Multiple necking phenomena in metal composites
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DV= [x~.Di~i + ( 1 - x ~ C e m e r
]
+din x~ /
[5]
w h e r e 7~. and x~ = a c t i v i t y coefficient and mole f r a c tion, res~pectively, of e i t h e r n i c k e l o r c h r o m i u m in /3, and the a p p r o x i m a t i o n of W a g n e r z7 has b e e n u s e d , i . e . , that growth is c o n t r o l l e d by the diffusivity at the c o m p o s i t i o n of the m a t r i x in c o n t a c t with the i n t e r p h a s e b o u n d a r y . T h e s e v a l u e s of D V a r e a l s o included in T a b l e II. The r a t i o of D V c a l c u l a t e d f r o m Eq. [4] to that o b t a i n e d f r o m Eq. [5] is s e e n to r a n g e f r o m 3 • 103 to 2 • 104. T h u s , the c o n t r i b u t i o n of v o l u m e diffusion to the growth of the c e l l u l a r s t r u c t u r e at the r e a c t i o n t e m p e r a t u r e s i n v e s t i g a t e d m u s t have been n e g l i g i b l e , and G m u s t a c c o r d i n g l y have been d e t e r m i n e d by c e l l b o u n d a r y d i f f u s i o n . A s is a p p r o p r i a t e for a D B - c o n t r o l l e d r e a c t i o n , t h i s r a t i o tends to d e c r e a s e with i n c r e a s i n g t e m p e r a t u r e b e c a u s e the a c t i v a t i o n enthalpy for v o l u m e diffusion is c o n s i d e r a b l y h i g h e r t h a n that for cell b o u n d a r y diffusion; but even at the h i g h e s t t e m p e r a t u r e u t i l i z e d v o l u m e diffusion does not play a d e t e c t a b l e r o l e in the growth p r o c e s s . K o s s o w s k y ' s finding that the v a l u e s of D B c a l c u lated f r o m the growth k i n e t i c s data lie within an o r d e r of m a g n i t u d e of the g r a i n b o u n d a r y s e l f - d i f f u s i v i t i e s of i r o n in 20 pct C r , 25 pct Ni s t a i n l e s s s t e e l z~ p r o b ably c o n s t i t u t e s a c c e p t a b l e d i r e c t evidence that growth of the c e l l u l a r s t r u c t u r e in N i - C r is D B - c o n t r o l l e d . The a c t i v a t i o n enthalpy for the v o l u m e diffusion of i r o n in t h i s s t e e l 2~ is n e a r l y the s a m e as those for D~i a n d D~r in N i - C r a l l o y s ; 21 s i m i l a r a c t i v a t i o n e n t h a l p i e s (and p r o b a b l y a l s o Do's) for b o u n d a r y diffusion a r e a c c o r d i n g l y to be a n t i c i p a t e d . The c i r c u m s t a n c e that AH for D B a s c o m p u t e d from the growth k i n e t i c s data is n e a r l y twice a s high as might r e a s o n ably be expected may well be due to r e l a t i v e l y s m a l l e x p e r i m e n t a l e r r o r s in the m e a s u r e m e n t of 6 , and e s p e c i a l l y of S. K o s s o w s k y ' s m i c r o g r a p h s of the c e l l u l a r s t r u c t u r e in the Ni-44 pct C r a l l o y indicate that the n o d u l e s of this s t r u c t u r e c a n be i r r e g u l a r in shape and that t h e r e a r e a p p r e c i a b l e v a r i a t i o n s in S w i t h i n an i n d i v i d u a l nodule. The p o s s i b i l i t y of a l i m i t e d a m o u n t of g e n e r a l p r e c i p i t a t i
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