Thermal conductivity in intermetallic clathrates: A first principles perspective

TL;DR

This study uses first-principles calculations to analyze phonon interactions and thermal conductivity in intermetallic clathrates, revealing the significant roles of various phonon modes and electronic contributions in heat transport.

Contribution

It introduces a systematic approach incorporating temperature-dependent interatomic force constants to accurately model thermal conductivity in complex clathrates, highlighting the importance of higher-energy phonon modes.

Findings

Modes with energy >10 meV contribute 50% to heat transport at room temperature.

Temperature-dependent force constants are essential for accurate thermal conductivity modeling.

Electronic thermal conductivity approximately follows the Wiedemann-Franz law.

Abstract

Inorganic clathrates such as Ba$_8$Ga$_{x}$Ge$_{46-x}$ and Ba$_8$Al$_{x}$Si$_{46-x}$ commonly exhibit very low thermal conductivities. A quantitative computational description of this important property has proven difficult, in part due to the large unit cell, the role of disorder, and the fact that both electronic carriers and phonons contribute to transport. Here, we conduct a systematic analysis of the temperature and composition dependence of low-frequency modes associated with guest species in Ba$_8$Ga$_{x}$Ge$_{46-x}$ and Ba$_8$Al$_{x}$Si$_{46-x}$ ("rattler modes"), as well as of thermal transport in stoichiometric Ba$_8$Ga$_{16}$Ge$_{30}$. To this end, we account for phonon-phonon interactions by means of temperature dependent effective interatomic force constants (TDIFCs), which we find to be crucial in order to achieve an accurate description of the lattice part of the thermal conductivity. While the analysis of the thermal conductivity is often largely focused on the rattler modes, here, it is shown that at room temperatures modes with $\hbar\omega\gtrsim\,10\,\text{meV}$ account for 50\%\ of lattice heat transport. Finally, the electronic contribution to the thermal conductivity is computed, which shows the Wiedemann-Franz law to be only approximately fulfilled. As a result, it is crucial to employ the correct prefactor when separating electronic and lattice contributions for experimental data.