Funct. Mater. 2015; 22 (1): 79-92.

Phonon densities of states, dielectric constants, the Born effective charges, interatomic force constants of stoichiometric apatites Me₁₀(PO₄)₆X₂, where Me = Ca or Cd and X = F, Cl, Br, OH, were calculated in the framework of DFPT with pseudopotential approach and plane wave basis sets. Phonon densities of states of all investigated apatites were proven to have similar structures which consist of four bands, consistently with previously reported phonon spectra of Ca10(PO₄)₆F₂ and Ca₁₀(PO₄)₆(OH)₂. Phonon frequencies for calcium apatites are well consistent with the experimental IR-absorption curves. We have established the effects of evolution in spatial charge distributions, electron energy structures of valence bands and band gaps for apatites of the series Me₁₀(PO₄)₆X₂, where Me = Ca or Cd and X = F, Cl, Br, OH. Band gaps in the calcium apatites were correctly described in the framework of density functional theory. Lattice constants and bond lengths in apatites Me₁₀(PO₄)₆X₂, where Me = Ca or Cd and X = F, Cl, Br, OH, were calculated in the framework of the density functional theory which are in a good concordance with the experimental observations. High stability of PO₄-anions with respect to substitution of column ions in the apatite structure was found, which means the small variation in volumes of PO₄ tetrahedra. We have calculated phonon dispersion curves for Ca₁₀(PO₄)₆F₂, and have shown that the speed of sound along the six-fold screw axis in Ca₁₀(PO₄)₆F₂, Ca₁₀(PO₄)₆Cl₂, Ca₁₀(PO₄)₆(OH)₂, Ca₁₀(PO₄)₆Br₂ was larger than that in the planes perpendicular to it.