Twin Laws and Energy in Monoclinic Hydroxyapatite, Ca5(PO4)3(OH)

The most frequent twin law of the monoclinic hydroxyapatite crystal (HAp, S.G.: P21/c) is examined from both the geometrical and reticular point of view. The A3 twin axis, parallel to the screw diad axis of the parent (P) crystal, generates two twinned (T) individuals, mutually rotated by 120°. The structure of the resulting twinned interfaces are hypothesized, following the Hartman–Perdok method for determining the most stable surface profiles. The twin energy for each interface, evaluated by ab initio calculation, indicates that the activation energy for the nucleation of a three-dimensional (3D) twin can be hardly distinguished from the one needed to nucleate a single 3D crystal. Moreover, a triple monoclinic twin simulates the structure of a trigonal-hexagonal HAp single crystal and the growth morphology of a monoclinic twin gradually approaches the hexagonal habit as much as the twin grooves disappear during growth.