A geometrical construction method of determining orientation of grain surfaces from (111) traces
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A Geometrical Construction Method of Determining Orientation of Grain Surfaces from {111}Traces H. S. FONG {111} t r a c e s o c c u r f r e q u e n t l y on s u r f a c e s of m e t a l g r a i n s of cubic l a t t i c e s t r u c t u r e a s twin b o u n d a r i e s , s l i p l i n e s , W l d m a n s t a t t e n s t r u c t u r e , and so forth, a n d s e r v e a s a r e a d y m e a n s of identifying the c r y s t a l l o g r a p h i c o r i e n t a t i o n of the g r a i n s u r f a c e s . This m a y be done b y c a l c u l a t i o n ( p r e f e r a b l y with c o m p u t e r s a s the m a t h e m a t i c a l e q u a t i o n s a r e complex) d e r i v e d f r o m the t r e a t m e n t of D r a z i n and Otte I o r of Fong; 2 o r r e f e r e n c e m a y b e m a d e to p r e v i o u s l y p r e p a r e d c h a r t s o r t a b l e s such a s t h o s e of T a k e u c h i , Honma, and l k e d a s and D r a z i n and Otte. 4 If c o m p u t e r s , c h a r t s , and t a b l e s a r e not a v a i l a b l e , one m a y adopt the m a n u a l g r a p h i c t e c h n i q u e s d e s c r i b e d b y B a r r e t t 5 and R e e d - H i l l and B a l d winfl Both t h e s e t e c h n i q u e s involve a t r i a l and e r r o r p r o c e d u r e and will not g e n e r a l l y be r e g a r d e d to be e a s y . In each s t e p of the t r i a l and e r r o r p r o c e s s , which c o n s i s t s of a r o t a t i o n of p o l e s about a Wulff net a x i s , a t t e n t i o n h a s to be p a i d to the d i s s i m i l a r m o v e m e n t s of f o u r p o l e s along g e n e r a l l y d i f f e r e n t l a t i t u d e l i n e s of the Wulff net. J u d g m e n t h a s s u b s e q u e n t l y to be m a d e a s to w h e t h e r each of t h e s e p o l e s h a s m o v e d to c e r t a i n c o r r e c t l o c a t i o n s . The p u r p o s e of t h i s p a p e r is to p r e s e n t a g e o m e t r i c a l c o n s t r u c t i o n m e t h o d which will be found l e s s taxing to a p p l y than the m e t h o d s d e s c r i b e d b y B a r r e t t and R e e d - H i l l and Baldwin. This p r o c e d u r e d e m a n d s in each step, a g a i n of a t r i a l and e r r o r p r o c e s s , only the r e a d i l y m a d e j u d g m e n t of w h e t h e r a H. S. FONG is Lecturer in the Faculty of Engineering, University o f Singapore, Singapore. Manuscript submitted August 28, 1973. METALLURGICAL TRANSACTIONS
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Fig. 1 - - T h e g r a i n s u r f a c e QRS w i t h t r a c e s QR, RS, and SQ p r o d u c e d by {111} p I a n e s RQT, SRT, a n d QST.
c e r t a i n e a s i l y i d e n t i f i e d length B A o is equal to a c e r taln length c o r not. T h r e e {111} t r a c e s of d i f f e r e n t d i r e c t i o n s on a g r a i n s u r f a c e m a y be i m a g i n e d to f o r m a t r i a n g l e QRS of s i d e s a, b, and c in length a s shown in F i g . 1, T h i s f i g u r e a l s o shows the {111} p l a n e s QST, S R T , and R Q T which have p r o d u c e d t h e s e t r a c e s . The o r i e n t a t i o n of the g r a i n s u r f a c e
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