Lattice dynamics and anharmonic self-energies for the lithium halides

Lattice-dynamical calculations, using both the modified deformation-dipole model and the breathing-shell model, of the lithium halides are presented. Using the phonon frequencies and eigenvectors generated from these calculations, the frequency and temperature dependence of the Hermitean and anti-Hermitean parts of the $q\approx 0$ transverse-optic-mode self-energy are calculated. The results of the anharmonic calculations reveal that the zero-frequency self-energy shift is dominated at low temperatures for all four halides by the first-order quartic anharmonicity, but that, as the temperature is increased, the second-order cubic and quartic anharmonic contributions become increasingly more dominant, causing a changeover in sign for the zero-frequency self-energy shift, a result observed experimentally for other alkali halides crystalizing in the NaCl structure. This same phenomenon is also found for the far-infrared self-energy shift for LiBr and LiI, but for LiF and LiCl it appears that the second-order cubic and quartic anharmonicity provides the dominant contribution to the far-infrared self-energy shift at all temperatures. For all four materials the second-order cubic anharmonicity provides the dominant contribution to the inverse lifetime at low temperatures, but as the temperature is increased the second-order quartic contribution becomes increasingly important and finally provides the dominant contribution. At low temperatures the calculations yield lifetimes which are much longer than are actually observed, but for LiF, where experimental data exist at temperatures up to 1100 K, the calculations are in reasonable agreement for the range 200-1100 K.