Phonon Viscosity and Its Effect on Acoustic Wave Attenuation and Dislocation Motion

Abstract

When dislocations move through a crystal, they are damped by some thermal mechanism. It is shown in this paper that good agreement with available measurements is obtained if the dislocations are damped by phonon viscosity. Phonons are quantized sound waves, which carry the thermal energy in an insulator. The interchange of energy between the longitudinal branch and the two shear branches occurs through the nonlinear elastic constants of the solid and requires a finite time τ. The effect of a shear wave, which is equivalent to a compression in one direction and an equal extension at right angles, is to raise the instantaneous temperatures for those phonons having components along the compressed direction and to lower the temperature for those having components along the extended direction. The flow of heat between the hot and cold phonons produces a damping of the sound wave corresponding to a viscosity η = E0K/CvV̄2 as long as the time of application of the shear wave is long compared to τ. When the product ωτ≫1 this source of loss disappears. Phonon viscosity contributes directly to the acoustic attenuation and indirectly produces a damping for dislocation motion. By using thermal and sound velocity measurements to evaluate the viscosity, it is shown that available data on the attenuation of sound in metals and nonconducting crystals are in agreement with the calculated values of dislocation damping by phonon viscosity. A direct check for both edge and screw dislocations is obtained from recent work on the velocity of dislocations in lithium fluoride. The variation of internal friction in quartz as a function of temperature is in agreement with the temperature variation of phonon viscosity, but is not in agreement with calculations by Eshelby and Leibfried on dislocation damping by thermoelastic effects and by phonon scattering.