First-principles calculations of the vibrational and thermal properties of the type-I clathrates Ba8 Ga16 Six Ge30-x and Sr8 Ga16 Six Ge30-x

We have performed density-functional calculations of the vibrational and thermal properties of some of the type-I semiconductor clathrate "alloys" Ba8 Ga16 Six Ge30-x and Sr8 Ga16 Six Ge30-x as a function of Si composition x. We find that the guest-atoms Ba and Sr produce localized vibrational modes lying below 80 cm-1, which tend to reduce the acoustic bandwidth of the host material. Our results also predict an upshift in the flat optic modes of the host framework as the Si content of the lattice increases and that the guest-atom-associated Einstein temperature in these materials varies with x. Our calculated isotropic atomic displacement parameters as functions of temperature for the guest Ba and Sr atoms in these clathrates predict that Sr has a larger isotropic displacement parameter than Ba, thus suggesting that Sr should be more efficient than Ba in suppressing the thermal conductivity. We have also calculated the temperature dependences of the vibrational contributions to the specific heat, the entropy, and the Helmholtz free energy in these materials. We find that the heat capacities of these clathrates increase smoothly with temperature and approach the Dulong-Petit value at around room temperature. As expected, we also find that in these materials, there is also a slight x dependence of the heat capacity, free energy, and vibrational entropy.