Configurational entropy and solute correlation in disordered alloys
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which s e t s the e x c e s s e n t r o p y p r o p o r t i o n a l to the m e a n v a l u e of the l o g a r i t h m of the i n t e n s i t y . A s an e x a m p l e of a p p l i c a t i o n , a c o n c i s e a n a l y s i s for p a i r c o r r e l a t i o n s and t h e r m o d y n a m i c p r o p e r t i e s at e q u i l i b r i u m i s c a r r i e d out. The r e s u l t c o i n c i d e s with the s p h e r i c a l m o d e l for a l l o y s , a v a r i a n t of the Ising m o d e l r e s e m b l i n g the G a u s s i a n m o d e l of Clapp and M o s s but far e x c e e d i n g it in a c c u r a c y . In t h i s m a n n e r the m e r i t of the p r o p o s e d e n t r o p y formulation is established, T H E c o n c e r n of the p r e s e n t i n v e s t i g a t i o n is with the t h e r m o d y n a m i c s of d i s o r d e r e d b i n a r y a l l o y c r y s t a l s a s a f f e c t e d by d e v i a t i o n s of the s o l u t e d i s t r i b u t i o n f r o m r a n d o m n e s s . The W a r r e n - C o w l e y s h o r t - r a n g e o r d e r c o e f f i c i e n t s 1 p r o v i d e a way of c h a r a c t e r i z i n g the s t a t i s t i c a l a r r a n g e m e n t of s o l u t e in such a m a t e r i a l . A p r i n c i p l e a t t r i b u t e of the s h o r t - r a n g e o r d e r c o e f f i c i e n t s is the d i r e c t r e l a t i o n between t h e i r F o u r i e r t r a n s f o r m and the diffuse i n t e n s i t y of X - r a y s o r t h e r m a l n e u t r o n s s c a t t e r e d by an a l l o y c r y s t a l . With the s h o r t - r a n g e o r d e r c o e f f i c i e n t s one can a l s o f o r m u l a t e the d e p e n d e n c e of a l l o y p r o p e r t i e s such a s the e n e r g y of m i x i n g 2'3 upon the s t a t e of a g g r e g a t i o n of the s o l u t e . L i k e w i s e C o w l e y h a s u s e d the s h o r t r a n g e o r d e r c o e f f i c i e n t s to f o r m u l a t e the c o n f i g u r a tional e n t r o p y of m i x i n g . 1'2 By s u i t a b l e m a n i p u l a t i o n the e x p r e s s i o n for the e n e r g y of m i x i n g can be c o n v e r t e d to an e q u i v a l e n t f o r m e m p l o y i n g the diffuse i n t e n s i t y in p l a c e of the s h o r t - r a n g e o r d e r c o e f f i c i e n t s . C e r t a i n p r a c t i c a l and conceptual a d v a n t a g e s a c c r u e by t h i s p r o c e d u r e , including the fact that the e l a s t i c f r e e e n e r g y , a r i s i n g when the component a t o m s d i f f e r in s i z e , i s r e a d i l y e x p r e s s e d in t e r m s of the s a m e i n t e n s i t y function. 4 The a i m of the p r e s e n t i n v e s t i g a t i o n i s to show that a d v a n t a g e i s a l s o gained by u t i l i z i n g the i n t e n s i t y to f o r m u l a t e the c o n f i g u r a t i o n a l e n t r o p y of m i x i n g . U s i n g C o w l e y ' s r e s u l t a s a guide, we p r o p o s e a m o r e c o m p a c t function in t e r m s of the diffuse i n t e n s i t y . The m e r i t of the p r o p o s e d e n t r o p y
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