On the growth kinetics of grain boundary ferrite allotriomorphs
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S E V E R A L y e a r s ago, K i n s m a n and A a r o n s o n 1 r e p o r t e d m e a s u r e m e n t s of the thickening k i n e t i c s of g r a i n b o u n d a r y a l l o t r i o m o r p h s of p r o e u t e c t o i d f e r r i t e in an F e - 0 . 1 1 pct C and in two F e - C - X a l l o y s , obtained by m e a n s of t h e r m i o n i c e m i s s i o n m i c r o s c o p y . The p a r a b o l i c r a t e c o n s t a n t , a , for these k i n e t i c s * *The parabolicrate constantis the constantof proportionalitybetweengrowth distanceand the squareroot of the growthtime. was d e t e r m i n e d f r o m the e x p e r i m e n t a l data and also c a l c u l a t e d f r o m the Dub62- Z e n e r 3 equation for the m i g r a t i o n k i n e t i c s of a p l a n a r , d i s o r d e r e d i n t e r p h a s e b o u n d a r y of infinite extent. T h i s equation was d e r i v e d u n d e r the a s s u m p t i o n that the d i f f u s i v i t y , D, in the m a t r i x phase is i n v a r i a n t with c o m p o s i t i o n . Since the diffusivity of c a r b o n in a u s t e n i t e i n c r e a s e s r a p i d l y with c a r b o n c o n t e n t , 4 a p a r t i c u l a r value of this d i f f u s i v i t y had to be c h o s e n . Following W a g n e r , 5 the one s e l e c t e d was that at the c a r b o n content of the A e 3 or 7 / ( a + 7) phase b o u n d a r y . In the F e - C alloy and even m o r e p r o n o u n c e d l y in one of the F e - C - X a l l o y s , howe v e r , many of the e x p e r i m e n t a l l y m e a s u r e d v a l u e s of a r e f l e c t e d growth k i n e t i c s f a s t e r than those c a l c u l a t e d . If the c a l c u l a t e d k i n e t i c s a r e accepted as exact, this r e s u l t i n d i c a t e s that the i n t e r f a c e c o m p o s i t i o n s at the b r o a d faces of the a l l o t r i o m o r p h s d e p a r t e d a p p r e c i a b l y f r o m t h e i r e q u i l i b r i u m v a l u e s d u r i n g growth. C. ATKINSON is Lecturer, Department of Mathematics, Imperial College of Science and Technology, London, United Kingdom. H. B. AARON, formerly with Scientific Research Staff, is now Chem-Met Specialist, Automotive Assembly Division, Ford Motor Company, Dearborn, Mich. 48121. K. R. KINSMAN is with the Scientific Research Staff, Ford Motor Company. H. I. AARONSON, formerly with Scientific Research Staff, Ford Motor Company, is now Professor, Department of Metallurgical Engineering, Michigan Technological University, Houghton, Mich. 49931. Manuscript submitted March 23, 1972. METALLURGICALTRANSACTIONS
In view of the s m a l l u n d e r c o o l i n g s b e l o w the A e 3 at which much of these data w e r e obtained and the p r e d o m i n a n t l y d i s o r d e r e d s t r u c t u r e which n o r m a l l y c h a r a c t e r i z e s the b r o a d faces of a l l o t r i o m o r p h s , this e x p l a n a t i o n s e e m s u n l i k e l y . The r e s u l t o b t a i n e d was, in fact, a l m o s t the r e v e r s e of that a n t i c i p a t e d . The e x p e r i m e n t a l
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