Anisotropic Klemens model for the thermal conductivity tensor

TL;DR

This paper extends the Klemens model to anisotropic materials, providing analytical formulas for directional thermal conductivity, validated against experimental data for graphite.

Contribution

It introduces an anisotropic Klemens model incorporating Onsager relations and anisotropic Debye dispersion, enabling analysis of heat transfer in layered and chainlike materials.

Findings

Model accurately predicts thermal conductivity in graphite

Analytical expressions match experimental data

Applicable to various anisotropic materials

Abstract

With the constraint from Onsager reciprocity relations, here we generalize the Klemens model for phonon-phonon Umklapp scattering from isotropic to anisotropic. Combined with the anisotropic Debye dispersion, this anisotropic Klemens model leads to analytical expressions for heat transfer along both ab-plane (k_ab) and c-axis (k_c), suitable for both layered and chainlike materials with any anisotropy ratio of the dispersion and the scattering. The model is justified by comparison with experimental k_ab and k_c of bulk graphite at high temperatures, as well as the thickness-dependent k_c of graphite thin films at room temperature.