Rattling guest atoms in Si, Ge, and Sn-based type-II clathrate materials

We have studied the vibrational properties of some of the compounds based on the Type II silicon, germanium, and tin-based clathrate materials using LDA electronic structure methods. The lattices in these framework materials have open cages which can contain weakly bound guest impurities, and these guests produce local ("rattling") vibrational modes. Such modes may scatter the extended, heat carrying acoustic vibrational modes of the framework, potentially reducing the thermal conductivity. We present results for the vibrational spectra of the Type II clathrate compounds Na₁₆Cs ₈Si₁₃₆, Na₁₆Cs₈Ge₁₃₆, and Cs₂₄Sn₁₃₆. We discuss trends in the vibrational spectra of the framework host material and of the localized, rattling frequencies of the guest modes as the host changes from Si to Ge to Sn.