Structure and vibrational frequencies (at the Γ point) of CaCO3 aragonite have been calculated from first principles, by using the hybrid Hartree-Fock/DFT B3LYP Hamiltonian, at different unit-cell volumes in the 185–242 Å3 range. By using the frequencies evaluated at such different volumes, the mode-γ Grüneisen’s parameters were estimated for each vibrational mode, and the zero point and thermal pressure contributions to the total pressure, at each volume and temperature, have then been determined by means of standard thermodynamic formulas, within the limits of the quasi-harmonic approximation. This allowed for the determination of (i) the equation of state at different temperatures; (ii) the thermal expansion as a function of pressure and temperature, and (iii) the evaluation of some thermodynamic properties (entropy and specific heat) together with their temperature dependences. Results were directly compared with relevant experimental data.
The agreement of the calculated frequencies with the experimental data, at variable pressure, shows that the ab initio simulation can reproduce, at a relatively low computational cost, the full vibrational spectra of crystalline compounds of mineralogical interest. Moreover, the elastic properties (bulk modulus in particular), thermal expansion and thermodynamic properties, which play an important role in the characterization and in the understanding of the stability relations between carbonate phases, at high-pressure and high-temperature conditions, can be satisfactorily estimated. Precisely, at room temperature and pressure conditions, the calculated bulk modulus was 64.7 GPa, to be compared with an experimental value of 65(1) GPa (mean of three different experimental determinations); the estimated thermal expansion was about 6.1 · 10−5 K−1, which is only slightly underestimated with respect to the experimental datum [6.3(2) · 10−5 K−1]; the calculated entropy (S) and the constant-pressure specific heat (CP) were 87.5 and 83.1 J mol−1 K−1 respectively, which are in close agreement with the experimental data [84(6) and 82.6 J mol−1 K−1, for S and CP respectively].