Density functional theory calculations of local ordering of hydroxy groups and fluoride ions in hydroxyapatite

Electronic structure calculations based on density functional theory are employed to investigate the effect of substitutional fluoride ions on the local ordering of hydroxy groups in hydroxyapatite. The calculated structural parameters of the two end-member minerals are in good agreement with the experimental hexagonal structures. Electronic density contour plots show the apatite structure to be an ionic crystal, where the phosphate and hydroxy groups behave like polyanions. The calculations on hydroxyapatite identified the oxygen and hydrogen positions of the hydroxyl groups in the crystal structure to be well-defined, alternating in a column in the c direction. Any disorder within the OH columns carries an energetic cost of 0.22 eV per OH- but comparison with the fully ordered monoclinic phase of hydroxyapatite shows that ordering between the columns has no energetic advantage. We therefore predict that the experimentally found oxygen and hydrogen disorder is due to the presence in the crystal of differently oriented locally ordered domains, giving rise to the average partial occupancy which is found in crystallographic studies. Replacement of OH- groups in hydroxyapatite by F- ions from fluorapatite, is exo-thermic (-0.10 eV per OH- for a 33% replacement and -0.07 eV per OH- for a 50% substitution compared to the lowest energy hydroxyapatite structure). The 33% substitution of OH groups by F ions leads to a structure with reversion of the OH- alignment within the column and the presence of F- hence stabilises randomisation of the hydroxy groups in the columns. The negative calculated excess heats of solid solution of fluor- and hydroxyapatite (-7 kJ mol(-1)) are in agreement with the uptake of F- ions in hydroxyapatite in dental enamel.