Grain boundary segregation, two dimensional compound formation, and precipitation
- PDF / 2,069,752 Bytes
- 19 Pages / 612 x 792 pts (letter) Page_size
- 86 Downloads / 220 Views
MICHELGUTTMANNis MaRrede Recherches,Centre des Mat6naux de l'Ecoledes Minesde Pans, 91003 EvryCedex, France. This paper is based on a presentahon made at a symposiumon "Fundamentals of Gram Boundary SegregaUon"held at the NiagaraFallsMeetingof The MetallurgicalSocietyof AIME,September21, t976, under the sponsorship of the Physical MetallurgyCommittee. METALLURGICAL TRANSACTIONSA
I - T H E GRAIN BOUNDARY AS A 2D SOLID SOLUTION In M c L e a n ' s w e l l known o r i g i n a l t r e a t m e n t of i n t e r g r a n u l a r s e g r e g a t i o n , 1 the g r a i n b o u n d a r y is r e p r e s e n t e d as a zone of the m a t e r i a l w h e r e the m e r e e l a s t i c d i s t o r t i o n of s o m e a t o m i c s i t e s m a k e s t h e m m o r e f a v o r a b l e to s o l u t e a t o m s than the c r y s t a l i n t e r i o r due to the s i z e d i f f e r e n c e b e t w e e n s o l u t e I and s o l v e n t A a t o m s . T h e r e f o r e the e l a s t i c e n e r g y r e l e a s e ZxQ a r o u n d an I a t o m when l e a v i n g a bulk (B) s i t e f o r a f a v o r a b l e g r a i n b o u n d a r y s i t e is the e s s e n t i a l r e a s o n why a l a r g e r p r o p o r t i o n (0) of the l a t t e r than of the f o r m e r (X/B) is o c c u p i e d by I: 0
xB
AQ
&V
(The v a r i a t i o n of a t o m i c i n t e r n a l ( v i b r a t i o n a l and so forth) e n t r o p y can be a c c o u n t e d f o r by r e p l a c i n g AQ by AGO = A Q - TAS ~ in Eq. [1]). The d e c r e a s e in t o t a l i n t e r n a l e n e r g y due to ZxQ b e ing c o m p e n s a t e d at e q u i l i b r i u m by the c o n f i g u r a t i o n a l e n t r o p y d e c r e a s e a s s o c i a t e d with this type of " o r d e r i n g " e x p e r i e n c e d by the e n t i r e s y s t e m , the t o t a l Gibbs f r e e e n e r g y is m i n i m i z e d when Eq. [1] is obeyed. In sp i t e of its f o r m a l identity with L a n g m u i r a d s o r p t i o n i s o t h e r m , which p e r t a i n s to the a d s o r p t i o n of g a s e s on f r e e s u r f a c e s , no h y p o t h e s i s r e f e r r i n g to the 2D n a t u r e of the b o u n d a r i e s has b e e n n e c e s s a r y to e s t a b l i s h Eq. [1]; r a t h e r , the i n t e r f a c e has b e e n d e s c r i b e d as a kind of p h a s e b e h a v i n g e s s e n t i a l l y l i k e a so l i d s o l u t i o n with a v e r y l a r g e s o l u b i l i t y f o r I. T h i s p h a s e - l i k e a s p e c t of g r a i n b o u n d a r i e s is c r i t i c a l to the p h y s i c a l u n d e r s t a n d i n g of t h e i r b e h a v i o r , but the f o r m a l i s m of s u r f a c e t h e r m o d y n a m i c s is a l s o r e l e v a n t to t h e m s i n c e it n a t u r a l l y i n t r o d u c e s and c a r r i e s along a n o t h e r e s s e n t i a l p r o p e r t y of g r a i n b o u n d a r i e s , i . e . , s u r f a c e tension, which is e s s e n t i a l l y of 2D c h a r a c t e r . T h e r e f o r e both a p p r o a c h e s have to be c o m b i n e d in o r d e r to obtain a c o n s i
Data Loading...
