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) 2024 International Union of CrystallographyInternational Union of CrystallographyInternational Union of CrystallographyActa 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/htmlurn:issn:0108-7673https://journals.iucr.orgOpen-access and free articles in Acta Crystallographica Section A Foundations and Advancestext2002-01-01T00:00+00:006yearlyurn:issn:0108-7673Acta Crystallographica Section A Foundations and AdvancesCopyright (c) 2024 International Union of Crystallographymed@iucr.orgOpen-access and free articles in Acta Crystallographica Section A: Foundations and Advanceshttp://journals.iucr.org/logos/rss10a.gif
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Still imageUniversal simulation of absorption effects for X-ray diffraction in reflection geometry
https://journals.iucr.org/paper?wo5048
Analytical calculations of absorption corrections for X-ray powder diffraction experiments on non-ideal samples with surface roughness, porosity or absorption contrasts from multiple phases require complex mathematical models to represent their material distribution. In a computational approach to this problem, a practicable ray-tracing algorithm is formulated which is capable of simulating angle-dependent absorption corrections in reflection geometry for any given rasterized sample model. Single or multiphase systems with arbitrary surface roughness, porosity and spatial distribution of the phases in any combination can be modeled on a voxel grid by assigning respective values to each voxel. The absorption corrections are calculated by tracing the attenuation of X-rays along their individual paths via a modified shear-warp algorithm. The algorithm is presented in detail and the results of simulated absorption corrections on samples with various surface modulations are discussed in the context of published experimental results.2024-06-07Analytical calculations of absorption corrections for X-ray powder diffraction experiments on non-ideal samples with surface roughness, porosity or absorption contrasts from multiple phases require complex mathematical models to represent their material distribution. In a computational approach to this problem, a practicable ray-tracing algorithm is formulated which is capable of simulating angle-dependent absorption corrections in reflection geometry for any given rasterized sample model. Single or multiphase systems with arbitrary surface roughness, porosity and spatial distribution of the phases in any combination can be modeled on a voxel grid by assigning respective values to each voxel. The absorption corrections are calculated by tracing the attenuation of X-rays along their individual paths via a modified shear-warp algorithm. The algorithm is presented in detail and the results of simulated absorption corrections on samples with various surface modulations are discussed in the context of published experimental results.text/htmldoi:10.1107/S2053273324003292enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733ABSORPTION CORRECTIONS; MICROSTRUCTURE; RAY-TRACING; SURFACE ROUGHNESS; POWDER DIFFRACTIONUniversal simulation of absorption effects for X-ray diffraction in reflection geometrytextJuly 20242053-27333282053-2733Acta Crystallographica Section A: Foundations and Advancesmed@iucr.orghttps://creativecommons.org/licenses/by/4.0/803152024-06-074research papersDallmann, J.Graetz, J.Hock, R.

GraphT–T (V1.0Beta), a program for embedding and visualizing periodic graphs in 3D Euclidean space
https://journals.iucr.org/paper?uv5025
Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212–233] and Day et al. [Acta Cryst. (2024), A80, 258–281], the program GraphT–T has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4− tetrahedra into 2D and 3D Euclidean space. During embedding, the distance between linked vertices (T–T distances) and the distance between unlinked vertices (T⋯T separations) in the resultant unit-distance graph are restrained to the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is restrained to be equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. The notional interactions between vertices are described by a 3D spring-force algorithm in which the attractive forces between linked vertices behave according to Hooke's law and the repulsive forces between unlinked vertices behave according to Coulomb's law. Embedding parameters (i.e. spring coefficient, k, and Coulomb's constant, K) are iteratively refined during embedding to determine if it is possible to embed a given graph to produce a unit-distance graph with T–T distances and T⋯T separations that are compatible with the observed T–T distances and T⋯T separations in crystal structures. The resultant unit-distance graphs are denoted as compatible and may form crystal structures if and only if all distances between linked vertices (T–T distances) agree with the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. If the unit-distance graph does not satisfy these conditions, it is considered incompatible and the corresponding chain of tetrahedra is unlikely to form crystal structures. Using GraphT–T, Day et al. [Acta Cryst. (2024), A80, 258–281] have shown that several topological properties of chain graphs influence the flexibility (and rigidity) of the corresponding chains of Si tetrahedra and may explain why particular compatible chain arrangements (and the minerals in which they occur) are more common than others and/or why incompatible chain arrangements do not occur in crystals despite being topologically possible.2024-04-29Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212–233] and Day et al. [Acta Cryst. (2024), A80, 258–281], the program GraphT–T has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4− tetrahedra into 2D and 3D Euclidean space. During embedding, the distance between linked vertices (T–T distances) and the distance between unlinked vertices (T⋯T separations) in the resultant unit-distance graph are restrained to the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is restrained to be equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. The notional interactions between vertices are described by a 3D spring-force algorithm in which the attractive forces between linked vertices behave according to Hooke's law and the repulsive forces between unlinked vertices behave according to Coulomb's law. Embedding parameters (i.e. spring coefficient, k, and Coulomb's constant, K) are iteratively refined during embedding to determine if it is possible to embed a given graph to produce a unit-distance graph with T–T distances and T⋯T separations that are compatible with the observed T–T distances and T⋯T separations in crystal structures. The resultant unit-distance graphs are denoted as compatible and may form crystal structures if and only if all distances between linked vertices (T–T distances) agree with the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. If the unit-distance graph does not satisfy these conditions, it is considered incompatible and the corresponding chain of tetrahedra is unlikely to form crystal structures. Using GraphT–T, Day et al. [Acta Cryst. (2024), A80, 258–281] have shown that several topological properties of chain graphs influence the flexibility (and rigidity) of the corresponding chains of Si tetrahedra and may explain why particular compatible chain arrangements (and the minerals in which they occur) are more common than others and/or why incompatible chain arrangements do not occur in crystals despite being topologically possible.text/htmldoi:10.1107/S2053273324002523enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733BOND TOPOLOGY; CHAINS OF TETRAHEDRA; (SIO4)4- TETRAHEDRA; GRAPH EMBEDDING PROGRAM; 3D EUCLIDEAN SPACE; 3D SPRING-FORCE ALGORITHM; GRAPHT-TGraphT–T (V1.0Beta), a program for embedding and visualizing periodic graphs in 3D Euclidean spacetextActa Crystallographica Section A: Foundations and Advancesmed@iucr.orghttps://creativecommons.org/licenses/by/4.0/802823research papers2024-04-292053-2733May 20242053-2733292Day, M.C.Rostami, A.Hawthorne, F.C.

Bond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO4)n− tetrahedra
https://journals.iucr.org/paper?uv5024
In Part I of this series, all topologically possible 1-periodic infinite graphs (chain graphs) representing chains of tetrahedra with up to 6–8 vertices (tetrahedra) per repeat unit were generated. This paper examines possible restraints on embedding these chain graphs into Euclidean space such that they are compatible with the metrics of chains of tetrahedra in observed crystal structures. Chain-silicate minerals with T = Si4+ (plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+) have a grand nearest-neighbour 〈T–T〉 distance of 3.06±0.15 Å and a minimum T⋯T separation of 3.71 Å between non-nearest-neighbour tetrahedra, and in order for embedded chain graphs (called unit-distance graphs) to be possible atomic arrangements in crystals, they must conform to these metrics, a process termed equalization. It is shown that equalization of all acyclic chain graphs is possible in 2D and 3D, and that equalization of most cyclic chain graphs is possible in 3D but not necessarily in 2D. All unique ways in which non-isomorphic vertices may be moved are designated modes of geometric modification. If a mode (m) is applied to an equalized unit-distance graph such that a new geometrically distinct unit-distance graph is produced without changing the lengths of any edges, the mode is designated as valid (mv); if a new geometrically distinct unit-distance graph cannot be produced, the mode is invalid (mi). The parameters mv and mi are used to define ranges of rigidity of the unit-distance graphs, and are related to the edge-to-vertex ratio, e/n, of the parent chain graph. The program GraphT–T was developed to embed any chain graph into Euclidean space subject to the metric restraints on T–T and T⋯T. Embedding a selection of chain graphs with differing e/n ratios shows that the principal reason why many topologically possible chains cannot occur in crystal structures is due to violation of the requirement that T⋯T > 3.71 Å. Such a restraint becomes increasingly restrictive as e/n increases and indicates why chains with stoichiometry TO<2.5 do not occur in crystal structures.2024-04-29In Part I of this series, all topologically possible 1-periodic infinite graphs (chain graphs) representing chains of tetrahedra with up to 6–8 vertices (tetrahedra) per repeat unit were generated. This paper examines possible restraints on embedding these chain graphs into Euclidean space such that they are compatible with the metrics of chains of tetrahedra in observed crystal structures. Chain-silicate minerals with T = Si4+ (plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+) have a grand nearest-neighbour 〈T–T〉 distance of 3.06±0.15 Å and a minimum T⋯T separation of 3.71 Å between non-nearest-neighbour tetrahedra, and in order for embedded chain graphs (called unit-distance graphs) to be possible atomic arrangements in crystals, they must conform to these metrics, a process termed equalization. It is shown that equalization of all acyclic chain graphs is possible in 2D and 3D, and that equalization of most cyclic chain graphs is possible in 3D but not necessarily in 2D. All unique ways in which non-isomorphic vertices may be moved are designated modes of geometric modification. If a mode (m) is applied to an equalized unit-distance graph such that a new geometrically distinct unit-distance graph is produced without changing the lengths of any edges, the mode is designated as valid (mv); if a new geometrically distinct unit-distance graph cannot be produced, the mode is invalid (mi). The parameters mv and mi are used to define ranges of rigidity of the unit-distance graphs, and are related to the edge-to-vertex ratio, e/n, of the parent chain graph. The program GraphT–T was developed to embed any chain graph into Euclidean space subject to the metric restraints on T–T and T⋯T. Embedding a selection of chain graphs with differing e/n ratios shows that the principal reason why many topologically possible chains cannot occur in crystal structures is due to violation of the requirement that T⋯T > 3.71 Å. Such a restraint becomes increasingly restrictive as e/n increases and indicates why chains with stoichiometry TO<2.5 do not occur in crystal structures.text/htmldoi:10.1107/S2053273324002432enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733BOND TOPOLOGY; [TO4]N- TETRAHEDRA; CHAINS OF TETRAHEDRA; CHAIN GRAPH; GRAPH EMBEDDING; EUCLIDEAN SPACEBond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO4)n− tetrahedratext2024-04-29research papers325880med@iucr.orghttps://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2812053-2733May 20242053-2733Day, M.C.Hawthorne, F.C.Rostami, A.

Permissible domain walls in monoclinic ferroelectrics. Part II. The case of MC phases
https://journals.iucr.org/paper?lu5034
Monoclinic ferroelectric phases are prevalent in various functional materials, most notably mixed-ion perovskite oxides. These phases can manifest as regularly ordered long-range crystallographic structures or as macroscopic averages of the self-assembled tetragonal/rhombohedral nanodomains. The structural and physical properties of monoclinic ferroelectric phases play a pivotal role when exploring the interplay between ferroelectricity, ferroelasticity, giant piezoelectricity and multiferroicity in crystals, ceramics and epitaxial thin films. However, the complex nature of this subject presents challenges, particularly in deciphering the microstructures of monoclinic domains. In Paper I [Biran & Gorfman (2024). Acta Cryst. A80, 112–128] the geometrical principles governing the connection of domain microstructures formed by pairing MAB type monoclinic domains were elucidated. Specifically, a catalog was established of `permissible domain walls', where `permissible', as originally introduced by Fousek & Janovec [J. Appl. Phys. (1969), 40, 135–142], denotes a mismatch-free connection between two monoclinic domains along the corresponding domain wall. The present article continues the prior work by elaborating on the formalisms of permissible domain walls to describe domain microstructures formed by pairing the MC type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for MC type domains. Each permissible domain wall is characterized by Miller indices, the transformation matrix between the crystallographic basis vectors of the domains and, crucially, the expected separation of Bragg peaks diffracted from the matched pair of domains. All these parameters are provided in an analytical form for easy and intuitive interpretation of the results. Additionally, 2D illustrations are provided for selected instances of permissible domain walls. The findings can prove valuable for various domain-related calculations, investigations involving X-ray diffraction for domain analysis and the description of domain-related physical properties.2024-04-29Monoclinic ferroelectric phases are prevalent in various functional materials, most notably mixed-ion perovskite oxides. These phases can manifest as regularly ordered long-range crystallographic structures or as macroscopic averages of the self-assembled tetragonal/rhombohedral nanodomains. The structural and physical properties of monoclinic ferroelectric phases play a pivotal role when exploring the interplay between ferroelectricity, ferroelasticity, giant piezoelectricity and multiferroicity in crystals, ceramics and epitaxial thin films. However, the complex nature of this subject presents challenges, particularly in deciphering the microstructures of monoclinic domains. In Paper I [Biran & Gorfman (2024). Acta Cryst. A80, 112–128] the geometrical principles governing the connection of domain microstructures formed by pairing MAB type monoclinic domains were elucidated. Specifically, a catalog was established of `permissible domain walls', where `permissible', as originally introduced by Fousek & Janovec [J. Appl. Phys. (1969), 40, 135–142], denotes a mismatch-free connection between two monoclinic domains along the corresponding domain wall. The present article continues the prior work by elaborating on the formalisms of permissible domain walls to describe domain microstructures formed by pairing the MC type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for MC type domains. Each permissible domain wall is characterized by Miller indices, the transformation matrix between the crystallographic basis vectors of the domains and, crucially, the expected separation of Bragg peaks diffracted from the matched pair of domains. All these parameters are provided in an analytical form for easy and intuitive interpretation of the results. Additionally, 2D illustrations are provided for selected instances of permissible domain walls. The findings can prove valuable for various domain-related calculations, investigations involving X-ray diffraction for domain analysis and the description of domain-related physical properties.text/htmldoi:10.1107/S2053273324002419enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733FERROELASTIC DOMAINS; MONOCLINIC SYMMETRY; X-RAY DIFFRACTIONPermissible domain walls in monoclinic ferroelectrics. Part II. The case of MC phasestext2053-27333042053-2733May 20243research papers2024-04-2980293Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/med@iucr.orgBiran, I.Gorfman, S.

N-representable one-electron reduced density matrix reconstruction with frozen core electrons
https://journals.iucr.org/paper?pl5038
Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.2024-03-21Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.text/htmldoi:10.1107/S2053273324001645enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733QUANTUM CRYSTALLOGRAPHY; REDUCED DENSITY MATRIX; COMPTON SCATTERING; X-RAY DIFFRACTIONN-representable one-electron reduced density matrix reconstruction with frozen core electronstext2024-03-213research papers80249Acta Crystallographica Section A: Foundations and Advancesmed@iucr.orghttps://creativecommons.org/licenses/by/4.0/2572053-2733May 20242053-2733Yu, S.Gillet, J.-M.

The single-atom R1: a new optimization method to solve crystal structures
https://journals.iucr.org/paper?ae5140
A crystal structure with N atoms in its unit cell can be solved starting from a model with atoms 1 to j − 1 being located. To locate the next atom j, the method uses a modified definition of the traditional R1 factor where its dependencies on the locations of atoms j + 1 to N are removed. This modified R1 is called the single-atom R1 (sR1), because the locations of atoms 1 to j − 1 in sR1 are the known parameters, and only the location of atom j is unknown. Finding the correct position of atom j translates thus into the optimization of the sR1 function, with respect to its fractional coordinates, xj, yj, zj. Using experimental data, it has been verified that an sR1 has a hole near each missing atom. Further, it has been verified that an algorithm based on sR1, hereby called the sR1 method, can solve crystal structures (with up to 156 non-hydrogen atoms in the unit cell). The strategy to carry out this calculation has also been optimized. The main feature of the sR1 method is that, starting from a single arbitrarily positioned atom, the structure is gradually revealed. With the user's help to delete poorly determined parts of the structure, the sR1 method can build the model to a high final quality. Thus, sR1 is a viable and useful tool for solving crystal structures.2024-03-18A crystal structure with N atoms in its unit cell can be solved starting from a model with atoms 1 to j − 1 being located. To locate the next atom j, the method uses a modified definition of the traditional R1 factor where its dependencies on the locations of atoms j + 1 to N are removed. This modified R1 is called the single-atom R1 (sR1), because the locations of atoms 1 to j − 1 in sR1 are the known parameters, and only the location of atom j is unknown. Finding the correct position of atom j translates thus into the optimization of the sR1 function, with respect to its fractional coordinates, xj, yj, zj. Using experimental data, it has been verified that an sR1 has a hole near each missing atom. Further, it has been verified that an algorithm based on sR1, hereby called the sR1 method, can solve crystal structures (with up to 156 non-hydrogen atoms in the unit cell). The strategy to carry out this calculation has also been optimized. The main feature of the sR1 method is that, starting from a single arbitrarily positioned atom, the structure is gradually revealed. With the user's help to delete poorly determined parts of the structure, the sR1 method can build the model to a high final quality. Thus, sR1 is a viable and useful tool for solving crystal structures.text/htmldoi:10.1107/S2053273324001554enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733STRUCTURE SOLUTION; GLOBAL MINIMIZATION; SINGLE-ATOM R1; MOLECULAR REPLACEMENTThe single-atom R1: a new optimization method to solve crystal structurestext2024-03-18research papers323780https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advances2482053-2733May 20242053-2733Zhang, X.Donahue, J.P.

ClusterFinder: a fast tool to find cluster structures from pair distribution function data
https://journals.iucr.org/paper?tw5008
A novel automated high-throughput screening approach, ClusterFinder, is reported for finding candidate structures for atomic pair distribution function (PDF) structural refinements. Finding starting models for PDF refinements is notoriously difficult when the PDF originates from nanoclusters or small nanoparticles. The reported ClusterFinder algorithm can screen 104 to 105 candidate structures from structural databases such as the Inorganic Crystal Structure Database (ICSD) in minutes, using the crystal structures as templates in which it looks for atomic clusters that result in a PDF similar to the target measured PDF. The algorithm returns a rank-ordered list of clusters for further assessment by the user. The algorithm has performed well for simulated and measured PDFs of metal–oxido clusters such as Keggin clusters. This is therefore a powerful approach to finding structural cluster candidates in a modelling campaign for PDFs of nanoparticles and nanoclusters.2024-02-29A novel automated high-throughput screening approach, ClusterFinder, is reported for finding candidate structures for atomic pair distribution function (PDF) structural refinements. Finding starting models for PDF refinements is notoriously difficult when the PDF originates from nanoclusters or small nanoparticles. The reported ClusterFinder algorithm can screen 104 to 105 candidate structures from structural databases such as the Inorganic Crystal Structure Database (ICSD) in minutes, using the crystal structures as templates in which it looks for atomic clusters that result in a PDF similar to the target measured PDF. The algorithm returns a rank-ordered list of clusters for further assessment by the user. The algorithm has performed well for simulated and measured PDFs of metal–oxido clusters such as Keggin clusters. This is therefore a powerful approach to finding structural cluster candidates in a modelling campaign for PDFs of nanoparticles and nanoclusters.text/htmldoi:10.1107/S2053273324001116enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733PAIR DISTRIBUTION FUNCTION ANALYSIS; NANOCLUSTERS; NANOMATERIALS; SCREENINGClusterFinder: a fast tool to find cluster structures from pair distribution function datatext2202053-2733March 20242053-27332024-02-29research papers2https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advances21380Anker, A.S.Friis-Jensen, U.Johansen, F.L.Billinge, S.J.L.Jensen, K.M.Ø.

Automated selection of nanoparticle models for small-angle X-ray scattering data analysis using machine learning
https://journals.iucr.org/paper?iv5034
Small-angle X-ray scattering (SAXS) is widely used to analyze the shape and size of nanoparticles in solution. A multitude of models, describing the SAXS intensity resulting from nanoparticles of various shapes, have been developed by the scientific community and are used for data analysis. Choosing the optimal model is a crucial step in data analysis, which can be difficult and time-consuming, especially for non-expert users. An algorithm is proposed, based on machine learning, representation learning and SAXS-specific preprocessing methods, which instantly selects the nanoparticle model best suited to describe SAXS data. The different algorithms compared are trained and evaluated on a simulated database. This database includes 75 000 scattering spectra from nine nanoparticle models, and realistically simulates two distinct device configurations. It will be made freely available to serve as a basis of comparison for future work. Deploying a universal solution for automatic nanoparticle model selection is a challenge made more difficult by the diversity of SAXS instruments and their flexible settings. The poor transferability of classification rules learned on one device configuration to another is highlighted. It is shown that training on several device configurations enables the algorithm to be generalized, without degrading performance compared with configuration-specific training. Finally, the classification algorithm is evaluated on a real data set obtained by performing SAXS experiments on nanoparticles for each of the instrumental configurations, which have been characterized by transmission electron microscopy. This data set, although very limited, allows estimation of the transferability of the classification rules learned on simulated data to real data.2024-02-29Small-angle X-ray scattering (SAXS) is widely used to analyze the shape and size of nanoparticles in solution. A multitude of models, describing the SAXS intensity resulting from nanoparticles of various shapes, have been developed by the scientific community and are used for data analysis. Choosing the optimal model is a crucial step in data analysis, which can be difficult and time-consuming, especially for non-expert users. An algorithm is proposed, based on machine learning, representation learning and SAXS-specific preprocessing methods, which instantly selects the nanoparticle model best suited to describe SAXS data. The different algorithms compared are trained and evaluated on a simulated database. This database includes 75 000 scattering spectra from nine nanoparticle models, and realistically simulates two distinct device configurations. It will be made freely available to serve as a basis of comparison for future work. Deploying a universal solution for automatic nanoparticle model selection is a challenge made more difficult by the diversity of SAXS instruments and their flexible settings. The poor transferability of classification rules learned on one device configuration to another is highlighted. It is shown that training on several device configurations enables the algorithm to be generalized, without degrading performance compared with configuration-specific training. Finally, the classification algorithm is evaluated on a real data set obtained by performing SAXS experiments on nanoparticles for each of the instrumental configurations, which have been characterized by transmission electron microscopy. This data set, although very limited, allows estimation of the transferability of the classification rules learned on simulated data to real data.text/htmldoi:10.1107/S2053273324000950enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733MACHINE LEARNING; NANOPARTICLES; SAXS; SMALL-ANGLE X-RAY SCATTERING; DATA ANALYSIS; MODEL SELECTIONAutomated selection of nanoparticle models for small-angle X-ray scattering data analysis using machine learningtextMarch 20242053-27332122053-273380202Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/med@iucr.org2024-02-292research papersMonge, N.Deschamps, A.Amini, M.-R.

Universal parameters of bulk-solvent masks
https://journals.iucr.org/paper?pl5035
The bulk solvent is a major component of biomacromolecular crystals that contributes significantly to the observed diffraction intensities. Accurate modelling of the bulk solvent has been recognized as important for many crystallographic calculations. Owing to its simplicity and modelling power, the flat (mask-based) bulk-solvent model is used by most modern crystallographic software packages to account for disordered solvent. In this model, the bulk-solvent contribution is defined by a binary mask and a scale (scattering) function. The mask is calculated on a regular grid using the atomic model coordinates and their chemical types. The grid step and two radii, solvent and shrinkage, are the three parameters that govern the mask calculation. They are highly correlated and their choice is a compromise between the computer time needed to calculate the mask and the accuracy of the mask. It is demonstrated here that this choice can be optimized using a unique value of 0.6 Å for the grid step irrespective of the data resolution, and the radii values adjusted correspondingly. The improved values were tested on a large sample of Protein Data Bank entries derived from X-ray diffraction data and are now used in the computational crystallography toolbox (CCTBX) and in Phenix as the default choice.2024-02-09The bulk solvent is a major component of biomacromolecular crystals that contributes significantly to the observed diffraction intensities. Accurate modelling of the bulk solvent has been recognized as important for many crystallographic calculations. Owing to its simplicity and modelling power, the flat (mask-based) bulk-solvent model is used by most modern crystallographic software packages to account for disordered solvent. In this model, the bulk-solvent contribution is defined by a binary mask and a scale (scattering) function. The mask is calculated on a regular grid using the atomic model coordinates and their chemical types. The grid step and two radii, solvent and shrinkage, are the three parameters that govern the mask calculation. They are highly correlated and their choice is a compromise between the computer time needed to calculate the mask and the accuracy of the mask. It is demonstrated here that this choice can be optimized using a unique value of 0.6 Å for the grid step irrespective of the data resolution, and the radii values adjusted correspondingly. The improved values were tested on a large sample of Protein Data Bank entries derived from X-ray diffraction data and are now used in the computational crystallography toolbox (CCTBX) and in Phenix as the default choice.text/htmldoi:10.1107/S2053273324000299enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733BULK-SOLVENT MODELLING; FLAT MODELS; SOLVENT MASKS; GRID STEPS; MASK PARAMETERSUniversal parameters of bulk-solvent maskstext2024-02-09research papers219480https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advances2012053-2733March 20242053-2733Urzhumtsev, A.Adams, P.Afonine, P.

Parameterized absorptive electron scattering factors
https://journals.iucr.org/paper?pl5034
In electron diffraction, thermal atomic motion produces incoherent scattering over a relatively wide angular range, which appears as a diffuse background that is usually subtracted from measurements of Bragg spot intensities in structure solution methods. The transfer of electron flux from Bragg spots to diffuse scatter is modelled using complex scattering factors f + if′ in the Bloch wave methodology. In a two-beam Einstein model the imaginary `absorptive' scattering factor f′ can be obtained by the evaluation of an integral containing f over all possible scattering angles. While more sophisticated models of diffuse scatter are widely used in the electron microscopy community, it is argued in this paper that this simple model is appropriate for current structure solution and refinement methods. The two-beam model is a straightforward numerical calculation, but even this simplistic approach can become time consuming for simulations of materials with large numbers of atoms in the unit cell and/or many incident beam orientations. Here, a parameterized form of f′ is provided for 103 elements as neutral, spherical atoms that reduces calculation time considerably.2024-01-25In electron diffraction, thermal atomic motion produces incoherent scattering over a relatively wide angular range, which appears as a diffuse background that is usually subtracted from measurements of Bragg spot intensities in structure solution methods. The transfer of electron flux from Bragg spots to diffuse scatter is modelled using complex scattering factors f + if′ in the Bloch wave methodology. In a two-beam Einstein model the imaginary `absorptive' scattering factor f′ can be obtained by the evaluation of an integral containing f over all possible scattering angles. While more sophisticated models of diffuse scatter are widely used in the electron microscopy community, it is argued in this paper that this simple model is appropriate for current structure solution and refinement methods. The two-beam model is a straightforward numerical calculation, but even this simplistic approach can become time consuming for simulations of materials with large numbers of atoms in the unit cell and/or many incident beam orientations. Here, a parameterized form of f′ is provided for 103 elements as neutral, spherical atoms that reduces calculation time considerably.text/htmldoi:10.1107/S2053273323010963enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733ELECTRON DIFFRACTION; ABSORPTION; 3D-ED; THREE-DIMENSIONAL ELECTRON DIFFRACTION; THERMAL DIFFUSE SCATTERINGParameterized absorptive electron scattering factorstext2research papers2024-01-2580146Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/med@iucr.org2053-27331502053-2733March 2024Thomas, M.Cleverley, A.Beanland, R.

Modelling dynamical 3D electron diffraction intensities. I. A scattering cluster algorithm
https://journals.iucr.org/paper?tw5006
Three-dimensional electron diffraction (3D-ED) is a powerful technique for crystallographic characterization of nanometre-sized crystals that are too small for X-ray diffraction. For accurate crystal structure refinement, however, it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D-ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Proposed here is an alternative method, the `scattering cluster algorithm' (SCA), that replaces the eigen-decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by intensity transfer (i.e. `scattering') from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to the multislice approach. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA are demonstrated on tri-isopropyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells.2024-01-25Three-dimensional electron diffraction (3D-ED) is a powerful technique for crystallographic characterization of nanometre-sized crystals that are too small for X-ray diffraction. For accurate crystal structure refinement, however, it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D-ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Proposed here is an alternative method, the `scattering cluster algorithm' (SCA), that replaces the eigen-decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by intensity transfer (i.e. `scattering') from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to the multislice approach. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA are demonstrated on tri-isopropyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells.text/htmldoi:10.1107/S2053273323010689enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733DYNAMICAL ELECTRON DIFFRACTION; BLOCH WAVES; STRUCTURE MATRIX; MULTISLICEModelling dynamical 3D electron diffraction intensities. I. A scattering cluster algorithmtext2053-2733March 20242053-273317716780https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advancesresearch papers22024-01-25Mendis, B.

Modelling dynamical 3D electron diffraction intensities. II. The role of inelastic scattering
https://journals.iucr.org/paper?tw5007
The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave–Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.2024-01-25The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave–Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.text/htmldoi:10.1107/S2053273323010690enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733INELASTIC DIFFUSE SCATTERING; PHONONS; PLASMONS; BLOCH WAVESModelling dynamical 3D electron diffraction intensities. II. The role of inelastic scatteringtext2053-2733March 20242053-273318880178Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/med@iucr.org2research papers2024-01-25Mendis, B.

Analytical models representing X-ray form factors of ions
https://journals.iucr.org/paper?ae5139
Parameters in analytical models for X-ray form factors of ions f0(s), based on the inverse Mott–Bethe formula involving a variable number of Gaussians, are determined for a wide range of published data sets {s, f0(s)}. The models reproduce the calculated form-factor values close to what is expected from a uniform statistical distribution with limits determined by their precision. For different ions associated with the same atom, the number of Gaussians in the models decreases with increasing net positive charge.2024-01-01Parameters in analytical models for X-ray form factors of ions f0(s), based on the inverse Mott–Bethe formula involving a variable number of Gaussians, are determined for a wide range of published data sets {s, f0(s)}. The models reproduce the calculated form-factor values close to what is expected from a uniform statistical distribution with limits determined by their precision. For different ions associated with the same atom, the number of Gaussians in the models decreases with increasing net positive charge.text/htmldoi:10.1107/S2053273323010550enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733X-RAY FORM FACTORS; INVERSE MOTT-BETHE FORMULA; ANALYTICAL REPRESENTATIONS; IONSAnalytical models representing X-ray form factors of ionstext2053-2733January 20242053-273313612980https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advancesresearch papers12024-01-01Thorkildsen, G.

Deep learning applications in protein crystallography
https://journals.iucr.org/paper?ae5136
Deep learning techniques can recognize complex patterns in noisy, multidimensional data. In recent years, researchers have started to explore the potential of deep learning in the field of structural biology, including protein crystallography. This field has some significant challenges, in particular producing high-quality and well ordered protein crystals. Additionally, collecting diffraction data with high completeness and quality, and determining and refining protein structures can be problematic. Protein crystallographic data are often high-dimensional, noisy and incomplete. Deep learning algorithms can extract relevant features from these data and learn to recognize patterns, which can improve the success rate of crystallization and the quality of crystal structures. This paper reviews progress in this field.2024-01-01Deep learning techniques can recognize complex patterns in noisy, multidimensional data. In recent years, researchers have started to explore the potential of deep learning in the field of structural biology, including protein crystallography. This field has some significant challenges, in particular producing high-quality and well ordered protein crystals. Additionally, collecting diffraction data with high completeness and quality, and determining and refining protein structures can be problematic. Protein crystallographic data are often high-dimensional, noisy and incomplete. Deep learning algorithms can extract relevant features from these data and learn to recognize patterns, which can improve the success rate of crystallization and the quality of crystal structures. This paper reviews progress in this field.text/htmldoi:10.1107/S2053273323009300enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733PROTEIN CRYSTALLOGRAPHY; DEEP LEARNING; ARTIFICIAL INTELLIGENCE; MACHINE LEARNINGDeep learning applications in protein crystallographytext2053-2733172053-2733January 2024lead articles12024-01-01med@iucr.orghttps://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances180Matinyan, S.Filipcik, P.Abrahams, J.P.

Permissible domain walls in monoclinic MAB ferroelectric phases
https://journals.iucr.org/paper?lu5030
The concept of monoclinic ferroelectric phases has been extensively used over recent decades for the understanding of crystallographic structures of ferroelectric materials. Monoclinic phases have been actively invoked to describe the phase boundaries such as the so-called morphotropic phase boundary in functional perovskite oxides. These phases are believed to play a major role in the enhancement of such functional properties as dielectricity and electromechanical coupling through rotation of spontaneous polarization and/or modification of the rich domain microstructures. Unfortunately, such microstructures remain poorly understood due to the complexity of the subject. The goal of this work is to formulate the geometrical laws behind the monoclinic domain microstructures. Specifically, the result of previous work [Gorfman et al. (2022). Acta Cryst. A78, 158–171] is implemented to catalog and outline some properties of permissible domain walls that connect `strain' domains with monoclinic (MA/MB type) symmetry, occurring in ferroelectric perovskite oxides. The term `permissible' [Fousek & Janovec (1969). J. Appl. Phys. 40, 135–142] pertains to the domain walls connecting a pair of `strain' domains without a lattice mismatch. It was found that 12 monoclinic domains may form pairs connected along 84 types of permissible domain walls. These contain 48 domain walls with fixed Miller indices (known as W-walls) and 36 domain walls whose Miller indices may change when free lattice parameters change as well (known as S-walls). Simple and intuitive analytical expressions are provided that describe the orientation of these domain walls, the matrices of transformation between crystallographic basis vectors and, most importantly, the separation between Bragg peaks, diffracted from each of the 84 pairs of domains, connected along a permissible domain wall. It is shown that the orientation of a domain wall may be described by the specific combination of the monoclinic distortion parameters r = [2/(γ − α)][(c/a) − 1], f = (π − 2γ)/(π − 2α) and p = [2/(π − α − γ)] [(c/a) − 1]. The results of this work will enhance understanding and facilitate investigation (e.g. using single-crystal X-ray diffraction) of complex monoclinic domain microstructures in both crystals and thin films.2024-01-01The concept of monoclinic ferroelectric phases has been extensively used over recent decades for the understanding of crystallographic structures of ferroelectric materials. Monoclinic phases have been actively invoked to describe the phase boundaries such as the so-called morphotropic phase boundary in functional perovskite oxides. These phases are believed to play a major role in the enhancement of such functional properties as dielectricity and electromechanical coupling through rotation of spontaneous polarization and/or modification of the rich domain microstructures. Unfortunately, such microstructures remain poorly understood due to the complexity of the subject. The goal of this work is to formulate the geometrical laws behind the monoclinic domain microstructures. Specifically, the result of previous work [Gorfman et al. (2022). Acta Cryst. A78, 158–171] is implemented to catalog and outline some properties of permissible domain walls that connect `strain' domains with monoclinic (MA/MB type) symmetry, occurring in ferroelectric perovskite oxides. The term `permissible' [Fousek & Janovec (1969). J. Appl. Phys. 40, 135–142] pertains to the domain walls connecting a pair of `strain' domains without a lattice mismatch. It was found that 12 monoclinic domains may form pairs connected along 84 types of permissible domain walls. These contain 48 domain walls with fixed Miller indices (known as W-walls) and 36 domain walls whose Miller indices may change when free lattice parameters change as well (known as S-walls). Simple and intuitive analytical expressions are provided that describe the orientation of these domain walls, the matrices of transformation between crystallographic basis vectors and, most importantly, the separation between Bragg peaks, diffracted from each of the 84 pairs of domains, connected along a permissible domain wall. It is shown that the orientation of a domain wall may be described by the specific combination of the monoclinic distortion parameters r = [2/(γ − α)][(c/a) − 1], f = (π − 2γ)/(π − 2α) and p = [2/(π − α − γ)] [(c/a) − 1]. The results of this work will enhance understanding and facilitate investigation (e.g. using single-crystal X-ray diffraction) of complex monoclinic domain microstructures in both crystals and thin films.text/htmldoi:10.1107/S205327332300921XenInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733FERROELASTIC DOMAINS; MONOCLINIC SYMMETRY; X-RAY DIFFRACTIONPermissible domain walls in monoclinic MAB ferroelectric phasestextJanuary 20242053-27331282053-273311280https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advances2024-01-01research papers1Biran, I.Gorfman, S.

Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures
https://journals.iucr.org/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.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.text/htmldoi:10.1107/S205327332300863XenInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733TENSOR TOMOGRAPHY; SAXS; SMALL-ANGLE X-RAY SCATTERING; SCATTERING; RECIPROCAL-SPACE MAPS; OPTIMIZATIONSmall-angle scattering tensor tomography algorithm for robust reconstruction of complex texturestext2023-10-196research papersActa Crystallographica Section A: Foundations and Advancesmed@iucr.orghttps://creativecommons.org/licenses/by/4.0/795155262053-2733November 20232053-2733Nielsen, L.C.Erhart, P.Guizar-Sicairos, M.Liebi, M.

Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctness
https://journals.iucr.org/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).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).text/htmldoi:10.1107/S2053273323008446enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733DEBYE SCATTERING EQUATION; SITE-OCCUPANCY FACTORS; DEFECTIVE NANOCRYSTALSSite-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctnesstext2053-27335962053-2733November 20236research papers2023-11-0279587Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/med@iucr.orgFerri, F.Bossuto, M.C.Anzini, P.Cervellino, A.Guagliardi, A.Bertolotti, F.Masciocchi, N.

Molecular replacement for small-molecule crystal structure determination from X-ray and electron diffraction data with reduced resolution
https://journals.iucr.org/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.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.text/htmldoi:10.1107/S2053273323008458enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733ELECTRON CRYSTALLOGRAPHY; SMALL MOLECULES; MOLECULAR REPLACEMENTMolecular replacement for small-molecule crystal structure determination from X-ray and electron diffraction data with reduced resolutiontextNovember 20232053-27335142053-273350479med@iucr.orghttps://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2023-10-19research papers6Gorelik, T.E.Lukat, P.Kleeberg, C.Blankenfeldt, W.Mueller, R.

Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals
https://journals.iucr.org/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.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.text/htmldoi:10.1107/S2053273323008276enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733CHIRAL PROPERTIES; SPIRAL STRUCTURES; CYCLIC TWINSChiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spiralstext2053-27335862053-2733November 20236research papers2023-10-3179570Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/med@iucr.orgHornfeck, W.

An efficient system matrix factorization method for scanning diffraction based strain tensor tomography
https://journals.iucr.org/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.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.text/htmldoi:10.1107/S2053273323008136enInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733X-RAY DIFFRACTION; STRAIN TENSOR; TOMOGRAPHY; DIFFRACTION IMAGINGAn efficient system matrix factorization method for scanning diffraction based strain tensor tomographytext2023-09-296research papersActa Crystallographica Section A: Foundations and Advancesmed@iucr.orghttps://creativecommons.org/licenses/by/4.0/795425492053-2733November 20232053-2733Henningsson, A.Hall, S.A.

TERSE/PROLIX (TRPX) – a new algorithm for fast and lossless compression and decompression of diffraction and cryo-EM data
https://journals.iucr.org/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.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.text/htmldoi:10.1107/S205327332300760XenInternational Union of Crystallographyhttps://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733COMPRESSION; TERSE/PROLIX; TRPX; LOSSLESS; DIFFRACTION DATA; CRYO-EM DATA; LOSSLESS DATA COMPRESSIONTERSE/PROLIX (TRPX) – a new algorithm for fast and lossless compression and decompression of diffraction and cryo-EM datatext5412053-2733November 20232053-27332023-09-25research papers6https://creativecommons.org/licenses/by/4.0/med@iucr.orgActa Crystallographica Section A: Foundations and Advances53679Matinyan, S.Abrahams, J.P.