The activity coefficient of nonmetallic solutes in ternary and higher order liquid alloys
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cording to Eq. [1] a r e :
x X ( A a B b . . . j j K ~ L l ) CC[a!b ! Z !
...j!k!l! ]
. i x AaXBb . . " "d~Jxk x lL ~ " e x p [ - ( A H x / R T ) ]
D. C. HU AND Y. A. CHANG The t h e r m o d y n a m i c s of n o n m e t a l l i c s o l u t e s such as oxygen and n i t r o g e n in b i n a r y liquid alloys has b e e n the s u b j e c t of e x t e n s i v e t h e o r e t i c a l and e x p e r i m e n t a l investigations.l-24 One of the t h e o r e t i c a l models p r o posed by W a g n e r 9 c o n s i s t s of one p a r a m e t e r . This model is able to d e s c r i b e the c o m p o s i t i o n a l v a r i a t i o n of the a c t i v i t y coefficients of oxygen and n i t r o g e n in dilute b i n a r y liquid a l l o y s . %1~ However, the value of the p a r a m e t e r for any b i n a r y alloy s y s t e m m u s t be obtained f r o m e x p e r i m e n t a l data in the p a r t i c u l a r alloy s y s t e m . Chiang and Chang 1~ p r o p o s e d a s e m i e m p i r i c a l c o r r e l a t i o n which allows one to p r e d i c t the v a l u e of this p a r a m e t e r for any b i n a r y alloy s y s t e m without knowing the a c t i v i t y coefficient of the n o n m e t a l l i c solute in this alloy s y s t e m . Based on this c o r r e lation, Chang and Hu 2~ had p r e d i c t e d v a l u e s of the i n t e r a c t i o n p a r a m e t e r s of oxygen and n i t r o g e n in a l a r g e n u m b e r of liquid a l l o y s . The p r e d i c t e d v a l u e s a r e g e n e r a l l y in good a g r e e m e n t with the l i t e r a t u r e data when they a r e a v a i l a b l e . Since a l l o y s of t e c h n o l o g i c a l i m p o r t a n c e u s u a l l y c o n s i s t of t h r e e and m o r e m e t a l l i c c o m p o n e n t s , it is d e s i r a b l e to p r e d i c t the activity coefficient of a solute in m u l t i c o m p o n e n t alloy s y s t e m s knowing that in the r e s p e c t i v e m e t a l c o m p o n e n t s . The W a g n e r m o d e l was extended to t e r n a r y liquid a l l o y s by Kapoor ~6 and Schwerdfeger and p i t s c h S The obj e c t i v e s of the p r e s e n t p a p e r a r e 1) to extend this model to q u a t e r n a r y and higher o r d e r alloy s y s t e m s and 2) to t e s t the v a l i d i t y of the t h e o r e t i c a l equations for m u l t i c o m p o n e n t a l l o y s using data a v a i l a b l e in the l i t e r a t u r e . T h e o r e t i c a l D e r i v a t i o n . The d e r i v a t i o n as given below follows the a p p r o a c h of W a g n e r for b i n a r y liquid a l l o y s with an a d d i t i o n a l a s s u m p t i o n that t e r n a r y and h i g h e r o r d e r i n t e r a c t i o n s in m u l t i c o m p o n e n t alloys are unimportant. The s o l u b i l i t y of a d i a t o m i c gas, Xe, in a m u l t i c o m ponent liquid alloy may be r e p r e s e n t e d by the following r e a c t i o n :
9 t~X2"1/2
[2]
where x X , XA, XB 9 9 9 a r e the atom f r a c t i o n s of X , A , B . . . , AHX is the enthalpy of d i s s o l u t i o n , R is the gas constan
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