Vacuum Refining Copper Melts to Remove Bismuth, Arsenic, and Antimony

RALPH HARRIS

Experiments were camed out on 35 kg melts of doped cathode copper and anode copper in a 3 m 3, 150 kW vacuum induction furnace. Rates of removal of bismuth, arsenic, and antimony were mea- sured over temperature and pressure ranges of 1450 to 1610 K and 3 to 30 pascals, respectively. Bismuth removal was found to be rapid: 1 to 18 • 10 -5 m/s. Arsenic and antimony removal were quite slow: 0.2 to 3 • 10 -5 and 0.1 • 10 -5 m/s, respectively, and evaporation controlled rates of refining. It is shown that, at typical concentrations of these elements in copper, monatomic evaporation is the predominant evaporation mechanism. An expression for the melt phase mass transport rate coefficient is developed from Machlin's model. In this expression, melt diffusion is a function of melt temperature, and melt surface velocity is a function of the square root of melt surface area to volume ratio and the square of melt temperature, i.e. : k = 1.11 • IO-7[(A/V)f] ' /4Tr '/2 exp( -2515/T) . This coefficient is used to examine rate control in previous small scale studies and in the present and previous pilot scale studies. The gas phase mass transport coefficient is found to be proportional to the overpressure ratio defined as: total initial melt vapor pressure/chamber pressure, and is also found to be dependent on the geometry of the gas space immediately above the melt.

I. INTRODUCTION

IMPURITIES such as bismuth, arsenic, and antimony which enter the copper-making process must be removed because of their deleterious effects on copper's electrical properties. The inability of electrolytic refining to remove large amounts of these impurities has led to investigation of alternative refining techniques. Small scale and pilot scale studies showed rapid elimination of bismuth is possible via vacuum refining, but published data are found to be widely scattered and often contrary to theoretical predictions.' s

The present experimental investigation reexamined bis- muth, arsenic, and antimony elimination from 35 kg melts of high-impurity anode copper. The results indicate that vacuum refining kinetics are complex, and gas phase mass transport resistance can be significant and quite variable at chamber pressures previously thought to yield negligible gas phase resistance.

In the present analysis, the basic vacuum refining crite- rion is reconsidered to establish the roles of monatomic and polyatomic evaporation, and a revision of the expression for melt phase mass transport coefficient is necessary to examine rate control. It is discovered that gas phase mass transport resistance is related to both melt parameters and gas phase parameters.

II. THEORETICAL MODEL OF VACUUM REFINING

Vacuum distillation occurs via 3-step mass transfer, i .e. , mass transport in the liquid phase to the liquid/vacuum inter- face, evaporation, and mass transport in the gas phase away from the liquid/vacuum interface. 6,7,8a Vacuum refining of commercial copper melts involves the evaporation of metal-

RALPH HARRIS is with the Department of Mining and Metallurgical Engineering, McGill University, 3450 University Street, Montreal, Quebec H3A 2A7, Canada.

Manuscript submitted December 21, 1982.

lic elements which are known to exist as both monatomic and polyatomic species in the vapor state. The mechanism of evaporation for a particular element can be determined by considering the volatility coefficient for each form of that element.

III. MONATOMIC/POLYATOMIC EVAPORATION

Olette 9 developed volatility coefficients for monatomic evaporation by forming the ratio of the evaporation fluxes of solutes and solvents into perfect vacuum, i .e . ,

[-1]

where n is the molar flux M is the molar mass P is the partial vapor pressure R is the gas constant T is the melt temperature

Substitution for the partial pressures in terms of mole frac- tions (N), activity coefficients (7), and vapor pressures of the pure species (P~ into the basic refining criterion: ni/nb >- Ni/Nb (from mass balance) yields Olette's volatility coefficient refining criterion, i .e . ,

yiP~ [Mb] v2 q~,=--~-L~ij e l [2]

The magnitude of the volatility coefficient from one solute to another roughly indicates relative rates of refining when monatomic evaporation controls rates of refining.

Polyatomic evaporation can be treated in a similar manner by substituting the vapor pressure of the polyatomic species in terms of known solute properties, m i.e.:

Pij = P? " ,j (-y, N y [3]

where j is the number of atoms in the polyatomic species, Pij and P? ,~ are the partial vapor pressures of the polyatomic

METALLURGICAL TRANSACTIONS B VOLUME 15B, JUNE 1984--251

species in solution and the pure polyatomic species, re- spectively, and (yiNi) is equivalent to the activity of species i in solution. Substitution into Eq. [1] gives:

_ _ �9 9 j Nij -~ [ 27rMbRT] ltz Pg('yiNi) [4] nb [ 27rMij R TJ P~,

Substitution of the polyatomic refining criterion: nifnb >>- (1/j) �9 (NJNb) (from mass balance) yields a general expres- sion for the polyatomic volatility coefficient:

It is clearly seen that for j = 1, the polyatomic volatility coefficient reduces to that of Olette and it is also seen that for j >_- 2, the volatility coefficient depends upon solute concentration,

Volatility coefficients for impurity species commonly encountered in copper smelting are listed in Table I. The values indicate that only monatomic evaporation is possible for the given concentrations of arsenic or bismuth and that removal of antimony is unlikely in either form. Thus, having established the form of the evaporating species of concern here, the Hertz-Langmuir-Knudsen model can be used for the evaporation mass transfer coefficient: 11-14

= [ 1 l l /2 .y iMb ke [2~r34,RT:J p____~__, po [6]

where Pb is the density of the melt.

IV. MELT PHASE MASS TRANSPORT IN INDUCTION STIRRED SYSTEMS

Present mass transfer models for induction stirred sys- tems T M a r e imprecise because the diffusion term and melt surface velocity term in the expression for the melt phase mass transfer coefficient:

kra = (SD'nvm) '/2 [ '7]

\ "n'rm /

where D,, is the melt diffusion coefficient v,. is the melt surface velocity rm is the melt radius

are generally assigned constant values based on the best estimate of expected behavior.

However, it is known "that the melt diffusion coefficient is temperature dependent and can be expressed as:

D m = Do" e x p ( - E o / R T ) [8]

Table I. Volatility Coefficients Evaluated at 1200 ~ for Various Species Encountered during Vacuum Refining

Copper Melts. Activity Coefficients Are Given in Appendix I.

Solute ppm Volatility Coefficient

Bi - - 7.94 • 10 3

Bi2 200 6.70 • 10 -1 As - - 7.30 • 101 As2 400 1.90 • 10 -1

As4 400 3.52 x 10 5 Sb - - 3.11 x 10 ~ Sb2 200 2.96 x 10 -4

2 5 2 - - V O L U M E 15B, JUNE 1984

where ED, the activation energy for melt diffusion, has a magnitude of about 40 kJ and Do has a value of 1.63 • 10 - 7 m 2 S - I . 8b

It is also known that the characteristic melt surface velocity depends on a number of factors as shown by the expression of Szekely et al.:17

1/2

,9,

where v is the characteristic velocity J0 is the coil current L is the characteristic length (melt diameter) f is the characteristic frequency or is the electrical conductivity ~ is the magnetic permeability of free space

Since furnace power (P) is proportional to J0 z, and tr, P,o, and p do not vary greatly, the expression can be rewritten:

v ~ (e .f)1/2. L 2 [101

Melt temperature can also be related to furnace power and melt dimensions as shown by the following argument.

For a melt in an induction furnace at steady temperature, furnace power input balances conduction and radiation heat losses. A small change in melt temperature would yield a change in conduction heat losses which are proportional to the temperature change, and it would yield a change in radiation losses which are proportional to the fourth power of the temperature change. As the change in radiation heat losses overwhelms the change in conduction losses and the losses must be made up by additional furnace power input, it can be argued that furnace power is proportional to T 4. Furthermore, for a melt of fixed radius but having various depths, furnace power input must be proportional to the melt surface area to volume ratio. Equation [9] can then be rewritten combining these relationships:

Vm --- Vo" [T 4�9 (A/V) . f]~/2 . L 2 [ l l l

where (A/V) is the melt area to volume ratio Vo is the proportionality constant

Typical values of melt surface velocity are given in Table II and an average value of v0 was obtained from that data.

Substituting Eqs. [8] and [11] into Eq. [7] yields a new expression for the melt phase mass transport coefficient for induction stirred systems:

k,, = 1.11 x 10 -7

�9 [(A/V) . f ] 1 / 4 . T" r ''2" exp( -2515/T) [121

This is an interesting result as Eq. [12] indicates that the melt phase mass transfer coefficient increases as the melt radius increases and that melt temperature is a significant factor in induction stirred melt phase mass transport.

Table II. Typical Values of Melt Surface Velocity under Various Experimental Conditions

Temp. (K) A/V, m I Freq., Hz L, m vm, m/s

1473 7 3000 0.2 0.09 1523 7 3000 0.2 0.10 1573 7 3000 0.2 0.11 1473 55 3000 0.04 0.13

METALLURGICAL TRANSACTIONS B

V. GAS PHASE MASS TRANSPORT

Previous models for gas phase mass transport have suf- fered from a number of shortcomings. Ward ' s model 18'~9,2~ was specific to a particular system, and Ohno ' s model re- quired a knowledge of a gas phase mass transfer coefficient. Two previous works by the author 3'21 also modeled gas phase mass transport. Unfortunately, the first was based on poor data and is now thought to be in error and the second was restrictive in its range of applicability. However, the latter found that the ratio of melt vapor pressure to chamber pres- sure was critical in determining the gas phase mass transport mechanism. A more recent paper 36 by the author found a correlation between this ratio (there defined as the Over- Pressure Ratio: OPR) and the refining rate for bismuth re- moval from copper melts.

VI. PREVIOUS STUDIES

Table III presents a summary of previous work on vacuum refining copper melts to remove bismuth. Large ranges of chamber pressure, melt temperature, and melt area/volume ratio have been studied in various types of furnaces.

Table IV lists for Ohno 's induction stirred experiments 2 calculated rate coefficients for melt phase mass transport

(Eq. [12]), evaporation (Eq. [6]), and gas phase mass trans- port (kg = 1/kexp - l /kr , - l ike) . Clearly, in some experi- ments there was mixed control from the melt phase and evaporation and in other cases, mixed control from these two and the gas phase. Therefore, it would have been ex- pected for Ohno ' s less stirred experiments (the melts were shielded from the induction field) that the refining rates would have been less. As Ohno ' s results did not demon- strate this expected decrease, it can be reasoned that either (i) the above values for melt phase mass transfer coefficients are incorrect and Ohno 's conclusion that refining rates were controlled by processes other than melt phase mass transport was correct, (ii) there was little change in stirring from one experimental configuration to the other or, (iii) gas phase resistance decreased from the stirred to the less stirred experiments to compensate for the increased melt phase resistance. However, there are insufficient data to draw a firm conclusion.

Ohno 's later work on copper melts, mechanical ly stirred at different speeds, z~ was also not definitive on this subject as it was carried out at chamber pressures under which gas phase mass transport was l ikely solely rate limiting. The effects of gas phase resistance can further be seen in the works of Ozberk and Guthrie 5 and Danovitch. 4 Both those studies were carried out in the one apparatus and differed

Table IH. Summary of Previous Studies on Bismuth Removal from Copper Melts under Vacuum

Source Year Mass Cu, kg Temp., K Press., Pa (A/V), m -~ ke~p x 105 m/s Comment

Danovitch 4 82 23 to 35 1500 to 1740 7 to 160 6.7 to 10.2 1.6 to 7.4 Ozberk 5 79 34 1423 to 1623 8 to 13 7.1 1,1 to 3.1 Kametani 22 78 0.6 to 6 1473 130 to 270 - - 2 to 12/(A/V) B r y a n 23 77 4 1473 to 1573 3 to 27 - - 50/ (A/V)

Ohno 24 77 0.5 1468/1573 1 to 13 18.1 6,1 to 12.3

Ohno 2 76 0.15 1473/1573 0.1 to 1 30 to 60 8 to 26 Komorova z5 73 0.03 1473 1 - - 10 to 22/ (A/V) Streltsov z6 73 0.04 1473 13 to 67 - - 2.8 / (A/V)

3 m 3 VIM/full crucible 3 m 3 VIM/0.5 full crucible vacuum lift refining VIM/no description of experiments/

(A/V) probably in range 10 to 20 resistance heating/

molybdenum stirrer VIM/with-without stirring

resistance heating/also 1000 kg VIM tests, but no Bi data

Kameda 29 63 0.03 1373/1473 13 - - 20 to 64/ (A/V)

*ke.v = ln(wt pet i initial/wt pet i final) �9 (V/A) �9 (l/t); where t is the duration of the experiment in seconds.

Table IV. Summary of Ohno's Induction Stirred Studies for Bismuth and Lead Elimination from Copper Melts under Vacuum. 2 Chamber Pressure Was Taken as 0.5 Pascal.

Exp. No. Temp., K (A/V) , m - l Time, Min. OPR kexp X 105 m/s km• 105 m/s ke • 105 m/s k s • 105 m/s

Bismuth Elimination

S-1A 1473 53.6 5 18 13.4 29.1 36.1 79.6 S-1B 1473 58.4 10 18 13.1 29.7 36.1 66.8 S-1C 1473 54.4 15 18 8.6 29.2 36.1 18.4

S-2A 1573 29.6 5 50 20.3 29.8 90.3 216 S-2B 1573 54.4 6 50 26.0 34.7 90.3 - - S-2C 1573 52.8 10 50 16.1 34.5 90.3 45.3

Lead Elimination

S-3A 1473 60.0 5 28 16.5 29.1 57.2 114 S-3B 1473 55.2 10 28 13.8 28.5 57.2 50.2 S-3C 1473 56.8 15 28 10.0 28.7 57.2 21.0

S-4A 1573 56.0 5 144 17.8 34.1 142 50.5 S-4B 1573 54.4 10 144 13.5 33.8 142 26.7

METALLURGICAL TRANSACTIONS B VOLUME 15B, JUNE 1984--253

Table V. Summary of Ozberk and Guthrie's Experiments s and Danovitch's Experiments 4 on Vacuum Refining Copper Melts

Exp. No. Temp., K Press., Pa (A /V) , m -~ OPR keB2p X 105 m/s k,, x 105 m/s k, x 105 m/s k s • 105 m/s

Ozberk and Guthrie

O-1 1423 8 7.1 0.06 1.3 0-2 1523 8 7.1 0.26 2.8 0-3 1623 8 7.1 0.82 3.1 0-4 1423 13 7.1 0.04 1.1 0-5 1523 13 7.1 0.12 1.9 0-6 1623 13 7.1 0.45 2.3

Danovitch

D-1 1625 11 6.8 0.89 7.6 D-2 1637 11 7.8 1.01 6.0 D-3 1635 11 8.6 1.10 6.2 D-4 1595 14 8.2 0.55 4.4 D-5 1607 10 9.7 0.43 2.2 D-6 1530 14 6.8 0.29 3.9 D-7 1505 11 8.3 0.09 2.0 D-8 1500 7 10.2 0.35 1.6 D-9 1690 33 6.7 0.55 7.4 D-10 1740 33 8.1 0.68 5.0 D-11 1740 28 9.0 0.79 6.1 D-12 1740 35 10.2 0.94 6.4 D-13 1645 125 6.9 0.08 1.9 D-14 1607 95 8.0 0.05 3.0 D-15 1625 108 9.4 0.08 3.2 D-16 1645 11 6.8 0.58 3.5

10.0 22 1.6 12.1 58 3.9 14.2 137 4.1 10.0 22 1.3 12.1 58 2.3 14.2 137 2.8

14.1 139 18.6 14.9 152 10.8 15.2 150 11.2 14.1 109 6.9 15.0 120 2.6 12.1 62 6.4 12.2 49 2.5 12.7 47 1.9 15.5 228 15.1 17.5 326 7.2 18.0 326 9.5 18.6 326 10.1 14.6 162 2.2 14.3 120 3.9 15.3 139 4.1 14.6 162 4.7

only slightly in experimental configuration and the ranges studied. Their results are summarized in Table V.

It is clear that Danovitch 's refining rates were greater than those of Ozberk for similar temperature and pressure conditions. This is attributed to the major difference that Danovitch 's work was carded out in filled crucibles whereas Ozberk 's work was carried out in half full crucibles of the same diameter (Figure 1). It is believed that the absence of dead space over the melt in Danovi tch 's work lowered gas phase mass transport resistance with respect to that for Ozberk 's work.

VII. E X P E R I M E N T A L

Pilot scale vacuum refining experiments were carried out on high-impurity anode copper melts in a 150 kW vacuum induct ion furnace which has been descr ibed in deta i l elsewhere ~'25 and is the same apparatus as used by Ozberk et al. and Danovitch. Removal of bismuth, arsenic, and antimony was investigated over a temperature range from 1450 to 1610 K and over a pressure range from 3 to 30 pascals. Experimental procedure was similar to that of the previously cited studies. The vacuum chamber had an inter- nal volume of 3 m 3 and an inside diameter of 1.8 m. The induction furnace top was 0.8 m from the chamber roof, and the melt surface was 0.2 m below the rim of the crucible which was level with the top of the furnace (similar to the configuration of Ozberk et a l . ) . Inside crucible diameter was 0.195 m and inside height was 0.35 m. Chamber evacuation was via a two-stage pumping system comprising 300 cfm mechanical pump with a 1300 cfm roots blower.

A

2

r CRUCIBLE

2-FURNACE COILS 3 -PA CK/NG 4-MOLTEN COPPER

E3

Fig. 1 - -Placement of crucibles in the induction furnace: A - - O z b e r k and Guthrie, B- -Danovi tch and present work.

254--VOLUME 15B, JUNE 1984 METALLURGICAL TRANSACTIONS B

The quoted chamber pressures were those in equilibrium full pumping capacity.

VIII. RESULTS

Results of the present invest igat ion are summar ized in Table VI. Bismuth removal was generally about 5 to 10 times faster than arsenic removal , and there was no removal of antimony. The latter was as expected from cal- culated values of ant imony 's volatili ty coefficient. The in- equality between the ratios of bismuth and arsenic volatility coefficients and their refining rates indicates that mecha- nisms other than evaporation control bismuth removal rate.

Bismuth Removal. Table VII lists measured rate coeffi- cients and calculated values for each of the mass transport

steps for bismuth removal . The present range of over- pressure ratio is large and allows examination of gas phase mass transport resistance as a function of this parameter (Figure 2). Also plotted are the results of Ozberk et al. and Danovitch. It is seen that the work of Danovitch is distinctly different from that of the author and Ozberk et al. Linear equations relating kg and overpressure ratio were derived for the two configurations:

. . . . ,,oh= 2.05 + 10.04.(OPR) [13]

k ~ = 1.94 + 3 .65 . (OPR) [14]

Clearly, for small values of OPR, gas phase resistance was roughly the same for both cases and rate limiting. However, Danovitch 's gas phase mass transport was about 2.7 times more sensitive to increases in OPR, or, for a given melt

Table VI. Experimental Conditions and Results for the Present Study. Experiments Are Grouped into Sets Which Were Carried Out on the One Charge during One Day of Experimentation. Temperature Variation Was Approximately -+ 10 K. Pressure Variation Was Approximately _+ 10 Pct. Rate Coefficients Were Derived from the Slope of the In (Wt Pct Solute) vs Time Plot.

Exp. Temp. Press. (A/V) Time Wt Pct Initial Wt Pct Final No. K Pa m -~ Min. Bi As Sb Bi As Sb ~ p x 105 m/s ~)p • 10 6 m/s

H-1 1487 20 7.2 90 0.040 0.318 0.035 0.014 0.318 0,035 2.63 2.41 H-2 1445 7 7.1 88 0.797 0.354 0.036 0.210 0.301 0.037 3,35 3.83 H-3 1509 9 6.8 88 0.939 2.743 0.039 0.111 2.056 0.040 5.80 4.92 H-4 1553 10 6.5 37 0.258 3,938 0.712 0.084 3.269 0.650 7.33 7.91

H-5 1558 25 7.1 119 0.031 0.332 0.031 0.007 0.258 0,031 3.00 5.46 H-6 1545 I0 7.1 100 0.410 0.270 0.030 0.050 0.195 0.031 4.45 8.07 H-7 1531 5 7.1 95 0.374 0.215 0.332 0.048 0.126 0.362 5.15 7.19 H-8 1545 3 6.9 65 0.164 3.180 0.718 0.042 1.408 0.745 5.24 23.50

H-9 1483 13 6.9 61 0.046 0.365 0.054 0.027 0.297 0.049 2.14 8.88 H-10 1473 27 7,0 60 0.138 0.323 0.048 0.086* 0.316 0.045 1.17 - - H-11 1480 5 7.0 60 0.103 0,316 0,043 0,054 0.235* 0,047 2.49 12.30 H-12 1549 27 6.9 40 0.143 0.848 0.160 0.099 0.619 0.154 2.34 19.10

H-13 1507 8 6.6 58 0.043 0.337 0,030 0.024 0.202 0.032 2.75 15.40 H-14 1469 7 6.5 60 0.331 1.816 0.351 0,136" 1.651 0.385 3.70 4.90 H-15a 1578 9 6.5 20 0.438 1.808 0.372 0.113 1.361 0.402 17.50 39.60 H-15b 1626 15 6.5 40 0.113 1.361 0.402 0.055 1.280 0.367 4.64 3.96

*Values interpolated from the above mentioned plot

Table VII. Summary of Measured Rate Coefficients and Calculated Rate Coefficients for Each of the Mass Transport Steps for Bismuth Removal from Copper Melts under Vacuum. Experimental Conditions Are Also Given.

Exp. No. Temp., K Press., Pa (A/V), m ~ OPR k~p • 10 5 m/s k,~ • 10 5 m/s ke • 10 5 m/s kg • 10 5 m/s

H-1 1487 20 7.2 0.07 2.6 11.4 41 3.7 H-2 1445 7 7.1 1.55 3.4 10.5 27 6.2 H-3 1509 9 6.8 2.90 5.8 11.7 51 14.9 H-4 1553 10 6.5 1.49 7.3 12.4 76 23.0

H-5 1558 25 7.1 0.14 3.0 12.8 79 4.1 H-6 1545 10 7.1 1.62 4.5 12.5 71 7.8 H-7 1531 5 7.1 2.59 5.2 12.2 62 10.6 H-8 1545 3 6.9 2.89 5.7 12.4 71 12.3

H-9 1483 13 6,9 0.12 2.1 I 1.2 40 2.8 H-10 1473 27 7.0 0.11 1.2 11.0 36 1.4 H-11 1480 5 7.0 0.50 2.5 11,1 39 3.5 H-12 1549 27 6.9 0.29 2.3 12.6 73 2.9

B I 3 1507 8 6.6 0.25 2.7 11.5 50 3.8 H-14 1467 7 6.5 0.92 3.0 10.7 35 4.7 H-15a 1578 9 6.5 3.13 17.5 13.2 94 * H-15b 1626 15 6.5 1.43 4.6 14.0 146 7.2

*Measured value exceeds maximum theoretical rate from Eq. [12].

METALLURGICAL TRANSACTIONS B VOLUME 15B, JUNE 1984--255

26 I I I I I

24 - �9 DANOVITCH - iO 5 �9 OZBERK & GUTHRIE kg x m/s �9 PRESENT

20

18 / --

16 - -

KDANOVITCH = 2'05 + IO'04(OPR) r[

" l!J/ : !.-I 10 T - -

'r I I I KOZBERK/HARRIS = 1 94 + 3'68(0PR) !

I tit i o I 2

Fig. 2 - - Plot of calculated gas phase mass transport rate coefficient against OPR for Refs. 4, 5, and the present work. Regression coefficients for 8k~ "~ and k ~ are 0.726 and 0.964, respectively. Error bars are the maximum range of variation in k s as caused by a 20 pct change in k,~, k~, o r k , .

Table VIII. Arsenic Removal Rates for Previous and Present Studies on Vacuum Purification of Molten

Copper. Other Work by Kim 3~ Showed 30 to 50 Pet Elimination but Gave No Experimental Details.

Source ~ s • 105 m/s

Danovitch ~ 2 to 3.5 Ozberk s <~0.1 Kametani 22 2 to 25/(A/V) Komorova 25 10 to 25/(A/V) Golovko z9 40/(A/V) Kameda z7 3 to 30/(A/V) Present work 0.24 to 2.9

composition and temperature, 2.7 times more sensitive to decreases in chamber pressure.

Ohno's induction stirred studies were considered an example of the Harris/Ozberk phenomenon, and substitu- tion of his overpressure ratios in Eq. [14] yields values in

Table IX. Summary of Antimony Removal from Copper Melts. Other Work by Kim 3~

Showed 40 Pet Antimony Elimination.

Source keS~p • 10 5 m/s

Danovitch 4 <0.5 Ozberk 5 ~0.1 Kametami 22 4 to 25/(A/V) Komorova z5 I0 to 20/(A/V) Golovko z9 40/(A/V) Kameda 27 10 to 20/(A/V) Present work <~0.1

agreement to the calculated values (Table III). Substitution of the overpressure ratios for Ohno's later work on mechani- cally stirred copper in Eq. [14] yields values for gas phase resistance which would be solely rate limiting.

Arsenic Removal. Table VIII summarizes arsenic re- moval data for previous studies on copper purification. Ranges of the present work are also given. Except for Danovitch's work and some of the present results, arsenic removal rates were very low and indicative of small value of arsenic evaporation rate coefficients.

Antimony Removal. Table IX summarizes studies of an- timony removal from copper melts. Uncertainty in removal rates due to high analytical imprecision preclude firm con- clusions. Antimony volatility coefficients (Table I) indicate, however, that removal of antimony by vacuum refining is unlikely at all temperatures and concentrations.

IX. CONCLUSIONS

1. Polyatomic evaporation is shown to be unimportant in vacuum refining of usual industrial copper melts.

2. Melt phase mass transfer coefficients are suggested to be melt temperature and geometry dependent, and a suitable expression is developed.

3. Present results in conjunction with previous studies indi- cate a role of gas phase geometry in gas phase mass transport resistance.

4. Bismuth removal was rate controlled during large scale refining by a mixture of melt phase/gas phase mass trans- port resistance. For smaller scale studies, there was mixed control from each of the three transport steps.

5. Arsenic elimination was evaporation rate controlled and as such, temperature dependent to a far greater extent than bismuth. Imprecision in arsenic analysis precluded detailed examination of rate control for arsenic.

6. Antimony removal was found to be negligible on large scale studies. This was in accord with the values of anti- mony's volatility coefficient.

256--VOLUME 15B, JUNE 1984 METALLURGICAL TRANSACTIONS B

APPENDIX I

Table AI. Thermodynamic Data for Commonly Encountered Species in Copper Refining. Constants A, B, and C Were Used to Calculate Vapor Pressures of the Pure Species v/a the Relationship: loglo(P~) = A / T + B Iog~o(T) + C

Where P~ Is the Vapor Pressure of the Pure Species in Pascals and T Is Temperature in Kelvin.

Species yi Reference A B C Reference

As 0.006 10 - 20540 0.00 17.67 4 As2 - - - - - 13634 0.00 16.24 10 As4 - - - - - 6904 0.00 12.92 10 Bi 2.2 31 to 33 - 1 0 4 0 0 - 1 . 2 6 14.47 34 Bi2 - - - - - 10700 - 3 . 0 2 20.22 34 Cu 1.0 - - - 17520 - 1.21 15.33 34 Pb 5.7 31 ,33 - 10130 - 0 . 9 8 5 13.28 34 Sb 0.02 33 - 12160 0.00 10.19 35 Sb2 - - - - - 8423 0.00 9.46 35

NOMENCLATURE

y raoultian activity coefficient d~ volatility coefficient p bulk density

A melt area, m 2 a activity of species b bulk species Do temperature independent factor relating Dm to T, m 2 s- D,. liquid phase diffusion coefficient, m 2 s -~ Eo activation energy for liquid diffusion, kJ i evaporating species j number of atoms in polyatomic species ke evaporation rate coefficient, m s-l kexp experimentally measured rate coefficient, m s -1 kg gas phase mass transport rate coefficient, m s -~ km liquid phase mass transport rate coefficient, m s L M molar mass, kg kg-mol- N mole fraction n molar flux, kg-mol m -z s -~ P vapor pressure, pascal P ~ vapor pressure of pure species, pascal R gas constant, J kg-mol -I K -~ r,. melt radius, m T melt temperature, K V melt volume, m 3 v0 temperature independent factor relating v to T and

(A/V), m 3n K -2 s -1

vm melt surface velocity, m s -~

A C K N O W L E D G M E N T S

The author wishes to thank Anaconda Minerals of Tucson, AZ, for their support of the present study. D. Danovitch's labor toward his master's dissertation, as well as support for that work from the Noranda Research Centre, Pointe Claire, Quebec, are also gratefully acknowledged.

REFERENCES

1. O. Winkler and R. Bakish: Vacuum Metallurgy, Elsevier, NY, 1974, ch. 1.

2. R. Ohno: Metall. Trans. B, 1976, vol. 7B, pp. 647-53. 3. R. Harris and W.G. Davenport: Can. Met. Q., 1979, vol. 18,

pp. 303-11. 4. D. Danovitch: M. Eng. Thesis, McGill University, Montreal, 1982. 5. E. Ozberk and R. I.L. Guthrie: Proc. 6th International Vacuum

Metallurgy Conference, G.K. Blatt and R. Schlatter, eds., San

METALLURGICAL TRANSACTIONS B

Diego, CA, April 1979, American Vacuum Society, New York, NY, pp. 248-67.

6. R.G. Ward: JISI, 1963, vol. 201, pp. 11-15. 7. R. Ohno: Liquid Metals Chemistry and Physics, S.Z. Beer, ed.,

Marcel Decker, New York, NY, 1972, pp. 38-79. 8. a, b. F.D. Richardson: Physical Chemistry of Melts in Metallurgy,

Academic Press, London, 1974, vols. 1 and 2, a: pp. 483-87; b: pp. 1-14.

9. M. Olette: Physical Chemistry of Process Metallurgy, Part 2, G. R. St-Pierre, ed., Interscience, New York, NY, 1961, pp. 1065-87.

10. D.C. Lynch: Metall. Trans. B, 1980, vol. I1B, pp. 623-29. 11. R. Harris: Ph.D. Thesis, McGill University, Montreal, 1980. 12. O. Knacke and I. N. Stranski: Progress in Metal Physics, B. Chalmers

and R. King, eds., Pergamon, New York, NY, 1956, pp. 181-233. 13. I. Langmuir: J. Am. Chem. Soc., a: 1914, vol. 36, p. 1708; b: 1915,

vol. 37, p. 415; c: 1916, vol. 38, pp. 1145-15. 14. M. Knudsen: Ann. Physic., Folge 2, a: vol. 31, p. 205; b: vol. 32,

p. 890; c: vol. 33, p. 14; d: vol. 34, p. 1910. 15. E.S. Machlin: Trans. TMS-AIME, 1960, vol. 218, pp. 314-26. 16. W.G. Davenport, A. V. Bradshaw, and E D. Richardson: JISI, 1967,

vol. 25, p. 1034. 17. J. Szekely, C. W. Chang, and W. E. Johnson: Metall. Trans. B, 1977,

vol. 8B, pp. 514-17. 18. T. R. A. Davey: J. Metals, 1953, vol. 197, pp. 991-96. 19. T.R.A. Davey: Vacuum, 1962, vol. 12, pp. 83-95. 20. T. R. A. Davey: Vacuum, 1964, vol. 14, pp. 227-30. 21. R. Harris and W. G. Davenport: Metall. Trans. B, a: 1982, vol. 13B,

pp. 581-88; b: 1982, vol. 13B, pp. 589-91. 22. H. Kametani and C. Yamauchi: Trans. JIM, 1972, vol. 13, pp. 13-20. 23. R. Bryan, D. M. Pollard, and G. M. Willis: Australia-Japan Extrac-

tive Metallurgy Syrup., Australasian Inst. Min. Met., Parkville, Vic., 1980, pp. 439-48.

24. R. Ohno: Trans. JIM, 1977, vol. 18, pp. 232-38. 25. L. Komorova: l-lutnicke Listy, 1973, vol. 8, pp. 577-82 (translation:

BISI 12425, The Metals Society, London, UK). 26. F.N. Streltsov, E.G. Trankovski, and O.D. Moldaviskii: Tsvetyne

Metally (Non-Ferrous Metals), August 1973, vol. 8, pp. 40-43. 27. M. Kameda and A. Yasawa: Tohoku Diagaku Senko Seiren Kenkyusho

lho, 1963, vol. 19, pp. 57-68. 28. H. Salomon de Friedburg and W. G. Davenport: Met. Soc. CIM, Ann.

Vol., 1977, pp. 225-31. 29. V.V. Golovko and R.A. Isakova: Trans. Inst. Met. i Obogashch.

Akad. Nauk Kaz. SSR, 1965, vol. 13, pp. 32-37. 30. G.V. Kim and A. N. Kvyatkovskii: Tr. Altaisk Gorno-Met. Nauchn-

Issled Inst., Akad. Nauk. Kaz. SSR, 1963, vol. 14, pp. 86-89. 31. T. Azakami and A. Yasawa: Can. Met. Q., 1976, vol. 15, pp. 111-21. 32. S. Arac and G.H. Geiger: Metall. Trans. B, 1981, vol. 12B,

pp. 569-78. 33. G .K. Sigworth and J.F. Elliot: Can. Met. Q., 1974, vol. 13,

pp. 455-61. 34. O. Kubashewski and C.B. Alcock: Metallurgical Thermochemistry,

5th edition, Pergamon, Oxford, 1979, pp. 358-77. 35. R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, and K. K. Kelly:

Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, OH, 1973, pp. 247-52.

36. R. Harris, R. McClincy, and E.F. Rebling: Paper Selection No. A83-19, 1983, TMS-AIME, Warrendale, PA, pp. 1-7.

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