The effect of silver on the activity coefficient of zinc in dilute liquid ZnSn alloys at 803 K
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IN a r e c e n t p a p e r ,
Chang e t al. ~ have developed a method to a c c o u n t for any c o n c e n t r a t i o n d i f f e r e n c e s between the bulk and b u l k - v a p o r i n t e r f a c e of an alloy d u r i n g the c o u r s e of a t o r s i o n - e f f u s i o n e x p e r i m e n t . V a p o r i z a t i o n s t u d i e s of zinc f r o m dilute liquid ZnSn alloys showed the r e l i a b i l i t y of this method in o b t a i n ing activity data as a function of c o m p o s i t i o n . ~'2 The p u r p o s e of the p r e s e n t study is to e x a m i n e the effect of s i l v e r on the activity coefficient of zinc in dilute liquid ZnSn alloys at 530~ u s i n g this approach. The i n t e r a c t i o n between s i l v e r and zinc in liquid tin will be t r e a t e d u s i n g the Wagner i n t e r a c t i o n p a r a m e t e r and c o r r e l a t e d with solution m o d e l s . EXPERIMENTAL a) T h e o r e t i c a l Background D u r i n g the c o u r s e of a t o r s i o n - e f f u s i o n e x p e r i m e n t , the a m o u n t of the volatile solute in a n alloy such a s zinc in tin is c o n t i n u a l l y d e c r e a s i n g with t i m e . As shown p r e v i o u s l y , ~ the amount of solute r e m a i n i n g in the alloy at any time t is n i = n ~ ---~7-KdP~ (1 - e - K ' t )
[2]
ni/Mi -xi = n i / M i + n ~ g / M A g + n ~ / M s
w h e r e n s and M s a r e r e s p e c t i v e l y the i n i t i a l a m o u n t of the solvent in the alloy and the atomic weight of the s o l v e n t . F r o m Eqs. [1] and [2], xi can be calculated a s a function of t. Also Pi a s a function of t may be obtained f r o m the t o r s i o n - e f f u s i o n equation given below. [3]
P i = K2dp
T h e s e t h r e e equations allow the c a l c u l a t i o n of the t h e r m o d y n a m i c a c t i v i t y of solute as a function of ~/. However, in o r d e r to obtain p r e c i s e t h e r m o d y n a m i c p r o p e r t i e s , it is e s s e n t i a l to know the solute c o n c e n t r a t i o n at the b u l k - v a p o r i n t e r f a c e s i n c e the m e a s u r e d p a r t i a l p r e s s u r e is d e t e r m i n e d by the solute c o n c e n t r a t i o n at the i n t e r f a c e r a t h e r than that in the bulk. T h u s at any time t, the c o n c e n t r a t i o n d i s t r i b u t i o n of the volatile solute within the bulk m u s t be known. As shown p r e v i o u s l y , 1 the c o n c e n t r a t i o n d i s t r i b u t i o n is
[1] xi (t, 4) = 2 (exp - 5 2 ?iF) Xi m=l
with K -= /s163 KI = 44.331 (A~f~ + A 2 f 2 ) ( M i / T ) ~'2 in g / s - a t .
[la]
2~K2 = A1 q~ f , + A2 q2 f 2 in a t m / a n g l e of twist
[lb]
5m + Si--~-m-mCOS5m/
• cos (Sm~)
[4]
with 6m b e i n g the ruth root of
w h e r e n i is the n u m b e r of g r a m s of the volatile solute in the alloy at any time t (s), KI and K2 a r e r e s p e c tively the K n u d s e n and t o r s i o n - e f f u s i o n c o n s t a n t s , q~ is the angle of t w i s t e x p r e s s e d in d e g r e e , A~ and A2 a r e o r i f i c e a r e a s in c m 2, f~
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