ab initio simulations were employed to investigate the crystal structure of carbonated apatite (CAp). Two possible sites for the carbonate ions in the apatite lattice were considered: carbonate substituting for OH-ion (type-A) and for PO43-ion (type-B). A combined type-AB substitution was also proposed and numerous possible charge compensation mechanisms were treated. The results show that the most stable type-A CAp had its carbonate triangular plane almost parallel to c-axis, making an angle of about 2° at z = 0.46. In the most stable type-B CAp structure, the nearest Ca (2) ion was replaced by a sodium ion and the carbonate group was lying almost flat inb/c-plane. Of all the models considered, mixed substitution type-AB where two carbonate ions replacing one phosphate group and one hydroxyl group shows the most stable structure.
On manifolds admitting stable type Ⅲ$_{\textbf1}$ Anosov diffeomorphisms