In addition to their ground state, diamond structure, Si, Ge and Sn can form crystalline solids called clathrates. As in the diamond structure, in the clathrates, the Group IV atoms are tetrahedrally coordinated and sp 3 covalently bonded to their neighbors. However, the clathrates contain pentagonal atomic rings and have open-framework lattices containing 20-, 24-and 28-atom ''cages''. There are two clathrate lattices: Type I, a SC lattice with 46 atoms per unit cell and Type II, a FCC lattice with 136 atoms per cubic cell. The pure clathrates are semiconductors.
The cages can contain weakly bound impurities (''guests''), usually alkali or alkaline earth atoms. The choice of guest may be used to tune the material properties. The guests are electronic donors, but because of their weak bonding, they have small effects on the electronic band structures. However, they can produce low frequency vibrational (''rattling'') modes which can strongly affect the vibrational properties. Some guest-containing clathrates have been shown to be excellent candidates for thermoelectric applications precisely because the guests only perturb the electronic properties weakly, while strongly affecting the vibrational (heat transport) properties. For thermoelectric applications, semiconductor materials are needed. When all cages are filled, the clathrates become semimetallic due to the excess valence electrons of the guests. To compensate for this, Group III atoms (usually Ga or In) are substituted on the framework sites.
After an introduction to clathrates, the results of calculations of the vibrational properties of some experimentally relevant Si-and Ge-based Type I and Type II clathrates are presented. The calculations were carried out using a first-principles, planewave, pseudopotential method. Results for the Si-based Type II materials Cs 8 Ga 8 Si 128 and Rb 8 Ga 8 Si 128 , and for the Ge-based Type I materials Ba 8 Ga 16 Ge 30 and Ba 8 Ga 16 Si 5 Ge 25 will be discussed with an emphasis on the very low frequency rattling modes of the guest impurities.