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ISSN: 2053-2733

November 2019 issue

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Cover illustration: Crystallography has the potential to be a powerful tool in various research fields as well as in materials science. Nishiyama [Acta Cryst. (2019), A75, 798-813] makes use of magnetic space groups to derive and analyse fluid flows with chirality, called Beltrami flows, in hexagonal cases. Their invariant tori, which are tube-like surfaces wound around by streamlines, are numerically observed to form various arrangements (as shown in the cover image). Some resemble arrangements that appear in studies of rod packings or weavings in materials.

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A new method that extends the Jayatilaka X-ray constrained wavefunction approach in the framework of the spin-coupled technique of the valence bond theory is presented. The proposed strategy enables the extraction of traditional chemical information (e.g. weights of resonance structures) from experimental X-ray diffraction data without imposing constraints a priori or performing further analyses a posteriori.

foundations

research papers


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Magnetic groups are applied to three-dimensional fluid flows with chirality, which are called Beltrami flows. Eight Beltrami flows are derived and studied using Wyckoff positions. The crystal-like structures of their tube-like surfaces, called invariant tori, are numerically observed.

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Perfect colorings of patterns with multiple orbits were characterized, with a focus on colorings where the orbits share colors. These results were then applied to construct perfect and non-perfect colorings of various symmetrical objects.

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A universal and effective algorithm is proposed for geometrical comparison of abstract sets of n points in Euclidean space. Applications of the algorithm for comparison of both finite (ligands) and periodic (nets) chemical objects are considered.

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The alleviation of subsurface machining damage in a thick-crystal neutron interferometer is investigated by testing the interferometer throughout an annealing and chemical etching post-fabrication process. Spatially varying Bragg-plane angular misalignments between diffracting components of the interferometer are lessened from 10−5 rad to less than 10−9 rad.

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In the waves emitted from the entrance, back and lateral surfaces of a very weakly bent plane-parallel perfect crystal with negative strain gradient, X-ray interference fringes between two refracted beams with different hyperbolic trajectories were observed when the strain was very weak, of the order of 10−7.

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The a posteriori probability densities of anomalous structure-factor amplitude differences were estimated by the Markov chain Monte Carlo machine-learning method. The model incorporated the correlation between the different Bijvoet pairs and the improved estimates were shown to be beneficial for SAD phasing.

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Relativistic electron diffraction depends on linear and quadratic terms in the electric potential, the latter being neglected in the frequently used relativistically corrected Schrödinger equation. Conventional tabulations for electron scattering and its large-angle extrapolations can be amended in closed form by a universal correction based on the screened Coulomb potential squared.

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In analogy to the original phenomenological theory of martensite crystallography, a double-shear theory for lath martensite is proposed which chooses the shearing systems as those that are macroscopically equivalent to double twinning. Using only the additional assumptions of overall small shape strain magnitude and a condition of maximal compatibility, this approach naturally gives rise to {5 5 7}γ habit planes and orientation relationships close to the Kurdjumov–Sachs model.

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A novel data-driven approach for synchrotron Laue X-ray microdiffraction scans is presented based on machine learning techniques.

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The de Wolff hypothesis concerning the orthorhombic symmetry of some rutile-type compounds is quantitatively confirmed for β-MnO2 and MnF2.

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This article describes the scattering behavior of electron vortices inside amorphous samples. It focuses on the vortex purity, net angular momentum transfer, and statistical variations due to random beam and atom positions.

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