Ab initio simulation on the crystal structure and elastic properties of carbonated apatite

Ab initio quantum mechanical (QM) calculations were employed to study the crystal structure and elastic properties of carbonated apatite (CAp). Two locations for the carbonate ion in the apatite lattice were considered: carbonate substituting for OH(-) ion (type-A), and for PO4(3-) ion (type-B) with possible charge compensation mechanisms. A combined type-AB substitution (two carbonate ions replacing one phosphate group and one hydroxyl group, respectively) was also investigated. The results show that the most energetically stable substitution is type-AB, followed by type-A and then type-B. The most stable configuration of type-A has its carbonate triangular plane almost parallel to c-axis at z=0.46. The lowest energy configuration of type-B is that with a sodium ion substituting for a calcium ion for charge balance and the carbonate lying on the b/c-plane of apatite. Lattice parameter changes after carbonate substitution in hydroxyapatite (HA) agree with reported experimental results qualitatively: for type-A, lattice parameter a increases but c decreases; and for type-B, lattice parameter a decreases but c increases. Using the calculated CAp stable structures, we also calculated the elastic properties of CAp and compared them with those of HA and biological apatites.