Molecular Dynamics Study of the Thermodynamic Properties of Calcium Apatites. 2. Monoclinic Phases

Structural and thermodynamic properties of crystalline monoclinic calcium apatites, Ca₁₀(PO₄)₆(X)₂ (X = OH, Cl), were investigated for the first time using a molecular dynamics (MD) technique under a wide range of temperature and pressure conditions. The accuracy of the model at room temperature and atmospheric pressure was checked against crystal structural data, yielding maximum deviations of ca. 2%. The standard molar lattice enthalpy of the apatites was also calculated and compared with previously published experimental and MD results for the hexagonal polymorphs. High-temperature simulation runs were used to estimate the isobaric thermal expansivity coefficient and study the behavior of the crystal structure under heating. The heat capacity at constant pressure, C_p, 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 = 635 ± 7 J·mol^-1·K^-1 and C_p,m = 608 ± 14 J·mol^-1·K^-1 for hydroxy- and chlorapatite, respectively. High-pressure MD experiments, in the 0.5−75 kbar range, were performed to estimate the isothermal compressibility. The Parsafar−Mason equation of state was successfully used to fit the high-pressure p−V_m data, with an accuracy better than 0.03%.