Ultrasonic attenuation and dislocation damping in helium crystals

Measurements of the attenuation of pulsed longitudinal sound at frequencies of 5, 15, 25, 35, and 45 MHz have been made in hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ crystals grown under constant pressure of 32.5 and 60.0 atm at molar volumes of 20.5 and 19.2 ${\mathrm{cm}}^3$/mole. The specimens used for the measurements were considered to be single crystals. The attenuation versus frequency dependence measured for a number of crystals always revealed a broad peak. The height of the peak was dependent on the crystallographic orientation of the specimens. When the temperature was suddenly changed, the peak gradually shifted to a new location. The frequency dependence of the attenuation was measured at various temperatures between 1.3 and 2.3 K, and the height and location of the peak were found to be dependent on temperature. It was also found that the attenuation increased markedly when the strain amplitude of ultrasound was increased above a certain level. By the analysis of these experimental results the following conclusions have been obtained: The main origin of the attenuation is the overdamped resonance of crystal dislocations; the slip plane of the dislocations is the basal plane; the dominant pinning points are jogs existing on the dislocations in thermal equilibrium; the damping of dislocation motion originates from the energy loss due to three-phonon processes between thermal phonons and quasilocal phonons around dislocations. The argument was essentially classical, and the quantum character of dislocations was thus far not taken into consideration.