Ca-vacancy effect on the stability of substitutional divalent cations in calcium-deficient hydroxyapatite

First-principles calculations were performed to reveal an effect of Ca vacancies on the stability of substitutional divalent cations M²⁺ (M = Mg, Zn, Sr) in Ca-deficient hydroxyapatite (dHAp). M²⁺ concentrations up to 20 mol% in dHAp were considered, and the most stable substitutional sites and their lowest energy configurations in the dHAp lattice were examined with the aid of a generic algorithm method. It was found that defect formation energies of substitutional M²⁺ are lower in dHAp than in stoichiometric HAp (sHAp) at all M²⁺ concentrations. This indicates that these M²⁺ ions are more favorably involved in dHAp than in sHAp, which is in reasonable agreement with experiment. Detailed analyses on atomic structures in dHAp show that the presence of a Ca vacancy varies its surrounding Ca–O bond lengths over a wide area so that Ca–O polyhedrons with various sizes are produced. As a result, M²⁺ ions can predominantly occupy Ca sites at which M²⁺ fits better, depending on the ionic radii of M²⁺. For Zn²⁺ substitution in dHAp, its defect formation energy decreases more with the increasing concentrations and has the minimum value at 15 mol%. Such a trend can be understood from changes in effective coordination numbers of Zn in dHAp.