LOW FREQUENCY ELASTIC PROPERTIES OF GLASSES AT LOW TEMPERATURE

Transcription

1 LOW FREQUENCY ELSTIC PROPERTIES OF GLSSES T LOW TEMPERTURE. Raychaudhuri, S. Hunklinger To cite this version:. Raychaudhuri, S. Hunklinger. LOW FREQUENCY ELSTIC PROPERTIES OF GLSSES T LOW TEMPERTURE. Journal de Physique Colloques, 1982, 43 (C9), pp.c9485c9488. < /jphyscol: >. <jpa > HL Id: jpa Submitted on 1 Jan 1982 HL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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 HL, 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.

2 JOURNL DE PHYSIQUE Colloque C9, supplément au n 12, Tome 43, décembre 1982 page C9485 LOW FREQUENCY ELSTIC PROPERTIES OF GLSSES T LOW TEMPERTURE.K. Raychaudhuri and S. Hunklinger MaxPlanckInstitute, 7000 Stuttgart 80, F.R.G. Résumé. Nous avons mesuré pour la première fois les propriétés élastiques (vitesse du son et frottement interne) de verres au dessous de 1 K dans le domaine des fréquences audibles (~IkHz). Les résultats obtenus sont discutés dans le schéma du modèle tunnel des verres. L'hypothèse essentielle du modèle tunnel concernant les états tunnel à grand temps de relaxation a été vérifiée. bstract. We have for the first time measured the elastic properties (sound velocity and internal friction) of glasses "below 1K in the audiofrequency range ( ~ 1 KHz). The results obtained are discussed in the frame work of the tunneling model of glasses. The major assumption of the tunneling model regarding tunneling states with long relaxation times has been verified. Low temperature properties of glasses have been studied extensively in recent years to understand the nature of low energy excitations which are commonly known as Two Level Systems or Tunneling Systems (TS) /1/. In this paper we report the first measurements of the elastic properties of a glass below 1K in the audiofrequency range ( ~ 1 KHz). We have studied sound velocity (V E ) and internal friction (Q ) in a silica based insulating glass, a metallic glass (PdSiCu) and a superconducting metallic glass (CuZr, T = 0.32K) at temperatures "between 10mK and 10K by using a vibrating reed technique. In this temperature range audiofrequencies are hitherto an unexplored frequency domain and we compare and contrast high and low frequency measurements in the light of the existing understanding of the glassy state. The present understanding of the low temperature properties of glasses is based on the Tunneling Model /2/. This model predicts that for a TS with energy splitting E, there exists a broad distribution of relaxation times (l). The distribution is given "by /2,3/ P (E, T ) = P/2(1 _T (E)/T) 1 ' 2, where T (E) is the relaxation time of the fastest TS with energy E and P is the constant density of states. P (E, T ) diverges both for small and large values of T. By doing the experiment at low frequency we are probing especially the region of very long relaxation times. This is for the first time, this region has been probed unambigously through dynamic elastic measurements. Before presenting our data we want to discuss briefly the theoretical predictions of the Tunneling Model. t low temperatures (T < 10K) internal friction in glasses arises from two different processes /1/. One of them is the resonant interaction between phonons and TS. In our experiment the measuring frequency is so low that its contribution is negligible, since Q^4 S <* w. The resonant interaction leads, however, to a logarithmic, but frequency independent increase of velocity. ^* * [fj d> where the constant is given by res = Py 2 /pv 2. Here y is the elastic coupling constant, p is the mass density and v the sound velocity. T Q is some arbitrary reference temperature. The second process is called the relaxation process. If T is the relaxation time of the fastest TS we can distinguish between two different regimes in the relaxation process, namely ore» 1 and OJT «1. When o>t «1, we are probing TS with very long relaxation time. In principle one could also study this regime with radio frequencies. But at radio frequencies the crossover (OJT = 1) occurs at T > 1K, where uncertainties arise due to contributions to the relaxation rate from other process. In the audiofrequency range the crossover occurs at T < 0.1K, where the above complications do not arise. rticle published online by EDP Sciences and available at

3 C9486 JOURNL DE PHYSIQUE t very low temperatures of high frequencies w'r >> 1. In this region the contribution of relaxation process to variation of soun?? velocity is negligible so the only contribution is due to the resonant process. However, the temperature dependence of QI reflects the energy dependence of the relaxation rate T'. In insulating glasses the relaxati n is via direct one phonon process and TI a E ~. One obtains in that case Q' a T 3. In metallic glasses /4/ below a few Kelvin the electrons dominate the relaxation process and 'rzl a E. In that case a T. lso in metallic glasses due to extremely large relaxation rate (T very small) one enters the regime w~ >> 1 at extremely low temperature (in our frequency range in the u K region!) t Tower frequencies or higher temperature wt << 1. In this regime independent of the relaxation mechanism (via phonons or efectrons) one obtains t&l1 = T es. This temperature independent region, known as the "plateau" depends only on tfie density of states. In this regime, the contribution of relaxation process to the sound velocity causes a decrease with increasing temperature following a lntrelation given by Eq.1, The prefactor depends on the relaxation mechanism. For phonons P =3/2 re,. So that the overall variation in v is given with = % + p = 1/2,. For ree s laxation by electrons = 1/2 he, and the resulting?refactor = 172 res. It is to be noted that above result depends crucially on the distribution of parameters as suggested in the tunneling model. In Fig. 1 we show the data on a silica based insulating glass (microscope cover slide) s we warm up from the lowest temperature the sound velocity increases first following a 1nTrelation. t these temperatures we are in the regime w'r >> 1, so the change in velocity can be identified with the resonant contribution? From the slope we find res = 3.'7~10~, which is in excellent agreement with res found in this type of glasses in high frequency measurements. t around.08k v/v passes through a maximum which signals the crossover (wc 1). fter passing through the maximum the sound velocity decreases again, sincemwe are in the regime wr << 1. From 0.2K to IK, v decreases following a 1nTrelation. From the slope wemfind = 1.9x10~, which is 1/2 res, as expected. It is to be noted that this prediction of the tunneling model has been verified for the first time and this has been made possible only by using low frequency measurements. The internal friction also shows the expected behaviour. Below 0.1K itincreases as the temperature increases and above O.2K when we enter the regime w~ << 1 (signified by the fall of sound velocity) we obtain a nice plateau which continuzs over a large temperature range. In metallic glass (PdSiCu; see Fig. 2) the sound velocity increases following a 1nTrelation from the lowest temperature to about 1.5K. fter that it falls again quite rapidly. In metallic glasses,~~ is very small and in the entire temperature range w'r << 1. So the logarithmic rise of sound velocity is attributed to a combined efyect of resonant and relaxation process and as explained earlier the prefactor of the 1nTterm is 1/2 res. Thus from the slope we obtain Tes = 6.4x10~ which is again in agreement with high frequency measurement. bove 1.5K the relaxation process is dominated by phonons and the sound velocity falls again. It is to be pointed out that in metallic glasses the maximum occurs when the dominant relaxation mechanism changes from electrons to phonons and therefore should be more or less independent of frequency. But in insulating glasses the maximum occurs at the crossover w'r = 1. So it should be dependent on the frequency of measurement. Since we are in?he regime w'c << 1, the internal friction QI is more or less temperature independent over themwhole range in the metallic glass. In superconducting glass (Cu~r, Tc = 0.32K ; see Fig. 3) the situation is rather involved due to complicated behaviour of the relaxation rate at different temperatures /4,5/. t the lowest temperatures (T << T ) all the electrons are effectively frozen out and they no longer take part in relax?ng TS. So the behaviour is similar to an insulating glass. Since wr >> 1 holds, we see a logarithmical rise in the sound vem locity due to the resonant process. round.05k w'c tends to unity and the velocity passes through a maximum. bove that temperature tge relaxation process dominates and velocity falls rather rapidly. Simultaneously increases rapidly below.08k and reaches a plateau showing that WT << 1. The fall of sound velocity in this region is rather rapid signifying tha? quasiparticles excited across the superconducting energy gap are also taking part in the relaxation mechanism /5/. This behaviour stops at T and above that temperature the sound velocity behaves like that of a metallic glasg. Since at T = Tc, w~ << 1, we do not expect any big change in QI. However, we observe a small kink atm~c. The origin of this is not known.

4 Fig. 1: Sound velocity ( 0) and internal friction ( ) of a silica based insulating glass. W > \ IW 4 i PdSiCu 1030 Hz I I l l,, I lo TEMPERTURE (K) Fig. 2: Sound velocity ( 0 ) and internal friction ( a) Pd Si Cu ' of the metallic glass

5 JOURNL DE PHYSIQUE... ' I I I I I I ' 1 1 8%. 7"" '"' fi n 1.6 >W 4 >" Q f 5 T, 4x10,L.. *%,J me.. CuZr 1564 HZ. I I I I I I I I l TEMPERTURE (K) 4 cs 0 F 1.2 px I CI 0.8 Fig. 3: Sound velocity ( a) shows Tc. and internal friction ( a) of C U ~ ~ The Z ~ arrow ~ ~. To conclude, we have for the first time verified the major assumption of the tunneling model regarding distribution of states at very long relaxation times. References /I/ See the articles in "morphous Solid Low Temperature Properties"; Ed. W.. Phillips; Springer Verlag, New York 1981 /2/ W.. Phillips, J. Low Temp. Physics 7, 351 (1972) and P.W. nderson, B.I. Halperin, C.M. Varma, Phil. Mag. 25, l (1972) /3/ J. Jackle, Z. Phys. m, 212 (1972) /4/ J.L. Black in "Glassy Metals", p. 167 (Ed. H.J. Guntherodt, H. Beck; Springer Verlag, New York 1981) /5/ J.L. Black, P. Fulde, Phys. Rev. Lett. 9, 453 (1979) + lexander von Humboldt fellow