Thermal conductivity in intermetallic clathrates: A first principles perspective

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.