First-principles calculations for thermodynamic properties of type-I silicon clathrate intercalated by sodium atoms

Abstract

The ground state properties of the silicon clathrate [Formula: see text] intercalated by alkali metal sodium atoms [Formula: see text] are investigated by first-principle methods. Birch–Murnaghan equation of state is fitted to two sets of the [Formula: see text]–[Formula: see text] data calculated by density functional theory based on the plane-wave basis set within both the local density approximation (LDA) and the generalized gradient approximation (GGA). Through quasi-harmonic Debye model, some thermodynamic properties comprise the heat capacity, the thermal expansion coefficient, Debye temperature and the Grüneisen parameter for this clathrate compounds [Formula: see text] are obtained, which agree well with experimental results. Comparing the calculated heat specific in two ways with experimental results, we find that it is more accurate to describe the “rattle” modes of gust Na atoms in the cages as Einstein oscillators. Moreover, the effects of high pressure on these thermodynamic properties are also investigated which will be very helpful for a synthesis of these clathrate compounds in experiments under high pressure and high temperature condition.