Correlation of proton patterns with crystal parameters
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atom s c a t t e r i n g f a c t o r s for e l e c t r o n d i f f r a c t i o n , and taking the s u m of all F 2 v a l u e s after m u l t i p l y i n g each by a r e a s o n a b l e t e m p e r a t u r e f a c t o r . 2,s It was pointed out that an i n t e n s i t y , Icalc, computed in this a r b i t r a r y way is by no m e a n s a valid computation of t r u e i n t e n s i t i e s , but a l l t e s t s made thus far indicate that it s e e m s to provide a c o n v e n i e n t and useful a p p r o x i m a tion to r i g o r o u s c a l c u l a t i o n s . We now propose that these c o m p u t a t i o n s provide a method for obtaining an a p p r o x i m a t e value of the atom position p a r a m e t e r of a o n e - p a r a m e t e r c r y s t a l , using v i s u a l e s t i m a t e s of the r e l a t i v e i n t e n s i t i e s of l i n e s on a film. In t e s t s of the method, the i n t e g r a t e d i n t e n s i t y dip for each line on a film was e s t i m a t e d by c o m p a r i n g it v i s u a l l y with an optically c a l i b r a t e d s c a l e , 4 choosing s e g m e n t s of each line that a r e r e m o v e d from i n t e r s e c t i n g l i n e s and in a r e a s of equal b a c k g r o u n d i n t e n s i t y w h e n e v e r p o s s i b l e . The p a t t e r n s were made with a c o l l i m a t e d b e a m of 100 key p r o t o n s s t r i k i n g clean c r y s t a l s u r f a c e s in n o n e h a n n e l i n g d i r e c t i o n s and s c a t t e r i n g to Kodak NTA f i l m s . In the case of a c r y s t a l of m a g n e t i t e , p r i n t s ( e n l a r g e m e n t s ) of the proton f i l m s were studied and only the s i m p l e s t o b s e r v a t i o n s of line i n t e n s i t i e s were used (equalities o r n e a r e q u a l i ties) b e c a u s e m o r e q u a n t i t a t i v e m e a s u r e s of i n t e n s i t i e s could add nothing to the solution proposed. MAGNETITE Back s c a t t e r i n g proton p a t t e r n s , 100 key, showed l i n e s of the following r e l a t i v e s t r e n g t h s , a sequence that was i d e n t i c a l in three p a t t e r n s of three different o r i e n t a t i o n s of the FesO4 c r y s t a l , which was a n a t u r a l c r y s t a l from Switzerland: (110) VS; (111) S; (100) M; (211), (210), (311), (310), (511) W[--These o b s e r v a t ~ - n s were c o m p a r e d with computed v a l u e s , Icalc, in which the t e m p e r a t u r e f a c t o r exponent was taken as for X - r a y diffraction, B = 0.49. Magnetite has a cubic s t r u c t u r e , Fd3m, 8 f o r m u l a units p e r unit cell of ao = 8.394, the i r o n in positions 8a and 16d and the oxygen in positions 32e with the p a r a m e t e r u = 0.2548. s The a t o m i c s c a t t e r i n g a m p l i t u d e s used for i r o n and oxygen were the s e l f - c o n s i s t e n t field v a l u e s for e l e c t r o n diffraction l i s t e d in the I n t e r n a t i o n a l T a b l e s for X - r a y C r y s t a l l o g r a p h y ; there was no a t t e m p t to diff e r e n t i a t e b e t w e e n Fe ~*+and
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