Discussion of grain growth in aluminum
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B. NOWAK
T h e d a t a of R h i n e s and C r a i g (RC) (Met Trans., 1974, vol. 5, pp. 413-25) a r e p a r t i a l l y r e i n t e r p r e t e d . F o r the f i r s t r e g i m e of g r a i n growth, a v e r a g e g r a i n v o l u m e is p r o p o r t i o n a l to t i m e , in a c c o r d a n c e with RC, but f o r the second, it i s p r o p o r t i o n a l to the t h r e e h a l v e s p o w e r of t i m e . The s t r u c t u r a l f a c t o r cr i s found to b e c o n s t a n t only in the f i r s t r e g i m e , and i t s v a l u e i s r e d e t e r m i n e d f r o m the d a t a to be about 2.65. T h e o r e t i c a l d e r i v a t i o n s of t h i s v a l u e a r e a l s o given and a r e found to be r e l a t e d to g r a i n f o r m (e.g. a t e t r a k a i d e c a h e d r o n ) . G r a i n b o u n d a r y m o t i o n in the s e c o n d r e g i m e i s c o n t r o l l e d by d r a g due to l a t t i c e d i f f u s i o n of solute a t o m s f r o m the b o u n d a r y , and an a c t i v a t i o n e n e r g y of about 27 k c a l / m o l e (113 k J / m o l e ) f o r t h i s p r o c e s s is c a l c u l a t e d f r o m the data.
IN a
r e c e n t p a p e r , R h i n e s and C r a i g 1 have e x a m i n e d i s o t h e r m a l (635~ g r a i n g r o w t h in a l u m i n u m by a c a r e f u l and e x t e n s i v e a p p l i c a t i o n of s e r i a l s e c t i o n i n g and innovative t o p o l o g i c a l a n a l y s i s . T h e y r e p o r t an i n c r e a s e of a v e r a g e g r a i n v o l u m e p r o p o r t i o n a l to t i m e , with the r a t e c o n s t a n t equal to the p r o d u c t of f o u r c o n s t a n t s , e a c h m e a s u r a b l e i n d e p e n d e n t l y of the g r o w t h e x p e r i m e n t : 1) a d i m e n s i o n l e s s t o p o l o g i c a l " s w e e p c o n s t a n t 0 " d e f i n e d a s the n u m b e r of a v e r a g e g r a i n s l o s t when the g r a i n b o u n d a r i e s s w e e p t h r o u g h 1 cc of m a t e r i a l p e r cubic c e n t i m e t e r and r e a d j u s t f o r e q u i a x e d g r a i n s , 2) the m o b i l i t y , ~, of the a v e r a g e g r a i n , 3) the s u r f a c e t e n s i o n , ~, of the a v e r a g e g r a i n b o u n d a r y , and 4) a d i m e n s i o n l e s s " s t r u c t u r a l g r a d i e n t a " which i s e x p e r i m e n t a l l y c o n s t a n t and is e q u a l to the p r o d u c t of t o t a l c u r v a t u r e p e r unit v o l u m e and the shared surface area per grain. T h e p u r p o s e of t h i s p a p e r i s to r e i n t e r p r e t p a r t i a l l y s o m e of the d a t a p r e s e n t e d b y RC. T h e s e a u t h o r s point out that t h e r e a r e two r e g i m e s f o r the t i m e d e p e n d e n c e of the g r a i n b o u n d a r y s u r f a c e a r e a p e r unit v o l u m e , SV, and the t o t a l s u r f a c e c u r v a t u r e p e r unit v o l u m e , MV (this quantity is the i n t e g r a l of the m e a n c u r v a t u r e at e v e r y point o v e r the t o t a l g r a i n b o u n d a r y a r e a p e r unit v o l u
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