On the use of single surface trace analysis
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On the Use of Single Surface Trace Analysis K.H.
ECKELMEYER
TRACEa n a l y s i s
i s f r e q u e n t l y u s e d in m e t a l l u r g i c a l i n v e s t i g a t i o n s to d e t e r m i n e t h e c o m p o s i t i o n p l a n e s of features such as slip lines, twins, precipitate particles, and m a r t e n s i t e p l a t e s . T w o s u r f a c e t r a c e a n a l y s i s i s e m p l o y e d w h e r e v e r p o s s i b l e b e c a u s e it y i e l d s a n u n ambiguous result for each measurement that is made. S o m e t i m e s , h o w e v e r , it i s e x p e r i m e n t a l l y i m p r a c t i c a l t o u s e a two s u r f a c e t e c h n i q u e . Such s i t u a t i o n s a r i s e either when the featuges being examined are too small to b e c l e a r l y r e s o l v e d on a d j a c e n t s u r f a c e s , o r w h e n t h e s p e c i m e n g e o m e t r y i s p r o h i b i t i v e , a s in t r a n s m i s s i o n e l e c t ~ o n m i c r o s c o p y . In s u c h c a s e s t h e d e s i r e d i n f o r m a t i o n can o f t e n b e o b t a i n e d u s i n g a s i n g l e s u r f a c e trace analysis.* *Techniquesof one and two surface trace analysisare reviewedin reference 1. A s e r i o u s s h o r t c o m i n g of a l l s i n g l e s u r f a c e t e c h n i q u e s i s t h a t t h e i n v e s t i g a t o r c a n n o t prove t h a t t h e s o l u t i o n he o b t a i n s i s t h e o n e a n d o n l y c o r r e c t s o l u t i o n . S i n c e e a c h m e a s u r e m e n t d o e s not g i v e an u n a m b i g u o u s r e s u l t , h e c a n only s a y t h a t h i s s o l u t i o n i s consistent w i t h a l l of t h e m e a s u r e m e n t s . * T h e q u e s t i o n of w h e t h e r *The pole-locusmethod2 is superior in that it allowsthe investigatorto state that no other solution appears to be consistent with the data. Since consistency depends on the arbitrarily established lirmt of acceptable error, however, the polelocus technique does not fundamentallyprove that no other solution is consistent, but rather indicateswtuch solution has the highestdegreeof consistency. this and/or other solutions are consistent, however, is s t r o n g l y d e p e n d e n t on t h e l i m i t of a c c e p t a b l e e r r o r , w h i c h i s a r b i t r a r i l y e s t a b l i s h e d by t h e i n v e s t i g a t o r . In v i e w of t h i s u n c e r t a i n t y it w o u l d b e v e r y h e l p f u l if s o m e m e a s u r e of s t a t i s t i c a l s i g n i f i c a n c e c o u l d b e a t t a c h e d to s o l u t i o n s o b t a i n e d by s i n g l e s u r f a c e t e c h n i q u e s . T h i s n o t e o u t l i n e s a m e t h o d by w h i c h t h i s c a n be done. In s i n g l e s u r f a c e t r a c e a n a l y s i s an i n d i v i d u a l t r a c e n o r m a l i s Said to b e c o n s i s t e n t w i t h t h e h y p o t h e s i s t h a t t h e c o m p o s i t i o n p l a n e i s of t h e f o r m {hkl} if t h e t r a c e K. H. ECKELMEYER is Staff Member, Sandia Laboratories, Albuquerque, N. Mex. Manuscript submitted Sep
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