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ISSN: 2053-2733

May 2020 issue

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Cover illustration: In their Lead Article, Power et al. [Acta Cryst. (2020). A76, 275-301] develop new mathematical tools to classify and enumerate isotopy types for 3-periodic nets. Isotopy types are aimed at distinguishing different aspects of (self-)catenation observed in crystal structures. As a first step, they classify 3-periodic bouquet nets and n-fold pcu nets up to periodic isotopy. The image illustrates some of the enumerated four- and fivefold pcu nets which could represent challenging targets for synthetic chemists.

scientific commentaries


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The article by Power et al. [Acta Cryst. (2020), A76, 275–301] on the isotopy classification of crystal nets is discussed.

advances

lead articles


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Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type.

research papers


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The Debye scattering equation (DSE) is generalized and augmented in order to account for moderate texture effects, yielding the differential cross section as a function of atomic coordinates and texture coefficients subject to symmetry constraints. Implications for the evaluation of the pair distribution function (PDF) as a direct transform of powder diffraction data from textured samples are also discussed.

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Physical quantities in arbitrary dimensional space can be classified into 41 types using three antisymmetries within the framework of Clifford algebra.

foundations

research papers


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Features of azimuthal plots for RHEED and its new counterpart, RHEPD, are discussed. The plots, for both electrons and positrons, are determined using dynamical diffraction theory.

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The application of groupoids to modular crystal structures is presented.

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A method is described for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films comprising various crystal orientations and/or polymorphs by measuring reciprocal-lattice vectors.

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A method is adapted to generate a full rank realization of an abstract regular polyhedron with automorphism group H3.

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An auto-indexing method for two-color X-ray diffraction data is presented, which has been tested on both simulated and experimental protein diffraction data. The indexing yield is increased significantly compared with the previous approach using conventional indexers.

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To describe multiple Bragg reflection from a thick, ideally imperfect crystal, the transport equations are reformulated in three-dimensional phase space and solved by spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially for finite detectors.

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A new type of X-ray LLL interferometer, a `hard' interferometer, which has both a base and a `ceiling', is tested for experimental investigations. The tested interferometer has no preliminary uncontrollable moiré and can be used for object and deformation investigations.

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Structure-mining finds and returns the best-fit structures from structural databases given a measured pair distribution function data set. Using databases and heuristics for automation, it has the potential to save experimenters a large amount of time as they explore candidate structures from the literature.

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A Landau theory for the wurtzite-based heterovalent ternary semiconductor ZnSnN2 is developed and a first-order reconstructive phase transition is proposed as the cause of observed crystal structure disorder. The model implies that the phase transition is paraelectric to antiferroelectric.

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The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect.

short communications


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Using mineralogical data, it is demonstrated that chemical simplicity measured as an amount of Shannon information per atom on average corresponds to higher symmetry measured as an order of the point group of a mineral, which provides a modern formulation of the Fedorov–Groth law.
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