Acta Crystallographica Section A
http://journals.iucr.org/a/issues/2017/01/00/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) 2017 International Union of Crystallography2016-12-08International 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 73, Part 1, 2017textweekly62002-01-01T00:00+00:001732016-12-08Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances1urn:issn:2053-2733med@iucr.orgDecember 20162016-12-08Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2017/01/00/isscontsbdy.html
Still imageA general algorithm for generating isotropy subgroups in superspace
http://scripts.iucr.org/cgi-bin/paper?vk5013
This paper presents a general algorithm for generating the isotropy subgroups of superspace extensions of crystallographic space groups involving arbitrary superpositions of multi-k order parameters from incommensurate and commensurate k vectors. Several examples are presented in detail in order to illuminate each step of the algorithm. The practical outcome is that one can now start with any commensurate parent crystal structure and generate a structure model for any conceivable incommensurate modulation of that parent, fully parameterized in terms of order parameters of irreducible representations at the relevant wavevectors. The resulting modulated structures have (3 + d)-dimensional superspace-group symmetry. Because incommensurate structures are now commonly encountered in the context of many scientifically and technologically important functional materials, the opportunity to apply the powerful methods of group representation theory to this broader class of structural distortions is very timely.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Stokes, H.T.Campbell, B.J.2017-01-01doi:10.1107/S2053273316017629International Union of CrystallographyIrreducible representations can now be used to derive the isotropy subgroups at irrational wavevectors, making it relatively easy to explore the (3 + d)-dimensional superspace-group symmetries that arise from incommensurate modulations of a parent crystal structure. A general algorithm capable of arbitrary superpositions of multiple incommensurate and commensurate order parameters is presented.ENirreducible representationsisotropy subgroupsincommensurate structuresmodulated structuressuperspace groupsorder parameterThis paper presents a general algorithm for generating the isotropy subgroups of superspace extensions of crystallographic space groups involving arbitrary superpositions of multi-k order parameters from incommensurate and commensurate k vectors. Several examples are presented in detail in order to illuminate each step of the algorithm. The practical outcome is that one can now start with any commensurate parent crystal structure and generate a structure model for any conceivable incommensurate modulation of that parent, fully parameterized in terms of order parameters of irreducible representations at the relevant wavevectors. The resulting modulated structures have (3 + d)-dimensional superspace-group symmetry. Because incommensurate structures are now commonly encountered in the context of many scientifically and technologically important functional materials, the opportunity to apply the powerful methods of group representation theory to this broader class of structural distortions is very timely.text/htmlA general algorithm for generating isotropy subgroups in superspacetext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Sphere packings as a tool for the description of martensitic phase transformations
http://scripts.iucr.org/cgi-bin/paper?td5036
Martensitic transformations which play an important role in metallurgical processes are analysed using group–subgroup relations and sphere-packing considerations. This approach is applied to the transformations between body-centred cubic (b.c.c.) and face-centred cubic (f.c.c.) phases and yields the orientation relations according to the Nishiyama–Wassermann, the Kurdjumov–Sachs and the Pitsch mechanisms. The models proposed by Pitsch and Schrader and by Burgers for the transition between b.c.c. and hexagonally closest-packed (h.c.p.) type structures can be interpreted analogously. In addition, two mechanisms for the transition between cubic f.c.c. and h.c.p. structures are described.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Sowa, H.2017-01-01doi:10.1107/S2053273316013425International Union of CrystallographyMartensitic phase transformations are described by means of group–subgroup relations and sphere-packing considerations.ENsphere packingsmartensitic transformationsorientation relationshipsgroup–subgroup relationsMartensitic transformations which play an important role in metallurgical processes are analysed using group–subgroup relations and sphere-packing considerations. This approach is applied to the transformations between body-centred cubic (b.c.c.) and face-centred cubic (f.c.c.) phases and yields the orientation relations according to the Nishiyama–Wassermann, the Kurdjumov–Sachs and the Pitsch mechanisms. The models proposed by Pitsch and Schrader and by Burgers for the transition between b.c.c. and hexagonally closest-packed (h.c.p.) type structures can be interpreted analogously. In addition, two mechanisms for the transition between cubic f.c.c. and h.c.p. structures are described.text/htmlSphere packings as a tool for the description of martensitic phase transformationstext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Revisiting La0.5Sr1.5MnO4 lattice distortion and charge ordering with multi-beam resonant diffraction
http://scripts.iucr.org/cgi-bin/paper?lk5012
Sinusoidal wave type distortions of La0.5Sr1.5MnO4 in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction (MRXD) with (7/4 7/4 0) fractional primary diffraction. Two four-beam diffractions with opposite asymmetry were measured at 6.5545 keV and compared with the curves simulated by the dynamical X-ray diffraction theory. This approach provides the possibility of resolving the distortion modes which are perpendicular to the momentum transfer by a single azimuthal scan. The paper also demonstrates the sensitivity of MRXD profiles versus incident X-ray energy in the vicinity of the Mn K edge to the charge disproportion between the two manganese sites, reconfirming the small charge disproportion feature.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Liu, W.-C.Chiu, Y.-H.Kung, Y.-Y.Liao, P.-Y.Cheng, C.-H.Chih, Y.-C.Tsai, Y.-W.Chu, C.-H.Lai, C.-H.Huang, D.-J.Soo, Y.-L.Chang, S.-L.2017-01-01doi:10.1107/S2053273316013759International Union of CrystallographySinusoidal wave type distortions of La0.5Sr1.5MnO4 in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction and dynamical theory.ENX-ray multiple diffractiondynamical X-ray diffraction theoryLa0.5Sr1.5MnO4Sinusoidal wave type distortions of La0.5Sr1.5MnO4 in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction (MRXD) with (7/4 7/4 0) fractional primary diffraction. Two four-beam diffractions with opposite asymmetry were measured at 6.5545 keV and compared with the curves simulated by the dynamical X-ray diffraction theory. This approach provides the possibility of resolving the distortion modes which are perpendicular to the momentum transfer by a single azimuthal scan. The paper also demonstrates the sensitivity of MRXD profiles versus incident X-ray energy in the vicinity of the Mn K edge to the charge disproportion between the two manganese sites, reconfirming the small charge disproportion feature.text/htmlRevisiting La0.5Sr1.5MnO4 lattice distortion and charge ordering with multi-beam resonant diffractiontext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Constraint-induced direct phasing method
http://scripts.iucr.org/cgi-bin/paper?ae5023
The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimetre in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented microcrystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern. Although single-crystal diffraction data consist of discrete spots or X-ray reflections, the diffraction of microcrystals in a powder forms rings so that the reflections overlap. Thus, the analysis is more challenging due to unavoidable errors in the structure-factor amplitudes and the low-resolution data available for structure determination. This paper introduces a constraint-induced phasing method that (i) improves structure solutions measured by success rate, quality of solutions and various figures of merit, and (ii) extends low-resolution powder diffraction data to atomic resolution by adding unmeasured reflections. Application results have shown clearly that the constraint-induced phasing method is an effective way to produce initial structure models that are suitable for further structural refinement and completion.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Xu, H.2017-01-01doi:10.1107/S2053273316013875International Union of CrystallographyA constraint-induced direct phasing method has been developed to improve structure-solution determination for low-resolution X-ray powder diffraction data.ENpowder diffractionpowder Shake-and-Bakedirect phasing methodslow-resolution dataThe best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimetre in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented microcrystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern. Although single-crystal diffraction data consist of discrete spots or X-ray reflections, the diffraction of microcrystals in a powder forms rings so that the reflections overlap. Thus, the analysis is more challenging due to unavoidable errors in the structure-factor amplitudes and the low-resolution data available for structure determination. This paper introduces a constraint-induced phasing method that (i) improves structure solutions measured by success rate, quality of solutions and various figures of merit, and (ii) extends low-resolution powder diffraction data to atomic resolution by adding unmeasured reflections. Application results have shown clearly that the constraint-induced phasing method is an effective way to produce initial structure models that are suitable for further structural refinement and completion.text/htmlConstraint-induced direct phasing methodtext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers002-Periodic self-dual tilings
http://scripts.iucr.org/cgi-bin/paper?eo5066
2-Periodic self-dual tilings are important in fields ranging from crystal chemistry to mathematical physics. They have been systematically enumerated using combinatorial tiling theory, and 1, 5 and 62 uninodal, binodal and trinodal self-dual tilings have been found. This paper illustrates all uninodal and binodal self-dual tilings and selected trinodal self-dual tilings. Most of these structures are described for the first time.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Delgado-Friedrichs, O.O'Keeffe, M.2017-01-01doi:10.1107/S2053273316013917International Union of CrystallographyAll uninodal, binodal and trinodal 2-periodic self-dual tilings are enumerated and described.ENnetsself-dual tilings2-Periodic self-dual tilings are important in fields ranging from crystal chemistry to mathematical physics. They have been systematically enumerated using combinatorial tiling theory, and 1, 5 and 62 uninodal, binodal and trinodal self-dual tilings have been found. This paper illustrates all uninodal and binodal self-dual tilings and selected trinodal self-dual tilings. Most of these structures are described for the first time.text/html2-Periodic self-dual tilingstext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Lattice reduction using a Euclidean algorithm
http://scripts.iucr.org/cgi-bin/paper?ae5025
The need to reduce a periodic structure given in terms of a large supercell and associated lattice generators arises frequently in different fields of application of crystallography, in particular in the ab initio theoretical modelling of materials at the atomic scale. This paper considers the reduction of crystals and addresses the reduction associated with the existence of a commensurate translation that leaves the crystal invariant, providing a practical scheme for it. The reduction procedure hinges on a convenient integer factorization of the full period of the cycle (or grid) generated by the repeated applications of the invariant translation, and its iterative reduction into sub-cycles, each of which corresponds to a factor in the decomposition of the period. This is done in successive steps, each time solving a Diophantine linear equation by means of a Euclidean reduction algorithm in order to provide the generators of the reduced lattice.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Mujica, A.2017-01-01doi:10.1107/S2053273316015539International Union of CrystallographyThe reduction of a crystal lattice is considered. The reduction associated with the existence of a commensurate translation that leaves the crystal invariant is addressed, and a practical scheme for it is provided.ENreduction of latticesab initio calculationsstructure searchEuclidean algorithmsupercellsThe need to reduce a periodic structure given in terms of a large supercell and associated lattice generators arises frequently in different fields of application of crystallography, in particular in the ab initio theoretical modelling of materials at the atomic scale. This paper considers the reduction of crystals and addresses the reduction associated with the existence of a commensurate translation that leaves the crystal invariant, providing a practical scheme for it. The reduction procedure hinges on a convenient integer factorization of the full period of the cycle (or grid) generated by the repeated applications of the invariant translation, and its iterative reduction into sub-cycles, each of which corresponds to a factor in the decomposition of the period. This is done in successive steps, each time solving a Diophantine linear equation by means of a Euclidean reduction algorithm in order to provide the generators of the reduced lattice.text/htmlLattice reduction using a Euclidean algorithmtext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?
http://scripts.iucr.org/cgi-bin/paper?mq5046
This paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Jahn, T.Wilke, R.N.Chushkin, Y.Salditt, T.2017-01-01doi:10.1107/S2053273316015114International Union of CrystallographyThe critical photon fluence for reconstructing objects from noisy diffraction patterns is computed by a maximum-likelihood estimator, for the optical near- and far-field regimes, of random binary bitmap images as a function of contrast value.ENcoherent X-ray diffractive imagingCDIimage reconstructionphase retrievalmaximum likelihoodThis paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.text/htmlHow many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?text1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00MPF, a multipurpose figure of merit for phasing procedures
http://scripts.iucr.org/cgi-bin/paper?sc5100
The efficient multipurpose figure of merit MPF has been defined and characterized. It may be very helpful in phasing procedures. Indeed, it might be used for establishing the centric or acentric nature of an unknown structure, for identifying the presence of some pseudotranslational symmetry, for recognizing the correct solution in multisolution approaches and for estimating the quality of structure models as they become available during the phasing process. Thus, phase improvement or deterioration may be monitored and useless models may be discarded to save computing time. It is also shown that MPF may be applied in different phasing approaches, no matter if ab initio or non ab initio.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Burla, M.C.Carrozzini, B.Cascarano, G.L.Giacovazzo, C.Polidori, G.2017-01-01doi:10.1107/S2053273316016521International Union of CrystallographyA new figure of merit, MPF, has been devised. It may be usefully applied in different contexts of a phasing procedure.ENfigure of meritphasingphase refinementdirect methodsThe efficient multipurpose figure of merit MPF has been defined and characterized. It may be very helpful in phasing procedures. Indeed, it might be used for establishing the centric or acentric nature of an unknown structure, for identifying the presence of some pseudotranslational symmetry, for recognizing the correct solution in multisolution approaches and for estimating the quality of structure models as they become available during the phasing process. Thus, phase improvement or deterioration may be monitored and useless models may be discarded to save computing time. It is also shown that MPF may be applied in different phasing approaches, no matter if ab initio or non ab initio.text/htmlMPF, a multipurpose figure of merit for phasing procedurestext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Ordering of convex polyhedra and the Fedorov algorithm
http://scripts.iucr.org/cgi-bin/paper?eo5068
A method of naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph has been previously suggested. A polyhedron can be built using its name. Classes of convex n-acra (i.e. n-vertex polyhedra) are strictly (without overlapping) ordered by their names. In this paper the relationship between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the above ordering is described. The convex n-acra are weakly ordered by the maximum extra valencies of their vertices. Thus, non-simple n-acra follow the simple ones for any n.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Voytekhovsky, Y.L.2017-01-01doi:10.1107/S2053273316017095International Union of CrystallographyThe relation between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the ordering of convex n-acra is found. A method to weakly order the convex n-acra by the maximum extra valencies of their vertices is suggested.ENconvex n-acraFedorov algorithmsimple and non-simple polyhedraextra valenciesweak ordering of n-acraA method of naming any convex polyhedron by a numerical code arising from the adjacency matrix of its edge graph has been previously suggested. A polyhedron can be built using its name. Classes of convex n-acra (i.e. n-vertex polyhedra) are strictly (without overlapping) ordered by their names. In this paper the relationship between the Fedorov algorithm to generate the whole combinatorial variety of convex polyhedra and the above ordering is described. The convex n-acra are weakly ordered by the maximum extra valencies of their vertices. Thus, non-simple n-acra follow the simple ones for any n.text/htmlOrdering of convex polyhedra and the Fedorov algorithmtext1732017-01-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Ashort communications00