A mathematical model study of the influence of degree of mixing and powder particle size variation on the homogenization
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the r a t e of homogenization in powder compacts. A s e c ondary goal of the study was to d e t e r m i n e the effects of s m a l l v a r i a t i o n s in solute powder p a r t i c l e s i z e on homogenization kinetics. An a n a l y t i c a l approach, r a t h e r than an e x p e r i m e n t a l one, was used in o r d e r to o b s e r v e blending and size v a r i a t i o n s on s y s t e m s containing s m a l l n u m b e r s of p a r t i c l e s (i.e., to a s s e s s the m a g n i tude of effects which occur on the scale of a few p a r t i cle d i a m e t e r s ) . Such information is n e c e s s a r y to d e t e r mine whether blending effects in powder compacts a r e local or long range, and to define subsequent e x p e r i m e n t s aimed at c h a r a c t e r i z i n g powder blends and r e l a t i n g such c h a r a c t e r i z a t i o n s to mixing techniques. The m a t h e m a t i c a l model that was developed does not consider volume change effects a s s o c i a t e d with a l loying, i n t e r p a r t i c l e p o r o s i t y , Kirkendall p o r o s i t y , and other g e o m e t r i c a l changes r e l a t e d to sintering. These effects can influence homogenization kinetics through v a r i a t i o n s in the amount of i n t e r p a r t i c l e contact (volume diffusion effects) and in the amount of internal s u r f a c e a r e a (surface diffusion effects). However, these c o m p l e x i t i e s a r e beyond the scope of the p r e s ent study.
M O D E LING P R O C E D U R E S The g e n e r a l t r e a t m e n t of diffusional homogenization p r o b l e m s has been reviewed r e c e n t l y by Purdy and Kirkaldy. 6 Their t r e a t m e n t , although s p e c i f i c a l l y d e signed to analyze homogenization of ingot segregation, is sufficiently g e n e r a l to be applicable to the p e r i o d i c VOLUME 6A, APRIL 1975-869
d i s t r i b u t i o n of h e t e r o g e n e i t i e s e x i s t i n g in c o m p a c t e d b l e n d s of p o w d e r s . The p r e s e n t s t u d y c o n s i d e r s the a p p l i c a t i o n of the f o r m a l i s m of v o l u m e diffusion c o n t r o l l e d h o m o g e n i z a t i o n to a o n e - d i m e n s i o n a l t r a n s p o r t m o d e l ( a l t e r n a t e s t a c k i n g of p l a t e s of two c o m p o s i t i o n s ) in o r d e r to a n a l y z e the e f f e c t s of blending and p a r t i c l e s i z e v a r i a t i o n s on h o m o g e n i z a t i o n k i n e t i c s . The o n e - d i m e n s i o n a l m o d e l has the a d v a n t a g e of c o m p u t a t i o n a l f l e x i b i l i t y o v e r the t h r e e - d i m e n s i o n a l m o d e l ( c o n c e n t r i c - s p h e r e ) in s t u d y i n g the e f f e c t s of i n t e r e s t and is c o n s i d e r a b l y s i m p l e r in t e r m s of c o m p u t a t i o n a l d e t a i l s . Although q u a n t i t a t i v e c o r r e l a t i o n s b e t w e e n o n e - d i m e n s i o n a l m o d e l s have b e e n e s t a b l i s h e d p r e v i o u s l y 3'7 f o r o n e - p a r t i c l e s y s t e m s , s u c h
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