On the observations of low angle boundaries in the field ion microscope
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p l an e of t h e b o u n d a r y is a p p r o x i m a t e l y 50 deg f r o m t he a x i s of m i s o r i e n t a t i o a and t h e b o u n d a r y is of t he m i x e d t y p e. A l s o , the B u r g e r s v e c t o r s of d i s l o c a t i o n s c o m p r i s i n g a tilt b o u n d a r y a r e n e c e s s a r i l y n o r m a l to the a x i s of m i s o r i e n t a t i o n . H e n c e , f o r t i l t b o u n d a r i e s w h e r e the m i s o r i e n t a t i o n is about [110], no s p i r a l s w i l l be s e e n on (110) p l a n e s s i n c e the p r o d u c t b 9 n m u s t eq u al z e r o . T h i s is o b v i o u s l y not the c a s e in F i g . 1, b e c a u s e s p i r a l s in (110) p l a n e s a r e p r e s e n t . Both t y p e s of o b s e r v a t i o n i m m e d i a t e l y p r e c l u d e the p r e s e n c e of e i t h e r a s i m p l e a r r a y of d i s l o c a t i o n s of one type o r an a r r a y of p a r a l l e l d i s l o c a t i o n s of two t y p e s , s i n c e t h e s e r e s u l t in t i l t b o u n d a r i e s . Th e p o s s i b i l i t y of an a r r a y of nonp~.rallel d i s l o c a t i o n s of two t y p e s c o m p r i s i n g the b o u n d a r y m a y be e x a m i n e d by u s e of F r a n k ' s e q u a t i o n , s w h i c h s t a t e s that: s = (~" •
2sinS/2
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On the Observations of Low Angle Boundaries in the Field Ion Microscope
w h e r e s is the s u m of the B u r g e r s v e c t o r s of t he d i s l o c a t i o n s w h i c h a r e i n t e r s e c t e d by an a r b i t r a r y v e c t o r r lying in the p l an e of the b o u n d a r y , u is the unit v e c t o r along t h e r o t a t i o n a x i s and 0 is the a n g l e of m i s o r i e n t a t i o n . By d e f i n i t i o n , s a l w a y s l i e s in the pl a ne d e fined by the r e s p e c t i v e B u r g e r s v e c t o r s bl and b2, and f r o m E q . [1] u m u s t a l w a y s be n o r m a l to the p l a ne d e fined by s ( h e n c e , by b~ and bz). T h e r e f o r e , f o r m i s o r i e n t a t i o n s about [110], w h e r e the b o u n d a r y is c o m p r i s e d of two t y p e s of n o n p a r a l l e l d i s l o c a t i o n s , both bl and b2 m u s t lie in the (110) plane and h a v e a z e r o dot p r o d u c t with the p l an e n o r m a l . C o n s e q u e n t l y , a s i t u a t i o n i d e n t i c a l f o r that of a t i l t b o u n d a r y e x i s t s in that no s p i r a l s w i l l be v i s i b l e on (110) p l a n e s . *
R. J . B A Y U Z I C K AND R. S. GOODRICH
*For a bcc structure, the only Burgersvectorssatisfyingthe criteriaare a/2 [] 11], a/2 [1~1], and a [001]. The visibilityof these dislocationsat other posi-
In m o s t i n s t a n c e s w h e r e the field ion m i c r o s c o p e is u s e d to o b s e r v e low a n g l e b o u n d a r i e s , the d i s l o c a t i o n s c o m p r i s i n g the b o u n d a r y , o r at l e a s t s o m e of t h e m , a r e not v i s i b l e . T h i s is r e a d i l y a c c o u n t e d f o r if we apply two b a s i c c r i t e r i a : we m u s t c o n s i d e r the
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