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r a n g e m e n t of a t o m s , Sv is the v i b r a t i o n a l e n t r o p y , and S e l is the e l e c t r o n i c e n t r o p y . T h e n the s t a c k i n g fault e n e r g y 7 of Eq. [2] can be w r i t t e n in the form Y a = 5Ufe + 6Uc + 8 u i + 5uv -- T ( S S e l + 5Sv + 6So)

[5]

In this m o d e l we a s s u m e the t e m p e r a t u r e - d e p e n d e n t t e r m s b u y , T S S e l , a n d T 6 s v to be n e g l i g i b l e for noble m e t a l - n o r m a l m e t a l alloys. It would a p p e a r that this a s s u m p t i o n is not u n r e a s o n a b l e . In p u r e s i l v e r , for which 5u i and 5So a r e z e r o by d e f i n i t i o n , ), is found to be independent of t e m p e r a t u r e , l ' 4 i m p l y i n g that the above t e r m s a r e not i m p o r t a n t . [6]

Y s ~- 6Ufe + 6Uc + 6ui -- T 6 s o

I) STACKING F A U L T ENERGY IN NOBLE M E T A L ALLOYS

A) F r e e E l e c t r o n C o n t r i b u t i o n

We write the free e n e r g y Gs of the a phase (fcc or hcp) with no i n t e r n a l d e f e c t s as [1]

Gc~ = U s + P V s - T S ~

F o r an infinite c r y s t a l the c r e a t i o n of a single infinite fault using an i s o t h e r m a l , c o n s t a n t p r e s s u r e p r o c e s s y i e l d s a change in free e n e r g y 6G a. Then y is defined as the free e n e r g y change per unit a r e a of the fault [2]

V s = 5 g s = 6 u s + P S v a - TSsc~

F o r n o r m a l c l o s e - p a c k e d m e t a l s , where 5u c = 8u i = 0 c a l c u l a t i o n s ~ b a s e d on the f r e e e l e c t r o n theory give r e a s o n a b l e a g r e e m e n t with e x p e r i m e n t a l m e a s u r e m e n t s for both fcc and hcp p h a s e s . The m o d e l is b a s e d on a p a i r - w i s e i n t e r a c t i o n b e t w e e n two a t o m s u s i n g an a s y m p t o t i c form of the i n t e r a c t i o n e n e r g y . 6 F o r fcc m e t a l s the i n t r i n s i c s t a c k i n g fault e n e r g y , yi, i s given by a s u m m a t i o n over the c l o s e packed planes with s p a c i n g d Yi = 5Ufe = ~ [3n~o (3nd) - (3n - 1). ~0(3nd - d)]

[7]

n=l

where 8g, 5u, 5v, and 8s a r e the changes in f r e e e n e r g y , i n t e r n a l e n e r g y , v o l u m e , and e n t r o p y p e r unit fault a r e a , r e s p e c t i v e l y . In g e n e r a l , the P S v t e r m is s m a l l and can be neglected. F o r a g e n e r a l solid the cohesion can be a s s u m e d s e p a r a b l e into t h r e e t e r m s , c o m p r i s i n g of the f r e e e l e c t r o n , covalent, and ionic c o n t r i b u t i o n s to bonding. T h u s , for our p u r p o s e s h e r e then the i n t e r n a l e n e r g y at t e m p e r a t u r e T c a n be w r i t t e n in a l i n e a r f o r m [3]

U = U [ e + Uc + U i + U v

where Ufe is the free e l e c t r o n , U c the c o v a l e n t , U i the ionic, and U v the v i b r a t i o n a l c o n t r i b u t i o n s to the i n t e r n a l e n e r g y . In a s i m i l a r fashion the e n t r o p y is w r i t t e n as S =Sel +S v +So

[4]

where So is the c o n f i g u r a t i o