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) 2014 International Union of Crystallography2014-03-31International 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 70, Part 3, 2014textyearly62002-01-01T00:00+00:003702014-03-31Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances203urn:issn:2053-2733med@iucr.orgMarch 20142014-03-31Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2014/03/00/isscontsbdy.html
Still imagePolyhedra, complexes, nets and symmetry
http://scripts.iucr.org/cgi-bin/paper?xo5017
Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zigzag or helical. A polyhedron or complex is regular if its geometric symmetry group is transitive on the flags (incident vertex–edge–face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well known to crystallographers and they are identified explicitly. There are also six infinite families of chiral apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits.Copyright (c) 2014 International Union of Crystallographyurn:issn:2053-2733Schulte, E.2014-03-12doi:10.1107/S2053273314000217International Union of CrystallographyThe recently classified 3-periodic regular apeirohedra and polygonal complexes in space all have well known crystal nets as edge graphs. These nets are determined explicitly.ENcrystal netsregular polyhedraapeirohedrapolygonal complexesSkeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zigzag or helical. A polyhedron or complex is regular if its geometric symmetry group is transitive on the flags (incident vertex–edge–face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well known to crystallographers and they are identified explicitly. There are also six infinite families of chiral apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits.text/htmlPolyhedra, complexes, nets and symmetrytext3702014-03-12Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Non-crystallographic nets: characterization and first steps towards a classification
http://scripts.iucr.org/cgi-bin/paper?xo5014
Non-crystallographic (NC) nets are periodic nets characterized by the existence of non-trivial bounded automorphisms. Such automorphisms cannot be associated with any crystallographic symmetry in realizations of the net by crystal structures. It is shown that bounded automorphisms of finite order form a normal subgroup F(N) of the automorphism group of NC nets (N, T). As a consequence, NC nets are unstable nets (they display vertex collisions in any barycentric representation) and, conversely, stable nets are crystallographic nets. The labelled quotient graphs of NC nets are characterized by the existence of an equivoltage partition (a partition of the vertex set that preserves label vectors over edges between cells). A classification of NC nets is proposed on the basis of (i) their relationship to the crystallographic net with a homeomorphic barycentric representation and (ii) the structure of the subgroup F(N).Copyright (c) 2014 International Union of Crystallographyurn:issn:2053-2733Moreira de Oliveira Jr, M.Eon, J.-G.2014-03-12doi:10.1107/S2053273314000631International Union of CrystallographyThe central role of bounded automorphisms of finite order in non-crystallographic nets is featured; it is shown that stable nets are crystallographic nets.ENnon-crystallographic netsunstable netslabelled quotient graphsNon-crystallographic (NC) nets are periodic nets characterized by the existence of non-trivial bounded automorphisms. Such automorphisms cannot be associated with any crystallographic symmetry in realizations of the net by crystal structures. It is shown that bounded automorphisms of finite order form a normal subgroup F(N) of the automorphism group of NC nets (N, T). As a consequence, NC nets are unstable nets (they display vertex collisions in any barycentric representation) and, conversely, stable nets are crystallographic nets. The labelled quotient graphs of NC nets are characterized by the existence of an equivoltage partition (a partition of the vertex set that preserves label vectors over edges between cells). A classification of NC nets is proposed on the basis of (i) their relationship to the crystallographic net with a homeomorphic barycentric representation and (ii) the structure of the subgroup F(N).text/htmlNon-crystallographic nets: characterization and first steps towards a classificationtext3702014-03-12Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Applications of direct methods in protein crystallography for dealing with diffraction data down to 5 Å resolution
http://scripts.iucr.org/cgi-bin/paper?mq5019
Apart from solving the heavy-atom substructure in proteins and ab initio phasing of protein diffraction data at atomic resolution, direct methods have also been successfully combined with other protein crystallographic methods in dealing with diffraction data far below atomic resolution, leading to significantly improved results. In this respect, direct methods provide phase constraints in reciprocal space within a dual-space iterative framework rather than solve the phase problem independently. Applications of this type of direct methods to difficult SAD phasing, model completion and low-resolution phase extension will be described in detail.Copyright (c) 2014 International Union of Crystallographyurn:issn:2053-2733Fan, H.Gu, Y.He, Y.Lin, Z.Wang, J.Yao, D.Zhang, T.2014-03-12doi:10.1107/S2053273313034864International Union of CrystallographyDirect methods applying to protein diffraction data below atomic resolution are described. Typical examples for SAD phasing, model completion and phase extension are given in detail.ENdirect methodsproteinsSAD phasingmodel completionphase extensionApart from solving the heavy-atom substructure in proteins and ab initio phasing of protein diffraction data at atomic resolution, direct methods have also been successfully combined with other protein crystallographic methods in dealing with diffraction data far below atomic resolution, leading to significantly improved results. In this respect, direct methods provide phase constraints in reciprocal space within a dual-space iterative framework rather than solve the phase problem independently. Applications of this type of direct methods to difficult SAD phasing, model completion and low-resolution phase extension will be described in detail.text/htmlApplications of direct methods in protein crystallography for dealing with diffraction data down to 5 Å resolutiontext3702014-03-12Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section Aresearch papers00About systematic errors in charge-density studies
http://scripts.iucr.org/cgi-bin/paper?kx5024
The formerly introduced theoretical R values [Henn & Schönleber (2013). Acta Cryst. A69, 549–558] are used to develop a relative indicator of systematic errors in model refinements, Rmeta, and applied to published charge-density data. The counter of Rmeta gives an absolute measure of systematic errors in percentage points. The residuals (Io − Ic)/σ(Io) of published data are examined. It is found that most published models correspond to residual distributions that are not consistent with the assumption of a Gaussian distribution. The consistency with a Gaussian distribution, however, is important, as the model parameter estimates and their standard uncertainties from a least-squares procedure are valid only under this assumption. The effect of correlations introduced by the structure model is briefly discussed with the help of artificial data and discarded as a source of serious correlations in the examined example. Intensity and significance cutoffs applied in the refinement procedure are found to be mechanisms preventing residual distributions from becoming Gaussian. Model refinements against artificial data yield zero or close-to-zero values for Rmeta when the data are not truncated and small negative values in the case of application of a moderate cutoff Io > 0. It is well known from the literature that the application of cutoff values leads to model bias [Hirshfeld & Rabinovich (1973). Acta Cryst. A29, 510–513].Copyright (c) 2014 International Union of Crystallographyurn:issn:2053-2733Henn, J.Meindl, K.2014-03-13doi:10.1107/S2053273314000898International Union of CrystallographyAn indicator of systematic errors based on theoretical R values is introduced and applied to charge-density data.ENsystematic errorstheoretical R valuesmeta-residual valuescharge-density studiesleast-squares refinementresidualsThe formerly introduced theoretical R values [Henn & Schönleber (2013). Acta Cryst. A69, 549–558] are used to develop a relative indicator of systematic errors in model refinements, Rmeta, and applied to published charge-density data. The counter of Rmeta gives an absolute measure of systematic errors in percentage points. The residuals (Io − Ic)/σ(Io) of published data are examined. It is found that most published models correspond to residual distributions that are not consistent with the assumption of a Gaussian distribution. The consistency with a Gaussian distribution, however, is important, as the model parameter estimates and their standard uncertainties from a least-squares procedure are valid only under this assumption. The effect of correlations introduced by the structure model is briefly discussed with the help of artificial data and discarded as a source of serious correlations in the examined example. Intensity and significance cutoffs applied in the refinement procedure are found to be mechanisms preventing residual distributions from becoming Gaussian. Model refinements against artificial data yield zero or close-to-zero values for Rmeta when the data are not truncated and small negative values in the case of application of a moderate cutoff Io > 0. It is well known from the literature that the application of cutoff values leads to model bias [Hirshfeld & Rabinovich (1973). Acta Cryst. A29, 510–513].text/htmlAbout systematic errors in charge-density studiestext3702014-03-13Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section Aresearch papers00A new theory for X-ray diffraction
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This article proposes a new theory of X-ray scattering that has particular relevance to powder diffraction. The underlying concept of this theory is that the scattering from a crystal or crystallite is distributed throughout space: this leads to the effect that enhanced scatter can be observed at the `Bragg position' even if the `Bragg condition' is not satisfied. The scatter from a single crystal or crystallite, in any fixed orientation, has the fascinating property of contributing simultaneously to many `Bragg positions'. It also explains why diffraction peaks are obtained from samples with very few crystallites, which cannot be explained with the conventional theory. The intensity ratios for an Si powder sample are predicted with greater accuracy and the temperature factors are more realistic. Another consequence is that this new theory predicts a reliability in the intensity measurements which agrees much more closely with experimental observations compared to conventional theory that is based on `Bragg-type' scatter. The role of dynamical effects (extinction etc.) is discussed and how they are suppressed with diffuse scattering. An alternative explanation for the Lorentz factor is presented that is more general and based on the capture volume in diffraction space. This theory, when applied to the scattering from powders, will evaluate the full scattering profile, including peak widths and the `background'. The theory should provide an increased understanding of the reliability of powder diffraction measurements, and may also have wider implications for the analysis of powder diffraction data, by increasing the accuracy of intensities predicted from structural models.Copyright (c) 2014 Paul F. Fewsterurn:issn:2053-2733Fewster, P.F.2014-03-27doi:10.1107/S205327331400117XInternational Union of CrystallographyBy considering the scattering distributed throughout space, there is an intensity enhancement at the Bragg angle even when the Bragg condition is not satisfied. This leads to an alternative explanation for the diffraction from powders and small crystals.ENdiffraction theorypowder diffractionsmall crystalsThis article proposes a new theory of X-ray scattering that has particular relevance to powder diffraction. The underlying concept of this theory is that the scattering from a crystal or crystallite is distributed throughout space: this leads to the effect that enhanced scatter can be observed at the `Bragg position' even if the `Bragg condition' is not satisfied. The scatter from a single crystal or crystallite, in any fixed orientation, has the fascinating property of contributing simultaneously to many `Bragg positions'. It also explains why diffraction peaks are obtained from samples with very few crystallites, which cannot be explained with the conventional theory. The intensity ratios for an Si powder sample are predicted with greater accuracy and the temperature factors are more realistic. Another consequence is that this new theory predicts a reliability in the intensity measurements which agrees much more closely with experimental observations compared to conventional theory that is based on `Bragg-type' scatter. The role of dynamical effects (extinction etc.) is discussed and how they are suppressed with diffuse scattering. An alternative explanation for the Lorentz factor is presented that is more general and based on the capture volume in diffraction space. This theory, when applied to the scattering from powders, will evaluate the full scattering profile, including peak widths and the `background'. The theory should provide an increased understanding of the reliability of powder diffraction measurements, and may also have wider implications for the analysis of powder diffraction data, by increasing the accuracy of intensities predicted from structural models.text/htmlA new theory for X-ray diffractiontext3702014-03-27Copyright (c) 2014 Paul F. FewsterActa Crystallographica Section Aresearch papers00Unified approach for determining tetragonal tungsten bronze crystal structures
http://scripts.iucr.org/cgi-bin/paper?ib5024
Tetragonal tungsten bronze (TTB) oxides are one of the most important classes of ferroelectrics. Many of these framework structures undergo ferroelastic transformations related to octahedron tilting deformations. Such tilting deformations are closely related to the rigid unit modes (RUMs). This paper discusses the whole set of RUMs in an ideal TTB lattice and possible crystal structures which can emerge owing to the condensation of some of them. Analysis of available experimental data for the TTB-like niobates lends credence to the obtained theoretical predictions.Copyright (c) 2014 International Union of Crystallographyurn:issn:2053-2733Smirnov, M.Saint-Grégoire, P.2014-04-01doi:10.1107/S2053273314003994International Union of CrystallographyThe whole set of rigid unit modes in tetragonal tetragonal bronze lattices is described. Structural distortions induced by condensation of the modes are discussed. Confrontation with available experimental data confirms the relevance of the rigid unit mode model.ENtetragonal tungsten bronzesrigid unit modesphase transitionsTetragonal tungsten bronze (TTB) oxides are one of the most important classes of ferroelectrics. Many of these framework structures undergo ferroelastic transformations related to octahedron tilting deformations. Such tilting deformations are closely related to the rigid unit modes (RUMs). This paper discusses the whole set of RUMs in an ideal TTB lattice and possible crystal structures which can emerge owing to the condensation of some of them. Analysis of available experimental data for the TTB-like niobates lends credence to the obtained theoretical predictions.text/htmlUnified approach for determining tetragonal tungsten bronze crystal structurestext3702014-04-01Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Seitz symbols for crystallographic symmetry operations
http://scripts.iucr.org/cgi-bin/paper?es0405
The aim of this report is to describe the Seitz notation for symmetry operations adopted by the Commission on Crystallographic Nomenclature as the standard convention for Seitz symbolism of the International Union of Crystallography. The established notation follows the existing crystallographic conventions in the descriptions of symmetry operations.Copyright (c) 2014 International Union of Crystallographyurn:issn:2053-2733Glazer, A.M.Aroyo, M.I.Authier, A.2014-03-14doi:10.1107/S2053273314004495International Union of CrystallographyThe Seitz notation for symmetry operations adopted by the Commission on Crystallographic Nomenclature as the standard convention for Seitz symbolism of the International Union of Crystallography is described.ENSeitz notationsymmetry operationscrystallographic groupsThe aim of this report is to describe the Seitz notation for symmetry operations adopted by the Commission on Crystallographic Nomenclature as the standard convention for Seitz symbolism of the International Union of Crystallography. The established notation follows the existing crystallographic conventions in the descriptions of symmetry operations.text/htmlSeitz symbols for crystallographic symmetry operationstext3702014-03-14Copyright (c) 2014 International Union of CrystallographyActa Crystallographica Section Ashort communications00