Theoretical Study of the Properties of the Type II Clathrate A$^{x}$Sn$^{136}$, (A = alkali atom; 0 $\le $ x $\le $ 24)

Motivated by recent experimental and theoretical interest in the x dependence of the properties of the Si and Ge-based Type II clathrate materials A$^{x}$Si$^{136 }$and A$^{x}$Ge$^{136}$ (A = alkali atom) [1,2] we are carrying out a systematic theoretical study of the properties of the Sn-based Type II clathrate system A$^{x}$Sn$^{136}$. Type II clathrates have cage-like lattices in which Si, Ge, or Sn atoms are tetrahedrally-coordinated and sp$_{3}$ covalently bonded. The cages can contain ``guests''; usually alkali or alkaline earth atoms. These materials are particularly interesting because of their potential use as thermoelectrics. Recent powder X-ray diffraction experiments have found the very interesting result that, for increasing x in the range 0 $\le $ x $\le $ 8 a lattice contraction occurs, and that x is increased further (8 $\le $ x $\le $ 24), a contrasting lattice expansion results. These observations have motivated us to study the behavior of the lattice constant and other properties as a function of guest concentration in other Type II clathrates. In the present paper, we report preliminary results of a density functional based theoretical study of the properties of K$^{x}$Sn$^{136}$ as a function of x. We present results for the x dependence of the lattice constant as well as for other structural and electronic properties of this material. \\[4pt] [1] S. Stefanoski and G. Nolas, Cryst. Growth Des. 2011, dx.doi.org/10.1021/cg200756r\\[0pt] [2] M. Beekman, E. Nenghabi, K. Biswas, C. Myles, M. Baitinger, Y. Grin, G.S. Nolas, Inorg. Chem. 49 2010, DOI: 10.1021/ic1005049