Influence of crystallography on aspects of solid-solid nucleation theory
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C. L. WHITE, K. C. RUSSELL,
P. E. MARTH, P. K. RUF, AND H. I. AARONSON
S. M. TUOMINEN,
E x p r e s s i o n s f o r the m a j o r v a r i a b l e s in the g e n e r a l r a t e equation f o r s o l i d - s o l i d n u c l e a tion w e r e d e v e l o p e d on the b a s i s of v a r i o u s m o d e l s of the c r i t i c a l n u c l e u s sh ap e d u r i n g h o m o g e n e o u s and h e t e r o g e n e o u s n u c le a t i o n . T h e s e m o d e l s a r e b a s e d upon s p h e r e s , but in s o m e a f a c e t was i n c o r p o r a t e d at one b o u n d a r y o r i e n t a t i o n to r e p r e s e n t the p r e s e n c e of a p a r t i a l l y o r fully c o h e r e n t s t r u c t u r e . Gibbs' r e l a t i o n s h i p f o r the c r i t i c a l r a d i u s is a p p l i c a b l e to all of the m o d e l s . The o t h e r v a r i a b l e s in the n u c l e a t i o n r a t e equation a r e a f f e c t e d by the m o d e l and by f a c e t i n g . R e d u c t i o n of AG* by f a c e t i n g is concluded to be the p r i m a r y c a u s e f o r the p r e s e n c e of r e p r o d u c i b l e l a t t i c e o r i e n t a t i o n r e l a t i o n s h i p s and fo r the e x i s t e n c e of t r a n s i t i o n p h a s e s during p r e c i p i t a t i o n f r o m so l i d s o l u t i o n s .
T H E g e n e r a l o c c u r r e n c e of s p e c i f i c l a t t i c e o r i e n t a t i o n r e l a t i o n s h i p s b e t w e e n p r e c i p i t a t e s and t h e i r m a t r i x c r y s t a l s , which allow the d e v e l o p m e n t of p l a n a r f a c e t s with o p t i m a l l y m a t c h i n g conjugate habit p l a n e s at one o r m o r e i n t e r p h a s e b o u n d a r y o r i e n t a t i o n s , has long b e e n e s t a b l i s h e d . 1'~ The e x i s t e n c e of t r a n s i t i o n p h a s e s has for many y e a r s b e e n a s s o c i a t e d with the s u p e r i o r l a t t i c e m a t c h i n g which such p h a s e s exhibit, at l e a s t at one b o u n d a r y o r i e n t a t i o n , with r e s p e c t to the m a t r i x phase. Both of t h e s e g e n e r a l o b s e r v a t i o n s s t r o n g l y i n d i c a t e that the c r i t i c a l n u c l e u s in a s o l i d - s o l i d t r a n s f o r m a t i o n is l i k e l y to be f a c e t e d w h e n e v e r t h e r e e x i s t s r e a s o n a b l e s i m i l a r i t y b e t w e e n the l a t t i c e s of the m a t r i x and p r e c i p i t a t e . L a t t i c e m a t c h i n g at the f a c e t s should n o r m a l l y be quite s e n s i t i v e to b o u n d a r y o r i e n tation when the two c r y s t a l s t r u c t u r e s i n v o l v e d a r e d i f f e r e n t , the c a s e with which this p a p e r is c o n c e r n e d . This i n d i c a t e s that t h e s e f a c e t s a r e l i k e l y to be p l a n a r and of the e n e r g y cusp type. D e s p i t e t h e s e long u n d e r s t o o d c o n s i d e r a t i o n s , all of the s u g g e s t e d c r i t i c a l n u c le u s s h a p e s f o r h o m o g e n e o u s , g r a i n b o u n d a r y and d i s l o c
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