Identification of two allotwins of mica polytypes in reciprocal space through the minimal rhombus unit

The X-ray investigation (precession method) of the Ruiz Peak oxybiotite, which is well known for the occurrence of a large number of polytypes and twins, revealed two complex diffraction patterns, which cannot be identified as long-period polytypes. These patterns are analysed in terms of the minimal rhombus, a geometrical asymmetric unit in reciprocal space which permits the decomposition of the composite reciprocal lattice of a twin or allotwin into the reciprocal lattices of the individuals. Both the recorded patterns correspond to a 1M-2M(1) allotwin: the relative rotation between the individuals is 120 degrees in one case and 60 degrees in the other. The geometrical criteria for evaluating the presence of twinning or allotwinning are analysed through these two natural examples.