Computational method for studying the thermal conductivity of molecular crystals in the course of condensed matter physics

Abstract

This paper presents a computational method for studying the thermal conductivity of molecular crystals that can be used in the educational course of condensed matter physics. This method is based on the Debye model of thermal conductivity in the approximation of the corresponding relaxation times and allows studying the heat transfer processes features in simple molecular crystals at temperatures close to or above Debye temperature. The thermal conductivity is analysed in the framework of modified Debye model in which heat is transferred by low-frequency phonons and above the phonon mobility edge by “diffusive” modes migrating randomly from site to site. The mobility edge ω0 is found from the condition that the phonon mean-free path cannot become smaller than half the phonon wavelength. The contributions of phonon-phonon, one-, and two-phonon scattering to the total thermal resistance of molecular crystals are calculated under the assumption that the different scattering mechanisms contribute additively. The presented computational method will be useful in pedagogical activities for teaching students of physical faculties.