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) 2019 International Union of Crystallography2019-01-01International 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 75, Part 1, 2019textweekly62002-01-01T00:00+00:001752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances1urn:issn:2053-2733med@iucr.orgJanuary 20192019-01-01Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageBounding the regularity radius for regular crystals
http://scripts.iucr.org/cgi-bin/paper?me6021
Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Frettloeh, D.2019-01-01doi:10.1107/S205327331801642XInternational Union of CrystallographyThe new lower bounds for the regularity radius for `regular systems' (orbits of a single point under a crystallographic group) in arbitrary dimension given by Baburin et al. [Acta Cryst. (2018) A74, 616–629] are discussed.ENDelone setsregularity radiuscrystallinityEngel setstext/htmlBounding the regularity radius for regular crystalstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Ascientific commentaries12Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings
http://scripts.iucr.org/cgi-bin/paper?vf5001
This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.Copyright (c) 2019 Erdal C. Oğuz et al.urn:issn:2053-2733Ogˇuz, E.C.Socolar, J.E.S.Steinhardt, P.J.Torquato, S.2019-01-01doi:10.1107/S2053273318015528International Union of CrystallographyThis work examines the long-wavelength scaling properties of self-similar substitution tilings, placing them in their hyperuniformity classes. Quasiperiodic, non-PV (Pisot–Vijayaraghavan number) and limit-periodic examples are analyzed. Novel behavior is demonstrated for certain limit-periodic cases.ENsubstitution tilinghyperuniformitydiffractionlimit-periodic tilingsnon-Pisot tilingsquasiperiodic tilingsThis work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.text/htmlHyperuniformity and anti-hyperuniformity in one-dimensional substitution tilingstext1752019-01-01Copyright (c) 2019 Erdal C. Oğuz et al.Acta Crystallographica Section Aresearch papers313Ultrafast calculation of diffuse scattering from atomistic models
http://scripts.iucr.org/cgi-bin/paper?vk5031
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391–399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 102, making refinement of atomistic models to large diffuse-scattering volumes practical.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Paddison, J.A.M.2019-01-01doi:10.1107/S2053273318015632International Union of CrystallographyA new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the fast Fourier transform can be used to perform such calculations rapidly, and a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations.ENdiffuse scatteringdisorderMonte Carlo simulationDiffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391–399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 102, making refinement of atomistic models to large diffuse-scattering volumes practical.text/htmlUltrafast calculation of diffuse scattering from atomistic modelstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers1424Ab initio phasing of the diffraction of crystals with translational disorder
http://scripts.iucr.org/cgi-bin/paper?ae5053
To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.Copyright (c) 2019 Andrew J. Morgan et al.urn:issn:2053-2733Morgan, A.J.Ayyer, K.Barty, A.Chen, J.P.J.Ekeberg, T.Oberthuer, D.White, T.A.Yefanov, O.Chapman, H.N.2019-01-01doi:10.1107/S2053273318015395International Union of CrystallographyThis article reports on the combined use of Bragg reflections and diffuse scatter for structure determination in crystallography.ENX-ray diffractiondiffuse scatteringphase retrievalmacromolecular crystallographyTo date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.text/htmlAb initio phasing of the diffraction of crystals with translational disordertext1752019-01-01Copyright (c) 2019 Andrew J. Morgan et al.Acta Crystallographica Section Aresearch papers2540Rotational switches in the two-dimensional fullerene quasicrystal
http://scripts.iucr.org/cgi-bin/paper?vf5003
One of the essential components of molecular electronic circuits are switching elements that are stable in two different states and can ideally be switched on and off many times. Here, distinct buckminsterfullerenes within a self-assembled monolayer, forming a two-dimensional dodecagonal quasicrystal on a Pt-terminated Pt3Ti(111) surface, are identified to form well separated molecular rotational switching elements. Employing scanning tunneling microscopy, the molecular-orbital appearance of the fullerenes in the quasicrystalline monolayer is resolved. Thus, fullerenes adsorbed on the 36 vertex configuration are identified to exhibit a distinctly increased mobility. In addition, this finding is verified by differential conductance measurements. The rotation of these mobile fullerenes can be triggered frequently by applied voltage pulses, while keeping the neighboring molecules immobile. An extensive analysis reveals that crystallographic and energetic constraints at the molecule/metal interface induce an inequality of the local potentials for the 36 and 32.4.3.4 vertex sites and this accounts for the switching ability of fullerenes on the 36 vertex sites. Consequently, a local area of the 8/3 approximant in the two-dimensional fullerene quasicrystal consists of single rotational switching fullerenes embedded in a matrix of inert molecules. Furthermore, it is deduced that optimization of the intermolecular interactions between neighboring fullerenes hinders the realization of translational periodicity in the fullerene monolayer on the Pt-terminated Pt3Ti(111) surface.Copyright (c) 2019 Paßens and Karthäuserurn:issn:2053-2733Paßens, M.Karthäuser, S.2019-01-01doi:10.1107/S2053273318015681International Union of CrystallographyLocal potential differences between the 36 and 32.4.3.4 vertex configurations are identified within a two-dimensional dodecagonal fullerene monolayer. In a local area of the 8/3 approximant, rotational switching fullerenes on 36 vertex sites are revealed by scanning tunneling microscopy.ENrotational switchesfullerenesinterfacial interactionsgeometric frustrationdodecagonal quasicrystalssquare–triangle tilingscanning tunneling microscopyOne of the essential components of molecular electronic circuits are switching elements that are stable in two different states and can ideally be switched on and off many times. Here, distinct buckminsterfullerenes within a self-assembled monolayer, forming a two-dimensional dodecagonal quasicrystal on a Pt-terminated Pt3Ti(111) surface, are identified to form well separated molecular rotational switching elements. Employing scanning tunneling microscopy, the molecular-orbital appearance of the fullerenes in the quasicrystalline monolayer is resolved. Thus, fullerenes adsorbed on the 36 vertex configuration are identified to exhibit a distinctly increased mobility. In addition, this finding is verified by differential conductance measurements. The rotation of these mobile fullerenes can be triggered frequently by applied voltage pulses, while keeping the neighboring molecules immobile. An extensive analysis reveals that crystallographic and energetic constraints at the molecule/metal interface induce an inequality of the local potentials for the 36 and 32.4.3.4 vertex sites and this accounts for the switching ability of fullerenes on the 36 vertex sites. Consequently, a local area of the 8/3 approximant in the two-dimensional fullerene quasicrystal consists of single rotational switching fullerenes embedded in a matrix of inert molecules. Furthermore, it is deduced that optimization of the intermolecular interactions between neighboring fullerenes hinders the realization of translational periodicity in the fullerene monolayer on the Pt-terminated Pt3Ti(111) surface.text/htmlRotational switches in the two-dimensional fullerene quasicrystaltext1752019-01-01Copyright (c) 2019 Paßens and KarthäuserActa Crystallographica Section Aresearch papers4149Aspherical scattering factors for SHELXL – model, implementation and application
http://scripts.iucr.org/cgi-bin/paper?ib5060
A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.Copyright (c) 2019 Jens Lübben et al.urn:issn:2053-2733Lübben, J.Wandtke, C.M.Hübschle, C.B.Ruf, M.Sheldrick, G.M.Dittrich, B.2019-01-01doi:10.1107/S2053273318013840International Union of CrystallographyA new aspherical scattering factor formalism was implemented in SHELXL. It relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. The automated atom-type assignment was derived from the invariom formalism.ENSHELXLinvariomsaspherical scattering factorsquantum crystallographyA new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.text/htmlAspherical scattering factors for SHELXL – model, implementation and applicationtext1752019-01-01Copyright (c) 2019 Jens Lübben et al.Acta Crystallographica Section Aresearch papers5062Modeling of energy-dispersive X-ray diffraction for high-symmetry crystal orientation
http://scripts.iucr.org/cgi-bin/paper?ae5052
The methods for X-ray crystal orientation are rapidly evolving towards versatility, fewer goniometry measurements, automation, high accuracy and precision. One method that attracts a lot of attention is energy-dispersive X-ray diffraction (EDXRD) which is based on detecting reflections from crystallographic planes in a crystal at fixed angles of a parallel polychromatic X-ray incident beam. In theory, an EDXRD peak can move in a diffraction pattern as a function of a crystallographic plane d-spacing and its orientation relative to a fixed direction in space can change also. This is equivalent to the possibility of measuring the orientation of single crystals. The article provides a modeling for the EDXRD method whose main feature is the nonmoving crystal in the sense of traditional goniometry where the angle measurements of diffracting planes are a must. The article defines the equation of orientation for the method and shows the derivation in great detail. It is shown that the exact solutions of the equations can be obtained using the generalized reduced gradient method, a mathematical subroutine that is implemented in Excel software. The significance and scientific impact of the work are discussed along with the validated tested results.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Dragoi, D.Dragoi, A.2019-01-01doi:10.1107/S2053273318013864International Union of CrystallographyThis article describes the modeling of energy-dispersive X-ray diffraction for high-symmetry crystal orientation. The work gives exact equations for determining the orientation. The results are discussed in terms of basic crystallography, formula applications without limitations, software for exact solutions and equipment.ENEDXRD methodextended stereographic projectionequation of orientationgeneralized reduced gradient methodevolving XRD methodsThe methods for X-ray crystal orientation are rapidly evolving towards versatility, fewer goniometry measurements, automation, high accuracy and precision. One method that attracts a lot of attention is energy-dispersive X-ray diffraction (EDXRD) which is based on detecting reflections from crystallographic planes in a crystal at fixed angles of a parallel polychromatic X-ray incident beam. In theory, an EDXRD peak can move in a diffraction pattern as a function of a crystallographic plane d-spacing and its orientation relative to a fixed direction in space can change also. This is equivalent to the possibility of measuring the orientation of single crystals. The article provides a modeling for the EDXRD method whose main feature is the nonmoving crystal in the sense of traditional goniometry where the angle measurements of diffracting planes are a must. The article defines the equation of orientation for the method and shows the derivation in great detail. It is shown that the exact solutions of the equations can be obtained using the generalized reduced gradient method, a mathematical subroutine that is implemented in Excel software. The significance and scientific impact of the work are discussed along with the validated tested results.text/htmlModeling of energy-dispersive X-ray diffraction for high-symmetry crystal orientationtext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers6370Determination of stacking ordering in disordered close-packed structures from pairwise correlation functions
http://scripts.iucr.org/cgi-bin/paper?ib5057
It is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures. First, of theoretical interest, the analytical formulation and solution of the problem are presented when the exact pairwise correlation counts are known. In the second part, the practical problem is approached. A simulated annealing procedure is developed to solve the problem using as initial guess approximate solutions from previous treatments. The robustness of the procedure is tested with synthetic data, followed by an experimental example. The developed approach performs robustly over different synthetic and experimental data, comparing favorably with the reported methods.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Serrano-Alfaro, P.Estevez-Rams, E.Lora-Serrano, R.Aragon-Fernandez, B.2019-01-01doi:10.1107/S2053273318014080International Union of CrystallographyIt is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures using a simulated annealing procedure. The robustness of the procedure is tested with synthetic data, followed by an experimental example.ENclose-packed structuresdisordercorrelation functionsIt is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures. First, of theoretical interest, the analytical formulation and solution of the problem are presented when the exact pairwise correlation counts are known. In the second part, the practical problem is approached. A simulated annealing procedure is developed to solve the problem using as initial guess approximate solutions from previous treatments. The robustness of the procedure is tested with synthetic data, followed by an experimental example. The developed approach performs robustly over different synthetic and experimental data, comparing favorably with the reported methods.text/htmlDetermination of stacking ordering in disordered close-packed structures from pairwise correlation functionstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers7181Reducing dynamical electron scattering reveals hydrogen atoms
http://scripts.iucr.org/cgi-bin/paper?td5055
Compared with X-rays, electron diffraction faces a crucial challenge: dynamical electron scattering compromises structure solution and its effects can only be modelled in specific cases. Dynamical scattering can be reduced experimentally by decreasing crystal size but not without a penalty, as it also reduces the overall diffracted intensity. In this article it is shown that nanometre-sized crystals from organic pharmaceuticals allow positional refinement of the hydrogen atoms, even whilst ignoring the effects of dynamical scattering during refinement. To boost the very weak diffraction data, a highly sensitive hybrid pixel detector was employed. A general likelihood-based computational approach was also introduced for further reducing the adverse effects of dynamic scattering, which significantly improved model accuracy, even for protein crystal data at substantially lower resolution.Copyright (c) 2019 Max T. B. Clabbers et al.urn:issn:2053-2733Clabbers, M.T.B.Gruene, T.van Genderen, E.Abrahams, J.P.2019-01-01doi:10.1107/S2053273318013918International Union of CrystallographyExperimental and computational reduction of dynamical electron scattering allows for visualizing of individual hydrogen atoms.ENdynamical scatteringelectron diffractionhydrogen atomsnanocrystalshybrid pixel detectorCompared with X-rays, electron diffraction faces a crucial challenge: dynamical electron scattering compromises structure solution and its effects can only be modelled in specific cases. Dynamical scattering can be reduced experimentally by decreasing crystal size but not without a penalty, as it also reduces the overall diffracted intensity. In this article it is shown that nanometre-sized crystals from organic pharmaceuticals allow positional refinement of the hydrogen atoms, even whilst ignoring the effects of dynamical scattering during refinement. To boost the very weak diffraction data, a highly sensitive hybrid pixel detector was employed. A general likelihood-based computational approach was also introduced for further reducing the adverse effects of dynamic scattering, which significantly improved model accuracy, even for protein crystal data at substantially lower resolution.text/htmlReducing dynamical electron scattering reveals hydrogen atomstext1752019-01-01Copyright (c) 2019 Max T. B. Clabbers et al.Acta Crystallographica Section Aresearch papers829318709801870981k-Isocoronal tilings
http://scripts.iucr.org/cgi-bin/paper?eo5087
In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s ≤ k. A tiling {\cal T} is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of {\cal T} is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k-transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then it is k-uniform. This article also presents the classification of isocoronal tilings in the Euclidean plane.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Taganap, E.De Las Peñas, M.L.A.2019-01-01doi:10.1107/S2053273318013992International Union of CrystallographyThis article presents a method to determine planar edge-to-edge k-isocoronal tilings – tilings whose vertex coronae form k orbits or k transitivity classes under the action of the symmetry group.ENk-isocoronal tilingsvertex-k-transitive tilingsk-uniform tilingsisocoronal tilingsuniform tilingsIn this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s ≤ k. A tiling {\cal T} is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of {\cal T} is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k-transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then it is k-uniform. This article also presents the classification of isocoronal tilings in the Euclidean plane.text/htmlk-Isocoronal tilingstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers94106Nonlinear optical organic–inorganic crystals: synthesis, structural analysis and verification of harmonic generation in tri-(o-chloroanilinium nitrate)
http://scripts.iucr.org/cgi-bin/paper?lk5035
The structural and nonlinear optical properties of a new anilinium hybrid crystal of chemical formula (C6H7NCl+·NO3−)3 have been investigated. The crystal structure was determined from single-crystal X-ray diffraction measurements performed at a temperature of 100 K which show that the compound crystallizes in a noncentrosymmetric space group (Pna21). The structural analysis was coupled with Hirshfeld surface analysis to evaluate the contribution of the different intermolecular interactions to the formation of supramolecular assemblies in the solid state that exhibit nonlinear optical features. This analysis reveals that the studied compound is characterized by a three-dimensional network of hydrogen bonds and the main contributions are provided by the O...H, C...H, H...H and Cl...H interactions, which alone represent ∼85% of the total contributions to the Hirshfeld surfaces. It is noteworthy that the halogen...H contributions are quite comparable with those of the H...H contacts. The nonlinear optical properties were investigated by nonlinear diffuse femtosecond-pulse reflectometry and the obtained results were compared with those of the reference material LiNbO3. The hybrid crystals exhibit notable second (SHG) and third (THG) harmonic generation which confirms its polarity is generated by the different intermolecular interactions. These measurements also highlight that the THG signal of the new anilinium compound normalized to its SHG counterpart is more pronounced than for LiNbO3.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Athmani, H.Kijatkin, C.Benali-Cherif, R.Pillet, S.Schaniel, D.Imlau, M.Benali-Cherif, N.Bendeif, E.-E.2019-01-01doi:10.1107/S2053273318014122International Union of CrystallographyThis work addresses the structure–property relationship of an interesting organic–inorganic material. The structural investigation is coupled with Hirshfeld surface analysis to examine the nonlinear optical properties.ENstructural analysisintermolecular interactionsHirshfeld surface analysisnonlinear optical propertiesThe structural and nonlinear optical properties of a new anilinium hybrid crystal of chemical formula (C6H7NCl+·NO3−)3 have been investigated. The crystal structure was determined from single-crystal X-ray diffraction measurements performed at a temperature of 100 K which show that the compound crystallizes in a noncentrosymmetric space group (Pna21). The structural analysis was coupled with Hirshfeld surface analysis to evaluate the contribution of the different intermolecular interactions to the formation of supramolecular assemblies in the solid state that exhibit nonlinear optical features. This analysis reveals that the studied compound is characterized by a three-dimensional network of hydrogen bonds and the main contributions are provided by the O...H, C...H, H...H and Cl...H interactions, which alone represent ∼85% of the total contributions to the Hirshfeld surfaces. It is noteworthy that the halogen...H contributions are quite comparable with those of the H...H contacts. The nonlinear optical properties were investigated by nonlinear diffuse femtosecond-pulse reflectometry and the obtained results were compared with those of the reference material LiNbO3. The hybrid crystals exhibit notable second (SHG) and third (THG) harmonic generation which confirms its polarity is generated by the different intermolecular interactions. These measurements also highlight that the THG signal of the new anilinium compound normalized to its SHG counterpart is more pronounced than for LiNbO3.text/htmlNonlinear optical organic–inorganic crystals: synthesis, structural analysis and verification of harmonic generation in tri-(o-chloroanilinium nitrate)text1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers1071141530349Selling reduction versus Niggli reduction for crystallographic lattices
http://scripts.iucr.org/cgi-bin/paper?ae5054
The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.Copyright (c) 2019 Lawrence C. Andrews et al.urn:issn:2053-2733Andrews, L.C.Bernstein, H.J.Sauter, N.K.2019-01-01doi:10.1107/S2053273318015413International Union of CrystallographyThe unit-cell reduction described by Selling and used by Delone (Delaunay) is explained in a simple form.ENunit-cell reductionDelaunayDeloneNiggliSellingThe unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.text/htmlSelling reduction versus Niggli reduction for crystallographic latticestext1752019-01-01Copyright (c) 2019 Lawrence C. Andrews et al.Acta Crystallographica Section Aresearch papers115120A coloring-book approach to finding coordination sequences
http://scripts.iucr.org/cgi-bin/paper?eo5090
An elementary method is described for finding the coordination sequences for a tiling, based on coloring the underlying graph. The first application is to the two kinds of vertices (tetravalent and trivalent) in the Cairo (or dual-32.4.3.4) tiling. The coordination sequence for a tetravalent vertex turns out, surprisingly, to be 1, 4, 8, 12, 16, …, the same as for a vertex in the familiar square (or 44) tiling. The authors thought that such a simple fact should have a simple proof, and this article is the result. The method is also used to obtain coordination sequences for the 32.4.3.4, 3.4.6.4, 4.82, 3.122 and 34.6 uniform tilings, and the snub-632 tiling. In several cases the results provide proofs for previously conjectured formulas.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Goodman-Strauss, C.Sloane, N. J. A.2019-01-01doi:10.1107/S2053273318014481International Union of CrystallographyThis article presents a simple method for finding formulas for coordination sequences, based on coloring the underlying graph according to certain rules. It is illustrated by applying it to several uniform tilings and their duals.ENcoordination sequencesuniform tilingdual tilingCairo tilingtetravalent verticestrivalent verticesAn elementary method is described for finding the coordination sequences for a tiling, based on coloring the underlying graph. The first application is to the two kinds of vertices (tetravalent and trivalent) in the Cairo (or dual-32.4.3.4) tiling. The coordination sequence for a tetravalent vertex turns out, surprisingly, to be 1, 4, 8, 12, 16, …, the same as for a vertex in the familiar square (or 44) tiling. The authors thought that such a simple fact should have a simple proof, and this article is the result. The method is also used to obtain coordination sequences for the 32.4.3.4, 3.4.6.4, 4.82, 3.122 and 34.6 uniform tilings, and the snub-632 tiling. In several cases the results provide proofs for previously conjectured formulas.text/htmlA coloring-book approach to finding coordination sequencestext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers121134Anomalous small viral shells and simplest polyhedra with icosahedral symmetry: the rhombic triacontahedron case
http://scripts.iucr.org/cgi-bin/paper?eo5089
The development of antiviral strategies requires a clear understanding of the principles that control the protein arrangements in viral shells. Considered here are those capsids that violate the paradigmatic Caspar and Klug (CK) model, and it is shown that the important structural features of such anomalous shells from the Picobirnaviridae, Flaviviridae and Leviviridae families can be revealed by models in the form of spherical icosahedral packings of equivalent rhombic structural units (SUs). These SUs are composed of protein dimers forming the investigated capsids which, as shown here, are based on the rhombic triacontahedron (RT) geometry. How to modify the original CK approach in order to make it compatible with the considered rhombic tessellations of a sphere is also discussed. Analogies between capsids self-assembled from dimers and trimers are demonstrated. This analysis reveals the principles controlling the localization of receptor proteins (which recognize the host cell) on the capsid surface.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Pimonov, V.V.Konevtsova, O.V.Rochal, S.B.2019-01-01doi:10.1107/S2053273318015656International Union of CrystallographyThe symmetry of the capsomers forming a viral shell determines the polyhedron underlying the shell structure. If the capsid is self-assembled from dimers, this is the rhombic triacontahedron with 30 equivalent rhombic faces.ENcapsid structuresCaspar and Klug modelspherical latticeicosahedral symmetryThe development of antiviral strategies requires a clear understanding of the principles that control the protein arrangements in viral shells. Considered here are those capsids that violate the paradigmatic Caspar and Klug (CK) model, and it is shown that the important structural features of such anomalous shells from the Picobirnaviridae, Flaviviridae and Leviviridae families can be revealed by models in the form of spherical icosahedral packings of equivalent rhombic structural units (SUs). These SUs are composed of protein dimers forming the investigated capsids which, as shown here, are based on the rhombic triacontahedron (RT) geometry. How to modify the original CK approach in order to make it compatible with the considered rhombic tessellations of a sphere is also discussed. Analogies between capsids self-assembled from dimers and trimers are demonstrated. This analysis reveals the principles controlling the localization of receptor proteins (which recognize the host cell) on the capsid surface.text/htmlAnomalous small viral shells and simplest polyhedra with icosahedral symmetry: the rhombic triacontahedron casetext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers135141Updating direct methods
http://scripts.iucr.org/cgi-bin/paper?sc5126
The standard method of joint probability distribution functions, so crucial for the development of direct methods, has been revisited and updated. It consists of three steps: identification of the reflections which may contribute to the estimation of a given structure invariant or seminvariant, calculation of the corresponding joint probability distribution, and derivation of the conditional distribution of the invariant or seminvariant phase given the values of some diffracted amplitudes. In this article the conditional distributions are derived directly without passing through the second step. A good feature of direct methods is that they may work in the absence of any prior information: that is also their weakness. Different types of prior information have been taken into consideration: interatomic distances, interatomic vectors, Patterson peaks, structural model. The method of directly deriving the conditional distributions has been applied to those cases. Some new formulas have been obtained estimating two-, three- and four-phase invariants. Special attention has been dedicated to the practical aspects of the new formulas, in order to simplify their possible use in direct phasing procedures.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Giacovazzo, C.2019-01-01doi:10.1107/S2053273318016443International Union of CrystallographyDirect methods techniques are revisited and new mathematical approaches are described.ENphasingdirect methodsjoint probability distributionsab initio techniquesprior informationThe standard method of joint probability distribution functions, so crucial for the development of direct methods, has been revisited and updated. It consists of three steps: identification of the reflections which may contribute to the estimation of a given structure invariant or seminvariant, calculation of the corresponding joint probability distribution, and derivation of the conditional distribution of the invariant or seminvariant phase given the values of some diffracted amplitudes. In this article the conditional distributions are derived directly without passing through the second step. A good feature of direct methods is that they may work in the absence of any prior information: that is also their weakness. Different types of prior information have been taken into consideration: interatomic distances, interatomic vectors, Patterson peaks, structural model. The method of directly deriving the conditional distributions has been applied to those cases. Some new formulas have been obtained estimating two-, three- and four-phase invariants. Special attention has been dedicated to the practical aspects of the new formulas, in order to simplify their possible use in direct phasing procedures.text/htmlUpdating direct methodstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers142157Model-independent extraction of the shapes and Fourier transforms from patterns of partially overlapped peaks with extended tails
http://scripts.iucr.org/cgi-bin/paper?sc5121
This work presents a technique for extracting the detailed shape of peaks with extended, overlapping tails in an X-ray powder diffraction pattern. The application discussed here concerns crystallite size broadening, though the technique can be applied to spectra of any origin and without regard to how the profiles are to be subsequently analyzed. Historically, the extraction of profile shapes has been difficult due to the complexity of determining the background under the peak, resulting in an offset of the low-frequency components of the Fourier transform of the peak known as the `hook' problem. The use of a carefully considered statistical weighting function in a non-linear least-squares fit, followed by summing the residuals from such a fit with the fit itself, allows one to extract the full shape of an isolated peak, without contributions from either the background or adjacent peaks. The extracted shape, consisting of the fit function recombined with the residuals, is not dependent on any specific shape model. The application of this to analysis of microstructure is performed independently of global parametric models, which would reduce the number of refined parameters; therefore the technique requires high-quality data to produce results of interest. The effectiveness of the technique is demonstrated by extraction of Fourier transforms of peaks from two sets of size-broadened materials with two differing pieces of equipment.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Mendenhall, M.H.Cline, J.P.2019-01-01doi:10.1107/S2053273318016935International Union of CrystallographyA new method of extracting the individual shapes of overlapping powder peaks with Lorentzian (or other long-range) tails is presented. This allows computation of microstructure directly in Fourier space, without the infamous `hook' problem at low frequency.ENFourier transformsmicrostructurehook effectpowder diffractionThis work presents a technique for extracting the detailed shape of peaks with extended, overlapping tails in an X-ray powder diffraction pattern. The application discussed here concerns crystallite size broadening, though the technique can be applied to spectra of any origin and without regard to how the profiles are to be subsequently analyzed. Historically, the extraction of profile shapes has been difficult due to the complexity of determining the background under the peak, resulting in an offset of the low-frequency components of the Fourier transform of the peak known as the `hook' problem. The use of a carefully considered statistical weighting function in a non-linear least-squares fit, followed by summing the residuals from such a fit with the fit itself, allows one to extract the full shape of an isolated peak, without contributions from either the background or adjacent peaks. The extracted shape, consisting of the fit function recombined with the residuals, is not dependent on any specific shape model. The application of this to analysis of microstructure is performed independently of global parametric models, which would reduce the number of refined parameters; therefore the technique requires high-quality data to produce results of interest. The effectiveness of the technique is demonstrated by extraction of Fourier transforms of peaks from two sets of size-broadened materials with two differing pieces of equipment.text/htmlModel-independent extraction of the shapes and Fourier transforms from patterns of partially overlapped peaks with extended tailstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers158164Report of the Executive Committee for 2017
http://scripts.iucr.org/cgi-bin/paper?es5004
The report of the Executive Committee for 2017 is presented.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Ashcroft, A.T.2019-01-01doi:10.1107/S205327331801330XInternational Union of CrystallographyThe report of the Executive Committee for 2017 is presented.ENInternational Union of CrystallographyExecutive CommitteeThe report of the Executive Committee for 2017 is presented.text/htmlReport of the Executive Committee for 2017text1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography165209Gjønnes Medal in Electron Crystallography – call for nominations
http://scripts.iucr.org/cgi-bin/paper?es5007
Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Meshi, L.2019-01-01doi:10.1107/S2053273318016674International Union of CrystallographyNominations for the Gjønnes Medal in Electron Crystallography are requested.ENGjønnes Medalelectron crystallographytext/htmlGjønnes Medal in Electron Crystallography – call for nominationstext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography210210Nominations for the Ewald Prize
http://scripts.iucr.org/cgi-bin/paper?es5008
Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Ashcroft, A.T.2019-01-01doi:10.1107/S2053273318016820International Union of CrystallographyNominations for the 11th Ewald Prize are invited.ENEwald PrizeInternational Union of Crystallographytext/htmlNominations for the Ewald Prizetext1752019-01-01Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography211211