A reanalysis of the kinetics of neck growth during liquid phase sintering
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I. INTRODUCTION
HEATt r e a t m e n t
of liquid p h a s e s i n t e r e d m a t e r i a l s f o r t i m e s in e x c e s s of t h o s e r e q u i r e d to p r o d u c e 100 p c t d e n s i f i c a t i o n r e s u l t s in a c o a r s e n i n g of the m i c r o s t r u c t u r e . If the liquid c o m p l e t e l y wets the d i s p e r s e d s o l i d , i.e., if the s o l i d p a r t i c l e s t r u l y r e m a i n i s o l a t e d , the c o a r s e n i n g should then b e d e s c r i b e d by the c l a s s i c a l e x p r e s s i o n s of W a g n e r ~ and L i f s h i t z and Slyozov 2 m o d i f i e d to t a k e into account the eff e c t s of the d i s p e r s e d p h a s e v o l u m e f r a c t i o n on the c o a r s e n i n g r a t e . 3-5 Indeed, m o s t r e c e n t e x p e r i m e n t a l r e s u l t s 4-14 on liquid p h a s e s i n t e r e d s y s t e m s have b e e n a n a l y z e d on the b a s i s of O s t w a l d r i p e n i n g cont r o l l i n g 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 and the f r e quently o b s e r v e d l i n e a r r e l a t i o n s h i p b e t w e e n the cube of a v e r a g e p a r t i c l e s i z e and the s i n t e r i n g t i m e has led t h e s e w o r k e r s to conclude that O s t w a l d r i p e n i n g d o m i n a t e s the c o a r s e n i n g p r o c e s s . M i c r o s t r u c t u r a l e x a m i n a t i o n of fully d e n s e liquid p h a s e s i n t e r e d s t r u c t u r e s , h o w e v e r , shows n u m e r o u s i n s t a n c e s of p a r t i c l e - p a r t i c l e c o n t a c t s even in s y s t e m s in which d e n s i f i c a t i o n a p p a r e n t l y o c c u r s by the " s o l u t i o n - p r e c i p i t a t i o n " m e c h a n i s m for which c o m p l e t e wetting i s a p r e r e q u i s i t e . Indeed, in the o r i g i n a l a n a l y s i s of the " s o l u t i o n - p r e c i p i t a t i o n " p r o c e s s , ~S K i n g e r y p r e d i c t e d e s t a b l i s h m e n t of p a r t i c l e - p a r t i c l e c o n t a c t s at the l a t e r s t a g e s of d e n s i f i c a t i o n . When s u c h c o n t a c t s o c c u r , 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 can still take place by Ostwald ripening wherein partic l e s not in c o n t a c t g r o w (or d i s s o l v e ) at the e x p e n s e of one a n o t h e r . A l t e r n a t i v e l y , the e s t a b l i s h m e n t of such c o n t a c t s 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 b y c o a l e s c e n c e ; that is two p a r t i c l e s can m a k e cont a c t , s u b s e q u e n t l y f u s e into one and the p r o c e s s cont i n u e s d y n a m i c a l l y . Indeed, P a r i k h and H u m e n i k 16 d e m o n s t r a t e d i n c o n t r o v e r t i b l y that c o a l e s c e n c e can a c c e l e r a t e 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 t h e i r e x p e r i m e n t s t h e y w e r e a b l e to v a r y the d e g r e e of wetting
(and t h e r e f o r e the e x t e n t of p a r t i c l e - p a r t i c l e contact) of the s o l i d by t
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