A thermodynamic analysis of the copper-lead-sulfur system at 1473 K
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Cu-S The value of 7~(Cu) = 3.97 (:h0.4) • I0 -s is from Sigworth and Elliott6 while those of X~(Cu ) = 0.0226 S = - 1 4 + 2 are from Kellogg. 7 T h e * 0.001 and ~S(Cu)
t e r m Y0S(Cu) is the l i m i t i n g a c t i v i t y c o e f f i c i e n t of s u l f u r in liquid c o p p e r ; x~(Cu ) i s the a t o m f r a c t i o n of s u l f u r a t s a t u r a t i o n ; and cS(cu) = (0 In Vs/0Xs) i s the G i b b s e n e r g y s e l f - i n t e r a c t i o n p a r a m e t e r of s u l f u r in l i q u i d c o p p e r . T h e s u p e r s c r i p t (*) d e s i g n a t e s the v a l u e at t h e m e t a l - r i c h b o u n d a r y and is a d o p t e d in
s t a t e s a r e Cu(l) and S(I). T h e change of s t a n d a r d s t a t e s f o r s u l f u r f r o m 1/2 Se(g) to S(I) i s m a d e u s i n g the d a t a f r o m J A N A F . a F r o m K e l l o g g , 7 the e q u i l i b r i u m c o n s t a n t , K c u s ~ / z , for the following reaction Cu(/) + 1 / 4 S2(g) = CuS1/2(l)
[1]
is found to be 32.3 and the v a l u e s of a c u , a S and pS 2 at the s t o i c h i o m e t r i c c o m p o s i t i o n CueS a r e 0.437 • 0.02, 3.36 • 10 -4 and 2.53 (+2) • 10 -s arm, r e s p e c t i v e l y .
Pb-S The phase relations and thermodynamic properties of the lead-sulfur system are not well established. F r o m D T A experiments, Miller and K o m a r e k v suggested a flat liquidus around 1330 K whereas Kullerud I~ 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. O n the other hand, vapor pressure m e a s urements of Yazawa, et al, n over the P b - P b S 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, 12 h a v e r e c e n t l y r e v i e w e d the t h e r -
m o d y n a m i c p r o p e r t i e s of the P b - S s y s t e m and have shown t h a t the P b - P b S s o l u t i o n t h e r m o d y n a m i c s c o n f o r m s to r e g u l a r b e h a v i o r . F r o m t h e i r r e c o m m e n d e d G i b b s e n e r g y of f o r m a t i o n of PbS(I) a c c o r d i n g to the following reaction Pb(/) + 1/2 S2(g) : PbS(/)
[2]
the e q u i l i b r i u m c o n s t a n t , K p b s , i s found to b e 23.3. VOLUME 8B, DECEMBER 1 9 7 7 - 5 4 1
and J e f f e s , the c o m p u t e d v a l u e s of In TS(Cu-Pb) o should be r e a s o n a b l e . F u r t h e r m o r e , the Gibbs e n e r g y i n t e r Cu a In YS a c t i o n p a r a m e t e r , ~S(Pb), defined a s ~ / Xpb ~ 1' Xcu 08
[~
CU
m a y be c a l c u l a t e d f r o m Eq. [3] a s - 5.8. T h i s value c o m p a r e s f a v o r a b l y with the value o f - 7 e x t r a p o l a t e d f r o m the equation s u g g e s t e d by G r a n t and R u s s e l l f o r t h e i r e x p e r i m e n t a l t e m p e r a t u r e r a n g e , 873 to 1173 K.
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-V ~ 03
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05 Xp b
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