Thermodynamics of binary metallic solutions: Application of the wilson equation
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c l e a r as to how f a r each of the t e r m i n a l r e g i o n s should be e x t e n d e d t o w a r d the c e n t e r of the d i a g r a m . 2) F o u r p a r a m e t e r s m u s t be e v a l u a t e d to d e t e r m i n e the a c t i v i t y c o e f f i c i e n t s of both c o m p o n e n t s in the t e r m i n a l r e g i o n s ; t h e s e p a r a m e t e r s a r e a12 , a21, and two integration constants. 3) A u s e f u l m a t h e m a t i c a l d e s c r i p t i o n of the t h e r m o d y n a m i c s of both c o m p o n e n t s o v e r the e n t i r e c o m p o s i tion r a n g e is not a c h i e v e d . The c e n t r a l o r t r a n s i t i o n r e g i o n is f o r a l l p r a c t i c a l p u r p o s e s undefined m a t h e matically. P r o b l e m s 1) and 3) a r e not i n h e r e n t in the Wilson equation and only two a r b i t r a r y c o n s t a n t s a r e r e q u i r e d to m a t h e m a t i c a l l y d e s c r i b e a b i n a r y s y s t e m o v e r its e n t i r e c o m p o s i t i o n r a n g e ; no new, e q u a l l y s e r i o u s p r o b l e m s a r e i n t r o d u c e d by the W i l s o n equation. A m o d i f i e d f o r m of the Wilson e q u a t i o n has been g i v e n by O r y e and P r a u s n i t z 5 as R T - - ~ X i In i=x
j=l
XjA i
[1]
w h e r e G E is the e x c e s s m o l a r Gibbs f r e e e n e r g y of the solution, X is the a t o m f r a c t i o n of a component, and A i j is a p o s i t i v e a d j u s t a b l e p a r a m e t e r (Aii = A j j = 1). It can be shown that f o r a b i n a r y s o l u t i o n Inyl=-ln(X'+A'aXa)+Xaix,+-~laX
z
Aa, X, + XaJ
[2a] lnr2=-ln(X~+&lX0
Thermodynamics of Binary Metallic Solutions: Application of the Wilson Equation S. K. TARBY
AND
F. P. STEIN
N U M E R O U S
t h e o r i e s and e m p i r i c a l s u g g e s t i o n s h a v e b e e n p r o p o s e d to c o r r e l a t e e x p e r i m e n t a l t h e r m o d y n a m i c data of b i n a r y s o l u t i o n s . The m o s t r e c e n t d e v e l o p m e n t of a f o r m a l i s m f o r b i n a r y m e t a l l i c s o l u t i o n s h a s b e e n made by D a r k e n and c o w o r k e r s . 1-s Although Darken's quadratic formalism correlates experimental d a t a r e a s o n a b l y well, it does have s o m e d e f i c i e n c i e s . The p o s s i b i l i t y of the e x i s t e n c e of a n o t h e r f o r m a l i s m s u i t a b l e f o r e x p r e s s i n g the t h e r m o d y n a m i c s of b i n a r y m e t a l l i c solutions should not be o v e r l o o k e d . This c o m m u n i c a t i o n c o n s i d e r s the a p p l i c a t i o n of a f o r m a l i s m p r o p o s e d by Wilson 4 to m e t a l l i c s y s t e m s . B e f o r e c o n s i d e r i n g the Wilson equation, a few b r i e f c o m m e n t s about the q u a d r a t i c f o r m a l i s m a r e o f f e r e d . We b e l i e v e that the f o ll o w in g i t e m s d e t r a c t f r o m the quadratic formalism: 1) If t h e r e is s i g n i f i c a n t s c a t t e r in the data u s e d to c o n s t r u c t a g rap h of log r i v s
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