Bone mineral: first principles study of carbonate substitutions in hydroxyapatite

Mineral components of bone and teeth are hydroxyapatite at varying crystallinities and impurity concentrations, with carbon as a CO$^{-2}_3$ ion being the most abundant. The impurities influence the biological properties of bone and a study of their electronic and structural nature will contribute to a full understanding of the biological aspects. We perform electron density functional theory calculations to investigate CO$^{-2}_3$ on different sites in periodic hydroxyapatite lattice, as well as various charge compensation mechanisms. These include substitutions on OH$^{-}$ (A-site) and PO$^{-3}_4$ (B-site), and compensation by V$_{OH}$ or V$_{Ca}$. Defect clustering and effects of impurity concentration are studied. Substitutions of two CO$^{-2}_3$ for two PO$^{-3}_4$, compensated by a V$_{Ca}$, were found to be the most favored energetically. The $a$ lattice parameter increases for A-site substitutions, while for the B-site it typically decreases. The implications on the material properties are discussed.