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) 2020 International Union of Crystallography2020-04-02International 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 76, Part 3, 2020textweekly62002-01-01T00:00+00:003762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances273urn:issn:2053-2733med@iucr.orgApril 20202020-04-02Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageIsotopy classes for 3-periodic net embeddings
http://scripts.iucr.org/cgi-bin/paper?ib5087
Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Power, S.C.Baburin, I.A.Proserpio, D.M.2020-03-05doi:10.1107/S2053273320000625International Union of CrystallographyEntangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type.ENperiodic netsembedded netscoordination polymersisotopy typescrystallographic frameworksEntangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.text/htmlIsotopy classes for 3-periodic net embeddingstext3762020-03-05Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Alead articles00Texture corrections for total scattering functions
http://scripts.iucr.org/cgi-bin/paper?vk5041
Many functional materials are today synthesized in the form of nanoparticles displaying preferred orientation effects to some small or large extent. The analysis of diffraction data of such kinds of systems is best performed in the framework of the total scattering approach that prescinds from translation symmetry assumptions. Therefore modified expressions were derived for the most common total scattering functions, in particular the Debye scattering equation (DSE) which yields the texture-averaged differential cross section as a function of atomic coordinates and texture parameters. The modified DSE encodes higher-order even spherical Bessel functions which account for the texture effect. Selection rules arising from experimental geometries and symmetries are discussed. In addition the duality of the texture effect is introduced showing the effects of texture on both the I(Q) and {\cal{G}}(r). The paper includes several definitions and appendices which are meant to be useful for those involved in the development of crystallographic computing.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Cervellino, A.Frison, R.2020-03-26doi:10.1107/S2053273320002521International Union of CrystallographyThe 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.ENDebye scattering equationtexturepair distribution functionMany functional materials are today synthesized in the form of nanoparticles displaying preferred orientation effects to some small or large extent. The analysis of diffraction data of such kinds of systems is best performed in the framework of the total scattering approach that prescinds from translation symmetry assumptions. Therefore modified expressions were derived for the most common total scattering functions, in particular the Debye scattering equation (DSE) which yields the texture-averaged differential cross section as a function of atomic coordinates and texture parameters. The modified DSE encodes higher-order even spherical Bessel functions which account for the texture effect. Selection rules arising from experimental geometries and symmetries are discussed. In addition the duality of the texture effect is introduced showing the effects of texture on both the I(Q) and {\cal{G}}(r). The paper includes several definitions and appendices which are meant to be useful for those involved in the development of crystallographic computing.text/htmlTexture corrections for total scattering functionstext3762020-03-26Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Comparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surface
http://scripts.iucr.org/cgi-bin/paper?iv5004
Azimuthal plots for RHEPD (reflection high-energy positron diffraction) and RHEED (reflection high-energy electron diffraction) were calculated using dynamical diffraction theory and then compared. It was assumed that RHEPD and RHEED azimuthal plots can be collected practically by recording the intensity while rotating the sample around the axis perpendicular to the surface (for the case of X-ray diffraction, such forms of data are called Renninger scans). It was found that RHEPD plots were similar to RHEED plots if they were compared at Bragg reflections of the same order. RHEPD plots can also be determined in the region of total external reflection and for such conditions multiple scattering effects turned out to be very weak. The findings for azimuthal plots are also discussed in the context of the formation mechanisms of Kikuchi patterns.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Mitura, Z.2020-03-26doi:10.1107/S2053273320001205International Union of CrystallographyFeatures 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.ENdynamical diffraction theoryazimuthal plotsRenninger scansKikuchi patternsAzimuthal plots for RHEPD (reflection high-energy positron diffraction) and RHEED (reflection high-energy electron diffraction) were calculated using dynamical diffraction theory and then compared. It was assumed that RHEPD and RHEED azimuthal plots can be collected practically by recording the intensity while rotating the sample around the axis perpendicular to the surface (for the case of X-ray diffraction, such forms of data are called Renninger scans). It was found that RHEPD plots were similar to RHEED plots if they were compared at Bragg reflections of the same order. RHEPD plots can also be determined in the region of total external reflection and for such conditions multiple scattering effects turned out to be very weak. The findings for azimuthal plots are also discussed in the context of the formation mechanisms of Kikuchi patterns.text/htmlComparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surfacetext3762020-03-26Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Groupoid description of modular structures
http://scripts.iucr.org/cgi-bin/paper?ug5004
Modular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Nespolo, M.Souvignier, B.Stöger, B.2020-04-02doi:10.1107/S2053273320000650International Union of CrystallographyThe application of groupoids to modular crystal structures is presented.ENmodular crystal structuresgroupoidssubperiodic groupssuperposition structurespolytypismModular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.text/htmlGroupoid description of modular structurestext3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers00An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films
http://scripts.iucr.org/cgi-bin/paper?wo5036
Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Simbrunner, J.Schrode, B.Domke, J.Fritz, T.Salzmann, I.Resel, R.2020-04-02doi:10.1107/S2053273320001266International Union of CrystallographyA 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.ENepitaxyindexingmathematical crystallographyCrystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.text/htmlAn efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin filmstext3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Geometric realizations of abstract regular polyhedra with automorphism group H3
http://scripts.iucr.org/cgi-bin/paper?eo5106
A geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Aranas, J.A.L.Loyola, M.L.2020-04-02doi:10.1107/S2053273320001564International Union of CrystallographyA method is adapted to generate a full rank realization of an abstract regular polyhedron with automorphism group H3.ENabstract regular polyhedrageometric realizationsnon-crystallographic Coxeter group H3string C-groupsA geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.text/htmlGeometric realizations of abstract regular polyhedra with automorphism group H3text3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers00SPIND-TC: an indexing method for two-color X-ray diffraction data
http://scripts.iucr.org/cgi-bin/paper?ib5084
Recent developments of two-color operation modes at X-ray free-electron laser facilities provide new research opportunities, such as X-ray pump/X-ray probe experiments and multiple-wavelength anomalous dispersion phasing methods. However, most existing indexing methods were developed for indexing diffraction data from monochromatic X-ray beams. Here, a new algorithm is presented for indexing two-color diffraction data, as an extension of the sparse-pattern indexing algorithm SPIND, which has been demonstrated to be capable of indexing diffraction patterns with as few as five peaks. The principle and implementation of the two-color indexing method, SPIND-TC, are reported in this paper. The algorithm was tested on both simulated and experimental data of protein crystals. The results show that the diffraction data can be accurately indexed in both cases. Source codes are publicly available at https://github.com/lixx11/SPIND-TC.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Li, X.Li, C.Liu, H.2020-04-02doi:10.1107/S2053273320001916International Union of CrystallographyAn 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.ENserial crystallographytwo-color diffractionindexing algorithmRecent developments of two-color operation modes at X-ray free-electron laser facilities provide new research opportunities, such as X-ray pump/X-ray probe experiments and multiple-wavelength anomalous dispersion phasing methods. However, most existing indexing methods were developed for indexing diffraction data from monochromatic X-ray beams. Here, a new algorithm is presented for indexing two-color diffraction data, as an extension of the sparse-pattern indexing algorithm SPIND, which has been demonstrated to be capable of indexing diffraction patterns with as few as five peaks. The principle and implementation of the two-color indexing method, SPIND-TC, are reported in this paper. The algorithm was tested on both simulated and experimental data of protein crystals. The results show that the diffraction data can be accurately indexed in both cases. Source codes are publicly available at https://github.com/lixx11/SPIND-TC.text/htmlSPIND-TC: an indexing method for two-color X-ray diffraction datatext3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers00