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, ΔlatH298°, 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, Cp,m, in the range 298−1298 K, was estimated from the plot of the molar enthalpy of the crystal as
a function of temperature, Hm = (Hm,298 − 298Cp,m) + Cp,mT, yielding Cp,m = 694 ± 68 J·mol-1·K-1, Cp,m =
646 ± 26 J·mol-1·K-1, Cp,m = 530 ± 34 J·mol-1·K-1, and Cp,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, κT, 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%.