Callaway's model of lattice thermal conductivity has been modified by introducing an arbitrary relation between the phonon frequency and the phonon wave vector, to take account of (i) the phonon dispersion, and (ii) the number of phonon states in the wave-vector space, allowing for separate contributions of the transverse and the longitudinal phonons. Three-phonon relaxation times that have different temperature dependence for different temperature ranges have been used. Application to silicon has been made successfully. It is observed that the four-phonon processes play an important role at high temperatures, and that the major contribution to the lattice thermal conductivity comes from the transverse phonons.

• Received 11 August 1969

DOI:https://doi.org/10.1103/PhysRevB.1.750