First-principles study of the biomineral hydroxyapatite

The biomineral hydroxyapatite Ca₁₀(PO₄)₆(OH)₂ is the main mineral constituent of mammal bone. Hydroxyapatite crystallizes in the hexagonal and monoclinic phases, the main difference between them being the orientation of the hydroxyl groups. Using density functional theory, we study the energetics of the hexagonal and monoclinic phases, along with the several hypothetical crystal structures of hydroxyapatite. The monoclinic phase has the lowest energy, with the hexagonal phase being only 22 meV/cell higher in energy. We identify a structural transition path from the hexagonal to monoclinic phase, with the activation energy of 0.66 eV per hexagonal cell. At room temperature, the transition occurs on a millisecond time scale. The electronic structures of the monoclinic and hexagonal phases are compared. For the hexagonal phase, we calculate the phonon frequencies at the {Γ}-point and elastic constants. Both are in good agreement with available experimental results.