Computer generation and automatic plotting of perfect and twinned electron diffraction patterns for cubic crystal struct
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C. M. MAUCIONE, D. L. FORMENTI, AND L . A . HELDT SOLUTIONS of e l e c t r o n diffraction p a t t e r n s g e n e r a l l y r e q u i r e a knowledge of p l a n a r s e c t i o n s through r e c i p r o c a l space. Meakin z has w r i t t e n a digital computation p r o g r a m for g e n e r a t i n g and plotting such s e c t i o n s for nontwinned c r y s t a l s . T w i n n e d p a t t e r n s , however, r e quire a more complex analysis; i.e., perfect patterns u s u a l l y c o n s i s t of the zero o r d e r Laue zone of the p l a n e n o r m a l to the e l e c t r o n b e a m , w h e r e a s twinned p a t t e r n s c o n s i s t of two zero o r d e r Laue z o n e s , one (the twinned projection) g e n e r a t e d by a 180 deg r o t a tion about the twin a x i s . The a u t h o r s have p r o d u c e d a p r o g r a m which g e n e r a t e s and plots any r e c i p r o c a l lattice s e c t i o n in twinned o r nontwinned cubic c r y s t a l s . The p r o g r a m was w r i t t e n in F o r t r a n IV, level G, for u s e with an IBM 360 Model 44 computing s y s t e m and a Benson and L e h n e r p l o t t e r . C o n v e r s i o n of end options in r e a d s t a t e m e n t s , logical I F ' s , type s t a t e m e n t s and plotting r o u t i n e may be r e q u i r e d for other s y s t e m s . The p a r e n t p r o g r a m conrains s u b r o u t i n e s for d e t e r m i n a t i o n of the d i s t a n c e s b e t w e e n points lying on a plane and for plotting. If plotting c a p a b i l i t i e s a r e not a v a i l a b l e , the plotting s u b r o u t i n e a n d the c a l l s t a t e m e n t s to this r o u t i n e may be r e m o v e d from the p r o g r a m . The X and Y d i s t a n c e s needed for m a n u a l c o n s t r u c t i o n a r e then r e a d d i r e c t l y from the c a l c u l a t e d output. The r e q u i r e d inputs a r e m a t r i x s i z e (the b o u n d a r i e s put o n r e c i p r o c a l s p a c e ) , l a t t i c e p a r a m e t e r (A), c r y s tal s t r u c t u r e ( s i m p l e c u b i c , fcc, bcc, o r diamond cubic) and the c r y s t a l l o g r a p h i c d i r e c t i o n p a r a l l e l to the e l e c t r o n b e a m . The p r o g r a m g e n e r a t e s the r e c i p r o c a l l a t tice s e c t i o n (plane) n o r m a l to the e l e c t r o n b e a m . If a twinned p r o j e c t i o n is r e q u i r e d , M i l l e r i n d i c e s of the twin p l a n e a r e included. The p r o g r a m g e n e r a t e s a r e g i o n of indexed r e c i p r o cal lattice points, the spacing of which a r e p r o p o r t i o n a l to 1/19, w h e r e D is the i n t e r p l a n a r d i s t a n c e in r e a l space. The r e f l e c t i o n s having s t r u c t u r e f a c t o r s n o n z e r o a r e then s e l e c t e d . It is d e t e r m i n e d which of t h e s e r e f
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