Temperature and frequency dependence of the velocity of sound in dielectric crystals

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Abstract
The temperature and frequency dependence of the velocity of sound in dielectric crystals have been calculated to lowest order in anharmonic terms by using the quasi-harmonic approximation and the phonon Boltzmarm equation. It is assumed that the quasi-harmonic approximation for the stress in a deformed crystal in microscopic equilibrium may be generalized to non-equilibrium situations in a simple way. It is found that at very low frequencies the velocity is determined by the adiabatic elastic constants in agreement with classical continuum theory. At high frequencies, however, the classical isothermal result is not obtained, and in contrast to the classical result it is found that there is a change in velocity in going from low frequencies to high frequencies for pure shear waves. A rough estimate is made of the magnitude of this effect and it is decided that it should be observable under suitable conditions.

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