Unravelling the specific site preference in doping of calcium hydroxyapatite with strontium from ab initio investigations and Rietveld analyses

Strontium can be substituted into the calcium sublattice of hydroxyapatite without a solubility limit. However, recent ab initio simulations carried out at 0 K report endothermic nature of this process. There is also striking discrepancy between experimentally observed preference of Sr doping at Ca-II sites and the first principles calculations, which indicate that a Ca-I site is preferred energetically for the Sr substitution. In this paper we combine insights from Density Functional Theory simulations and regular configurational entropy calculations to determine the site preference of Sr doping in the range of 0-100 at% at finite temperatures. In addition, samples of Sr-HA are synthesized and refinement of the relevant structural information provides benchmark information on the experimental unit cell parameters of Sr-HA. We find that the contribution of the entropy of mixing can efficiently overcome the endothermic excess energy at a temperature typical of the calcining step in the synthesis route of hydroxyapatite (700-950 °C). We observe that the most preferential substitution pattern is mixed substitution of Sr regardless of the concentration. For a wet chemical method, carried out at a moderate temperature (90 °C), the mixed doping is still slightly favourable at higher Sr-concentrations, except the range at 20% Sr, where Site II substitution is not restricted energetically and equally possible as the mixed doping. We observe a close correspondence between our theoretical results and available experimental data. Hence it should be possible to apply this theory to other divalent dopants in HA, such as Zn ²⁺, Mg ²⁺, Pb ²⁺, Cu ²⁺, Ba ²⁺, Cd ²⁺etc.