

0 0-15

1100 C

0-2 0 0-25 0-30 N A S

The activity data of Jones and Philipp converted to a

liquid arsenic standard state

Figure 35

9n Arsenic Activity

dAs*io"2

154

8 4

7 1 3 8 7 K /

This investigation

4 - I

3 4

1 -

1 3 7 3 K

Data of Jones and Philipp

0 I 0-125 0-150

N As

0-200 0-250 0-300

Comparison of the results of this investigation with those

of Jones and Philipp; relative to a liquid arsenic standard state

Figure 56

I 155

niques is to plot activity aguiusb mole fraction. In some

instances, the variation in activity is very large and the log P

of the activity coefficient is plotted against (1 - mole fraction),

A regular solution yields a straight line of constant slope. Two

more general results of such plots are; two linear portions or a

linear portion and a curved portion. Where there is a linear

relationship it is easier to describe the activity as a function

of composition. The calculation of log ^ A s and (1 - a r e

given in tables 31, 32 and 3 3 for each of the experimental

temperatures and the results are shown on figures 57, 58 and 59 ,

Each of the graphs is linear over a range and here the equation

of the best straight line has been calculated.

At 900°C, in the range N A g = 0-210 to 0-280, l o^10 ^As = - 2 , 9 9 2 ^ C u + ° ' 7 4 5 9

At 1000°C, in the range = 0-160 to 0-310,

l o S l 0 y A s = - 2 ' 9 7 5 N 2 C u + 0-8555

At 1114°C, in the range NAs = 0-195 to 0-285

L O S L 0 V = ~ 3 . 5 5 7 ^ + 1 . 1 6 7 '

The revised data of Jones and Philipp were also treated this

way and the results are shown in figure 40, No linear fit was

found to be suitable over a reasonable range.

4.2,2 The Activity of Copper in Copper-Arsenic Alloys

The activity of the second component in a binary system may

be determined from the activity of the other by application of

the Gibbs - Duhem equation, which was given as;

^ d In a^ + N 2 d. ln a 2 = 0 (1)

N A S 4 aAs ^As l 0 ^ A s

0.277 0.5230 4.180 x 10""2 0.1510 -0.821

0.256 0.5441 3.308 x 10~ 2 0.1294 -0.888

0.251 0.5661 2.862 x 10" 2 0.1140 -0.943

0.241 0.5764 2.475 x 10~2 0.1023 -0.990

0.227 0.5980 2.067 x 10" 2 0.0912 - 1 . 0 4 0

0.210 0.6246 1.573 x 10"2 0.0750 -1.125

Calculation of arsenic activity coefficient at 1173 K

Table 31

137

- 0 - 8

-0-94

-1-04-

-1-1

-1-2

Lg Y y10 As

-I 1-

0-64 0-62 0-60 0-58 0-56 0-54 0-52

N Cu Variation of activity coefficient with composition

Figure 37

138

N. N 2 aA VA logV. As Cu As As & As

0.160 0.7059 9.10 x 10~5 5.69 x 10~2 -1.245

0.194 0.6501 1.67 x 10"2 8 . 6 3 x 10"2 -1.064

0.223 0.6033 2.29 x 10"2 0.1027 -0.988

0.217 0.6134 2.34 x 10"2 0.1077 -0.968

0.248 0.5661 3.58 x 10~2 0.1446 -0.840

0.288 0.5075 6.31 x 10~2 0.2207 -0.658

0.312 0.4740 8.68 x 10~2 0.2787 -0.555

Calculation of arsenic activity coefficient at 1273 K

Table 32

1000 c t

f / /

- F

% /

/

1-C 0-9 0-8 o r 0-5 0-5

N R Cu Variation of activity coefficient with composition

Figure 58

140

N A S N C U aAs l 0 ^ A s 2

aAs

v - 2 0.285 0.5122 8.72 x 10 0.2870 -0.5422

0.247 0.5670 5-01 x 10""2 0.2029 -0.6928

0.250 0.5627 5.07 x 10~2 0.2030 -0.6926

0.221 0.6067 3.22 x 10""2 0.1459 -0.8360

0.195 0.6480 1.97 x 10"2 0.1011 -0.9954

0.162 0.7022 1.16 x 10"2 7.185 x 10"2 -1.144

0.136 0.7465 8.90 x 10"2 6.547 x 10""2 -1.190

Calculation of arsenic activity coefficient at 1387 K

Table 33 / I / Y V

141

Lg V 10 As 1114- C

- 0 - 5

-0-7

-0-9

- M

1-3

-1-5 1 0 0-9

V 0 - 8 0-7 0 6 0-5

N Cu

Variation of activity coefficient with composition

I Figure 39

I G y I<> As

- V O H

Revised data of Jones and Philipp

Figure 40

143

which leads to;

In a1

and similarly

I n K , = -

rN = N / v riN1 W1 N 2 d In a 2 (2)

~ N1 N 2 d In 2 (3)

Unfortunately this integration would involve the evaluation of

the area under a curve which extends to infinity. To improve

the accuracy it is possible to use a function, such that

(X = In Y± (4)

(1 - N.)2

2 2 For a two component system (1 - N^) = N 2 so

/>( = In 1 and o^ = in 2 (5) P 2

V N 1

By combination of the equations (3) and (5) Darken and Gurry (44)

arrived at;

In 1 <Z \ <Z \

K 1

= "" ° 2 N 1 N 2 " P 1 " N L ^ D N 1 ( 6 )

V = 1

The activity data from the transpiration experiments can

now be used to calculate the activity of copper by substitution

of the data for arsenic as component 2 into equation (6). The

(/function was calculated for arsenic at each experimental

temperature, and then the values of D(were plotted against N ^

in order that the area bounded by the curve could be measured.

The results are given in tables 34, 35 and 36 and figures 41 ,

42 and 43. Application of equation (6) to the copper-arsenic

system gives;

144

N A N P N 2 logi( ciK As Cu Cu 6 As As

0.277 0.723 0.523 -0.821 -1.570

0.256 0.744 0.554 -0.888 -1.603

0.251 0.749 0.561 -0.943 -1.681

0.242 0.758 0.575 -0.990 -1.723

0.227 0.773 0.598 -1.040 -1.739

0.210 0.790 0.625 -1.125 -1.801 Y ° - 2 Extrapolated values, 0 = 1.122 x 10

oU -1.95 Calculation of oC function at 1173 K

Table 34

145

N A N P N 2 log £ <* As Cu Cu & As As

0.160 O.84O 0.706 - 1 . 2 4 5 - 1 . 7 6 4

0.194 0.806 O.65O -1.064 -1.637

0.223 0.777 0.603 -0.988 -1.638

0.217 0.783 0.613 -0.968 -1.578

0.248 0.752 O . 5 6 6 -0.840 -1.484

0.288 0.712 0.508 -0.658 -1.297 0.312 0.689 0.474 -0.555 -1.171

Extrapolated values, X = 1.58 x 10~

<X°= - 1 . 8 0

Calculation of (X function at 1273 K

Table 35

146

N a N N 2 log*' As Cu Cu & As As

0.285 0.715 0.511 -0.5422 -1.059

0.247 0.753 0.567 -0.6928 -1.222

0 . 2 5 0 0.750 O . 5 6 5 - 0 . 6 9 2 6 -1.231

0.221 0.779 0.607 -0.8360 -1.378

0.195 0.805 0.648 -0.9954 -1.455

0.162 0.838 0.702 -1.144 -1.629

0.136 O.864 0.746 -1.190 -1.549

Extrapolated values, )! = 2.20 x 10~2

= - 1 . 6 6

Calculation of <X function at 1387 K

Table 3 6

Variation of d( function with composition

- 1 - 5 H

H S

-1-7-1

1-0 0-9

Figure 41

900 C

0-8

—J

Figure 42 OO

Variation of d function with composition

1-3 r

1 - 5 !-

1 :7 L

1 - 0 0 - 9 N

C U

Figure 43

1114 °C

0-8 0 - 7

150

1 0 B „ X . = " * N.. * "fNCu = V 0fAs d N J

N„ = N, 10 Cu Cu As As | As As

N„ = 1 Cu Calculated values of 311(1 h e nce a C u are given in table

37. The activity of copper in solution in copper-arsenic alloys

with N A s up to 0*30 at 1114°C is shown in figure 44.

The results for the activity of copper can be compared with

the measurements of Azakami and Yazawa (26), they used an

electrochemical technique to measure the activity of copper at

1273 K. They found that the activity coefficient could be

represented by log = -5.285 N^ 2 + 0.0853 (N A g> 0.025). The

The activities of copper calculated from this investigation are

slightly higher at each composition, for example at N^ = 0.8,

a^ is 0.65 compared to 0.60 reported by Azakami and Yazawa.

The corresponding arsenic activities are similarly higher with

= 1.6 x 10~2 compared with = 4.0 x 10~~5 in the earlier

investigation, both relative to a liquid arsenic standard state.

T/ °C N As Nn xN. Cu As As Value of integral

- 2 1114 °C 0.95 7.8708 x 10~2 -8.285 x

1114 °C 0.90 0.14805 -0.1655 1114 °C 0.80 0.2320 -0.32175 1114 °C 0.70 0.1995 -0.4550 1000 ° c 0.95 8.5358 x 10~2 -8.985 x 1000 ° c 0.90 0.1611 -0.17962 1000 ° c 0.80 • 0.2728 -0.3630 1000 ° c 0.70 0.25725 -0.5060 900 °C 0.95' 9.253 x 10"5 -9.740 X 900 ° c 0.90 0.1746 -0.19471 900 °C 0.80 0.2936 -0.3850 900 ° c 0.70 0.2982 -0.5490

, - 2

. - 2

Calculation of copper activity in copper - arsenic alloys

Table 37

log10*Cu YCu aCu

•4.143 x 10~"3 0.9905 0.9410 •1.745 x 10"2 0.9606 0.8646 •8.975 x 10"2 0.8132 0.6506 •0.2455 0.5682 0.3977 4.4925 x 10-5 0.9897 0.9402 •1.852 x 10"2 0.9583 0.8625 •9.02 x 10""2 0 .8124 0.6499 •0.2486 0.5641 0.3949 •4.87 x 10"3 0.9888 0.9394 •2.011 x 10"2 0.9548 0.8593 •9.140 x 10"2 0.8102 0.6482 •0.2508 0.5613 0.3929

The a c t i v i t y of copper i n c o p p e r - a r s e n i c a l l o y s a t 1 1 1 4

Figure 44

155

4.3 The Lead-Copper-Arsenic System

The activity measurements in the. lead-copper-arsenic system cannot be compared with any other investigation. The results are interesting because of the large amounts of arsenic in the alloys for a set arsenic activity even when the proportion of lead is high. It was possible that at 900°C the experiments may have become more liable to problems due to the high vapour pressure of lead. In some instances the vapour pressure of lead was comparable to that of the arsenic in the incoming argon. It appears that rather than the rate of arsenic arrival being a major factor, the rate of arsenic evaporation from the alloy became predominant. There are two observations to support this view, firstly the very short equilibration time, and secondly the very fast rate at which the arsenic activity rises as its mole fraction is increased. This means that the vapour pressure of arsenic above the alloys, in this range is relatively high. As the vapour pressure of arsenic was so much higher than lead, for most of the experimental time the mode of operation was similar to a transpiration experiment where arsenic loss from a lead-copper-arsenic alloy in a pure gas stream is found. These experiments were carried out close to equilibrium. The variation of the isoactivity curves with temperature may be seen by comparing the 0*1 activity contour at 800°C with that at 900°C(Figure 45). The upper curve represents the results at 800°C, increasing the temperature tends to decrease the mole fraction of arsenic at each Pb/Cu ratio, at a constant arsenic activity which was the expected result. The effect of temperature is greatest in the region where the Pb/Cu ratio is around unity. The same effect may be seen by comparing the 0*05 arsenic activity contours at 800 and 900°C (Figure 46). The

1

D O

t As

0-05 As Activity at 800 and 900° C

F i g u r e 46

156

upper line represents the results at 800°C. The amount of diver-gence between the lines is smaller than for the 0-1 activity lines.

As was noted earlier there is a miscibility gap in the Pb-Cu-As system up to a temperature of around 1065°C. None of the droplets showed any signs of having separated into two phases, to any serious extent, so that it is considered likely that all of the experiments were conducted outside the miscibility gap. When samples were accidentally produced within the miscibility gap, the fact was easily detected by the appearance of the sample.

The position of the miscibility gaps quoted from earlier investigations may be compared with the position of the isoacv tivity lines. The initial comparisons are between the 0-1 arsenic activity contour at 800°C and the reported miscibility gaps from three previous investigations. The first figure (Figure 47) shows the miscibility gap at 900°C as determined by Hino, Azakami and Yazawa (34). The activity line rises through the miscibility gap at the high lead end and then runs parallel to its edge. The second figure shows the same activity contour and the miscibility gap found by Dice, Oldbright and Brighton (31) at 700°C (Figure 48 )# The edge of the miscibility gap moves up to run parallel to the activity contour, from the lead rich end, they cross for a short distance before diverging. Increasing the temperature would have caused the miscibility gap to recede, and its edge would probably have run parallel to the activity curve. The third figure shows the data of Jacobs, Maes, and de Stryker (33) also at 800°C. This time the two sets of data are close at the high lead side of the diagram, and the general trend is for the two sets of data to converge in the copper rich region, (Figure 49).

f As

Comparison of the position of the 0-1 arsenic activity line at 800 °C and the miscibility gap found by Hino, Azakami and lazawa at 900 °C

Figure 47

f As

N —> Pb Comparison of the position of the 0«1 arsenic activity line at 800 °C and the

miscibility gap found by Dice, Oldbright and Brighton

F i g u r e 46

t As

N Pb

Comparison of the 0.1 arsenic activity line at 800 C with the miscibility gap found by Jacobs, Maes and de Stryker at 800 °C

Figure 49

160

4.4 Practical Results and Implications

As a result of this work, the cooling of metal tapped from a complex smelter is better understood. If a purely Pb-Cu-As bullion is tapped, it is unlikely to contain a mole fraction of arsenic greater than 0.05. Whatever the Pb:Cu ratio the arsenic activity is very low. The metal is tapped at around 1150 °C, above the temperature at which the miscibility gap exists. As the metal cools it enters the miscibility gap and separates into two phases one copper-rich with the majority of the arsenic, the other a lead-rich phase. The composition of the two equilibrium phases • changes as the temperature falls and the position of the miscibility gap alters.

The activity of arsenic will be the same in each of the phases if they are at equilibrium, so the general position of the tie-lines can be predicted. The activity of arsenic is far lower in copper than in the corresponding lead alloy, so if the metal were to separate into two binary, lead-arsenic and copper-arsenic, phases then the tie-lines would cross the miscibility gap radiating out from the lead rich corner across towards the copper-arsenic side of the phase diagram. The presence of lead in the copper-rich phase and vice versa tends to cause the tie-lines to become more parallel to the lead-copper side of the ternary phase diagram.

The very low activity of arsenic in copper leads to the formation of the speiss phase, and as the lead-rich phase cools the copper comes out of solution and the products are a low arsenic lead bullion phase and the copper arsenide with some entrained lead.

161

Appendix 1

A programme was written in the "FORTRAN" programming language for use on the time-shared facility of the college computer (Cyber 174)• The programme calculated the extent of dissociation of As^ molecules on being heated from evaporation temperature to the furnace hot zone temperature. The required data for the execution of the programme were the source vapour pressure of arsenic and the hot zone temperature. The programme works by converging on the correct value and the programme terminates when consecutive values are equal. The values produced by each iterative step are printed, an example of the execution of the programme and a listing of it are given overleaf.

10

20

50 40 50 60

70 80

90 1 0 0

110

1 2 0

130 140 150 1 6 0

170 1 8 0

1 9 0

200 210 220 230

240

250

260

270

280

290

PROGRAM AS (INPUT,OUTPUT) REAL C1,C2,C3,V,F1,G1,G2,G 24 PRINT, "HOT ZONE TEMP IN CENTIGRADE ?" PRINT, "800,900,1000,OR, 1100,ANY OTHER TO TERMINATE CPROGRAM" READ(5,*)T IF(T.EQ.800) GO TO 66 IF(T.EQ.900) GO TO 77 IF(T.EQ.IOOO) GO TO 88 IF(T.EQ.HOO) GO TO 99 GO TO 10 66 C1=1.091E-32

C2=5.678E-7 C3=1.021E-5

GO TO 23 77CC1=2.750E-28

C2=8.689E-6 C3=6.729E-5

GO TO 23 88 C1=1.411E-24

C2=8.719E-5 C3=3.298E-4

GO TO 23 99 C1=2.084E-21

C2=6.156E-4

C3=1.282E-3 23 ¥RITE(6,100) 100 FORMAT(*INPUT VP AS4*) READ(5, *)V

2059

500 PRINT, "AS4 AS5 AS2 AS »

510 X=1E-12

520 DO 500 1=1,20

330 F1=X+0.75*((X*C5)**0.75)+0.5*((X*C2)**0.5)

340 F2=0.25*((X*C1 )**0.25)-V

350 F=F1+F2

560 G1=1 +0.5625*C5*( (X*C5)**(-0.25) )+C2*0.25*(X*C2 )**(-0.5)

370 G2=0.0625*01*((X*C1)**(-0.75))

580 G=G1 +G2

390 A=X

400 X=X-F/G

410 IF(A.EQ.X) GO TO 82

420 Y=(C1*X)**0.25

430 Z=(C2*X)**0.5

440 T=(C5*X)**0.75

450 VJRITE(6,53)X,Y,Z,T

460 55 FORMAT (1X,E12.6,4X,E12.6,4X,E12.6,4X,E12.6)

470 500 CONTINUE

480 82 PRINT, "INPUT 1 IF NEXT- READING AT SAME TEMP"

490 READ(5,*) K

500 IF(K.EQ.1) GO TO 25

510 GO TO 24

520 10 STOP

530 END

164

HnT 7PNF TFMP TN rFNTTFPFmF ? s n n, 'H n n, 1 rin n . np • 11 n n, rnv dthfp tp tfpm tnptf ppcifprm

V- son TNPIIT VP RR4 •:•• R F - 4

R : " " 4 . 1 S 7 7 Q 4 F - I " I F . . P A I'I 0 1 R F - 0 3 . P R R P R P E - 0 3 . F Q : - : P 4 4 F - N " : . P ' Z , P P 4 4 F - L T " : , ; - ' 9 ~ : ; - 4 4 F — O R INPUT 1 TF NFXT PFPT"iTNR RT SPME TFMP

R:"' 1 RS? PR 3 Ap 2PP F-H9 . 94F,fi4RF— AR .8 04149E-08

. 1 ?9 7 R I*I F-0? . 121.P07F-04 .3A9848E-OA

. 1 739F-08 .129034F-04 . 4I-I4742E-OA

. 1 741E-OR . 1 ?9 03 AF-04 .4 04754E-OA

. 1 74 1 F-O.R .1P903AF-04 .4 04754F-OA

. 1 741F-OR .129ORAF-04 .4 04754E-OA

HnT 7PNF TFMP TN I'FNTTGRPPF ? Rfi0, Rfifi, 1 finfi,PR,11 nn, RNV riTHFP TO TERMT NRTE • 11. o o

PRHGRRM TNPIIT v p V 3 E - 4

R S 4

R.--4 PR 1 RS? RS3 . 4PP4RRF— 07 . '3RP4P8F- 07 . f<c7777F-o5 .210193E-07 .R773AAF-OF .3777ROF-OA .775A7PF-04 .118429F-OP . '1 7AA4F-04 .AA1P95F-OA .237A79F—OR .A35PP7F-OP .141R37F-03 .737347E-OA .295491E-03 .83058OF-OP .1X41FQF-03 . 74 ORP' F— OA .P9791 OF-OR .891395F-OP .14417?F-u3 . 74 03A4F-OA .P97914F-03 ..99J41 1E-np . 14417?F — OR .74 0RA4F—OA .P97914F-03 .891411E-OP TNPIIT 1 TF NF T pfrotnf rt srme TFMP •

c. HPT 7PNF TFMP TN CFNT TPPHTIF 7 R fl fl * I'l fl, 1 I'l 0 I'l, PP. 11 no,rnv dthfp TCI tfpmtnrtf pppg PRM

CP 1.1i*i? SFCS.

PUN rPMPI FTF.

PYE

165

Appendix 1

A computer programme was written in the "FORTRAN" programming language for use on the college computer (Cyber 174) time-shared facility. The programme used the derived analytical function of AGevap for 4As^?=iAs4£gj against temperature in K. The vapour pressure of arsenic was calculated at one degree intervals in the range from 473 to 683 K. The time to transport 1 gramme of arsenic at various gas flow rates was also calculated by varying the value of GASF in the programme.

The programme is given overleaf.

166

10 PROGRAM VA?OUR(INPUT,OUTPUT,TAPE 5=INPUT,TAPE 6=0UTPUT) 20 GASF =75 30 FLOW = GASF/22400 40 DO 1 N=473,683 50 T=N 60 Y1=-1.75181E-7*((T)**3) 70 12=1.517244E-3* ((T)**2) 80 Y3=-1.173787E1*T 90 Y4=9.23726E3 100 Y=Y1+Y2-+Y3+Y4 110 P=EXP(-Y/(1.9872 *T)) 120 p=p**4

130 VAPN=P*FLOW/(1 -P) 140 GSAS=VAPN*74•92*4 150 T1=1/GSAS 160 N1=N-273 170 VJRITE(6,20) N,N1,P,T1 180 20 F0RMAT(1X,I3,10X,I3,10X,E12.6,10X,E12.6) 190 1 CONTINUE 200 STOP 210 END

167

Appendix 1

A programme was written in "FORTRAN" for use on the time-shared facilty of the college computer (Cyber 174). The programme was used to calculate the final composition of alloys of lead, copper and arsenic which had equilibrated with the vapour phase. The data required for the execution of the programme are; 1) Start weight of the droplet 2) Final weight of the droplet 3) Alloy number 4) Vapour pressure of lead at the hot zone temperature 5) Duration of the experiment

The output from the programme are; 1) The final composition of the alloy assuming no lead loss 2) The final composition of the alloy assuming that the lead in the

alloy forms a Raoultian solution

The data on the alloys is stored in a..file called "datal". This data is loaded by using a short procedure file which then executes the programme. The procedure file, the data file and the programme are given overleaf, together with an example of the output from the execution of the programme. The. first line of output is the calculated composition assuming that there is no lead loss.

The procedure file is executed by typing "-alloy" The input data are preceded by "?" A typical run follows ;

-alloy INPUT START WEIGHT IN GRAMMES ? .3544 INPUT ALLOY NUMBER ? 5 INPUT FINAL WEIGHT IN GRAMMES ? .3480 MAX.LEAD LOSS IS 8.09741E-4

GIVEN BELOW ARE MOLE FRACTIONS OF EACH IN FINAL DROPLET MOLES AS MOLES CU MOLES PB .284431 .315844 .399725 .285065 .312313 .402622

INPUT START WEIGHT IN GRAMMES ? 1

.101 CP SECONDS EXECUTION TIME /

:" ETFL»500 oo RFT/CHRNRF MNF5. T =f'HRNFF. fc". F:=F'PnR 1 i"FT* PR TR 1

PRPR1 ^DRTpr:, PFROV.

F'FRTIV.

•0. 3886 . 3347 . 3 1 1 £ .31 12

. pp. 06 p 9 pe,

. 8 ' 6 J 4

. P4-4.F

. 5 3 1 * 1 5

. 5 4 I " I Q

. 48:57

. 4 O*5:?

. 3065 - 86 05 . 81 03 . 1 444 . 0784 . 1 4 06: . 1 846 . 88 01 .8786 . 38:76 . 458:7 . 4 6 6 8 . 5641 . 6 6 1 8

10 PROGRAM CHANGE (INPUT, OUTPUT, DATA1, TAPE7=DATA1) 20 DIMENSION A(9),P(9),WA(9),WP(9),WC(9) 30 REAL LOSS,MA,MC,MP 40 READ (7,*)A 50 READ (7,*)C 60 READ (7,*)P 70 20 PRINT, "INPUT START WEIGHT IN GRAMMES" 80 READ (5,*)X 90 IF(X.GT.0.95) GO TO 50 100 PRINT,"INPUT ALLOY NUMBER" 110 READ(5,*)I 120 PRINT"INPUT TIME IN MINUTES" 130 READ (5,*)N 140 Z=A(I)*74.92 150 V=P(I)*207.2 160 F=C(I)*63.5 170 T=Z+V+F 180 WA(I)=Z/T*X 190 VJP(I)=V/T*X 200 WC(I)=F/T*X 210 G=WA(I) 220 PRINT, "INPUT FINAL WEIGHT IN GRA14MES" 230 READ(5,*)Y 240 IOSS=X-Y 250 ALE=G-L0SS 260 WTP=WP(I) 270 PLOSS=P(I)*N*4.175E~4 280 PRINT,"MAX.LEAD LOSS IS"

2 9 0 WRITE(6,*)PLOSS 300 WTC=WC(I) 310 WTA=ALE 320 MP=WTP/207.2

330 MC=WTC/63.5 340 MA=WTA/74.92 350 T=MA+MC+MP 360 MA=MA/T 370 MP=MP/T 380 MC=MC/T 390 /HRINT, "GIVEN BELOW ARE MOLE FRACTIONS OF EACH IN 400 CFINAL DROPLET" 410 PRINT, " MOLES AS MOLES CU MOLES PB" 420 WRITE(6,*)MA,MC,MP 430 WTC=WC(I) 440 WTP=WP (I) -PLOSS 450 WTA=WA(I)-L0SS+PL0SS 460 MP=WTP/207.2 470 MC=WTC/63.5 480 MA=WTA/74 • 92 490 T=MA+MC+MP 500 MA=MA/T 510 MC=MC/T 520 MP=MP/T

530 WRITE(6,*)MA,MC,MP 540 WRITE(6,33) 550 33 FORMAT(///) 560 GO TO 20 570 50 STOP 580 END

1

2

5

4 5

6

7

8

9 10

11 12

15

14

15 16

172

REFERENCES

T.R.A.Davey, Bull.Inst.Min.Met., 72, part 678, 1963, 553-620. A.G.Matyas, Trans.1 .M.M., 8 6 c , 1977, 190-194. S.E.Woods and D.A.Temple, Trans.I.M.M., 74C, 1965, 297-518. J.L.Bryson and P.M.J.Gray, Trans.I.M.M., 77C, 1968, 72-84. J.L.Leroy, P.J.Lenoir and L.E.Escoyez, A.I.M.E. World Symposium on Mining and Metallurgy of Lead & Zinc, Volume 2 Ed. C.Cotterill and J.Cigan, New York, A.I.M.E. 1970, 824-852. L.Fontainas, M.Cousement and R.Maes, Some Metallurgical Principles in the Smelting of Complex Materials, Complex Metallurgy '78, London, I.M.M., 1978, 15-23. D .A .Temple and G.O.John, Can. Min .Met. Bull., February 1971, 58-66. J.B.See, N.I.M. Report 1888, 1977. R.C.Crease and G.W.Healy, Can.Met.Qu., 14, 1975, 175-181. G.Preuner and I.Brockmuller, Z.Phys.Chem., 8H, 1912, 29-70. S.Horiba, Z.Phys.Chem., J06, 1923, 295-502. L.Brewer and J.Kane, J.Phys.Chem., 59, 1955, 105-109. P.Goldfinger and M.JeuneKomme, Adv.Mass Spec., J_, 1959, 554-546. A.Nesmeyanov, Vapour Pressure of the Elements, Elsevier, London, 1965. J.Arthur, J.Phys.Chem.Solids, 28, 1 9 6 7 , 2257-2267. C.Herrick and R.Feber, J.Phys.Chem., 72, 1968, 1102-1110.

17 18

19 20

21

22

2 3

24

25 26

27 28 29

30 31

32 33

34

2069

J.Hudson, Ph.D Thesis, Pennsylvannia State University, 1969.

E.H.Baker, Trans.1 .M.M., 80C, 1971, 93-98. H.Rau, J.Chem.Thermodynamics, 7, 1975, 27-32. Hultgren and others, Selected Values for the Thermodynamic Properties of the Elements, American Society for Metals, 1973. W.Hume-Rothery' and J.Burris, Phil.Mag., 2, 1957, 1177-96. R.Heyding and G.Despaut, Can.J.Chem., 38, 1960, 2477-81. R.Juza, K.von Benda, Z.Anorg.Allgem.Chem., 357, 1968, 238-246.

nd M.Hansen, Constitution of Binary Alloys, 2 Edition, New York, McGraw-Hill. D.Jones and D.Philipp, Trans.I.M.M., 88C, March 1979, 7-10. T.Azakami and A.Yazawa, Nippon Kogyo Kaishi, 85, 1969, 97-102. J.Bode, J.Gerlach,F.Pawlek, Erzmetall., 24, 1971, 480-485. D.Lynch, Met.Trans., 11B, December 1980, 623-629.

st M.Hansen, Constitution of Binary Alloys, 1 Edition, New York, McGraw-Hill. B.Predel and A.Emam, Z.fur Metallkunde, 64, 1973, 647-652 C.Dice, G.Oldbright and T.Brighton, Trans.T.M.S.-A.I.M.E., 121, 1936, 1.27-159 H.Kleinheisterkamp, Erzmetall., 1948, 65-72. J.Jacobs,R.Maes and R. de Stryker, Trans.T.M.S.-A.I.M.E., 239, 1967, 1166-1171. M.Hino, T.Azakami and A.Yazawa, The Liquid Miscibility Gap and. the distribution of Silver between Speiss and Metallic Lead in the Pb-Fe-As and Pb-Cu-As Ternary Systems, presented

174

th at 16 CIM Annual Conference, Vancouver, 1977.

35 R.A.Rapp , Physicochemical Measurements in Metals Research, New York, 1970.

36 Ed. O.Kubaschewski, Metallurgical Chemistry, H.M.S.O. 37 O.Kubaschewski, C.Alcock, E.Evans, Metallurgical

Thermochemistry, Pergammon Press, 19&7-38 G.Belton and R.Fruehan, J.Phys.Chem., 71, 1967,1403-1409. 39 G.Beiton and R.Fruehan, Met.Trans., 2,1971, 291-296. 40 R.Fruehan, Met.Trans., 2, 1971, 1213-1218. 41 U.Merten, J.Phys.Chem., 63, 1959, 443-445. 42 L.Gillespie, J.Chem.Phys., 7, 1939, 530-535. 43 F.D.Richardson, Physical Chemistry of Melts In Metallurgy,

Academic Press, London. 44 L.Darken and R.Gurry, Physical Chemistry of Metals, New

York, McGraw-Hill, 1953.

175

Acknowledgements

The author wishes to thank many past and present members of the Department of Metallurgy and Materials Science for many helpful discussions and suggestions in the course of this research. He is particularly grateful to Professor J.H.E.Jeffes for super-vision, encouragement and understanding throughout the course of the work.

He is also indebted to Metallurgie Hoboken-Overpelt for their assistance in preparing the lead copper arsenic alloys and in carrying out chemical analyses.

Finally the author would like to acknowledge the financial support he received from the Science and Engineering Research Council.