Solution of the general phonon Boltzmann equation: boundary and mass defect scattering

Abstract

The phonon Boltzmann equation is considered in its general form in the presence of mass defect interactions and boundary scattering. A variational method is applied to calculate the phonon thermal conductivity for a non-metallic slab of finite thickness and fixed temperatures at its two faces. In comparison with previous work the present study has the advantage that the different phonon polarizations are taken into account. Moreover, it has been shown that the operator involved in the study is positive definite which, in turn, implies that the variational method yields an upper bound on the phonon thermal conductivity.