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

Structural and thermodynamic properties of crystal hexagonal calcium apatites, Ca<sub>10</sub>(PO<sub>4</sub>)<sub>6</sub>(X)<sub>2</sub> (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<sub>lat</sub><i>H</i><sub>29</sub><sub>8</sub>°, 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, <i>C</i><i><sub>p</sub></i><sub>,m</sub>, in the range 298−1298 K, was estimated from the plot of the molar enthalpy of the crystal as a function of temperature, <i>H</i><sub>m</sub> = (<i>H</i><sub>m,298</sub> − 298<i>C</i><i><sub>p</sub></i><sub>,m</sub><i>)</i> + <i>C</i><i><sub>p</sub></i><sub>,m</sub><i>T</i>, yielding <i>C</i><i><sub>p</sub></i><sub>,m</sub> = 694 ± 68 J·mol<sup>-1</sup>·K<sup>-1</sup>, <i>C</i><i><sub>p</sub></i><sub>,m</sub> = 646 ± 26 J·mol<sup>-1</sup>·K<sup>-1</sup>, <i>C</i><i><sub>p</sub></i><sub>,m</sub> = 530 ± 34 J·mol<sup>-1</sup>·K<sup>-1</sup>, and <i>C</i><i><sub>p</sub></i><sub>,m</sub> = 811 ± 42 J·mol<sup>-1</sup>·K<sup>-1</sup> 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<sub>T</sub>, 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 <i>p</i>−<i>V</i> data were fitted to the Parsafar−Mason equation of state with an accuracy better than 1%.