Determination of dislocation density and stacking fault probability from X-ray powder pattern peak profiles

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An a n a l y s i s of X - r a y powder p a t t e r n peaks of p l a s t i c a l l y d e f o r m e d fcc m e t a l s and alloys allows the d e t e r m i n a t i o n of the s t a c k i n g fault p r o b a b i l i t y 5 and the d i s l o c a t i o n d e n s i t y p. The changes in p o s i t i o n of the peak m a x i m a a r e p r o d u c e d by r e s i d u a l o r applied s t r e s s e s a, by 5, and b y a r e d i s t r i b u t i o n of the alloying e l e m e n t s , w h e r e a s the b r o a d e n i n g of the peak p r o f i l e s r e s u l t s f r o m the r e d u c t i o n of the s i z e of the c o h e r e n t l y d i f f r a c t i n g d o m a i n s , f r o m the m i c r o s t a i n s r and f r o m 5 . Values of p a r e deduced from ~, and 5 is c o r r e l a t e d with the faulted a r e a in the cold worked c r y s t a l s , p / 5 is d i r e c t l y p r o p o r t i o n a l to the s t a c k i n g fault e n e r g y ),. E s t i m a t e s of the p r o p o r t i o n a l i t y c o n s t a n t a r e made which lead to v a l u e s of y c o n s i s t e n t with d i s l o c a t i o n node m e a s u r e m e n t s . P L A S T I C d e f o r m a t i o n of p o l y c r y s t a l l i n e m e t a l s o r a l loys p r o d u c e s s t r u c t u r a l c h a n g e s that influence m a n y p h y s i c a l p r o p e r t i e s of the m a t e r i a l , e.g., the d e f o r m i n g f o r c e s i n t r o d u c e lattice s t r e s s e s and g e n e r a t e d i s l o c a t i o n s and stacking faults. The final state depends on m a n y p a r a m e t e r s , such as c r y s t a l s t r u c t u r e , c h e m i c a l c o m p o s i t i o n , t h e r m a l h i s t o r y , and mode, extent, and r a t e of d e f o r m a t i o n , h~ X - r a y d i f f r a c t i o n t e c h n i q u e s p r o v i d e useful and s e n s i t i v e methods of e v a l u a t i n g n o n d e s t r u c t i v e l y the effect of p l a s t i c d e f o r m a t i o n on the m i c r o s t r u c t u r e of bulk m a t e r i a l s . The b r o a d e n i n g of powder p a t t e r n peaks 3'4 can be d i r e c t l y r e l a t e d to a r e d u c t i o n in the size of the c o h e r e n t l y diffracting d o m a i n s , to faulting on c e r t a i n (uvw) p l a n e s , and to s t r a i n s p r o d u c e d by d i s l o c a t i o n s within t h e s e d o m a i n s . Changes in the p o s i t i o n s of the powder p a t t e r n peaks can be c o r r e l a t e d with l a t t i c e s t r e s s e s in p o l y c r y s t a l l i n e s a m p l e s , 5-7 with s t a c k i n g or l a y e r faults 3'4's in the c a s e of fcc c r y s t a l s and with l a t t i c e p a r a m e t e r changes due to the p r e s e n c e of d i s l o c a t i o n s o r r e d i s t r i b u t i o n of the c h e m i c a l c o m p o n e n t s within this m a t e r i a l . 9 The l a t t i c e s t r a i n s might be the r e s u l t of applied o r r e s i d u a l s t r e s s e s in the d e f o r m e d m a t e r i a l . The d i s t r i b u t i o n of r e s i d u a l s t r e s s e s within the body can be quite c o m p l i c a t e d , and n