Operational nucleation in martensitic transformations
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T H O S E of us who have followed E d g a r B a i n ' s c a r e e r over s o m e d e c a d e s a r e p r i v i l e g e d to take p a r t in this S y m p o s i u m to c o m m e m o r a t e his eightieth b i r t h d a y . His opening p a p e r has p r o v i d e d m u c h - n e e d e d p e r s p e c tive for those who will c a r r y on. In a r e a l s e n s e , the p a n o r a m a he has m o d e s t l y unfolded b e a r s i m p r e s s i v e w i t n e s s to his l i f e ' s f u l f i l l m e n t as one of m e t a l l u r g y ' s m o s t p r o l i f i c p i o n e e r s . Few m o r t a l s a r e d e s t i n e d to leave such l a n d m a r k s and to r e a c h such heights in any field. I know f r o m m a n y c o n v e r s a t i o n s with D r . Bain that he has long b e e n f a s c i n a t e d with the p r o b l e m of n u c l e a tion in the solid s t a t e , p a r t i c u l a r l y as applied to m a r t e n s i t i c t r a n s f o r m a t i o n s . D u r i n g one of our e v e n i n g talks not long ago, I happened to m e n t i o n that the n u c l e a t i o n b a r r i e r could be d e s c r i b e d as the saddle point in a f r e e - e n e r g y s u r f a c e ; he had n e v e r h e a r d the t e r m " s a d d l e p o i n t " in the n u c l e a t i o n context b e f o r e , and he asked w h e t h e r anything specific could be d e duced f r o m this concept. In fact, he wanted to p u r s u e s e v e r a l r e l a t e d a s p e c t s of the n u c l e a t i o n p r o b l e m . L a t e r in the e v e n i n g , I told him I would deal with that v e r y s u b j e c t in my p a p e r for the Bain S y m p o s i u m .
r* = 4Ao/(AE) 2 AG*
= 32~A2~3/3(Ag)
[3 ] [4]
4
However, when AG* is c a l c u l a t e d f r o m Eq. [4], u s i n g a v a i l a b l e v a l u e s of Ag, A, and ~,1 the s a d d l e - p o i n t b a r r i e r is found to be o r d e r s of m a g n i t u d e too l a r g e to p e r m i t n u c l e a t i o n u n d e r the c o n d i t i o n s w h e r e m a r t e n sitic transformations are actually observed. To c i r c u m v e n t this difficulty, we p o s t u l a t e that m a r t e n s i t i c e m b r y o s of s u p e r c r i t i c a l size somehow e x i s t in the p a r e n t phase p r i o r to the t r a n s f o r m a t i o n . U n d e r these c i r c u m s t a n c e s , the effective n u c l e a t i o n e v e n t is not identified with the j u m p i n g of a s a d d l e - p o i n t b a r r i e r , but r a t h e r with the growth s t a r t - u p of an e x i s t i n g
9
Ac.
9IL "'" GROWTH S T A R T - U P IN OPERATIONAL NUCLEATION The f r e e - e n e r g y s u r f a c e in q u e s t i o n is i l l u s t r a t e d in F i g . 1. It is r e p r e s e n t e d by the equation: 1'2 4
4
AG = -~ 7rr2cAg + ~ ~rrc2A + 27rr2a
[1]
w h e r e AG is the o v e r a l l f r e e - e n e r g y change a c c o m p a n y i n g the f o r m a t i o n of a s e m i c o h e r e n t p a r t i c l e of m a r t e n s i t e with an a s s u m e d o b l a t e - s p h e r o i d a l shape of r a d i u s r and s e m i t h i c k n e s s c; Ag is t
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