Anharmonic phonon renormalization and thermal transport in the type-I Ba$_{\rm 8}$Ga$_{\rm 16}$Sn$_{\rm 30}$ clathrate from first principles

Abstract: Effects of strong phonon anharmonicity of a type-I clathrate Ba${\rm 8}$Ga${\rm 16}$Sn$_{\rm 30}$ induced by quadruple-well potential of guest atoms were investigated. Phonon transport including coherent interbranch component was analyzed using a first-principles-based self-consistent phonon (SCP) theory that gives temperature-dependent harmonic interatomic force constants and by solving off-diagonal components of group velocity operator. Experimentally observed thermal conductivities have been reasonably reproduced by considering both lattice and electron contributions. Through the analysis with the SCP theory, we found that hardening of guest modes leads to an increase in lattice thermal conductivity at frequencies below those of framework-dominant flat modes (< 40 cm$^{\rm -1}$), which finally results in the slow decay and slight increase in the total lattice thermal conductivity with increasing temperature. Detailed analyses revealed that the increase in lattice thermal conductivity at low frequency is attributed to (a) the increase in group velocities of phonon modes located at frequencies below that of the flat guest modes and (b) abnormal increase in lifetimes of phonon modes located between frequencies of the flat guest and framework modes with increasing temperature. From an engineering point of view, this effect may lead to an intriguing phenomenon, a larger decrease in thermal conductivity due to nanostructuring at higher temperatures.