High temperature elastic properties of polycrystalline niobium, tantalum, and vanadium
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T h e s e m e a s u r e m e n t s have now b e e n m a d e and a r e r e p o r t e d in t h i s w o r k .
1. INTRODUCTION
IN
r e c e n t work, 1 the t e m p e r a t u r e d e p e n d e n c e of the Y o u n g ' s modulus of p u r e n i c k e l , p l a t i n u m , and m o l y b d e n u m has b e e n m e a s u r e d up to ~1250 K using a p u l s e - e c h o technique involving a high t e m p e r a t u r e wave g u i d e . T h e m o t i v a t i o n for t h o s e m e a s u r e m e n t s w a s b a s e d upon d e p a r t u r e s f r o m l i n e a r i t y in the A r r h e n i u s p l o t s of the d i f f u s i v i t y D of i n t e r s t i t i a l a t o m s , C and N, in m o l y b d e n u m . K i m u r a and Y o s h i o k a 2 have a s c r i b e d the p o s i t i v e d e v i a t i o n f r o m l i n e a r i t y in the A r r h e n i u s plot for the d i f f u s i v i t y of C in Mo to a s i n g l e s t a g e m e c h a n i s m in which the m e t a l l a t t i c e s o f t e n s at high t e m p e r a t u r e s l e a d i n g to a d e c r e a s e in the a c t i v a t i o n e n e r g y f o r the diffusion of the i n t e r s t i t i a l s p e c i e s . It is e a s y to show that the s h e a r modulus m u s t d e c r e a s e in a nonlinear m a n n e r a s the t e m p e r a t u r e i n c r e a s e s in o r d e r f o r t h i s m o d e l to be a p o s s i b l e e x p l a n a t i o n f o r the o b s e r v e d diffusion b e h a v i o r f l T h e m e a s u r e m e n t s of K S s t e r 4 in Mo do indeed show a f a s t e r than l i n e a r d e c r e a s e of the s h e a r modulus with t e m p e r a t u r e . H o w e v e r the m o r e r e c e n t d a t a on Mo show a linea~" d e c r e a s e of the Young's modulus and s h e a r modulus with t e m p e r a t u r e in the r a n g e 300 to 1250 K. 1 The m o t i v a t i o n for the p r e s e n t s e t of e l a s t i c m e a s u r e m e n t s l i e s in s o m e r e c e n t findings c o n c e r n i n g the d i f f u s i v i t y of i n t e r s t i t i a l a t o m s in the G r o u p V e l e m e n t s at high t e m p e r a t u r e s . T h e e x p e r i m e n t a l findings have b e e n s u m m a r i z e d r e c e n t l y . 5 Stated b r i e f l y , the e x p e r i m e n t a l e v i d e n c e f r o m both m a s s - f l o w and anelastic measurements for a positive deviation from t h e A r r h e n i u s plot of In D vs 1/T i s c l e a r in t h e c a s e of O - N b , O - T a , and C - N b and t h e r e is s o m e i n d i c a t i o n of the s a m e b e h a v i o r in N - T a . 5 Now p r e l i m i n a r y s t u d i e s in the t e m p e r a t u r e r a n g e 300 to 1270 K f o r T a and Nb, and in the t e m p e r a t u r e r a n g e 300 to 1050 K for V have not r e v e a l e d any d e p a r t u r e f r o m l i n e a r i t y in the t e m p e r a t u r e d e p e n d e n c e of the e l a s t i c c o n s t a n t s . H o w e v e r the a n o m a l i e s found o c c u r o v e r h i g h e r t e m p e r a t u r e r a n g e s . While the l a t t i c e softening m o d e l i s doubtful v a l i d i t y for o t h e r r e a
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