The role of quenched-ln embryos in solid-state nucleation processes
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u s u a l theories of nucleation a s s u m e that n u c l e u s f o r m a t i o n o c c u r s a t t h e r e a c t i o n t e m p e r a t u r e . It i s w e l l k n o w n , h o w e v e r , t h a t c e r t a i n f e a t u r e s m a y be r e t a i n e d in a r a p i d q u e n c h f r o m t h e s o l u t i o n a n n e a l i n g t e m p e r a t u r e t o s e r v e as nucleation e m b r y o s at t h e r e a c t i o n t e m p e r a t u r e . T h e e m b r y o s m a y be of v a r i o u s k i n d s a n d are here c l a s s i f i e d as c o n c e n t r a t i o n fluctuat i o n s , diffusional nuclei, a n d d i s l o c a t i o n t a n g l e s . The c o n d i t i o n s f o r e x i s t e n c e of t h e s e e m b r y o s a r e d i s c u s s e d , especially as r e g a r d s t h e p e a r l i t e a n d m a r t e n site reactions. CONCENTRATION FLUCTUATIONS S o l i d solutions are nonuniform, even u n d e r e q u i l i b rium conditions. Microscopic c o n c e n t r a t i o n fluctuat i o n s a l w a y s e x i s t b e c a u s e of t h e r a n d o m m o t i o n o f the i n d i v i d u a l a t o m s . T h e s e e q u i l i b r i u m f l u c t u a t i o n s i n c o n c e n t r a t i o n a r e s e l d o m e x t e n s i v e e n o u g h t o be o b s e r v e d d i r e c t l y . T h e i n t e n s i t y o f f l u c t u a t i o n s is in g e n e r a l e x p e c t e d t o be t e m p e r a t u r e d e p e n d e n t . B e c a u s e o f t h i s , i t h a s b e e n s u g g e s t e d that a f l u c t u a t i o n s p e c t r u m f r o z e n i n by q u e n c h i n g a s o l u t i o n f r o m a h i g h t e m p e r a t u r e m i g h t be m o r e f a v o r a b l e t o c e r t a i n n u c l e a t i o n p r o c e s s e s t h a n the f l u c t u a t i o n s c h a r a c t e r i s t i c of t h e l o w e r t e m p e r a t u r e . L a n d a u a n d L i f s h i t z x g i v e t h e p r o b a b i l i t y to(x) of a f l u c t u a t i o n i n a p h y s i c a l q u a n t i t y x a s the G a u s s i a n 1 co(x) dx = (27r~:z)x/2 e x p ( - ( x - x ) 2 / 2 ~-~) . d x
[1]
w h e r e ~ a n d x a r e t h e m e a n s q u a r e f l u c t u a t i o n in a n d m e a n v a l u e o f t h e q u a n t i t y . T h e n u m b e r of f l u c t u a t i o n s p e r u n i t v o l u m e i n n u m b e r of s o l u t e a t o m s , n , i n a r e g i o n c o n t a i n i n g N s o l v e n t a t o m s i s g i v e n by to(v/)
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e x p ( - ( n - ~-)2
[2]
w h e r e to(n) i s t h e n u m b e r o f f l u c t u a t i o n s p e r u n i t v o l u m e , No i s t h e n u m b e r o f a t o m i c s i t e s p e r u n i t v o l u m e , a n d ~- i s t h e a v e r a g e n u m b e r o f s o l u t e a t o m s i n a r e KENNETH C. RUSSELL is Associate Professor, Department of Metallurgy and Materials Science and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Mass. This paper is based on a presentation made at a symposium on Altering the T i m e Cycle of Heat Treatment, held at the Philadelphia meeting of T h e Metallurgical Society o f A IME, October
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