Acta Crystallographica Section A
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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.enCopyright (c) 2018 International Union of Crystallography2018-05-01International Union of CrystallographyInternational Union of Crystallographyhttp://journals.iucr.orgurn:issn:2053-2733Acta 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/htmlActa Crystallographica Section A: Foundations and Advances, Volume 74, Part 3, 2018textweekly62002-01-01T00:00+00:003742018-05-01Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances157urn:issn:2053-2733med@iucr.orgMay 20182018-05-01Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imagePartially coherent ptychography by gradient decomposition of the probe
http://scripts.iucr.org/cgi-bin/paper?lk5027
Coherent ptychographic imaging experiments often discard the majority of the flux from a light source to define the coherence of the illumination. Even when the coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. This article proposes the gradient decomposition of the probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. An efficient first-order splitting algorithm (GDP-ADMM) for solving the proposed nonlinear optimization problem is described. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM using nanoprobes produces satisfactory results even when the ratio between the kernel width and the beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Chang, H.Enfedaque, P.Lou, Y.Marchesini, S.2018-04-11doi:10.1107/S2053273318001924International Union of CrystallographyPartially coherent effects in ptychography are addressed by using a simple and efficient model with only one coherent probe, its gradient and the variance of a convolution kernel.ENptychographypartial coherencephase retrievalwavefront metrologyCoherent ptychographic imaging experiments often discard the majority of the flux from a light source to define the coherence of the illumination. Even when the coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. This article proposes the gradient decomposition of the probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. An efficient first-order splitting algorithm (GDP-ADMM) for solving the proposed nonlinear optimization problem is described. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM using nanoprobes produces satisfactory results even when the ratio between the kernel width and the beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.text/htmlPartially coherent ptychography by gradient decomposition of the probetext3742018-04-11Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aresearch papers157169A method to estimate statistical errors of properties derived from charge-density modelling
http://scripts.iucr.org/cgi-bin/paper?ae5043
Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.Copyright (c) 2018 Bertrand Fournier et al.urn:issn:2053-2733Fournier, B.Guillot, B.Lecomte, C.Escudero-Adán, E.C.Jelsch, C.2018-05-03doi:10.1107/S2053273318004308International Union of CrystallographyErrors on molecular properties including the topology of electron density and electrostatics are estimated from a sample of deviating models generated using the variance–covariance matrix issued at the end of the charge-density refinement.ENMonte Carlo methodselectron densityuncertaintytopologyintermolecular interactionsEstimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.text/htmlA method to estimate statistical errors of properties derived from charge-density modellingtext3742018-05-03Copyright (c) 2018 Bertrand Fournier et al.Acta Crystallographica Section Aresearch papers1701831829445AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals
http://scripts.iucr.org/cgi-bin/paper?ae5042
Determination of the symmetry profile of structures is a persistent challenge in materials science. Results often vary amongst standard packages, hindering autonomous materials development by requiring continuous user attention and educated guesses. This article presents a robust procedure for evaluating the complete suite of symmetry properties, featuring various representations for the point, factor and space groups, site symmetries and Wyckoff positions. The protocol determines a system-specific mapping tolerance that yields symmetry operations entirely commensurate with fundamental crystallographic principles. The self-consistent tolerance characterizes the effective spatial resolution of the reported atomic positions. The approach is compared with the most used programs and is successfully validated against the space-group information provided for over 54 000 entries in the Inorganic Crystal Structure Database (ICSD). Subsequently, a complete symmetry analysis is applied to all 1.7+ million entries of the AFLOW data repository. The AFLOW-SYM package has been implemented in, and made available for, public use through the automated ab initio framework AFLOW.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Hicks, D.Oses, C.Gossett, E.Gomez, G.Taylor, R.H.Toher, C.Mehl, M.J.Levy, O.Curtarolo, S.2018-05-03doi:10.1107/S2053273318003066International Union of CrystallographyAFLOW-SYM is a comprehensive crystal-symmetry analysis suite catering to automated computational workflows and presenting a wealth of symmetry descriptions. This platform employs robust mapping techniques, validates calculated symmetry elements and resolves self-consistent tolerances for each system to yield results more commensurate with experiments compared with other common symmetry packages.ENcrystal structure analysisautomationmaterials genomicsAFLOW-SYMDetermination of the symmetry profile of structures is a persistent challenge in materials science. Results often vary amongst standard packages, hindering autonomous materials development by requiring continuous user attention and educated guesses. This article presents a robust procedure for evaluating the complete suite of symmetry properties, featuring various representations for the point, factor and space groups, site symmetries and Wyckoff positions. The protocol determines a system-specific mapping tolerance that yields symmetry operations entirely commensurate with fundamental crystallographic principles. The self-consistent tolerance characterizes the effective spatial resolution of the reported atomic positions. The approach is compared with the most used programs and is successfully validated against the space-group information provided for over 54 000 entries in the Inorganic Crystal Structure Database (ICSD). Subsequently, a complete symmetry analysis is applied to all 1.7+ million entries of the AFLOW data repository. The AFLOW-SYM package has been implemented in, and made available for, public use through the automated ab initio framework AFLOW.text/htmlAFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystalstext3742018-05-03Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aresearch papers184203Dependence of X-ray plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Laue case
http://scripts.iucr.org/cgi-bin/paper?td5047
For the asymmetrical Laue case the X-ray plane-wave transmission and reflection coefficients and rocking curves are analysed as a function of the deviation angles from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane. New peculiarities of the rocking curves are obtained. The peculiarities of both the effective absorption coefficient and rocking curves in thick crystals are also investigated.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Balyan, M.K.2018-03-14doi:10.1107/S205327331800181XInternational Union of CrystallographyThe dependence of X-ray rocking curves on the deviation angle from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane is investigated for the asymmetrical Laue case.ENX-ray rocking curvesdynamical diffractionLaue diffractiondeviation angleFor the asymmetrical Laue case the X-ray plane-wave transmission and reflection coefficients and rocking curves are analysed as a function of the deviation angles from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane. New peculiarities of the rocking curves are obtained. The peculiarities of both the effective absorption coefficient and rocking curves in thick crystals are also investigated.text/htmlDependence of X-ray plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Laue casetext3742018-03-14Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aresearch papers204215The fundamentals of crystal orientation
http://scripts.iucr.org/cgi-bin/paper?ae5040
The method described in this paper improves the old methods of crystal orientation, applies new parametric equations for crystallography, and increases the precision and accuracy of measurements. The method applies to inorganic and organic crystals. A breakthrough in crystal orientation happened about 25 years ago when two equations dependent on the Bragg angle and an arbitrary direction in the crystal were developed. Unfortunately, they were analytically insolvable and their unique solution was found numerically. Finding the numerical solution of crystal orientation is challenging from a mathematical point of view. In these conditions the numerical solution was found using the Newton method. The Newton method required a specific programming that limits the full benefit of the method in the laboratory. In recent years, a new numerical technique called GRG (generalized reduced gradient), which can be run on many inexpensive computers, was found to be a good fit for these equations. The solutions that can be found with the GRG method are now completed with additional parametric equations; they are easy to use with computers in many laboratories. In this way, parametrization of nonlinear equations for X-ray crystal orientation determines the positions of a reference surface of the single crystal relative to its crystallographic system and to a goniometer setting with two perpendicular axes of rotation. This approach was successfully validated and checked for different Si wafers with (111) and (004) orientation. The paper shows an innovative approach through the parametric equations in conjunction with exact solutions found with a GRG subroutine. The results of the method demonstrate the potential for new applications in industry and research.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Dragoi, D.2018-03-14doi:10.1107/S2053273317017594International Union of CrystallographyNew parametric equations are developed for crystal orientation, the solutions of which are free of constraints or approximations and are well suited for determination of crystal orientation with high accuracy and precision. These equations are validated and checked for orienting of single crystals with high precision and accuracy.ENexact solution for crystal orientationparametric crystal orientationstereographic projectionextended stereographic projectionlinked spherical trianglesThe method described in this paper improves the old methods of crystal orientation, applies new parametric equations for crystallography, and increases the precision and accuracy of measurements. The method applies to inorganic and organic crystals. A breakthrough in crystal orientation happened about 25 years ago when two equations dependent on the Bragg angle and an arbitrary direction in the crystal were developed. Unfortunately, they were analytically insolvable and their unique solution was found numerically. Finding the numerical solution of crystal orientation is challenging from a mathematical point of view. In these conditions the numerical solution was found using the Newton method. The Newton method required a specific programming that limits the full benefit of the method in the laboratory. In recent years, a new numerical technique called GRG (generalized reduced gradient), which can be run on many inexpensive computers, was found to be a good fit for these equations. The solutions that can be found with the GRG method are now completed with additional parametric equations; they are easy to use with computers in many laboratories. In this way, parametrization of nonlinear equations for X-ray crystal orientation determines the positions of a reference surface of the single crystal relative to its crystallographic system and to a goniometer setting with two perpendicular axes of rotation. This approach was successfully validated and checked for different Si wafers with (111) and (004) orientation. The paper shows an innovative approach through the parametric equations in conjunction with exact solutions found with a GRG subroutine. The results of the method demonstrate the potential for new applications in industry and research.text/htmlThe fundamentals of crystal orientationtext3742018-03-14Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aresearch papers216222Surface embeddings of the Klein and the Möbius–Kantor graphs
http://scripts.iucr.org/cgi-bin/paper?eo5078
This paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the Möbius–Kantor graph on the torus, the genus-2 bitorus and the genus-3 tritorus, as well as the two-dimensional, 7-valent Klein graph on the tritorus (and its dual: the 3-valent Klein graph). The genus-2 and -3 embeddings describe quotient graphs of 2- and 3-periodic reticulations of hyperbolic surfaces. This invariant is used to identify infinite nets related to the Möbius–Kantor and 7-valent Klein graphs.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Pedersen, M.C.Delgado-Friedrichs, O.Hyde, S.T.2018-03-27doi:10.1107/S2053273318002036International Union of CrystallographyUsing a simple invariant representation scheme for graphs, a number of reticular networks are identified as surface embeddings of the famous Klein and Möbius–Kantor graphs on periodic surfaces.ENperiodic netsKlein graphMöbius–Kantor graphThis paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the Möbius–Kantor graph on the torus, the genus-2 bitorus and the genus-3 tritorus, as well as the two-dimensional, 7-valent Klein graph on the tritorus (and its dual: the 3-valent Klein graph). The genus-2 and -3 embeddings describe quotient graphs of 2- and 3-periodic reticulations of hyperbolic surfaces. This invariant is used to identify infinite nets related to the Möbius–Kantor and 7-valent Klein graphs.text/htmlSurface embeddings of the Klein and the Möbius–Kantor graphstext3742018-03-27Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aresearch papers223232Quantitative theory of diffraction by cylindrical scroll nanotubes
http://scripts.iucr.org/cgi-bin/paper?td5048
A quantitative theory of Fraunhofer diffraction by right- and left-handed multiwalled cylindrical scroll nanotubes is developed on the basis of the kinematical approach. The proposed theory is mainly dedicated to structural studies of individual nanotubes by the selected-area electron diffraction technique. Strong and diffuse reflections of the scroll nanotube were studied and explicit formulas that govern relations between the direct and reciprocal lattice of the scroll nanotube are achieved.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Khadiev, A.Khalitov, Z.2018-05-03doi:10.1107/S2053273318003169International Union of CrystallographyA quantitative theory of Fraunhofer diffraction by a cylindrical scroll nanotube based on the kinematical approach is presented. The reciprocal lattice of a cylindrical scroll nanotube and its relation to the nanotube lattice parameters are determined on the basis of the proposed theory.ENmultiwall nanotubesscroll nanotubesnanoscrollsdiffraction by nanotubesA quantitative theory of Fraunhofer diffraction by right- and left-handed multiwalled cylindrical scroll nanotubes is developed on the basis of the kinematical approach. The proposed theory is mainly dedicated to structural studies of individual nanotubes by the selected-area electron diffraction technique. Strong and diffuse reflections of the scroll nanotube were studied and explicit formulas that govern relations between the direct and reciprocal lattice of the scroll nanotube are achieved.text/htmlQuantitative theory of diffraction by cylindrical scroll nanotubestext3742018-05-03Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aresearch papers233244Report of the Executive Committee for 2016
http://scripts.iucr.org/cgi-bin/paper?es0427
The report of the Executive Committee for 2016 is presented.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Dacombe, M.Ashcroft, A.T.2018-05-03doi:10.1107/S2053273317009780International Union of CrystallographyThe report of the Executive Committee for 2016 is presented.ENInternational Union of CrystallographyExecutive CommitteeThe report of the Executive Committee for 2016 is presented.text/htmlReport of the Executive Committee for 2016text3742018-05-03Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography245286B. T. M. (Terry) Willis (1927–2018)
http://scripts.iucr.org/cgi-bin/paper?es5002
Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Lander, G.Carlile, C.2018-03-27doi:10.1107/S2053273318004291International Union of CrystallographyObituary for Terry WillisENobituaryneutron diffractionHarwellSummer Schools on Neutron Scatteringtext/htmlB. T. M. (Terry) Willis (1927–2018)text3742018-03-27Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Aobituaries287288Shattered Symmetry. Group Theory From the Eightfold Way to the Periodic Table. By Pieter Thyssen and Arnout Ceulemans. Oxford University Press, 2017. Pp. 528. Price GBP 52.00 (hardback). ISBN 9780190611392.
http://scripts.iucr.org/cgi-bin/paper?xo0091
Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Assfeld, X.2018-03-14doi:10.1107/S2053273318000141International Union of CrystallographyENbook reviewgroup theoryLie groupstext/htmlShattered Symmetry. Group Theory From the Eightfold Way to the Periodic Table. By Pieter Thyssen and Arnout Ceulemans. Oxford University Press, 2017. Pp. 528. Price GBP 52.00 (hardback). ISBN 9780190611392.text3742018-03-14Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section Abook reviews289290