Lattice Thermal Conductivity

Consideration of the anharmonic properties of a linear chain suggests that the dimensionless quantity $\ensuremath{\alpha}\ensuremath{\gamma}T$ is in general a measure of the anharmonicity of a lattice ($\ensuremath{\alpha}$ is the thermal expansion coefficient and $\ensuremath{\gamma}$ the Gr\"uneisen parameter). It is therefore proposed that the mean free path for lattice vibrations in an insulator should, in the classical temperature region, be approximately $\frac{{A}_{0}}{\ensuremath{\alpha}\ensuremath{\gamma}T}$, where ${A}_{0}$ is the lattice spacing. Reasonably good agreement with experiment is found.