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 pressuredriven 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.