Impact of Rattlers on Thermal Conductivity of a Thermoelectric Clathrate: A First-Principles Study

We investigate the role of rattling guest atoms on the lattice thermal-conductivity of a type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ by first-principles lattice dynamics. Comparing phonon properties of filled and empty clathrates, we show that rattlers cause 10-fold reductions in the relaxation time of phonons by increasing the phonon-phonon scattering probability. Contrary to the resonant scattering scenario, the reduction in the relaxation time occurs in a wide frequency range, which is crucial for explaining unusually low thermal-conductivities of clathrates. We also find that the impact of rattlers on the group velocity of phonons is secondary because the flattening of phonon dispersion occurs only in a limited phase space in the Brillouin zone.