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THE ν PEAK IN DEFORMED HIGH-PURITY α-IRON STUDIED BY FORCED VIBRATIONS OUT
OF RESONANCE
H. Mizubayashi, H. Kronmüller, A. Seeger
To cite this version:
H. Mizubayashi, H. Kronmüller, A. Seeger. THE ν PEAK IN DEFORMED HIGH-PURITY α-IRON
STUDIED BY FORCED VIBRATIONS OUT OF RESONANCE. Journal de Physique Colloques,
1985, 46 (C10), pp.C10-309-C10-312. �10.1051/jphyscol:19851069�. �jpa-00225454�
THE v PEAK IN DEFORMED HIGH-PURITY a-IRON STUDIED BY FORCED VIBRATIONS OUT OF RESONANCE
M a x - P l a n c k - I n s t i t u t fiir M e t a l l f o r s c h u n g ,
I n s t i t u t
f i i r P h y s i k , 7000S t u t t g a r t
80, F . R . G .A b s t r a c t
-
The y peak i n h i g h - p u r i t y a - i r o n was i n v e s t i g a t e d u s i n g f r e q u e n c i e s o v e r t h r e e d e c a d e s , i.e. 7.4H2, O.Ol5Hz and 0.007Hz. For 7.4H2, t h e u s u a l r e s o n a n t v i b r a t i o n mode was u s e d and f o r 0.015 o r 0.007Hz, t h e f o r c e d v i b r a t i o n mode was a p p l i e d . The observed v a l u e s of t h e e n t h a l p y , H, and of t h e p r e - e x p o n e n t i a l f a c t o r , l / r o , of t h e y peak b o t h showed t h e tendency of i n c r e a s e w i t h a n n e a l i n g a f t e r t h e low t e m p e r a t u r e s m a l l d e f o r m a t i o n , i . e . from 0.825eV and 4 . 0 ~ 1 0 ~ 3 ~ - 1 t o 0.910eV and 1 . 2 ~ 1 0 ~ 5 ~ - 1 , r e s p e c t i v e l y . From t h e a m p l i t u d e dependence, 2Hk was e s t i m a t e d a s about 0.940eV, where Hk d e n o t e s t h e e n t h a l p y of a n i s o l a t e d s i n g l e k i n k i n s c r e w - d i s l o c a t i o n s i n a - i r o n .I - INTRODUCTION
I n deformed h i g h - p u r i t y bcc m e t a l s , t h e s o - c a l l e d a ( a l ) and t h e y peaks a r e commonly observed and a r e b e l i e v e d t o b e a s s o c i a t e d w i t h i n t r i n s i c motions of d i s l o - c a t i o n s ( s e e r e v i e w s / l , 2 / and a l s o 1 3 1 ) . Among them t h e y peak i s c o n s i d e r e d t o b e t h e r e l a x a t i o n p r o c e s s of screw d i s l o c a t i o n s t h r o u g h k i n k p a i r formation(KPF)/4/.
However, t h e p r e s e n t knowledge of t h e a c t i v a t i o n p a r a m e t e r s , t h e a c t i v a t i o n e n t h a l p y , H, and t h e p r e - e x p o n e n t i a l f a c t o r , l / r o , of t h e y peak o r of KPF i s v e r y l i m i t e d y e t . The aim of t h e p r e s e n t work i s t o i n v e s t i g a t e t h e s e a c t i v a t i o n p a r a m e t e r s of t h e y peak i n deformed h i g h - p u r i t y a - i r o n .
I n deformed h i g h - p u r i t y a - i r o n , Shimada and Sakamoto/5/ observed t h e y peak a t a b o u t 340K(%lHz) and o b t a i n e d 0.7810.leV f o r H and l 0 ~ ( l / ~ ~ ) = 1 2 . 4 * 1 . 5 ( l / r ~ i n s - l ) . The peak t e m p e r a t u r e , Tp, of t h e y peak r e p o r t e d i n l i t e r a t u r e s , however, shows a s t r o n g dependence on t h e a u t h o r s o r on t h e e x p e r i m e n t a l c o n d i t i o n s u s e d , e.g. a t a b o u t 300K(0.5Hz) by H i v e r t e t a 1 . / 6 / and a t a b o u t 290K(%2Hz) by M a t s u i and S c h u l t z / 7 / . These r e s u l t s s u g g e s t t h a t t h e v a l u e s of H and of
1 1 ~ ~
themselves may depend on t h e e x p e r i m e n t a l c o n d i t i o n s u s e d a s was a l s o s u g g e s t e d by t h e o r e t i c a l s t u d i e s / 8 , 9 / .An i n v e s t i g a t i o n c o v e r i n g wider f r e q u e n c y r a n g e g i v e s more p r e c i s e v a l u e s of H and of l / r 0 . F o r t h e r e l a x a t i o n p r o c e s s e s of d i s l o c a t i o n s , however, a change of f r e q u e n c i e s s h o u l d b e made w i t h o u t any h a n d l i n g e f f e c t s on a specimen. For s u c h a n i n v e s t i g a t i o n , a method u s i n g f o r c e d v i b r a t i o n s o u t of r e s o n a n c e / l O , l l / may b e s u i t - a b l e , which i t s e l f c a n c o v e r a v e r y wide f r e q u e n c y r a n g e , p r a c t i c a l l y 1% 1 0 - ~ ~ z / l l / . I n t h e p r e s e n t work, a h y b r i d measurement u s i n g b o t h t h e r e s o n a n t v i b r a t i o n a t about
' p e r m a n e n t a d d r e s s : I n s t i t u t e of Materials S c i e n c e , U n i v e r s i t y
of
T s u k u b a , S a k u r a - m u r a , I b a r a k i 305, Japan
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851069
C10-310 JOURNAL
DE PHYSIQUE
10Hz (R-mode) and t h e f o r c e d v i b r a t i o n s a t t h e o r d e r o f
10-L HZ
(F-mode) was performed.Using t h e p r e s e n t method one c a n i n v e s t i g a t e a r e l a x a t i o n p r o c e s s o v e r f r e q u e n c i e s o f 3 d e c a d e s w i t h o u t any h a n d l i n g e f f e c t s and a l s o i n r e a s o n a b l e measuring t i m e s . I1 - EXPERIMENTAL PROCEDURES
The specimen u s e d was a p o l y c r y s t a l l i n e w i r e of a - i r o n w i t h RRR=3800. The s i z e was 0.9mm$x32mm. B e f o r e i n t e r n a l f r i c t i o n ( 1 F ) measurements, t h e specimen w a s d e f o m e d by 2.0% i n t e n s i o n a t room t e m p e r a t u r e s ( R T ) . Then, a s m a l l d e f o r m a t i o n by 0.1% i n t o r s i o n a t 80K and warming up t o %420K were performed two t i m e s s u c c e s s i v e l y i n o r d e r t o o b t a i n a good r e p r o d u c i b i l i t y of t h e y peak/12/. I n t h e f o l l o w i n g s , t h i s specimen, t h e specimen
A
pre-deformed by2.0%
a t RT, w i l l b e c a l l e d a se.
IF-measurements were performed by an i n v e r t e d t o r s i o n pendulum u s i n g R-mode a t 7.4Hz and a l s o F-mode a t 0.015, 0.007 o r 0.006Hz. I F was d e t e r m i n e d from f r e e decay c u r v e s i n R-mode and from l a g a n g l e s between t h e v i b r a t i o n s of t h e a p p l i e d f o r c e and of t h e pendulum i n F-mode. The s t r a i n a m p l i t u d e , €0, u s e d was 7x10-6 b u t f o r a n amp- l i t u d e dependence, 28x10-6 was a l s o used. During t h e IF-measurements, t h e specimen was s u b j e c t e d t o a n a x i a l m a g n e t i c f i e l d o f 1 5 0 0 e .
It h a s been r e p o r t e d 1 5 1 t h a t t h e y peak i n h i g h - p u r i t y a - i r o n i s observed w i t h a peak h e i g h t , Q - l p , of a b o u t 4x10-3 immediately a f t e r a low t e m p e r a t u r e s m a l l deforma- t i o n , s a y t h e ' v i r g i n f y peak, b u t w i t h a much d e c r e a s e d Q - l p a f t e r warming up t o s400K d u e t o r e c o v e r y a n d / o r p i n n i n g phenomena, s a y t h e ' a n n e a l e d ' y peak. I n t h e p r e s e n t work, b o t h t h e ' v i r g i n 1 and t h e ' a n n e a l e d ' y p e a k s were i n v e s t i g a t e d .
The measuring c o n d i t i o n s f o r t h e ' v i r g i n ' y peak were a s f o l l o w s : ( 1 ) The s p e c i - men, A20, was deformed by 0.05% i n t o r s i o n a t 80K(in t h e f o l l o w i n g s , 0.05%(80K)) and t h e n , (2) a warming up measurement was performed up t o a b o u t 420K. These p r o c e d u r e s were r e p e a t e d l y performed f o r v a r i o u s f r e q u e n c i e s . F o r t h e ' a n n e a l e d ' y peak, a f t e r (21, t h e r e p e a t e d measurements between 80K and 390K b u t w i t h o u t 0.05%(80K) were made f o r v a r i o u s f r e q u e n c i e s . A20 was f i r s t l y s u b j e c t e d t o t h e i n v e s t i g a t i o n o f t h e
' v i r g i n ' y peak w i t h ~ ~ = 7 x 1 0 - 6 . These measuring r u n s w i l l b e c a l l e d a s A2O-1 and s o on. A f t e r A20-1, t h e specimen was once warmed up t o 500K and t h e n , t h e ' v i r g i n ' y peak was a g a i n i n v e s t i g a t e d w i t h ~ ~ = 7 x 1 0 - ~ , i . e . A20-2. Following A20-2, t h e 'an- n e a l e d ' y peak was i n v e s t i g a t e d w i t h t h e same € 0 , i . e . A20-2a. The s i m i l a r i n v e s t i - g a t i o n s a s were made i n A20-2 and A20-2a w e r e a l s o performed b u t w i t h t h e i n c r e a s e d EO of 28x10-6, i . e . A20-3 and A20-3a, r e s p e c t i v e l y . A f t e r A20-3a, €0 was d e c r e a s e d t o 7x10-6 and t h e i n v e s t i g a t i o n of t h e ' a n n e a l e d ' y peak was c o n t i n u e d , i . e . A20-3b.
I11
-
EXPERIMENT& RESULTS AND DISCUSSIONF i g . l ( a ) and ( b ) show examples of t h e r e s u l t s observed a t 7.4Hz and 0.015Hz f o r A20-1, r e s p e c t i v e l y . I n F i g . l ( a ) , o b s e r v e d c h a n g e s of p e r i o d , P , and of I F , Q-l, w e r e shown a g a i n s t t e m p e r a t u r e s , T, by t h e symbols f o r t h e warming r a t e , T , of 3K/min o r of 10K/min. Here, t h e ' v i r g i n ' y p e a k was observed a t a b o u t 347K w i t h Q - l p of a b o u t
F o r t h e d e t a i l e d i n v e s t i g a t i o n , t h e o b s e r v e d y peak was compared w i t h t h e c a l c u l a t e d o n e drawn by t h e s o l i d c u r v e s and a l s o w i t h a s i n g l e Debye p e a k by d o t t e d and broken c u r v e s . F o r t h e c a l c u l a t e d y peak, it was assumed that t h e y p e a k c a n b e e x p l a i n e d by a broadened Debye peak, where t h e r e l a x a t i o n s t r e n g t h , A , h a s a Gaussian d i s t r i b u t i o n on l o g a r i t h m s of t h e p r e - e x p o n e n t i a l f a c t o r around l / r o . l / r o used was t h e v a l u e o b t a i n e d i n Fig.3. The background v a l u e s u s e d w e r e shown by t h e broken l i n e s . One c a n s e e i n F i g . l ( a ) that t h e o b s e r v e d y p e a k was o f a n e a r l y s i n g l e Debye peak. F u r t h e r a t t h e h i g h e r t e m p e r a t u r e s i d e , a d e c r e a s e of t h e y peak was s t a r t e d . Such t h e d e c r e a s e of t h e y peak i s commonly obseved i n h i g h - p u r i t y bcc m e t a l s and i s s u r m i s e d t o b e due t o a r e a r r a n g e m e n t of d i s l o c a t i o n s t r u c t u r e s i n t r o d u c e d by t h e low t e m p e r a t u r e d e f o r m a t i o n / 3 / . Here, t h e observed y peak s e e n in F i g . l ( a ) w a s o v e r l a p p e d by t h e e a r l y s t a g e of t h e r e c o v e r y . For s u c h a c a s e , o n e c a n e x p e c t t h a t w i t h i n c r e - a s i n g
!k,
t h e t e m p e r a t u r e s o f r e c o v e r y i n c r e a s e s and a t t h e l i m i t of i n f i n i t e T, t h e t r u e ' v i r g i n ' y peak may b e o b t a i n e d . Indeed in F i g . l ( a ) , o n e can see from t h e o u r v e s f o r P that t h e t e m p e r a t u r e of r e c o v e r y was i n c r e a s e d from %360K f o r 3K/min t o s370K f o r 10K/min, and a l s o from t h e c u r v e s f o r Q - ~ that Tp and Q - 1 w e r e i n c r e a s e d from 3 4 6 . 1 t l K and s 3 . 9 ~ 1 0 - 3 f o r 3K/min t o 348.3tlK and ~ 4 . 4 ~ 1 0 - 3 f o r 10K/min, r e s p e c t i v e l y . P From t h e r e p e a t e d measurements w i t h'k
i n between 3Klmin and 12K/min, t h e t r u e Tp and?-lp
f o r 7.4Hz i n A20-1 were d e t e r m i n e d a s 349.0flK and *4.7x10-3, r e s p e c t i v e l y . The v l r g i n l y peak f o r 0.015Hz s e e n i n F i g . l ( b ) was observed a t 284.8flK w i t h Q - l p oft h e l o w e r - t e m p e r a t u r e s i d e . T h e r e f o r e , t h e measurements h e r e were performed w i t h a v e r y low T t o complete t h e d i s l o c a t i o n p i n n i n g s f a r below Tp. B e s i d e s t h e y peak, one can a l s o s e e a s m a l l s h o u l d e r a t about 230K. From t h e r e p e a t e d measurements,TpVs determined were 284.6'1K f o r 0.015Hz and 277.4f1.5K f o r 0.007Hz, r e s p e c t i v e l y , and
averaged o<er f o r 0.015Hz and 0.007Hz was %5.2x10-3 i n A20-1.
S i m i l a r i n v e s t i g a t i o n a s mentioned above was a l s o made i n A20-2 and i n A20-3.
The o b t a i n e d r e s u l t s f o r Tp v s f r e q u e n c y , f , f o r t h e ' v i r g i n ' y p e a k a r e s e e n i n F i g , 3 . F i g . 2 shows examples of t h e ' a n n e a l e d ' y peak observed a t 7.4Hz and a t 0.015Hz i n A20-2a a f t e r A20-2. For t h e r e p e a t e d measurements f o l l o w i n g 0.05%(80K), t h e 'an- n e a l e d ' y peak showed t r a n s i e n t changes o f T and Q-lp i n e a r l y r u n s , t h e r e f o r e t h e s e v a l u e s were determined from t h e r e s u l t s o b t a l n e d a f t e r t h e t r a n s i e n t changes were
P
completed. S i m i l a r i n v e s t i g a t i o n was a l s o performed i n A20-3a and i n A20-3b a f t e r A20-3, and t h e o b t a i n e d r e s u l t s f o r Tp v s f f o r t h e ' a n n e a l e d ' y peak a r e a l s o shown in Fig.3.
For a r e l a x a t i o n peak, t h e r e l a t i o n of q - l p a l / T can b e e x p e c t e d / l O / . I n t h e p r e s e n t work, t h e observed r a t i o of
(Q;lp
f o r 0.015 an: 0.007Hz /9-1
f o r 7.4Hz), Q - l p - r a t i o , was always found i n between 1 . 0 and 1 . 3 e x c e p t 1 . 8 i n d o - 3 and t h a t of (Tp f o r 7.4Hz1%
f o r 0.015 and 0.007Hz), T p - r a t i o , was always a b o u t 1 . 2 . That i s , t h e r e l a t i o n of Q - l p - r a t i o = T p - r a t i o was observed w i t h i n e x p e r i m e n t a l e r r o r s t h r o u g h t h e p r e s e n t work, but i n A20-3, Q-lp f o r 7.4Hz was much s m a l l e r t h a n t h a t e x p e c t e d from t h e r e s u l t s f o r 0.015 and 0.007Hz. Combining t h e s e r e s u l t s w i t h t h e f a c t s t h a t t h e ' v i r g i n ' y peak f o r 7.4Hz was p a r t l y o v e r l a p p e d by t h e r e c o v e r y p r o c e s s and i n A20-3, t h e i n c r e a s e d € 0 of 28x10-6 was u s e d , o n e can s a y t h a t t h e i n c r e a s e d E O might a c c e l e r a t e t h e r e c o v e r y p r o c e s s . T h e r e f o r e , H and l / r o i n A20-3 o b t a i n e d i n Fig.3 w i l l n o t b e d i s c u s s e d and on t h e o t h e r hand, one can say t h a t t h e r e c o v e r y was more proceeded a f t e r A20-3, i.e. i n A20-3a and A20-3b, t h a n a f t e r A20-2, i . e . i n A20-2a.Fig.4 shows t h e p l o t f o r l o g ( l / r o ) vs. H which were o b t a i n e d i n F i g . 3. From t h e a m p l i t u d e dependence i n v e s t i g a t e d i n A20-3a and A20-3b, i n c r e a s e s of b o t h H and
l / r o
w i t h d e c r e a s i n g E O can be s e e n . Combining t h i s a m p l i t u d e dependence of H w i t h S e e g e r ' s t h e o r y on KPF-process/8/, 2Hk was e s t i m a t e d a s about 0.940eV, where Hk de- n o t e s t h e e n t h a l p y of a n i s o l a t e d s i n g l e k i n k i n s c r e w - d i s l o c a t i o n s in a - i r o n . On t h e o t h e r hand, f o r t h e e f f e c t of a n n e a l i n g which was i n v e s t i g a t e d i n A20-1 o r A20-2, A20-2a and A20-3b, one c a n s e e t h e tendency of i n c r e a s e s of b o t h H and
l / r o
w i t h a n n e a l i n g proceeded. F u r t h e r , comparing t h e e f f e c t of a n n e a l i n g seen between in A20- 2a and i n A20-3b w i t h t h a t of a m p l i t u d e , i n A20-3a and in A20-3b, one c a n s e e t h a t t h e s e e f f e c t s were a l m o s t t h e same f o r A20. T h i s r e s u l t c a n b e r e a s o n a b l y understood a f t e r t h e f o l l o w i n g c o n s i d e r a t i o n ; t h e i n t e r n a l s t r e s s a p p l i e d t o t h e ' v i r g i n ' y peak h e r e might be mainly i n t r o d u c e d by 0.05%(80K) and b e d e c r e a s e d w i t h a n n e a l i n g . T h e r e f o r e , it is concluded in t h e p r e s e n t work t h a t b o t h H and l / r o i n c r e a s e w i t h de- c r e a s i n g s t r e s s a p p l i e d t o t h e y peak p r o c e s s . D e t a i l e d r e s u l t s i n c l u d i n g t h e e f f e c t of p r e - d e f o r m a t i o n s a t RT and f u r t h e r d i s c u s s i o n s w i l l be r e p o r t e d elsewhere.ACKNOWLEDGEMENTS
The a u t h o r s w i s h t o e x p r e s s t h e i r g r a t i t u d e t o Messors H. Waldmann and J. Wolf f o r t h e i r i n v a l u a b l e h e l p s t h r o u g h o u t t h e e x p e r i m e n t s and t o P r o f e s s o r s H. S c h u l t z and S. Okuda f o r d i s c u s s i o n s . One of t h e a u t h o r s (H.M.) acknowledges d e e p l y f i n a n - c i a l s u p p o r t from t h e Alexander von Humboldt Foundation.
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/9/ G . F a n t o z z i , C. Esnouf, W. Benoit and I.G. R i t c h i e , Prog. Mater. S c i . z ( 1 9 8 2 ) 311.
/ l o /
A.S. Nowick and B.S. B e r r y , A n e l a s t i c R e l a x a t i o n i n C r y s t a l l i n e S o l i d s , Academ P r e s s , New York and London, 1972./11/ J. Woirgard, P. Mazot and A. R i v i S r e , J . P h y s i q u e %(1981), C5-1135.
1121 L.B. Magalas and P. Moser, i b i d . %(l.981), C5-97.
T ( K l
% - -
Fig.2 Examples of t h e ' a n n e a l e d ' y peaki n A20-2a f o r 7.4Hz and f o r 0.015Hz w i t h
-
o ~ ~ = 7 x 1 0 - 6 ( s e e t e x t ) .F i g . l ( b )
350 330 Tp 31;K, 290 280
T (n)
F i g . 1 Examples of t h e ' v i r g i n ' y peak i n A20-1 f o r 7.4Hz(a) and f o r 0.015Hz (b) w i t h ~ ~ = 7 x 1 0 - ~ ( s e e t e x t ) .
-
FI,0
I"
-
2.8 3.0 3.2 3.4 3.6
130.80 0.85 0.90 10001 Tp ( K-l)
H (eV)
Fig.4 L o g ( l / ~ o ) vs. H, Ghich were F i g . 3 A r r h e n i u s p l o t f o r t h e y peak ob- o b t a i n e d in F i g . 3 . s e r v e d f o r v a r i o u s e x p e r i m e n t a l c o n d i t i o n s .
