Piecewise-linear embeddings of knots and links with rotoinversion symmetry
This article describes the simplest members of an infinite family of knots and links that have achiral piecewise-linear embeddings in which linear segments (sticks) meet at corners. The structures described are all corner- and stick-2-transitive – the smallest possible for achiral knots. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - July 29, 2021 Category: Chemistry Authors: O'Keeffe, M. Treacy, M.M.J. Tags: knots links decussate structures piecewise-linear embedding research papers Source Type: research
Sidney C. Abrahams (1924 – 2021)
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 28, 2021 Category: Chemistry Authors: Brock, C.P. Glazer, A.M. Tags: obituary lithium niobate lithium tantalate ferroelectricity tungsten bronzes obituaries Source Type: research
Space Group Visualizer. By Eckhard Hitzer and Christian Perwass. Independently published, 2021. Paperback, pp. 162. Price EUR 22.25, USD 24.99. ISBN 979-8719838618.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 21, 2021 Category: Chemistry Authors: M ü ller, U. Tags: space-group theory crystallographic software book reviews Source Type: research
An Invitation to Applied Category Theory. Seven Sketches in Compositionality. By Brendan Fong and David I. Spivak. Cambridge University Press, 2019. Paperback, pp. 348. Price GBP 37.99. ISBN 9781108711821.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 21, 2021 Category: Chemistry Authors: St ö ger, B. Tags: book review category theory book reviews Source Type: research
A new density-modification procedure extending the application of the recent | ρ |-based phasing algorithm to larger crystal structures
The incorporation of the new peakness-enhancing fast Fourier transform compatible ipp procedure (ipp = inner-pixel preservation) into the recently published SM algorithm based on | ρ | [Rius (2020). Acta Cryst A76, 489 – 493] improves its phasing efficiency for larger crystal structures with atomic resolution data. Its effectiveness is clearly demonstrated via a collection of test crystal structures (taken from the Protein Data Bank) either starting from random phase values or by using the randomly shifted modulus function (a Patterson-type synthesis) as initial ρ estimate. It has been found that in the presence of med...
Source: Acta Crystallographica Section A - June 21, 2021 Category: Chemistry Authors: Rius, J. Torrelles, X. Tags: SM phasing algorithm ipp procedure ρ -based phasing residual direct methods origin-free modulus sum function structure solution research papers Source Type: research
Magnetic modes compatible with the symmetry of crystals
A classification of magnetic point groups is presented which gives an answer to the question: which magnetic groups can describe a given magnetic mode? There are 32 categories of magnetic point groups which describe 64 unique magnetic modes: 16 with a ferromagnetic component and 48 without. This classification focused on magnetic modes is helpful for finding the magnetic space group which can describe the magnetic symmetry of the material. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 21, 2021 Category: Chemistry Authors: Fabrykiewicz, P. Przenios ł o, R. Sosnowska, I. Tags: magnetic ordering magnetic space groups symmetry site symmetry point group spin reorientation research papers Source Type: research
A topological proof of the modified Euler characteristic based on the orbifold concept
The notion of the Euler characteristic of a polyhedron or tessellation has been the subject of in-depth investigations by many authors. Two previous papers worked to explain the phenomenon of the vanishing (or zeroing) of the modified Euler characteristic of a polyhedron that underlies a periodic tessellation of a space under a crystallographic space group. The present paper formally expresses this phenomenon as a theorem about the vanishing of the Euler characteristic of certain topological spaces called topological orbifolds. In this new approach, it is explained that the theorem in question follows from the fundamental ...
Source: Acta Crystallographica Section A - June 21, 2021 Category: Chemistry Authors: Naskr ę cki, B. Dauter, Z. Jaskolski, M. Tags: Euler characteristic orbifolds space-filling polyhedra space groups asymmetric units research papers Source Type: research
Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain
The X-ray Bragg coherent diffractive imaging (CDI) technique assumes that the structure factor holds constant over the measured crystal. This approximation breaks down for materials exhibiting variations in the unit-cell configuration, such as piezo- and ferroelectrics. In that case, the strain field cannot be reliably determined from the reconstruction because the lattice deformation and the structure factor contribute concomitantly. Proposed here is a solution to this problem achieved by combining Bragg CDI and the multiwavelength anomalous diffraction approach that measures a Friedel pair of reflections at two different...
Source: Acta Crystallographica Section A - June 21, 2021 Category: Chemistry Authors: Shabalin, A.G. Shpyrko, O.G. Tags: coherent X-ray diffractive imaging multiwavelength anomalous diffraction imaging polarization domains atomic displacement lattice deformation short communications Source Type: research
On symmetry breaking of dual polyhedra of non-crystallographic group H3
The study of the polyhedra described in this paper is relevant to the icosahedral symmetry in the assembly of various spherical molecules, biomolecules and viruses. A symmetry-breaking mechanism is applied to the family of polytopes {\cal V}_{H_{3}}(\lambda) constructed for each type of dominant point λ . Here a polytope {\cal V}_{H_{3}}(\lambda) is considered as a dual of a {\cal D}_{H_{3}}(\lambda) polytope obtained from the action of the Coxeter group H3 on a single point \lambda\in{\bb R}^{3}. The H3 symmetry is reduced to the symmetry of its two-dimensional subgroups H2, A1 × A1 and A2 that are used to exami...
Source: Acta Crystallographica Section A - June 16, 2021 Category: Chemistry Authors: Myronova, M. Tags: Coxeter groups dual polytopes orbit decompositions fullerenes nanotubes stellated polyhedra research papers Source Type: research
Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions
A local structure analysis method based on convergent-beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low-order structure factors with sin θ / λ ≤ 0.28 Å − 1 of potassium tantalate (KTaO3). Comparison between structure factors determined from CBED patterns taken at the zone-axis (ZA) and Bragg-excited conditions is made in order to discuss their precision and sensitivities. Bragg-excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg-e...
Source: Acta Crystallographica Section A - June 10, 2021 Category: Chemistry Authors: Aryal, B. Morikawa, D. Tsuda, K. Terauchi, M. Tags: CBED structure factors electron density electrostatic potential precision research papers Source Type: research
From crystal color symmetry to quantum spacetime
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - May 28, 2021 Category: Chemistry Authors: Bojowald, M. Saxena, A. Tags: color symmetry quantum spacetime renormalized blended spacetime relativistic spacetime crystals scientific commentaries Source Type: research
A reference-based multi-lattice indexing method integrating prior information correction and iterative refinement in protein crystallography
A new multi-lattice indexing method based on the principle of whole-pattern matching given cell dimensions and space-group symmetry is presented for macromolecular crystallography. The proposed method, termed the multi-crystal data processing suite (MCDPS), features a local correction for prior information accompanied by iterative refinement of experimental parameters, both of which are numerically and experimentally demonstrated to be critical for accurately identifying multiple crystal lattices. Further analysis of data reduction and structure determination with conventional single-crystal programs reveals that the proce...
Source: Acta Crystallographica Section A - May 27, 2021 Category: Chemistry Authors: Zhou, Q. Gao, Z.-Q. Dong, Z. Jiang, Y.-M. She, Z. Geng, Z. Dong, Y.-H. Tags: multi-crystal diffraction indexing algorithm multi-crystal data processing suite MCDPS protein crystallography data reduction research papers Source Type: research
Resolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon
The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters: (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, distance to a detector, and anisotropic elastic constants of the chosen crystal. The results allow the optimization of the parameters of bent-crystal spectrometers for the hard X-ray free-electron laser sources. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - May 27, 2021 Category: Chemistry Authors: Kaganer, V.M. Petrov, I. Samoylova, L. Tags: X-ray free-electron lasers X-ray spectroscopy bent crystals diamond crystal optics femtosecond X-ray diffraction research papers Source Type: research
Polarization effects of X-ray monochromators modeled using dynamical scattering theory
The difference in the diffracted intensity of the σ - and π -polarized components of an X-ray beam in powder diffraction has generally been treated according to equations based on dipole scattering, also known as kinematic X-ray scattering. Although this treatment is correct for powders and post-sample analyzers known to be of high mosaicity, it does not apply to systems configured with nearly perfect crystal incident-beam monochromators. Equations are presented for the polarization effect, based on dynamical diffraction theory applied to the monochromator crystal. The intensity of the π component relative to the σ com...
Source: Acta Crystallographica Section A - May 27, 2021 Category: Chemistry Authors: Mendenhall, M.H. Black, D. Windover, D. Cline, J.P. Tags: dynamical diffraction powder diffraction incident-beam monochromators polarization research papers Source Type: research
Relativistic spacetime crystals
Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other hand need to account for the mixing of space and time in special relativity through Lorentz transformation, and have been listed only in 2D. This work shows that there exists a transformation between the conventional Minkowski spacetime (MS) and what is referred to here as renormalized blended spacetime (RBS); they are shown to be equivalent descriptions of relativistic physics in flat spac...
Source: Acta Crystallographica Section A - May 27, 2021 Category: Chemistry Authors: Gopalan, V. Tags: spacetime special relativity renormalized blended spacetime relativistic spacetime crystals research papers Source Type: research
