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EFFECTS OF THERMAL CYCLING ON
ULTRASONICALLY MEASURED TLS
PARAMETERS OF A METALLIC GLASS
G. Cibuzar, A. Hikata, C. Elbaum
To cite this version:
JOURNAL
DE
PHYSIQUEColloque
CIO,
supplément au n o 12, Tome 46, décembre 1985 page '210-461EFFECTS OF THERMAL CYCLING ON ULTRASONICALLY MEASURED TLS PARAMETERS OF A METALLIC GLASS
G. CIBUZAR',
A.
HIKATA and C. ELBAUMBrown University,Department of Physics, Providence, R.I. 02912,
U.S.A.
Résumé
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En utilisant des mesures de la vitesse du son en fonction de la température en dessous de 1 K, nous avons étudié les effets de relaxation structurelle, ainsi que la reversibilité des charactéristiques de l'effet tunnel dans les systèmes à deux niveaux du verre metallique PdSiCu. L'existence de réversibilité du produit de la densité d'états et du potentiel de déformation a été confirmé entre les températures de 610 Ket 510 K.
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Abstract - Velocity changes as a function of temperature, at T < 1 K, were used to study the effects of structural relaxation and reversibility of two-level tunneling systems characteristics of the metallic glass PdSiCu. The existence of reversibility of the product of density of states and de- formation potential for TLS has been confirmed between the temperatures of 610 K and 510 K.
1
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INTRODUCTIONMany low temperature properties of amorphous materials have been accounted for by the two-level tunneling systems (TLS) mode; (11. One such feature is the linear increase of sound velocity with InT for T < 1 K. We report here a study in which this property was used to investigate, at low temperatures, the effects of struc- tural relaxation of glasses.
The TLS mode1 predicts that at low temperatures (UT, >> 1). the sound velocity change (Avlv) is given by
and at high temperatures (UT, << l),
where n is the density of states of TLS, M is the deformation potential, p is the material density and Tg is an arbitrary reference temperature. T~ is the relax- ation r i m e of fastest relaxing TLS with energy splitting E {2}. Thus, as the tem- perature is raised, (Av/v) initially increases with 1nT and then goes through a maximum and decreases proportionally to -1nT.
The density of a glass is usually smaller than that of the corresponding crystal- line solid; i-e., glass has an excess volume, and changes in this excess volume are an important factor in structural relaxation of glasses. The amount of excess vol-
'~resent address : Sperry ~ o m g a n y , Eagen, MN, U.S.A.
CIO-462
JOURNAL
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PHYSIQUE
Ume is a function of the thermal history of the glass. The higher the rate of the original quenching of the liquid, the more excess volume is formed. The amount of excess volume can also be varied after the glass has been formed by applying heat treatments at temperatures low enough to prevent crystallization, yet allow struc- tural relaxation.
Thë amount of strvctural relaxation depends on the annealing temperatvre Ta and on the cooling rate Q after annealing. If the sample is cooled slowly (Q < 1 K/sec), thus allowing significant structural changes while cooling, then the resulting structures would correspond to those which would be obtained by a lower original quench rate of the liquid during the formation of the original glass. For a given cooling rate, the higher Ta the more time the sample has to relax.
Measurements of many properties of the glass have been found to be reversible when the glass is subjected to temperature cycling and rapid quenching (3-6). By a re- versible change we do not mean reversible in the thermodynamic sense, but changes in a metastable state due to non-equilibriurn rapid quenching. We have studied revers- ibility by annealing experiments on the metallic glass PdSiCu, as follows. The first annealing was done at 610 K for two hours, followed by a quench in ice-water. Subsequent annealings, st 510 K, 610 K and 510 K were done for 20 minutes each, also followed by a quench in ice-water. Our results for the change in nM2 deduced from measurements of the sound velocity change are shown in Table 1. The value of nM2 was found to change reversibly by about 15% while cycling between 610 and 510 K. The only other experimental data on the reversibility of nM2 is the work of Cotts, Anderson and Poon (7). They found that cycling a sample of PdSiCu between 520 and 570 K resulted in a 7% change in nM2 as deduced from thermal conductivity measure- ments. If we assume that the effect of the annealing is the same for al1 the TLS in this range of energy splittings, since the temperature range of the two experi- ments overlapped, the results of the two experiments should be consistent in terms of the amount of reversibility. The difference between the two annealing tempera- tures for Our experimenl: is twice that of the experiment of Cotts et al, and we find the amount of reversible change of Our measurement to be twice that of theirs.
Table 1
Change in nM2 as a function of annealing temperature T
2 2 a'
Ta measured nM lpv
Theoretical predictions of the cause of the reversible changes have centered on both chemical short-range ordering (CSRO) and excess volume. We are not aware of any quantitative CSRO model which make's predictions with which we can compare Our experimental data. There is, however, a quantitative prediction based on the free volume model of Cohen and Turnbull ( 8 ) . (Free volume is the term reserved for that part of the excess volume which can be distributed randomly in the glass without changing the interna1 energy). Recently, Cohen and Grest (91 extended the free volume model to account for thermodynamic properties (such as specific heat) as well as transport properties. Using molecular dynamics calculations they developed a theory of the amorphous phase, and in the process developed a more rigorous basis for the free volume model. They obtained the following expression for the amount of the free volume vf as a function of temperature
where A (dimensions of volume/temperature), B, and T (a temperature) are constants, and Tl > Tg. Notice that vf goes to zero as T goes &O zero. We are concerned with the relationship between the amount of free volume as a function of annealing tem- perature. Using the estimate for v
,
for T << T < Tl, we have v T, where Tformed. S i n c e we r a p i d l y quench t h e sample a f t e r a n n e a l i n g , we r e t a i n t h e s t r u c - t u r e c h a r a c t e r i s t i c of t h e a n n e a l i n g t e m p e r a t u r e T
,
hence we have T = Ta, and vf a T.
On t h e a s s u m p t i o n t h a t M~ i s c o n s t a n t , tfie work of Cohen and G r e s t {IO)s u g g e s ? s t h a t t h e TLS d e n s i t y o f s t a t e s n i s p r o p o r t i o n a l t o T
,
which i s c o n s i s - t e n t w i t h t h e - s u l t s shown i n Table 1. The r e v e r s - i l i t y o f t h e changes i n nM2 c a n be e x p ï a k e d by r e v e r g i b l e c h a n g e s i n n due t o t h e r e v e r s i b l e f r e e volume changes b r o u g h t a b o u t by r a p i d quenching a f t e r a n n e a l i n g a t d i f f e r e n t T.
The r e s u l t s of o u r e x p e r i m e n t s on s l o w and r a p i d c o o l i n g a f t e r a n n e a l i n g i n a i c a t e t h a t t h e TLS a r e a s s o c i a t e d w i t h r e g i o n s o f f r e e volume.T h i s r e s e a r c h was s u p p o r t e d by t h e N a t i o n a l S c i e n c e Foundation t h r o u g h t h e m a t e r i - a l s R e s e a r c h L a b o r a t o r y o f Brown U n i v e r s i t y .
III - REFERENCES
P.W. Anderson, B . I . H a l p e r i n and C.M. Varma, P h i l . Mag.
25,
1 (1972); W.A. P h i l l i p s . J. Low Temp. Phys. 7, 351 (1972).J. J a c k l e , Z . Phys.
257,
212 (1972). T. Egami, Mat. Res. B u l l .g,
557 ( 1 9 7 8 ) .A. Kursumovic, M.G. S c o t t , E. G i r t , and R.W. Cahn, S c r i p t a M e t a l l .
s,
1303 (1980).M. R a l a n z a t , S c r i p t a M e t a l l .
14,
1 7 3 (1980).A.C. Anderson, C.C. Koch, and J . O . Scarbrough, Phys. Rev. B z , 1156 (1982). E . J . C o t t s , A.C. Anderson and S. Poon, Phys. Rev. B E , 6127 (1983).
M. Cohen and D. T u r n b u l l , J. Chem. Phys.
