Exponential approximation of the coherence contribution to the thermal conductivity of complex clathrate-type crystals

Abstract

The low-temperature properties of guest-host crystals, such as clathrates and skutterudites, offer a rich playground for discovering novel physical phenomena and developing new materials with unique properties. The temperature dependence of thermal conductivity in these materials can exhibit both crystal-like and glass-like behavior, which reflects the properties of the phonon excitations and various scattering mechanisms. The ultra-low thermal conductivity of clathrate crystals is closely related to the concept of minimal thermal conductivity, which is determined by the intrinsic phonon scattering in the material. In this work, the temperature dependence of thermal conductivity for both crystal-like and glass-like behavior of different structural types of clathrates and skutterudites was analyzed using the ”Unified theory of thermal transport in crystals and glasses” of M. Simoncelli, N. Marzari & F. Mauri. A method was proposed and tested for the coherence contribution related to wave-like tunneling and loss of coherence between different vibrational eigenstates. The temperature dependence of the coherence contribution to thermal conductivity was approximated by the exponential function of an Arrhenius type with characteristic energy E and characteristic minimal thermal conductivity parameter κ0. The coherence contribution is intertwined with other phonon scattering mechanisms, and over a wide temperature range, its temperature dependence is universal with parameters depending on the crystal structure, positional disorder, and impurity doping. This work provides insights into the temperature dependence of thermal conductivity in guest-host materials and its importance for designing and optimizing their properties for various applications, such as thermoelectric generators.