STUDY ON SPECTRUM OF DISLOCATION RELAXATION IN Nb

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STUDY ON SPECTRUM OF DISLOCATION RELAXATION IN Nb

S. Okuda, T. Motoyama, N. Kuramochi, T. Arai

To cite this version:

S. Okuda, T. Motoyama, N. Kuramochi, T. Arai. STUDY ON SPECTRUM OF DISLOCA- TION RELAXATION IN Nb. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-281-C10-284.

�10.1051/jphyscol:19851062�. �jpa-00225446�

STUDY ON SPECTRUM OF DISLOCATION RELAXATION IN Nb S. OKUDA, T. MOTOYAMA, N. KURAMOCHI AND T. ARAI I n s t i t u t e of Materials Science, U n i v e r s i t y of T s u k u b a ,

Sakura-mura, I b a r a k i 305, Japan

A b s t r a c t - The a 1 peak i n Nb was s t u d i e d by e l a s t i c a f t e r - e f f e c t and i n t e r n a l f r i c t i o n . R e l a x a t i o n spectrum a n a l y s i s u s i n g computer program SALS was made on t h e s e d a t a . The r e s u l t s show t h a t t h e a 1 peak i s composed of more t h a n t e n sub-peaks of n e a r l y s i n g l e r e l a x a t i o n w i t h T O = 10-14s.

I - INTRODUCTION

R e l a x a t i o n peaks a s s o c i a t e d w i t h d i s l o c a t i o n motion i n m e t a l s a r e known t o be much b r o a d e r i n w i d t h t h a n a s i n g l e r e l a x a t i o n p e a k / l / . For example, a w i d t h of t h e Bordoni peak i n Cu i s u s u a l l y more t h a n two t i m e s l a r g e r t h a n t h a t of s i n g l e r e l a x a - t i o n . S i n c e t h e P e i e r l s s t r e s s of d i s l o c a t i o n s can change w i t h d i s l o c a t i o n l i n e d i r e c t i o n s r e l a t i v e t o t h e i r B u r g e r ' s v e c t o r s , t h e d i s l o c a t i o n r e l a x a t i o n peak may b e composed of many sub-peaks. Thus, Thompson and Holmes/Z/ have s u c c e s s f u l l y d i v i d e d t h e Bordoni peak i n t o s e v e r a l component sub-peaks by a n a l y s i n g step-wise changes observed i n e l a s t i c modulus curve. On t h e o t h e r hand, i n deformed m e t a l s , t h e d i s l o - c a t i o n s a r e c o n s i d e r e d t o l i e i n v a r i o u s i n t e r n a l s t r e s s e s and a l s o t o have a v a r i e t y of l i n e l e n g t h . These f a c t o r s i n c r e a s e t h e b r o a d e n e s s of t h e r e l a x a t i o n peak and i n t h i s c a s e a c o n t i n u o u s d i s t r i b u t i o n i n t h e a c t i v a t i o n energy E a n d / o r p r e - e x p o n e n t i a l f a c t o r T O would b e expected f o r t h e peak. Whether t h e broadeness of t h e peak should be a t t r i b u t e d t o sub-peaks of almost s i n g l e r e l a x a t i o n o r t h e c o n t i n u o u s d i s t r i b u t i o n i n E a n d / o r

is s t i l l a m a t t e r of d i s p u t e . E x p e r i m e n t a l l y , i t was r a t h e r d i f f i c u l t t o d i s t i n g u i s h t h e s e f a c t o r s / l / .

T h i s i s a l s o t r u e f o r t h e a peak i n bcc m e t a l s which i s c o n s i d e r e d t o be a s s o c i - a t e d w i t h t h e k i n k d i f f u s i o n a l o n g screw d i s l o c a t i o n s ( t h e a 1 peak) and t h e k i n k p a i r f o r m a t i o n on non-screw d i s l o c a t i o n s ( t h e a2 p e a k ) / 3 , 4 / . The a 1 and a2 peaks a r e some t i m e s c a l l e d a s t h e a and a ' peaks, r e s p e c t i v e l y / 3 / . From a c l o s e i n s p e c t i o n of t h e e l a s t i c modulus c u r v e , t h e a 1 peak i n Ta i s suggestedtobecompossd~fseveral sub- p e a k s / 5 / . On t h e one hand, based on computer s i m u l a t i o n of d i s l o c a t i o n c o r e s t r u c - t u r e s i n bcc m e t a l s , Seeger and WiirthrichI61 have proposed t h a t t h e r e c o u l d b e s i x k i n d s of k i n k s t r u c t u r e s i n screw d i s l o c a t i o n s i n bcc, and s i m i l a r c a l c u l a t i o n s have been made i n d e t a i l by Duesberg/7/. On t h e o t h e r hand, Cost/8/ have r e c e n t l y developed a method of spectrum a n l y s i s f o r e l a s t i c a f t e r - e f f e c t ( E A E ) r e s p o n s e c u r v e s . T h e r e f o r e , it i s of i n t e r e s t t o o b s e r v e whether t h e al peak i s composed of many sub- peaks.

I n t h e p r e s e n t work, t h e a 1 peak i n Nb was s t u d i e d by means of EAE and i n t e r n a l f r i c t i o n ( 1 F ) . An a n a l y s i s of EAE r e a p o n s e c u r v e s was made u s i n g a computer program SALS ( S t a t i s t i c a l A n a l y s i s w i t h L e a s t Squares f i t t i n g ) / 9 / i n a s i m i l a r way a s t h a t of Cost181 and s p e c t r a of r e l a x a t i o n t i m e s of t h e a 1 peak were o b t a i n e d . P r e l i m i n a r y r e s u l t s have been g i v e n i n /lo/. F u r t h e r , a s i m i l a r a n a l y s i s was a l s o a p p l i e d t o I F c u r v e s .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851062

JOURNAL DE PHYSIQUE

I1 - EXPERIMENTAL

P o l y c r y s t a l l i n e w i r e of p u r e Nb of 0.5mm i n d i a m e t e r was c a r e f u l l y a n n e a l e d i n UHV and c o a t e d by Pd on t h e s u r f a c e . RRR of t h i s w i r e was %2500. T h i s w i r e was c u t i n t o specimens, deformed a t RT and f i n a l l y a n n e a l e d a t 150°C i n a i r t o remove r e s i - d u a l hydrogen/4/. EAE was measured i n t o r s i o n a l modello/ and I F , by f l e x u r a l v i b r a - t i o n a t %600Hz/4/.

R e l a x a t i o n c u r v e s of EAE were measured f o r b3600s a t v a r i o u s t e m p e r a t u r e s around t h e a peak, w i t h s t a r i n a m p l i t u d e 1x10-4 and spectrum a n a l y s i s of t h e s e c u r v e s were made by SALS. Following t h e a n a l y s i s method a f t e r C o s t / 8 / , a n e l a s t i c s t r a i n r e c o v e r e d a t t j ( i n s ) a f t e r t h e s t r e s s was removed c a n a p p r o x i m a t e l y b e e x p r e s s e d a s

where a d i s t r i b u t i o n i n r e l a x a t i o n t i m e T i s d i v i d e d i n t o e q u a l l y spaced b i n s of 1n.c ; Ai, t h e r e l a t i v e spectrum a m p l i t u d e i n t h e i - t h b i n ; m, t h e number of d a t a p o i n t s , and X o , t h e a d j u s t a b l e c o n s t a n t . S o l u t i o n s of e q . ( l ) f o r A i were o b t a i n e d by SALS and p r o v i d e d t h e d e s i r e d s p e c t r a of r e l a x a t i o n t i m e . I n t h e p r e s e n t experiments, r l = 8.5, T40" 3600s, n=40 and m=190.

For spectrum a n a l y s i s of I F c u r v e s / l l / , I F v a l u e a t t e m p e r a t u r e T; is g i v e n by

J

n

Q-'(T~) = i = 1 E A j w~~ / ( l + w 2 r i 2 ) st^^^ + ^BTj + ^y , ^{(j =} 1, m and n < m ) (2) where r i = r 0 exp ( Ei/kTj ) and r i s d i v i d e d i n t o n b i n s of e q u a l l y spaced a c t i v a t i o n e n e r g i e s E. w i s a n a n g u l a r f r e q u e n c y of v i b r a t i o n . The l a s t t h r e e t e r m s r e p r e s e n t a background component. Again, s o l u t i o n s of e q . ( 2 ) f o r A i o b t a i n e d by SALS p r o v i d e d t h e r e l a x a t i o n s p e c t r a . I n t h e p r e s e n t e x p e r i m e n t s , E .= (1+2i)meV, n = 8 0 and m = 220.

1

111 - RESULTS AND DISCUSSION

EAE measurements were made on t h e specimen deformed 8 % by t o r s i o n and a l s o a d d i - t i o n a l l y deformed 4%. An example of t h e r e s u l t s of t h e EAE spectrum a n a l y s i s i s shown i n F i g . l ( a ) . Here t h e spectrum component a t upper and lower T l i m i t s a r e n o t r e l i a b l e and should be abandoned. Comparison between t h e c a l c u l a t e d c u r v e u s i n g t h i s spectrum w i t h t h e e x p e r i m e n t a l c u r v e i s g i v e n i n F i g . l ( b ) and a n agreement i s s e e n t o be r e a s o n a b l y good. R e l a x a t i o n t i m e s ~ ' a t peaks i n t h e s e s p e c t r a o b t a i n e d a t e a c h s t e m p e r a t u r e a r e g i v e n i n t h e A r r h e n i u s p l o t i n F i g . 2 .

I F measurements were made on t h e specimen deformed 7% by bending. An example of

Relaxation time T in s Time in s

F i g . 1 - ( a ) R e l a x a t i o n s t r e n g t h h i s t o g r a m o b t a i n e d by spectrum a n a l y s i s of EAE r e l a x a t i o n c u r v e measured a t 25.6K f o r Nb deformed 8 + 4 % by t o r s i o n a t RT. Number shows t h e r e l a t i v e r e l a x a t i o n s t r e n g t h C A i f o r each sub-peak components.

(b) Comparison of t h e r e l a x a t i o n c u r v e c a l c u l a t e d i n ( a ) (smooth l i n e ) w i t h t h a t

observed e x p e r i m e n t a l l y ( j e r k y l i n e ) .

was o b t a i n e d from I F measured w i t h s t r a i n a m p l i t u d e € 0 " 1 . 1 ~ 1 0 - 6 , but t h e spectrum f o r

1 . 7 ~ 1 0 - ~ was found t o be almost t h e same. T h e r e f o r e , t h e spectrum i s n o t v e r y a m p l i t u d e dependent. These r e s u l t s show t h a t t h e a 1 peak i s composed of many sub-peaks which a r e n e a r l y of s i n g l e r e l a x a t i o n . The peak v a l u e s of E ' s i n F i g . 3 were c o n v e r t e d t o t h e v a l u e s of T assuming T O = 1x10-x4s and t h e s e

a r e a g a i n p l o t t e d i n Fig.2. T h i s v a l u e of T O was o b t a i n e d from t h e peak s h i f t of t h e a 1 peak a s a whole shown i n F i g . 2 , and i s i n agreement w i t h T O of sub-peaks determined from EAE s p e c t r a a s shown below.

I n F i g . 3 , t h e n u m e r i c a l f i g u r e i n d i c a t e d on e a c h p o i n t of EAE s p e c t r a shows a r e l a t i v e spectrum a m p l i t u d e C A i , examples of which a r e shown i n F i g . 1 ( a ) . ( P o i n t s w i t h o u t t h e f i g u r e s a r e s m a l l e r i n s t r e n g t h . ) T h i s C A i c o u l d b e used t o d e t e r m i n e t h e correspondence among v a r i o u s components of r e l a x a t i o n on t h e A r r h e n i u s p l o t s . With t h i s and o t h e r f a c t o r s i n mind, t h e most p r o b a b l e l i n e s through e a c h p o i n t of EAE s p e c t r a were drawn i n Fig.3. These l i n e s a r e s e e n t o be i n f a i r agreement w i t h components o b t a i n e d i n I F s p e c t r a . Some of t h e c o r r e s p o n d i n g component s e e n t o b e m i s s i n g , s i n c e t h e r e s o l u t i o n i n t h e IF s p e c t r a i s n o t a s good a s i n EAE,

F i n a l l y , t e m p e r a t u r e s of t h e s e sub-peaks would a l s o b e observed a s s m a l l d i p s i n t e m p e r a t u r e d e r i v a t i v e of e l a s t i c modulus (dE/E) /dT v s . temperaure i n I F measurements These a r e n o t s o a c c u r a t e a s t h o s e o b t a i n e d from SALS a n a l y s i s , b u t a r e shown i n Fig.2. Again, a f a i r l y good agreement i s s e e n .

I n c o n c l u s i o n , t h e spectrum a n a l y s i s of EAE and I F d a t a i n Nb showed t h a t t h e a 1 peak i n Nb is composed of many sub-peaks of n e a r l y s i n g l e r e l a x a t i o n . Even t h e number of sub-peaks w i t h f a i r l y l a r g e s t r e n g t h i n t e n which i s more t h a n t h e number of k i n k t y p e s expected from t h e p r e s e n t t h e o r y . The a v e r a g e r e l a x a t i o n p a r a m e t e r s of t h e a 1 peak i n Nb were o b t a i n e d a s T O = 1x10-14s and E x 80meV.

F i g . 2 - A r r h e n i u s p l o t s of v a r i o u s r e l a x a t i o n d a t a o b t a i n e d i n t h e p r e s e n t

experiments. P o i n t s i n t h e upper h a l f were o b t a i n e d from i n t e r n a l f r i c t i o n and

t h o s e i n lower h a l f were o b t a i n e d from EAE. See t e x t f o r d e t a i l .

JOURNAL DE PHYSIQUE

0

Activation energy (meV) 0 20 40 60 80 100

Temperature ( K )

(b)

F i g . 3 - (a) R l a x a t i o n s t r e n g t h h i s t o g r a m o b t a i n e d by .spectrum a n a l y s i s of t h e a 1 peak o b t a i n e d i n i n t e r n a l f r i c t i o n . The Nb specimen was deformed 7 % by bending a t RT .

(b) Comparison of t h e a 1 peak c a l c u l a t e d i n ( a ) (broken l i n e ) w i t h t h a t observed e x p e r i m e n t a l l y ( s o l i d l i n e ) . They a r e almost on t h e same c u r v e .

ACKNOWLEDGEMENT

The a u t h o r s would l i k e t o t h a n k P r o f . Y . Oyanagi f o r v a l u a b l e a d v i c e s i n computer c a l c u l a t i o n s and P r o f . H. Mizubayashi f o r d i s c u s s i o n .

REFERENCES

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/2/ D.O. Thompson and D.K. Holmes, J . Appl. Phys. 2 ( 1 9 5 9 ) , 525.

131 G. F a n t o z z i and I.G. R i t c h i e , J . P h y s i q u e 2 ( 1 9 8 1 ) , C5-3.

/ 4 / N. Kuramochi and S. Okuda, i n t h i s c o n f e r e n c e .

/5/ H. Mizubayashi and S. Okuda, phys. s t a t . s o l . ( a ) z ( 1 9 8 2 ) , 257.

161 A. Seeger and C. Wiithrich, Nuovo Cimento =(1976), 38.

/ 7 / M.S. Duesberg, Acta M e t a l l . =(1983), 1747, 1759.

/ 8 / J.R. C o s t , J. Appl. Phys. x ( 1 9 8 3 ) , 2137; Acta M e t a l l . =(1984),123.

/ 9 / T . Nakagawa and Y . Oyanagi, i n Recent Developments i n S t a t i s t i c a l I n f e r e n c e and Data A n a l y s i s , Ed. K. M a t u s i t a (North-Holland, 1980) p.221.

/ l o / S. Okuda, N. Kuramochi, T . Motoyama, T. A r a i and N. Matsumoto, i n D i s l o c a t i o n s

in S o l i d s , Ed. H. Suzuki, T. Ninomiya, K. Sumino and S. Takeuchi, (Univ. of Tokyo P r e s s , 1985) p.595.

1111 T. A r a i and S. Okuda, t o b e p u b l i s h e d .