Modelling dynamical 3D electron diffraction intensities. I. A scattering cluster algorithm
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 m...
Source: Acta Crystallographica Section A - January 25, 2024 Category: Chemistry Authors: Mendis, B. Tags: dynamical electron diffraction Bloch waves structure matrix multislice research papers Source Type: research
Parameterized absorptive electron scattering factors
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...
Source: Acta Crystallographica Section A - January 25, 2024 Category: Chemistry Authors: Thomas, M. Cleverley, A. Beanland, R. Tags: electron diffraction absorption 3D-ED three-dimensional electron diffraction thermal diffuse scattering research papers Source Type: research
Double-slit asymmetrical dynamical diffraction of X-rays in ideal crystals
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 asymmet...
Source: Acta Crystallographica Section A - January 23, 2024 Category: Chemistry Authors: Balyan, M. Tags: double-slit dynamical diffraction Young's fringes X-ray diffraction interferometer asymmetrical diffraction research papers Source Type: research
Deep learning applications in protein crystallography
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 relevan...
Source: Acta Crystallographica Section A - January 1, 2024 Category: Chemistry Authors: Matinyan, S. Filipcik, P. Abrahams, J.P. Tags: protein crystallography deep learning artificial intelligence machine learning lead articles Source Type: research
Analytical models representing X-ray form factors of ions
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. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - January 1, 2024 Category: Chemistry Authors: Thorkildsen, G. Tags: X-ray form factors inverse Mott – Bethe formula analytical representations research papers Source Type: research
Symmetry groups of two-way twofold and three-way threefold fabrics
This work discusses the symmetry groups of two classes of woven fabrics, two-way twofold fabrics and three-way threefold fabrics. A method to arrive at a design of a fabric is presented, employing methods in color symmetry theory. Geometric representations of all possible layer group or diperiodic symmetry structures of the fabrics are derived. There are 50 layer symmetry groups corresponding to two-way twofold fabrics and 27 layer symmetry groups corresponding to three-way threefold fabrics. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - December 19, 2023 Category: Chemistry Authors: De Las Pe ñ as, M.L.A. Tomenes, M. Liza, K. Tags: two-way twofold and three-way threefold fabrics bi-axial and tri-axial weaves layer groups weavings research papers Source Type: research
Realizations of crystal nets. I. (Generalized) derived graphs
A crystal net can be derived from a `generalized' voltage graph representing a graph analog of a fundamental domain of that crystal net along with a sufficient collection of its symmetries. The voltage assignments include not only isometries to the (oriented) edges, but also `weight' groups assigned to vertices for generating the vertex figures around those vertices. By varying the voltage assignments, one obtains geometrically distinct – and occasionally topologically distinct – Euclidean graphs. The focus here is on deriving simple graphs, i.e. graphs with no loops or lunes, especially uninodal edge transitive graphs...
Source: Acta Crystallographica Section A - December 19, 2023 Category: Chemistry Authors: McColm, G. Tags: crystal nets parametrization realizations of graphs voltage graphs periodic graphs research papers Source Type: research
Professor Dr Hendrik (Henk) Schenk (1939 – 2023)
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - December 8, 2023 Category: Chemistry Authors: Reiss, C.A. Tags: International Union of Crystallography direct methods powder diffraction International Tables for Crystallography obituaries Source Type: research
Periodic diffraction from an aperiodic monohedral tiling
The diffraction pattern from the recently reported aperiodic `einstein', or `hat', monohedral tiling [Smith et al. (2023). arXiv:2303.10798v1] has been analyzed. The structure is the hexagonal mta net, a kite tiling, with aperiodic vertex deletions. A large model's diffraction pattern displays a robust sixfold periodicity in plane group p6. A repeating, roughly triangular motif of `diffused intensity' arises between the strongest Bragg peaks. The motif contains high-density regions of discrete `satellite' peaks, rather than continuous `diffuse scattering', breaking mirror symmetry, consistent with the chiral hat tiling. (S...
Source: Acta Crystallographica Section A - December 7, 2023 Category: Chemistry Authors: Kaplan, C.S. O'Keeffe, M. Treacy, M.M.J. Tags: quasicrystalline tiling hat monotiling quasiperiodic diffraction research papers Source Type: research
Permissible domain walls in monoclinic MAB ferroelectric phases
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 ...
Source: Acta Crystallographica Section A - December 7, 2023 Category: Chemistry Authors: Biran, I. Gorfman, S. Tags: ferroelastic domains monoclinic symmetry X-ray diffraction research papers Source Type: research
Isogonal 2-periodic polycatenanes: chain mail
For 2-periodic polycatenanes with isogonal (vertex-transitive) embeddings, the basic units linked are torus knots and links including the unknots (untangled polygons). Twenty-four infinite families have been identified, with hexagonal, tetragonal or rectangular symmetry. The simplest members of each family are described and illustrated. A method for determining the catenation number of a ring based on electromagnetic theory is described. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - November 30, 2023 Category: Chemistry Authors: O'Keeffe, M. Treacy, M.M.J. Tags: chain mail polycatenanes layered structures isogonal structures Gauss linking number research papers Source Type: research
Identification of Kikuchi lines in electron diffraction patterns collected in small-angle geometry
It is demonstrated that Kikuchi features become clearly visible if reflection high-energy electron diffraction (RHEED) patterns are filtered using digital image processing software. The results of such pattern transformations are shown for SrTiO3 with mixed surface termination for data collected at different azimuths of the incident electron beam. A simplified analytical approach for the theoretical description of filtered Kikuchi patterns is proposed and discussed. Some examples of raw and filtered patterns for thin films are shown. RHEED patterns may be treated as a result of coherent and incoherent scattering of electro...
Source: Acta Crystallographica Section A - November 30, 2023 Category: Chemistry Authors: Mitura, Z. Szwachta, G. Kokosza, Ł . Przybylski, M. Tags: reflection high-energy electron diffraction RHEED Kikuchi patterns perovskites nanostructured materials digital images research papers Source Type: research
Algorithm for spin symmetry operation search
A spin space group provides a suitable way of fully exploiting the symmetry of a spin arrangement with a negligible spin – orbit coupling. There has been a growing interest in applying spin symmetry analysis with the spin space group in the field of magnetism. However, there is no established algorithm to search for spin symmetry operations of the spin space group. This paper presents an exhaustive algorithm for determining the spin symmetry operations of commensurate spin arrangements. The present algorithm searches for spin symmetry operations from the symmetry operations of a corresponding nonmagnetic crystal structur...
Source: Acta Crystallographica Section A - November 23, 2023 Category: Chemistry Authors: Shinohara, K. Togo, A. Watanabe, H. Nomoto, T. Tanaka, I. Arita, R. Tags: spin space groups spin symmetry operations spin arrangements Procrustes problems Hermite normal forms research papers Source Type: research
Periodic Borromean rings, rods and chains
This article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2-periodic vertex-, edge- and ring-transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1- and 3-periodic ring-transitive (isonemal) families. A second isonemal 2-periodic family is identified, as is a unique 3-periodic Borromean assembly of equilateral triangles. Also reported is a notable 2-periodic structure comprising chains of linked rings in which the chains are locked in place but no two chains are directly interlinked, being held in...
Source: Acta Crystallographica Section A - November 23, 2023 Category: Chemistry Authors: O'Keeffe, M. Treacy, M.M.J. Tags: polycatenanes Borromean property ring-transitive family edge-transitive family vertex-transitive family research papers Source Type: research
Hierarchical topological analysis of crystal structures: the skeletal net concept
Topological analysis of crystal structures faces the problem of the `correct' or the `best' assignment of bonds to atoms, which is often ambiguous. A hierarchical scheme is used where any crystal structure is described as a set of topological representations, each of which corresponds to a particular assignment of bonds encoded by a periodic net. In this set, two limiting nets are distinguished, complete and skeletal, which contain, respectively, all possible bonds and the minimal number of bonds required to keep the structure periodicity. Special attention is paid to the skeletal net since it describes the connectivity of...
Source: Acta Crystallographica Section A - November 23, 2023 Category: Chemistry Authors: Blatova, O.A. Blatov, V.A. Tags: crystal structures topology periodic nets hierarchical analysis research papers Source Type: research
