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 minimum-energy 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.