A first-principles lattice dynamical study of type-I, type-II, and type-VIII silicon clathrates

The pristine crystalline type-I, type-II, and type-VIII silicon clathrates have been studied using state of the art first-principles calculations based on density functional theory and density functional perturbation theory. We apply quasi-harmonic approximation to study structural stability, the possibility of temperature or pressure-driven phase transitions, along with Grüneisen parameters, coefficients of thermal expansion and thermal conductivities to estimate the degree of phonon anharmonicity for selected silicon clathrates. It is shown that a pressure-driven phase transition between type-I and type-II silicon clathrates may occur, and a temperature-driven phase transition between type-I and type-VIII Si clathrates at high temperature is likely. We further show that the relatively high Grüneisen parameters (1.5, 1.65, and 1.29, respectively for Si₄₆-I, Si₁₃₆-II, Si₄₆-VIII), the existence of negative regions in the thermal expansion coefficient curves and very low thermal conductivities all indicate that the phonon anharmonicity in these silicon clathrates is high.