A Molecular Dynamics Study of the Thermodynamic Properties of Calcium Apatites. 1. Hexagonal Phases

Structural and thermodynamic properties of crystal hexagonal calcium apatites, Ca₁₀(PO₄)₆(X)₂ (X = OH, F, Cl, Br), were investigated using an all-atom Born−Huggins−Mayer potential by a molecular dynamics technique. The accuracy of the model at room temperature and atmospheric pressure was checked against crystal structural data, with maximum deviations of ca. 4% for the haloapatites and 8% for hydroxyapatite. The standard molar lattice enthalpy, Δ_latH₂₉₈°, of the apatites was calculated and compared with previously published experimental results, the agreement being better than 2%. The molar heat capacity at constant pressure, C_p,m, in the range 298−1298 K, was estimated from the plot of the molar enthalpy of the crystal as a function of temperature, H_m = (H_m,298 − 298C_p,m) + C_p,mT, yielding C_p,m = 694 ± 68 J·mol^-1·K^-1, C_p,m = 646 ± 26 J·mol^-1·K^-1, C_p,m = 530 ± 34 J·mol^-1·K^-1, and C_p,m = 811 ± 42 J·mol^-1·K^-1 for hydroxy-, fluor-, chlor-, and bromapatite, respectively. High-pressure simulation runs, in the range 0.5−75 kbar, were performed in order to estimate the isothermal compressibility coefficient, κ_T, of those compounds. The deformation of the compressed solids is always elastically anisotropic, with BrAp exhibiting a markedly different behavior from those displayed by HOAp and ClAp. High-pressure p−V data were fitted to the Parsafar−Mason equation of state with an accuracy better than 1%.