A Molecular Dynamics Study of the Thermodynamic Properties of Calcium Apatites. 1.
Hexagonal Phases
J. A. L. CruzFernando
N. Canongia LopesJosé
CaladoJorge C. G.
E. Minas da PiedadeManuel
2005
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%.