First-principles calculations of divalent substitution of Ca2+ in tricalcium phosphates

First-principles calculations were carried out to reveal local atomic arrangements and thermodynamic stability of substitutional divalent cations of Mg(2+), Zn(2+), Sr(2+) and Ba(2+) in tricalcium phosphates (TCPs). There are two modifications of α-TCP and β-TCP, and a number of inequivalent Ca sites are present in the crystal structures. It was found that each divalent cation has energetically preferential Ca sites for substitution. For instance, Mg(2+) and Zn(2+) favor the substitution at the Ca-5 site of β-TCP while Sr(2+) and Ba(2+) tend to occupy Ca-3 and Ca-4 in the β-type crystal structure. The calculated site preference of these cations was in reasonable agreement with available experimental data. Moreover, it was found that these cations have negative formation energies at specific Ca sites especially in β-TCP, indicating the stabilization of the β phase.