Effect of Guest Atom Composition on the Structural and Vibrational Properties of the Type II Clathrate-Based Materials A(x)Si(136), A(x)Ge(136) and A(x)Sn(136) (A = Na, K, Rb, Cs; 0 ≤ x ≤ 24)

Type II clathrates are interesting due to their potential thermoelectric applications. Powdered X-ray diffraction (XRD) data and density functional calculations for Na(x)Si(136) found a lattice contraction as x increases for 0 < x < 8 and an expansion as x increases for x > 8. This is explained by XRD data that shows that as x increases, the Si(28) cages are filled first for x < 8 and the Si(20) cages are then filled for x > 8. Motivated by this work, here we report the results of first-principles calculations of the structural and vibrational properties of the Type II clathrate compounds A(x)Si(136), A(x)Ge(136), and A(x)Sn(136). We present results for the variation of the lattice constants, bulk moduli, and other structural parameters with x. These are contrasted for the Si, Ge, and Sn compounds and for guests A = Na, K, Rb, and Cs. We also present calculated results of phonon dispersion relations for Na(4)Si(136), Na(4)Ge(136), and Na(4)Sn(136) and we compare these for the three materials. Finally, we present calculated results for the elastic constants in Na(x)Si(136), Na(x)Ge(136), and Na(x)Sn(136) for x = 4 and 8. These are compared for the three hosts, as well as for the two compositions.