A thermodynamic analysis of the copper-lead-sulfur system at 1473 K
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Cu-S The value of Y~(Cu) = 3.97 (~0.4) x 10-3 is from Sigworth and Elliott6 while those of x.~(Cu~ = 0.0226 4- 0.001 and ~S(cu) = - 1 4 +2 are frOm'Kellogg.7 The term r°S(Cu) is the limiting activity coefficient of sulfur in liquid copper; x~(Cu) is the atom fraction of sulfur at saturation; and ES(cu) = (8 In ~s/aXS) is the Gibbs energy self-interaction parameter of sulfur in liquid copper. The superscript (*) designates the value at the metal-rich boundary and is adopted in the present s t u d y . Employing these values of ~ ( C u ) , X~(Cu) and ¢~(Cu), the values of acu, a s and Ps~ at X~fCu) are found t o be 0.981 + 0.002, 6.53 x 10-° and 9.37 (±1.5) x 10-7 atm, respectively. The standard states are Cu(l) and S(I). The change of standard states for sulfur from 1//2 S2(g) t o S(I) is made u s i n g the data from JANAF.8 From Kellogg, 7 the equilibrium constant, Kcusl/2, for the following reaction Cu(/) + 1/4 S2(g) = CuS~n(/)
[I]
is found to be 32.3 and the values of acu, as and ps2 at the stoichiometric composition CueS are 0.437 ± 0.02, 3.36 x I0-4 and 2.53 (~2) x 10-5 atm, respectively.
Pb-S The phase relations and thermodynamic properties of the lead-sulfur system are not well established. From DTA experiments, Miller and Komarek9 suggested a flat liquidus around 1330 K whereas KullerudI° postulated a monotectic reaction. Kullerud's suggested phase diagram for the Pb-S system shows a miscibility gap in the concentration range, 0.25 < x s < 0.32 at 1473 K. On the other hand, vapor pressure measurements of Yazawa, e t al, ~ over the Pb-PbS solutions in the temperature range 1333 to 1473 K do not suggest the existence of a miscibility gap. For the present analysis, lead and lead sulfide are taken to be completely miscible in the liquid state at 1473 K. Schuhmann, e t al,~2 have recently reviewedthe thermodynamic properties of the Pb-S system and have shown that the lab-labS solution thermodynamics conforms to regular behavior. From their recommended Gibbs energy of formation of PbS(1) according to the following reaction Pb(/) + 1//2 Se(g) = PbS(/)
[2]
the equilibrium constant, Kpbs, is found t o be 23.3. VOLUME 8B, DECEMBER 1977-541
and Jeffes, the computed values of In "YS(Cu-Pb) o should be reasonable. Furthermore, the Gibbs energy interCu 0 In YS~ action parameter, ES(Pb) , defined as ~ / xpb ~ 1 ' 0
.3
XCu
XS
0.8
0.2
/Q9 Cu
QI
OI
02
0.3
0.4
0,5 Xpb
06
07
Q8
09
may be calculated from Eq. [3] as - 5.8. This value compares favorably with the value o f - 7 extrapolated from the equation suggested by Grant and Russell for t h e i r experimental temperature r a n g e , 873 to 1173 K.
Pb
THERMODYNAMIC CALCULATIONS AND DISCUSSION
F i g . 1--Experimental tie-line distributions along the t e r n a r y miscibility gap of the C u - P b - S s y s t e m at 1473 K.
The individual activities of lead and sulfur r e f e r r e d to the Raoultian standard states at the stoichiometric composition of PbS(l) are not known. Experimental values for the limiting activity coefficient of sulfur in lead at hig
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