HAL Id: jpa-00225420
https://hal.archives-ouvertes.fr/jpa-00225420
Submitted on 1 Jan 1985
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
UNDERDAMPED DISLOCATION RESONANCE IN
Cu
E. Drescher-Krasicka, R. Jemielniak, J. Królikowski
To cite this version:
JOURNAL DE PHYSIQUE
C o l l o q u e C I O ,
supplément
au
n o 1 2 , Tome 46,décembre
1985 p a g e C10-159U N D E R D A M P E D DISLOCATION RESONANCE IN
Cu
E. DRESCHER-KRASICKA, R. JEMIELNIAK AND J. KROLIKOWSKI
Institute of Fundamental Technological Research, Polish
Academy of Sciences, Warsaw, Poland
A b s t r a c t Measurements of d i s l o c a t i o n dependent a t t e n u a t i o n (aD) i n Cu and A l a r e o b s c u r r e d a t t e m p e r a t u r e s below 50 K bj t h e a t t e n u a t i o n due t o electron-phonon i n t e r a c t i o n s (aE). T h i s paper p r e s e n t s t h e measurements on A l and+Cu f i n g l e c r y s t a l s i n which aE is e l i m i n a t e d by u s i n g a magnetic f i e l d H 1 q p e r p e n d i c u l a r t o t h e d i r e c t i o n of p r o p a g a t i o n of t h e a c o u s t i c waves. Underdamped resonance peak i n a D was o b t a i n e d a t 4.2 K i n a s l i g h t l y deformed Cu sample. The r e s u l t s a r e d i s c u s s e d i n t h e framework of t h e Granato-Lucke theory
.
I n t r o d u c t i o n At low t e m p e r a t u r e s , t h e t o t a l measured a t t e n u a t i o n a of a c o u s t i c waves i n pure s i n g l e c r y s t a l s of Cu has t h r e e components:
where a* i s a background a t t e n u a t i o n , a D is t h e d i s l o c a t i o n a t t e n u a t i o n , and a E
is
t h e a t t e n u a t i o n due t o t h e electron-phonon i n t e r a c t i o n s . In pure s i n g l e c r y s t a l s of Cu, t h e component aE becomes s i g n i f i c a n t a t t e m p e r a t u r e s below 50 K, and i n c r e a s e s l i n e a r l y with t h e c o n d u c t i v i t y a c c o r d i n g t o P i p p a r d ' s Law [ l ] when t h e t e m p e r a t u r e d e c r e a s e s . In o r d e r t o s e e t h e d i s l o c a t i o n resonance b e h a v i o r a t low t e m p e r a t u r e (4.2 K) t h e electron-phonon c o n t r i b u t i o n t o t h e t o t a l a t t e n u a t i o n of u l t r a s o n i c waves muSt be somehow e l i m i n a t e d . It was a l r e a d y done i n l e a d by D. Read [2], R. B. Schwarz, R. D. I s a a c and A. V. Granato [ 3 ] bj u s i n g t h e s u p e r c o n d u c t i n g property of t h i s metal. In t h i s paper a magnetic f i e l d p e r p e n d i c u l a r t o t h e d i r e c t i o n of p r o p a g a t i o n of u l t r a s o n i c waves was a p p l i e d , and t h e f i e l d a t which t h e e l e c t r o n - phonon i n t e r a c t i o n s i n Cu samples became n e g l i g i b l e was e x p e r i m e n t a l l y e v a l u a t e d f o r each frequency. Underdamped d i s l o c a t i o n resonance was s e e n a t l i q u i d helium
t e m p e r a t u r e s f o r a p u r e copper sample w i t h r e l a t i v e l y l o n g l o o p l e n g t h s . The magnetic f i e l d e f f e c t s a r e d i s c u s s e d and compared w i t h r e s u l t s found by Morse [ l ] . Theory The e f f e c t of magnetic f i e l d on u l t r a s o n i c a t t e n u a t i o n depends on t h e v a l u e of q 2 , when q is t h e wave v e c t o r of t h e u l t r a s o n i c wave and L is t h e mean f r e e p a t h of e l e c t r o n s i n t h e sample [ I l . When t h e v a l u e of qll i s e q u a l o r l e s s t h a n u n i t y , t h e a t t e n u a t i o n d e c r e a s e s monotonically a s t h e f i e l d i n c r e a s e s . When t h e magnetic f i e l d i s p e r p e n d i c u l a r t o b o t h t h e p a r t i c l e v e l o c i t y and t h e p r o p a g a t i o n d i r e c t i o n - t h e r a t i o of t h e a t t e n u a t i o n t o t h e z e r o f i e l d a t t e n u a t i o n i s found t o be: a(H) - = 1 2 (2) a(0) 1+(2w r )
whare T is t h e r e l a x a t i o n f i m e i n t h e absence of t h e f i e l d , and w c , t h e c y c l o t r o n f requency
,
where e i s t h e e l e c t r o n i c c h a r g e , m t h e mass, and c t h e v e l o c i t y of l i g h t . These e q u a t i o n s have been confirmed bj Morse e t a l . (1958) on Cu s i n g l e c r y s t a l s and t h e r e s u l t s a r e shown i n Fig. 1.
JOURNAL
DE
PHYSIQUE* O TRANSVERSE WAVES
A
LONGITUOINAL WAVESO 1 2
3
4 5 6Fig. 1. Observed magnetic f i e l d dependence of t h e a t t e n u a t i o n i n copper a t a frequency of 8.6 Mc/sec. The d o t t e d l i n e is a p l o t of Eq. (2). ( A f t e r Morse, 1959).
Experimental Procedure Two pure s i n g l e c r y s t a l copper samples were c u t i n a < I l l > d i r e c t i o n , w i t h a c r y s t a l o g r a p h i c o r i e n t a t i o n b e t t e r t h a n 2 degrees. The samples were lapped, e t c h e d and annealed and l a t e r i r r a d i a t e d i n a Co6@ s o u r c e with a dose of 30 MRad. This i r r a d i a t i o n was s u f f i c i e n t t o p i n t h e d i s l o c a t i o n loops i n o r d e r t o o b t a i n t h e background a t t e n u a t i o n a t room temperature. One of t h e Cu samples was deformed up t o 1% bj u n i a x i a l compression. The second sample remained undeformed, b u t t h e r e s u l t i n g deformation due t o t h e thermal s t r e s s e s of c o o l i n g i n a sample h o l d e r was e v a l u a t e d a f t e r t h e low t e m p e r a t u r e experiment and found t o be 0.1%. The samples were mounted i n a c r y o s t a t c o n t a i n i n g a superconducting magnet. A Matec 6600 system w i t h an a t t e n u a t i o n r e c o r d e r were used t o monitor t h e a t t e n u a t i o n changes a s a f u n c t i o n of f requency a t c o n s t a n t t e m p e r a t u r e e q u a l t o 4 . 2 K. For each measured f requency; 10; 30, 50, 70, 90, 110, 130 and 150 MHz t h e a t t e n u a t i o n a s a f u n c t i o n of i n c r e a s i n g magnetic f i e l d was recorded, and t h e r e s u l t s a r e p r e s e n t d i n Fig. 2.
A 4lnethyl-1-pentane bond was a p p l i e d over l i q u i d n i t r o g e n temperature. T h i s procedure does n o t produce an u n d e s i r a b l e c o n t r i b u t i o n t o t h e t o t a l d i s l o c a t i o n a t t e n u a t i o n .
R e s u l t s F i g u r e 2 p r e s e n t s t h e t o t a l u l t r a s o n i c a t t e n u a t i o n a s a f u n c t i o n of t h e i n c r e a s i n g magnetic f i e l d f o r d i f f e r e n t f r e q u e n c i e s . At z e r o f i e l d t h e t o t a l measured u l t r a s o n i c a t t e n u a t i o n has t h e h i g h e s t v a l u e f o r a l 1 measured f r e q u e n c i e s except f o r 150 MHz. In t h i s c a s e , qQ becomes g r e a t e r t h a n u n i t y , and s m a l l o s c i l l a t i o n s i n t h e range between O 5 5 KGauss a r e seen. T h i s i s t h e e x p e r i m e n t a l l i m i t of t h e a p p l i c a t i o n of Eq. (Z), which was formulated f o r qQ
<
1. But t h e c h a r a c t e r of t h e changes of t h e u l t r a s o n i c a t t e n u a t i o n f o r i n c r e a s i n g magnetic f i e l di s t h e same. In a l 1 experiments t h e a p p l i e d magnetic f i e l d reduces t h e u l t r a s o n i c a t t e n u a t i o n t o a c o n s t a n t low v a l u e compared t o t h e z e r o f i e l d case. Above 8.6 KGauss, t h e a t t e n u a t i o n f o r a l 1 measured f r e q u e n c i e s i s n o t a f f e c t e d by a f u r t h e r i n c r e a s e of t h e f i e l d , t h i s means, a c c o r d i n g t o Eq. ( 2 ) t h a t t h e electron-phonon i n t e r a c t i o n i s e l i m i n a t e d by t h e f i e l d . F i g u r e 3 p r e s e n t s t h e d i s l o c a t i o n
a t t e n u a t i o n aD a s a f u n c t i o n of frequency a t c o n s t a n t magnetic f i e l d H = 8.6 KGauss a t 4.2 K on a double l o g a r i t h m i c s c a l e .
SPECIMEN A . u i
g l H T-4.2K
70 M H z
Fig. 2 Attenuation yersus magnetic f i e l d for d i f f e r e n t frequencies. S l i g h t l y deformed Cu sample, E = 0 . 1 % ; T = 4 . 2 K.
C10-162 JOURNAL DE
PHYSIQUE
The frequency dependence found i n Fig. 3 i s t o o s t e e p f o r a n overdamped resonance, but is c o n s i s t e n t w i t h t h a t expected f o r an underdamped resonance. S i m i l a r r e s u l t s were found f o r A l .
D i s c u s s i o n Using t h e e x p e r i m e n t a l l y o b t a i n e d resonance frequency f o
-
150 MfIz one can e s t i q t e t h e a v e r a g e loop l e n g t h L of t h e d i s l o c a t i o n s u s i n g t h e theory of Granato-Luckev
2F
150 MHz f o - - =where vs i s t h e s h e a r wave v e l o c i t y . T h i s g i v e s L
-
1 0 - ~ cm. Knowing L, one can e s t i m a t e t h e c r i t i c a l d i s l o c a t i o n v i s c o u s d r a g c o n s t a n t Bc a t T = 4.2 K fromB = 2 m
where A is t h e d i s l o c a t i o n mass p e r u n i t l e n g t h and k i s t h e r e s t o r i n g f o r c e
9
where G i s t h e e l a s t i c s h e a r modulus and b i s t h e B u r g e r ' s v e c t o r . BL = 4 f i . A vS = 1.2 x 10"
B
-
1 0 - ~ i n cgs u n i t sThese a r e r e a s o n a b l e v a l u e s , [ 4 ] and show t h a t even r e l a t i v e l y l o n g l o o p l e n g t h s can be underdamped a t low enough temperatures.
Acknowledgments
We thagk Prof e s s o r Granato f o r v a l u a b l e s u g g e s t i o n s and h e l p f u f d i s c u s s i o n s , P r o f e s s o r Lucke and Alexander von Humboldt Foundation f o r h e l p with t h e samples and t h e Matec equipment, and John Meder f o r a s s i s t a n c e w i t h p r e p a r a t i o n o f t h i s paper.
R e f e r e n c e s
1. Phy s i c a l ~ c o u s t i c s .
W. P. Mason, Vol.
N ,
A p p l i c a t i o n t o Quantum and S o l i d S t a t e P h y s i c s , P a r t A, Academic P r e s s , Ni', LONDON (1968).2. D. Read; Ph.D. T h e s i s ; U n i v e r s i t y of I l l i n o i s (1978).
3. R.
