Acta Crystallographica Section A: Foundations and Advances最新文献

{"title":"N-representable one-electron reduced density matrix reconstruction with frozen core electrons.","authors":"Sizhuo Yu, Jean Michel Gillet","doi":"10.1107/S2053273324001645","DOIUrl":"10.1107/S2053273324001645","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"249-257"},"PeriodicalIF":1.8,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11067946/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140173648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A digital distance on the kisrhombille tiling.","authors":"Fatma Kablan, Béla Vizvári, Benedek Nagy","doi":"10.1107/S2053273323010628","DOIUrl":"10.1107/S2053273323010628","url":null,"abstract":"<p><p>The kisrhombille tiling is the dual tessellation of one of the semi-regular tessellations. It consists of right-angled triangle tiles with 12 different orientations. An adequate coordinate system for the tiles of the grid has been defined that allows a formal description of the grid. In this paper, two tiles are considered to be neighbors if they share at least one point in their boundary. Paths are sequences of tiles such that any two consecutive tiles are neighbors. The digital distance is defined as the minimum number of steps in a path between the tiles, and the distance formula is proven through constructing minimum paths. In fact, the distance between triangles is almost twice the hexagonal distance of their embedding hexagons.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"226-236"},"PeriodicalIF":1.8,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140092997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO₄)^n- tetrahedra.","authors":"Maxwell Christopher Day, Frank Christopher Hawthorne, Ali Rostami","doi":"10.1107/S2053273324002432","DOIUrl":"10.1107/S2053273324002432","url":null,"abstract":"<p><p>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 (m_v); if a new geometrically distinct unit-distance graph cannot be produced, the mode is invalid (m_i). The parameters m_v and m_i 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.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":"80 Pt 3","pages":"258-281"},"PeriodicalIF":1.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11067949/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140846471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Permissible domain walls in monoclinic ferroelectrics. Part II. The case of M_C phases.","authors":"Ido Biran, Semën Gorfman","doi":"10.1107/S2053273324002419","DOIUrl":"https://doi.org/10.1107/S2053273324002419","url":null,"abstract":"<p><p>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 M_AB 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 M_C type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for M_C 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.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":"80 Pt 3","pages":"293-304"},"PeriodicalIF":1.8,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11067950/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140849018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ClusterFinder: a fast tool to find cluster structures from pair distribution function data.","authors":"Andy S Anker, Ulrik Friis-Jensen, Frederik L Johansen, Simon J L Billinge, Kirsten M Ø Jensen","doi":"10.1107/S2053273324001116","DOIUrl":"10.1107/S2053273324001116","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"213-220"},"PeriodicalIF":1.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10913672/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139988764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parameterized absorptive electron scattering factors.","authors":"M Thomas, A Cleverley, R Beanland","doi":"10.1107/S2053273323010963","DOIUrl":"10.1107/S2053273323010963","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"146-150"},"PeriodicalIF":1.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10913675/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139544955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Understanding extended homometry based on complementary crystallographic orbit sets.","authors":"Zeyue Zhang, Yihan Shen, Junliang Sun","doi":"10.1107/S205327332400007X","DOIUrl":"10.1107/S205327332400007X","url":null,"abstract":"<p><p>Extended homometry is a phenomenon in which distinct structures have the same X-ray diffraction (XRD) intensities, which may lead to incorrect results of structural analysis based on XRD methods. It is proposed and proved herein that half of a crystallographic orbit has the same powder X-ray diffraction intensity as its complementary set; three more theorems are deduced. These results are conducive to understanding the formation of extended homometric structures. Also analyzed are some reported or potential homometric or weakly homometric structures in the Inorganic Crystal Structure Database to confirm the theorems. This work presents a quick approach to analyze and construct extended homometric structures based on crystallographic orbits.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"151-160"},"PeriodicalIF":1.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139701218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advanced implication theory. Symmetry tables.","authors":"Frantisek Pavelcik","doi":"10.1107/S2053273324000846","DOIUrl":"10.1107/S2053273324000846","url":null,"abstract":"<p><p>The MIF (multiple implication function) group symmetry was assigned to all 230 space groups. Knowledge of MIF symmetry allows the calculation of an asymmetric unit. A more accurate procedure for calculating MIFs has been developed. Extensive tables of MIF symmetry and asymmetric units were computer generated. The development of implication theory for crystal structure determination seems to have reached completion.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"189-193"},"PeriodicalIF":1.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139701217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Double-slit asymmetrical dynamical diffraction of X-rays in ideal crystals.","authors":"Minas Balyan","doi":"10.1107/S2053273323010331","DOIUrl":"10.1107/S2053273323010331","url":null,"abstract":"<p><p>The theoretical investigation of double-slit asymmetrical dynamical diffraction of X-rays in perfect crystals establishes that Young's interference fringes on the exit surface are formed. The position of the fringes in the cross section of the beam depends on deviation from the Bragg exact orientation and asymmetry angle. An equation for the period of the fringes is presented, according to which the period is polarization sensitive. The period increases with increasing the absolute value of the asymmetry angle. In its turn, the size of the interference region also increases with increasing the absolute value of the asymmetry angle. However, the ratio of interference region size to period, i.e. the number of observed fringes, decreases with increasing the absolute value of the asymmetry angle. The size of the interference region can be of the order of a few tens of mm, which can be used for obtaining Fourier dynamical diffraction holograms of a large size. This type of diffraction can also be used for obtaining double-slit dynamical diffraction contrast of defects and deformations. Due to the phase difference information, in comparison with single-slit diffraction, double-slit diffraction is more sensitive to the existence of objects and deformations in the path of the wave.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"161-166"},"PeriodicalIF":1.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139519271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling dynamical 3D electron diffraction intensities. II. The role of inelastic scattering.","authors":"Budhika Mendis","doi":"10.1107/S2053273323010690","DOIUrl":"10.1107/S2053273323010690","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"178-188"},"PeriodicalIF":1.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10913673/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139544989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}