Dislocation dynamics in niobium-oxygen
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[1]
w h e r e ~ is the m e a n v e l o c i t y of d i s l o c a t i o n s , 7-* is the effective s h e a r s t r e s s (the d i f f e r e n c e b e t w e e n the a p p l i e d s h e a r s t r e s s 7" and the a t h e r m a l s h e a r s t r e s s ru) and B is a c o n s t a n t . The s h e a r s t r a i n r a t e ~ is r e l a t e d to ~ and ~'* by 6 ~r
=pro b
Ivl
(_
exp \
kT
/j
[21
w h e r e P m i s the d e n s i t y of m o b i l e d i s l o c a t i o n s , b is the B u r g e r s v e c t o r , u i s the d i s l o c a t i o n a t t e m p t f r e q u e n c y , l is the length c o v e r e d by each s u c c e s s f u l d i s l o c a t i o n e x c u r s i o n , Z~G is the Gibbs free e n e r g y of a c t i v a t i o n , k is the B o l t z m a n n c o n s t a n t and T is the a b s o l u t e t e m p e r a t u r e . Thus m* can be evaluated (and i s g e n e r a l l y defined) a s
m*
l
]r
[3]
p r o v i d e d m* and P m a r e not functions of s t r e s s or s t r a i n r a t e . F u r t h e r m o r e , m* can be r e l a t e d to t h e r m a l l y a c t i v a t e d d e f o r m a t i o n p a r a m e t e r s , i . e . the a c t i v a t i o n enthalpy AH and the a c t i v a t i o n a r e a A* by r e l a t i o n s h i p s such a s 7 ra* k T = - \ 8---i-n-~-n~'*J T = T*bA*
[4]
Here AG = AH -- T AS w h e r e AS is the e n t r o p y of activation. K. V. RAVI, formerly Graduate Assistant, Divisionof Metallurgy and Materials Science, Case Western Reserve University, Cleveland, Ohio 44106, is now with Semiconductor Products Division,Central Research Laboratory, Motorola, Inc., Phoenix, Ariz. R. GIBALAis Associate Professor, Divisionof Metallurgyand Materials Science, Case Western Reserve University,Cleveland,Ohio. Manuscript submitted May 11, 1972. METALLURGICALTRANSACTIONS
T h e r e have been a l a r g e n u m b e r of s t u d i e s of the d i s l o c a t i o n d y n a m i c s of b o d y - c e n t e r e d cubic (bcc) m e t a l s , s'9 T h e s e s t u d i e s have a t t e m p t e d not only to c l a r i f y p r o b l e m s a s s o c i a t e d with the p h y s i c a l u n d e r s t a n d i n g of m* a s a m a t e r i a l s p a r a m e t e r but also to u n d e r s t a n d the r a t e c o n t r o l l i n g d e f o r m a t i o n m e c h a n i s m s at low t e m p e r a t u r e s T < 0.15Tin, w h e r e T m is the m e l t i n g t e m p e r a t u r e . In this l a t t e r a r e a t h e r e has b e e n a long and c o n t i n u i n g c o n t r o v e r s y c o n c e r n i n g w h e t h e r the high s t r e n g t h of bcc m a t e r i a l s at low t e m p e r a t u r e s is a l a t t i c e ( P e i e r l s - N a b a r r o ) h a r d e n i n g or h a r d e n i n g c a u s e d by r e s i d u a l i n t e r s t i t i a l impurities. 8 U n f o r t u n a t e l y , only in a few i n v e s t i g a t i o n s has the effect of i n t e r s t i t i a l additions on the d i s l o c a t i o n d y n a m i c s of high p u r i t y m a t e r i a l s been e x a m i n e d in a s y s t e m a t i c way. T u r n e r and V r e e l a n d 1~ have m e a s u r
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