First-Principles Study of Guest-Host Bonding in the Type-II Clathrate Compounds A$_{\mathrm{x}}$Si$_{\mathrm{136}}$ (A $=$ Na, K, Rb, Cs; 0 $\le $ x $\le $ 24)

The Type II clathrate-based materials are interesting due to their potential thermoelectric applications. Recently, a synthesis and characterization of Na$_{\mathrm{x}}$Si$_{\mathrm{136\thinspace }}$for various x has been reported [1]. Powdered X-Ray diffraction (XRD) data and density functional theory (DFT) studies of Na$_{\mathrm{x}}$Si$_{\mathrm{136}}$ have found a lattice contraction as x increases for 0 \textless x \textless 8 and an expansion as x increases for x \textgreater 8. This is explained by XRD data showing that, as x increases, the 28-atom Si cages are filled first for x \textless 8 and the 20-atom Si cages are then filled for x \textgreater 8. We report results of first-principles calculations focused on analyzing the underlying mechanisms relevant to guest-host interactions and to understanding the role of the guest atom to host atom size ratio in this material. We have also studied the compounds A$_{\mathrm{x}}$Si$_{\mathrm{136}}$ (A $=$ Na, K, Rb, Cs; 0 $\le $ x $\le $ 24). Our LDA calculations for K$_{\mathrm{x}}$Si$_{\mathrm{136}}$ (0 \textless x \textless 16) predict that this material should exhibit a non-monotonic structural response similar to that in Na$_{\mathrm{x}}$Si$_{\mathrm{136}}$; the lattice should contract and then expand as x increases. We find that the heavier guests (Rb, Cs) vibrate nearer to the center of the Si$_{\mathrm{28}}$ cages than do Na and K. Our results also show that Na and K are both strongly coupled to the Si framework in A$_{\mathrm{x}}$Si$_{\mathrm{136}}$ (A $=$ Na, K; x $=$ 4, 8). [1] S. Sefanoski, C.D. Malliakas, M.G. Kanatzidis, G.S. Nolas, \underline {\textit{Inorg. Chem.}} \underline {51}, 8686 (2012).