Relationship between Adiabatic Elastic Constants and the Slopes of Phonon Dispersion Curves for Rare-Gas Solids

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Abstract
The velocity of first sound is calculated from the adiabatic elastic constants using the lowest-order self-consistent phonon scheme. The velocity of sound is also calculated from the limiting slopes of phonon dispersion curves using a conserving approximation. Results are presented for models appropriate to solid Kr and solid Xe. The maximum difference appears to be of order 4% or less at the respective melting temperatures. This has the important consequence that the limiting slopes of phonon dispersion curves should be in agreement at least to this accuracy with conventional ultrasonic measurements and Brillouin-scattering experiments. Thus the apparent discrepancies between ultrasonic and neutron data in solid Ar do not appear to be due to this effect.