Amorphous-like acoustical properties of Na doped β-Al2O 3

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Abstract
Ultrasonic attenuation and velocity measurements are reported for the superionic conductor Na β-alumina for a wide range of temperatures (1.7-80 K) and frequencies (0.5-2.0 GHz). Three acoustic modes were propagated perpendicular to the c-axis : longitudinal, transverse polarized perpendicular to the c-axis, and transverse polarized parallel to the c-axis. In the lower temperature range (T < 10 K) the attenuation for all three modes is independent of the ultrasonic frequency and varies as the cube of the temperature. At higher temperatures the attenuation reaches a temperature independent plateau, the height of which depends linearly on frequency. The acoustic phase velocities for the longitudinal mode and the transverse mode polarized perpendicular to the c-axis increase logarithmically with temperature at low temperatures, pass through a maximum at approximately 8 K, and then decrease nearly linearly with temperature. The velocity behaviour of the other transverse mode is more complicated. All the experimental results and particularly the velocity variations, but for one mode, are well-explained in terms of the theory of two-level systems developed for amorphous systems. The logarithmic temperature dependence of the velocity and the T 3 temperature dependence of the attenuation are well-known, both theoretically and experimentally, for amorphous insulators. The plateau in the attenuation is not usually observed in amorphous materials. We show that this plateau places restrictions on the distribution function describing the two-level systems and, further, indicates that even for two-level systems of a given energy there is a spectrum of two-level system-phonon coupling constants. To describe the attenuation data at temperatures above 10 K, the direct relaxation process of the two-level system does not lead to a sufficiently rapid increase with the temperature. The introduction of a Raman relaxation process gives the correct temperature dependence. Then, the experimentally observed quasi-linear temperature variations of the phase velocity is well accounted for if a T4 contribution, due to the elastic anharmonicity, is added to the effects of the Raman process. Thus the two-level system theory, developed for amorphous materials, explains all the acoustical properties (attenuation and phase velocity) of the sodium doped fi-alumina up to 70 K. More, these experiments confirm the relevance of the two-level system theory for the description of both resonant and relaxation effects on the acoustical properties of truly amorphous compounds