The prediction method for standard enthalpies of apatites using the molar volume, lattice energy, and linear correlations from existing experimental data

Abstract

Experimental data of thermodynamic state functions and molar volume for phosphate, arsenate, and vanadate apatites containing Ca, Sr, Ba, Pb, end Cd at the cationic positions Me2+ and F, OH, Cl, Br, and I at the halide position X were collected. The apatite supergroup splits into distinct subgroups (populations) constituted by Me10(AO4)6X2 with the same Me2+ cations and tetrahedral AO43− anions but with different anions at the X position. Linear relationships between various parameters within apatite subgroups are observed. The prediction method for standard enthalpies of apatites (ΔHºf,el) is based on regression analysis of the linear correlations within the subgroups between ΔH°f,el of apatites and their molar volume Vm, lattice energy UPOT, and ΔH°f,el of their anions AO43− or X−. This allowed to predict 22 new ΔH°f,el values for apatites and materials with an apatite structure. The prediction precision is comparable to the experimental uncertainty obtained when reproducing experimental data using calorimetric measurements or dissolution experiments and can be applied to a wider range of apatites than other methods.