Lattice Dynamics of Lithium Hydride

Abstract

Crystalline lithium hydride, with four electrons per primitive unit cell, has the simplest electronic configuration of all ionic crystals with the sodium-chloride-type structure, and thus represents an excellent test case for existing theories of lattice dynamics of these substances. Lattice vibrations in this system have been studied by measuring the phonon dispersion curves along the three high-symmetry directions in a single crystal of $^{7}\mathrm{LiD}$, using the techniques of coherent inelastic scattering of thermal neutrons. The isotopes $^{7}\mathrm{Li}$ and D were chosen over normal Li and H because of their more favorable neutron cross sections. All measurements were taken at room temperature, using a triple-axis neutron spectrometer operating in the constant-Q mode. Uncertainties in the measured frequencies are estimated to be no greater than 3-5%. The transverse zone center frequency is in excellent agreement with infrared absorption data. The experimental dispersion curves have been least-squares-fitted to several versions of the rigid-ion and shell models of lattice dynamics. A seven-parameter shell model fits the data to within the experimental accuracy. In this model, the ionic charge was variable and only the hydride ions were polarizable. Short-range forces were assumed between nearest neighbors (${\mathrm{Li}}^{+}$ and ${\mathrm{H}}^{\ensuremath{-}}$) and between negative second neighbors (${\mathrm{H}}^{\ensuremath{-}}$ and ${\mathrm{H}}^{\ensuremath{-}}$). The ionic charge obtained from the fit indicates that the bonding in $^{7}\mathrm{LiD}$ is about 88% ionic, in good agreement with estimates obtained from electronegativity considerations. The second-neighbor bond-stretching force constant was found to be about 7% of that obtained for the nearest neighbors. The model parameters obtained for $^{7}\mathrm{LiD}$ were used to calculate dispersion curves for $^{7}\mathrm{LiH}$, and frequency distribution functions for both substances. The frequency distribution for $^{7}\mathrm{LiH}$ has a gap between the acoustic and optic modes, whereas that for $^{7}\mathrm{LiD}$ does not.