Conducting a thermal conductivity survey

A physically transparent approximate theory of phonon decay rates is presented starting from a pair potential model of the interatomic forces in an insulator or semiconductor. The theory applies in the classical regime and relates the 3-phonon decay rate to the third derivative of the pair potential. Phonon dispersion relations do not need to be calculated, as sum rules relate all the needed quantities directly to the pair potential. The Brillouin zone averaged phonon lifetime turns out to involve a dimensionless measure of the anharmonicity multiplied by an effective density of states for 3-phonon decay. Results are given for rare gas and alkali halide crystals. For rare gases, the results are in good agreement with more elaborate perturbation calculations. Comparison to experimental data on phonon linewidths and thermal conductivity are made.