Structural, vibrational and thermal properties of some type II tin-based clathrates
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ABSTRACT This work is based on a theoretical study of some type II Sn-based clathrates. It includes a systematic study of some structural, electronic and vibrational properties of the type II tin-based clathrate materials Sn136, AxSn136 (A = Na, K, Cs; x = 8, 16, 24) For the structural properties the equilibrium volume V0, and the lattes constant ao have been calculated. The results show that for all compounds considered, the predicted lattice constant and the equilibrium energy increases with x. Also, the slope of the lattice constant as a function of x is predicted to become larger as the guest atom atomic number increases. These results agree with some other research on type II clathrates . I have also presented and discussed the results of the phonon dispersion relations for the mentioned materials and made qualitative and quantitative comparisons of the vibrational spectra for all the materials. Also, I have presented the results of the calculations of the low frequency elastic constants and the longitudinal and transverse sound velocities and I have compared these results for these three different guest atoms. Finally, the temperature dependence of the vibrational contributions to the free energy, the entropy and the specific heat capacity at constant volume (CV) have been predicted and discussed for the Type II Sn clathrate based materials Sn136, AxSn136 (A = Na, K, Cs; X = 8, 16, 24) in the temperature range (0 – 500) K.