Using the Ziman scheme of considering a drifting Planck’s distribution, as the eigenvector of the linearized phonon collision operator, the anharmonic relaxation of phonons is discussed. The earlier arbitrariness in the phonon-phonon coupling parameters is removed by formulating explicit expressions for different allowed processes in terms of measurable quantities. Low and high temperature approximations of relaxation rates are also discussed: the results differ from earlier calculations. At low temperatures superthermal or high frequency phonons, which have temperature-independent and equal N- and U-relaxation rates, play important roles in thermal conduction in pure insulators.

Anharmonic phonon relaxation times in Ge are calculated using (i) an isotropic continuum model, and (ii) a dispersive model. A complete spectrum of calculated results is presented. Frequency-averaged values for normal- and umklapp-three-phonon relaxation times are also calculated. A comparison is made between our findings and some earlier works, and disagreements are discussed. The results are applied in calculating some results in the theory of lattice thermal conductivity.

We present a comparison of high-temperature three-phonon resistivities from the relaxation time methods due to Klemens, Callaway, and Debye, and the variational method due to Leibfried and Schlömann. All the calculations are based upon the same choice of anharmonic crystal potential; and hence the results are suitable for comparison on quantitative basis. We find that the resistivities in increasing order of magnitude come from the methods due to Klemens, Callaway Debye, and Leibfried and Schlömann respectively.