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) 2015 International Union of Crystallography2015-06-30International 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 71, Part 4, 2015textyearly62002-01-01T00:00+00:004712015-06-30Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances351urn:issn:2053-2733med@iucr.orgJune 20152015-06-30Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageAccessible atomic structures from sub-micron protein crystals
http://scripts.iucr.org/cgi-bin/paper?me0583
Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Rodriguez, J.A.2015-07-01doi:10.1107/S2053273315012206International Union of CrystallographyA guide to the collection and processing of MicroED data invites X-ray crystallographers and electron microscopists to solve atomic structures from tiny protein crystals.ENMicroEDnanocrystalselectron diffractiontext/htmlAccessible atomic structures from sub-micron protein crystalstext4712015-07-01Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Ascientific commentaries351352MicroED data collection and processing
http://scripts.iucr.org/cgi-bin/paper?mq5031
MicroED, a method at the intersection of X-ray crystallography and electron cryo-microscopy, has rapidly progressed by exploiting advances in both fields and has already been successfully employed to determine the atomic structures of several proteins from sub-micron-sized, three-dimensional crystals. A major limiting factor in X-ray crystallography is the requirement for large and well ordered crystals. By permitting electron diffraction patterns to be collected from much smaller crystals, or even single well ordered domains of large crystals composed of several small mosaic blocks, MicroED has the potential to overcome the limiting size requirement and enable structural studies on difficult-to-crystallize samples. This communication details the steps for sample preparation, data collection and reduction necessary to obtain refined, high-resolution, three-dimensional models by MicroED, and presents some of its unique challenges.Copyright (c) 2015 Johan Hattne et al.urn:issn:2053-2733Hattne, J.Reyes, F.E.Nannenga, B.L.Shi, D.de la Cruz, M.J.Leslie, A.G.W.Gonen, T.2015-07-01doi:10.1107/S2053273315010669International Union of CrystallographyThe collection and processing of MicroED data are presented.ENMicroEDelectron diffractioncrystallographycryo-EMnanocrystalsMicroED, a method at the intersection of X-ray crystallography and electron cryo-microscopy, has rapidly progressed by exploiting advances in both fields and has already been successfully employed to determine the atomic structures of several proteins from sub-micron-sized, three-dimensional crystals. A major limiting factor in X-ray crystallography is the requirement for large and well ordered crystals. By permitting electron diffraction patterns to be collected from much smaller crystals, or even single well ordered domains of large crystals composed of several small mosaic blocks, MicroED has the potential to overcome the limiting size requirement and enable structural studies on difficult-to-crystallize samples. This communication details the steps for sample preparation, data collection and reduction necessary to obtain refined, high-resolution, three-dimensional models by MicroED, and presents some of its unique challenges.text/htmlMicroED data collection and processingtext4712015-07-01Copyright (c) 2015 Johan Hattne et al.Acta Crystallographica Section Afeature articles353360Identification of inversion domains in KTiOPO4via resonant X-ray diffraction
http://scripts.iucr.org/cgi-bin/paper?pc5051
A novel method is presented for the identification of the absolute crystallographic structure in multi-domain polar materials such as ferroelectric KTiOPO4. Resonant (or `anomalous') X-ray diffraction spectra collected across the absorption K edge of Ti (4.966 keV) on a single Bragg reflection demonstrate a huge intensity ratio above and below the edge, providing a polar domain contrast of ∼270. This allows one to map the spatial domain distribution in a periodically inverted sample, with a resolution of ∼1 µm achieved with a microfocused beam. This non-contact, non-destructive technique is well suited for samples of large dimensions (in contrast with traditional resonant X-ray methods based on diffraction from Friedel pairs), and its potential is particularly relevant in the context of physical phenomena connected with an absence of inversion symmetry, which require characterization of the underlying absolute atomic structure (such as in the case of magnetoelectric coupling and multiferroics).Copyright (c) 2015 Federica Fabrizi et al.urn:issn:2053-2733Fabrizi, F.Thomas, P.A.Nisbet, G.Collins, S.P.2015-05-14doi:10.1107/S2053273315007238International Union of CrystallographyThe identification and high-resolution mapping of the absolute crystallographic structure in multi-domain ferroelectric KTiOPO4 is achieved through a novel synchrotron X-ray diffraction method. On a single Bragg reflection, the intensity ratio in resonant diffraction below and above the Ti absorption K edge demonstrates a domain contrast up to a factor of ∼270, thus implementing a non-contact, non-destructive imaging technique with micrometre spatial resolution, applicable to samples of arbitrarily large dimensions.ENresonant X-ray diffractionsynchrotron radiationimagingabsolute structureinversion symmetryinversion domainsferroelectricsA novel method is presented for the identification of the absolute crystallographic structure in multi-domain polar materials such as ferroelectric KTiOPO4. Resonant (or `anomalous') X-ray diffraction spectra collected across the absorption K edge of Ti (4.966 keV) on a single Bragg reflection demonstrate a huge intensity ratio above and below the edge, providing a polar domain contrast of ∼270. This allows one to map the spatial domain distribution in a periodically inverted sample, with a resolution of ∼1 µm achieved with a microfocused beam. This non-contact, non-destructive technique is well suited for samples of large dimensions (in contrast with traditional resonant X-ray methods based on diffraction from Friedel pairs), and its potential is particularly relevant in the context of physical phenomena connected with an absence of inversion symmetry, which require characterization of the underlying absolute atomic structure (such as in the case of magnetoelectric coupling and multiferroics).text/htmlIdentification of inversion domains in KTiOPO4via resonant X-ray diffractiontext4712015-05-14Copyright (c) 2015 Federica Fabrizi et al.Acta Crystallographica Section Aresearch papers361367Theoretical study of the properties of X-ray diffraction moiré fringes. I
http://scripts.iucr.org/cgi-bin/paper?td5025
A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997). Acta Cryst. A53, 810–812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.Copyright (c) 2015 Jun-ichi Yoshimuraurn:issn:2053-2733Yoshimura, J.2015-05-14doi:10.1107/S2053273315004970International Union of CrystallographyA detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory, where the effect of the Pendellösung intensity oscillation on the moiré pattern is explained in detail.ENdiffraction moiré fringesPendellösung oscillationphase jumpgap phaseA detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997). Acta Cryst. A53, 810–812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.text/htmlTheoretical study of the properties of X-ray diffraction moiré fringes. Itext4712015-05-14Copyright (c) 2015 Jun-ichi YoshimuraActa Crystallographica Section Aresearch papers368381Diaphony, a measure of uniform distribution, and the Patterson function
http://scripts.iucr.org/cgi-bin/paper?sc5088
This paper reviews the number-theoretic concept of diaphony, a measure of uniform distribution for number sequences and point sets based on a Fourier theory approach, and its relation to crystallographic concepts like the largest interplanar spacing of a lattice, the structure-factor equation and the Patterson function.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Hornfeck, W.Kuhn, P.2015-05-29doi:10.1107/S2053273315007123International Union of CrystallographyThe number-theoretic concept of diaphony, as a measure of uniform distribution, is reviewed, highlighting its relation to crystallographic concepts like the largest interplanar spacing of a lattice, the structure-factor equation and the Patterson function.ENuniform distributiongeometric discrepancydiaphonystructure-factor equationPatterson functionThis paper reviews the number-theoretic concept of diaphony, a measure of uniform distribution for number sequences and point sets based on a Fourier theory approach, and its relation to crystallographic concepts like the largest interplanar spacing of a lattice, the structure-factor equation and the Patterson function.text/htmlDiaphony, a measure of uniform distribution, and the Patterson functiontext4712015-05-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers382391Algorithm for systematic peak extraction from atomic pair distribution functions
http://scripts.iucr.org/cgi-bin/paper?vk5002
The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python program SrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Granlund, L.Billinge, S.J.L.Duxbury, P.M.2015-05-29doi:10.1107/S2053273315005276International Union of CrystallographyThis paper describes a method for unbiased peak extraction from atomic pair distribution functions using the information-theoretic Akaike information criterion.ENpair distribution functionpeak extractionmodel selectionAkaike information criterioncomputer programThe study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python program SrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.text/htmlAlgorithm for systematic peak extraction from atomic pair distribution functionstext4712015-05-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers392409Approximation of virus structure by icosahedral tilings
http://scripts.iucr.org/cgi-bin/paper?eo5047
Viruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tiles via projection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Salthouse, D.G.Indelicato, G.Cermelli, P.Keef, T.Twarock, R.2015-05-29doi:10.1107/S2053273315006701International Union of CrystallographyA procedure for the approximation of viral capsids by icosahedral tilings is proposed and illustrated for a range of viruses from different families. The output tilings can be used as coarse-grained models of viral capsids, providing a basis for further mathematical modelling of their dynamic behaviour and assembly.ENvirus capsid structureicosahedral tilingspolygonal approximationViruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tiles via projection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications.text/htmlApproximation of virus structure by icosahedral tilingstext4712015-05-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers410422Pairwise correlations in layered close-packed structures
http://scripts.iucr.org/cgi-bin/paper?vk5001
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, analytical expressions are developed for the pairwise correlation functions between the layers. These may be calculated analytically as explicit functions of model parameters or the expressions may be used as a fast, accurate and efficient way to obtain numerical values. Several examples are presented, finding agreement with previous work as well as deriving new relations.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Riechers, P.M.Varn, D.P.Crutchfield, J.P.2015-06-02doi:10.1107/S2053273315005264International Union of CrystallographyA closed-form method is developed to calculate correlation functions of arbitrarily stacked close-packed structures.ENX-ray diffractionplanar disorderstacking faultz-transformationspectral decompositionpair distribution functionGiven a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, analytical expressions are developed for the pairwise correlation functions between the layers. These may be calculated analytically as explicit functions of model parameters or the expressions may be used as a fast, accurate and efficient way to obtain numerical values. Several examples are presented, finding agreement with previous work as well as deriving new relations.text/htmlPairwise correlations in layered close-packed structurestext4712015-06-02Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers423443Topological crystallography of gas hydrates
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A new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Gudkovskikh, S.V.Kirov, M.V.2015-06-02doi:10.1107/S2053273315008864International Union of CrystallographyFor investigation of the proton-disordered structure of clathrate hydrates, a new approach is presented which is based on topological crystallography.ENtopological crystallographyquotient graphclathrate hydratesproton disorderA new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out.text/htmlTopological crystallography of gas hydratestext4712015-06-02Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers444450Iterative projection algorithms in protein crystallography. II. Application
http://scripts.iucr.org/cgi-bin/paper?sc5089
Iterative projection algorithms (IPAs) are a promising tool for protein crystallographic phase determination. Although related to traditional density-modification algorithms, IPAs have better convergence properties, and, as a result, can effectively overcome the phase problem given modest levels of structural redundancy. This is illustrated by applying IPAs to determine the electron densities of two protein crystals with fourfold non-crystallographic symmetry, starting with only the experimental diffraction amplitudes, a low-resolution molecular envelope and the position of the non-crystallographic axes. The algorithm returns electron densities that are sufficiently accurate for model building, allowing automated recovery of the known structures. This study indicates that IPAs should find routine application in protein crystallography, being capable of reconstructing electron densities starting with very little initial phase information.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Lo, V.L.Kingston, R.L.Millane, R.P.2015-06-06doi:10.1107/S2053273315005574International Union of CrystallographyIterative projection algorithms are used to determine the structures of two tetrameric proteins starting with only a low-resolution envelope and the position of the non-crystallographic axes.ENiterative projection algorithmsphasingdensity modificationphase determinationIterative projection algorithms (IPAs) are a promising tool for protein crystallographic phase determination. Although related to traditional density-modification algorithms, IPAs have better convergence properties, and, as a result, can effectively overcome the phase problem given modest levels of structural redundancy. This is illustrated by applying IPAs to determine the electron densities of two protein crystals with fourfold non-crystallographic symmetry, starting with only the experimental diffraction amplitudes, a low-resolution molecular envelope and the position of the non-crystallographic axes. The algorithm returns electron densities that are sufficiently accurate for model building, allowing automated recovery of the known structures. This study indicates that IPAs should find routine application in protein crystallography, being capable of reconstructing electron densities starting with very little initial phase information.text/htmlIterative projection algorithms in protein crystallography. II. Applicationtext4712015-06-06Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers451459Temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals
http://scripts.iucr.org/cgi-bin/paper?sc5090
This paper reports temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals, involving forbidden (002) and weak (222) reflections. Phase determination based on multiple-beam diffraction is employed to estimate phase shifts from (002)-based \{(002)(375)(37\overline{3})\} four-beam cases and (222)-based \{ (222)(\overline{5}3\overline{3})\} three-beam cases in the vicinity of the Ge K edge for temperatures from 20 K up to 300 K. The forbidden/weak reflections enhance the sensitivity of measuring phases at resonance. At room temperature, the resonance triplet phases reach a maximum of 8° for the four-beam cases and −19° for the three-beam cases. It is found that the peak intensities and triplet phases obtained from the (002) four-beam diffraction are related to thermal motion induced anisotropy and anomalous dispersion, while the (222) three-beam diffraction depends on the aspherical covalent electron distribution and anomalous dispersion. However, the electron–phonon interaction usually affects the forbidden reflections with increasing temperatures and seems to have less effect on the resonance triplet phase shifts measured from the (002) four-beam diffraction. The resonance triplet phase shifts of the (222) three-beam diffraction versus temperature are also small.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Liao, P.-Y.Liu, W.-C.Cheng, C.-H.Chiu, Y.-H.Kung, Y.-Y.Chang, S.-L.2015-06-06doi:10.1107/S2053273315009006International Union of CrystallographyTemperature (20–300 K)- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals, involving forbidden (002) and weak (222) reflections, are reported.ENresonant phase shiftstemperature dependenceenergy dependenceX-ray multiple diffractionGe crystalsThis paper reports temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals, involving forbidden (002) and weak (222) reflections. Phase determination based on multiple-beam diffraction is employed to estimate phase shifts from (002)-based \{(002)(375)(37\overline{3})\} four-beam cases and (222)-based \{ (222)(\overline{5}3\overline{3})\} three-beam cases in the vicinity of the Ge K edge for temperatures from 20 K up to 300 K. The forbidden/weak reflections enhance the sensitivity of measuring phases at resonance. At room temperature, the resonance triplet phases reach a maximum of 8° for the four-beam cases and −19° for the three-beam cases. It is found that the peak intensities and triplet phases obtained from the (002) four-beam diffraction are related to thermal motion induced anisotropy and anomalous dispersion, while the (222) three-beam diffraction depends on the aspherical covalent electron distribution and anomalous dispersion. However, the electron–phonon interaction usually affects the forbidden reflections with increasing temperatures and seems to have less effect on the resonance triplet phase shifts measured from the (002) four-beam diffraction. The resonance triplet phase shifts of the (222) three-beam diffraction versus temperature are also small.text/htmlTemperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystalstext4712015-06-06Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers460466The atomic anisotropic displacement tensor – completing the picture
http://scripts.iucr.org/cgi-bin/paper?kx5044
A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representation U to point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011), International Tables for Crystallography, Vol. A, Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Thorkildsen, G.Larsen, H.B.2015-05-29doi:10.1107/S2053273315008372International Union of CrystallographySome properties of the anisotropic displacement tensor have been revised. Complete tables for site-symmetry restrictions covering all special positions as listed in International Tables for Crystallography, Vol. A, are provided.ENanisotropic displacement tensortransformations among tensor representationssite-symmetry restrictionsequivalent isotropic displacement parameterA simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representation U to point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011), International Tables for Crystallography, Vol. A, Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].text/htmlThe atomic anisotropic displacement tensor – completing the picturetext4712015-05-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Ashort communications467470From a Grain of Salt to the Ribosome. The History of Crystallography as Seen Through the Lens of the Nobel Prize. Series in Structural Biology, Volume 4, edited by Ivar Olovsson, Anders Liljas and Sven Lidin. World Scientific, 2014. Pp. 536. Price GBP 98.00. ISBN 978-981-4623-11-7.
http://scripts.iucr.org/cgi-bin/paper?xo0015
Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Viterbo, D.2015-07-01doi:10.1107/S2053273315010529International Union of CrystallographyENbook reviewhistory of crystallographyNobel Prizetext/htmlFrom a Grain of Salt to the Ribosome. The History of Crystallography as Seen Through the Lens of the Nobel Prize. Series in Structural Biology, Volume 4, edited by Ivar Olovsson, Anders Liljas and Sven Lidin. World Scientific, 2014. Pp. 536. Price GBP 98.00. ISBN 978-981-4623-11-7.text4712015-07-01Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Abook reviews471472