Lattice Dynamics of Lithium Fluoride
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Abstract
The frequency wave-vector dispersion relation for the normal modes of vibration of ${\mathrm{Li}}^{7}$F at 298\ifmmode^\circ\else\textdegree\fi{}K has been measured by means of slow-neutron inelastic scattering techniques. Triple-axis crystal spectrometers at two reactor facilities at the Oak Ridge National Laboratory were employed, mostly in the "constant-Q" mode of operation. The results can be satisfactorily fitted by a seven-parameter dipole approximation model involving nearest-neighbor and second-nearest-neighbor ${\mathrm{F}}^{\ensuremath{-}}$-${\mathrm{F}}^{\ensuremath{-}}$ short-range forces, a variable ionic charge, and the polarizability of the ${\mathrm{F}}^{\ensuremath{-}}$ ions only. The applicability of other force models to ${\mathrm{Li}}^{7}$F is also discussed. Certain inconsistencies have been found between the slopes of the acoustic branches near q=0 and the appropriate velocities of sound as measured by ultrasonic techniques. It is believed that these arise from anharmonic effects. The frequency distribution of the normal modes has been computed with high precision from the best-fit dipole approximation model, together with related quantities such as the lattice heat capacity, entropy, and Debye-Waller factors for each ion. Combined (two-phonon) density-of-states functions have also been calculated; comparisons are made between these one- and two-phonon distribution functions and certain features observed in optical and infrared absorption experiments on LiF.