Ultrasonic attenuation in glasses of SiO2GeO2 mixture

Ultrasonic attenuation in glasses of SiO2GeO2 mixture

ELSEVIER Physica B 219&220 (1996) 261 263 Ultrasonic attenuation in glasses of SiO2-GeO2 mixture T. Kosugi a'*, H. Kobayashi b, Y. Kogure c "Faculty...

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ELSEVIER

Physica B 219&220 (1996) 261 263

Ultrasonic attenuation in glasses of SiO2-GeO2 mixture T. Kosugi a'*, H. Kobayashi b, Y. Kogure c "Faculty qf Seience, Hiroshima University, Higashi-Hiroshima 739, Japan bNational Research Laborato~ of Metrolog3,, Tsukuba 305, Japan ~The Nishi Tokyo University, Kitatsuru-gun, Yamanashi 409-01. Japan

Abstract Ultrasonic absorption on SIO2-5 mole% GeO2 and SiO2-10 mole% GeO2 glasses between 1.6-250 K shows that the most probable origin of the structural relaxation of SiO2 glass is the transverse motion of the oxygen atom in Si O Si bridge among existing models. In addition it is also suggested that the same structure is the origin of two-level system (TLS) phenomena below 10 K.

I. Introduction

2. Experimental

The glassy state, as often represented by SiO2 glass, has characteristic thermal and acoustic properties at low temperatures, i.e., the specific heat dependent on T linearly below l K and the thermal conductivity proportional to T2 around 1 K, acoustic properties explained by the tunneling two-level system (TLS) around or below 1 K, and the large acoustic relaxation peak around the liquid nitrogen temperature El]. These properties are generally considered to be due to the existence of the double-well potential (DWP) in some atomic configuration [2 5]. However, we do not have the definite solution on the actual atomic configuration fiJr DWP until now in any kind of glasses. Our approach for seeking a solution is very simple but may be appropriate [6], i.e., we have tried to measure precisely the ultrasonic absorption or the internal friction (IF) of mixed glasses of SiO2 and GeO2, where the sites of Si atoms in pure 8i02 glass are expected to be replaced randomly by Ge atoms [7, 8].

Internal friction is measured by a composite oscillator method using - 18.5 ~ X-cut quartz transducer (50 x 3.5 x 3.5 mm, 51 kHz), which produces longitudinal waves [9]. Samples are SiO2-5mole% GeO2 and SiO2 10 mole% GeO2 glasses made by the VAD process. Fig. 1 shows the IF ( = nQ- 1) of SiO2 5% and 10% GeO2 glasses. The result of pure SiO2 is also shown as the reference. At low temperatures below 5 K, the IF is almost independent on temperature, which is explained to be due to the TLS relaxation [10]. The magnitude at 2 K is 1.49x 103, 1.22x 10 3 and 1.26x 10 -3 for pure SiO2, 5% GeO2 and 10% GeO2, respectively. By introducing GeO2, the low temperature IF below 25 K becomes smaller relative to that of pure SiO2. At relatively high temperatures where the IF is due to the thermally activated relaxation [2], the IF peak shifts to higher temperatures with introducing GeO2, i.e., 33 K, 40 K, and 48 K for pure SiO2, 5% GeO2 and 10% GeO2. If we assume 'structural units' (SU) as the origin of the relaxation, we may say that the initial SU in pure SiO2 glass decreases by introducing GeO2 and another type (a new type) of SU is newly produced. It is, however, not easy to discuss precisely the absolute magnitude of IF. For

*Corresponding author.

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Fig. 1. Internal friction of pure SiO2, SIO2-5% GeO2 and SIO2-10% GeOz glasses.

instance, the I F of SIO2-5% GeOz is smaller than that of SIO2-10% GeO2 in the whole temperature range of the measurements. In fact, it is known that the magnitude of I F is influenced at most 20 % by different annealing conditions [11].

3. D i s c u s s i o n

The following assumptions are made in order to analyze our data: (1) The temperature dependence of I F is little influenced by annealing, although the absolute value is not. (2) The initial structural units (ISU) which originate the relaxation in SiO2 glass, and the new structural units (NSU) produced by SiO2-GeO2 mixing have little influence on each other. This means that the I F can be given as the simple addition of each contribution from ISU and NSU. Fig. 2 shows the I F normalized to that at 2 K. The differences between the I F of a mixed glass and the pure SiO2 glass are also shown as D5 and D10 for 5% GeO2 and 10% GeO2, respectively. Points to be noted are; (1) The temperature dependence is the same below 25 K for three samples. (2) D5 and D10, which show almost the same temperature dependence, have the IF peaks at 65 K. (3) D10 is about two times large as D5. These results seem to be consistent with the assumptions we have made above. We next consider the microscopic meaning of ISU and NSU. The I F due to the relaxation in D W P for the one kind of structural units is given as I F = pcZk-~ (I -4- o92T2) \8-J sech2 2kT '

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Fig. 2. Normalized IF at 2 K for pure SiOz, SIO2-5% GeO/ and SIO2-10% GeO> The differences between the normalized IF of SIO2-5% GeO2 and pure SiOz, and between SIO2-10% GeO2 and pure SiOz are also shown.

where N is the number density of the active structural units, V the deformation potential, p the density of glass, c the sound velocity, co the angular frequency, T the relaxation time, A the asymmetry energy of DWP, e the energy difference between two ground states in DWP, and k T has usual meaning [10]. By mixing, the number density N and Young's modulus E ( = pc 2) will be changed, which will result in the change of IF. There are three plausible atomic models proposed for the D W P which produces the relaxation in SiO2 glass. First is the transverse motion of bridging oxygen (O) atom across the Si-O Si bridge (T-model) [2]. Second is the longitudinal motion of O atom along the S i - O - S i bridge (L-model) [3]. Third is the rotation of the relatively rigid SiO4 tetrahedra (R-model) I-4, 5]. First we consider the models T and L. By the mixing, the number of S i - O - S i bridges is reduced to 90.2% and 81% for 5 % GeO2 and 10% GeO20 respectively. Instead, the S i - O - G e bridge is newly produced by 9.5% and 18% in concentration for 5% and 10% GeO2. According to Eq. (1), the IF due to ISU is expected to be reduced to 92% and 85% of that of pure SiO2 for 5% and 10% GeOz. For SIO2-10% GeO/ this value agrees well the experimental result, i.e., the I F of 10% GeOz to pure SiO2 is 85% at the temperatures below 25 K (Fig. 1). For 5% GeO2, the experimental result is 82% which is 12% smaller than the expected value (92%). This difference may be due to the annealing condition, i.e., the effective annealing temperature for the 5 % GeOz sample might be higher than usual [11]. The IF peaks D5 and D10 could be due to NSU. The fraction of the concentration of S i - O - G e to S i - O - S i is expected to be 10.5% and 22.2% for 5% and 10% GeOz, respectively. The ratio between these fractions

?2 Kosugi et al. /Physica B 219&220 (1996) 261-263

.> Fig. 3. Schematic (two-dimensional)model for the relaxation in SiO 2 glass. Silicon atoms are shown as full circles and oxygen atoms (not shown apparently) are located at the corners of triangles. A large displacement is localizednear the oxygen atom at the center. (10.5/22.2 = 48%) should agree with the ratio of 65 K peak height between D5 and D10 in Fig. 2. The result supports this reasoning. Furthermore it is probable that the relaxation of NSU corresponds to the relaxation due to the transverse motion of O atom in S i - O - G e bridge, because the peak temperature Tp ( = 65 K) is reasonably located when we see the fact that Tp in pure SiO2 and pure GeO2 glasses will be about 33 K and 100 K for 51 kHz, respectively [2,12]. On the other hand, L-model is denied strongly, because the DWP for longitudinal motion of O atom in the S i - O - G e bridge must be too largely asymmetric to produce a successive relaxation between its two wells. Next let us consider the recently proposed R-model, i.e., the coupled rotation of five tetrahedra, which consist of one centered tetrahedron and four surrounding tetrahedra [53. For 8 i 0 2 - 5 % and 10% GeO2, the number of the group of five SiO4, which might correspond to ISU for the relaxation in this model, is reduced to 77.4% and 59%, respectively. Instead, the group of the centered SiO4 with surrounding three SiO4 and one GeO4 will be mainly produced by 16% and 26% in concentration for 5% and 10% GeO2. This result does not seem to support R-model, because the second largest group of R-model should have a similar activation energy to that for the five SiO4 tetrahedra when we suppose its configuration. Thus R-model is not likely to be satisfactory for the relaxation.

263

We summarize our understanding of the actual structure which originates the relaxation in SiO2 glass as follows. The new structural unit (NSU) in SiO2-GeO2 mixed glasses could be assigned as the transverse motion of O atom in the Si-O Ge bridge among existing structural models as discussed above. As a result, the initial structural unit (ISU) can be considered to be also the transverse motion of the O atom in the Si O-Si bridge. In addition the TLS phenomena may originate from the same structure as the high-temperature relaxation in SiO2 glass, because the magnitude of the IF due to ISU between 1.6 and 200 K is changed in the same manner against mixing with Ge atoms. The transverse motion of an oxygen atom in Si O-Si bridge may be considered as a part of the libration of SiO4 tetrahedra (Fig. 3). However, our proposal is different from that by Vukcevich or Buchenau in that the actual potential barrier for the relaxation should be localized near one oxygen atom which is easiest to move in the four oxygen atoms in a SiO4.

Acknowledgements We would like to thank The Furukawa Electric Co., Ltd. and Fujikura Ltd. for supplying us the SiO2 10% GeO2 sample and the SIO2-5% GeO2 sample.

References [1] W.A. Phillips (ed.), Amorphous Solids - Low Temperature Properties (Springer, Berlin, 1981). [2] O.L. Anderson and H.E. B6mmel, J. Am. Ceram. Soc. 38 (1955) 125. [3] R.E. Strakna, Phys. Rev. 123 (1961) 2020. [4] M.R. Vukcevich, J. Non-Cryst. Solids 11 (1972) 25. [5] U. Buchenau, H.M. Zhou, N. Nucker, K.S. Gilroy and W.A. Phillips, Phys. Rev. Lett. 28 (1988) 1318. [6] T. Kosugi, H. Kobayashi and Y. Kogure, Phonon Scattering in Condenced Matter VII, eds. M. Meissner and R.O. Pohl (Springer, Berlin, 1993) p. 277. [7] N.F. Borrelli, Phys. Chem. Glasses 10 (1969) 43. [8] T. Edahiro, M. Kawachi, S. Sudo and S. Tomaru, Jpn. J. Appl. Phys. 19 (1980) 2047. [9] T. Kosugi, Jpn. J. Appl. Phys. 33 (1994) 2862. [10] J. J/ickle, L. Piche, W. Arnold and S. Hunklinger, J. NonCryst. Solids 20 {1976) 365. [11] J.T. Krause, J. Appl. Phys. 42 {1971) 3035. [12] K. Sakai, P.K. Choi and K. Takagi, J. Non-Cryst. Solids 109 (1989) 47.