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

Abstract

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° in one case and 60° in the other. The geometrical criteria for evaluating the presence of twinning or allotwinning are analysed through these two natural examples.