Acta Crystallographica Section A
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.enCopyright (c) 2024 International Union of Crystallography2023-11-30International Union of CrystallographyInternational Union of Crystallographyhttp://journals.iucr.orgurn:issn:2053-2733Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlActa Crystallographica Section A: Foundations and Advances, Volume 80, Part 1, 2024textweekly62002-01-01T00:00+00:001802023-11-30Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances1urn:issn:2053-2733med@iucr.orgNovember 20232023-11-30Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
//journals.iucr.org/a/issues/2024/01/00/index.html
Still imageMaximal independence and symmetry in crystal chemistry of natural tectosilicates
http://scripts.iucr.org/cgi-bin/paper?ae5134
Löwenstein's avoidance rule in aluminosilicates is reinterpreted on the basis of the fourth Pauling rule. It is shown that avoidance of Si–O–Si bridges may account for avoidance of Al–O–Al bridges. In view of this interpretation, it is proposed that the most favourable distributions of cations entering in substitution of silicon in the framework are associated to maximal independent sets of the respective 3-periodic nets. Among all possible solutions, only those with maximal symmetry are realized. The applicability of the concept is demonstrated for a few natural tectosilicates, which have been analysed through the prism of their labelled quotient graph.Copyright (c) 2024 International Union of Crystallographyurn:issn:2053-2733Moreira de Oliveira Jr, M.Eon, J.-G.2024-01-01doi:10.1107/S2053273323008665International Union of CrystallographyThe distribution of aluminium cations in natural tectosilicates is shown to satisfy the concepts of maximal independence and maximum symmetry.ENnetszeolitesquotient graphsmaximal independent setsLöwenstein's avoidance rule in aluminosilicates is reinterpreted on the basis of the fourth Pauling rule. It is shown that avoidance of Si–O–Si bridges may account for avoidance of Al–O–Al bridges. In view of this interpretation, it is proposed that the most favourable distributions of cations entering in substitution of silicon in the framework are associated to maximal independent sets of the respective 3-periodic nets. Among all possible solutions, only those with maximal symmetry are realized. The applicability of the concept is demonstrated for a few natural tectosilicates, which have been analysed through the prism of their labelled quotient graph.text/htmlMaximal independence and symmetry in crystal chemistry of natural tectosilicatestext1802024-01-01Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Hierarchical topological analysis of crystal structures: the skeletal net concept
http://scripts.iucr.org/cgi-bin/paper?nv5012
Topological analysis of crystal structures faces the problem of the `correct' or the `best' assignment of bonds to atoms, which is often ambiguous. A hierarchical scheme is used where any crystal structure is described as a set of topological representations, each of which corresponds to a particular assignment of bonds encoded by a periodic net. In this set, two limiting nets are distinguished, complete and skeletal, which contain, respectively, all possible bonds and the minimal number of bonds required to keep the structure periodicity. Special attention is paid to the skeletal net since it describes the connectivity of a crystal structure in the simplest way, thus enabling one to find unobvious relations between crystalline substances of different composition and architecture. The tools for the automated hierarchical topological analysis have been implemented in the program package ToposPro. Examples, which illustrate the advantages of such analysis, are considered for a number of classes of crystalline substances: elements, intermetallics, ionic and coordination compounds, and molecular crystals. General provisions of the application of the skeletal net concept are also discussed.Copyright (c) 2024 International Union of Crystallographyurn:issn:2053-2733Blatova, O.A.Blatov, V.A.2024-01-01doi:10.1107/S2053273323008975International Union of CrystallographyThe skeletal net concept is introduced into the scheme of hierarchical topological analysis of crystal structures to provide the simplest way of describing structure connectivity. Examples, which illustrate the advantages of such analysis, are considered for elements, intermetallics, ionic and coordination compounds, and molecular crystals.ENcrystal structurestopologyperiodic netshierarchical analysisTopological analysis of crystal structures faces the problem of the `correct' or the `best' assignment of bonds to atoms, which is often ambiguous. A hierarchical scheme is used where any crystal structure is described as a set of topological representations, each of which corresponds to a particular assignment of bonds encoded by a periodic net. In this set, two limiting nets are distinguished, complete and skeletal, which contain, respectively, all possible bonds and the minimal number of bonds required to keep the structure periodicity. Special attention is paid to the skeletal net since it describes the connectivity of a crystal structure in the simplest way, thus enabling one to find unobvious relations between crystalline substances of different composition and architecture. The tools for the automated hierarchical topological analysis have been implemented in the program package ToposPro. Examples, which illustrate the advantages of such analysis, are considered for a number of classes of crystalline substances: elements, intermetallics, ionic and coordination compounds, and molecular crystals. General provisions of the application of the skeletal net concept are also discussed.text/htmlHierarchical topological analysis of crystal structures: the skeletal net concepttext1802024-01-01Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Periodic Borromean rings, rods and chains
http://scripts.iucr.org/cgi-bin/paper?nv5009
This article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2-periodic vertex-, edge- and ring-transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1- and 3-periodic ring-transitive (isonemal) families. A second isonemal 2-periodic family is identified, as is a unique 3-periodic Borromean assembly of equilateral triangles. Also reported is a notable 2-periodic structure comprising chains of linked rings in which the chains are locked in place but no two chains are directly interlinked, being held in place as a novel `quasi-Borromean' set of four repeating components.Copyright (c) 2024 International Union of Crystallographyurn:issn:2053-2733O'Keeffe, M.Treacy, M.M.J.2024-01-01doi:10.1107/S2053273323009269International Union of CrystallographyThe synthesis of molecular Borromean rings and other links is an active area of chemical research. Hypothetical 1-, 2- and 3-periodic molecular structures are described with the Borromean property that, although no two rings or chains are linked, the structures are interlocked and do not fall apart.ENpolycatenanesBorromean propertyring-transitive familyedge-transitive familyvertex-transitive familyThis article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2-periodic vertex-, edge- and ring-transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1- and 3-periodic ring-transitive (isonemal) families. A second isonemal 2-periodic family is identified, as is a unique 3-periodic Borromean assembly of equilateral triangles. Also reported is a notable 2-periodic structure comprising chains of linked rings in which the chains are locked in place but no two chains are directly interlinked, being held in place as a novel `quasi-Borromean' set of four repeating components.text/htmlPeriodic Borromean rings, rods and chainstext1802024-01-01Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Algorithm for spin symmetry operation search
http://scripts.iucr.org/cgi-bin/paper?ib5119
A spin space group provides a suitable way of fully exploiting the symmetry of a spin arrangement with a negligible spin–orbit coupling. There has been a growing interest in applying spin symmetry analysis with the spin space group in the field of magnetism. However, there is no established algorithm to search for spin symmetry operations of the spin space group. This paper presents an exhaustive algorithm for determining the spin symmetry operations of commensurate spin arrangements. The present algorithm searches for spin symmetry operations from the symmetry operations of a corresponding nonmagnetic crystal structure and determines their spin-rotation parts by solving a Procrustes problem. An implementation is distributed under a permissive free software license in spinspg Version 0.1.1, available at https://github.com/spglib/spinspg.Copyright (c) 2024 International Union of Crystallographyurn:issn:2053-2733Shinohara, K.Togo, A.Watanabe, H.Nomoto, T.Tanaka, I.Arita, R.2024-01-01doi:10.1107/S2053273323009257International Union of CrystallographyAn algorithm is presented for determining the spin symmetry operations of a given spin arrangement. Spin symmetry operations of a spin space group act simultaneously on both the spatial and spin coordinates of the spin arrangement.ENspin space groupsspin symmetry operationsspin arrangementsProcrustes problemsHermite normal formsA spin space group provides a suitable way of fully exploiting the symmetry of a spin arrangement with a negligible spin–orbit coupling. There has been a growing interest in applying spin symmetry analysis with the spin space group in the field of magnetism. However, there is no established algorithm to search for spin symmetry operations of the spin space group. This paper presents an exhaustive algorithm for determining the spin symmetry operations of commensurate spin arrangements. The present algorithm searches for spin symmetry operations from the symmetry operations of a corresponding nonmagnetic crystal structure and determines their spin-rotation parts by solving a Procrustes problem. An implementation is distributed under a permissive free software license in spinspg Version 0.1.1, available at https://github.com/spglib/spinspg.text/htmlAlgorithm for spin symmetry operation searchtext1802024-01-01Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Identification of Kikuchi lines in electron diffraction patterns collected in small-angle geometry
http://scripts.iucr.org/cgi-bin/paper?wo5045
It is demonstrated that Kikuchi features become clearly visible if reflection high-energy electron diffraction (RHEED) patterns are filtered using digital image processing software. The results of such pattern transformations are shown for SrTiO3 with mixed surface termination for data collected at different azimuths of the incident electron beam. A simplified analytical approach for the theoretical description of filtered Kikuchi patterns is proposed and discussed. Some examples of raw and filtered patterns for thin films are shown. RHEED patterns may be treated as a result of coherent and incoherent scattering of electron waves. The effects of coherent scattering may be considered as those occurring due to wave diffraction by an idealized crystal and, usually, only effects of this type are analysed to obtain structural information on samples investigated with the use of RHEED. However, some incoherent scattering effects mostly caused by thermal vibrations of atoms, known as Kikuchi effects, may also be a source of valuable information on the arrangements of atoms near the surface. Typically, for the case of RHEED, Kikuchi features are hidden in the intensity background and researchers cannot easily recognize them. In this paper, it is shown that the visibility of features of this type can be substantially enhanced using computer graphics methods.Copyright (c) 2024 International Union of Crystallographyurn:issn:2053-2733Mitura, Z.Szwachta, G.Kokosza, Ł.Przybylski, M.2024-01-01doi:10.1107/S2053273323009385International Union of CrystallographySome advantages of filtering of digital reflection high-energy electron diffraction (RHEED) patterns are shown.ENreflection high-energy electron diffractionRHEEDKikuchi patternsperovskitesnanostructured materialsdigital imagesIt is demonstrated that Kikuchi features become clearly visible if reflection high-energy electron diffraction (RHEED) patterns are filtered using digital image processing software. The results of such pattern transformations are shown for SrTiO3 with mixed surface termination for data collected at different azimuths of the incident electron beam. A simplified analytical approach for the theoretical description of filtered Kikuchi patterns is proposed and discussed. Some examples of raw and filtered patterns for thin films are shown. RHEED patterns may be treated as a result of coherent and incoherent scattering of electron waves. The effects of coherent scattering may be considered as those occurring due to wave diffraction by an idealized crystal and, usually, only effects of this type are analysed to obtain structural information on samples investigated with the use of RHEED. However, some incoherent scattering effects mostly caused by thermal vibrations of atoms, known as Kikuchi effects, may also be a source of valuable information on the arrangements of atoms near the surface. Typically, for the case of RHEED, Kikuchi features are hidden in the intensity background and researchers cannot easily recognize them. In this paper, it is shown that the visibility of features of this type can be substantially enhanced using computer graphics methods.text/htmlIdentification of Kikuchi lines in electron diffraction patterns collected in small-angle geometrytext1802024-01-01Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Isogonal 2-periodic polycatenanes: chain mail
http://scripts.iucr.org/cgi-bin/paper?pl5030
For 2-periodic polycatenanes with isogonal (vertex-transitive) embeddings, the basic units linked are torus knots and links including the unknots (untangled polygons). Twenty-four infinite families have been identified, with hexagonal, tetragonal or rectangular symmetry. The simplest members of each family are described and illustrated. A method for determining the catenation number of a ring based on electromagnetic theory is described.Copyright (c) 2024 International Union of Crystallographyurn:issn:2053-2733O'Keeffe, M.Treacy, M.M.J.2024-01-01doi:10.1107/S2053273323009543International Union of CrystallographyTwo-periodic chain mail polycatenane structures with one kind of vertex are presented. Twenty-four infinite families are identified, with hexagonal, tetragonal or rectangular symmetry.ENchain mailpolycatenaneslayered structuresisogonal structuresGauss linking numberFor 2-periodic polycatenanes with isogonal (vertex-transitive) embeddings, the basic units linked are torus knots and links including the unknots (untangled polygons). Twenty-four infinite families have been identified, with hexagonal, tetragonal or rectangular symmetry. The simplest members of each family are described and illustrated. A method for determining the catenation number of a ring based on electromagnetic theory is described.text/htmlIsogonal 2-periodic polycatenanes: chain mailtext1802024-01-01Copyright (c) 2024 International Union of CrystallographyActa Crystallographica Section Aresearch papers00