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

Abstract

Calcium apatites with the general chemical formula (Ca, X) 10 (PO 4 , Y) 6 Z 2 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, Ca 10 (PO 4 ) 6 CO 3 , 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 V 0 = 538.14(5) Å 3 , K 0 = 106.2(7) GPa, and K 0 = 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 K T0 = 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. K E Y W O R D S bone mineralogy, carbonated apatite, DFT, Gaussian-type orbitals, quasiharmonic approximation

Equation of state of hexagonal hydroxylapatite (P63) as obtained from density functional theory simulations

“…To quantify the anisotropy on the lattice axis, we fitted the a ( P ) and c ( P ) data using a linearized BM3 equation, obtaining M(a) 0 = 300(15), M(a)' = 13.4(3.8), and a 0 = 9.386(9) and M(c) 0 = 514(26), M(c)' = 9.2(6.1), and c 0 = 6.872(4), respectively. These results are in very good agreement with the axial moduli previously calculated from the second‐order elastic constants …”

“…Recently, the structural, vibrational, surface properties and second‐order elastic constants of hydroxylapatite by ab initio quantum mechanical approach were investigated, obtaining results in good agreement with available experimental data. The aim of the present work is to further extend the research and calculate the equation of state of stoichiometric OHAp (space group P6 3 ) by using the well‐known quasi‐harmonic approximation (QHA), to fill the knowledge gap on the thermomechanical behavior of this mineral phase.…”

“…We employed the same all‐electron basis sets used in previous simulations of the bulk, vibrational and surface properties of hydroxylapatite and related carbonate‐doped minerals, where Ca, P, O, and H atoms are described by 86–511G(2d), 85‐21G(d), 6–31G*, and 6–31G* contractions, respectively.…”

“…Hydroxylapatite equilibrium volume was preliminarily calculated with the inclusion of dispersive forces in a previous work, obtaining lattice parameters a = 9.3859 Å and c = 6.8709 Å. This initial geometry was then employed to derive the equation of state of the mineral.…”

First‐principles investigation of structural, electronic, and optical properties of transition metal‐dopedC40 CrSi2

“…It is well known that the first-principles calculations are an effective tool to study the physical properties of a solid at the atomic or electronic level. [47][48][49][50][51][52] To reveal the physical properties of TM-doped C40 CrSi 2 silicide, the total energy, electronic, and optical properties of TM-doped C40 CrSi 2 silicide were assessed using the first-principles calculations, as implemented in the CASTEP code. [53,54] The interactions between the ionic core and valence electron of TM-doped C40 CrSi 2 silicide were described by the ultra-soft pseudopotentials.…”