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) 2017 International Union of Crystallography2017-09-01International Union of CrystallographyInternational Union of Crystallographyhttp://journals.iucr.orgurn:issn:2053-2733Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlActa Crystallographica Section A: Foundations and Advances, Volume 73, Part 5, 2017textweekly62002-01-01T00:00+00:005732017-09-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances373urn:issn:2053-2733med@iucr.orgSeptember 20172017-09-01Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imagePhilip Coppens (1930–2017)
http://scripts.iucr.org/cgi-bin/paper?es0429
Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Becker, P.2017-09-01doi:10.1107/S2053273317012475International Union of CrystallographyObituary for Philip Coppens.ENobituarycharge-density studiestime-resolved crystallographyInternational Union of Crystallographytext/htmlPhilip Coppens (1930–2017)text5732017-09-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aobituaries373374Davide Viterbo (1939–2017)
http://scripts.iucr.org/cgi-bin/paper?es0428
Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Mealli, C.Milanesio, M.2017-08-15doi:10.1107/S2053273317011500International Union of CrystallographyObituary for Davide ViterboENobituarydirect methodsSIRAssociazione Italiana CristallografiaEuropean Crystallographic AssociationInternational Union of Crystallographytext/htmlDavide Viterbo (1939–2017)text5732017-08-15Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aobituaries375376Close-packed structure dynamics with finite-range interaction: computational mechanics with individual layer interaction
http://scripts.iucr.org/cgi-bin/paper?lk5017
This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B (2000), 218, 425–430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Rodriguez-Horta, E.Estevez-Rams, E.Lora-Serrano, R.Neder, R.2017-08-15doi:10.1107/S2053273317008968International Union of CrystallographyThis is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. Instead of using an Ising model over spins defined by the Hägg coding, a Hamiltonian considering direct interaction between the close-packed layers is assumed. The results of the phase diagram and the appearance of disorder are compared with the previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed.ENpolytypescomputational mechanicsclose-packed structure dynamicsThis is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B (2000), 218, 425–430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.text/htmlClose-packed structure dynamics with finite-range interaction: computational mechanics with individual layer interactiontext5732017-08-15Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers377386Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces
http://scripts.iucr.org/cgi-bin/paper?sc5102
In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Chirikjian, G.S.Sajjadi, S.Shiffman, B.Zucker, S.M.2017-08-15doi:10.1107/S2053273317007227International Union of CrystallographyThe minimal-volume search space in molecular replacement can be expressed in multiple ways wherein there is a trade-off between the sizes of rotation and translation subspaces. In particular, if the space group is a semi-direct product of a point group and a Bieberbach group, then the search space can be represented as a product of two manifolds: a spherical space form and a Euclidean space form.ENfundamental domainmolecular replacementmeasure theorycoset spacediscrete subgroupIn molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.text/htmlMathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spacestext5732017-08-15Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers387402The wavevector substar group in reciprocal space and its representation
http://scripts.iucr.org/cgi-bin/paper?kx5058
A new concept of the wavevector substar group is established which, in the study of translational symmetry breaking of a crystal, only considers the particular arms of the wavevector star taking part in the phase transition; this is in contrast with the traditional Landau theory which considers all of the arms of the wavevector star. It is shown that this new concept can be used effectively to investigate the interesting physical properties of crystals associated with translational symmetry breaking. It is shown that studies on complicated phase transitions related to reducible representations, such as those in perovskite KMnF3 multiferroics and the high-temperature superconductor La2/3Mg1/2W1/2O3 (La4Mg3W3O18), are much simplified by the new concept. The theory of the wavevector substar group and its representation is a powerful mathematical tool for the study of various symmetry-breaking phenomena in solid-state crystals.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Kim, I.H.Pak, J.Kim, I.H.Kim, S.W.Li, L.2017-08-15doi:10.1107/S205327331700688XInternational Union of CrystallographyA new concept of the wavevector substar group and its representation is established.ENwavevector substar grouprepresentation of wavevector substar groupstar channel grouptranslational symmetry breakingphase transitionsA new concept of the wavevector substar group is established which, in the study of translational symmetry breaking of a crystal, only considers the particular arms of the wavevector star taking part in the phase transition; this is in contrast with the traditional Landau theory which considers all of the arms of the wavevector star. It is shown that this new concept can be used effectively to investigate the interesting physical properties of crystals associated with translational symmetry breaking. It is shown that studies on complicated phase transitions related to reducible representations, such as those in perovskite KMnF3 multiferroics and the high-temperature superconductor La2/3Mg1/2W1/2O3 (La4Mg3W3O18), are much simplified by the new concept. The theory of the wavevector substar group and its representation is a powerful mathematical tool for the study of various symmetry-breaking phenomena in solid-state crystals.text/htmlThe wavevector substar group in reciprocal space and its representationtext5732017-08-15Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers403413Real-time detection and resolution of atom bumping in crystallographic models
http://scripts.iucr.org/cgi-bin/paper?ae5037
A basic principle in crystal structure determination is that there should be proper distances between adjacent atoms. Therefore, detection of atom bumping is of fundamental significance in structure determination, especially in the direct-space method where crystallographic models are just randomly generated. Presented in this article is an algorithm that detects atom bonding in a unit cell based on the sweep and prune algorithm of axis-aligned bounding boxes and running in the O(n log n) time bound, where n is the total number of atoms in the unit cell. This algorithm only needs the positions of individual atoms in the unit cell and does not require any prior knowledge of existing bonds, and is thus suitable for modelling of inorganic crystals where the bonding relations are often unknown a priori. With this algorithm, computation routines requiring bonding information, e.g. anti-bumping and computation of coordination numbers and valences, can be performed efficiently. As an example application, an evaluation function for atom bumping is proposed, which can be used for real-time elimination of crystallographic models with unreasonably short bonds during the procedure of global optimization in the direct-space method.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Liu, Y.2017-09-01doi:10.1107/S2053273317011548International Union of CrystallographyAn O(n log n) algorithm that detects atom bonding in a unit cell is presented. As an application of this algorithm, an evaluation function for atom bumping is proposed, which can be used for real-time elimination of crystallographic models with unreasonable bond lengths during the procedure of crystal structure determination in direct space.ENreal-time collision detectionsweep and prune algorithmdirect-space methodsanti-bumping algorithmA basic principle in crystal structure determination is that there should be proper distances between adjacent atoms. Therefore, detection of atom bumping is of fundamental significance in structure determination, especially in the direct-space method where crystallographic models are just randomly generated. Presented in this article is an algorithm that detects atom bonding in a unit cell based on the sweep and prune algorithm of axis-aligned bounding boxes and running in the O(n log n) time bound, where n is the total number of atoms in the unit cell. This algorithm only needs the positions of individual atoms in the unit cell and does not require any prior knowledge of existing bonds, and is thus suitable for modelling of inorganic crystals where the bonding relations are often unknown a priori. With this algorithm, computation routines requiring bonding information, e.g. anti-bumping and computation of coordination numbers and valences, can be performed efficiently. As an example application, an evaluation function for atom bumping is proposed, which can be used for real-time elimination of crystallographic models with unreasonably short bonds during the procedure of global optimization in the direct-space method.text/htmlReal-time detection and resolution of atom bumping in crystallographic modelstext5732017-09-01Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers414422Accelerated scattering of convex polyhedra
http://scripts.iucr.org/cgi-bin/paper?eo5074
The formulas for the minimum (minn) and maximum (maxn) names in the classes of convex n-acra (i.e. n-vertex polyhedra) are found for any n. The asymptotic behaviour (as n → ∞) for maxn+1/maxn, minn+1/minn, minn+1/maxn and maxn/minn is established. They characterize in detail the accelerated scattering of [minn, maxn] ranges on a real line.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Voytekhovsky, Y.L.2017-08-15doi:10.1107/S2053273317009196International Union of CrystallographyThe formulas for minn and maxn names in the classes of convex n-acra, as well as asymptotic relationships (as n → ∞) between them, are found. These explain the distribution of [minn, maxn] ranges on the real line.ENconvex polyhedra and polyacraminimum and maximum namesasymptotic relationshipsThe formulas for the minimum (minn) and maximum (maxn) names in the classes of convex n-acra (i.e. n-vertex polyhedra) are found for any n. The asymptotic behaviour (as n → ∞) for maxn+1/maxn, minn+1/minn, minn+1/maxn and maxn/minn is established. They characterize in detail the accelerated scattering of [minn, maxn] ranges on a real line.text/htmlAccelerated scattering of convex polyhedratext5732017-08-15Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Ashort communications423425