Duals of Frank-Kasper structures as C, Si and Ge clathrates: Energetics and structure

The four-connected clathrate structures derived as the duals of some of the tetrahedrally close-packed intermetallic structures (Frank-Kasper structures) are considered as possible structures for elemental C, Si and Ge. The minimumenergy structures are found using empirical potentials. The type II structure is found to have the lowest energy, but other clathrate structures have only a slightly higher energy within a few kT of the energy of the diamond form. Explicit coordinates are given for some Si structures.