A quantitative analysis of hydrogen trapping
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S I N C E its e x i s t e n c e was s u g g e s t e d by D a r k e n and S m i t h 1 in 1949, h y d r o g e n t r a p p i n g has been w e l l subs t a n t i a t e d , both e x p e r i m e n t a l l y and t h e o r e t i c a l l y . T r a p s that have now been identified in i r o n and o t h e r m e t a l s include d i s l o c a t i o n s , 2,~ g r a i n b o u n d a r i e s , 3,4 v o i d s , %6 and p a r t i c l e - m a t r i x i n t e r f a c e s . S,4,7 Th e i m p o r t a n c e of such i n t e r n a l t r a p s on h y d r o g e n diffusion and on d e t e r m i n i n g an a l l o y ' s s u s c e p t i b i l i t y t o w a r d s h y d r o g e n e m b r i t t l e m e n t is a l s o w e l l d o c u m e n t e d , s-l~ What is lacking, h o w e v e r , is a r e l i a b l e te c h n i qu e f o r not only identifying such t r a p s , but a l s o of p r e d i c t i n g what t h e i r e f f e c t will be. It is u s u a l to a t t e m p t to obtain t r a p p i n g p a r a m e t e r s f r o m an a n a l y s i s of the p e r m e a t i o n r a t e of h y d r o g e n t h r o u g h a m a t e r i a l , d r a w i n g upon one of s e v e r a l e x i s t i n g t h e o r i e s , the m o s t g e n e r a l b e i n g that of McNabb and F o s t e r , n in which F i c k ' s f i r s t and s e c o n d laws have been modified to include a t r a p p i n g r e a c t i o n . Although the r e s u l t i n g d i f f e r e n t i a l e q u at i o n s cannot be s o l v e d e x p l i c i t l y , n u m e r i c a l so l u tions have been p r o p o s e d in the l i t e r a t u r e m o s t r e cently by C a s k e y and P i l l i n g e r . 12 While o t h e r t h e o r i e s o r m o d e l s , in p a r t i c u l a r t h o s e of O r i a n i , 13 Koiwa, 14 and P r e s s o u y r e and B e r n s t e i n , 15 a l s o t r e a t the s a m e p r o b l e m they r e q u i r e s i m p l i f y i n g a s s u m p t i o n s which m a y o r m a y not apply to a l l r e a l i s t i c cases.1~ A f u r t h e r p r o b l e m c o m m o n to a ll t h e s e m o d e l s , is that due to t h e i r i n t r i n s i c g e n e r a l i t y and the l a r g e n u m b e r of a s s o c i a t e d p a r a m e t e r s , n or due to the c o m p l e x i t y of the m a t e r i a l i ts e lf , it is often d if f i c u lt to d i s t i n g u i s h b e t w e e n the t r a p p i n g c h a r a c t e r i s t i c s of d i f f e r e n t t r a p s , thus making it d if f i c u lt to d e t e r m i n e the t r a p ping and r e l e a s e r a t e s , t r a p e f f i c i e n c y , and the i n t e r a c t i o n e n e r g y b e t w e e n v a r i o u s t r a p s and h y d ro g en . In this p a p e r we d e s c r i b e an a p p r o a c h f r o m which quant i t a t i v e t r a p p i n g p a r a m e t e r s can be obtained. Th e key is the use of a m o d e l s y s t e m in which the t r a p population is not only known but c o n t r o l l a b l e . In fact, we
will be able to a n a l y z e a quite c o m p l e x t r a p p i n g s i t u a tion w h e r e both r e v e r s i b l e and i r r e v e r s i b l e t r a p p i
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