Stress-induced interaction of pairs of point defects in bcc solutions
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1. ~ T R O D U C T I O N
c a l c u l a t e d by m e a n s of the i n v e r s e F o u r i e r - t r a n s f o r mation:
A s is known, the i n t e r a c t i o n b e t w e e n point defects is a v e r y i m p o r t a n t effect for u n d e r s t a n d i n g such phen o m e n a as s h o r t - r a n g e and l o n g - r a n g e o r d e r , diffusion, aging in i r r a d i a t e d m a t e r i a l s , i n t e r n a l friction, and so on. T h i s i n t e r a c t i o n is e s p e c i a l l y s t r o n g b e tween i n t e r s t i t i a l a t o m s in a bcc host lattice s i n c e each i n t e r s t i t i a l atom p r o d u c e s a l a r g e c r y s t a l - l a t t i c e d i s t o r t i o n r e s u l t i n g in the s t r e s s - i n d u c e d i n t e r a c tion (the e s t i m a t i o n of a t y p i c a l p a i r w i s e s t r e s s - i n duced i n t e r a c t i o n e n e r g y in a bcc host lattice gives a value of the o r d e r of 1 eV). The p u r p o s e of this p a p e r is the c a l c u l a t i o n of s t r e s s - i n d u c e d i n t e r a c t i o n e n e r g i e s of the i n t e r s t i t i a l i n t e r s t i t i a l , and i n t e r s t i t i a l - h o s t a t o m v a c a n c y p a i r s ( i n t e r s t i t i a l s in o c t a h e d r a l as well as t e t r a h e d r a l i n t e r s t i c e s ) . C o n s i d e r a t i o n 1 of employed static c r y s t a l l a t t i c e s takes into account the d i s c r e t e a t o m i c s t r u c t u r e of a host lattice in the a n a l y s i s of e l a s t i c a t o m i c d i s p l a c e m e n t s and c o r r e s p o n d i n g s t r e s s - i n duced e n e r g i e s , and t h e r e f o r e e n a b l e s the c a l c u l a t i o n of p a i r - w i s e e n e r g i e s of p a i r s whose s e p a r a t i o n v e c t o r is c o m m e n s u r a b l e with i n t e r a t o m i c d i s t a n c e s . C o m p u t e r c a l c u l a t i o n s a r e c a r r i e d out in the g e n e r a l f o r m which e n a b l e s obtaining the s t r e s s induced e n e r g i e s for any kind of i n t e r s t i t i a l a t o m s (for e x a m p l e , H, O, N, C) in V, NC, Ta, a F e , and t h e r e f o r e a r e u n i v e r s a l for these m e t a l s . 2. CALCULATION TECHNIQUE The c a l c u l a t i o n technique employed in this p a p e r is b a s e d on the lattice s t a t i c s t h e o r y f o r m u l a t e d in Ref. 1. The r e a l s t r e s s - i n d u c e d p a i r w i s e i n t e r a c t i o n e n e r gies Wpq(R) b e t w e e n p - t y p e and q-type defects s e p a r a t e d by the bcc lattice t r a n s l a t i o n v e c t o r R is M. S. BLANTERis affiliated with the Institute for Machine Construction, Moscow, and A. G. KHACHATURYANis Professor, Institute of Crystallography, Academy of Sciences of the USSR, Moscow, USSR. Manuscript submitted June 20, 1977. METALLURGICALTRANSACTIONSA
1 Wpq(R) = Nr ~ Vpq(k) e -/KR
[1]
where N is a total n u m b e r of the host a t o m s , the s u m m a t i o n is c a r r i e d out over all N points of q u a s i c o n t i n u u m i n s i d e the f i r s t B r i l l o u i n of t
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