Inelastic Neutron Scattering from Solid Neon

Abstract

The phonon dispersion curves of a neon sample with a lattice spacing of 4.454 ± 0.002 Å have been measured in the [100], [110], and [111] symmetry directions at 5 °K. Accuracies between 0.5 and 2% are evidenced except for high-energy modes near the zone boundary, i.e., for modes with energies greater than ≈ 6 meV. The data can be fit extremely well with an axially symmetric four-neighbor force-constant model of eight parameters. Measurements made at $\zeta <0.2\mathrm{}$ allowed an accurate determination of the zero-sound elastic constants $C_{11}=166.1\mathrm{}\pm 1.7$, $C_{12}=85.5\mathrm{}\pm 2.1$, and $C_{44}=95.2\mathrm{}\pm 0.5\times {10}^8$ dyn ${\mathrm{cm}}^{-2\mathrm{}}$. The latter give a value for the zero-sound bulk modulus $B_0=\frac{1}{3}(C_{11}+2\mathrm{}{C}_{12})=112.4\mathrm{}\pm 1.7\times {10}^8$ dyn ${\mathrm{cm}}^{-2\mathrm{}}$ which agrees with the adiabatic first-sound bulk modulus. Phonon measurements have also been obtained at 22 °K in the [100] direction with no change in sample density. The isochoric temperature shift varies between 1 and 2% for the longitudinal mode and between - 3.5 and 0% for the transverse mode as $\zeta$ changes from 0.1 to 0.5, respectively. The measured phonon line shapes have also been compared with the instrumental resolution in order to determine intrinsic phonon lifetimes. In most instances, upper limits to the broadening are obtained. For $\zeta <0.1\mathrm{}$, all branches have widths $\mathrm{}\left[100\right]T$ phonon at $\zeta =0.2\mathrm{}$ has an energy of 1.45 meV and a width of ≈ 0.3 meV, whereas at 5 °K only an upper limit for the width of $\mathrm{}\left[100\right]T$ phonons. The detailed measurement of phonons near the zone boundary with energies greater than 6 meV was not accomplished due to substantial broadening (>1 meV) of the single-phonon response and its superposition by multiphonon scattering, which is broad in energy and of comparable intensity.