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Submitted on 1 Jan 1982
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THERMOELASTIC AND RELAXATIONAL PROPERTIES OF DIELECTRIC AND METALLIC
GLASSES AT LOW TEMPERATURE
H. Tietje, M.V. Schickfus, E. Gmelin
To cite this version:
H. Tietje, M.V. Schickfus, E. Gmelin. THERMOELASTIC AND RELAXATIONAL PROPERTIES
OF DIELECTRIC AND METALLIC GLASSES AT LOW TEMPERATURE. Journal de Physique
Colloques, 1982, 43 (C9), pp.C9-529-C9-532. �10.1051/jphyscol:19829105�. �jpa-00222409�
THERMOELASTIC AND RELAXATIONAL PROPERTIES OF DIELECTRIC AND METALLIC GLASSES AT LOW TEMPERATURE
H. Tietje, M.v. Schickfus and E. Gmelin
Max-Planak-Institut fur Festkorperforsahung, Hei-senbergstr. 1, D-7000 Stuttgart 80, F.R.G.
Résumé.- Nous avons étudié le paramètre de Grûneisen à basse tem- pérature et le comportement relaxationnel à temps long des exci- tations tunnel dans la silice vitreuse et dans le verre métallique PdSiCu en mesurant l'effet thermoélastique. Dans le cas de la si- lice vitreuse, nos résultats sont en accord qualitatif avec les mesures précédentes de dilatation thermique, et nous avons obser- vé des temps de relaxation atteignant 600 s. Pour PdSiCu, une contribution relaxationnelle importante a été mise en évidence.
Abstract. - We have investigated the low-temperature Gruneisen parameter and the long-time relaxational behaviour of the tunneling excitations in vitreous silica and in the metallic glass PdSiCu through the thermoelastic effect. In the case of a-Si02, our data agree qualitatively with previous measurements of the thermal ex- pansion, and relaxation times of up to 600 s have been detected.
For PdSiCu a large relaxational contribution was found.
The low-temperature properties of amorphous solids differ completely from those of crystalline materials. Characteristic anomalies are the well-known linear temperature dependence of the specific heat, a In- dependence of the thermal conductivity and an enhanced and saturable ultrasonic absorption / 1 / . These effects, which have been observed in dielectric and metallic glasses as well, are caused by low-energy tun- neling systems which seem to be present in all glasses with a low co- ordination number. These tunneling systems are supposed to be atoms or groups of atoms moving in a double-well potential.
In this work we have studied the influence of the tunneling systems on- to the Gruneisen parameter and onto the long-time relaxational behavi- our of amorphous materials by the elasto-caloric effect. The Gruneisen parameter characterizes the non-harmonic behaviour of a material and is defined as y = -31n E/31n V, i.e. the change of energy associated with a change of volume. For a "macroscopic" y this value has to be weighted with the specific heat of the excitation under consideration.
The usual technique to study the Gruneisen parameter is through a mea- surement of the thermal expansion, since y = B / < X C y ) - A t very low tem- peratures the thermal expansion becomes very small and therefore diffi- cult to measure. We chose a different approach, which was essentially to measure the temperature variation associated with a change of strain.
In this case the macroscopic Gruneisen parameter turns out to be 3 AT
Y T-x"Acr l 1 )
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19829105
C9-530 JOURNAL DE PHYSIQUE
where
x
i s t h e c o m p r e s s i b i l i t y and o t h e a p p l i e d s t r e s s .I n t h e p r e s e n c e of an e x t e r n a l s t r a i n f i e l d , a n i n t e r a c t i o n term H I i s added t o t h e Hamiltonian H o of t h e u n d i s t u r b e d t u n n e l i n g system, r e - s u l t i n g i n a t o t a l Hamiltonian H:
Then t h e e n e r g y of t h e t u n n e l i n g system i s E = / A 2 + A 2 . Here A i s t h e asymmetry of t h e double-well p o t e n t i a l and A t h e enerEjy s p l i t t i n g due t o t h e t u n n e l i n g . A. i s g i v e n a s A = 5fl-xp ( - A )
,
where h = d J 2 m ~ / f i ~.
hR i s t h e v i b r a t i o n a l energy o f t h g p a r t i c l e i n one w e l l , d t h e d i s t a n c e between t h e two w e l l s , and V t h e h e i g h t of t h e energy b a r r i e r between them. A s t r a i n f i e l d c a u s e s changes i n b o t h t h e asymmetry and t h e t u n n e l s p l i t t i n g 6 A = BAe and 6A = B e .
I n o r d e r t o e x p l a r n t h e thgrmalA"and a c o u s t i c p r o p e r t i e s of g l a s s e s , a d i s t r i b u t i o n of t h e p a r a m e t e r s A and X I P(A,X) = P = c o n s t h a s been i n t r o d u c e d / I / . T h i s l e a d s t o a d i s t r i b u t i o n of t h e r e l a x a t i o n t i m e s T
i n which t h e t u n n e l i n g systems r e t u r n i n t o t h e r m a l e q u i l i b r i u m a f t e r a p e r t u r b a t i o n / 2 / :
-
1-
PP ( E , T ) =
-
1T-1 ( I - Tmin T - l ) 112
where ~~i~ (' 10 -8 s a t 2 K ) i s t h e r e l a x a t i o n time f o r t h o s e t u n n e l i n g systems w l t h A = E . For A o < < ~ v e r y l o n g r e l a x a t i o n t i m e s a r e e x p e c t e d .
0
I n o u r experiment t h e samples were e i t h e r r o d s of v i t r e o u s s i l i c a Su- p r a s i l I w i t h a l e n g t h of 120 mm and a d i a m e t e r of 4 mm, o r r i b b o n s o f t h e m e t a l l i c g l a s s Pdo. 775Si0.1 65Cu0 06 w i t h dimensions 1 4 0 ~ 1 . 5 ~ 0.03 mm. The samples were mounted i n t h e vacuum chamber of a c r y o s t a t and clamped a t b o t h e n d s t o c o p p e r b l o c k s a t c o n s t a n t t e m p e r a t u r e . S t r e s s was a p p l i e d from o u t s i d e t h e c r y o s t a t t h r o u g h a b e l l o w s - s e a l e d s t a i n l e s s s t e e l w i r e . The t e m p e r a t u r e v a r i a t i o n was measured w i t h an exposed-element germanium thermometer and a Wheatstone b r i d g e and r e - c o r d e d by a d e s k t o p computer. T y p i c a l s t r e s s e s were 500 N/cm2 f o r v i t r e o u s s i l i c a and 2x104 N/cm2 f o r PdSiCu, t h e a s s o c i a t e d t e m p e r a t u r e changes were of t h e o r d e r of 1 mK and 50 mK, r e s p e c t i v e l y . The r i s e - t i m e of t h e s t r e s s was a b o u t 0.5 s .
F i g . 1: Temperature change of v i t r e o u s s i l i c a a t 3.5 K a f t e r a p p l y i n g and r e l e a s i n g of s t r e s s .
A 1
-
-
YE -
u
I-
-
a -
I
10 20 30 40
Unloading t ( s )
F i g . 1 shows a t y p i c a l t e m p e r a t u r e r e s p o n s e AT( t ) f o r a-Si02 a t 3.5 K . Temperature r i s e s when s t r e s s i s a p p l i e d and d e c r e a s e s when s t r e s s i s r e l e a s e d , c o r r e s p o n d i n g t o a n e g a t i v e Gruneisen p a r a m e t e r . It can c l e a r - l y be s e e n t h a t t h i s e f f e c t , which should b e r e v e r s i b l e i n an i d e a l e l a s t i c s o l i d , i s superimposed by a n i r r e v e r s i b l e h e a t i n g . The i r r e v e r - s i b l e h e a t i n g i s n e g l i g i b l e a t h i g h e r t e m p e r a t u r e s (T> 6 K ) , whereas it masks t h e r e v e r s i b l e c o n t r i b u t i o n below T-2 K . The two c o n t r i b u t i o n s
F i g . 2: Temperature depen- dence o f t h e Griineisen p a r a - meter o f a-Si02. The s o l i d l i n e r e p r e s e n t s t h e r e s u l t s
of / 3 , 4 , 5 / .
>
-
8L
I 1 I II
2 4 6 T (K)
From t h e r e v e r s i b l e c o n t r i b u t i o n we have e v a l u a t e d t h e t e m p e r a t u r e dependence of t h e Gruneisen p a r a m e t e r shown i n F i g . 2. Our d a t a a r e q u a l i t a t i v e l y s i m i l a r t o t h o s e r e p o r t e d i n t h e l i t e r a t u r e /3,4,5/, a l - though s m a l l e r by a f a c t o r of two. The d i f f e r e n c e may i n p a r t b e due t o t h e f a c t t h a t our e x p e r i m e n t i s a " s h o r t - t i m e " e x p e r i m e n t compared w i t h a measurement of t h e t h e r m a l e x p a n s i o n .
F o r a d i s c u s s i o n of t h e i n f l u e n c e of t h e t u n n e l i n g systems o n t o t h e Griineisen p a r a m e t e r , t h e c o n t r i b u t i o n s of BA and Baa have t o be e v a l u - a t e d . We assume BA t o b e composed of two c o n t r i b u t i o n s : A d i r e c t v a r i - a t i o n o f t h e asymmetry w i t h s t r a i n , r e s u l t i n g i n B A z 1 eV, and a s m a l l c o n t r i b u t i o n due t o a dependence of t h e asymmetry f r o m t h e d i s t a n c e d of t h e w e l l s . We e x p e c t no c o r r e l a t i o n between A and BA and t h e r e f o r e no macroscopic c o n t r i b u t i o n of t h e f i r s t p a r t . The second p a r t y i e l d s y =-I / 6 / . The i n f l u e n c e of BAo h a s been d i s c u s s e d by Lyon e t a l . / 3 / , i t s c o n t r i b u t i o n t o y i s e s t i m a t e d t o b e between -1 and - 1 0 .
The i r r e v e r s i b l e h e a t i n g c a n be u n d e r s t o o d a s a r e l a x a t i o n e f f e c t of t h e t u n n e l i n g s y s t e m s . When s t r e s s i s a p p l i e d t o t h e sample, t h e t u n - n e l i n g systems w i l l change energy and r e a c h t h e i r new t h e r m a l e q u i l i - brium w i t h i n t h e i r r e l a x a t i o n t i m e T . Those t u n n e l ~ n g systems w i t h T
s m a l l e r t h a n t s , t h e t i m e i n which s t r e s s i s a p p l i e d o r r e l e a s e d , w i l l always be i n t h e r m a l e q u i l i b r i u m w i t h t h e phonon b a t h of t h e sample.
They may c o n t r i b u t e t o t h e r e v e r s i b l e h e a t i n g . Those systems w i t h T r t , w i l l s l o w l y r e l a x i n t o t h e new e q u i l i b r i u m l e a d i n g t o a c r e e p o f t h e
sample which produces h e a t , r e g a r d l e s s of t h e s i g n of t h e s t r e s s . F i g . 3 shows t h a t even a t t
=
10 min t h e h e a t produced by d e c a y i n g t u n n e l i n g systems can b e observed a t t e m p e r a t u r e s around 3 X. Numerical i n t e g r a - t l o n shows a remarkable agreement of t h e i r r e v e r s i b l y produced h e a t w i t h t h e p r e d i c t i o n of equ. 3.F i g . 3: I r r e v e r s i b l y produced
h e a t a s a f u n c t i o n of t i m e
0.6h
C9-532 JOURNAL DE PHYSIQUE
I n t h e c a s e of t h e m e t a l l i c g l a s s PdSiCu, o n l y a n i r r e v e r s i b l e h e a t i n g c o u l d be o b s e r v e d a t a l l t e m p e r a t u r e s ( F i g . 4 ) . I f we assume t h a t t h i s e f f e c t i s due t o t h e t u n n e l i n g s y s t e m s , it i s i n c o n t r a s t t o t h e v e r y s h o r t r e l a x a t i o n t i m e s e x p e c t e d b e c a u s e of t h e i r c o u p l i n g t o t h e con- d u c t i o n e l e c t r o n s . We t h e n would have t o assume a dependence of t h e c o u p l i n g between e l e c t r o n s and t u n n e l i n g s y s t e m s on t h e t u n n e l s p l i t - t i n g A,. A f u r t h e r p o s s i b i l i t y i s t h e a c t i v a t i o n of d i s l o c a t i o n - l i k e d e f e c t s . F i n a l l y t h e p o s s i b i l i t y of c r e e p h a s t o be t a k e n i n t o a c c o u n t , a l t h o u g h o u r s t r e s s was below t h e room-temperature c r e e p l i m i t by a f a c t o r of two. F u r t h e r e x p e r i m e n t s , e s p e c i a l l y a t lower t e m p e r a t u r e s and w i t h s u p e r c o n d u c t i n g m e t a l l i c g l a s s e s w i l l h e l p t o c l a r i f y t h e s i t u a t i o n .
F i g . 4 : Temperature v a r i a t i o n of PdSiCu a t 3 . 5 K. The s t r e s s
i s a p p l i e d a t t = 0 s e c and
T -
r e l e a s e d a t t = 40 s e c .
t
Unloading 20 4 0 60
tCsl
R e f e r e n c e s .
/ 1 / f o r a r e c e n t r e v i e w s e e : T o p i c s i n C u r r e n t P h y s i c s 24 (Amorphous S o l i d s , W.A. P h i l l i p s e d . )
,
S p r i n g e r , B e r l i n 1981./ 2 / J . J a c k l e : 2. P h y s i k
257,
212 ( 1 9 7 2 ) ./ 3 / K . G . Lyon, G.L. S a l i n g e r , C.A. Swenson: Phys. Rev. B E , 4231 ( 1 9 7 9 ) . / 4 / G . K . White: Phys. Rev. L e t t .
2 ,
204 ( 1 9 7 5 ) ./ 5 / O.B. Wright, W.A. P h i l l i p s : P h y s i c a
z,
859 ( 1 9 8 1 ) ./ 6 / M.v.Schickfus, S. H u n k l i n g e r , K. D r a n s f e l d : i n "Fundamentals and A p p l i c a t i o n s of N o n m e t a l l i c M a t e r i a l s a t Low T e m p e r a t u r e s " , G . Hartwig, D. Evans, R.L. Kolek e d . , Plenum P r e s s 1981.
