First principle investigation of the thermomechanical properties of type A carbonated apatite

Calcium apatites with the general chemical formula (Ca, X)10(PO4, Y)6Z2 represent a mineral family of utmost importance in several fields, for example, bone biology, biomaterials, and mineralogy. However, few works have focused on the mechanical properties of these phases, and in particular, no data are available on the thermomechanical and thermodynamic properties of carbonate-bearing (hydroxyl)apatites. In the present work, the equation of state of type A carbonated apatite (CAp, Ca10(PO4)6CO3, space group P1) was calculated by ab initio quantum mechanical methods within the density functional theory (DFT) framework. Starting from athermal results (at 0 K), the combined effect of temperature and pressure was investigated through the quasiharmonic approximation (QHA). In athermal conditions, the equation of state of the CAp unit cell volume can be described by a third-order Birch-Murnaghan formulation, with parameters V0 = 538.14(5) Å3, K0 = 106.2(7) GPa, and K′ = 4.6(4). The QHA well described the temperature and pressure dependence of the thermodynamics and mechanical properties of the mineral. For instance, the bulk modulus at 0 GPa and ambient temperature (300 K) is KT0 = 102.95 GPa, which is lower than that of stoichiometric apatite by about 6%. The unit cell thermal expansion coefficient between 0 and 600 K was also calculated and reported. The results are in line with the few available experimental data reported in literature on type AB carbonated hydroxylapatite. The reported findings further extend the knowledge of the mechanical and thermal behaviors of this important mineral found in biological environments, results that are useful for biotechnological and other applications of the (C)OHAp phases.