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ISSN: 2053-2733

May 2024 issue

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Cover illustration: In a previous paper [Acta Cryst. (2022), A78, 212–233] Day and Hawthorne used graph theoretic methods to generate topological representations of some observed and hypothetical chains of [SiO4]4− tetrahedra. In this issue Day et al. consider possible restraints on embedding these chain graphs into two- and three-dimensional Euclidean space such that they are compatible with the metrics of chains of tetrahedra observed in real crystal structures [Acta Cryst. (2024), A80, 258–281; Acta Cryst. (2024), A80, 282–292]. The two chain arrangements shown are not observed in silicates: when embedded in two dimensions, they form planar curves that force unrealistic TT distances between vertices ([SiO4]4− tetrahedra). When embedded in three dimensions, they form helical arrangements which allow realistic TT distances.

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research papers


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The kisrhombille tiling is the dual of one of the eight semi-regular tilings and is built up by right-angled triangles in 12 orientations. In this paper, an appropriate coordinate system is presented and the digital distance is defined and computed by the number of steps of neighboring triangles, where two triangles are considered to be neighbors if they share at least one point on their border.

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A new optimization method based on a new concept of single-atom R1 (sR1) for solving crystal structures is presented.

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An improved method of one-electron reduced density matrix reconstruction from structure factors and directional Compton profiles is tested on a urea crystal. Novel restrictions accounting for molecular symmetry and freezing of core electrons are introduced.

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It is shown that all possible topologically distinct chain graphs of tetrahedra may be embedded into 3D Euclidean space. In minerals, separations between linked T cations are 3.06 (15) Å and between unlinked T cations are >3.71 Å, and these distances constrain the ability of embedded chain graphs to occur as structural entities in crystals. Software (GraphT-T) allows this embedding to be tested for stereochemical viability.

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The program GraphTT (V1.0Beta) has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4− tetrahedra into 2D and 3D Euclidean space.

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Following the previous work [Biran & Gorfman (2024). Acta Cryst. A80, 112–128], all the possibilities for permissible (mismatch-free) walls between monoclinic domains of pseudocubic ferroelectric perovskites of MC type are analyzed. The study yields analytical expressions for the orientation of such walls, the orientation relationship between the lattice vectors and for the separation between Bragg peaks diffracted from matched domains.
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