Structural identification of cubic iron-oxide nanocrystal mixtures: X-ray powder diffraction versus quasi-kinematic transmission electron microscopy

Two novel (and proprietary) strategies for the structural identification of a nanocrystal from either a single high-resolution (HR) transmission electron microscopy (TEM) image or a single precession electron diffraction pattern are proposed and their advantages discussed in comparison to structural fingerprinting from powder X-ray diffraction patterns. Simulations for cubic magnetite and maghemite nanocrystals are used as examples. This is an expanded and updated version of a conference paper that has been published in Suppl. Proc. of TMS 2008, 137th Annual Meeting & Exhibition, Volume 1, Materials Processing and Properties, pp. 25-32.Comment: 7 pages, 3 figures, 1 table, expanded and updated version of a conference paper that has been published in Suppl. Proc. of TMS 2008, 137th Annual Meeting & Exhibition, Volume 1, Materials Processing and Properties, pp. 25-3

Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review

Objective Distinctions Between Genuine Plane Symmetries and Pseudosymmetries in Crystal Patterns of Graphic Artwork

A recently developed method for the objective identification of the plane symmetry group of a noisy crystal pattern is briefly described and subsequently applied to two pieces of graphic art. Pseudo-symmetries do not distract from the beauty of graphic art but add to it. They are here distinguished from the genuine symmetries that combine to form the best-fitting plane symmetry group. The gray-value deviations of the individual pixel values of graphic artworks from their perfectly symmetric abstractions are considered to be chiefly due to the handiwork and employed creative procedures of an individual artists. As different graphic techniques/procedures were employed in the creation of the here classified crystal patterns, one may glean insights on how well a particular technique or procedure supports the realization of an intended crystallographic symmetry group in a graphic work of art.Comment: 8 pages, 3 figure