Thermal and Electronic Attenuations and Dislocation Drag in the Hexagonal Crystal Cadmium

Abstract

Thermal attenuations for dielectric crystals due to the Akheiser effect show characteristic patterns connected with crystal structure. For cubic crystals, the nonlinearity constants D—which determine the coupling of acoustic waves with the thermal phonons—are all larger for the longitudinal waves than they are for the shear waves by ratios that vary from 5 to 17. On the other hand, for trigonal and hexagonal crystals, the constants are in the same order. It is the purpose of this paper to investigate whether these conclusions hold for metal crystals. For these crystals, there are three sources of square-law attenuation for longitudinal waves and two for shear waves. These are the thermoelastic effect, the phonon viscosity (Akheiser effect), and the electron-damping effect. Previous measurements for the cubic crystals lead, aluminum, and copper, made over a temperature range, are analyzed for these three components, and it is shown that the phonon viscosity D values vary from 5.3 to 17.5 for the ratio of longitudinal to shear values in agreement with the results for dielectric crystals. New measurements are presented for the hexagonal single crystal cadmium. It is shown that all dislocation motions, generated by the small strains used, lie in the direction of easy glide, i.e., in a plane perpendicular to the c axis. The longitudinal wave along the c axis and the three waves perpendicular to c all have only a square law attenuation. When the thermoelastic effect and the electronic damping effect are subtracted out, the nonlinearity constants have the same order of magnitude for both longitudinal and shear waves. Dislocation damping appears in the shear wave in the c direction. The ratio of the number of dislocations to the damping constant is evaluated and is shown to be smaller than that for other pure crystals. This is consistent with phonon damping of dislocations on account of the large nonlinearity constant D found for shear motion in the glide plane. When an attempt was made to measure this damping over a temperature range, it was found that a sudden increase in the attenuation occurs for shear waves controlled by the c44 elastic constant.