Empirical potential description of energetics and thermodynamic properties in expanded-volume silicon clathrates

Energetics and thermodynamic properties of some expanded-volume silicons have been investigated using an empirical bond-order potential developed by Tersoff. For the most important silicon clathrate networks (formula presented) and (formula presented) we report on their elastic properties, vibrational properties, thermodynamic properties (free energy, entropy, heat capacity, and melting temperature), and the formation energies of vacancy, using the harmonic approximation and/or molecular-dynamics simulations. In order to illustrate relations between energetics and geometrical properties in expanded-volume silicons, we have calculated optimized geometries and energetics for more than 60 kinds of silisils, “zeolite without oxygen,” introduced by the Arizona State University group. A simple relation between cohesive energies and geometrical properties is found in these systems. It is also found that bulk moduli in these structures strongly depend on the density (or the atomic volume) and a simple theory deduced from the pseudopotential total-energy formalism by Lam et al. [Phys. Rev. B 35, 9190 (1987)] holds in the relation between them.