Interpolation between linearized and atomistic models for accurate calculation of the lattice thermal conductivity in the full temperature range -

Abstract

In this thesis, we developed a model for the lattice thermal conductivity (κ). For the calculation of κ for a single crystal over a full temperature range, the model uses the full Callaway's solution to Boltzmann equation that discriminates between the physical nature of the various phonon mechanisms. However, it uses temperature-dependent lattice vibration parameters, phonon group velocity calculated from a dynamical matrix, and intrinsic phonon relaxation time calculated from Fermi's golden rule. With these modifications, the developed model accounts for the dependence of κ on the crystallographic direction over a wide temperature range. For the calculation of the effect of phonon boundary scattering, the model uses the relationship established by Casimir. This relation considers a diffuse scattering, i.e., it ignores the dependence of the wave vector on the phonon-boundary scattering. The model considers the localized mass fluctuation as a perturbation Hamiltonian to account for the effect of point defect on κ. The developed model is applied to calculate the effects of crystallographic orientation and isotope composition on κ of Ge. A satisfactory agreement is obtained between theory and experiment.