First-principles study on structural, electronic, vibrational and thermodynamic properties of Sr10(PO4)6X2 (X = F, Cl, Br)

Abstract

A theoretical investigation on the structural stability, electronic, vibrational, and thermodynamic properties of the strontium apatites Sr₁₀(PO₄)₆X₂ (X = F, Cl, Br) is systematically conducted by the first-principles calculations. Results of cohesive energies and formation enthalpies suggest that the thermal stability of strontium apatites decreases from Sr₁₀(PO₄)₆F₂ (Sr-FAP) to Sr₁₀(PO₄)₆Cl₂ (Sr-ClAP) and further to Sr₁₀(PO₄)₆Br₂ (Sr-BrAP); such a tendency is also be observed with regard to the band gaps. Using linear-response approach, the detailed vibrational properties of Sr₁₀(PO₄)₆X₂ (X = F, Cl, Br) are obtained. According to the calculated phonon dispersions, it is concluded that strontium apatites Sr₁₀(PO₄)₆X₂ (X = F, Cl, Br) are dynamically stable, and the phonon behaviors are generally similar to these apatites, but most of the vibrational frequencies decrease from Sr-FAP, Sr-ClAP to Sr-BrAP. The assignment of the vibrational modes at the gamma point demonstrate that all the silent mode B_g, B_u and E_2u are affected and the only optically active mode involved is the Raman active mode E_2g with the replacement of larger Cl⁻ and Br⁻ for F⁻. The results calculated with the quasi-harmonic approximation (QHA) show that Sr₁₀(PO₄)₆X₂ (X = F, Cl, Br) exhibits similar but slightly different behaviors in terms of its thermodynamic properties, which is expected because the halogen atoms F, Cl and Br are in the same VIIA group. Significantly, all the present calculation results are satisfactory compared to the existing experimental and theoretical results.