The stability of lamellar structures
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AND
G. C. WEATHERLY
The t h e r m a l s t a b i l i t y of l a m e l l a r s t r u c t u r e s u n d e r c r e e p or h o t - w o r k i n g conditions is cons i d e r e d . It is suggested that the m i c r o s t r u c t u r a l s t a b i l i t y of the t w o - p h a s e alloy can be a l t e r e d by the i n t r o d u c t i o n of b o u n d a r i e s f o r m e d by d e f o r m a t i o n and r e c o v e r y p r o c e s s e s . E x p r e s s i o n s a r e d e r i v e d for the r a t e of growth at t r i p l e points f o r m e d in this way. T h e s e e x p r e s s i o n s a r e r e l a t e d to the s t a b i l i t y of u n i d i r e c t i o n a l l y grown e u t e c t i c s under c r e e p conditions, and s p h e r o i d i z a t i o n o b s e r v e d u n d e r hot working conditions. Under c e r t a i n l i m iting conditions the r e s u l t s r e d u c e d to those of M u l l i n s for " g r o o v i n g " at g r a i n b o u n d a r y f r e e s u r f a c e j u n c t i o n s by v o l u m e and s u r f a c e diffusion. ~-~ J k W O - p h a s e l a m e l l a r s t r u c t u r e s , e.g. p e a r l i t e or those p r o d u c e d by u n i d i r e c t i o n a l s o l i d i f i c a t i o n f r o m the m e l t , show e x c e l l e n t t h e r m a l s t a b i l i t y in the a s grown state. 1'2 T h e r e is a growing amount of evidence s u g g e s t i n g that this t h e r m a l s t a b i l i t y i s c o n t r o l l e d by faults in the s t r u c t u r e , 1'3 and if these faults could be e l i m i n a t e d the s t r u c t u r e would not c o a r s e n . However, u n d e r conditions of s e v e r e d e f o r m a t i o n at high t e m p e r a t u r e s it has been known for many y e a r s that the l a m e l t a r s t r u c t u r e i s u n s t a b l e and s p h e r o i d i z e s . 4 This s p h e r o i d i z a t i o n is exploited in m a n y of the hot working p r o c e s s e s of s t e e l s . The m e c h a n i s m for s p h e r o i d i z a t i o n is not obvious. The p r o b l e m l i e s in the i n h e r e n t s t a b i l i t y of p l a n a r m o r p h o l o g i e s ; except in the p r e s e n c e of a high d r i v i n g force, e.g. chemical supersaturation, a perturbation on a p l a n a r i n t e r f a c e will decay with t i m e , and the p l a n a r morphology is s t a b l e . 5'6 T h i s c o n c l u s i o n is not a l t e r e d by the p r e s e n c e of a s t r e s s p e r se. If the n o r m a l s t r e s s at any s e g m e n t of an i n t e r f a c e is pn, the c h e m i c a l potential Px of a solute s p e c i e s x will be given by ~x = Po--pn6~2
w h e r e Po is the c h e m i c a l potential for the s t r e s s free state and 5f~ is the d i f f e r e n c e in a t o m i c v o l u m e of the solute in the two p h a s e s . The p r e s e n c e of s t r e s s e s can affect the c h e m i c a l potential of a solute s p e c i e s at an i n t e r f a c e , but the n a t u r e of these s t r e s s e s a r e such that the p e r t u r b a t i o n will s t i l l decay. To i l l u s t r a t e t h i s , c o n s i d e r the s i m
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