The magnetoelastic interaction of dislocations and ferromagnetic domain walls in iron and nickel
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A t h e o r y i s d e v e l o p e d which p e r m i t s the m a g n e t o e l a s t i c i n t e r a c t i o n of domain walls and d i s l o c a t i o n s to be c o m p u t e d as a function of t h e i r r e l a t i v e s e p a r a t i o n . The m e t h o d c o r r e s p o n d s to a two constant t h e o r y of m a g n e t o s t r i c t i o n and i s ap p l i ed to m o r e than sixty c a s e s f o r i r o n and n i c k e l . The c a l c u l a t i o n s indicate that d i s l o c a t i o n s in i r o n i n t e r a c t m o r e s t r o n g l y by a s much a s an o r d e r of m a g n i tu d e with 180 deg w a l l s than with 90 deg Type B w a l l s , i . e . , w al l s with n o r m a l c o m p o n e n t of m a g n e t i z a t i o n but equal z e r o . The situation f o r n i c k e l is just the opposite. The r e s u l t s a r e d i s c u s s e d in t e r m s of the e f f e c t s of domain walls on individual d i s l o c a t i o n s and the e f f e c t of e x t e n s i v e a r r a y s of d i s l o c a t i o n s on m a g n e t i c p r o p e r t i e s . Y Y O R K E R S in the f i e l d of soft f e r r o m a g n e t i c m a t e r i a l s have d e v o t e d i n c r e a s i n g attention in the past decade and a half to the e f f e c t s of d i s l o c a t i o n s on m a g netic p r o p e r t i e s . F r o m a p r a c t i c a l point of v i e w , it h as b e e n p r o p o s e d that an u n d e r s t a n d i n g of the i n t e r p l a y of the two would l ead , on the one hand, to a s i m p l e , nondestructive means for estimating mechanical p r o p e r t i e s and, on the o t h e r hand, to c l o s e r c o n t r o l of m a g n e t i c p r o p e r t i e s of m a t e r i a l s s u b j e c t e d to m e c h a n i c a l d e f o r m a t i o n during p r o c e s s i n g . F r o m a t h e o r e t i c a l point of v i e w , h o w e v e r , the b a s i c p r o b l e m of a n a l y z i n g the i n t e r a c t i o n s of d i s l o c a t i o n s with the m a g n e t i c d et a i l s of a m a t e r i a l is r a t h e r f o r m i d a b l e . A d i s l o c a t i o n is a line l o c a l i z e d e r r o r in the c r y s t a l s t r u c t u r e , with an a s s o c i a t e d long range l a t t i c e d i s t o r t i o n , so that one should w o r r y about the c o n s e q u e n c e s of this on each of the s e v e r a l f o r m s of i n t e r n a l e n e r g y of a f e r r o m a g ne t i c s y s t e m . The e f f e c t of d i s l o c a t i o n s on f e r r o m a g n e t i c p r o p e r t i e s was f i r s t t r e a t e d by B r o w n , ~ who d e v e l o p e d a t h e ory of the i n f l u en c e of s m a l l i n h o m o g e n e i t i e s of m a g n e t i z a t i o n a s s o c i a t e d with " i n t e r n a l " s t r e s s e s on the r a t e of a p p r o a c h to s a t u r a t i o n (the e f f e c t of cold work on s u s c e p t i b i l i t y at high f i e l d s ) . S e e g e r and K r Sn m u l l e r 2 have c a r r i e d B r o w n ' s t r e a t m e n t f u r t h e r , taking into acco u n t a n i s o t r o p y of m a g n e t o s t r i c t i o n and
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