Inelastic neutron scattering from solidAr36

Abstract

The phonon dispersion relations of $^{36}\mathrm{Ar}$ have been measured in the [100], [110], and [111] symmetry directions at 10 K using a triple-axis neutron spectrometer. A comparison of the measured dispersion curves and the best available theoretical calculations based on the Bobetic-Barker (BB) potential shows small systematic discrepancies for the [100]L, [110]${\mathrm{T}}_{2}$, [110]L, and [111]L branches. Otherwise the agreement between experiment and theory is remarkably good. The data are well described by several harmonic Born-von K\'arm\'an models the most general of which (a three-neighbor general-force model with nine parameters) has been used to deduce values of zero-sound elastic constants. At 10 K (lattice constant $a=5.313\ifmmode\pm\else\textpm\fi{}0.002$ \AA{}), these are ${c}_{11}=(424\ifmmode\pm\else\textpm\fi{}5)\ifmmode\times\else\texttimes\fi{}{10}^{8}$, ${c}_{12}=(239\ifmmode\pm\else\textpm\fi{}5)\ifmmode\times\else\texttimes\fi{}{10}^{8}$, and ${c}_{44}=(225\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ dyn ${\mathrm{cm}}^{\ensuremath{-}2}$ which imply a deviation from the Cauchy relation with $\ensuremath{\delta}=\ensuremath{-}0.06\ifmmode\pm\else\textpm\fi{}0.02$. From the energies of phonons of small wave vector measured just below the melting point at 82 K ($a=5.463\ifmmode\pm\else\textpm\fi{}0.002$ \AA{}), the zero-sound elastic constants were determined to be ${c}_{11}=(248\ifmmode\pm\else\textpm\fi{}6)\ifmmode\times\else\texttimes\fi{}{10}^{8}$, ${c}_{12}=(153\ifmmode\pm\else\textpm\fi{}5)\ifmmode\times\else\texttimes\fi{}{10}^{8}$, and ${c}_{44}=(124\ifmmode\pm\else\textpm\fi{}4)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ dyn ${\mathrm{cm}}^{\ensuremath{-}2}$ ($\ensuremath{\delta}=\ensuremath{-}0.19\ifmmode\pm\else\textpm\fi{}0.04$). In both the 10- and 82-K measurements, particular care has been taken to remove the systematic errors introduced by finite instrumental resolution. The measured elastic constants have been compared with several calculations and with results obtained from ultrasonic and Brillouin scattering experiments. Calculations of elastic constants based on the BB potential with the Axilrod-Teller three-body interactions are in good agreement with our data at both temperatures. The energies of some typical phonons have been measured at temperatures of 10, 35, 55, and 75 K. In the only case in which these measurements can be compared with an existing calculation (the [100]T mode at $\ensuremath{\zeta}=0.4$, our results show a slightly larger shift of the phonon energy than that computed by Klein et al. from the BB potential.