Theoretical equilibrium shape of hydroxyapatite, revised

Abstract

The theoretical equilibrium shape (ES) of the monoclinic hydroxyapatite (HAp) crystal is revised, having taken into account, for the first time, a new set of {h0l} pinacoids: {10}, {102} and {04}. The corresponding surface profiles are determined by applying the morphological Hartman–Perdok method. Surface energy values (γ_h0l) are evaluated at 0 K, with respect to the vacuum. Crystal surfaces are simulated by using the 2D periodic slab model and the ab initio CRYSTAL14 code. Calculations are performed at the DFT (density functional theory) level: the B3LYP Hamiltonian was adopted. From the comparison between the set of the γ_h0l values previously obtained for the pinacoids: {100}, {001} and {02} and those calculated in this work, a completely new ES is obtained. This striking result brings into question: (i) the geometrical laws of the growth twins; (ii) the predicted growth shape of HAp in pure aqueous solutions; (iii) the habit change of HAp crystals growing in aqueous solutions and doped with impurities that could make 2D-epitaxies on selected crystal faces.