Lattice Thermal Conductivity

Consideration of the anharmonic properties of a linear chain suggests that the dimensionless quantity $\alpha \gamma T$ is in general a measure of the anharmonicity of a lattice ($\alpha$ is the thermal expansion coefficient and $\gamma$ the Grüneisen parameter). It is therefore proposed that the mean free path for lattice vibrations in an insulator should, in the classical temperature region, be approximately $\frac{A_0}{\alpha \gamma T}$, where $A_0$ is the lattice spacing. Reasonably good agreement with experiment is found.