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March 2021 issue
Cover illustration: Until recently, virtually all experimental electron densities have been determined using single-crystal data. In this issue, Svane et al. [Acta Cryst. (2021), A77, 85-95] show that powder diffraction data collected using the overlapped high-grade intelligencer setup (OHGI) at SPring-8, which uses 15 MYTHEN strip modules, can yield comparable electron-density information to that obtained using the Aarhus vacuum imaging-plate diffractometer (AVID). The cover image shows the static deformation densities (top row) and residual densities (bottom row) for urea, showing that multipole electron densities can be obtained from powder diffraction even without a dedicated setup.
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The advantages of a powerful new tool for determining the electron density of small inorganic systems using high-quality powder diffraction data from the MYTHEN microstrip detector [Svane et al. (2021). Acta Cryst. A77, 85–95] are considered.
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Multipole electron densities and structural parameters of inorganic and organic materials were evaluated on the basis of synchrotron powder X-ray diffraction data obtained with a MYTHEN detector system (OHGI).
A new crystallographic method to refine a spin-resolved atomic orbital model against X-ray and polarized neutron diffraction data is reported. Radial extension of atomic orbitals, and their orientations and populations, are obtained for each atom in the YTiO3 perovskite crystal.
foundations
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A generalization of Penrose tiling to 3D Euclidean space with icosahedral symmetry is proposed. The dodecahedral tiling system composed of four prototiles with faces of Robinson triangles determines the 3D quasicrystallographic structures.
The diffraction of an X-ray microbeam in a crystal with boundary conditions in the cases of both geometrical optics and the Fresnel approximation was studied theoretically. Reciprocal-space maps and the distribution of the diffraction intensity of the microbeam inside the crystal were calculated.
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A mathematical proof based on arithmetic argument is presented for the modified Euler characteristic ![[\chi_{\rm m}=\sum_{i=0}^N (-1)^i \sum _{j=1}^{n(i)} 1/m(ij)=0]](/a/issues/2021/02/00/pl5009/teximages/pl5009fi1.svg)
(where the first summation runs from 0-dimensional vertices to the N-dimensional cell or `interior'), applicable to symmetrically arranged space-filling polytopes in N-dimensional space, where the contribution of each jth i-dimensional element of the polytope is weighted by a factor inversely proportional to its multiplicity m(ij).
(where the first summation runs from 0-dimensional vertices to the N-dimensional cell or `interior'), applicable to symmetrically arranged space-filling polytopes in N-dimensional space, where the contribution of each jth i-dimensional element of the polytope is weighted by a factor inversely proportional to its multiplicity m(ij).
Crystallographic descriptions of isogonal piecewise linear embeddings of 1-periodic weaves and links (chains) are presented. Many of these are interesting synthetic targets for reticular chemistry methods.
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It is proved that the coordination sequence of the graph obtained from a crystal is of quasi-polynomial type, as had been postulated by Grosse-Kunstleve et al. [Acta Cryst. (1996), A52, 879–889] in their study of coordination sequences of zeolites.
The dynamical diffraction Talbot effect behind a crystal in free space is considered. The theoretical predictions of the effect are confirmed by numerical calculations.
A classification of the symmetry of magnetic modulations is presented. Helical magnetic ordering is possible only in magnetic superspace groups with proper rotations only, i.e. from classes 1, 2, 222, 4, 422, 3, 32, 6 and 622. Cycloidal modulations are possible in groups from crystal classes 1, 2, m and mm2.
