Direct observations of lamellar fault migration in the Pb-Sn eutectic
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L a m e l l a r m i c r o s t r u c t u r e s a r e i n t r i n s i c a l l y shape s t a b l e in the s e n s e that g r o w t h of a l a r g e l a m e l l a at the e x p e n s e of a s m a l l e r one i s not a s s o c i a t e d with a d e c r e a s e in the s u r f a c e to v o l u m e (S/V) r a t i o of the s y s t e m . This i s in c o n t r a s t to g l o b u l a r and r o d l i k e s t r u c t u r e s in which the g r o w t h of a l a r g e p a r t i c l e at the e x p e n s e of a s m a l l e r one is c o n c u r r e n t with a c o n t i n u a l l y d e c r e a s i n g S/V. L a m e l l a r s t r u c t u r e s a r e a l s o not s u s c e p t i b l e to the l a m e l l a r analog of R a y l e i g h i n s t a b i l i t i e s which c a n l e a d to the b r e a k d o w n of a r o d l i k e p a r t i c l e into a r o w of s p h e r e s . In the a b s e n c e of substructural effects therefore, lamellar structures would b e e x p e c t e d to c o a r s e n at e l e v a t e d t e m p e r a t u r e only b y the m o t i o n of l a m e l l a r t e r m i n a t i o n s . Such a d e f e c t ( a l s o known a s a fault) can l e a d to m i c r o s t r u c t u r a l c o a r s e n i n g in the m a n n e r s u g g e s t e d b y Cline 1 and G r a h a m and K r a f t , 2 a s noted in F i g . 1. The c u r v a t u r e at the l a m e l l a r t e r m i n a t i o n is a s s o c i a t e d with an i n c r e a s e in s o l u b i l i t y of c o m p o n e n t A in the /3 p h a s e at t h i s p o s i t i o n . This p r o d u c e s a c o n c e n t r a t i o n g r a d i e n t of A in the /3 p h a s e such that c o m p o n e n t A diffuses f r o m the t e r m i n a t i o n to a d j a c e n t l a m e l l a e . This m a s s flux, t o g e t h e r with the r e q u i r e m e n t of l o c a l e q u i l i b r i u m at the t e r m i n a t i o n i n t e r f a c e , p r o d u c e s a r e c e s s i o n o r m o t i o n of the fault. Cline ~ h a s t h e o r e t i c a l l y p r e d i c t e d the v e l o c i t y of fault m i g r a t i o n and t h i s m e c h a n i s m of c o a r s e n i n g w a s a l s o s u g g e s t e d b y G r a h a m and K r a f t 2 to e x p l a i n e l e v a t e d t e m p e r a t u r e m i c r o s t r u c t u r a l b r e a k down in the A1-CuA12 l a m e l l a r e u t e c t i c . Although G r a h a m and K r a f t did not develop an a n a l y t i c a l e x p r e s s i o n f o r the v e l o c i t y at which f a u l t s r e c e d e , t h e i r m o d e l c a n be c o m b i n e d with e s t i m a t e s a s to the diffusion g e o m e t r y to o b t a i n such an e x p r e s s i o n a s follows. T h e i r e x p r e s s i o n (Eq. [4]) for the m a s s t r a n s f e r r a t e , dQ/dt, m u s t f i r s t be c o n v e r t e d to a f a u l t m i g r a tion r a t e t h r o u g h the f o r m u l a , dQ/dr (unit l a m e l l a r length) = ~up'V F, By a s s u m i n g the diffusion a r e a p e r unit l a m e l l a r length is X and the diffusion d i s t a n c e ~ , ( c o m p a r e with G r a h a m and K r a f t ' s Eqs. [5] and [7]i d i r e c t e x p r
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