Open-access and free articles in Acta Crystallographica Section A: Foundations and Advances
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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.en-gbCopyright (c) 2023 International Union of CrystallographyInternational Union of CrystallographyInternational Union of CrystallographyOpen-access and free articles in Acta Crystallographica Section A Foundations and Advanceshttps://journals.iucr.orgurn:issn:0108-7673Acta 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.texttext/html62002-01-01T00:00+00:00yearlymed@iucr.orgActa Crystallographica Section A Foundations and AdvancesCopyright (c) 2023 International Union of Crystallographyurn:issn:0108-7673Open-access and free articles in Acta Crystallographica Section A: Foundations and Advanceshttp://journals.iucr.org/logos/rss10a.gif
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Still imageSmall-angle scattering tensor tomography algorithm for robust reconstruction of complex textures
http://scripts.iucr.org/cgi-bin/paper?ae5133
The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For such a method to be employed by researchers from a wide range of backgrounds, it is crucial that its reliance on prior knowledge about the system is minimized, and that it is robust under various conditions. Here, a method is presented that employs band-limited spherical functions to enable the reconstruction of reciprocal-space maps of a wide variety of nanostructures. This method has been thoroughly tested and compared with existing methods in its ability to retrieve known reciprocal-space maps, as well as its robustness to changes in initial conditions, using both simulations and experimental data. It has also been evaluated for its computational performance. The anchoring of this method in a framework of integral geometry and linear algebra highlights its possibilities and limitations.https://creativecommons.org/licenses/by/4.0/Nielsen, L.C.Erhart, P.Guizar-Sicairos, M.Liebi, M.Small-angle scattering tensor tomography algorithm for robust reconstruction of complex texturesurn:issn:2053-2733doi:10.1107/S205327332300863XThe development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. The paper presents a method tested against both simulations and experimental data, and compared with existing methods, demonstrating its ability to handle several different classes of nanostructures.2023-10-19The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For such a method to be employed by researchers from a wide range of backgrounds, it is crucial that its reliance on prior knowledge about the system is minimized, and that it is robust under various conditions. Here, a method is presented that employs band-limited spherical functions to enable the reconstruction of reciprocal-space maps of a wide variety of nanostructures. This method has been thoroughly tested and compared with existing methods in its ability to retrieve known reciprocal-space maps, as well as its robustness to changes in initial conditions, using both simulations and experimental data. It has also been evaluated for its computational performance. The anchoring of this method in a framework of integral geometry and linear algebra highlights its possibilities and limitations.textentext/htmlTENSOR TOMOGRAPHY; SAXS; SMALL-ANGLE X-RAY SCATTERING; SCATTERING; RECIPROCAL-SPACE MAPS; OPTIMIZATIONInternational Union of Crystallography6Acta Crystallographica Section A: Foundations and AdvancesNovember 20232053-2733med@iucr.org5152053-2733research papers2023-10-19https://creativecommons.org/licenses/by/4.0/52679Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctness
http://scripts.iucr.org/cgi-bin/paper?lu5032
The Debye scattering equation (DSE) [Debye (1915). Ann. Phys. 351, 809–823] is widely used for analyzing total scattering data of nanocrystalline materials in reciprocal space. In its modified form (MDSE) [Cervellino et al. (2010). J. Appl. Cryst. 43, 1543–1547], it includes contributions from uncorrelated thermal agitation terms and, for defective crystalline nanoparticles (NPs), average site-occupancy factors (s.o.f.'s). The s.o.f.'s were introduced heuristically and no theoretical demonstration was provided. This paper presents in detail such a demonstration, corrects a glitch present in the original MDSE, and discusses the s.o.f.'s physical significance. Three new MDSE expressions are given that refer to distinct defective NP ensembles characterized by: (i) vacant sites with uncorrelated constant site-occupancy probability; (ii) vacant sites with a fixed number of randomly distributed atoms; (iii) self-excluding (disordered) positional sites. For all these cases, beneficial aspects and shortcomings of introducing s.o.f.'s as free refinable parameters are demonstrated. The theoretical analysis is supported by numerical simulations performed by comparing the corrected MDSE profiles and the ones based on atomistic modeling of a large number of NPs, satisfying the structural conditions described in (i)–(iii).https://creativecommons.org/licenses/by/4.0/Ferri, F.Bossuto, M.C.Anzini, P.Cervellino, A.Guagliardi, A.Bertolotti, F.Masciocchi, N.Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctnessurn:issn:2053-2733doi:10.1107/S2053273323008446The modified Debye scattering equation, often used for characterizing defective nanoparticle ensembles, has been theoretically analyzed with a special focus on the significance and correctness of the site-occupancy factors, oi's.2023-11-02The Debye scattering equation (DSE) [Debye (1915). Ann. Phys. 351, 809–823] is widely used for analyzing total scattering data of nanocrystalline materials in reciprocal space. In its modified form (MDSE) [Cervellino et al. (2010). J. Appl. Cryst. 43, 1543–1547], it includes contributions from uncorrelated thermal agitation terms and, for defective crystalline nanoparticles (NPs), average site-occupancy factors (s.o.f.'s). The s.o.f.'s were introduced heuristically and no theoretical demonstration was provided. This paper presents in detail such a demonstration, corrects a glitch present in the original MDSE, and discusses the s.o.f.'s physical significance. Three new MDSE expressions are given that refer to distinct defective NP ensembles characterized by: (i) vacant sites with uncorrelated constant site-occupancy probability; (ii) vacant sites with a fixed number of randomly distributed atoms; (iii) self-excluding (disordered) positional sites. For all these cases, beneficial aspects and shortcomings of introducing s.o.f.'s as free refinable parameters are demonstrated. The theoretical analysis is supported by numerical simulations performed by comparing the corrected MDSE profiles and the ones based on atomistic modeling of a large number of NPs, satisfying the structural conditions described in (i)–(iii).textentext/htmlDEBYE SCATTERING EQUATION; SITE-OCCUPANCY FACTORS; DEFECTIVE NANOCRYSTALSInternational Union of Crystallography2053-2733November 2023Acta Crystallographica Section A: Foundations and Advances6587med@iucr.org2053-2733research papershttps://creativecommons.org/licenses/by/4.0/2023-11-0259679Molecular replacement for small-molecule crystal structure determination from X-ray and electron diffraction data with reduced resolution
http://scripts.iucr.org/cgi-bin/paper?lu5029
The resolution of 3D electron diffraction (ED) data of small-molecule crystals is often relatively poor, due to either electron-beam radiation damage during data collection or poor crystallinity of the material. Direct methods, used as standard for crystal structure determination, are not applicable when the data resolution falls below the commonly accepted limit of 1.2 Å. Therefore an evaluation was carried out of the performance of molecular replacement (MR) procedures, regularly used for protein structure determination, for structure analysis of small-molecule crystal structures from 3D ED data. In the course of this study, two crystal structures of Bi-3812, a highly potent inhibitor of the oncogenic transcription factor BCL6, were determined: the structure of α-Bi-3812 was determined from single-crystal X-ray data, the structure of β-Bi-3812 from 3D ED data, using direct methods in both cases. These data were subsequently used for MR with different data types, varying the data resolution limit (1, 1.5 and 2 Å) and by using search models consisting of connected or disconnected fragments of BI-3812. MR was successful with 3D ED data at 2 Å resolution using a search model that represented 74% of the complete molecule.https://creativecommons.org/licenses/by/4.0/Gorelik, T.E.Lukat, P.Kleeberg, C.Blankenfeldt, W.Mueller, R.Molecular replacement for small-molecule crystal structure determination from X-ray and electron diffraction data with reduced resolutionurn:issn:2053-2733doi:10.1107/S2053273323008458Molecular replacement as implemented in Phaser was applied to structure analysis of small-molecule single-crystal X-ray and electron diffraction data.2023-10-19The resolution of 3D electron diffraction (ED) data of small-molecule crystals is often relatively poor, due to either electron-beam radiation damage during data collection or poor crystallinity of the material. Direct methods, used as standard for crystal structure determination, are not applicable when the data resolution falls below the commonly accepted limit of 1.2 Å. Therefore an evaluation was carried out of the performance of molecular replacement (MR) procedures, regularly used for protein structure determination, for structure analysis of small-molecule crystal structures from 3D ED data. In the course of this study, two crystal structures of Bi-3812, a highly potent inhibitor of the oncogenic transcription factor BCL6, were determined: the structure of α-Bi-3812 was determined from single-crystal X-ray data, the structure of β-Bi-3812 from 3D ED data, using direct methods in both cases. These data were subsequently used for MR with different data types, varying the data resolution limit (1, 1.5 and 2 Å) and by using search models consisting of connected or disconnected fragments of BI-3812. MR was successful with 3D ED data at 2 Å resolution using a search model that represented 74% of the complete molecule.textentext/htmlELECTRON CRYSTALLOGRAPHY; SMALL MOLECULES; MOLECULAR REPLACEMENTInternational Union of Crystallography504med@iucr.org2053-27336November 2023Acta Crystallographica Section A: Foundations and Advances2053-27335142023-10-19research papershttps://creativecommons.org/licenses/by/4.0/79Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals
http://scripts.iucr.org/cgi-bin/paper?ae5132
A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ. By means of their specific parameterization they comprise local features of both periodic and aperiodic crystals. In particular, chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes, each discrete spiral being generated from an integer inclination sequence. The geometry of circle involutes does not only provide for a constant orthogonal separation distance between adjacent spiral branches but also yields an approximate delineation of the intrinsically periodic twin domains as well as a single aperiodic core domain interconnecting them. Apart from its mathematical description and analysis, e.g. concerning its circle packing densities, the toy model is studied in association with the crystallography and crystal chemistry of α-uranium and CrB-type crystal structures.https://creativecommons.org/licenses/by/4.0/Hornfeck, W.Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spiralsurn:issn:2053-2733doi:10.1107/S2053273323008276A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ, comprising local features of both periodic and aperiodic crystals. Chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes.2023-10-31A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ. By means of their specific parameterization they comprise local features of both periodic and aperiodic crystals. In particular, chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes, each discrete spiral being generated from an integer inclination sequence. The geometry of circle involutes does not only provide for a constant orthogonal separation distance between adjacent spiral branches but also yields an approximate delineation of the intrinsically periodic twin domains as well as a single aperiodic core domain interconnecting them. Apart from its mathematical description and analysis, e.g. concerning its circle packing densities, the toy model is studied in association with the crystallography and crystal chemistry of α-uranium and CrB-type crystal structures.textentext/htmlCHIRAL PROPERTIES; SPIRAL STRUCTURES; CYCLIC TWINSInternational Union of Crystallography2053-2733med@iucr.org570Acta Crystallographica Section A: Foundations and Advances6November 20232053-273379586research papers2023-10-31https://creativecommons.org/licenses/by/4.0/An efficient system matrix factorization method for scanning diffraction based strain tensor tomography
http://scripts.iucr.org/cgi-bin/paper?vk5050
Diffraction-based tomographic strain tensor reconstruction problems in which a strain tensor field is determined from measurements made in different crystallographic directions are considered in the context of sparse matrix algebra. Previous work has shown that the estimation of the crystal elastic strain field can be cast as a linear regression problem featuring a computationally involved assembly of a system matrix forward operator. This operator models the perturbation in diffraction signal as a function of spatial strain tensor state. The structure of this system matrix is analysed and a block-partitioned factorization is derived that reveals the forward operator as a sum of weighted scalar projection operators. Moreover, the factorization method is generalized for another diffraction model in which strain and orientation are coupled and can be reconstructed jointly. The proposed block-partitioned factorization method provides a bridge to classical absorption tomography and allows exploitation of standard tomographic ray-tracing libraries for implementation of the forward operator and its adjoint. Consequently, RAM-efficient, GPU-accelerated, on-the-fly strain/orientation tensor reconstruction is made possible, paving the way for higher spatial resolution studies of intragranular deformation.https://creativecommons.org/licenses/by/4.0/Henningsson, A.Hall, S.A.An efficient system matrix factorization method for scanning diffraction based strain tensor tomographyurn:issn:2053-2733doi:10.1107/S2053273323008136Matrix analysis is used to provide a computationally efficient mathematical framework for diffraction-based strain tomography.2023-09-29Diffraction-based tomographic strain tensor reconstruction problems in which a strain tensor field is determined from measurements made in different crystallographic directions are considered in the context of sparse matrix algebra. Previous work has shown that the estimation of the crystal elastic strain field can be cast as a linear regression problem featuring a computationally involved assembly of a system matrix forward operator. This operator models the perturbation in diffraction signal as a function of spatial strain tensor state. The structure of this system matrix is analysed and a block-partitioned factorization is derived that reveals the forward operator as a sum of weighted scalar projection operators. Moreover, the factorization method is generalized for another diffraction model in which strain and orientation are coupled and can be reconstructed jointly. The proposed block-partitioned factorization method provides a bridge to classical absorption tomography and allows exploitation of standard tomographic ray-tracing libraries for implementation of the forward operator and its adjoint. Consequently, RAM-efficient, GPU-accelerated, on-the-fly strain/orientation tensor reconstruction is made possible, paving the way for higher spatial resolution studies of intragranular deformation.textentext/htmlX-RAY DIFFRACTION; STRAIN TENSOR; TOMOGRAPHY; DIFFRACTION IMAGINGInternational Union of Crystallography2053-2733med@iucr.org542Acta Crystallographica Section A: Foundations and AdvancesNovember 202362053-273379549https://creativecommons.org/licenses/by/4.0/research papers2023-09-29TERSE/PROLIX (TRPX) – a new algorithm for fast and lossless compression and decompression of diffraction and cryo-EM data
http://scripts.iucr.org/cgi-bin/paper?lu5031
High-throughput data collection in crystallography poses significant challenges in handling massive amounts of data. Here, TERSE/PROLIX (or TRPX for short) is presented, a novel lossless compression algorithm specifically designed for diffraction data. The algorithm is compared with established lossless compression algorithms implemented in gzip, bzip2, CBF (crystallographic binary file), Zstandard(zstd), LZ4 and HDF5 with gzip, LZF and bitshuffle+LZ4 filters, in terms of compression efficiency and speed, using continuous-rotation electron diffraction data of an inorganic compound and raw cryo-EM data. The results show that TRPX significantly outperforms all these algorithms in terms of speed and compression rate. It was 60 times faster than bzip2 (which achieved a similar compression rate), and more than 3 times faster than LZ4, which was the runner-up in terms of speed, but had a much worse compression rate. TRPX files are byte-order independent and upon compilation the algorithm occupies very little memory. It can therefore be readily implemented in hardware. By providing a tailored solution for diffraction and raw cryo-EM data, TRPX facilitates more efficient data analysis and interpretation while mitigating storage and transmission concerns. The C++20 compression/decompression code, custom TIFF library and an ImageJ/Fiji Java plugin for reading TRPX files are open-sourced on GitHub under the permissive MIT license.https://creativecommons.org/licenses/by/4.0/Matinyan, S.Abrahams, J.P.TERSE/PROLIX (TRPX) – a new algorithm for fast and lossless compression and decompression of diffraction and cryo-EM dataurn:issn:2053-2733doi:10.1107/S205327332300760XThis article presents a fast and lossless algorithm for compressing diffraction data, achieving up to 85% reduction in file size while processing up to 2000 512 × 512 frames s−1. This breakthrough in compression technology is a significant step towards more efficient analysis and storage of large diffraction data sets.2023-09-25High-throughput data collection in crystallography poses significant challenges in handling massive amounts of data. Here, TERSE/PROLIX (or TRPX for short) is presented, a novel lossless compression algorithm specifically designed for diffraction data. The algorithm is compared with established lossless compression algorithms implemented in gzip, bzip2, CBF (crystallographic binary file), Zstandard(zstd), LZ4 and HDF5 with gzip, LZF and bitshuffle+LZ4 filters, in terms of compression efficiency and speed, using continuous-rotation electron diffraction data of an inorganic compound and raw cryo-EM data. The results show that TRPX significantly outperforms all these algorithms in terms of speed and compression rate. It was 60 times faster than bzip2 (which achieved a similar compression rate), and more than 3 times faster than LZ4, which was the runner-up in terms of speed, but had a much worse compression rate. TRPX files are byte-order independent and upon compilation the algorithm occupies very little memory. It can therefore be readily implemented in hardware. By providing a tailored solution for diffraction and raw cryo-EM data, TRPX facilitates more efficient data analysis and interpretation while mitigating storage and transmission concerns. The C++20 compression/decompression code, custom TIFF library and an ImageJ/Fiji Java plugin for reading TRPX files are open-sourced on GitHub under the permissive MIT license.textentext/htmlCOMPRESSION; TERSE/PROLIX; TRPX; LOSSLESS; DIFFRACTION DATA; CRYO-EM DATA; LOSSLESS DATA COMPRESSIONInternational Union of Crystallography79541https://creativecommons.org/licenses/by/4.0/research papers2023-09-252053-2733med@iucr.org536Acta Crystallographica Section A: Foundations and Advances6November 20232053-2733Optimal estimated standard uncertainties of reflection intensities for kinematical refinement from 3D electron diffraction data
http://scripts.iucr.org/cgi-bin/paper?pl5027
Estimating the error in the merged reflection intensities requires a full understanding of all the possible sources of error arising from the measurements. Most diffraction-spot integration methods focus mainly on errors arising from counting statistics for the estimation of uncertainties associated with the reflection intensities. This treatment may be incomplete and partly inadequate. In an attempt to fully understand and identify all the contributions to these errors, three methods are examined for the correction of estimated errors of reflection intensities in electron diffraction data. For a direct comparison, the three methods are applied to a set of organic and inorganic test cases. It is demonstrated that applying the corrections of a specific model that include terms dependent on the original uncertainty and the largest intensity of the symmetry-related reflections improves the overall structure quality of the given data set and improves the final Rall factor. This error model is implemented in the data reduction software PETS2.https://creativecommons.org/licenses/by/4.0/Khouchen, M.Klar, P.B.Chintakindi, H.Suresh, A.Palatinus, L.Optimal estimated standard uncertainties of reflection intensities for kinematical refinement from 3D electron diffraction dataurn:issn:2053-2733doi:10.1107/S2053273323005053Several models for estimating the standard uncertainties of reflection intensities are analysed for refinement against 3D electron diffraction data. A new model is proposed which results in more accurate structure models.2023-08-14Estimating the error in the merged reflection intensities requires a full understanding of all the possible sources of error arising from the measurements. Most diffraction-spot integration methods focus mainly on errors arising from counting statistics for the estimation of uncertainties associated with the reflection intensities. This treatment may be incomplete and partly inadequate. In an attempt to fully understand and identify all the contributions to these errors, three methods are examined for the correction of estimated errors of reflection intensities in electron diffraction data. For a direct comparison, the three methods are applied to a set of organic and inorganic test cases. It is demonstrated that applying the corrections of a specific model that include terms dependent on the original uncertainty and the largest intensity of the symmetry-related reflections improves the overall structure quality of the given data set and improves the final Rall factor. This error model is implemented in the data reduction software PETS2.textentext/htmlERROR MODELLING; ERROR ANALYSIS; DATA REDUCTION; ELECTRON DIFFRACTIONInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/4395427med@iucr.org2023-08-14research papers792053-2733Acta Crystallographica Section A: Foundations and AdvancesSeptember 20232053-2733Patch frequencies in rhombic Penrose tilings
http://scripts.iucr.org/cgi-bin/paper?nv5007
This exposition presents an efficient algorithm for an exact calculation of patch frequencies for rhombic Penrose tilings. A construction of Penrose tilings via dualization is recalled and, by extending the known method for obtaining vertex configurations, the desired algorithm is obtained. It is then used to determine the frequencies of several particularly large patches which appear in the literature. An analogous approach works for a particular class of tilings and this is also explained in detail for the Ammann–Beenker tiling.https://creativecommons.org/licenses/by/4.0/Mazáč, J.Patch frequencies in rhombic Penrose tilingsurn:issn:2053-2733doi:10.1107/S2053273323004990An algorithm is presented for an exact calculation of patch frequencies for a family of tilings which can be obtained via dualization.2023-07-24This exposition presents an efficient algorithm for an exact calculation of patch frequencies for rhombic Penrose tilings. A construction of Penrose tilings via dualization is recalled and, by extending the known method for obtaining vertex configurations, the desired algorithm is obtained. It is then used to determine the frequencies of several particularly large patches which appear in the literature. An analogous approach works for a particular class of tilings and this is also explained in detail for the Ammann–Beenker tiling.textentext/htmlPATCH FREQUENCY; TILING; DUALIZATION METHODInternational Union of Crystallography411https://creativecommons.org/licenses/by/4.0/399med@iucr.org52023-07-24research papers792053-2733September 2023Acta Crystallographica Section A: Foundations and Advances2053-2733Algorithms for magnetic symmetry operation search and identification of magnetic space group from magnetic crystal structure
http://scripts.iucr.org/cgi-bin/paper?ib5114
A crystal symmetry search is crucial for computational crystallography and materials science. Although algorithms and implementations for the crystal symmetry search have been developed, their extension to magnetic space groups (MSGs) remains limited. In this paper, algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types of given MSGs, searching for transformations to a Belov–Neronova–Smirnova (BNS) setting, and symmetrizing the magnetic crystal structures using the MSGs are presented. The determination of magnetic symmetry operations is numerically stable and is implemented with minimal modifications from the existing crystal symmetry search. Magnetic space-group types and transformations to the BNS setting are identified by a two-step approach combining space-group-type identification and the use of affine normalizers. Point coordinates and magnetic moments of the magnetic crystal structures are symmetrized by projection operators for the MSGs. An implementation is distributed with a permissive free software license in spglib v2.0.2: https://github.com/spglib/spglib.https://creativecommons.org/licenses/by/4.0/Shinohara, K.Togo, A.Tanaka, I.Algorithms for magnetic symmetry operation search and identification of magnetic space group from magnetic crystal structureurn:issn:2053-2733doi:10.1107/S2053273323005016This paper presents algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types from a given magnetic space group (MSG), searching for transformations to a Belov–Neronova–Smirnova setting, and symmetrizing the magnetic crystal structures on the basis of the determined MSGs.2023-09-06A crystal symmetry search is crucial for computational crystallography and materials science. Although algorithms and implementations for the crystal symmetry search have been developed, their extension to magnetic space groups (MSGs) remains limited. In this paper, algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types of given MSGs, searching for transformations to a Belov–Neronova–Smirnova (BNS) setting, and symmetrizing the magnetic crystal structures using the MSGs are presented. The determination of magnetic symmetry operations is numerically stable and is implemented with minimal modifications from the existing crystal symmetry search. Magnetic space-group types and transformations to the BNS setting are identified by a two-step approach combining space-group-type identification and the use of affine normalizers. Point coordinates and magnetic moments of the magnetic crystal structures are symmetrized by projection operators for the MSGs. An implementation is distributed with a permissive free software license in spglib v2.0.2: https://github.com/spglib/spglib.textentext/htmlMAGNETIC SPACE GROUP; MAGNETIC SPACE-GROUP TYPE; MAGNETIC STRUCTURE; CRYSTAL STRUCTURE ANALYSIS; AFFINE NORMALIZERInternational Union of Crystallography2023-09-06research papers792053-2733September 2023Acta Crystallographica Section A: Foundations and Advances2053-2733https://creativecommons.org/licenses/by/4.0/3985390med@iucr.orgMachine learning for classifying narrow-beam electron diffraction data
http://scripts.iucr.org/cgi-bin/paper?lu5027
As an alternative approach to X-ray crystallography and single-particle cryo-electron microscopy, single-molecule electron diffraction has a better signal-to-noise ratio and the potential to increase the resolution of protein models. This technology requires collection of numerous diffraction patterns, which can lead to congestion of data collection pipelines. However, only a minority of the diffraction data are useful for structure determination because the chances of hitting a protein of interest with a narrow electron beam may be small. This necessitates novel concepts for quick and accurate data selection. For this purpose, a set of machine learning algorithms for diffraction data classification has been implemented and tested. The proposed pre-processing and analysis workflow efficiently distinguished between amorphous ice and carbon support, providing proof of the principle of machine learning based identification of positions of interest. While limited in its current context, this approach exploits inherent characteristics of narrow electron beam diffraction patterns and can be extended for protein data classification and feature extraction.https://creativecommons.org/licenses/by/4.0/Matinyan, S.Demir, B.Filipcik, P.Abrahams, J.P.van Genderen, E.Machine learning for classifying narrow-beam electron diffraction dataurn:issn:2053-2733doi:10.1107/S2053273323004680Neural networks were trained for robust classification of narrow electron beam diffraction patterns and may significantly decrease the need for storage space.2023-06-20As an alternative approach to X-ray crystallography and single-particle cryo-electron microscopy, single-molecule electron diffraction has a better signal-to-noise ratio and the potential to increase the resolution of protein models. This technology requires collection of numerous diffraction patterns, which can lead to congestion of data collection pipelines. However, only a minority of the diffraction data are useful for structure determination because the chances of hitting a protein of interest with a narrow electron beam may be small. This necessitates novel concepts for quick and accurate data selection. For this purpose, a set of machine learning algorithms for diffraction data classification has been implemented and tested. The proposed pre-processing and analysis workflow efficiently distinguished between amorphous ice and carbon support, providing proof of the principle of machine learning based identification of positions of interest. While limited in its current context, this approach exploits inherent characteristics of narrow electron beam diffraction patterns and can be extended for protein data classification and feature extraction.textentext/htmlDIFFRACTION; SINGLE-MOLECULE ELECTRON DIFFRACTION; TEM; TRANSMISSION ELECTRON MICROSCOPY; MACHINE LEARNING; NEURAL NETWORKSInternational Union of Crystallography79research papers2023-06-202053-2733July 2023Acta Crystallographica Section A: Foundations and Advances2053-2733368https://creativecommons.org/licenses/by/4.0/med@iucr.org3604New benchmarks in the modelling of X-ray atomic form factors
http://scripts.iucr.org/cgi-bin/paper?ae5130
Analytical representations of X-ray atomic form factor data have been determined. The original data, f0(s;Z), are reproduced to a high degree of accuracy. The mean absolute errors calculated for all s = sin θ/λ and Z values in question are primarily determined by the precision of the published data. The inverse Mott–Bethe formula is the underlying basis with the electron scattering factor expressed by an expansion in Gaussian basis functions. The number of Gaussians depends upon the element and the data and is in the range 6–20. The refinement procedure, conducted to obtain the parameters of the models, is carried out for seven different form factor tables published in the span Cromer & Mann [(1968), Acta Cryst. A24, 321–324] to Olukayode et al. [(2023), Acta Cryst. A79, 59–79]. The s ranges are finite, the most common span being [0.0, 6.0] Å−1. Only one function for each element is needed to model the full range. This presentation to a large extent makes use of a detailed graphical account of the results.https://creativecommons.org/licenses/by/4.0/Thorkildsen, G.New benchmarks in the modelling of X-ray atomic form factorsurn:issn:2053-2733doi:10.1107/S2053273323003996Improved analytical representations of X-ray atomic form factors are put forward based on the inverse Mott–Bethe formula. Applying these representations, the mean absolute errors calculated for the complete set of form factors given in Table 6.1.1.1 in International Tables for Crystallography, Vol. C, 3rd ed., are reduced by a factor of ∼50 from previous published analyses. Various form factor compilations are examined to record the applicability of the approach outlined.2023-06-02Analytical representations of X-ray atomic form factor data have been determined. The original data, f0(s;Z), are reproduced to a high degree of accuracy. The mean absolute errors calculated for all s = sin θ/λ and Z values in question are primarily determined by the precision of the published data. The inverse Mott–Bethe formula is the underlying basis with the electron scattering factor expressed by an expansion in Gaussian basis functions. The number of Gaussians depends upon the element and the data and is in the range 6–20. The refinement procedure, conducted to obtain the parameters of the models, is carried out for seven different form factor tables published in the span Cromer & Mann [(1968), Acta Cryst. A24, 321–324] to Olukayode et al. [(2023), Acta Cryst. A79, 59–79]. The s ranges are finite, the most common span being [0.0, 6.0] Å−1. Only one function for each element is needed to model the full range. This presentation to a large extent makes use of a detailed graphical account of the results.textentext/htmlATOMIC FORM FACTORS; ANALYTICAL REPRESENTATIONS; INVERSE MOTT-BETHE FORMULAInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/3304318med@iucr.orgresearch papers2023-06-02792053-2733Acta Crystallographica Section A: Foundations and AdvancesJuly 20232053-2733Crystallography of homophase twisted bilayers: coincidence, union lattices and space groups
http://scripts.iucr.org/cgi-bin/paper?nv5002
This paper presents the basic tools used to describe the global symmetry of so-called bilayer structures obtained when two differently oriented crystalline monoatomic layers of the same structure are superimposed and displaced with respect to each other. The 2D nature of the layers leads to the use of complex numbers that allows for simple explicit analytical expressions of the symmetry properties involved in standard bicrystallography [Gratias & Portier (1982). J. Phys. Colloq. 43, C6-15–C6-24; Pond & Vlachavas (1983). Proc. R. Soc. Lond. Ser. A, 386, 95–143]. The focus here is on the twist rotations such that the superimposition of the two layers generates a coincidence lattice. The set of such coincidence rotations plotted as a function of the lengths of their coincidence lattice unit-cell nodes exhibits remarkable arithmetic properties. The second part of the paper is devoted to determination of the space groups of the bilayers as a function of the rigid-body translation associated with the coincidence rotation. These general results are exemplified with a detailed study of graphene bilayers, showing that the possible symmetries of graphene bilayers with a coincidence lattice, whatever the rotation and the rigid-body translation, are distributed in only six distinct types of space groups. The appendix discusses some generalized cases of heterophase bilayers with coincidence lattices due to specific lattice constant ratios, and mechanical deformation by elongation and shear of a layer on top of an undeformed one.https://creativecommons.org/licenses/by/4.0/Gratias, D.Quiquandon, M.Crystallography of homophase twisted bilayers: coincidence, union lattices and space groupsurn:issn:2053-2733doi:10.1107/S2053273323003662A general scheme is proposed to classify and determine the crystallographic properties of twisted bilayers of any homophase 2D structures using complex numbers.2023-06-02This paper presents the basic tools used to describe the global symmetry of so-called bilayer structures obtained when two differently oriented crystalline monoatomic layers of the same structure are superimposed and displaced with respect to each other. The 2D nature of the layers leads to the use of complex numbers that allows for simple explicit analytical expressions of the symmetry properties involved in standard bicrystallography [Gratias & Portier (1982). J. Phys. Colloq. 43, C6-15–C6-24; Pond & Vlachavas (1983). Proc. R. Soc. Lond. Ser. A, 386, 95–143]. The focus here is on the twist rotations such that the superimposition of the two layers generates a coincidence lattice. The set of such coincidence rotations plotted as a function of the lengths of their coincidence lattice unit-cell nodes exhibits remarkable arithmetic properties. The second part of the paper is devoted to determination of the space groups of the bilayers as a function of the rigid-body translation associated with the coincidence rotation. These general results are exemplified with a detailed study of graphene bilayers, showing that the possible symmetries of graphene bilayers with a coincidence lattice, whatever the rotation and the rigid-body translation, are distributed in only six distinct types of space groups. The appendix discusses some generalized cases of heterophase bilayers with coincidence lattices due to specific lattice constant ratios, and mechanical deformation by elongation and shear of a layer on top of an undeformed one.textentext/htmlBICRYSTALLOGRAPHY WITH COMPLEX NUMBERS; BILAYERS; COINCIDENCE LATTICES; SPACE GROUPSInternational Union of Crystallography2053-2733Acta Crystallographica Section A: Foundations and AdvancesJuly 20232053-273379research papers2023-06-02med@iucr.org3014317https://creativecommons.org/licenses/by/4.0/Efficient structure-factor modeling for crystals with multiple components
http://scripts.iucr.org/cgi-bin/paper?pl5025
Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi-ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two-component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components.https://creativecommons.org/licenses/by/4.0/Afonine, P.V.Adams, P.D.Urzhumtsev, A.G.Efficient structure-factor modeling for crystals with multiple componentsurn:issn:2053-2733doi:10.1107/S205327332300356XA multi-component description of the unit-cell content is introduced. Efficient algorithms to define the contribution of these components to structure factors are described and implemented in CCTBX and Phenix.2023-06-20Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi-ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two-component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components.textentext/htmlSTRUCTURE FACTORS; MULTIPLE COMPONENTS; SCATTERING FUNCTIONS; BULK SOLVENT; REFINEMENT; DENSITY MAPSInternational Union of Crystallography352https://creativecommons.org/licenses/by/4.0/345med@iucr.org479research papers2023-06-202053-27332053-2733Acta Crystallographica Section A: Foundations and AdvancesJuly 2023A note on the wedge reversion antisymmetry operation and 51 types of physical quantities in arbitrary dimensions
http://scripts.iucr.org/cgi-bin/paper?ib5117
The paper by Gopalan [(2020). Acta Cryst. A76, 318–327] presented an enumeration of the 41 physical quantity types in non-relativistic physics, in arbitrary dimensions, based on the formalism of Clifford algebra. Gopalan considered three antisymmetries: spatial inversion, 1, time reversal, 1′, and wedge reversion, 1†. A consideration of the set of all seven antisymmetries (1, 1′, 1†, 1′†, 1†, 1′, 1′†) leads to an extension of the results obtained by Gopalan. It is shown that there are 51 types of physical quantities with distinct symmetry properties in total.https://creativecommons.org/licenses/by/4.0/Fabrykiewicz, P.A note on the wedge reversion antisymmetry operation and 51 types of physical quantities in arbitrary dimensionsurn:issn:2053-2733doi:10.1107/S2053273323003303It is shown that there are 51 types of physical quantities in arbitrary dimensions with distinct transformations by wedge reversion symmetry. In the paper by Gopalan [(2020). Acta Cryst. A76, 318–327] only 41 types were enumerated.2023-06-05The paper by Gopalan [(2020). Acta Cryst. A76, 318–327] presented an enumeration of the 41 physical quantity types in non-relativistic physics, in arbitrary dimensions, based on the formalism of Clifford algebra. Gopalan considered three antisymmetries: spatial inversion, 1, time reversal, 1′, and wedge reversion, 1†. A consideration of the set of all seven antisymmetries (1, 1′, 1†, 1′†, 1†, 1′, 1′†) leads to an extension of the results obtained by Gopalan. It is shown that there are 51 types of physical quantities with distinct symmetry properties in total.textentext/htmlMULTIVECTORS; WEDGE REVERSION; ANTISYMMETRY; CLIFFORD ALGEBRAInternational Union of Crystallography79short communications2023-06-052053-27332053-2733Acta Crystallographica Section A: Foundations and AdvancesJuly 2023384https://creativecommons.org/licenses/by/4.0/381med@iucr.org4Approximating lattice similarity
http://scripts.iucr.org/cgi-bin/paper?uv5018
A method is proposed for choosing unit cells for a group of crystals so that they all appear as nearly similar as possible to a selected cell. Related unit cells with varying cell parameters or indexed with different lattice centering can be accommodated.https://creativecommons.org/licenses/by/4.0/Andrews, L.C.Bernstein, H.J.Sauter, N.K.Approximating lattice similarityurn:issn:2053-2733doi:10.1107/S2053273323003200A method is proposed for transforming unit cells for a group of crystals so that they all appear as similar as possible to a selected cell.2023-07-24A method is proposed for choosing unit cells for a group of crystals so that they all appear as nearly similar as possible to a selected cell. Related unit cells with varying cell parameters or indexed with different lattice centering can be accommodated.textentext/htmlLATTICE MATCHING; DELAUNAY; DELONE; NIGGLI; SELLINGInternational Union of Crystallography484https://creativecommons.org/licenses/by/4.0/480med@iucr.org579research papers2023-07-242053-27332053-2733September 2023Acta Crystallographica Section A: Foundations and AdvancesFourier-synthesis approach for static charge-density reconstruction from theoretical structure factors of CaB6
http://scripts.iucr.org/cgi-bin/paper?pl5022
In a pilot study, electron-density (ED) and ED Laplacian distributions were reconstructed for the challenging case of CaB6 (Pearson symbol cP7) with conceptually fractional B—B bonds from quantum-chemically calculated structure-factor sets with resolutions 0.5 Å–1 ≤ [sin(θ)/λ]max ≤ 5.0 Å–1 by means of Fourier-synthesis techniques. Convergence of norm deviations of the distributions obtained with respect to the reference ones was obtained in the valence region of the unit cell. The QTAIM (quantum theory of atoms in molecules) atomic charges, and the ED and ED Laplacian values at the characteristic critical points of the Fourier-synthesized distributions have been analysed for each resolution and found to display a convergent behaviour with increasing resolution. The presented method(exponent) (ME) type of Fourier-synthesis approach can qualitatively reconstruct all characteristic chemical bonding features of the ED from valence-electron structure-factor sets with resolutions of about 1.2 Å–1 and beyond, and from all-electron structure-factor sets with resolutions of about 2.0 Å–1 and beyond. Application of the ME type of Fourier-synthesis approach for reconstruction of ED and ED Laplacian distributions at experimental resolution is proposed to complement the usual extrapolation to infinite resolution in Hansen–Coppens multipole model derived static ED distributions.https://creativecommons.org/licenses/by/4.0/Bergner, C.Grin, Y.Wagner, F.R.Fourier-synthesis approach for static charge-density reconstruction from theoretical structure factors of CaB6urn:issn:2053-2733doi:10.1107/S2053273323002644A novel type of Fourier-synthesis approach is reported for determining electron-density distributions and their Laplacians from static structure factors of CaB6. The approach relies on mathematical weighting functions to yield a data set, reproducing all characteristic chemical bonding features of the original quantum-chemically calculated distributions.2023-05-05In a pilot study, electron-density (ED) and ED Laplacian distributions were reconstructed for the challenging case of CaB6 (Pearson symbol cP7) with conceptually fractional B—B bonds from quantum-chemically calculated structure-factor sets with resolutions 0.5 Å–1 ≤ [sin(θ)/λ]max ≤ 5.0 Å–1 by means of Fourier-synthesis techniques. Convergence of norm deviations of the distributions obtained with respect to the reference ones was obtained in the valence region of the unit cell. The QTAIM (quantum theory of atoms in molecules) atomic charges, and the ED and ED Laplacian values at the characteristic critical points of the Fourier-synthesized distributions have been analysed for each resolution and found to display a convergent behaviour with increasing resolution. The presented method(exponent) (ME) type of Fourier-synthesis approach can qualitatively reconstruct all characteristic chemical bonding features of the ED from valence-electron structure-factor sets with resolutions of about 1.2 Å–1 and beyond, and from all-electron structure-factor sets with resolutions of about 2.0 Å–1 and beyond. Application of the ME type of Fourier-synthesis approach for reconstruction of ED and ED Laplacian distributions at experimental resolution is proposed to complement the usual extrapolation to infinite resolution in Hansen–Coppens multipole model derived static ED distributions.textentext/htmlELECTRON DENSITY; FOURIER TRANSFORMATION; FOURIER SYNTHESIS; HEXABORIDES; LAPLACIANInternational Union of Crystallography272https://creativecommons.org/licenses/by/4.0/246med@iucr.org3research papers2023-05-05792053-2733May 2023Acta Crystallographica Section A: Foundations and Advances2053-2733On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity
http://scripts.iucr.org/cgi-bin/paper?uv5014
Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom. In this case, they share the same value for their Shannon entropy based subdivision complexity. The enumeration of Wyckoff sequences with this property is a combinatorial problem solved in this work, first in the general case of fixed subdivision complexity but non-specified Wyckoff sequence length, and second for the restricted case of Wyckoff sequences of both fixed subdivision complexity and fixed Wyckoff sequence length. The combinatorial results are accompanied by calculations of the combinatorial, coordinational, configurational and subdivision complexities, performed on Wyckoff sequences representing actual crystal structures.https://creativecommons.org/licenses/by/4.0/Hornfeck, W.Červený, K.On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexityurn:issn:2053-2733doi:10.1107/S2053273323002437The number of Wyckoff sequences of a given subdivision complexity is calculated by means of a generating polynomial approach and a dynamic programming approach. The result depends on the choice of space-group symmetry (which is obligatory) and Wyckoff sequence length (which is optional). It also takes into account specified values for the total number of combinatorial and coordinational degrees of freedom, thereby representing crystal structures of invariant subdivision complexity.2023-05-11Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom. In this case, they share the same value for their Shannon entropy based subdivision complexity. The enumeration of Wyckoff sequences with this property is a combinatorial problem solved in this work, first in the general case of fixed subdivision complexity but non-specified Wyckoff sequence length, and second for the restricted case of Wyckoff sequences of both fixed subdivision complexity and fixed Wyckoff sequence length. The combinatorial results are accompanied by calculations of the combinatorial, coordinational, configurational and subdivision complexities, performed on Wyckoff sequences representing actual crystal structures.textentext/htmlWYCKOFF SEQUENCES; COMBINATORICS; SHANNON ENTROPY; STRUCTURAL COMPLEXITYInternational Union of Crystallographyresearch papers2023-05-1179May 2023Acta Crystallographica Section A: Foundations and Advances2053-27332053-2733https://creativecommons.org/licenses/by/4.0/2943med@iucr.org280Crystal search – feasibility study of a real-time deep learning process for crystallization well images
http://scripts.iucr.org/cgi-bin/paper?ik5007
To avoid the time-consuming and often monotonous task of manual inspection of crystallization plates, a Python-based program to automatically detect crystals in crystallization wells employing deep learning techniques was developed. The program uses manually scored crystallization trials deposited in a database of an in-house crystallization robot as a training set. Since the success rate of such a system is able to catch up with manual inspection by trained persons, it will become an important tool for crystallographers working on biological samples. Four network architectures were compared and the SqueezeNet architecture performed best. In detecting crystals AlexNet accomplished a better result, but with a lower threshold the mean value for crystal detection was improved for SqueezeNet. Two assumptions were made about the imaging rate. With these two extremes it was found that an image processing rate of at least two times, but up to 58 times in the worst case, would be needed to reach the maximum imaging rate according to the deep learning network architecture employed for real-time classification. To avoid high workloads for the control computer of the CrystalMation system, the computing is distributed over several workstations, participating voluntarily, by the grid programming system from the Berkeley Open Infrastructure for Network Computing (BOINC). The outcome of the program is redistributed into the database as automatic real-time scores (ARTscore). These are immediately visible as colored frames around each crystallization well image of the inspection program. In addition, regions of droplets with the highest scoring probability found by the system are also available as images.https://creativecommons.org/licenses/by/4.0/Thielmann, Y.Luft, T.Zint, N.Koepke, J.Crystal search – feasibility study of a real-time deep learning process for crystallization well imagesurn:issn:2053-2733doi:10.1107/S2053273323001948Four deep learning architectures were applied and SqueezeNet scored best. It was combined with the grid programming system BOINC to realize automatic real-time scoring of crystallization well images. Scores are written to a database and displayed to facilitate image inspection for users.2023-06-02To avoid the time-consuming and often monotonous task of manual inspection of crystallization plates, a Python-based program to automatically detect crystals in crystallization wells employing deep learning techniques was developed. The program uses manually scored crystallization trials deposited in a database of an in-house crystallization robot as a training set. Since the success rate of such a system is able to catch up with manual inspection by trained persons, it will become an important tool for crystallographers working on biological samples. Four network architectures were compared and the SqueezeNet architecture performed best. In detecting crystals AlexNet accomplished a better result, but with a lower threshold the mean value for crystal detection was improved for SqueezeNet. Two assumptions were made about the imaging rate. With these two extremes it was found that an image processing rate of at least two times, but up to 58 times in the worst case, would be needed to reach the maximum imaging rate according to the deep learning network architecture employed for real-time classification. To avoid high workloads for the control computer of the CrystalMation system, the computing is distributed over several workstations, participating voluntarily, by the grid programming system from the Berkeley Open Infrastructure for Network Computing (BOINC). The outcome of the program is redistributed into the database as automatic real-time scores (ARTscore). These are immediately visible as colored frames around each crystallization well image of the inspection program. In addition, regions of droplets with the highest scoring probability found by the system are also available as images.textentext/htmlBIOCRYSTALLIZATION; HIGH-THROUGHPUT SCREENING; DEEP LEARNING; NEURAL NETWORK; U-NET; ALEXNET; VGGNET; RESNET; SQUEEZENET; BOINCInternational Union of Crystallography2023-06-02research papers79July 2023Acta Crystallographica Section A: Foundations and Advances2053-27332053-2733338https://creativecommons.org/licenses/by/4.0/med@iucr.org3314Boris Gruber's contributions to mathematical crystallography
http://scripts.iucr.org/cgi-bin/paper?uv5015
Boris Gruber made fundamental contributions to the study of crystal lattices, leading to a finer classification of lattice types than those of Paul Niggli and Boris Delaunay before him.Grimmer, H.Boris Gruber's contributions to mathematical crystallographyurn:issn:2053-2733doi:10.1107/S2053273323001961Boris Gruber's fundamental contributions to the classification of crystal lattices are reviewed.2023-05-05Boris Gruber made fundamental contributions to the study of crystal lattices, leading to a finer classification of lattice types than those of Paul Niggli and Boris Delaunay before him.textentext/htmlBORIS GRUBER; CRYSTAL LATTICES; LATTICE CHARACTERS; BUERGER CELLS; NIGGLI CELL; BRAVAIS TYPES; GENERAInternational Union of Crystallography792023-05-05scientific commentaries2053-2733Acta Crystallographica Section A: Foundations and AdvancesMay 20232053-2733300med@iucr.org2953Crystal 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.https://creativecommons.org/licenses/by/4.0/Brehm, W.White, T.Chapman, H.N.Crystal diffraction prediction and partiality estimation using Gaussian basis functionsurn:issn:2053-2733doi:10.1107/S2053273323000682Reflection position, size and shape prediction and partiality estimation of crystal diffraction by integrating using a Gaussian basis are described.2023-02-17The 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.textentext/htmlPARTIALITY ESTIMATION; DIFFRACTION PREDICTION; MERGING; SERIAL SNAPSHOT CRYSTALLOGRAPHYInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/1622145med@iucr.org2023-02-17research papers792053-2733Acta Crystallographica Section A: Foundations and AdvancesMarch 20232053-2733Dynamic 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.https://creativecommons.org/licenses/by/4.0/Handley, C.M.Ward, R.E.Freeman, C.L.Reaney, I.M.Sinclair, D.C.Harding, J.H.Dynamic tilting in perovskitesurn:issn:2053-2733doi:10.1107/S2053273322011949A new computational program to analyse and extract tilt data from molecular dynamics simulations of perovskites is presented and results compared with experimental data.2023-01-23A 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.textentext/htmlPEROVSKITES; TILT; DIFFRACTION; MOLECULAR DYNAMICS; SUPERLATTICEInternational Union of Crystallography792023-01-23research papers2053-2733March 2023Acta Crystallographica Section A: Foundations and Advances2053-2733https://creativecommons.org/licenses/by/4.0/1702med@iucr.org163Dynamical 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.https://creativecommons.org/licenses/by/4.0/Drevon, T.R.Waterman, D.G.Krissinel, E.Dynamical diffraction of high-energy electrons by light-atom structures: a multiple forward scattering interpretationurn:issn:2053-2733doi:10.1107/S2053273322011779The 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.2023-02-09Because 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.textentext/htmlHIGH-ENERGY ELECTRON DIFFRACTION; T-MATRIX; MULTIPLE SCATTERING; INDEPENDENT ATOM APPROXIMATIONInternational Union of Crystallography79research papers2023-02-092053-27332053-2733March 2023Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/1912180med@iucr.orgA phase retrieval algorithm for triply periodic minimal surface like structures
http://scripts.iucr.org/cgi-bin/paper?ik5006
A method to solve the crystallographic phase problem of materials with triply periodic minimal surface like structures, such as lyotropic liquid crystal bicontinuous cubic phases, is reported. In triply periodic minimal surface like structures, the difference between the maximum and minimum electron densities tends to be the smallest for the true phase combination among the possible combinations [Oka (2022). Acta Cryst. A78, 430–436]. Using this feature, a new iterative phase retrieval algorithm for structure determination was developed. The algorithm modifies electron densities outside the upper and lower thresholds in the iterative Fourier transformation process with fixed amplitudes for the structure factors, and efficiently searches for the structure with the smallest difference between the maximum and minimum electron densities. The proper structure was determined by this algorithm for all tested data for lyotropic liquid crystal bicontinuous cubic phases and mesoporous silicas. Although some cases required constraints such as the volume fraction for structure determination, more than half could be determined without any constraints, including space groups.https://creativecommons.org/licenses/by/4.0/Oka, T.A phase retrieval algorithm for triply periodic minimal surface like structuresurn:issn:2053-2733doi:10.1107/S2053273322010786A method to solve the crystallographic phase problem of materials with triply periodic minimal surface like structures, such as lyotropic liquid crystal bicontinuous cubic phases, is reported.2023-01-01A method to solve the crystallographic phase problem of materials with triply periodic minimal surface like structures, such as lyotropic liquid crystal bicontinuous cubic phases, is reported. In triply periodic minimal surface like structures, the difference between the maximum and minimum electron densities tends to be the smallest for the true phase combination among the possible combinations [Oka (2022). Acta Cryst. A78, 430–436]. Using this feature, a new iterative phase retrieval algorithm for structure determination was developed. The algorithm modifies electron densities outside the upper and lower thresholds in the iterative Fourier transformation process with fixed amplitudes for the structure factors, and efficiently searches for the structure with the smallest difference between the maximum and minimum electron densities. The proper structure was determined by this algorithm for all tested data for lyotropic liquid crystal bicontinuous cubic phases and mesoporous silicas. Although some cases required constraints such as the volume fraction for structure determination, more than half could be determined without any constraints, including space groups.textentext/htmlCRYSTALLOGRAPHIC PHASE RETRIEVAL; LYOTROPIC LIQUID CRYSTALS; MESOPOROUS SILICA; TRIPLY PERIODIC MINIMAL SURFACESInternational Union of Crystallography792023-01-01research papers2053-27332053-2733Acta Crystallographica Section A: Foundations and AdvancesJanuary 2023https://creativecommons.org/licenses/by/4.0/58151med@iucr.org