Thermodynamics of stacking faults

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The Gibbs t r e a t m e n t of i n t e r f a c i a l f r e e e n e r g y is r e v i e w e d and a p p l i e d to t h e s p e c i f i c c a s e of s t a c k i n g f a u l t s in a l l o y s . The a l t e r n a t i v e m o d e l of v i e w i n g the fault r e g i o n a s a s e c o n d p h a s e i s b r i e f l y r e v i e w e d . P r i o r t r e a t m e n t s of the topic u s i n g the l a t t e r a p p r o a c h a r e shown to have l e d to t h e r m o d y n a m i c i n c o n s i s t e n c i e s in s o m e c a s e s . The r e l a t i o n b e t w e e n s t a c k i n g fault e n e r g y and e q u i l i b r i u m s e p a r a t i o n of p a r t i a l d i s l o c a t i o n s is e s t a b l i s h e d . The s t r e s s r e q u i r e d to m o v e p a r t i a l d i s l o c a t i o n s o r p e r f e c t d i s l o c a t i o n s in a l l o y s is d e v e l o p e d on the b a s i s of a v i r t u a l displacement from equilibrium approach. h n u m b e r of a u t h o r s x-n h a v e c o n s i d e r e d the t h e r m o d y n a m i c s of s t a c k i n g f a u l t s , with i n t e r e s t c e n t e r i n g about the a d s o r p t i o n of s o l u t e a t o m s to f a u l t s , the s o c a l l e d Suzuki s e g r e g a t i o n . H o w e v e r , a s shown in l a t e r s e c t i o n s , m a n y of t h e s e t r e a t m e n t s contain q u e s t i o n a b l e t h e r m o d y n a m i c a s s u m p t i o n s . The c o r r e c t t r e a t m e n t of the s p e c i f i c i n t e r f a c i a l f r e e e n e r g y of the s t a c k i n g fault is i n h e r e n t in the o r i g i n a l w o r k of G i b b s . ta Indeed, t h e s t a c k i n g fault is s i m p l y a s p e c i f i c e x a m p l e of the g e n e r a l s u r f a c e d i s c u s s e d by G i b b s . A c c o r d i n g l y , we f i r s t r e v i e w G i b b s ' t r e a t m e n t of i n t e r f a c i a l f r e e e n e r g y o r , f o r b r e v i t y , s u r f a c e e n e r g y . T h i s a p p r o a c h i s then a p p l i e d s p e c i f i c a l l y to s t a c k i n g f a u l t s . The v a r i o u s o t h e r t r e a t m e n t s of the s u b j e c t a r e then c o n s i d e r e d and c o m p a r e d to the p r e s ent r e s u l t s . The n e x t s e c t i o n of the p a p e r i n v o l v e s m e t h o d s f o r e s t i m a t i n g s t a c k i n g fault e n e r g i e s in t e r m s of t h e r m o d y n a m i c q u a n t i t i e s . The p o s s i b i l i t y of v a c a n c i e s a c t i n g a s a Suzuki a d s o r b a t e is d i s c u s s e d . F i n a l l y , we c o n s i d e r the influence of s t a c k i n g fault e n e r g y on d i s l o c a tion m o t i o n i n s o f a r a s it r e l a t e s to v i r t u a l d i s p l a c e ments from thermodynamic equilibrium. A) A P P L I C A T I O N O F GIBBS' T R E A T M E N T We t r e a t ~,, the s t a c k i n g fault e n e r g y , a s a s p e c i f i c c a s e of a Gibbs i n t e r f a c e . B e c a u s e ~, is e x t r e m e l y a n i s o t r o p i c with r e s p e c t to o r i e n t a t i o n of the s u r f a c e in a c r y s t a l , e s s e n t i

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