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Effects of strong phonon anharmonicity of a type-I clathrate Ba$_{\rm8}$Ga$_{\rm 16}$Sn$_{\rm 30}$ induced by quadruple-well potential of guestatoms were investigated. Phonon transport including coherent interbranchcomponent was analyzed using a first-principles-based self-consistent phonon(SCP) theory that gives temperature-dependent harmonic interatomic forceconstants and by solving off-diagonal components of group velocity operator.Experimentally observed thermal conductivities have been reasonably reproducedby considering both lattice and electron contributions. Through the analysiswith the SCP theory, we found that hardening of guest modes leads to anincrease in lattice thermal conductivity at frequencies below those offramework-dominant flat modes (< 40 cm$^{\rm -1}$), which finally results inthe slow decay and slight increase in the total lattice thermal conductivitywith increasing temperature. Detailed analyses revealed that the increase inlattice thermal conductivity at low frequency is attributed to (a) the increasein group velocities of phonon modes located at frequencies below that of theflat guest modes and (b) abnormal increase in lifetimes of phonon modes locatedbetween frequencies of the flat guest and framework modes with increasingtemperature. From an engineering point of view, this effect may lead to anintriguing phenomenon, a larger decrease in thermal conductivity due tonanostructuring at higher temperatures.

Strong Phonon Anharmonicity of Clathrate Compound at High Temperature