Zero sound, first sound and second sound of solids

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The response of an anharmonic crystal to low-frequency and long wavelength probes is discussed. The difference between the velocities of sound in the zero sound and first sound regions is emphasized. In the zero sound region, it is shown that measured elastic constants may, unlike the macroscopic elastic constants, not have the symmetry of a second-rank tensor in addition to the point group symmetry of the crystal. The size of the deviations from the symmetry of a second-rank tensor is calculated for alkali halides and shown to be about a per cent at 300 °K. In the first sound region the elastic constants and ultrasonic attenuation are calculated. The difference between these elastic constants and those of the zero sound region is shown to be about 10% for some elastic constants of alkali halides at 300 °K. The extent to which the propagation of first sound is adiabatic is also discussed. The velocity of the second sound mode is calculated as a function of temperature, but calculations suggest it is very heavily damped in alkali halides. Finally, the thermal conductivity of KBr is computed and compared with experiment. The extension of these results to the dielectric response function is also described.