Twist boundaries in ordered alloys
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MARCINKOWSKI, AND WEN FENG TSENG
A d e t a i l e d a n a l y s i s has been made of the e q u i l i b r i u m c o n f i g u r a t i o n of s o m e of the s i m p l e r types of twist b o u n d a r i e s a n t i c i p a t e d in o r d e r e d a l l o y s . S i m i l a r to the c a s e of tilt boundar i e s , it is found that the extension of the s u p e r l a t t i c e d i s l o c a t i o n s d e c r e a s e s with i n c r e a s i n g angle of m i s f i t of the b o u n d a r y . F u r t h e r m o r e , at s u f f i c i e n t l y high a n g l e , the b o u n d a r y bec o m e s c o m p l e t e l y d i s o r d e r e d . An e x a m i n a t i o n of twist b o u n d a r i e s i n o r d e r e d FeCo shows them to c o n s i s t of s u p e r l a t t i c e d i s l o c a t i o n s in a l l c a s e s , but somewhat m o r e c o m p l e x than those t r e a t e d t h e o r e t i c a l l y and d e s c r i b e d above.
IN
an e a r l i e r paper ~ it was shown that for a low a n g l e tilt b o u n d a r y in an o r d e r e d alloy, the s u p e r l a t t i c e d i s l o c a t i o n s c o m p r i s i n g the wall may be extended p a r a l l e l o r p e r p e n d i c u l a r to the w a l l , depending upon the v a r i a tion of a n t i p h a s e b o u n d a r y e n e r g y with o r i e n t a t i o n . F u r t h e r m o r e , a s the a n g l e of m i s f i t i n c r e a s e s , the wall of v e r t i c a l l y a l i g n e d d i s l o c a t i o n s is f o r m e d in a l l c a s e s , with the extension between the s u p e r l a t t i c e d i s l o c a t i o n s being equal to the s e p a r a t i o n between the s u p e r l a t t i c e d i s l o c a t i o n s t h e m s e l v e s . The walt thus e s s e n t i a l l y b e c o m e s d i s o r d e r e d . It was p o s t u l a t e d , t h e r e f o r e , that this r e l a t i v e l y high e n e r g y b o u n d a r y would s e r v e a s an easy c r a c k propagation path so that i n t e r g r a n u l a r f r a c t u r e should be a n t i c i p a t e d in o r d e r e d a l l o y s . This postulate was shown to be in g e n e r a l a g r e e m e n t with e x p e r i m e n t a l observations.Z The q u e s t i o n now a r i s e s a s to whether the above a n a l y s i s also a p p l i e s to the o t h e r e x t r e m e in g r a i n b o u n d a r y type, n a m e l y , the p u r e twist b o u n d a r y . It will, t h e r e f o r e , be the p u r p o s e in what follows to develop a t h e o r e t i c a l m o d e l of twist b o u n d a r i e s in s u p e r lattices.
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TWIST BOUNDARY CONFIGURATIONS Fig. l(a) shows a p a r a l l e l a r r a y of s u p e r l a t t i c e s c r e w d i s l o c a t i o n s lying along the z a x i s . The a n t i p h a s e b o u n d a r y between the p a i r of o r d i n a r y d i s l o c a t i o n s with B u r g e r s v e c t o r b z c o m p r i s i n g the s u p e r l a t l i c e d i s l o c a t i o n is shown shaded. In e q u i l i b r i u m , the e x t e n s i o n of each s u p
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