Acta Crystallographica Section A
http://journals.iucr.org/a/issues/2016/05/00/isscontsbdy.html
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 Crystallography2016-08-31International 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 5, 2016textweekly62002-01-01T00:00+00:005722016-08-31Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances515urn:issn:2053-2733med@iucr.orgAugust 20162016-08-31Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2016/05/00/isscontsbdy.html
Still imageMiniaturized beamsplitters realized by X-ray waveguides
http://scripts.iucr.org/cgi-bin/paper?mq5045
This paper reports on the fabrication and characterization of X-ray waveguide beamsplitters. The waveguide channels were manufactured by electron-beam lithography, reactive ion etching and wafer bonding techniques, with an empty (air) channel forming the guiding layer and silicon the cladding material. A focused synchrotron beam is efficiently coupled into the input channel. The beam is guided and split into two channels with a controlled (and tunable) distance at the exit of the waveguide chip. After free-space propagation and diffraction broadening, the two beams interfere and form a double-slit interference pattern in the far-field. From the recorded far-field, the near-field was reconstructed by a phase retrieval algorithm (error reduction), which was found to be extremely reliable for the two-channel setting. By numerical propagation methods, the reconstructed field was then propagated along the optical axis, to investigate the formation of the interference pattern from the two overlapping beams. Interestingly, phase vortices were observed and analysed.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Hoffmann-Urlaub, S.Salditt, T.2016-08-10doi:10.1107/S205327331601144XInternational Union of CrystallographyMiniaturized X-ray beamsplitters based on lithographic waveguide channels have been fabricated and tested. Numerical simulations of beam propagation and splitting by finite difference calculations have been confirmed by near-field reconstructions from the measured far-field interference pattern, using an error reduction algorithm. The device enables novel nano-interferometric and off-axis holography applications.ENX-ray waveguidesX-ray interferometryphase retrievalcoherencecoherent imagingThis paper reports on the fabrication and characterization of X-ray waveguide beamsplitters. The waveguide channels were manufactured by electron-beam lithography, reactive ion etching and wafer bonding techniques, with an empty (air) channel forming the guiding layer and silicon the cladding material. A focused synchrotron beam is efficiently coupled into the input channel. The beam is guided and split into two channels with a controlled (and tunable) distance at the exit of the waveguide chip. After free-space propagation and diffraction broadening, the two beams interfere and form a double-slit interference pattern in the far-field. From the recorded far-field, the near-field was reconstructed by a phase retrieval algorithm (error reduction), which was found to be extremely reliable for the two-channel setting. By numerical propagation methods, the reconstructed field was then propagated along the optical axis, to investigate the formation of the interference pattern from the two overlapping beams. Interestingly, phase vortices were observed and analysed.text/htmlMiniaturized beamsplitters realized by X-ray waveguidestext5722016-08-10Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers515522The crystallographic chameleon: when space groups change skin
http://scripts.iucr.org/cgi-bin/paper?sc5097
Volume A of International Tables for Crystallography is the reference for space-group information. However, the content is not exhaustive because for many space groups a variety of settings may be chosen but not all of them are described in detail or even fully listed. The use of alternative settings may seem an unnecessary complication when the purpose is just to describe a crystal structure; however, these are of the utmost importance for a number of tasks, such as the investigation of structure relations between polymorphs or derivative structures, the study of pseudo-symmetry and its potential consequences, and the analysis of the common substructure of twins. The aim of the article is twofold: (i) to present a guide to expressing the symmetry operations, the Hermann–Mauguin symbols and the Wyckoff positions of a space group in an alternative setting, and (ii) to point to alternative settings of space groups of possible practical applications and not listed in Volume A of International Tables for Crystallography.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Nespolo, M.Aroyo, M. I.2016-07-15doi:10.1107/S2053273316009293International Union of CrystallographyAlternative settings of space groups are explored: what they are, why they can be useful and how to obtain them.ENspace groupsaxial settingHermann–Mauguin symbolsVolume A of International Tables for Crystallography is the reference for space-group information. However, the content is not exhaustive because for many space groups a variety of settings may be chosen but not all of them are described in detail or even fully listed. The use of alternative settings may seem an unnecessary complication when the purpose is just to describe a crystal structure; however, these are of the utmost importance for a number of tasks, such as the investigation of structure relations between polymorphs or derivative structures, the study of pseudo-symmetry and its potential consequences, and the analysis of the common substructure of twins. The aim of the article is twofold: (i) to present a guide to expressing the symmetry operations, the Hermann–Mauguin symbols and the Wyckoff positions of a space group in an alternative setting, and (ii) to point to alternative settings of space groups of possible practical applications and not listed in Volume A of International Tables for Crystallography.text/htmlThe crystallographic chameleon: when space groups change skintext5722016-07-15Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers523538Improving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithm
http://scripts.iucr.org/cgi-bin/paper?sc5096
An iterative transform method proposed previously for direct phasing of high-solvent-content protein crystals is employed for enhancing the molecular-replacement (MR) algorithm in protein crystallography. Target structures that are resistant to conventional MR due to insufficient similarity between the template and target structures might be tractable with this modified phasing method. Trial calculations involving three different structures are described to test and illustrate the methodology. The relationship of the approach to PHENIX Phaser-MR and MR-Rosetta is discussed.Copyright (c) 2016 Hongxing He et al.urn:issn:2053-2733He, H.Fang, H.Miller, M.D.Phillips Jr, G.N.Su, W.-P.2016-07-15doi:10.1107/S2053273316010731International Union of CrystallographyAn iterative transform algorithm is proposed to improve the conventional molecular-replacement method for solving the phase problem in X-ray crystallography. Several examples of successful trial calculations carried out with real diffraction data are presented.ENmolecular replacementhybrid input–output algorithmab initio phasingprotein crystallographyAn iterative transform method proposed previously for direct phasing of high-solvent-content protein crystals is employed for enhancing the molecular-replacement (MR) algorithm in protein crystallography. Target structures that are resistant to conventional MR due to insufficient similarity between the template and target structures might be tractable with this modified phasing method. Trial calculations involving three different structures are described to test and illustrate the methodology. The relationship of the approach to PHENIX Phaser-MR and MR-Rosetta is discussed.text/htmlImproving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithmtext5722016-07-15Copyright (c) 2016 Hongxing He et al.Acta Crystallographica Section Aresearch papers539547On representing rotations by Rodrigues parameters in non-orthonormal reference systems
http://scripts.iucr.org/cgi-bin/paper?ae5020
A Rodrigues vector is a triplet of real numbers used for parameterizing rotations or orientations in three-dimensional space. Because of its properties (e.g. simplicity of fundamental regions for misorientations) this parameterization is frequently applied in analysis of orientation maps of polycrystalline materials. By conventional definition, the Rodrigues parameters are specified in orthonormal coordinate systems, whereas the bases of crystal lattices are generally non-orthogonal. Therefore, the definition of Rodrigues parameters is extended so they can be directly linked to non-Cartesian bases of a crystal. The new parameters are co- or contravariant components of vectors specified with respect to the same basis as atomic positions in a unit cell. The generalized formalism allows for redundant crystallographic axes. The formulas for rotation composition and the relationship to the rotation matrix are similar to those used in the Cartesian case, but they have a wider range of applicability: calculations can be performed with an arbitrary metric tensor of the crystal lattice. The parameterization in oblique coordinate frames of lattices is convenient for crystallographic applications because the generalized parameters are directly related to indices of rotation-invariant lattice directions and rotation-invariant lattice planes.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Morawiec, A.2016-07-28doi:10.1107/S2053273316009426International Union of CrystallographyVectorial parameterizations of proper rotations in three-dimensional space are generalized so the parameters are directly linked to non-orthonormal bases of crystal lattices or to frames with redundant crystallographic axes.ENlatticesrotation representationRodrigues parametersquaternionsframesA Rodrigues vector is a triplet of real numbers used for parameterizing rotations or orientations in three-dimensional space. Because of its properties (e.g. simplicity of fundamental regions for misorientations) this parameterization is frequently applied in analysis of orientation maps of polycrystalline materials. By conventional definition, the Rodrigues parameters are specified in orthonormal coordinate systems, whereas the bases of crystal lattices are generally non-orthogonal. Therefore, the definition of Rodrigues parameters is extended so they can be directly linked to non-Cartesian bases of a crystal. The new parameters are co- or contravariant components of vectors specified with respect to the same basis as atomic positions in a unit cell. The generalized formalism allows for redundant crystallographic axes. The formulas for rotation composition and the relationship to the rotation matrix are similar to those used in the Cartesian case, but they have a wider range of applicability: calculations can be performed with an arbitrary metric tensor of the crystal lattice. The parameterization in oblique coordinate frames of lattices is convenient for crystallographic applications because the generalized parameters are directly related to indices of rotation-invariant lattice directions and rotation-invariant lattice planes.text/htmlOn representing rotations by Rodrigues parameters in non-orthonormal reference systemstext5722016-07-28Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers548556Indirect Fourier transform in the context of statistical inference
http://scripts.iucr.org/cgi-bin/paper?vk5006
Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Muthig, M.Prévost, S.Orglmeister, R.Gradzielski, M.2016-07-28doi:10.1107/S2053273316009657International Union of CrystallographyThe indirect Fourier transform is discussed in the context of complementary statistical inference frameworks in order to determine a solution objectively, which then allows one to automate model-free analysis of small-angle scattering data. Modern machine-learning methods are used to obtain the most robust solution.ENindirect Fourier transform (IFT)Bayesian statistical inferencemodel selectionfrequentist statistical inferenceInferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.text/htmlIndirect Fourier transform in the context of statistical inferencetext5722016-07-28Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers557569A topological coordinate system for the diamond cubic grid
http://scripts.iucr.org/cgi-bin/paper?eo5061
Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Čomić, L.Nagy, B.2016-08-31doi:10.1107/S2053273316011700International Union of CrystallographyThe diamond cubic grid is one of the usual cubic crystal structures. The Voronoi cells are triakis truncated tetrahedra having four hexagon and 12 triangle faces, 30 edges and 16 vertices. A symmetric coordinate system is presented that addresses not only the voxels, but also the faces, edges and vertices between them. In this way, not only volumes, but also surfaces, or paths containing edges can be easily described and visualized.ENdiamond cubic gridtopological coordinate systemtopological operationsabstract cell complexesnon-traditional three-dimensional gridsTopological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.text/htmlA topological coordinate system for the diamond cubic gridtext5722016-08-31Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aresearch papers570581How to name and order convex polyhedra
http://scripts.iucr.org/cgi-bin/paper?eo5063
In this paper a method is suggested for naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph. A polyhedron is uniquely fixed by its name and can be built using it. Classes of convex n-acra (i.e. n-vertex polyhedra) are strictly ordered by their names.Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Voytekhovsky, Y.L.2016-08-10doi:10.1107/S2053273316010846International Union of CrystallographyA method is suggested to build a digital name for any convex polyhedron by using the adjacency matrix of its edge graph and vice versa. Thus, the problem of how to discern and order the overwhelming majority of combinatorially asymmetric (i.e. primitive triclinic) polyhedra is solved.ENconvex polyhedraadjacency matrixdigital nameorderingcombinatorial asymmetryIn this paper a method is suggested for naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph. A polyhedron is uniquely fixed by its name and can be built using it. Classes of convex n-acra (i.e. n-vertex polyhedra) are strictly ordered by their names.text/htmlHow to name and order convex polyhedratext5722016-08-10Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Ashort communications582585Vojtech Jaroslav Kopský (1936–2016)
http://scripts.iucr.org/cgi-bin/paper?es0420
Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Litvin, D.B.Janovec, V.2016-08-31doi:10.1107/S2053273316011852International Union of CrystallographyObituary for Vojtech Jaroslav Kopský.ENobituarygroup theoryphase transitionssubperiodic groupsInternational Tables for Crystallographytext/htmlVojtech Jaroslav Kopský (1936–2016)text5722016-08-31Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Aobituaries586587Mathematical Stereochemistry. By Shinsaku Fujita. De Gruyter, 2015. Pp. xviii + 437. Price EUR 129.95, USD 182.00, GBP 97.99. ISBN 978-3-11-036669-3.
http://scripts.iucr.org/cgi-bin/paper?xo0030
Copyright (c) 2016 International Union of Crystallographyurn:issn:2053-2733Chirikjian, G.2016-08-31doi:10.1107/S2053273316010779International Union of CrystallographyENbook reviewstereochemistrygroup theorytext/htmlMathematical Stereochemistry. By Shinsaku Fujita. De Gruyter, 2015. Pp. xviii + 437. Price EUR 129.95, USD 182.00, GBP 97.99. ISBN 978-3-11-036669-3.text5722016-08-31Copyright (c) 2016 International Union of CrystallographyActa Crystallographica Section Abook reviews588588