Lattice Dynamics of Neon at Two Densities from Coherent Inelastic Neutron Scattering

Abstract

Phonon dispersion relations for two single crystals of neon were measured by inelastic neutron scattering. Growth of the crystals by a high-pressure technique permitted a study of Ne lattice dynamics at densities differing by 4%. Measurements in the principal symmetry directions of the fcc lattice were made at 4.7\ifmmode^\circ\else\textdegree\fi{}K on a crystal with a lattice parameter of 4.462\ifmmode\pm\else\textpm\fi{}0.002 \AA{}. These data could be well fitted with a spectrum calculated by self-consistent phonon theory with a Lennard-Jones pair potential. An all-neighbor quasi-harmonic calculation with the Lennard-Jones potential also provided a good match after calculated energies were adjusted for a difference in theoretical and experimental lattice parameters. The two models utilized different values for the Lennard-Jones parameters in the calculations. A Born-von K\'arm\'an analysis indicated that interatomic forces are short-range and predominantly central. Dispersion curves in the [001] direction were measured for a second sample at 4.7 and 25\ifmmode^\circ\else\textdegree\fi{}K at constant volume (lattice parameter 4.402\ifmmode\pm\else\textpm\fi{}0.002 \AA{}). The temperature shift of the frequencies was small, averaging (-2.3\ifmmode\pm\else\textpm\fi{}1.3)% for the transverse and (2.3\ifmmode\pm\else\textpm\fi{}2.4)% for the longitudinal mode. A Born-von K\'arm\'an analysis of data for this higher-density sample indicated the appearance of significant noncentral forces. Comparison of phonon measurements at 4.7\ifmmode^\circ\else\textdegree\fi{}K for the two samples yielded average quasiharmonic-mode Gr\uneisen parameters ${\ensuremath{\gamma}}_{j}$ of 2.9\ifmmode\pm\else\textpm\fi{}0.5 and 4.2\ifmmode\pm\else\textpm\fi{}0.6, respectively, for the [001] transverse and longitudinal branches.