Abstract
The neutron-inelastic-scattering technique was used to measure the phonon dispersion relations in two high-density crystals of hcp $^{4}\mathrm{He}$ with molar volumes of 11.61 and 9.41 ${\mathrm{cm}}^{3}$/mol. These densities are on the order of twice that of $^{4}\mathrm{He}$ at 30 bars. The crystals were grown from the melt in the fcc phase, and cooled across the fcc-hcp phase transition. The observed phonon spectra show anharmonic effects much less prominent than those observed in earlier measurements at 21 ${\mathrm{cm}}^{3}$/mol. In particular, multiphonon interference effects were not found to be very pronounced, while multiphonon scattering appeared to influence phonon line shapes strongly for large wave-vector and energy transfers. Elastic constants d\ifmmode \dot{e}\else \.{e}\fi{}termined from the initial slopes of the dispersion curves were found to be in good agreement with those calculated by Goldman using the first-order self-consistent-phonon theory. The dependence on volume of the phonon energies is discussed with reference to the earlier studies at 21.1 and 16.0 ${\mathrm{cm}}^{3}$/mol. No significant dispersion of mode Gr\uneisen parameters was found unlike the case of fcc He. Gr\uneisen parameters were found to depend on volume approximately in a manner given by Ahlers for the thermodynamic Gr\uneisen parameter.
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