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I H E n e c e s s i t y t o be a b l e t o d e s c r i b e t h e t h e r m o d y n a m i c properties of multicomponent alloy s y s t e m s u s i n g a m i n i m u m a m o u n t o f e x p e r i m e n t a l d a t a i s well k n o w n . S e v e r a l b i n a r y s o l u t i o n m o d e l s~-s h a v e b e e n proposed and have s h o w n v a r i e d amounts of success when u s e d t o calculate t e r n a r y solution c h a r a c t e r istics. In o r d e r t o p r e d i c t t h e t e r n a r y h e a t s o f m i x i n g , t h e b i n a r y h e a t s m u s t be d e s c r i b e d by s u i t a b l e e q u a t i o n s . T h e equations d e s c r i b i n g b i n a r y h e a t s of m i x i n g can be d i v i d e d into t w o b r o a d c a t e g o r i e s : t h o s e w h i c h a r e d e s i g n e d t o deal solely with t h e d i l u t e solution r e g i o n a n d t h o s e w h i c h d e s c r i b e t h e h e a t of f o r m a t i o n o v e r l a r g e c o m p o s i t i o n a l r a n g e s . T h i s p a p e r w i l l be c o n c e r n e d only w i t h t h e l a t t e r c a t e g o r y . S i n c e i t i s d e s i r a b l e t o find an equation with a finite n u m b e r of t e r m s t o apply t o most b i n a r y l i q u i d and s o l i d metallic s o l u t i o n s , ; t h o s e m o d e l s b a s e d o n s e r i e s e x p a n s i o n s will also b e excluded. T h e m o d e l s in t h e l a t t e r c a t e g o r y a r e b a s e d p r i m a r i l y upon a bonding e n e r g y analysis. T h e s e m o d e l s are as follows: 1) H i l d e b r a n d ' s r e g u l a r s o l u t i o n m o d e l~ (&H M = a X A X B ), 2) H a r d y ' s s u b r e g u l a r m o d e le ( A H M = o Q X ~ XB + o~2XAX~), 3) G u g g e n h e i m ' s 3 a n d R u s h b r o o k e ' s 4 q u a s i - c h e m i c a l m o d e l ( A n = a X A X B [1 - 2 O t X A X B / ( z R T ) ] , a n d 4) D a r k e n ' s m o d e l5 t o d e s c r i b e t h e e x c e s s f r e e e n e r g y of m i x i n g o v e r t h e c o m p o s i t i o n a l r a n g e w h e r e t h e e x c e s s s t a b i l i t y f u n c t i o n is c o n s t a n t r e g i o n = R T X B I n 7 B -- a x e ) . I n t h e s e e q u a t i o n s , A H M is t h e h e a t o f m i x i n g in c a l o r i e s p e r m o l e of s o l u t i o n , A F X s i s t h e d i f f e r e n c e b e t w e e n t h e a c t u a l a n d i d e a l f r e e e n e r g y of m i x i n g , e , al, and a2 a r e constants, X A and X B a r e t h e mole f r a c t i o n s of c o m p o n e n t s A a n d B , r e s p e c t i v e l y , z i s t h e c o o r d i n a t i o n n u m b e r o f t h e c r y s t a l s t r u c t u r e of t h e s o l i d s o l u t i o n ( o r t h e a v e r a g e n u m b e r of n e a r e s t neighbors for l i q u i d solutions), R i s the g a s constant,

T i s t h e a b s o l u t e t e m p e r a t u r e , a n d 7~ i s t h e a c t i v i t y c o e f f i c i e n t of c o m p o n e n t i i n t h e H e n r i a n L a w r e g i o n f o r c o m p o n e n t i. T h e r e g u l a r solution m o d e l h o l d s for only a s m a l l n u m b e r of b i n a r y meta