Temperature dependence of microwave phonon attenuation

Abstract

Measurements of the temperature dependence of the attenuation of 9-Gc/sec phonons are presented. They include measurements on crystals of quartz, CdS, GaAs, Ge, Si, CaF2, Al2O3, and MgO in several directions and modes of polarization. The attenuation in most of the materials is proportional to Tn, where the average value of n=4.11.2 for the fast transverse waves, 4.01.7 for the slow transverse waves, 4.81.4 for the longitudinal waves. For MgO and Al2O3 the attenuation is proportional to the frequency of the sound between 3 and 9 Gc/sec. An empirical correlation of the data is that the attenuation of 9-Gc/sec phonons is 3 dB/cm when (T)0.1, where =Debye temperature of the crystal. Values of the third-order elastic constants are used to make absolute comparisons of the theory of attenuation by three-phonon processes with the data. The agreement is good in some cases but not in others. © 1965 The American Physical Society.