Anharmonic Three-Phonon Processes in Lithium Fluoride

Abstract

The ultrasonic attenuation was measured in lithium fluoride for longitudinal and both transverse waves along the [110] axis at 0.4 and 1.0 Gc/sec from liquid-helium to room temperatures. After subtracting the low-temperature residual attenuation, the anharmonic attenuation of the slow transverse mode was found to vary linearly with frequency and as $T^{3.5}$ below 30°K. For the fast transverse and the longitudinal modes, the temperature variation is more rapid and not expressible as a single power of temperature. The attenuation of the longitudinal mode showed some dependence on beam intensity. The attenuation of the slow transverse waves at 15°K was found to be somewhat higher than predicted by the Landau-Rumer theory. The strength of three-phonon processes had been deduced by Berman and Brock from the isotope thermal resistance of lithium fluoride. These results refer to phonons of frequencies around 300 Gc/sec. Assuming a linear variation with frequency, the present attenuation values agree to almost within a factor 2 with the values deduced by Berman and Brock at the same temperatures. Velocities of the three modes are given as functions of crystallographic direction.