Short range order structure in a copper 16 atomic percent aluminum alloy
- PDF / 1,082,602 Bytes
- 8 Pages / 612 x 783.28 pts Page_size
- 57 Downloads / 200 Views
T H E diffuse s c a t t e r i n g of X - r a y s p r o v i d e s the p r i m a r y s o u r c e of s t r u c t u r a l i n f o r m a t i o n of s o l i d s o l u t i o n s . One m a y obtain i n f o r m a t i o n about the n o n r a n d o m n e s s and about the f a i l u r e of the a t o m s to s i t p r e c i s e l y on the lattice sites. The c o h e r e n t diffuse i n t e n s i t y is c o m p o s e d of t h r e e t e r m s , that due to the n o n r a n d o m n e s s , i.e., s h o r t r a n g e o r d e r (SRO), that due to the a t o m i c d i s p l a c e m e n t and that due to the s q u a r e of the d i s p l a c e m e n t s . T h e r e a r e h i g h e r t e r m s in the i n t e n s i t y e x p a n s i o n so the o b s e r v a t i o n s should b e r e s t r i c t e d to the r e g i o n w h e r e only the f i r s t t h r e e c o m p o n e n t s a r e i m p o r t a n t . T h e r m a l motion, which g i v e s r i s e to t h e r m a l diffuse s c a t t e r i n g (TDS), h a s a z e r o t i m e a v e r a g e and cannot c o n t r i b u t e to the f i r s t o r d e r d i s p l a c e m e n t t e r m s but is the p r i n c i p l e c o n t r i b u t i o n to the q u a d r a t i c t e r m . B o r i e 1 o r i g i n a l l y showed how it is p o s s i b l e to s e p a r a t e the SRO i n t e n s i t y f r o m the f i r s t o r d e r d i s p l a c e m e n t i n t e n s i t y a s a r e s u l t of the d i f f e r e n c e in s y m m e t r y , and s u b s e q u e n t l y B o r i e and S p a r k s 2 showed how one can s i m i l a r l y s e p a r a t e a l l t h r e e c o n t r i b u t i o n s . This was an i m p o r t a n t a d v a n c e s i n c e one did not then have to m a k e a t e m p e r a t u r e e x t r a p o l a t i o n to e l i m i n a t e the TDS. Having done the s e p a r a t i o n , one o b t a i n s the parameters from a Fourier analysis. As the i n t e n s i t y is a l i n e a r c o m b i n a t i o n of the p a r a m e t e r s which r e p r e s e n t t h e s e t e r m s , it is a l s o p o s s i b l e to a p p l y s t a n d a r d s t a t i s t i c a l t e c h n i q u e s to o b t a i n the n u m e r i c a l solution. A c o m p u t e r p r o g r a m h a s b e e n w r i t t e n to c a r r y out such a s o l u t i o n and is d o c u m e n t e d e l s e w h e r e , s The a d v a n t a g e s of u s i n g a m u l t i p l e r e g r e s s i o n s o l u t i o n i n s t e a d of the s e p a r a t i o n t e c h n i q u e a r e t h a t a) the o b s e r v a t i o n s m a y b e m a d e in an a r b i t r a r y m a n n e r in a s m a l l e r v o l u m e in r e c i p r o c a l s p a c e , b) no a p p r o x i m a t i o n s c o n c e r n i n g the s t r u c t u r e f a c t o r s a r e r e q u i r e d , c) the o b s e r v a t i o n s a r e w e i g h t e d to r e f l e c t t h e i r v a r y i n g p r e c i s i o n , d) c o n s t r a i n t s can b e i n c o r p o r a t e d to i m p r o v e the q u a l i t y of the solution, and e) p a r a m e t e r e r r o r s and t h e i r c o r r e l a t i o n a r e obtained. In both t h e s e t y p e s
Data Loading...
