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Acta Crystallographica. Section A, Foundations of Crystallography

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https://www.readbyqxmd.com/read/24132223/incommensurate-crystallography-by-sander-van-smaalen-iucr-monographs-on-crystallography-no-21-oxford-university-press-2012-pp-284-price-paperback-gbp-37-50-isbn-978-0-19-965923-4
#1
Gervais Chapuis
No abstract text is available yet for this article.
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132222/spin-line-groups
#2
Nataša Lazić, Marko Milivojević, Milan Damnjanović
Spin line groups describe the symmetries of spin arrangements in quasi-one-dimensional systems. These groups are derived for the first family of line groups. Among them, magnetic groups are singled out as a special case. Spin arrangements generated by the derived groups are first discussed for single-orbit systems and then the conclusions are extended to multi-orbit cases. The results are illustrated by the examples of a CuO2 zigzag chain, a (13)C nanotube and the hexaferrite Ba2Mg2Fe12O22. Applications to neutron diffraction and classical ground-state determination are indicated...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132221/distribution-rules-of-systematic-absences-on-the-conway-topograph-and-their-application-to-powder-auto-indexing
#3
R Oishi-Tomiyasu
This paper presents several general properties of systematic absences that are available before unit-cell parameters and the space group have been determined. The properties are given in the form of distribution rules of Miller indices corresponding to systematic absences on a topograph. A topograph is a graph whose edges are associated with a set of four lattice vectors satisfying Ito's equation 2(|l1(*)|(2) + |l2(*)|(2)) = |l1(*) + l2(*)|(2) + |l1(*) - l2(*)|(2). It is possible to integrate global information about extinct reflections by using topographs...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132220/platonic-solids-generate-their-four-dimensional-analogues
#4
Pierre Philippe Dechant
This paper shows how regular convex 4-polytopes - the analogues of the Platonic solids in four dimensions - can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the Cartan-Dieudonné theorem, the reflective symmetries of the Platonic solids generate rotations. In a Clifford algebra framework, the space of spinors generating such three-dimensional rotations has a natural four-dimensional Euclidean structure. The spinors arising from the Platonic solids can thus in turn be interpreted as vertices in four-dimensional space, giving a simple construction of the four-dimensional polytopes 16-cell, 24-cell, the F4 root system and the 600-cell...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132219/c70-c80-c90-and-carbon-nanotubes-by-breaking-of-the-icosahedral-symmetry-of-c60
#5
Mark Bodner, Jiří Patera, Marzena Szajewska
The icosahedral symmetry group H3 of order 120 and its dihedral subgroup H2 of order 10 are used for exact geometric construction of polytopes that are known to exist in nature. The branching rule for the H3 orbit of the fullerene C60 to the subgroup H2 yields a union of eight orbits of H2: four of them are regular pentagons and four are regular decagons. By inserting into the branching rule one, two, three or n additional decagonal orbits of H2, one builds the polytopes C70, C80, C90 and nanotubes in general...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132218/comparative-study-of-x-ray-charge-density-data-on-cosb3
#6
Mette Stokkebro Schmøkel, Lasse Bjerg, Finn Krebs Larsen, Jacob Overgaard, Simone Cenedese, Mogens Christensen, Georg K H Madsen, Carlo Gatti, Eiji Nishibori, Kunihisa Sugimoto, Masaki Takata, Bo Brummerstedt Iversen
CoSb3 is an example of a highly challenging case for experimental charge-density analysis due to the heavy elements (suitability factor of ∼0.01), the perfect crystallinity and the high symmetry of the compound. It is part of a family of host-guest structures that are potential candidates for use as high-performance thermoelectric materials. Obtaining and analysing accurate charge densities of the undoped host structure potentially can improve the understanding of the thermoelectric properties of this family of materials...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132217/direct-phasing-of-nanocrystal-diffraction
#7
Veit Elser
Recent experiments at free-electron laser X-ray sources have been able to resolve the intensity distributions about Bragg peaks in nanocrystals of large biomolecules. Information derived from small shifts in the peak positions augment the Bragg samples of the particle intensity with samples of its gradients. Working on the assumption that the nanocrystal is entirely generated by lattice translations of a particle, an algorithm is developed that reconstructs the particle from intensities and intensity gradients...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132216/more-about-residual-values
#8
Julian Henn, Andreas Schönleber
The usual residual values are complemented by expectation values based solely on the experimental data and the number of model parameters. These theoretical R values serve as benchmark values when all of the basic assumptions for a least-squares refinement, i.e. no systematic errors and a fully adequate model capable of describing the data, are fulfilled. The prediction of R values as presented here is applicable to any field where model parameters are fitted to data with known precision. For crystallographic applications, F(2)-based residual benchmark values are given...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132215/homometry-in-the-light-of-coherent-beams
#9
Sylvain Ravy
Two systems are homometric if they are indistinguishable by diffraction. A distinction is first made between Bragg and diffuse scattering homometry, and it is shown that in the last case coherent diffraction can allow the diffraction diagrams to be differentiated. The study of the Rudin-Shapiro sequence, homometric to random sequences, allows one to manipulate independently two-point and four-point correlation functions, and to show their effect on the statistics of speckle patterns. This study provides evidence that long-range order in high-order correlation functions has a measurable effect on the speckle statistics...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132214/nets-with-collisions-unstable-nets-and-crystal-chemistry
#10
Olaf Delgado-Friedrichs, Stephen T Hyde, Shin Won Mun, Michael O'Keeffe, Davide M Proserpio
Nets in which different vertices have identical barycentric coordinates (i.e. have collisions) are called unstable. Some such nets have automorphisms that do not correspond to crystallographic symmetries and are called non-crystallographic. Examples are given of nets taken from real crystal structures which have embeddings with crystallographic symmetry in which colliding nodes either are, or are not, topological neighbors (linked) and in which some links coincide. An example is also given of a crystallographic net of exceptional girth (16), which has collisions in barycentric coordinates but which also has embeddings without collisions with the same symmetry...
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/24132213/a-new-vision-for-acta-crystallographica-section-a
#11
Simon J L Billinge, Jianwei Miao
No abstract text is available yet for this article.
November 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778103/primo-levi-william-henry-bragg-and-the-atomic-theory-of-matter
#12
Davide Viterbo
No abstract text is available yet for this article.
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778102/on-subgroups-of-crystallographic-coxeter-groups
#13
Eden Delight B Provido, Ma Louise Antonette N De Las Peñas, Rene P Felix
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.
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778101/nonequivalent-periodic-subsets-of-the-lattice
#14
W Cocke
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...
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778100/symmetry-group-of-two-special-types-of-carbon-nanotori
#15
Mihai D Staic, Alina Petrescu-Nita
This paper studies the symmetry group of two special types of carbon nanotori. The construction is motivated by a group-theoretical result.
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778099/digital-electron-diffraction-seeing-the-whole-picture
#16
Richard Beanland, Paul J Thomas, David I Woodward, Pamela A Thomas, Rudolf A Roemer
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...
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778098/inferring-planar-disorder-in-close-packed-structures-via-%C3%AE%C2%B5-machine-spectral-reconstruction-theory-examples-from-simulated-diffraction-patterns
#17
D P Varn, G S Canright, J P Crutchfield
A previous paper detailed a novel algorithm, ε-machine spectral reconstruction theory (εMSR), 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 εMSR 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, εMSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an ε-machine...
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778097/a-new-interpretation-of-the-%C3%AF-a-parameter
#18
B Carrozzini, G L Cascarano, C Giacovazzo, A Mazzone
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.
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778096/application-of-%C3%AE-recycling-to-electron-automated-diffraction-tomography-data-from-inorganic-crystalline-nanovolumes
#19
Jordi Rius, Enrico Mugnaioli, Oriol Vallcorba, Ute Kolb
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...
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
https://www.readbyqxmd.com/read/23778095/tabulation-of-irreducible-representations-of-the-crystallographic-space-groups-and-their-superspace-extensions
#20
Harold T Stokes, Branton J Campbell, Ryan Cordes
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 P(s)...
July 2013: Acta Crystallographica. Section A, Foundations of Crystallography
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