Electronic and atomic structures of vacancies and protons in hydroxyapatite (HAp) are analyzed by using first-principles band structure calculations. From total energies of supercells for monoclinic HAp, defect formation energies and equilibrium concentrations are evaluated, assuming chemical equilibrium between HAp and aqueous solution saturated with respect to HAp. It is found that interstitial and Ca-substitutional protons form ${\mathrm{H}}_2\mathrm{O}$ groups or acid phosphates of ${\mathrm{HPO}}_4^{2-}$ and are stabilized by making hydrogen bonding with adjacent ${\mathrm{PO}}_4^{3-}$ groups. Moreover, defect association considerably decreases the defect formation energies, and, in particular, interstitial protons bonded to ${\mathrm{OH}}^{-}$ groups become most stable when associated with Ca-substitutional protons. Due to abundant formation of the associated defect comprising interstitial and Ca-substitutional protons, Ca contents in HAp decrease with lowering pH, which explains pH dependence of $\mathrm{Ca}∕\mathrm{P}$ molar ratios of HAp observed experimentally.

• Received 31 August 2007

DOI:https://doi.org/10.1103/PhysRevB.77.104106