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Structure determination without Fourier inversion. V. A concept based on parameter spaceEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The parameter-space concept for solving crystal structures from reflection amplitudes (without employing or searching for their phases) is described on a theoretically oriented basis. Emphasis is placed on the principles of the method, on selecting one of three types of parameter spaces discussed in this paper, and in particular on the structure model employed (equal-atom point model, however usually reduced to one-dimensional projections) and on the system of `isosurfaces' representing experimental `geometrical structure amplitudes' in an orthonormal parameter space of as many dimensions as unknown atomic coordinates. The...
Source: Acta Crystallographica Section A - October 17, 2009 Category: Chemistry Authors: Zimmermann, H.Fischer, K.F. Tags: structure determination parameter spaces unique solution homometric solutions phase problem eliminated research papers Source Type: journals

Prices of IUCr journalsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Dacombe, M.H. Tags: prices of journals international union of crystallography Source Type: journals

Gjønnes Medal in Electron Crystallography – call for nominationsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Marks, L.D. Tags: Gj ø nnes Medal international union of crystallography Source Type: journals

Foundations of Crystallography with Computer Applications. By Maureen M. Julian. Boca Raton: CRC Press, 2008. Pp. xxvi + 340. Price (hardback) GBP 55.00. ISBN 978-1-4200-6075-1.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Aroyo, M.I. Tags: book review book reviews Source Type: journals

Multiplicative congruential generators, their lattice structure, its relation to lattice–sublattice transformations and applications in crystallographyEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
An analysis of certain types of multiplicative congruential generators – otherwise known for their application to the sequential generation of pseudo-random numbers – reveals their relation to the coordinate description of lattice points in two-dimensional primitive sublattices. Taking the index of the lattice–sublattice transformation as the modulus of the multiplicative congruential generator, there are special choices for its multiplier which induce a symmetry-preserving permutation of lattice-point coordinates. From an analysis of similar sublattices with hexagonal and square symmetry it is conjectured that the c...
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Hornfeck, W.Harbrecht, B. Tags: multiplicative congruential generators lattice – sublattice transformation lattice points crystallographic orbits research papers Source Type: journals

Improving the direct-methods sign-unconstrained S-FFT algorithm. XVEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In order to extend the application field of the direct-methods S-FFT phase-refinement algorithm to density functions with positive and negative peaks, the equal-sign constraint was removed from its definition by combining ρ2 with an appropriate density function mask [Rius & Frontera (2008). Acta Cryst. A64, 670–674]. This generalized algorithm (S2-FFT) was shown to be highly effective for crystal structures with at least one moderate scatterer in the unit cell but less effective when applied to structures with only light scatterers. To increase the success rate in this second case, the mask has been improved and the con...
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Rius, J.Frontera, C. Tags: direct methods S-FFT algorithm phase refinement research papers Source Type: journals

Molecular replacement: the probabilistic approach of the program REMO09 and its applicationsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The method of joint probability distribution functions has been applied to molecular replacement techniques. The rotational search is performed by rotating the reciprocal lattice of the protein with respect to the calculated transform of the model structure; the translation search is performed by fast Fourier transform. Several cases of prior information are studied, both for the rotation and for the translation step: e.g. the conditional probability density for the rotation or the translation of a monomer is found both for ab initio and when the rotation and/or the translation values of other monomers are given. The new a...
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Caliandro, R.Carrozzini, B.Cascarano, G.L.Giacovazzo, C.Mazzone, A.Siliqi, D. Tags: molecular replacement protein crystallography joint probability distribution functions research papers Source Type: journals

The OD interpretation of the crystal structure of kettnerite CaBiOFCO3Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The mineral kettnerite, CaBi(OFCO3), is a rare example of an order–disorder (OD) structure with a quadratic net. The lattice parameters of the simplest possible 1O polytype are a = 5.3641 (1), b = 5.3641 (1), c = 13.5771 (2) Å, and the space group is Pbaa. There are three kinds of OD layers, identical to structure-building layers. Two of them are non-polar: the Bi—O and Ca—F at z = 0 and z = 1/2, respectively, with the layer-group symmetry C2/m2/m(4/a,b)21/m21/m. The third kind of OD layer of CO3 groups (located between the Bi—O and Ca—F layers) is polar, with alternating sense of polarity. The layer gro...
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Hybler, J.Ďurovič, S. Tags: kettnerite OD structure polytypism research papers Source Type: journals

Experimental charge-density study of paracetamol – multipole refinement in the presence of a disordered methyl groupEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A high-resolution single-crystal X-ray study of paracetamol has been performed at 85 K. Different approaches to modeling the experimental electron density (ED) were tested for the dynamically disordered portions of the molecule in order to check to what extent it is possible to obtain a proper ED distribution in the ordered part. Models were examined in which the methyl-group ED was built from pseudoatoms taken from the University at Buffalo Pseudoatom Databank or the Invariom database, with multipole parameters for the remaining atoms being obtained from free refinement. The κ′ restricted multipolar model (KRMM) and ...
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Bąk, J.M.Dominiak, P.M.Wilson, C.C.Woźniak, K. Tags: experimental charge density University at Buffalo Pseudoatom Databank Invariom database aspherical atom model paracetamol research papers Source Type: journals

Multiresolution of quasicrystal diffraction spectraEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A method for analyzing and classifying two-dimensional pure point diffraction spectra (i.e. a set of Bragg peaks) of certain self-similar structures with scaling factor β > 1, such as quasicrystals, is presented. The two-dimensional pure point diffraction spectrum Π is viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity. Then, by using a nested sequence of self-similar subsets called β-lattices, we implement a multiresolution analysis of the spectrum Π. This analysis yields a partition of Π simultaneously in geometry, in scale and in intensity (the `fingerp...
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Elkharrat, A.Gazeau, J.-P.Dénoyer, F. Tags: quasicrystals diffraction spectra self-similar structures multiresolution analysis research papers Source Type: journals

On symmetry classes of crystal structuresEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
An open-ended classification scheme for crystal structures based on Wyckoff sets and affine normalizer groups is proposed. It is free of metrical and geometrical considerations. All structures of one structure type belong to the same symmetry class. An application is given for the Inorganic Crystal Structure Database (version 2, 2007). (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 16, 2009 Category: Chemistry Authors: Burzlaff, H.Zimmermann, H. Tags: crystal structure classification Wyckoff positions Wyckoff sets affine normalizers research papers Source Type: journals

International Union of Crystallography Twenty-First General Assembly and International Congress of Crystallography, Osaka, Japan, 23–31 August 2008Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
(Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - August 13, 2009 Category: Chemistry Authors: IUCr Tags: international union of crystallography Source Type: journals

Louis Pasteur's discovery of molecular chirality and spontaneous resolution in 1848, together with a complete review of his crystallographic and chemical workEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Pasteur's chemical and crystallographic work is described. The article commences with a brief overview of related science (chemical structure, crystallography, optical activity) before and after 1848, the year of the discovery of molecular chirality and spontaneous resolution. Concerning this discovery, three separate and varying reports are described. These are: (i) the publications in the scientific literature, (ii) the early (auto)biographies and (iii) Pasteur's handwritten laboratory notebooks. The three versions give differing views on the topic. Subsequently all of Pasteur's crystallographic and chemical work is pass...
Source: Acta Crystallographica Section A - August 11, 2009 Category: Chemistry Authors: Flack, H.D. Tags: Pasteur molecular chirality spontaneous resolution dissymmetry research papers Source Type: journals

Using dynamically scattered electrons for three-dimensional potential reconstructionEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Three-dimensional charge-density maps computed by first-principles methods provide information about atom positions and the bonds between them, data which are particularly valuable when trying to understand the properties of point defects, dislocations and interfaces. This paper presents a method by which three-dimensional maps of the electrostatic potential, related to the charge-density map by the Poisson equation, can be obtained experimentally at 1 Å resolution or better, especially at low accelerating voltages. The method requires data acquired by holographic transmission electron microscopy methods such as off-axi...
Source: Acta Crystallographica Section A - July 30, 2009 Category: Chemistry Authors: Koch, C.T. Tags: three-dimensional potential reconstruction dynamically scattered electrons transmission electron microscopy electron holography research papers Source Type: journals

Differential geometry: a natural tool for describing symmetry operationsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group operation is a one-to-one map acting on the manifold, whereas a point-group operation is a linear map acting between two tangent spaces of the manifold. Manifold theory proves particularly powerful as a unified formalism describing symmetry operations of conventional as well as modulated crystals without requiring a higher-dimensional space. We show, in particular, that a ...
Source: Acta Crystallographica Section A - July 30, 2009 Category: Chemistry Authors: Kocian, P.Schenk, K.Chapuis, G. Tags: differential geometry manifold theory modulated structures tangent space research papers Source Type: journals

Edge-transitive lattice netsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Lattice nets have one vertex in the topological unit cell. Some two- and three-periodic lattice nets with one kind of edge (edge-transitive) are described. Simple expressions for the topological density of the two-periodic nets are found empirically. Thirteen infinite families of three-periodic cubic lattice nets and hexagonal, trigonal and tetragonal families are identified. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - July 29, 2009 Category: Chemistry Authors: Delgado-Friedrichs, O.O'Keeffe, M. Tags: periodic nets research papers Source Type: journals

Phase modulation effects in X-ray diffraction from a highly deformed crystal with variable strain gradientEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The X-ray interbranch scattering by lattice distortions is studied for a thin crystal whose thickness is appreciably less than the conventional X-ray extinction length. The concept of interbranch phase modulation of the X-ray wavefield is extended to the case of a large gradient which depends on depth inside the crystal. The prominent interbranch features of the diffracted intensity are also established within this concept. Numerical calculations of the diffracted intensity are presented for an exponential strain gradient model to illustrate this. Diffraction (extinction) contrast is discussed for a strongly deformed speci...
Source: Acta Crystallographica Section A - July 29, 2009 Category: Chemistry Authors: Shevchenko, M. Tags: X-ray diffraction deformation protein crystal research papers Source Type: journals

Point substitution processes for decagonal quasiperiodic tilingsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A general construction principle for the inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of expansion and division of the tiles, where the expanded tiles can be divided arbitrarily as long as the set of prototiles is maintained. A certain kind of point decoration process turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new fa...
Source: Acta Crystallographica Section A - July 29, 2009 Category: Chemistry Authors: Fujita, N. Tags: quasiperiodic tilings point decorations decagonal tilings prototiles research papers Source Type: journals

Three new types of interpenetrating sphere packingsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Three new types of homogeneous interpenetrating sphere packings are described. In the general position of space group Ccce, two sphere packings of type 3/10/o1 can be combined to form interpenetrating sphere packings of type o[3/10/o1]2. The other two types of interpenetrating sphere packings show symmetry Fddd: two packings of type 3/10/t4 are intertwined in o[3/10/t4]2 and three packings of type 3/4/t1 in o[3/4/t1]3. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - June 16, 2009 Category: Chemistry Authors: Sowa, H. Tags: interpenetrating sphere packings short communications Source Type: journals

Towards the best model for H atoms in experimental charge-density refinementEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The consequences of different treatments of H atoms in experimental charge-density studies are discussed. Geometric and topological parameters obtained after applying four different H-atom models in multipolar refinement on high-resolution X-ray data only were compared with the results obtained for a reference joint high-resolution X-ray/neutron refinement. The geometry and the topological critical point and integrated parameters closest to the reference values were obtained after a mixed refinement (high-order refinement of heavy atoms, low-angle refinement of H atoms and elongation of the X—H distance to the average ne...
Source: Acta Crystallographica Section A - June 16, 2009 Category: Chemistry Authors: Hoser, A.A.Dominiak, P.M.Woźniak, K. Tags: experimental charge density high-order refinement H-atom models anisotropic atomic displacement parameter estimation elastic neutron diffraction topological properties research papers Source Type: journals

Determination of molecular envelopes from solvent contrast variation dataEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
An algorithm is described for determining macromolecular envelopes from crystal diffraction amplitudes measured from a solvent contrast variation series. The method uses solvent contrast variation data that have been preprocessed to represent the structure-factor amplitudes of the envelope. The amplitudes are phased using an iterative projection algorithm that incorporates connectivity and compactness constraints on the envelope. The algorithm is tested by simulation on two protein envelopes and shown to be effective even in the absence of the very low resolution data, which are difficult to access experimentally. (Source:...
Source: Acta Crystallographica Section A - June 10, 2009 Category: Chemistry Authors: Lo, V.Kingston, R.L.Millane, R.P. Tags: macromolecular crystallography molecular envelopes solvent contrast variation research papers Source Type: journals

MAD techniques applied to powder data: finding the structure given the substructureEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The joint probability distribution function method is applied to multiple-wavelength anomalous dispersion (MAD) powder data. The distributions are calculated by assuming prior knowledge of the scattering intensities at two wavelengths and of the anomalous-scatterer substructure. The method leads to formulas estimating the full structure phases and their reliability. The procedure has been applied to two structures, one unknown and one known; the second was used as a control for the phasing procedure. In spite of the unavoidable peak overlapping in the diffraction pattern, the formulas proved to be very effective. Combined ...
Source: Acta Crystallographica Section A - June 10, 2009 Category: Chemistry Authors: Altomare, A.Burla, M.C.Cuocci, C.Giacovazzo, C.Gozzo, F.Moliterni, A.Polidori, G.Rizzi, R. Tags: multiple-wavelength anomalous dispersion powder diffraction data structure solution joint probability distribution function method research papers Source Type: journals

On a minimum tetrahedron in a three-dimensional lattice. Part I. Lattices with a shortest basis fulfilling b · c ≥ 0, a · c ≥ 0, a · b ≥ 0Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The problem of a representative body of a three-dimensional lattice is considered. The cell fulfilling a + b + c = min is clearly not unique: even five mutually non-congruent such cells can exist in some lattices [Gruber (1973). Acta Cryst. A29, 433–440]. The idea that this number could be reduced by replacing the cell (i.e. a parallelepiped) by another, possibly more suitable, geometrical object is considered. For this object a lattice tetrahedron fulfilling the condition a + b + c + d + e + f = min is chosen, a to f being the lengths of its edges. It is called the minitetrahedron of the lattice. In this article, the pr...
Source: Acta Crystallographica Section A - June 10, 2009 Category: Chemistry Authors: Gruber, B. Tags: lattice basis Niggli cell minimum tetrahedra research papers Source Type: journals

Investigations of the bond-selective response in a piezoelectric Li2SO4·H2O crystal to an applied external electric fieldEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Piezoelectric lithium sulfate monohydrate, Li2SO4·H2O, was analyzed with respect to the relationship between the static structural properties of the crystal and its response to an external electric field. The static electron density was determined via standard low-temperature X-ray data collection at 90 (5) K using an Enraf–Nonius CAD-4 diffractometer, Mo Kα radiation and multipole model refinement. Then a synchrotron-radiation experiment using the D3 beamline at HASYLAB was conducted in order to investigate the structural deformations in Li2SO4·H2O caused by an applied external electric field. In particular, the sh...
Source: Acta Crystallographica Section A - June 10, 2009 Category: Chemistry Authors: Schmidt, O.Gorfman, S.Bohatý, L.Neumann, E.Engelen, B.Pietsch, U. Tags: lithium sulfate monohydrate piezoelectricity multipole refinement distortions research papers Source Type: journals

Formation of interference fringes in the Bragg–(Bragg)m–Laue modeEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
X-ray interference fringes in the beams diffracted from a lateral surface of a thin plane-parallel crystal are measured and analyzed using Wagner's approach [Wagner (1956), Z. Phys. 146, 127–168]. It is found that the fringes are caused by the interference between the internal waves excited by the incident beam in both the Bragg–Laue case and the Bragg–Bragg–Laue case. The period of the interference fringes is shown to be proportional to the distance between the incident point of the X-ray and the crystal edge, and to be inversely proportional to the crystal thickness. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - May 16, 2009 Category: Chemistry Authors: Hirano, K.Fukamachi, T.Yoshizawa, M.Negishi, R.Hirano, K.Kawamura, T. Tags: interference fringes Bragg – Laue case research papers Source Type: journals

Concise intensity statistics of Friedel opposites and classification of the reflectionsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A previous extensive analysis of the mean-square intensity difference of Friedel opposites [Shmueli et al. (2008). Acta Cryst. A64, 476–483] is here concisely re-examined and confirmed by purely statistical methods. The analysis applies to noncentrosymmetric crystals only. For special reflections and centered lattices both mean-square intensity difference and average intensity of Friedel opposites depend on the centering factor of the crystal lattice and/or on the isotropy subgroup of the reflection. A complete classification of the reflections, based on the above intensity statistics, is presented. It is also shown that...
Source: Acta Crystallographica Section A - May 12, 2009 Category: Chemistry Authors: Shmueli, U.Flack, H.D. Tags: reflection intensities Friedel opposites noncentrosymmetric crystals Bijvoet ratio short communications Source Type: journals

Probability plots based on Student's t-distributionEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The validity of the normal distribution as an error model is commonly tested with a (half) normal probability plot. Real data often contain outliers. The use of t-distributions in a probability plot to model such data more realistically is described. It is shown how a suitable value of the parameter ν of the t-distribution can be determined from the data. The results suggest that even data that seem to be modeled well using a normal distribution can be better modeled using a t-distribution. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - May 12, 2009 Category: Chemistry Authors: Hooft, R.W.W.Straver, L.H.Spek, A.L. Tags: Student's t-distribution probability plot short communications Source Type: journals

The relationship of the hyperspherical harmonics to SO(3), SO(4) and orientation distribution functionsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The expansion of an orientation distribution function as a linear combination of the hyperspherical harmonics suggests that the analysis of crystallographic orientation information may be performed entirely in the axis–angle parameterization. Practical implementation of this requires an understanding of the properties of the hyperspherical harmonics. An addition theorem for the hyperspherical harmonics and an explicit formula for the relevant irreducible representatives of SO(4) are provided. The addition theorem is useful for performing convolutions of orientation distribution functions, while the irreducible representa...
Source: Acta Crystallographica Section A - May 12, 2009 Category: Chemistry Authors: Mason, J.K. Tags: orientation distribution functions hyperspherical harmonics irreducible representatives research papers Source Type: journals

60 years of IUCr journalsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In the 60 years since its birth in 1948, the number of journals published by the International Union of Crystallography has risen from one to eight. A brief account of the history of the forerunner of the IUCr journals, Zeitschrift für Kristallographie, is given. The context of the birth of the IUCr and the first of its journals, Acta Crystallographica, is recalled. The circumstances which led to the growth of Acta into several sections, at first A and B then, successively, C, D, E and F, and the launch of two new journals, the Journal of Applied Crystallography and the Journal of Synchrotron Radiation, are described. The...
Source: Acta Crystallographica Section A - April 11, 2009 Category: Chemistry Authors: Authier, A. Tags: publishing Acta Crystallographica Journal of Applied Crystallography Journal of Synchrotron Radiation International Tables for Crystallography International Union of Crystallography feature articles Source Type: journals

The full symmetry and irreducible representations of nanotoriEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The full symmetry groups of carbon nanotori are investigated. It is shown that that the symmetry group of a chiral (n1, n2) nanotorus is isomorphic to D2mq/n, where m and q are the number of lattice points on the torus circumference vector and the number of graphene hexagons in the nanotorus unit cell, respectively, and n = gcd(n1, n2). It is also shown that the symmetry group of zigzag and armchair (achiral) nanotori is D_{4m} \times {\bb Z}_{2}, where D2k and {\bb Z}_{k} are the dihedral group of order 2k and the cyclic group of order k, respectively. The irreducible representations and characters of these groups are dis...
Source: Acta Crystallographica Section A - April 1, 2009 Category: Chemistry Authors: Arezoomand, M.Taeri, B. Tags: full symmetry group carbon nanotorus representation theory research papers Source Type: journals

Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of nanoparticlesEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The relationship between the equations used in the atomic pair distribution function (PDF) method and those commonly used in small-angle-scattering (SAS) analyses is explicitly shown. The origin of the sloping baseline, −4πrρ0, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The nonlinear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - April 1, 2009 Category: Chemistry Authors: Farrow, C.L.Billinge, S.J.L. Tags: atomic pair distribution function small-angle scattering nanoparticles modeling research papers Source Type: journals

Topological relations between three-periodic nets. II. Binodal netsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The TOPOS program package was used to generate all subnets of 3- to 12-coordinated binodal nets taken from the Reticular Chemistry Structure Resource database. 38 304 binodal nets with novel topologies were revealed and stored in the TTD collection. A new invariant, the adjacency matrix of the shell graph of a node, is proposed to distinguish the node local topology. With this invariant, the first six examples of binodal-quasi-uninodal nets were discovered. 4604 organic and metal-organic frameworks were analyzed to find examples of the topologies generated. It was shown that many edge-transitive nets as well as unknown t...
Source: Acta Crystallographica Section A - April 1, 2009 Category: Chemistry Authors: Blatov, V.A.Proserpio, D.M. Tags: topological relations three-periodic nets binodal nets edge-transitive nets research papers Source Type: journals

Depth profiling of polymer films with grazing-incidence small-angle X-ray scatteringEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A model-free method of reconstructing depth-specific lateral scattering from incident-angle-resolved grazing-incidence small-angle X-ray scattering (GISAXS) data is proposed. The information on the material which is available through variation of the X-ray penetration depth with incident angle is accessed through reference to the reflected branch of the GISAXS process. Reconstruction of the scattering from lateral density fluctuations is achieved by solving the resulting Fredholm integral equation with minimal a priori information about the experimental system. Results from simulated data generated for hypothetical multila...
Source: Acta Crystallographica Section A - April 1, 2009 Category: Chemistry Authors: Singh, M.A.Groves, M.N. Tags: depth profiling grazing-incidence small-angle X-ray scattering block copolymers research papers Source Type: journals

Correcting electron-density resolution bias in reciprocal spaceEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Fourier syntheses are always affected by series-termination errors, which generate sets of positive and negative ripples around each main peak in the map. The interaction among the ripples distorts the profile of the map and moves peaks away from their correct positions. In a previous paper [Altomare et al. (2008). Acta Cryst. A64, 326–336] an algorithm was described which reduces the resolution bias by removing the effects of the ripples in direct space. In this paper the correction is performed in reciprocal space: the effect of the ripples on the atomic scattering factors is calculated and subtracted from the usual at...
Source: Acta Crystallographica Section A - March 16, 2009 Category: Chemistry Authors: Altomare, A.Cuocci, C.Giacovazzo, C.Maggi, S.Moliterni, A.Rizzi, R. Tags: electron-density maps resolution series-termination errors bias research papers Source Type: journals

Temperature-dependent Debye–Waller factors for semiconductors with the wurtzite-type structureEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We computed Debye–Waller factors in the temperature range from 0.1 to 1000 K for AlN, GaN, InN, ZnO and CdO with the wurtzite-type structure. The Debye–Waller factors were derived from phonon densities of states obtained from Hellmann–Feynman forces computed within the density-functional-theory formalism. The temperature dependences of the Debye–Waller factors were fitted and fit parameters are given. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - March 13, 2009 Category: Chemistry Authors: Schowalter, M.Rosenauer, A.Titantah, J.T.Lamoen, D. Tags: Debye – Waller factors semiconductors density functional theory wurtzite-type structures research papers Source Type: journals

Discrete tomography of icosahedral model setsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The discrete tomography of mathematical quasicrystals with icosahedral symmetry is investigated, placing emphasis on reconstruction and uniqueness problems. The work is motivated by the requirement in materials science for the unique reconstruction of the structures of icosahedral quasicrystals from a small number of images produced by quantitative high-resolution transmission electron microscopy. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - March 13, 2009 Category: Chemistry Authors: Huck, C. Tags: icosahedral quasicrystals discrete tomography icosahedral symmetry high-resolution transmission electron microscopy research papers Source Type: journals

Crystal topologies – the achievable and inevitable symmetriesEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The link between the crystal topology and symmetry is examined, focusing on the conditions under which a structure with a given topology can exhibit a certain symmetry. By defining embeddings for quotient graphs (finite representations of crystal topologies) and the corresponding nets (the graph-theoretical equivalents of structures), a strong relationship between the automorphisms of the quotient graphs and the symmetry of the embedded net is established. This allows one to constrain the relative node positions under the premise that an embedding of a net has a certain symmetry, and allows one to assign nodes to equivalen...
Source: Acta Crystallographica Section A - March 13, 2009 Category: Chemistry Authors: Thimm, G. Tags: crystal topologies quotient graphs nets symmetry research papers Source Type: journals

Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examplesEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We present a method for geometric construction of periodic three-dimensional Euclidean nets by projecting two-dimensional hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMSs). Our techniques extend the combinatorial tiling theory of Dress, Huson & Delgado-Friedrichs to enumerate simple reticulations of these TPMSs. We include a taxonomy of all networks arising from kaleidoscopic hyperbolic tilings with up to two distinct tile types (and their duals, with two distinct vertices), mapped to three related TPMSs, namely Schwarz's primitive (P) and diamond (D) surfaces, and Schoen's gyroid (G). (Source: A...
Source: Acta Crystallographica Section A - January 28, 2009 Category: Chemistry Authors: Ramsden, S.J.Robins, V.Hyde, S.T. Tags: three-dimensional Euclidean nets two-dimensional hyperbolic tilings triply periodic minimal surfaces kaleidoscopic hyperbolic tilings lead articles Source Type: journals

Comments on tables of magnetic space groupsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Litvin [Acta Cryst. (2008), A64, 419–424 and supplementary material] extends much of the information contained in Volume A of International Tables for Crystallography for the 230 space-group types to the 1651 types of Shubnikov space groups, using Opechowski–Guccione (OG) notation for the space groups with a black–white lattice. It is pointed out that OG notation has crucial disadvantages compared to Belov–Neronova–Smirnova (BNS) notation. It is shown how Litvin's diagrams of symmetry elements for the orthorhombic Shubnikov space groups can be interpreted in terms of BNS symbols and how those containing e-glides ...
Source: Acta Crystallographica Section A - January 23, 2009 Category: Chemistry Authors: Grimmer, H. Tags: magnetic space groups Belov – Neronova Smirnova notation Opechowski Guccione notation black white space groups research papers Source Type: journals

Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group typeEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The Dirichlet generating functions for the number of sublattices fixed under each symmetry operation of the parent Patterson group may be combined to count the number of crystallographically nonequivalent sublattices, in total, by sublattice point group and by colour lattice group type. The combinatorial formulae used imply the existence of various congruences among the corresponding arithmetic functions. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - January 23, 2009 Category: Chemistry Authors: Rutherford, J.S. Tags: sublattice enumeration crystallographically nonequivalent sublattices colour lattice group Dirichlet generating functions research papers Source Type: journals

A general approach for determining the diffraction contrast factor of straight-line dislocationsEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Dislocations alter perfect crystalline order and produce anisotropic broadening of the X-ray diffraction profiles, which is described by the dislocation contrast factor. Owing to the lack of suitable mathematical tools to deal with dislocations in crystals of any symmetry, contrast factors are so far only known for a few slip systems in high-symmetry phases and little detail is given in the literature on the calculation procedure. In the present paper a general approach is presented for the calculation of contrast factors for any dislocation configuration and any lattice symmetry. The new procedure is illustrated with prac...
Source: Acta Crystallographica Section A - January 23, 2009 Category: Chemistry Authors: Martinez-Garcia, J.Leoni, M.Scardi, P. Tags: diffraction contrast factors dislocations elastically anisotropic crystals metrics research papers Source Type: journals

On the determination of fiber tilt angles in fiber diffractionEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The common digital method that is used to eliminate the effect of fiber tilt from fiber diffraction patterns is based on an approximation given by Franklin & Gosling [Acta Cryst. (1953), 6, 678–685]. The estimate of the tilt angle is iteratively optimized in the so-called `Fraser correction'. Building on the fundamental work of Polanyi [Z. Phys. (1921), 7, 149–180], the exact solution is presented. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - November 4, 2008 Category: Chemistry Authors: Stribeck, N. Tags: fiber tilt fiber diffraction short communications Source Type: journals

Deconvolution of the interatomic vector set using a convolution tableEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The deconvolution of the interatomic vector set (the ideal Patterson function) with the superposition technique is not complete because of the vector overlaps: multiple images and false peaks usually exist in the superposition map. Here, a new method for the deconvolution of the interatomic vector set is presented. This method involves constructing a table termed the `convolution table' from vectors in a superposition map and then sorting the table so that vectors belonging to different images are separated, and thus the overlaps are naturally solved. This method does not use the symmetry information. (Source: Acta Crystal...
Source: Acta Crystallographica Section A - November 4, 2008 Category: Chemistry Authors: Feng, J. Tags: interatomic vector set Patterson function deconvolution superposition vector overlap short communications Source Type: journals

Detection and characterization of ultra-thin films with neutron reflectometryEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Specular reflectometry, being a technique based on interference between coherent X-ray or neutron beams, is considered to have a fundamental limit in sensing the presence of films that are too thin for the maximum momentum transfer, Qmax, to which reflectivity has been measured. However, it is known both experimentally and from simulations that an ultra-thin film, with thickness t (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - November 4, 2008 Category: Chemistry Authors: Tun, Z. Tags: reflectometry thin films contrast matching research papers Source Type: journals

How to multiply a matrix of normal equations by an arbitrary vector using FFTEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This paper describes a novel algorithm for multiplying a matrix of normal equations by an arbitrary real vector using the fast Fourier transform technique. The algorithm allows full-matrix least-squares refinement of macromolecular structures without explicit calculation of the normal matrix. The resulting equations have been implemented in a new computer program, FMLSQ. A preliminary version of the program has been tested on several protein structures. The consequences for crystallographic refinement of macromolecules are discussed in detail. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 7, 2008 Category: Chemistry Authors: Strokopytov, B.V. Tags: computer programs FMLSQ fast Fourier transforms structure refinement macromolecules research papers Source Type: journals

Bijective mapping between the eigenvalue spectrum of a Karle–Hauptman matrix and its phasesEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
For any particular Karle–Hauptman matrix, a bijective mapping exists between the eigenvalue spectrum of the matrix and the set of structure-factor phases, given enough phase constraints. For a matrix of order n + 1 with no symmetry-equivalent reflections, n + 1 phases need to be fixed. Only a small subset of matrices derived from centric reflections from trigonal or hexagonal space groups have a bijective mapping without any fixed phases. (Source: Acta Crystallographica Section A)
Source: Acta Crystallographica Section A - October 7, 2008 Category: Chemistry Authors: Ralph, A.C. Tags: Karle – Hauptman matrix bijective mapping eigenvalues phases short communications Source Type: journals

Retrieving low- and medium-resolution structural features of macromolecules directly from the diffraction intensities – a real-space approach to the X-ray phase problemEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A simple mathematical algorithm is proposed to generate electron-density functions whose Fourier amplitudes match the diffraction intensities. The function is by construction everywhere positive. Using appropriate averaging procedures, the high-density regions of such functions could yield important structural information about macromolecular crystals. Trial calculations on protein crystals show that the protein envelope plus other structural motifs such as barrels and secondary structures could be recognized in the density maps. As such, the algorithm could provide a basis for new phasing methods or supplement existing ph...
Source: Acta Crystallographica Section A - October 7, 2008 Category: Chemistry Authors: Su, W.-P. Tags: phase problem macromolecules diffraction intensities phasing methods research papers Source Type: journals

Reliability of Monte Carlo simulations of disordered structures optimized with evolutionary algorithms exemplified with diffuse scattering from La0.70(1)(Al0.14(1)I0.86(1))Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Complex disorder and corresponding diffuse scattering from La0.70(1)(Al0.14(1)I0.86(1)) was taken as basis for investigating the reliability, reproducibility and influence of the refinement parameters of evolutionary algorithm refinements of Monte Carlo simulations. Using the same diffuse-scattering data set, a model relying on reasonable a priori knowledge about the real structure was used, as well as one that includes no presumptions except the average structure and the chemical composition. To strengthen the complementary character of the approaches, different evolutionary algorithms (`differential' and `cooperative' ev...
Source: Acta Crystallographica Section A - October 7, 2008 Category: Chemistry Authors: Weber, T.Simon, A.Mattausch, H.Kienle, L.Oeckler, O. Tags: disorder diffuse scattering evolutionary algorithm refinements Monte Carlo simulations research papers Source Type: journals

Elastic scattering of high-energy electrons by dopant atoms within a crystal in transmission electron microscopyEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A Bloch-wave model of dopant-atom scattering is developed using perturbation theory for parallel illumination in a transmission electron microscope. Dopant-atom scattering causes a change in the Bloch-wave excitations, with transitions from one Bloch state to another being governed by the amplitudes of the Bloch states at the dopant-atom position. The scattering mechanisms therefore depend on whether the dopant atom is substitutional or interstitial as well as the orientation of the crystal. The model is used to calculate the electron wavefunction for substitutional and interstitial Mo atoms in [111]- and [001]-oriented bo...
Source: Acta Crystallographica Section A - October 7, 2008 Category: Chemistry Authors: Mendis, B.G. Tags: dopant atoms Bloch waves Howie – Whelan equation perturbation theory research papers Source Type: journals

Measurement of X-ray rocking curves in the Bragg–Laue caseEmail this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
X-ray rocking curves in the Bragg–Laue case diffracting from the side surface of a plane-parallel crystal have been measured using a high-resolution optical system. The full width at half-maximum of the rocking curves is approximately three times narrower than that measured from the top surface. The characteristics of the transmitted beam from the side surface are almost the same as those through a thin crystal in the Bragg case. The rocking curves and the direction of X-ray energy flow in the crystal observed in the experiment can be reproduced using Wagner's approach [Wagner (1956), Z. Phys. 146, 127–168]. (Source: A...
Source: Acta Crystallographica Section A - August 14, 2008 Category: Chemistry Authors: Yoshizawa, M.Fukamachi, T.Hirano, K.Oba, T.Negishi, R.Hirano, K.Kawamura, T. Tags: Bragg – Laue case X-ray dynamical diffraction rocking curve research papers Source Type: journals