Twinning in niobium, a continuous nucleation theory

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M E C H A N I C A L twinning is u s u a l l y d e s c r i b e d in t e r m s of p a r t i a l d i s l o c a t i o n m o v e m e n t , s i n c e it i s t h e o r e t i c a l l y i m p o s s i b l e f o r whole c r y s t a l l a t t i c e p l a n e s to s p o n t a n e o u s l y twin at the o b s e r v e d twinning s t r e s s e s .1,2 A m o n g c u r r e n t t h e o r i e s f o r e x a m p l e , V e n a b l e s 3'4 p r o p o s e d a m e c h a n i s m f o r fcc m e t a l s in which one p a r t i a l d i s l o c a t i o n r o t a t e s about a n o t h e r to p r o d u c e a twin with the o b s e r v e d l e n t i c u l a r s h a p e . S l e e s w y k S'6 described a very elegant mechanism for bcc metals, in which c o m b i n e d p a r t i a l d i s l o c a t i o n m o v e m e n t allowed a twin to be e a s i l y a c c o m m o d a t e d in the m a t r i x . T h i s a l s o a c c o u n t e d for the e x p e r i m e n t a l l y o b s e r v e d s l i p s o m e t i m e s found p r e c e d i n g a twin in the twinning p l a n e . U n f o r t u n a t e l y t h e s e and s i m i l a r d i s l o c a t i o n t h e o r i e s do not account f o r the fact that s t r e s s induced twins m o v e with a v e l o c i t y c o m p a r a b l e with the s p e e d of sound in the m e t a l 7 F o r c o m p a r i s o n , d i s l o c a t i o n v e l o c i t i e s for s l i p in n i o b i u m , d e d u c e d f r o m an e t c h - p i t t e c h n i q u e , 8 l i e b e t w e e n 2 • 10 -v and 3 • 10-2 c m / s . T h e s e v e l o c i t i e s a r e a f a c t o r of 107 s l o w e r than the s p e e d of sound. E v e n though the e t c h - p i t m e a s u r e m e n t s l e a d to a v e r a g e d i s l o c a t i o n v e l o c i t i e s , and s o m e m a y m o v e f a s t e r than 3 • 10 -2 cm//s, t h e r e i s c l e a r l y a s i g n i f i c a n t d i f f e r e n c e in the c h a r a c t e r i s t i c s of s l i p d i s l o c a t i o n s and p a r t i a l d i s l o c a t i o n s which f o r m a twin-matrix interface. It i s t h e r e f o r e r e a s o n a b l e to q u e s t i o n the v a l i d i t y of d i s l o c a t i o n t h e o r i e s f o r m a c r o s c o p i c twinning and e x p l o r e the p o s s i b i l i t y of a l t e r n a t i v e m e c h a n i s m s . I n d e e d , Venables,~ in d i s c u s s i n g t h i s p r o b l e m , s t a t e s that " T h e f o r m a t i o n of m a c r o s c o p i c twins m u s t be p r o d u c e d by q u a s i - s i m u l t a n e o u s n u c l e a t i o n of m a n y m i c r o s c o p i c t w i n s . H e n c e , the m a c r o s c o p i c twins m a y a p p e a r to f o r m f a s t e r than the m e c h a n i c s of a s i n g l e pole m e c h a n i s m would a l l o w . " P r o b a b l y the s a m e c o m m e n t should be e x t e n d e d to m a c r o s c o p i c twin f o r m a t i o n in b c c m e t a l s . The a p p r o a c h u s e d for the p r e s e n t study was to e v a l u a t e the e n e r g y r e q u i r e d to f o r m a c o m p l e t e twin and c o m p a r e t h i s with e s t i m a t e s f o r the t w i n -