Temperature dependence of the zero-sound elastic constants of crystalline xenon

Neutron inelastic scattering has been used to measure the low-frequency phonon dispersion relations for a single crystal of xenon at temperatures of 159.6, 111.0, and 10.0 K. From these data, the sound speeds and zero-sound elastic constants have been deduced, as well as the bulk modulus, anisotropy, and deviation from the Cauchy relation. The data are compared against Brillouin-scattering measurements at 156 K with the result that there are differences in $c_{11}$ and $c_{12}$ which cannot be explained as zero-sound-first-sound differences. The experimentally observed temperature dependence of the elastic constants is not well described by theory, although good agreement is found for a Monte Carlo calculation near the melting temperature. Our result for the departure from the Cauchy relation at low temperature indicates that calculations of many-body effects probably overestimate their importance for xenon.