A new formalism for representation of binary thermodynamic data
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T h e e q u a t i o n s a r e used in i n t e r p r e t i n g e x p e r i m e n t a l data f o r s e v e r a l r e l a t i v e l y w e a k l y i n t e r a c t i n g b i n a r y s y s t e m s . F o r the p u r p o s e of c o m p a r i s o n , a c t i v i t y c o e f f i c i e n t s o b t a i n e d by the s u b r e g u l a r m o d e l and K r u p k o w s k i ' s f o r m a l i s m have a l s o b e e n c o m p u t e d . The p r e s e n t e q u a t i o n s m a y b e c o n s i d e r e d to be c o n v e n i e n t in d e s c r i b i n g the t h e r m o d y n a m i c b e h a v i o r of m e t a l l i c s o l u t i o n s .
V A R I O U S a n a l y t i c a l e q u a t i o n s have b e e n p r o p o s e d to e x p r e s s a c t i v i t y c o e f f i c i e n t s a s f u n c t i o n s of c o m p o s i t i o n f o r l i q u i d a l l o y s . S i n c e e x t r a p o l a t i o n s of a c t i v i t y c o e f f i c i e n t s with r e s p e c t to c o m p o s i t i o n a r e s o m e t i m e s m e t with d i f f i c u l t i e s b e c a u s e of l a c k of e n o u g h d a t a , the e q u a t i o n s a r e of i m p o r t a n c e in a n a l y z i n g the t h e r m o d y n a m i c b e h a v i o r of m e t a l l i c solutions.
In~'2 = w ( T ) ( 1 - x l ) rn - - m - 1 (1 - x l ) m - I
+
and h e n c e A F x s is r e p r e s e n t e d as: AFXS
T H E O R E T I C A L CONSIDERATIONS AND F O R M A L I S M S
METALLURGICAL
TRANSACTIONS B
[4]
THE P R E S E N T E Q U A T I O N
AFXS
xl(1 - x~) = a ° f ( x )
[51
T h e l a t t e r f u n c t i o n is f r e q u e n t l y e x p r e s s e d in the f o r m of a p o l y n o m i a l c o n s i s t i n g of c o m p o s i t i o n a l t e r m s and c o r r e s p o n d i n g c o e f f i c i e n t s w h i c h a r e i m p o r t a n t in d e s c r i b i n g the t h e r m o d y n a m i c b e h a v i o r of s o l u t i o n s . T h e p o l y n o m i a l in the p r e s e n t investigation is c o n s i d e r e d to be a n e x p o n e n t i a l f u n c t i o n of c o m p o s i t i o n xx. H e n c e A F x s m a y b e e x p r e s s e d a s :
w h e r e a~ = R T l n y f ; az = R T ( i n ]/° - In y o ) and xx tool f r a c t i o n of c o m p o n e n t 1 . T h e o t h e r e q u a t i o n involving two p a r a m e t e r s h a s been p r o p o s e d by K r u p k o w s k i .3 He has e m p l o y e d the following e q u a t i o n s for a c t i v i t y c o e f f i c i e n t s f o r c o m p o n e n t s 1 and 2: [2]
J . P . HAJRA is Lecturer, Department of Metallurgy, Indian Institute of Science, Bangalore - 560 012, India. Manuscript submitted April 30, 1979.
(1--xx)[(1--x,) m - x - l ]
T h e p r e s e n t s t u d y i n v e s t i g a t e s the f o r m of the f u n c tion f ( x ) i n E q . [5], r e s p o n s i b l e f o r the a s y m m e t r i c b e h a v i o r of the e x c e s s i n t e g r a l f r e e e n e r g i e s of mixing f o r v a r i o u s b i n a r y s o l u t i o n s :
[1]
In ~'x : w ( T ) ( 1 - x l ) m
w(T)
A s y m m e t r y is due to a p a r a m e t e r rn in Eq. [4]. D a r k e n4 h a s s h o w n that for c
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