Calculated Evaluation of the Energies of Point Defects in α- and β-Ca3(PO4)2

A comparative semi-empirical calculation of the energies of heterovalent substitution of Na+ or K+ ions for Ca2+ and SO42- or SiO44- ions for PO43- in alpha- and beta-Ca-3(PO4)(2) and the energies of point defects accompanying this substitution has been carried out. The energy of substitution of Na or K for Ca and vacancies in different Ca positions in beta-Ca-3(PO4)(2) (the whitlockite structure) is, in general, consistent with the sizes of the substitutes and the geometry of their coordination environment. For alpha-Ca-3(PO4)(2) (the glaserite-type cation-deficient structure), the energy of incorporation of cations (Na, K, and Ca) into six vacant structural positions relative to the glaserite structure has been calculated. The defect energies obtained are qualitatively consistent with the available phase diagrams of the investigated systems under the assumption of a significant entropy factor.