Infrared Optical Properties ofLi7F and Natural LiF at Various Temperatures, Calculated with Shell-Model Lattice-Dynamical Data

The infrared optical properties of ${\mathrm{Li}}^7$F, including the real and imaginary dielectric constants, the extinction and absorption coefficient, the refractive index, conductivity, reflectivity, and phase angle, have been calculated absolutely, assuming two-phonon "summation" or "difference" relaxation of the transverse optic (TO) resonance with near-zero wave vector. A shell model, fitted to inelastic-neutron-scattering data from ${\mathrm{Li}}^7$F at 298 °K, was used to generate the lattice-dynamical data with a density of 256 000 points per zone. The form of the potential derivatives used in the cubic-anharmonic-coupling coefficient took into account, in an approximate fashion, the long-range Coulombic coupling between other-than-nearest neighbors. The calculated constants were then compared with various experimental data, including both direct-transmission-absorption measurements and reflectivity-analysis data. The agreement in intensity and structure is generally very good, and two-phonon assignments have been made of the features in the calculated spectra. It is thought that the result of the approximation made in the cubic coupling coefficient is an overaccentuation of these features. At room temperature, there is further evidence for the need to include at least three-phonon relaxation terms, arising from quartic anharmonicity, both underneath the main resonance and above the two-phonon energy limit. At 7.5 °K the discrepancy in the width and peak height of the TO resonance between the calculated spectra, strictly applicable only to ${\mathrm{Li}}^7$F, and the experimental data, obtained primarily from natural LiF crystals containing 7.5 at.% of the ${\mathrm{Li}}^6$ isotope, is very large. This extreme behavior is due to the fact that two-phonon relaxation of the TO resonance is almost entirely through "difference" processes, which disappear as 0 °K is approached. The damping due to the isotope-induced one-phonon processes has therefore been calculated, using once again the 298 °K shell-model data, and added to the two-phonon damping. The absorption coefficient, refractive index, and reflectivity were then calculated for natural LiF at 7.5 °K, and very satisfactory agreement was obtained with experiment.