Structural, Electronic and Vibrational Properties of Na$_{x}$Si$_{136 }$(0 $<$ x $<$ 24) Clathrates

CRAIG HIGGINS, EMMANUEL NENGHABI$^{\dag }$, CHARLES W. MYLES, Texas Tech U.; KOUSHIK BISWAS, Oak Ridge National Lab; MATT BEEKMAN, U. of Oregon; GEORGE S. NOLAS, U. of South Florida - Na$_{x}$Si$_{136}$ is a Type II clathrate with important thermoelectric properties. It's face-centered cubic lattice contains polyhedral ``cages'' of silicon atoms with Na atom ``guests'' in the cages. This material is very interesting because powder X-ray diffraction experiments$^{1 }$for differing Na content x have shown that, for increasing x in the range 0 $<$ x $<$ 8, lattice contraction occurs. After all Si$_{28}$ cages in the unit cell are filled (x = 8) and x is increased further, causing a filling of the Si$_{20}$ cages, a contrasting lattice expansion results. Using the local density approximation, we have calculated the x dependences of the structural, electronic and vibrational properties of Na$_{x}$Si$_{136}$. Results are presented for the x dependences of the lattice constant, electronic bands, and vibrational modes. Our results for the x dependence of the lattice constant are in agreement with our X-ray data$^{1}$. $^{\dag }$Deceased. $^{1}$M. Beekman, E.N. Nenghabi, K. Biswas, C.W. Myles, M. Baitinger, Y. Grin, G.S. Nolas, Inorg. Chem. 49, 5338--5340 (2010).