Void growth rates in irradiated materials at the peak swelling temperature
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Void Growth Rates in Irradiated Materials at the Peak Swelling Temperature A. D. BRAILSFORD The p r o b l e m of void growth in i r r a d i a t e d m a t e r i a l s is of g r e a t technological i m p o r t a n c e and h a s a t t r a c t e d c o n s i d e r a b l e a t t e n t i o n over the past decade. 1'2 While it i s doubtful that a c o m p l e t e t h e o r e t i c a l u n d e r s t a n d i n g of the p h e n o m e n o n can be achieved without confronting the c o m p l e x i t i e s of s t r u c t u r a l m a t e r i a l s , c e r t a i n i n g r e d i e n t s in any growth m o d e l can be p e r c e i v e d and a b s t r a c t e d for s e p a r a t e a n a l y s i s . One such topic is the extent to which i n t e r f a c e control of v a c a n c y (and i n t e r s t i t i a l ) flow into a void can inhibit void growth in i r r a d i a t e d m a t e r i a l s , together with the dose dependence of the s w e l l i n g in this case as c o n t r a s t e d to d i f f u s i o n c o n t r o l l e d growth. T h i s is the s u b j e c t of the p r e s e n t note. It will be shown that in both i n s t a n c e s an a p p r o x i m a t e l y l i n e a r d e p e n d e n c e of s w e l l i n g upon dose is p r e d i c t e d in bulk s o l u t i o n - t r e a t e d m a t e r i a l s at the peak swelling t e m p e r a t u r e , p r o v i d i n g t h e r e is no s i g n i f i c a n t l o s s of the i r r a d i a t i o n - i n d u c e d d i s l o c a t i o n d e n s i t y due to r e c o v e r y p r o c e s s e s , 3 o r d e c r e a s e of void d e n s i t y as a r e s u l t of void c o a l e s c e n c e . ~ We c o n s i d e r an idealized s y s t e m c o n s i s t i n g of a fixed v o l u m e c o n c e n t r a t i o n C v of i d e n t i c a l voids; r a d i u s r v , of i d e n t i c a l i n t e r s t i t i a l d i s l o c a t i o n loops, of r a d i u s r L , at a v o l u m e c o n c e n t r a t i o n N/;, and d e f o r m a t i o n d i s l o c a t i o n s at a d e n s i t y pod. Then if the i r r a d i a t i o n p r o d u c e s i n t e r s t i t i a l s and v a c a n c i e s at a r a t e K ( d i s p l a c e m e n t s p e r atom p e r second), at the peak s w e l l i n g t e m p e r a t u r e , where i n t r i n s i c r e c o m b i n a tion and t h e r m a l g e n e r a t i o n effects may be neglected to a f i r s t a p p r o x i m a t i o n , the s w e l l i n g S ( i . e . t h e f r a c tional void volume) at time t is given by the i n t e g r a l of ~ dS ~-
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K p d f l v C ~ ( P d + t3vCv) ~
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