ATTENUATION AND VELOCITY CHANGE OF ACOUSTIC WAVES IN THE AMORPHOUS METAL PdSiCu FROM 0.05 K TO 90 K

HAL Id: jpa-00221302

https://hal.archives-ouvertes.fr/jpa-00221302

Submitted on 1 Jan 1981

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.

ATTENUATION AND VELOCITY CHANGE OF

ACOUSTIC WAVES IN THE AMORPHOUS METAL

PdSiCu FROM 0.05 K TO 90 K

P. Doussineau

To cite this version:

JOURNAL DE PHYSIQUE

CoZloque C6, suppldment au n012, Tome 42, de'cernbre 1981 page C6-72

A T T E N U A T I O N AND V E L O C I T Y CHANGE OF ACOUSTIC WAVES I N THE AMORPHOUS M E T A L P d S i C u FROM 0 . 0 5

K

TO 90

K

P. Doussineau

Laboratoire dfUZtrasons, Universite' Pierre e t Marie Curie, Tour 13, 4 place Jussieu, 75230 Paris Cedes 05, France

Abstract.

-

Previous a c o u s t i c experiments i n a-PdSiCu were extended. Attenua-

--

-

t i o n and v e l o c i t y change were measured a t v a r i o u s f r e q u e n c i e s around 500 MHz from 0.05 K t o 90 K

.

The a t t e n u a t i o n i s i n t e r p r e t e d a s t h e sum of two c o n t r i - b u t i o n s : one due t o t h e r e l a x a t i o n of t h e TLS and t h e o t h e r due t o an a c t i v a - t e d process. The v e l o c i t y change i s explained w i t h t h e same two preceding c o n t r i b u t i o n s ; however i t i s n e c e s s a r y t o add n o t only t h e r e s o n a n t c o n t r i b u - t i o n b u t a l s o an e l e c t r o n i c term v a r y i n g a s T ~ .

1.

Experiments.

-

I t i s now w e l l e s t a b l i s h e d t h a t two-level systems (TLS) a r e pre- s e n t i n amorphous m e t a l s [ I ] . Among o t h e r experimental methods u l t r a s o n i c waves have proved t h a t t h e y a r e one of t h e b e s t t o o l t o s t u d y TLS i n amorphous m e t a l s . I p r e s e n t h e r e an e x t e n s i o n of p r e v i o u s a c o u s t i c experiments i n amorphous Pd0.775Si0.165C~0.06

[ 2 ] . The a t t e n u a t i o n and phase v e l o c i t y change of t r a n s v e r s e a c o u s t i c waves a t f o u r f r e q u e n c i e s from 185 t o 852 MHz have been measured i n t h e temperature range 0.05 t o 90 K

.

The r e s u l t s a r e shown i n F i g u r e s 1 and 2 f o r t h e a t t e n u a t i o n and t h e v e l o c i t y change r e s p e c t i v e l y . The main f e a t u r e s a r e : - i n t h e temperature range below 6 K

t h e a t t e n u a t i o n v a r i e s l i n e a r l y w i t h t h e temperature and w i t h t h e frequency. - A t

h i g h e r t e m p e r a t u r e s t h e a t t e n u a t i o n s t i l l i n c r e a s e s , goes through a broad maximum n e a r 20 - 2 5 K and t h e n d e c r e a s e s slowly (Fig. 1 ) . A s i m i l a r peak h a s been p r e v i o u s l y r e p o r t e d i n a Pd0.775Si0.165Ag0.06 sample f o r l o n g i t u d i n a l waves [ 3 ] . - A t t h e lowest t e m p e r a t u r e s (T < 2 K ) t h e v e l o c i t y f i r s t i n c r e a s e s roughly l o g a r i t h m i c a l l y when t h e temperature i n c r e a s e s (Fig. 2 ) . T h i s behavior i s now w e l l known f o r amor- phous m e t a l s [ I ] . - Then t h e v e l o c i t y goes through a maximum and d e c r e a s e s on a l l

t h e temperature range explored (up t o 70 K ) . T h i s d e c r e a s e cannot b e s a i d l i n e a r i f t h e e n t i r e temperature range ( 4 t o 70 K ) i s considered, c o n t r a r y t o what was claimed f o r t h e same m a t e r i a l i n t h e range 4 t o 20 K

[41.

2 .

Theory.

-

The preceding r e s u l t s a r e e x p l a i n e d i n t h e framework of t h e TLS theo- r y . I r e c a l l h e r e o n l y t h e r e s u l t s u s e f u l t o what f o l l o w s . D e t a i l s can be found e l s e - where [1,5]. The r e s o n a n t i n t e r a c t i o n between TLS and u l t r a s o n i c wave l e a d s t o a ve- v e l o c i t y change g i v e n by

Av/v,,

= C I n T / T o , where

To

i s an a r b i t r a r y r e f e r e n c e t e m p e r a t u r e , ?I,, t h e sound v e l o c i t y , C = y2

/

p ~ : w i t h p t h e d e n s i t y , y an e l a s t i c deformation p o t e n t i a l and t h e d e n s i t y of s t a t e s o f t h e TLS. Besides t h e r e s o n a n t i n t e r a c t i o n , t h e e l a s t i c wave undergoes a r e l a x a t i o n a l a t t e n u a t i o n (and d i s p e r s i o n ) . I n terms of t h e complex change of. t h e e l a s t i c c o n s t a n t c

,

it i s given by

where

6

= 1 / k T

,

E i s t h e s p l i t t i n g between t h e two-levels,

r =

(Ao/E12

with

A,

t h e t u n n e l i n g m a t r i x element

153,

(11/21i is t h e frequency o f t h e u l t r a s o n i c wave, and T , i s

t h e l o n g i t u d i n a l r e l a x a t i o n time of t h e TLS.

T,

c h a r a c t e r i z e s t h e r e t u r n towards e q u i l i b r i u m of t h e TLS p o p u l a t i o n . I n a m e t a l two channels a r e p o s s i b l e , v i a t h e thermal phonons o r v i a t h e conduction e l e c t r o n s [ I ] . Consequently

BE

4 k 3

Y z

=

:I

[.

-'

+

[.:I-'

where

[TI)-'

= pK3

T3[y]

c o t h

,

w i t h K3 =

-

1

2

.rr

o h 4 VT5 (T = L o r ?' s t a n d s f o r t h e p o l a r i z a t i o n ) and (T,E)-' = T K ,

T

-

BE

2 coth-,

6

2

E

w i t h

K , =

~

(G

K, )

.

5

i s t h e e l e c t r i c d e n s i t y of s t a t e s a t t h e Fermi l e v e l and I(, an

2 h _w

Ac

e l e c t r i c deformation p o t e n t i a l . I n t h e g e n e r a l c a s e t h e a t t e n u a t i o n ( a = - I m

-

)

Ac

v

Oo

and t h e v e l o c i t y change

₍₀₂₁

_v

₌ Re

-)

a r e given by a numerical c a l c u l a t i o n . 2 c,

B e s i d e s t h i s f i r s t r e l a x a t i o n a l e f f e c t t h e a c o u s t i c a t t e n u a t i o n i n amorphous m a t e r i a l s g e n e r a l l y p r e s e n t s a broad peak a t t r i b u t e d t o some a c t i v a t i o n p r o c e s s e s above energy b a r r i e r s [ 6 ] . The corresponding change i n t h e e l a s t i c c o n s t a n t i s given

-

-

n ( U )

dU

where E i s t h e r e l a x a t i o n s t r e n g t h ,

r

(U)

i s a r e l a x - a t i o n time g i v e n by the Arrhenius law

r(U)

= To exp

BU

,

n ( U )

c h a r a c t e r i z e s t h e d i s - t r i b u t i o n of energy b a r r i e r s

U.

Usually

n(U)

i s t a k e n a s a c o n s t a n t . I found it i s

u2

b e t t e r t o choose a g a u s s i a n d i s t r i b u t i o n

n(U)

=

$

exp- 7 where o h a s t o b e

IT u 2 G

determined by t h e experiment.

C6-74 JOURNAL DE PHYSIQUE

3 . Interpretation.

-

The whole s e t o f r e s u l t s p r e s e n t e d i n F i g u r e s 1 and 2 i s

d e s c r i b e d with t h e t h e o r y o u t l i n e d above.

C,

K , ,

K g , E , To and 0 a r e used a s f r e e parameters i n t h e numerical computation. I n f a c t

C

i s given by t h e l o g a r i t h m i c i n c r e a s e o f t h e v e l o c i t y a t t h e lowest t e m p e r a t u r e s , while t h e product KIC i s d e t e r - mined from t h e a t t e n u a t i o n i n t h e same t e m p e r a t u r e range 121. I t was p o s s i b l e t o o b t a i n a good f i t (shown by t h e s o l i d l i n e s i n Fig. 1) of t h e a t t e n u a t i o n r e s u l t s when t h e a t t e n u a t i o n due t o an Arrhenian p r o c e s s w i t h a g a u s s i a n d i s t r i b u t i o n o f t h e energy b a r r i e r s was added t o t h e r e l a x a t i o n a l a t t e n u a t i o n due t o t h e TLS. The b e s t agreement was o b t a i n e d w i t h

CT

= 5.5

,

K 1 = 1.5 101°

f'

s - l ,

K3

=

2 l o 8 K - ~ s-'

,

E = 4.4 10-\ ,a = 5

lo-''

e r g and T,, = 3.5 lo-" s . Then t h e v e l o c i t y change was c a l c u l a t e d w i t h t h e same s e t of parameters. The l o g a r i t h m i c r e s o n a n t c o n t r i b u t i o n was a l s o added. A good f i t was o b t a i n e d f o r temper- a t u r e s up t o 4 K . A t h i g h e r t e m p e r a t u r e s t h e observed d e c r e a s e of t h e v e l o c i t y was f a s t e r t h a n t h e c a l c u l a t e d one. A good f i t (shown by t h e s o l i d l i n e s i n Fig. 2) up t o 40 K was o b t a i n e d when a d e c r e a s i n g term v a r y i n g a s 1.6 ' 'T was added t o t h e t h r e e preceding c o n t r i b u t i o n s . Such a v e l o c i t y v a r i a t i o n was expected i n a metal a s an e l e c t r o n i c c o n t r i b u t i o n t o t h e e l a s t i c c o n s t a n t [71.

Thus a s a t i s f a c t o r y agreement i s o b t a i n e d between t h e c a l c u l a t e d c u r v e s and t h e experimental r e s u l t s i n PdSiCu f o r both t h e a t t e n u a t i o n and t h e v e l o c i t y change a t v a r i o u s f r e q u e n c i e s i n an extended temperature range. From t h e p r e c e d i n g i n t e r p r e t a - t i o n a q u e s t i o n a r i s e s . Have t h e TLS and t h e p a r t i c l e s involved i n t h e Arrhenius p r o c e s s a common o r i g i n ? The procedure given above assumes t h e answer i s n e g a t i v e because t h e d i f f e r e n t c o n t r i b u t i o n s of t h e a t t e n u a t i o n ( o r v e l o c i t y ) a r e added. I n t h e o p p o s i t e c a s e n o t t h e a t t e n u a t i o n ( o r v e l o c i t y ) b u t t h e r e l a x a t i o n r a t e s have t o be added. Such a p o s s i b i l i t y h a s n o t n e t been explored, b u t i t w i l l be t h e purpose of f u r t h e r r e s e a r c h .

REFERENCES

111

BLACK, J . L . , i n

M e t a l l i c G Z a s s e s ,

e d i t e d b y H . J . Guntherodt and H. Bech ( S p r i n g e r Verlag, B e r l i n , 1980)

[21 DOUSSINEAU, P . , J.

P h y s i q u e L e t t .

42 (1981) L-83, and r e f e r e n c e s t h e r e i n .

131

DUTOIT, M . ,

Phys. L e t t .

50 A (1974) 221.

143

BELLESSA, G . ,

Phys. Rev. L e t t .

40 (1978) 1456.

151 DOUSSINEAU, P. F&NOIS, C . , LEISURE, R. G . , LEVELUT, A . , and PRIEUR, J .

Y.,

J.

P h y s i q u e

40 (1980) 1193.

[ 6 ] BELLESSA, G . , J .

P h y s i q u e ColZ.

40 (1980) C8-723.