A computer technique for the solution of laue back reflection patterns of cubic crystals. Part I
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CHRISTENSEN, AND R . J .
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A computer a l g o r i t h m has been developed for the rapid solution of Laue back r e f l e c t i o n patt e r n s of cubic s t r u c t u r e s . Reflections of planes having indices (333) and lower a r e indexed d i r e c t l y without the use of s p e c i a l c h a r t s , nets o r t a b l e s . The c o m p u t a t i o n a l s c h e m e c o m p a r e s the angles a s s o c i a t e d with r e f l e c t i o n s from the X - r a y p a t t e r n s and the t r u e i n t e r p l a n a r angles which a r e calculated by the p r o g r a m . Any f i l m - t o - s p e c i m e n d i s t a n c e may be used and the s y s t e m a t i c e r r o r s a s s o c i a t e d with m e a s u r e m e n t of this d i s t a n c e a r e m i n i m i z e d to determine the best value.
T H E routine for indexing Laue back r e f l e c t i o n patt e r n s can be tedious and expensive. Even an o p e r a t o r skilled in the use of the Wulff and G r e n i n g e r nets and the s t e r e o g r a p h i c p r o i e c t i o n often r e q u i r e s c o n s i d e r able time and e x p e r i e n c e b e f o r e difficult p a t t e r n s can be solved. The p r e s e n t paper d e s c r i b e s an a l g o r i t h m capable of a s s i g n i n g i n d i c e s to the r e f l e c t i o n s on Laue back r e f l e c t i o n p a t t e r n s of cubic c r y s t a l s . The prog r a m based upon the a l g o r i t h m is s u i t a b l e for t i m e s h a r e d , o r batch p r o c e s s i n g c o m p u t e r s . A totally u n skilled o p e r a t o r can a c c o m p l i s h the e n t i r e p r o c e d u r e and a r r i v e at the solution within a few m i n u t e s . The a l g o r i t h m d u p l i c a t e s the t r a d i t i o n a l technique of matching the angles between p r o m i n e n t r e f l e c t i o n s on the film with the true values of i n t e r p l a n a r a n g l e s . The p r o g r a m seeks a solution by a s s i g n i n g t r i a l indices to a pair of r e f l e c t i o n s , g e n e r a t i n g a function of the t r u e i n t e r p l a n a r angle and c o m p a r i n g it with its c o u n t e r p a r t from the X - r a y p a t t e r n . As a c c e p t a b l e indices a r e d e veloped, additional r e f l e c t i o n s and t h e i r a n g l e s a r e admitted to the s e a r c h . T r i a l indices up to (333) a r e considered. U n c e r t a i n t i e s r e s u l t i n g from the spot size on the Xray film and tilting of the film plane a r e a c c o m m o d a t e d by p e r m i t t i n g e x p e r i m e n t a l a n g l e s within a s m a l l r a n g e , E , of the t r u e i n t e r p t a n a r angle to be accepted a s a match. E , which is typically +2 deg, may be s p e cified as p r o g r a m input. The s y s t e m a t i c e r r o r r e s u l t ing from i n a c c u r a c i e s in d e t e r m i n i n g the f i l m - t o - s p e c imen dista,lce is a d j u s t e d by the p r o g r a m and the best e s t i m a t e for this d i s t a n c e is p r i n t e d out. The p r o g r a m does not r e q u i r e that a p a r t i c
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