Thermodynamic behavior in binary metallic solutions
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l-X1)
rn
m -m 1 ( 1 -
Xl) ~-~ + m-
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 is shown for s e v e r a l b i n a r y s y s t e m s . Both dilute and c o n c e n t r a t e d s o l u t i o n s a r e c o n s i d e r e d . In dilute solutions ( H e n r y ' s law r e g i o n ) t h e s e equations ex c lu d e constant v a l u e s of the a c t i v i t y c o e f f i c i e n t s . T h e s e f o r m u l a e with m > 1 s a t i s f y R ao u l t s law and H e n r y ' s law as l i m i t i n g c a s e s . However, e x p e r i m e n t a l data i n d i 0 cate that only in two s y s t e m s , n a m e l y Zn-Sn and Z n - B i , YZn = YZn o v e r a finite c o m p o s i tion r a n g e . When rn is c l o s e to unity, as is the c a s e for the Zn-Sn and Z n - B i s y s t e m s R a o u l t ' s law is not s a t i s f i e d until Xzn is i n f i n i t e s i m a l l y c l o s e to unity. Data for c o n c e n t r a t e d zinc s o l u t i o n s for both s y s t e m s s u p p o r t this conclusion. A c o m p a r i s o n of K r u p k o w s k i ' s m e t h o d with D a r k e n ' s q u a d r a t i c f o r m a l i s m was also c a r r i e d out, and it was shown that both m e t h o d s give s i m i l a r r e s u l t s when m = 2.
ANALYTICAL
equations of the f o r m log Yi = f ( T , X ) a r e e m p l o y e d for r e p r e s e n t i n g t e m p e r a t u r e - c o m p o s i t i o n d e p e n d e n c e of 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 b i n a r y m e t a l l i c s o l u t i o n s . The u s e of t h e s e r e l a t i o n s in e x t r a p ol a ti ng to infinite dilution and in a p p l ic a t io n of b i n a r y data to the a n a l y s i s of m u l t i c o m p o n e n t s y s t e m s r a i s e s the q u e s t i o n of the p r o p e r r a n g e of t h e i r applicability. Two such f o r m a l i s m a r e e x a m i n e d in this p a p e r , n a m e l y D a r k e n ' s ~ q u a d r a t i c f o r m a l i s m and K r u p k o w s k i ' s 2 f o r malism. DARKEN'S
QUADRATIC
FORMALISM
D a r k e n ~ has shown that for m a n y b i n a r y s y s t e m s a plot of log y1 v s (1 - Xt) 2 l e a d s to t h r e e d i s t i n c t r e g i o n s , two t e r m i n a l r e g i o n s in which a l i n e a r r e l a t i o n e x i s t s and an i n t e r m e d i a t e r e g i o n which is difficult to r e p r e s e n t by any s i m p l e p o l y n o m i a l r e l a t i o n . F o r each of the t e r m i n a l r e g i o n s D a r k e n e m p l o y s the r e l a t i o n s : Y2
log ~
2
= ~ 1 2 ( X , - 1)
[1]
Y2
[2]
log vl : ~ , x ~ ~12-
2.303RT
2.303 R
where the subscript 1 denotes solvent and 2 solute, ~ is the activity coefficient and No its value at infinite dilution, X is the molar fraction, ~ ~2 and 5~2 are the parameters of heat and entropy, respectively and are determined from the temperature dependence of ~2. KRUPKOWSKI'S FORMALISM Krupkowski 2 has e m p l o y e d for b i n a r y s o lu ti o n s the following f o r m u l a e : Z. MOSER is Associate Professor at Institute for Metal Research, Polish Academy of Sciences, Chairma
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