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) 2023 International Union of Crystallography2023-03-01International 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 79, Part 2, 2023textweekly62002-01-01T00:00+00:002792023-03-01Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances132urn:issn:2053-2733med@iucr.orgMarch 20232023-03-01Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageA general force field by machine learning on experimental crystal structures. Calculations of intermolecular Gibbs energy with FlexCryst
http://scripts.iucr.org/cgi-bin/paper?lu5022
Machine learning was employed on the experimental crystal structures of the Cambridge Structural Database (CSD) to derive an intermolecular force field for all available types of atoms (general force field). The obtained pairwise interatomic potentials of the general force field allow for the fast and accurate calculation of intermolecular Gibbs energy. The approach is based on three postulates regarding Gibbs energy: the lattice energy must be below zero, the crystal structure must be a local minimum, and, if available, the experimental and the calculated lattice energy must coincide. The parametrized general force field was then validated regarding these three conditions. First, the experimental lattice energy was compared with the calculated energies. The observed errors were found to be in the order of experimental errors. Second, Gibbs lattice energy was calculated for all structures available in the CSD. Their energy values were found to be below zero in 99.86% of the cases. Finally, 500 random structures were minimized, and the change in density and energy was examined. The mean error in the case of density was below 4.06%, and for energy it was below 5.7%. The obtained general force field calculated Gibbs lattice energies of 259 041 known crystal structures within a few hours. Since Gibbs energy defines the reaction energy, the calculated energy can be used to predict chemical–physical properties of crystals, for instance, the formation of co-crystals, polymorph stability and solubility.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Hofmann, D.W.M.Kuleshova, L.N.2023-02-09doi:10.1107/S2053273323000268International Union of CrystallographyMachine learning was employed on the Cambridge Structural Database to derive a general force field for all observed atom–atom interactions. The force field parameters, i.e. interatomic potentials and `critical bond distances', are derived to calculate the intermolecular Gibbs energy, which is important for the prediction of crystal structures, solubility and other thermodynamic properties.ENmachine learningGibbs energycrystal structure analysisforce fieldintermolecular interactionsMachine learning was employed on the experimental crystal structures of the Cambridge Structural Database (CSD) to derive an intermolecular force field for all available types of atoms (general force field). The obtained pairwise interatomic potentials of the general force field allow for the fast and accurate calculation of intermolecular Gibbs energy. The approach is based on three postulates regarding Gibbs energy: the lattice energy must be below zero, the crystal structure must be a local minimum, and, if available, the experimental and the calculated lattice energy must coincide. The parametrized general force field was then validated regarding these three conditions. First, the experimental lattice energy was compared with the calculated energies. The observed errors were found to be in the order of experimental errors. Second, Gibbs lattice energy was calculated for all structures available in the CSD. Their energy values were found to be below zero in 99.86% of the cases. Finally, 500 random structures were minimized, and the change in density and energy was examined. The mean error in the case of density was below 4.06%, and for energy it was below 5.7%. The obtained general force field calculated Gibbs lattice energies of 259 041 known crystal structures within a few hours. Since Gibbs energy defines the reaction energy, the calculated energy can be used to predict chemical–physical properties of crystals, for instance, the formation of co-crystals, polymorph stability and solubility.text/htmlA general force field by machine learning on experimental crystal structures. Calculations of intermolecular Gibbs energy with FlexCrysttext2792023-02-09Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers132144Crystal diffraction prediction and partiality estimation using Gaussian basis functions
http://scripts.iucr.org/cgi-bin/paper?ik5005
The recent diversification of macromolecular crystallographic experiments including the use of pink beams, convergent electron diffraction and serial snapshot crystallography has shown the limitations of using the Laue equations for diffraction prediction. This article gives a computationally efficient way of calculating approximate crystal diffraction patterns given varying distributions of the incoming beam, crystal shapes and other potentially hidden parameters. This approach models each pixel of a diffraction pattern and improves data processing of integrated peak intensities by enabling the correction of partially recorded reflections. The fundamental idea is to express the distributions as weighted sums of Gaussian functions. The approach is demonstrated on serial femtosecond crystallography data sets, showing a significant decrease in the required number of patterns to refine a structure to a given error.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Brehm, W.White, T.Chapman, H.N.2023-02-17doi:10.1107/S2053273323000682International Union of CrystallographyReflection position, size and shape prediction and partiality estimation of crystal diffraction by integrating using a Gaussian basis are described.ENpartiality estimationdiffraction predictionmergingserial snapshot crystallographyThe recent diversification of macromolecular crystallographic experiments including the use of pink beams, convergent electron diffraction and serial snapshot crystallography has shown the limitations of using the Laue equations for diffraction prediction. This article gives a computationally efficient way of calculating approximate crystal diffraction patterns given varying distributions of the incoming beam, crystal shapes and other potentially hidden parameters. This approach models each pixel of a diffraction pattern and improves data processing of integrated peak intensities by enabling the correction of partially recorded reflections. The fundamental idea is to express the distributions as weighted sums of Gaussian functions. The approach is demonstrated on serial femtosecond crystallography data sets, showing a significant decrease in the required number of patterns to refine a structure to a given error.text/htmlCrystal diffraction prediction and partiality estimation using Gaussian basis functionstext2792023-02-17Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers145162Dynamic tilting in perovskites
http://scripts.iucr.org/cgi-bin/paper?lu5021
A new computational analysis of tilt behaviour in perovskites is presented. This includes the development of a computational program – PALAMEDES – to extract tilt angles and the tilt phase from molecular dynamics simulations. The results are used to generate simulated selected-area electron and neutron diffraction patterns which are compared with experimental patterns for CaTiO3. The simulations not only reproduced all symmetrically allowed superlattice reflections associated with tilt but also showed local correlations that give rise to symmetrically forbidden reflections and the kinematic origin of diffuse scattering.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Handley, C.M.Ward, R.E.Freeman, C.L.Reaney, I.M.Sinclair, D.C.Harding, J.H.2023-01-23doi:10.1107/S2053273322011949International Union of CrystallographyA new computational program to analyse and extract tilt data from molecular dynamics simulations of perovskites is presented and results compared with experimental data.ENperovskitestiltdiffractionmolecular dynamicssuperlatticeA new computational analysis of tilt behaviour in perovskites is presented. This includes the development of a computational program – PALAMEDES – to extract tilt angles and the tilt phase from molecular dynamics simulations. The results are used to generate simulated selected-area electron and neutron diffraction patterns which are compared with experimental patterns for CaTiO3. The simulations not only reproduced all symmetrically allowed superlattice reflections associated with tilt but also showed local correlations that give rise to symmetrically forbidden reflections and the kinematic origin of diffuse scattering.text/htmlDynamic tilting in perovskitestext2792023-01-23Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers163170Dynamical theory of X-ray diffraction by crystals with different surface relief profiles
http://scripts.iucr.org/cgi-bin/paper?iv5027
A dynamical theory is developed of X-ray diffraction on a crystal with surface relief for the case of high-resolution triple-crystal X-ray diffractometry. Crystals with trapezoidal, sinusoidal and parabolic bar profile models are investigated in detail. Numerical simulations of the X-ray diffraction problem for concrete experimental conditions are performed. A simple new method to resolve the crystal relief reconstruction problem is proposed.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Karpov, A.V.Kazakov, D.V.Punegov, V.I.2023-01-23doi:10.1107/S2053273322012062International Union of CrystallographyA dynamical theory of X-ray diffraction is presented for a crystal with surface relief operated in a single-mode regime.ENdynamical theory of X-ray diffractioncrystal surface reliefreciprocal-space mappingrocking curvesrelief bar reconstructionA dynamical theory is developed of X-ray diffraction on a crystal with surface relief for the case of high-resolution triple-crystal X-ray diffractometry. Crystals with trapezoidal, sinusoidal and parabolic bar profile models are investigated in detail. Numerical simulations of the X-ray diffraction problem for concrete experimental conditions are performed. A simple new method to resolve the crystal relief reconstruction problem is proposed.text/htmlDynamical theory of X-ray diffraction by crystals with different surface relief profilestext2792023-01-23Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers171179Dynamical diffraction of high-energy electrons by light-atom structures: a multiple forward scattering interpretation
http://scripts.iucr.org/cgi-bin/paper?lu5020
Because of the strong electron–atom interaction, the kinematic theory of diffraction cannot be used to describe the scattering of electrons by an assembly of atoms due to the strong dynamical diffraction that needs to be taken into account. In this paper, the scattering of high-energy electrons by a regular array of light atoms is solved exactly by applying the T-matrix formalism to the corresponding Schrödinger's equation in spherical coordinates. The independent atom model is used, where each atom is represented by a sphere with an effective constant potential. The validity of the forward scattering approximation and the phase grating approximation, assumed by the popular multislice method, is discussed, and an alternative interpretation of multiple scattering is proposed and compared with existing interpretations.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Drevon, T.R.Waterman, D.G.Krissinel, E.2023-02-09doi:10.1107/S2053273322011779International Union of CrystallographyThe T-matrix is used to compute the scattering of fast electrons by a regular array of effective spherical potential wells. An assessment of the forward scattering approximation and a real-space multiple scattering interpretation are provided.ENhigh-energy electron diffractionT-matrixmultiple scatteringindependent atom approximationBecause of the strong electron–atom interaction, the kinematic theory of diffraction cannot be used to describe the scattering of electrons by an assembly of atoms due to the strong dynamical diffraction that needs to be taken into account. In this paper, the scattering of high-energy electrons by a regular array of light atoms is solved exactly by applying the T-matrix formalism to the corresponding Schrödinger's equation in spherical coordinates. The independent atom model is used, where each atom is represented by a sphere with an effective constant potential. The validity of the forward scattering approximation and the phase grating approximation, assumed by the popular multislice method, is discussed, and an alternative interpretation of multiple scattering is proposed and compared with existing interpretations.text/htmlDynamical diffraction of high-energy electrons by light-atom structures: a multiple forward scattering interpretationtext2792023-02-09Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers180191Three-periodic nets, tilings and surfaces. A short review and new results
http://scripts.iucr.org/cgi-bin/paper?pl5023
A brief introductory review is provided of the theory of tilings of 3-periodic nets and related periodic surfaces. Tilings have a transitivity [p q r s] indicating the vertex, edge, face and tile transitivity. Proper, natural and minimal-transitivity tilings of nets are described. Essential rings are used for finding the minimal-transitivity tiling for a given net. Tiling theory is used to find all edge- and face-transitive tilings (q = r = 1) and to find seven, one, one and 12 examples of tilings with transitivity [1 1 1 1], [1 1 1 2], [2 1 1 1] and [2 1 1 2], respectively. These are all minimal-transitivity tilings. This work identifies the 3-periodic surfaces defined by the nets of the tiling and its dual and indicates how 3-periodic nets arise from tilings of those surfaces.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Delgado-Friedrichs, O.O'Keeffe, M.Proserpio, D.M.Treacy, M.M.J.2023-02-13doi:10.1107/S2053273323000414International Union of CrystallographyAfter a brief review of tilings of 3-periodic nets, the use of essential rings is proposed to identify transitive tilings.ENtilingsnets3-periodic nets3-periodic tilingsessential ringsA brief introductory review is provided of the theory of tilings of 3-periodic nets and related periodic surfaces. Tilings have a transitivity [p q r s] indicating the vertex, edge, face and tile transitivity. Proper, natural and minimal-transitivity tilings of nets are described. Essential rings are used for finding the minimal-transitivity tiling for a given net. Tiling theory is used to find all edge- and face-transitive tilings (q = r = 1) and to find seven, one, one and 12 examples of tilings with transitivity [1 1 1 1], [1 1 1 2], [2 1 1 1] and [2 1 1 2], respectively. These are all minimal-transitivity tilings. This work identifies the 3-periodic surfaces defined by the nets of the tiling and its dual and indicates how 3-periodic nets arise from tilings of those surfaces.text/htmlThree-periodic nets, tilings and surfaces. A short review and new resultstext2792023-02-13Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers192202A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data
http://scripts.iucr.org/cgi-bin/paper?ae5124
This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Gu, R.Billinge, S.J.L.Du, Q.2023-02-24doi:10.1107/S2053273323000761International Union of CrystallographyA fast two-stage algorithm developed for highly efficient and accurate non-negative matrix factorization in smoothly varying data, such as atomic pair distribution function data, is reported.ENnon-negative matrix factorizationsmoothly varying datapair distribution functioninterior point methodThis article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.text/htmlA fast two-stage algorithm for non-negative matrix factorization in smoothly varying datatext2792023-02-24Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers203216Borromean rings redux. A missing link found – a Borromean triplet of Borromean triplets
http://scripts.iucr.org/cgi-bin/paper?pl5024
This paper describes a nine-component Borromean structure – a Borromean triplet of Borromean triplets – that was missing from an earlier enumeration.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733O'Keeffe, M.Treacy, M.M.J.2023-02-17doi:10.1107/S2053273323001122International Union of CrystallographyA nine-component Borromean triplet of Borromean triplets is described.ENBorromean structureBorromean triplet of Borromean tripletscatenanesThis paper describes a nine-component Borromean structure – a Borromean triplet of Borromean triplets – that was missing from an earlier enumeration.text/htmlBorromean rings redux. A missing link found – a Borromean triplet of Borromean tripletstext2792023-02-17Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Ashort communications217219Twenty-Fifth General Assembly and International Congress of Crystallography, Prague, Czech Republic, 14–21 August 2021
http://scripts.iucr.org/cgi-bin/paper?es5024
Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Ashcroft, A.T.2023-02-16doi:10.1107/S205327332300058XInternational Union of CrystallographyA report of the Twenty-Fifth General Assembly and International Congress of Crystallography is given.ENInternational Union of CrystallographyIUCrGeneral AssemblyInternational Congress of Crystallographytext/htmlTwenty-Fifth General Assembly and International Congress of Crystallography, Prague, Czech Republic, 14–21 August 2021text2792023-02-16Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography220228