The initial stages of the cellular reaction
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AND
H. B. AARON
Both the n u c l e a t i o n p r o c e s s p e r s e and the o r g a n i z a t i o n of n e a r b y n u c l e i or p r e c i p i t a t e s f o r m e d a t a given d i s o r d e r e d g r a i n b o u n d a r y into a v i a b l e c e l l s t r u c t u r e a r e c o n s i d e r e d . When the c r i t i c a l n u c l e u s i s m o d e l e d in s i m p l e f a s h i o n , b a s e d upon a r e c t a n g u l a r p a r a l l e l e p i p e d , the r a t e of n u c l e a t i o n by the " c o n v e n t i o n a l " m e c h a n i s m , in which the g r a i n b o u n d a r y i s e s s e n t i a l l y i m m o b i l e d u r i n g the n u c l e a t i o n p r o c e s s , f a r e x c e e d s that by the T u - T u r n b u l l " p u c k e r " m e c h a n i s m , in which the g r a i n b o u n d a r y is d e f l e c t e d so that i t s p l a n e i s p a r a l l e l to the h a b i t p l a n e of the n u c l e u s . A m o r e r i g o r o u s m o d e l of the c r i t i c a l n u c l e u s , b a s e d upon the s o m e w h a t s p e c i a l i z e d a s s u m p t i o n that an e n e r g y c u s p f a c e t f o r m s at only one b o u n d a r y o r i e n t a t i o n but d e v e l o p e d without a p r e c o n c e i v e d view of the n u c l e u s m o r p h o l o g y , l e a d s to this r e s u l t only when the f a c e t e n e r g y is g r e a t e r than o n e - h a l f the e n e r g y of a d i s o r d e r e d g r a i n b o u n d a r y . In the r e v e r s e e n e r g e t i c s i t u a t i o n , the n u c l e u s m o r p h o l o g y is e f f e c t i v e l y that s u p p o s e d by the p u c k e r m e c h a n i s m . T h e i n i t i a l s t a g e of c e l l u l a r g r o w t h is e x a m i n e d in the f r a m e w o r k of the question: why do a l l o t r i o m o r p h s f o r m a t d i s o r d e r e d g r a i n b o u n d a r i e s under s o m e conditions of a l l o y c o m p o s i t i o n and t e m p e r a t u r e and c e l l s d e v e l o p u n d e r o t h e r c o n d i t i o n s ? The conditions f o r the two r e a c t i o n p a t h s a r e e s t a b l i s h e d on the b a s i s of two key i d e a s : the d i r e c t i o n in which the torque t e r m a s s o c i a t e d with a f a c e t d e f l e c t s a g r a i n b o u n d a r y m e e t i n g the edge of the f a c e t (deduced f r o m the c o n s i d e r a t i o n s of Hoffman and Cahn), and the e x i s t e n c e of a d r i v i n g f o r c e f o r the b r e a k a w a y of a g r a i n b o u n d a r y f r o m such a junction r e s u l t i n g f r o m the r e q u i r e m e n t of continuity of path to a n o t h e r junction l o c a t e d n e a r b y .
C ~DERIOUS r e s e a r c h on the i n i t i a l s t a g e s of the c e l l u l a r (or d i s c o n t i n u o u s p r e c i p i t a t i o n ) r e a c t i o n can be c o n s i d e r e d to have begun in 1967, with the p u b l i c a t i o n of the f i r s t two of an i m p o r t a n t s e r i e s of p a p e r s by Tu and T u r n b u l l 1'2 b a s e d upon a thorough study of the c e l l u l a r r e a c t i o n in o r i e n t e d
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