First-Principles Computational Study of the Properties of the Clathrate Compounds A$_{\mathrm{8}}$Al$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$(A$=$Na,Rb,Cs)

Our recent study [1] of the properties of the Type-II binary clathrate compounds A$_{\mathrm{x}}$Si$_{\mathrm{136}}$, A$_{\mathrm{x}}$Ge$_{\mathrm{136}}$ and A$_{\mathrm{x}}$Sn$_{\mathrm{136}}$ (A$=$Na, K, Rb, Cs; 0$\le $x$\le $24) has increased the understanding of the role of the guest atoms and their composition x in determining the properties of these materials. For Na$_{\mathrm{x}}$Si$_{\mathrm{136}}$, our results have helped to explain the observed dependence of the lattice constant on x, which has a very unusual, distinct minimum at x $=$ 8. In this case, we have also found a ``Mexican-hat'' shaped effective potential curve for the Na atom motion in the large, (28-atom) Si cages. Motivated by these fascinating results for Na$_{\mathrm{x}}$Si$_{\mathrm{136}}$, we have extended our study of the effects of alkali guests on the properties of the Type-II clathrates to include their effects on the properties of the Type-II the ternary clathrate compounds A$_{\mathrm{8}}$Al$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$(A$=$Na,Rb,Cs). An earlier study of similar compounds, (Rb,Cs)$_{\mathrm{8}}$Ga$_{\mathrm{8}}$Si$_{\mathrm{128}}$, has found low frequency guest rattling modes (\textasciitilde 41-51 cm$^{\mathrm{-1}})$. Here, we report the results of a first-principles computational study of the electronic, structural and vibrational properties of the compounds A$_{\mathrm{8}}$Al$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$(A$=$Na,Rb,Cs). We contrast our results with those for (Rb,Cs)$_{\mathrm{8}}$Ga$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$, as well as with our recent results for the binary clathrates A$_{\mathrm{x}}$Si$_{\mathrm{136\thinspace }}$(A$=$Na,Rb,Cs). Our calculations are based on the Local Density Approximation to Density Functional Theory, as implemented by the VASP code. [1] D. Xue, C. Myles, C. Higgins; Materials 2016, \textbf{9}(8), 691.