Information-theoretic point symmetry classifications/quantifications of an electron diffraction spot pattern from a crystal with strong translational pseudosymmetry

Abstract

The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the analysis of an experimental selected-area transmission electron diffraction spot pattern. The extracted lattice parameters of this crystal are within experimental error bars consistent with a metric tensor that suggests the presence of hexagonal translation symmetry. The point symmetry of the combined low, medium, and high resolution spots is, however, no higher than 2mm. The likelihood of this electron diffraction pattern belonging to a rectangular-centered crystal rather than a hexagonal crystal is quantified on the basis of its information-theoretic point group symmetry classifications. Presumably due to a slight misorientation away from the exact [001] zone axis combined with the curvature of the Ewald sphere and a real structure that includes intergrowth of quadruple NbO and triple BaNbO3 blocks of varying sizes and orientations, the group of highest resolution spots, i.e. d-spacings between 0.125 to 0.085 nm, feature point symmetry .m. only. The crystallographic Rsym values of traditional classifications into the point groups that are compatible with the experimentally obtained primitive lattice parameters are provided for comparison purposes. As it is common practice in diffraction based crystallography, point symmetry classification and quantification results for the group of highest resolution spots are provided separately from their counterparts for the combined low, medium, and high resolution spots.