Determination of twinning relationships between diopside dendrites

Electron backscattered diffraction, used to determine the orientations of dendritic crystals of synthetic diopside, revealed novel twinning relationships between three dendrite crystals. The three crystals, considered pairwise, are related by two twinning laws: for two pairs, twin plane {51} and twin axis <42> perpendicular to the twin plane; and for the third pair, twin plane {21} and twin axis <56> perpendicular to the twin plane. The twin axes and twin planes between the latter pair of crystals closely match the twofold axis and symmetry plane inside the third crystal. The distribution of the three dendrite crystals in the twin structure shows overall 2/m symmetry, so the point group of diopside controls the whole combination of three crystals. The twin laws have been analysed using the theories of Mallard and Friedel, and twin indices and twin obliquity calculated. The complex twin laws yield a good lattice coincidence, and lattice relationship analysis based on the {201} plane confirms the twin laws.