Electronic and crystallographic structure of apatites

An ab initio study of four different stoichiometric apatites (oxyapatite, hydroxyapatite, fluorapatite, and chlorapatite) is presented. The calculations were performed using density-functional theory with the local-density approximation for exchange and correlation, and a full relaxation of the electronic structure, the atomic arrangement, and the unit cell. Hexagonal unit cells were obtained for all four apatites, and the calculated atomic arrangements are in close agreement with observation in those cases for which the structure is firmly established. A zero-temperature structure is predicted for oxyapatite, and two possible configurations were found for the ${\mathrm{Cl}}^{-}$ ions in chlorapatite. The possibility of the monoclinic structure in hydroxyapatite and chlorapatite was also studied but no indication of greater stability with respect to the hexagonal structure was found. A relationship between the structure of the apatites and that of pure calcium is discussed.