ULTRASONIC STUDIES OF METALLIC GLASSES AT LOW TEMPERATURES

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ULTRASONIC STUDIES OF METALLIC GLASSES

AT LOW TEMPERATURES

G. Park, A. Hikata, C. Elbaum

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque

C S ,

suppZ6ment au nolO, Tome

4 2 ,

octobre 1981

page

~ 5 - 5 1 7

U L T R A S O N I C S T U D I E S O F M E T A L L I C GLASSES A T LOW TEMPERATURES

G. Park, A . Hikata and C. Elbaum

Metals Research Laboratory, Brown University, Providence,

R I

02912,

U.S.A.

A b s t r a c t . - R e s u l t s a r e r e p o r t e d o f u l t r a s o n i c s t u d i e s o f amorphous Pd

.82Si . l $ ' Pd.40Ni P and Pd

.40 .20 . 7 7 5 S i . 1 6 5 C ~ 0 . 0 6 ~ a t f r e q u e n c i e s from 1 0 MIIz t o 600 MHz ( t r a n s v e r s e ) and t e m p e r a t u r e s down t o 0.27 K. The a t t e n u a t i o n i s found t o c o n t a i n an amplitude dependent ( s a t u r a b l e ) component. These o b s e r v a t i o n s , a s w e l l a s t h e temperature dependence of t h e v e l o c i t y changes, a r e c o n s i s t e n t w i t h t h e p r e d i c t i o n s of t h e two l e v e l t u n n e l i n g systems (TLS) t h e o r y . Con- t r a r y t o t h e p r e d i c t i o n s of t h i s t h e o r y , however, l i n e a r frequency dependence and e s s e n t i a l l y no temperature dependence o f s a t u r a b l e a t t e n u a t i o n changes were observed a t very low t e m p e r a t u r e s .

1. I n t r o d u c t i o n . - The Two Level System (TLS) t u n n e l i n g seems t o account f o r most o f t h e low t e m p e r a t u r e p r o p e r t i e s i n i n s u l a t i n g g l a s s e s 4 , i . e . , l i n e a r tem- p e r a t u r e dependence of t h e excess s p e c i f i c h e a t , q u a d r a t i c t e m p e r a t u r e dependence of t h e t h e r m a l c o n d u c t i v i t y , s a t u r a t i o n of u l t r a s o n i c a t t e n u a t i o n and l o g a r i t h m i c tem- p e r a t u r e dependence of sound v e l o c i t y changes. S i m i l a r b e h a v i o r o f t h e r m a l and u l - t r a s o n i c p r o p e r t i e s was a l s o observed i n m e t a l l i c glasses5-15. However, i n t h e c a s e of m e t a l l i c g l a s s e s , s e v e r a l s e r i o u s d i s c r e p a n c i e s were r e p o r t e d w i t h t h e p r e d i c t i o n of t h e TLS t h e o r y 5313-15. U l t r a s o n i c p r o p e r t i e s p r e d i c t e d by t h e TLS t h e o r y a r e

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summarized a s follows

.

The resonance a t t e n u a t i o n , which i s amplitude dependent, i s d e s c r i b e d a s

where J i s t h e a c o u s t i c i n t e n s i t y and Jc i s t h e c r i t i c a l i n t e n s i t y . The frequency and temperature dependences of a

A0 are

2

a = - _nnM3U, t a n h

-

hw

ov 2kT

Here M i s t h e deformation p o t e n t i a l , p i s t h e mass d e n s i t y , v i s t h e sound v e l o c i t y , and n i s t h e d e n s i t y of s t a t e s of TLS, which i s u s u a l l y assumed t o b e independent o f energy. With r e g a r d t o v e l o c i t y changes, t h i s t h e o r y g i v e s f o r t h e resonance con-

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JOURNAL DE PHYSIQUE

For m e t a l l i c g l a s s e s one of t h e s e r i o u s d i s c r e p a n c i e s w i t h t h i s t h e o r y , r e p o r t - e d s o f a r , i s t h e frequency and t e m p e r a t u r e dependence of t h e amplitude dependent p a r t 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 changes, aAO, i n t h e m e t a l l i c g l a s s Pd

.775si . l 7 5 06 13'14 ( h e r e a f t e r PdSiCu). I n Ref. 1 3 and 1 4 t h e a u t h o r s showed t h a t i n amorphous PdSiCu t h e e x p e r i m e n t a l l y observed aA f i t s v e r y w e l l t o t h e t h e o r e t i c a l l y p r e - d i c t e d form (Eq. ( l ) ) . However, t h e q u a n t i t i e s aAO o b t a i n e d from t h a t f i t t i n g were found t o have a l i n e a r dependence on frequency ( r a t h e r t h a n q u a d r a t i c dependence) i n t h e frequency range s t u d i e d (10 t o 600

MHz).

Moreover, aAO d i s p l a y e d a t most a very weak dependence on temperature ( r a t h e r t h a n 1/T dependence) below about 1 K. It i s , t h e r e f o r e , i n t e r e s t i n g t o e x p l o r e t h e u l t r a s o n i c p r o p e r t i e s i n m e t a l l i c g l a s s e s of d i f f e r e n t chemical compositions i n o r d e r t o v e r i f y whether t h e s e frequency and tem- p e r a t u r e dependences a r e c h a r a c t e r i s t i c p r o p e r t i e s of a l l m e t a l l i c g l a s s e s o r only o f PdSiCu. G e n e r a l i z a t i o n of t h e s e o b s e r v a t i o n s i s important i n understanding t h e

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p r o p e r t i e s of m e t a l l i c g l a s s e s s i n c e w /T dependence of aAO seems t o b e r a t h e r w e l l 4

e s t a b l i s h e d i n i n s u l a t i n g g l a s s e s

.

Here we r e p o r t t h e r e s u l t s of u l t r a s o n i c measurements on two o t h e r bulky m e t a l l i c g l a s s e s and compare them w i t h t h o s e of PdSiCu.

2 . Experimental.- The c a n d i d a t e s were pd. 82Si

.18

and Pd.40Ni.40P.20 ( h e r e a f t e r PdSi and PdNiP, r e s p e c t i v e l y ) . Samples 2 mm (PdSi) and 3 mm (PdNip) i n diameter and sev- e r a l cm l o n g were o b t a i n e d by w a t e r quenching t h e molten a l l o y c o n t a i n e d i n t h i n - w a l l s i l i c a t u b e s ( w a l l t h i c k n e s s down t o 0.05

mm

o b t a i n e d by e t c h i n g s i l i c a t u b e s i n h y d r o f l u o r i c a c i d ) . According t o I I a v i e s l 6 , t h e c r i t i c a l c o o l i n g r a t e of P m i P was e s t i m a t e d t o be t h e lowest o f a l l g l a s s forming a l l o y s p r e s e n t l y known. As f a r a s we know, t h i s i s t h e f i r s t r e p o r t on p r e p a r a t i o n of amorphous PdNiP b u l k samples 3 mm i n diameter. The g l a s s y n a t u r e of t h e samples t h u s o b t a i n e d was e s t a b l i s h e d by x-ray d i f f r a c t i o n . Lithium n i o b a t e c r y s t a l s and Dow Corning g r e a s e d i l u t e d w i t h t r i c h l o r o e t h y l e n e were used a s t r a n s d u c e r s and bonding a g e n t s , r e s p e c t i v e l y . De- t a i l s of t h e experimental s e t u p were d e s c r i b e d i n Ref.

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f o r simultaneous measurements of t h e a t t e n u a t i o n and v e l o c i t y changes below 200

MHz

( ~ d ~ i ) . Only t h e a t t e n - u a t i o n changes were measured on t h e PdNiP u s i n g t h e c o n v e n t i o n a l p u l s e d - o s c i l l a t o r t e c h n i q u e . The a c o u s t i c i n t e n s i t i e s covered i n t h e s e experiments were about t h e

1 3 same a s t h o s e f o r PdSiCu

.

3. R e s u l t s and D i s c u s s i o n .

-

Q u a l i t a t i v e l y , t h e r e s u l t s of u l t r a s o n i c measurements f o r pdsi15 and P I ~ N ~ P ' ~ a r e very s i m i l a r t o t h o s e of PdSiCu, i . e . , t h e e x c e l l e n t f i t s

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Pd.82Si.1, Pd.775Si.165Cu.06 TRANSVERSE T = 0.3 K 5

10

50 100 500 1000

FREQUENCY

(MHz)

Fig.

1. Frequency dependence of s a t u r a b l e a t t e n u a t i o n , aAO, a t T = 0 . 3 K i n Pd

.775

Si.165C~,06(0), Pd.8eSi.,8(0) and Pd-40Ni . 4 0 P * 2 0 ( ~ ) . The s t r a i g h t l i n e shows a l i n e a r dependence and t h e dashed l i n e r e p r e s e n t s U* dependence

p r e d i c t e d by t h e t h e o r y ( s e e Eq.

( 3 ) ) .

0.05 0.1 0.5

1 TEMPERATURE

(K)

Fig.

2. Temperature dependence of aAO of t r a n s v e r s e waves f o r Pd .775Si . 1 6 5 C U . 0 ~

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C5-520

JOURNAL DE PHYSIQUE

a d i s c u s s i o n of cc,, (An a n a l y s i s o f t h e v e l o c i t y measurements appeared e l s e -

nu

whereL3 'l5 ). F i g . 1 shows t h e frequency dependences of ccAO at 0.3 K f o r PdSi and

-.,

.1 l .

PdNiP, t o g e t h e r w i t h t h e p r e v i o u s r e s u l t o n PdSiCu f o r c ~ m ~ a r i s o n ~ ' ~ ~ + . Examples of t e m p e r a t u r e dependences o f ccAO a r e shown i n F i g . 2 a t s e v e r a l f r e q u e n c i e s f o r t h e s e t h r e e d i f f e r e n t samples. It i s obvious t h a t temperature dependences do n o t f o l l o w Eq. ( 3 ) , i . e . , 1 / T , a t l e a s t below 1 K , where aAO t e n d s t o a c o n s t a n t v a l u e . I n F i g . 2 , f o r convenience o f r e p r e s e n t a t i o n , o n l y one frequency was chosen f o r each a l l o y . S i m i l a r t e m p e r a t u r e dependence, however, was observed f o r a l l t h r e e a l l o y s , a t a l l f r e q u e n c i e s s t u d i e d 13-15 'l7. T h e r e f o r e , t h e l i n e a r dependence on frequency and, below % 1 K, t h e e s s e n t i a l l y t e m p e r a t u r e independent behavior o f ccA0 a r e be-

l i e v e d t o be i n t r i n s i c f e a t u r e s of m e t a l l i c g l a s s e s i n g e n e r a l , i n c o n t r a s t t o t h o s e 2 -1

of d i e l e c t r i c g l a s s e s ( i . e . , w T ).

4. Conclusions.- I n c o n c l u s i o n , t h e g e n e r a l f e a t u r e s o f u l t r a s o n i c a t t e n u a t i o n and v e l o c i t y changes i n amorphous Pd

_.

8ZSi.

18'

Pd. 4oNi .40P. 20 and 775Si. 1 6 5 C u ~ . ~ 6 Show v e r y s i m i l a r behavior w i t h r e g a r d t o amplitude, frequency and t e m p e r a t u r e depen- d e n c e ~ . T h e r e f o r e , we conclude t h e form

l / h

+

J / J of amplitude dependence of s a t - u r a b l e a t t e n u a t i o n

,

ccAO, and t h e l o g a r i t h m i c t e m p e r a t u r e dependence o f v e l o c i t y changes, Av/v, a r e c o n s i s t e n t w i t h t h e c u r r e n t TLS t h e o r y . On t h e o t h e r hand, t h e magnitude, frequency and t e m p e r a t u r e dependences of t h e t o t a l change of s a t u r a b l e

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a t t e n u a t i o n , aAO (WT' r a t h e r t h a n w /T) and t h e e x i s t e n c e o f amplitude and frequency dependence of v e l o c i t y changes, Av/v, a r e n o t c o n s i s t e n t w i t h t h e p r e d i c t i o n s of t h e t h e o r y . And a l l t h e s e p r o p e r t i e s (some c o n s i s t e n t and some i n c o n s i s t e n t w i t h t h e TLS t u n n e l i n g t h e o r y ) seem t o b e i n t r i n s i c t o m e t a l l i c g l a s s e s .

5 . Acknowled6gnents.- This work was s u p p o r t e d i n p a r t by t h e NSF under Grant No. DMR~T-12249 and through t h e M a t e r i a l s Research Laboratory of Brown U n i v e r s i t y . 6

.'

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