Structural, electronic, and vibrational properties of some type-II tin based clathrates
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In addition to forming the two common forms of crystalline tin, α-tin and β-tin, tin can crystallize into the metastable clathrate structures. These structures contain large 20, 24, or 28-atom “cages” which allow for the introduction of loosely bound guest atoms into the cages. In general, clathrate lattices of Group 14 elements, and the guests are either alkaline metal or alkaline earth metal atoms. The introduction of certain guests allows the tuning of the electronic and vibrational properties of the material to suit certain needs. Due to this ability for tuning the material properties, one of the main areas of focus for the clathrates is in thermoelectrics. Clathrates often have low thermal conductivities and have the electronic properties of semiconductors, both of which are important for a good thermoelectric material. Both silicon and germanium based Types I and II clathrates have been extensively studied both experimentally and theoretically. Tin based clathrates, especially those with the Type-II lattice structure, have not been as extensively studied, mostly due to the difficulty of synthesizing them. However, some new Type-II tin based clathrates have been recently synthesized. Several different compounds have been synthesized, but the ones of interest in this study are of the form X8Ba16Ga40Sn96, with X=K, Rb, or Cs, as well as the empty clathrate Ga40Sn96. Tin based clathrates are of interest due to the high atomic weight of tin itself, which results in a shrinking in phonon band widths and thus a lower thermal conductivity. In this thesis, the properties of some of the Type II tin-based clathrate compounds are investigated from first principles. The calculations are based on the Local Density Approximation to Density Functional theory. Here, results are reported for the equilibrium lattice constant and other equilibrium structural properties, the electronic band structures, the phonon dispersion curves, and the vibrational densities of states. Results of the latter calculations are used to find the low-lying vibrational modes of the guest atoms. Further, the results for the vibrational properties are used to approximately determine atomic displacement parameters, the thermodynamic properties of the materials, and the lattice thermal conductivity.