The electronic structure and transport properties of clathrates: a density functional study

We have used density functional theory to study the electronic properties of the clathrates Sr/sub 8/Ga/sub 16/Ge/sub 30/, Ba/sub 8/Ga/sub 16/Ge/sub 30/, and Ba/sub 8/Ga/sub 16/Si/sub 30/. We found that these compounds have a number of unexpected properties. The atoms inside the large cages (Sr or Ba) undergo large amplitude motion, especially in the direction parallel to the six-atom windows; the Sr atom in Sr/sub 8/Ga/sub 16/Ge/sub 30/ is practically neutral while the Ba atom in Ba/sub 8/Ga/sub 16/Ge/sub 30/ donates practically two electrons to the frame; Sr/sub 8/Ga/sub 16/Ge/sub 30/ is a metal while Ba/sub 8/Ga/sub 16/Ge/sub 30/ and Ba/sub 8/Ga/sub 16/Si/sub 30/ are semiconductors. The Sr bands in Sr/sub 8/Ga/sub 16/Ge/sub 30/ are located near the Fermi level, are very flat, and do not contribute to the Seebeck coefficient or the conductivity (there is thus no conductivity through the one-dimensional Sr wires in the structure); most electron transport takes place through one band whose electrons are located on the frame. We also find that the transport properties are sensitive to chemical modifications: deliberate errors in stoichiometry, doping with charge donors or acceptors, and changes in location of the group-III elements in the lattice can cause changes of a factor of two or more in the Seebeck coefficient. Finally, total energy calculations show that the clathrates have lower energy than the elemental solids (Sr, Ba, and Ge). This implies that the clathrates are not thermodynamically metastable and therefore one does not have to fight thermodynamics during synthesis; given a chance by kinetics the elements will prefer to form a clathrate. This suggests that clathrates can be formed by crystallization from a melt containing the elements in the appropriate stoichiometry.