http://journals.iucr.org/a/issues/2013/04/00/isscontsbdy.html Acta Crystallographica Section A: Foundations of Crystallography 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. en Copyright (c) 2013 International Union of Crystallography 2013-06-17 International Union of Crystallography International Union of Crystallography http://journals.iucr.org urn:issn:0108-7673 Acta Crystallographica Section A: Foundations of Crystallography 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/html Acta Crystallographica Section A: Foundations of Crystallography, Volume 69, Part 4, 2013 text yearly 6 2002-01-01T00:00+00:00 4 69 2013-06-17 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography 365 urn:issn:0108-7673 med@iucr.org June 2013 2013-06-17 http://journals.iucr.org/logos/rss10a.gif http://journals.iucr.org/a/issues/2013/04/00/isscontsbdy.html Still image http://scripts.iucr.org/cgi-bin/paper?sc5058 Femtosecond X-ray pulses from X-ray free-electron laser sources make it feasible to conduct room-temperature solution scattering experiments far below molecular rotational diffusion timescales. Owing to the ultra-short duration of each snapshot in these fluctuation scattering experiments, the particles are effectively frozen in space during the X-ray exposure. In contrast to standard small-angle scattering experiments, the resulting scattering patterns are anisotropic. The intensity fluctuations observed in the diffraction images can be used to obtain structural information embedded in the average angular correlation of the Fourier transform of the scattering species, of which standard small-angle scattering data are a subset. The additional information contained in the data of these fluctuation scattering experiments can be used to determine the structure of macromolecules in solution without imposing symmetry or spatial restraints during model reconstruction, reducing ambiguities normally observed in solution scattering studies. In this communication, a method that utilizes fluctuation X-ray scattering data to determine low-resolution solution structures is presented. The method is validated with theoretical data calculated from several representative molecules and applied to the reconstruction of nanoparticles from experimental data collected at the Linac Coherent Light Source. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Liu, H. Poon, B.K. Saldin, D.K. Spence, J.C.H. Zwart, P.H. 2013-05-08 doi:10.1107/S0108767313006016 International Union of Crystallography Ab initio model reconstruction from fluctuation X-ray scattering data is described. EN three-dimensional Zernike polynomials fluctuation X-ray scattering femtosecond X-ray diffraction structure Femtosecond X-ray pulses from X-ray free-electron laser sources make it feasible to conduct room-temperature solution scattering experiments far below molecular rotational diffusion timescales. Owing to the ultra-short duration of each snapshot in these fluctuation scattering experiments, the particles are effectively frozen in space during the X-ray exposure. In contrast to standard small-angle scattering experiments, the resulting scattering patterns are anisotropic. The intensity fluctuations observed in the diffraction images can be used to obtain structural information embedded in the average angular correlation of the Fourier transform of the scattering species, of which standard small-angle scattering data are a subset. The additional information contained in the data of these fluctuation scattering experiments can be used to determine the structure of macromolecules in solution without imposing symmetry or spatial restraints during model reconstruction, reducing ambiguities normally observed in solution scattering studies. In this communication, a method that utilizes fluctuation X-ray scattering data to determine low-resolution solution structures is presented. The method is validated with theoretical data calculated from several representative molecules and applied to the reconstruction of nanoparticles from experimental data collected at the Linac Coherent Light Source. text/html Three-dimensional single-particle imaging using angular correlations from X-ray laser data text 4 69 2013-05-08 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 365 373 http://scripts.iucr.org/cgi-bin/paper?dm5032 It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non-modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell (i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Kocian, P. 2013-05-17 doi:10.1107/S0108767313005990 International Union of Crystallography By using Lie group theory, the symmetry of displacively modulated structures may be described in the usual three-dimensional space. Moreover, when calculating the Fourier transform of such crystals, the structure factor may be clearly exhibited without requiring additional dimensions. EN modulated structures Lie groups structure factors It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non-modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell (i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions. text/html Incommensurate crystallography without additional dimensions text 4 69 2013-05-17 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 374 387 http://scripts.iucr.org/cgi-bin/paper?pc5025 New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part Ps. Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Stokes, H.T. Campbell, B.J. Cordes, R. 2013-05-08 doi:10.1107/S0108767313007538 International Union of Crystallography A tabulation of complete irreducible representations at all k points of three-dimensional crystallographic space groups and their extensions to (3 + d)-dimensional superspace groups is presented. EN irreducible representations space groups distortions order parameter New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part Ps. Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms. text/html Tabulation of irreducible representations of the crystallographic space groups and their superspace extensions text 4 69 2013-05-08 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 388 395 http://scripts.iucr.org/cgi-bin/paper?sc5059 δ Recycling is a simple procedure for directly extracting phase information from Patterson-type functions [Rius (2012). Acta Cryst. A68, 399–400]. This new phasing method has a clear theoretical basis and was developed with ideal single-crystal X-ray diffraction data. On the other hand, introduction of the automated diffraction tomography (ADT) technique has represented a significant advance in electron diffraction data collection [Kolb et al. (2007). Ultramicroscopy, 107, 507–513]. When combined with precession electron diffraction, it delivers quasi-kinematical intensity data even for complex inorganic compounds, so that single-crystal diffraction data of nanometric volumes are now available for structure determination by direct methods. To check the tolerance of δ recycling to missing data-collection corrections and to deviations from kinematical behaviour of ADT intensities, δ recycling has been applied to differently shaped nanocrystals of various inorganic materials. The results confirm that it can phase ADT data very efficiently. In some cases even more complete structure models than those derived from conventional direct methods and least-squares refinement have been found. During this study it has been demonstrated that the Wilson-plot scaling procedure is largely insensitive to sample thickness variations and missing absorption corrections affecting electron ADT intensities. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Rius, J. Mugnaioli, E. Vallcorba, O. Kolb, U. 2013-05-15 doi:10.1107/S0108767313009549 International Union of Crystallography The tolerance of δ recycling phases to missing data-collection corrections and to deviations from kinematical behaviour of electron ADT intensities is analysed in detail. It has been found that Wilson-plot scaling is largely insensitive to sample thickness variations and missing absorption corrections. EN δ recycling direct methods structure solution electron diffraction automated diffraction tomography nano electron diffraction precession electron diffraction nanocrystals δ Recycling is a simple procedure for directly extracting phase information from Patterson-type functions [Rius (2012). Acta Cryst. A68, 399–400]. This new phasing method has a clear theoretical basis and was developed with ideal single-crystal X-ray diffraction data. On the other hand, introduction of the automated diffraction tomography (ADT) technique has represented a significant advance in electron diffraction data collection [Kolb et al. (2007). Ultramicroscopy, 107, 507–513]. When combined with precession electron diffraction, it delivers quasi-kinematical intensity data even for complex inorganic compounds, so that single-crystal diffraction data of nanometric volumes are now available for structure determination by direct methods. To check the tolerance of δ recycling to missing data-collection corrections and to deviations from kinematical behaviour of ADT intensities, δ recycling has been applied to differently shaped nanocrystals of various inorganic materials. The results confirm that it can phase ADT data very efficiently. In some cases even more complete structure models than those derived from conventional direct methods and least-squares refinement have been found. During this study it has been demonstrated that the Wilson-plot scaling procedure is largely insensitive to sample thickness variations and missing absorption corrections affecting electron ADT intensities. text/html Application of δ recycling to electron automated diffraction tomography data from inorganic crystalline nanovolumes text 4 69 2013-05-15 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 396 407 http://scripts.iucr.org/cgi-bin/paper?pc5026 A new study of the σA parameter has been undertaken to understand its behaviour when the diffraction amplitude distributions are far from the standard Wilson distributions. The study has led to the formulation of a new statistical interpretation of σA, expressed in terms of a correlation factor. The new formulas allow a more accurate use of σA in electron-density modification procedures. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Carrozzini, B. Cascarano, G.L. Giacovazzo, C. Mazzone, A. 2013-05-15 doi:10.1107/S010876731300768X International Union of Crystallography A new statistical interpretation of the σA parameter is provided. EN σA estimate joint probability distribution approach structure-factor distributions correlation factors A new study of the σA parameter has been undertaken to understand its behaviour when the diffraction amplitude distributions are far from the standard Wilson distributions. The study has led to the formulation of a new statistical interpretation of σA, expressed in terms of a correlation factor. The new formulas allow a more accurate use of σA in electron-density modification procedures. text/html A new interpretation of the σA parameter text 4 69 2013-05-15 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 408 412 http://scripts.iucr.org/cgi-bin/paper?eo5021 A previous paper detailed a novel algorithm, ∊-machine spectral reconstruction theory (∊MSR), that infers pattern and disorder in planar-faulted, close-packed structures directly from X-ray diffraction patterns [Varn et al. (2013). Acta Cryst. A69, 197–206]. Here ∊MSR is applied to simulated diffraction patterns from four close-packed crystals. It is found that, for stacking structures with a memory length of three or less, ∊MSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an ∊-machine. For stacking structures with a memory length larger than three, ∊MSR returns a model that captures many important features of the original stacking structure. These include multiple stacking faults and multiple crystal structures. Further, it is found that ∊MSR is able to discover stacking structure in even highly disordered crystals. In order to address issues concerning the long-range order observed in many classes of layered materials, several length parameters are defined, calculable from the ∊-machine, and their relevance is discussed. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Varn, D.P. Canright, G.S. Crutchfield, J.P. 2013-05-17 doi:10.1107/S0108767313008738 International Union of Crystallography ∊-Machine spectral reconstruction theory, a method for finding planar disorder in close-packed structures, is applied to four simulated diffraction patterns. EN X-ray diffraction diffuse scattering one-dimensional disorder polytypes planar faults computational mechanics A previous paper detailed a novel algorithm, ∊-machine spectral reconstruction theory (∊MSR), that infers pattern and disorder in planar-faulted, close-packed structures directly from X-ray diffraction patterns [Varn et al. (2013). Acta Cryst. A69, 197–206]. Here ∊MSR is applied to simulated diffraction patterns from four close-packed crystals. It is found that, for stacking structures with a memory length of three or less, ∊MSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an ∊-machine. For stacking structures with a memory length larger than three, ∊MSR returns a model that captures many important features of the original stacking structure. These include multiple stacking faults and multiple crystal structures. Further, it is found that ∊MSR is able to discover stacking structure in even highly disordered crystals. In order to address issues concerning the long-range order observed in many classes of layered materials, several length parameters are defined, calculable from the ∊-machine, and their relevance is discussed. text/html Inferring planar disorder in close-packed structures via ∊-machine spectral reconstruction theory: examples from simulated diffraction patterns text 4 69 2013-05-17 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 413 426 http://scripts.iucr.org/cgi-bin/paper?td5013 The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Beanland, R. Thomas, P.J. Woodward, D.I. Thomas, P.A. Roemer, R.A. 2013-05-21 doi:10.1107/S0108767313010143 International Union of Crystallography Computer control of beam tilt and image capture allows the collection of electron diffraction patterns over a large angular range, without any overlap in diffraction data and from a region limited only by the size of the electron beam. This results in a significant improvement in data volumes and ease of interpretation. EN electron diffraction symmetry determination CBED LACBED computer control The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters. text/html Digital electron diffraction – seeing the whole picture text 4 69 2013-05-21 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 427 434 http://scripts.iucr.org/cgi-bin/paper?eo5022 This paper studies the symmetry group of two special types of carbon nanotori. The construction is motivated by a group-theoretical result. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Staic, M.D. Petrescu-Nita, A. 2013-05-22 doi:10.1107/S0108767313010325 International Union of Crystallography The symmetry group of two special types of carbon nanotori is studied using a group-theoretical result. EN carbon nanotori Cayley hypergraphs This paper studies the symmetry group of two special types of carbon nanotori. The construction is motivated by a group-theoretical result. text/html Symmetry group of two special types of carbon nanotori text 4 69 2013-05-22 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 435 439 http://scripts.iucr.org/cgi-bin/paper?eo5023 The use of Pólya's theorem in crystallography and other applications has greatly simplified many counting and coloring problems. Given a group of equivalences acting on a set, Pólya's theorem equates the number of unique subsets with the orbits of the group action. For a lattice and a given group of periodic equivalences, the number of nonequivalent subsets of the lattice can be solved using Pólya's counting on the group of relevant symmetries acting on the lattice. When equivalence is defined via a sublattice, the use of Pólya's theorem is equivalent to knowing the cycle index of the action of the group elements on a related finite group structure. A simple algebraic method is presented to determine the cycle index for a group element acting on a lattice subject to certain periodicity arguments. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Cocke, W. 2013-06-05 doi:10.1107/S0108767313011926 International Union of Crystallography A technique to calculate the number of nonequivalent subsets of a lattice subject to periodic boundary conditions is presented. EN lattice periodic subsets equivalences Pólya's theorem The use of Pólya's theorem in crystallography and other applications has greatly simplified many counting and coloring problems. Given a group of equivalences acting on a set, Pólya's theorem equates the number of unique subsets with the orbits of the group action. For a lattice and a given group of periodic equivalences, the number of nonequivalent subsets of the lattice can be solved using Pólya's counting on the group of relevant symmetries acting on the lattice. When equivalence is defined via a sublattice, the use of Pólya's theorem is equivalent to knowing the cycle index of the action of the group elements on a related finite group structure. A simple algebraic method is presented to determine the cycle index for a group element acting on a lattice subject to certain periodicity arguments. text/html Nonequivalent periodic subsets of the lattice text 4 69 2013-06-05 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 440 444 http://scripts.iucr.org/cgi-bin/paper?eo5024 A framework is presented based on color symmetry theory that will facilitate the determination of the subgroup structure of a crystallographic Coxeter group. It is shown that the method may be extended to characterize torsion-free subgroups. The approach is to treat these groups as groups of symmetries of tessellations in space by fundamental polyhedra. Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Provido, E.D.B. De Las Peñas, M.L.A.N. Felix, R.P. 2013-06-18 doi:10.1107/S010876731301283X International Union of Crystallography A method is presented that will facilitate the determination of the subgroup structure of crystallographic Coxeter groups, including determining torsion-free subgroups. EN crystallographic Coxeter groups crystallographic groups subgroups of crystallographic groups torsion-free subgroups color symmetry A framework is presented based on color symmetry theory that will facilitate the determination of the subgroup structure of a crystallographic Coxeter group. It is shown that the method may be extended to characterize torsion-free subgroups. The approach is to treat these groups as groups of symmetries of tessellations in space by fundamental polyhedra. text/html On subgroups of crystallographic Coxeter groups text 4 69 2013-06-18 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 445 451 http://scripts.iucr.org/cgi-bin/paper?mq5011 Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Viterbo, D. 2013-05-08 doi:10.1107/S0108767313006508 International Union of Crystallography Sir W. H. Bragg was an outstanding teacher capable of exciting the minds of intelligent young people and addressing them to science in general and chemistry in particular. Both Primo Levi, a well known Italian writer, and Dorothy Hodgkin, Nobel laureate for her pioneering work in crystallography, decided that they would become chemists after reading, at the age of sixteen, Bragg's book Concerning the Nature of Things. EN Primo Levi William Henry Bragg atomic theory of matter text/html Primo Levi, William Henry Bragg and the atomic theory of matter text 4 69 2013-05-08 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography essays 452 456 http://scripts.iucr.org/cgi-bin/paper?pf0109 Copyright (c) 2013 International Union of Crystallography urn:issn:0108-7673 Nespolo, M. 2013-06-18 doi:10.1107/S0108767313006624 International Union of Crystallography EN book review text/html Crystallography – An Introduction, 3rd ed. By Walter Borchardt-Ott. Springer, 2012. Pp. xvi + 357. Price (paperback) EUR 42.75. ISBN 978-3-642-16451-4. text 4 69 2013-06-18 Copyright (c) 2013 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography book reviews 457 458