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Microsized hydroxyapatite (HAp), we synthesized under mild hydrothermal conditions, shows both monoclinic and hexagonal polymorphs made by rod-shaped single crystals along with simple and multiple twins. The theoretical morphology, obtained through the Hartman-Perdok analysis on the P21/c polymorph, allowed to predict the stable surfaces of the main {hkl} forms. Their surface energies have been evaluated, at 0 K, by ab initio quantum-mechanical calculations. The resulting HAp equilibrium shape (ES) [1] is dominated by a pseudo-hexagonal prism formed by the the {001}, {100} and {-102} forms (having close energy values), all developing around the OH channels of the structure. The basal {010} form truncates the pseudo-hexagonal prism perpendicularly to the OH channels, while three other less important prisms {012}, {110} and {11-2}, lying in between the pseudo-hexagonal prism and the basal pinacoid, enter the ES. A simple kinetic model based on 2D nucleation is proposed to explain the morphology of the single crystals [1]. Assuming [2, 3] that the simplest twin law for the monoclinic phase is generated by a threefold rotation about the 21 axis, we found that the three original composition planes (OCP) of the twin coincide with the faces of the {001}, {100} and {-102} forms. For each OCP there are two different surface terminations, according to whether the frontier between parent (P) and twinned (T) crystals intercepts (or not) the centers of mass of PO4 and Ca ions and of the O atoms of the OH groups. We examined, as an example, the two kinds of interfaces for the twin (100)P/(001)T. The calculated twin energies result to be very close and low (3.3 and 4.2 erg cm-2), when compared to the value of the HAp surface energy in the [010] zone (≍ 1500 erg cm-2). This means that the probability of formation of a 2D-nucleus oriented in twin position on all the [010] zone is practically equivalent to that needed to generate a normally oriented 2D nucleus in the same zone
