The kinetics of martensite formation in small particles
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T H E quantitative kinetic p a r a m e t e r s d e s c r i b i n g the nucleation of martensite have been d e r i v e d for the most part from a n a l y s i s of isothermal transformation e x p e r iments. T h e characteristics of i s o t h e r m a l martensite f o r m a t i o n w e r e f i r s t d o c u m e n t e d c o m p l e t e l y by S h i h , A v e r b a c h , a n d C o h e n ~ a n d t h e i r r e s u l t s a r e shown in F i g . 1 . In o r d e r t o a n a l y z e t h e s e d a t a , i t i s a s s u m e d t h a t t h e h e t e r o g e n e o u s n u c l e a t i o n r a t e , * Nv (the t i m e *The problems associated with converting the measured transformation rates t o nucleation rates are covered elsewhere.2-4 d e r i v a t i v e o f t h e n u m b e r of m a r t e n s i t e p l a t e s p e r u n i t v o l u m e , N v) c a n b e w r i t t e n a s a p r o d u c t of the n u m b e r o f nucleation s i t e s per unit volume, n t , a n d a r a t e o f c o n v e r s i o n o f t h e s e s i t e s . T h e r a t e is w r i t t e n as a product o f a t t e m p t s p e r unit t i m e , u, a n d a B o l t z m a n f a c t o r e x p ( - Q / R T ) w h e r e Q is t h e a c t i v a t i o n e n e r g y for nucleation; t h u s ,
N v = nt u e x p -q/R T
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U s i n g t h i s f o r m a l i s m , e x p e r i m e n t a l d a t a c a n be a n a l y z e d t o y i e l d a n a c t i v a t i o n e n e r g y by e s t i m a t i n g t h e n u m b e r of active nucleation s i t e s and the attempt frequency. T h e d e r i v e d activation e n e r g i e s a n d t h e i r dep e n d e n c e on r e a c t i o n t e m p e r a t u r e ( i . e . , d r i v i n g f o r c e ) h a v e been used as t h e p r i m a r y quantities f o r c o m p a r i n g t h e o r y w i t h e x p e r i m e n t . 5'2 A p a r t i c u l a r l y difficult p r o b l e m a r i s e s in a s s e s s i n g t h e n u m b e r o f a c t i v e s i t e s b e c a u s e t h e i r n u m b e r is c o n s t a n t l y c h a n g i n g due t o t h e p o t e n t a u t o c a t a l y s i s a c companying transformation ( p r i o r transformation g r e a t l y i n c r e a s e s the n u c l e a t i o n r a t e , i . e . , i n c r e a s e s t h e n u m b e r o f s i t e s ) . 6 T h e p u r p o s e of t h e p r e s e n t p a p e r is to r e p o r t r e s u l t s f r o m a k i n e t i c t e c h n i q u e that i s c a p a b l e of m e a s u r i n g t h e n u c l e a t i o n r a t e f r o m
t h e i n i t i a l s i t e s a l o n e . It i s t h u s p o s s i b l e t o d e t e r m i n e independently the n u m b e r of active s i t e s and h e n c e reduce t h e l e v e l o f a s s u m p t i o n r e q u i r e d in e v a l u a t i n g Q . P e r h a p s m o r e i m p o r t a n t l y , t h e t e c h n i q u e m a k e s it p o s s i b l e to t e s t s e v e r a l a s s u m p t i o n s i n h e r e n t to t h e a n a l y s i s u s i n g E q . [1]. In p a r t i c u l a r , i t i s p o s s i b l e t o d e t e r m i n e t h e r e l a t i v e e f f e c t i v e n e s s of t h e v a r i o u s transformation s i
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