Electronic and vibrational properties of framework-substituted type-II silicon clathrates

Framework substitution has not been widely reported among the type-II group-IV clathrates. We have performed a theoretical study of the Cs8 Ga8 Si128 and Rb8 Ga8 Si128 clathrates, using the local-density approximation (LDA) to density-functional theory. In Rb8 Ga8 Si128 and Cs8 Ga8 Si128, eight Si atoms are substituted by Ga at the 8a crystallographic sites of the framework. We predict that both Rb8 Ga8 Si128 and Cs8 Ga8 Si128 are semiconductors with LDA indirect band gaps in the range of 0.73-0.77 eV. Similar substitution with Ge (instead of Ga) rendered the materials metallic. We have compared the electronic and vibrational properties of these Ga-substituted materials with those of the partially filled Rb8 Si136 and completely filled Na16 Rb8 Si136 clathrates. The phonon-dispersion curves show low-frequency guest "rattling" modes for each material. We have used these results to estimate the temperature-dependent values of the isotropic mean-square displacement amplitude (Uiso) for the various guest atoms in Na16 Rb8 Si136, Rb8 Ga8 Si128, and Cs8 Ga8 Si128. Our estimates for Na and Rb in Na16 Rb8 Si136 are in good agreement with experiment. We predict that the Rb guests will have low-frequency vibrational modes and higher values of Uiso than the Cs guests. The large values of Uiso, the localized low-frequency modes, and the semiconducting properties of Rb8 Ga8 Si128 indicate that this type of framework-substituted type-II clathrate may be potentially useful for thermoelectric applications.