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) 2016 International Union of Crystallography2016-07-01International 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 72, Part 4, 2016textweekly62002-01-01T00:00+00:004722016-07-01Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances459urn:issn:2053-2733med@iucr.orgJuly 20162016-07-01Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2016/04/00/isscontsbdy.html
Still imageCoherent diffraction imaging: consistency of the assembled three-dimensional distribution
http://scripts.iucr.org/cgi-bin/paper?mq5044
The short pulses of X-ray free-electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. From the recorded diffraction patterns the structure of particles or molecules can be determined on the nano- or even atomic scale. In a coherent diffraction imaging experiment thousands of diffraction patterns of identical particles are recorded and assembled into a three-dimensional distribution which is subsequently used to solve the structure of the particle. It is essential to know, but not always obvious, that the assembled three-dimensional reciprocal-space intensity distribution is really consistent with the measured diffraction patterns. This paper shows that, with the use of correlation maps and a single parameter calculated from them, the consistency of the three-dimensional distribution can be reliably validated.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Tegze, M.Bortel, G.2016-06-08doi:10.1107/S2053273316008366International Union of CrystallographyIn coherent diffraction experiments many diffraction images of randomly oriented particles are recorded and assembled into a three-dimensional scattering intensity distribution. In this paper a method is presented to test the consistency of the assembled three-dimensional distribution.ENsingle-particle imagingcoherent diffraction imagingX-ray free-electron lasersXFELsorientationThe short pulses of X-ray free-electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. From the recorded diffraction patterns the structure of particles or molecules can be determined on the nano- or even atomic scale. In a coherent diffraction imaging experiment thousands of diffraction patterns of identical particles are recorded and assembled into a three-dimensional distribution which is subsequently used to solve the structure of the particle. It is essential to know, but not always obvious, that the assembled three-dimensional reciprocal-space intensity distribution is really consistent with the measured diffraction patterns. This paper shows that, with the use of correlation maps and a single parameter calculated from them, the consistency of the three-dimensional distribution can be reliably validated.text/htmlCoherent diffraction imaging: consistency of the assembled three-dimensional distributiontext4722016-06-08Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers459464Faces of root polytopes in all dimensions
http://scripts.iucr.org/cgi-bin/paper?kx5052
In this paper the root polytopes of all finite reflection groups W with a connected Coxeter–Dynkin diagram in {\bb R}^n are identified, their faces of dimensions 0 ≤ d ≤ n − 1 are counted, and the construction of representatives of the appropriate W-conjugacy class is described. The method consists of recursive decoration of the appropriate Coxeter–Dynkin diagram [Champagne et al. (1995). Can. J. Phys. 73, 566–584]. Each recursion step provides the essentials of faces of a specific dimension and specific symmetry. The results can be applied to crystals of any dimension and any symmetry.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Szajewska, M.2016-05-13doi:10.1107/S2053273316004551International Union of CrystallographyThe reflection group W can be specified by a connected Coxeter–Dynkin diagram consisting of either one or two orbits of W. An individual orbit is viewed as the set of vertices of a polytope (root polytope) generated by its W from any one point of the orbit.ENfinite Coxeter groupsroot polytopesLie groupsLie algebraIn this paper the root polytopes of all finite reflection groups W with a connected Coxeter–Dynkin diagram in {\bb R}^n are identified, their faces of dimensions 0 ≤ d ≤ n − 1 are counted, and the construction of representatives of the appropriate W-conjugacy class is described. The method consists of recursive decoration of the appropriate Coxeter–Dynkin diagram [Champagne et al. (1995). Can. J. Phys. 73, 566–584]. Each recursion step provides the essentials of faces of a specific dimension and specific symmetry. The results can be applied to crystals of any dimension and any symmetry.text/htmlFaces of root polytopes in all dimensionstext4722016-05-13Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers465471Properties of X-ray resonant scattering in the Bragg case revealed on the Riemann surface
http://scripts.iucr.org/cgi-bin/paper?td5033
Continuing the work described in the previous paper [Saka (2016). Acta Cryst. A72, 338–348], the dynamical theory for perfect crystals in the Bragg case is reformulated using the Riemann surface. In particular, diffraction under resonant scattering conditions is investigated. The characteristic features of the dispersion surface and the rocking curve are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg conditions and the reflection strength. Characteristic properties that have been deduced through numerical analysis are derived analytically using these four parameters. Visualization of the geometric relationships between the four parameters on the Riemann surface is useful for understanding many properties such as symmetry and sharpness of the rocking curve under special conditions. Therefore, employing the Riemann surface is instructive for numerical analysis and useful for understanding dynamical diffraction in the Bragg case.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Saka, T.2016-05-13doi:10.1107/S2053273316005404International Union of CrystallographyProperties of X-ray resonant scattering in the Bragg case are revealed analytically using the Riemann surface.ENX-ray diffractiondynamical theoryBragg caseRiemann surfacedispersion surfacerocking curveresonant scatteringContinuing the work described in the previous paper [Saka (2016). Acta Cryst. A72, 338–348], the dynamical theory for perfect crystals in the Bragg case is reformulated using the Riemann surface. In particular, diffraction under resonant scattering conditions is investigated. The characteristic features of the dispersion surface and the rocking curve are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg conditions and the reflection strength. Characteristic properties that have been deduced through numerical analysis are derived analytically using these four parameters. Visualization of the geometric relationships between the four parameters on the Riemann surface is useful for understanding many properties such as symmetry and sharpness of the rocking curve under special conditions. Therefore, employing the Riemann surface is instructive for numerical analysis and useful for understanding dynamical diffraction in the Bragg case.text/htmlProperties of X-ray resonant scattering in the Bragg case revealed on the Riemann surfacetext4722016-05-13Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers472479Volumic omit maps in ab initio dual-space phasing
http://scripts.iucr.org/cgi-bin/paper?sc5098
Alternating-projection-type dual-space algorithms have a clear construction, but are susceptible to stagnation and, thus, inefficient for solving the phase problem ab initio. To improve this behaviour new omit maps are introduced, which are real-space perturbations applied periodically during the iteration process. The omit maps are called volumic, because they delete some predetermined subvolume of the unit cell without searching for atomic regions or analysing the electron density in any other way. The basic algorithms of positivity, histogram matching and low-density elimination are tested by their solution statistics. It is concluded that, while all these algorithms based on weak constraints are practically useless in their pure forms, appropriate volumic omit maps can transform them to practically useful methods. In addition, the efficiency of the already useful reflector-type charge-flipping algorithm can be further improved. It is important that these results are obtained by using non-sharpened structure factors and without any weighting scheme or reciprocal-space perturbation. The mathematical background of volumic omit maps and their expected applications are also discussed.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Oszlányi, G.Sütő, A.2016-06-17doi:10.1107/S2053273316008846International Union of CrystallographyNew omit maps are introduced that delete some subvolume of the unit cell without analysing the electron density. Applied as periodic perturbations these significantly improve the stagnating behaviour of alternating-projection-type dual-space algorithms.ENomit mapsiterative projection algorithmsdual-space methodsstructure determinationAlternating-projection-type dual-space algorithms have a clear construction, but are susceptible to stagnation and, thus, inefficient for solving the phase problem ab initio. To improve this behaviour new omit maps are introduced, which are real-space perturbations applied periodically during the iteration process. The omit maps are called volumic, because they delete some predetermined subvolume of the unit cell without searching for atomic regions or analysing the electron density in any other way. The basic algorithms of positivity, histogram matching and low-density elimination are tested by their solution statistics. It is concluded that, while all these algorithms based on weak constraints are practically useless in their pure forms, appropriate volumic omit maps can transform them to practically useful methods. In addition, the efficiency of the already useful reflector-type charge-flipping algorithm can be further improved. It is important that these results are obtained by using non-sharpened structure factors and without any weighting scheme or reciprocal-space perturbation. The mathematical background of volumic omit maps and their expected applications are also discussed.text/htmlVolumic omit maps in ab initio dual-space phasingtext4722016-06-17Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers480488Dynamical focusing by bent, asymmetrically cut perfect crystals in Laue geometry
http://scripts.iucr.org/cgi-bin/paper?td5030
A semi-analytical approach based on the influence functions of a point source located on the crystal surface has been adopted to show that the focusing ability of cylindrically bent Laue crystals may be strongly enhanced by replacing symmetrically cut crystals with asymmetrically cut crystals. This approach is generally applicable to any distance between the X-ray source and the focusing bent crystal. A mathematically straightforward method to simplify the derivation of the already known expression of the influence functions in the case of deformed crystals with a constant strain gradient (e.g. cylindrically bent crystals) is also presented.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Guigay, J.P.Ferrero, C.2016-06-29doi:10.1107/S2053273316006549International Union of CrystallographyThe focusing performances of bent Laue crystals are shown to be strongly sensitive to a small degree of asymmetry.ENinfluence functionsdynamical focusingbent perfect crystalsLaue asymmetric geometryA semi-analytical approach based on the influence functions of a point source located on the crystal surface has been adopted to show that the focusing ability of cylindrically bent Laue crystals may be strongly enhanced by replacing symmetrically cut crystals with asymmetrically cut crystals. This approach is generally applicable to any distance between the X-ray source and the focusing bent crystal. A mathematically straightforward method to simplify the derivation of the already known expression of the influence functions in the case of deformed crystals with a constant strain gradient (e.g. cylindrically bent crystals) is also presented.text/htmlDynamical focusing by bent, asymmetrically cut perfect crystals in Laue geometrytext4722016-06-29Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers489499Frequency analysis for modulation-enhanced powder diffraction
http://scripts.iucr.org/cgi-bin/paper?mq5042
Periodic modulation of external conditions on a crystalline sample with a consequent analysis of periodic diffraction response has been recently proposed as a tool to enhance experimental sensitivity for minor structural changes. Here the intensity distributions for both a linear and nonlinear structural response induced by a symmetric and periodic stimulus are analysed. The analysis is further extended for powder diffraction when an external perturbation changes not only the intensity of Bragg lines but also their positions. The derived results should serve as a basis for a quantitative modelling of modulation-enhanced diffraction data measured in real conditions.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Chernyshov, D.Dyadkin, V.van Beek, W.Urakawa, A.2016-06-29doi:10.1107/S2053273316008378International Union of CrystallographyA periodic modulation of experimental conditions would affect both intensities and Bragg angles for the diffraction lines. A frequency response (a series of harmonics) has been derived analytically and compared with a simulated modulation experiment.ENpowder diffractionmodulation-enhanced diffractionperiodic modulationfrequency responsePeriodic modulation of external conditions on a crystalline sample with a consequent analysis of periodic diffraction response has been recently proposed as a tool to enhance experimental sensitivity for minor structural changes. Here the intensity distributions for both a linear and nonlinear structural response induced by a symmetric and periodic stimulus are analysed. The analysis is further extended for powder diffraction when an external perturbation changes not only the intensity of Bragg lines but also their positions. The derived results should serve as a basis for a quantitative modelling of modulation-enhanced diffraction data measured in real conditions.text/htmlFrequency analysis for modulation-enhanced powder diffractiontext4722016-06-29Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers500506Robert Farrell Stewart (1936–2015)
http://scripts.iucr.org/cgi-bin/paper?es0418
Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Spackman, M.A.2016-06-08doi:10.1107/S2053273316008020International Union of CrystallographyObituary for Robert Farrell Stewart.ENobituaryscattering factorscharge densitymultipole modelVALRAYtext/htmlRobert Farrell Stewart (1936–2015)text4722016-06-08Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aobituaries507509Crystal Clear. The Autobiographies of Sir Lawrence & Lady Bragg. Edited by A. M. Glazer and Patience Thomson. Oxford University Press, 2015. Pp. xx + 427. Hardback. Price GBP 35.00. ISBN 978-0-19-874430-6.
http://scripts.iucr.org/cgi-bin/paper?xo0024
Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Ferraris, G.2016-05-13doi:10.1107/S2053273315024018International Union of CrystallographyENbook reviewSir William Lawrence BraggAlice Grace Jenny Braggtext/htmlCrystal Clear. The Autobiographies of Sir Lawrence & Lady Bragg. Edited by A. M. Glazer and Patience Thomson. Oxford University Press, 2015. Pp. xx + 427. Hardback. Price GBP 35.00. ISBN 978-0-19-874430-6.text4722016-05-13Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Abook reviews510511Perspectives in Crystallography. By John R. Helliwell. CRC Press, 2016. Hardback, Pp. xv + 155. Price GBP 75.65. ISBN 978-1-4987-3210-9.
http://scripts.iucr.org/cgi-bin/paper?xo0047
Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Ferraris, G.2016-05-13doi:10.1107/S2053273316003831International Union of CrystallographyENbook reviewbiocrystallographysynchrotron radiationtext/htmlPerspectives in Crystallography. By John R. Helliwell. CRC Press, 2016. Hardback, Pp. xv + 155. Price GBP 75.65. ISBN 978-1-4987-3210-9.text4722016-05-13Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Abook reviews512513