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  • 1
    Electronic Resource
    Electronic Resource
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 736-738 
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 31 (1998), S. 789-797 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The application of resonant (anomalous) scattering techniques to ab initio structure solution from powder data is demonstrated for the compound SrSO4. This material is orthorhombic, in space group Pnma (a = 8.359, b = 5.351, c = 6.869 Å, Z = 4), with 11 variable atomic positional parameters, and gives a fairly complex powder pattern with many overlapping peaks. Accurate high-resolution synchrotron X-ray powder diffraction data were obtained at three energies: 14, 225 and 5133 eV below the Sr K edge. From combinations of two of the three data-sets, partial Patterson densities were derived and used to phase the 71 uniquely resolved reflections, allowing a complete solution of the rest of the structure. Maximum entropy methods were found to be far superior to standard Fourier methods in the reconstruction of the electron-density distribution. The techniques of data collection, analysis and phase determination required for resonant scattering experiments of this type are described in detail.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 276 (1978), S. 593-594 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] In the simplest astrophysical model, the 45-µm feature can be observed in emission from hot sources or in absorption through cold dust against a hot background. In the Northern Hemisphere, the bright Kleinmann-Low (KL) nebula is particularly suitable2. Observations were made using a grating ...
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 450-455 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Diffraction experiments provide information on the Fourier components of microscopic density distributions in crystals. To obtain the spatial densities themselves, an inverse Fourier problem has to be solved. The procedure is complicated by the presence of noise and incompleteness of the data. The application of the maximum-entropy (MaxEnt) principle was a breakthrough in density reconstruction, allowing high-quality density maps to-be obtained without involving any a priori information concerning what the reconstructed density should look like. In this work, a procedure is proposed that incorporates a priori (e.g. theoretical) information into MaxEnt reconstructions of spin density distributions. It allows, on the one hand, the evaluation of the existing density models and, on the other, the precise investigation of what new information the experiment brings. Unlike traditional parameter-refinement techniques, the new method does not impose any strict constraints on the density to be reconstructed and is thus much more flexible. At the same time, it suppresses artifacts and yields high-quality density maps. The advantages of the new methods are illustrated by an example of spin density reconstruction based on real polarized neutron diffraction data.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 244-246 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The inverse Fourier transform is a most prominent and widely used tool in crystallography. Used to retrieve Patterson densities and densities from measured intensities or phased structure factors, it is well known to suffer from major drawbacks among which is the neglect of known error bars. In this paper, it is shown how to incorporate measured experimental error bars in the computation of the Fourier syntheses. This simple novel procedure should be useful when a proper maximum-entropy analysis proves infeasible, due to either a high dynamical range of the data or a high dimension of the direct space in which the density is sought (at least five or six dimensions for quasicrystallography).
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 295-300 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: When density distributions in crystals are reconstructed from three-dimensional diffraction data, a problem sometimes occurs when the spatial resolution in one given direction is very small compared to that in perpendicular directions. In this case, a two-dimensional projected density is usually reconstructed. For this task, the conventional Fourier inversion method only makes use of those structure factors measured in the projection plane. All the other structure factors contribute zero to the reconstruction of a projected density. On the contrary, the maximum-entropy method uses all the three-dimensional data, to yield three-dimensional-enhanced two-dimensional projected density maps. It is even possible to reconstruct a projection in the extreme case when not one structure factor in the plane of projection is known. In the case of poor resolution along one given direction, a Fourier inversion reconstruction gives very low quality three-dimensional densities `smeared' in the third dimension. The application of the maximum-entropy procedure reduces the smearing significantly and reasonably well resolved projections along most directions can now be obtained from the MaxEnt three-dimensional density. To illustrate these two ideas, particular examples based on real polarized neutron diffraction data sets are presented.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 176-188 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Bragg intensities from neutron and X-ray diffraction data of C60 single crystals were used to determine the nuclear- and electron-density distributions of C60 at room temperature. The anisotropic density distribution is reconstructed by the maximum-entropy method and evaluated in terms of symmetry-adapted spherical harmonics. From this analysis, the orientational probability density function f(ω) has been calculated and the rotational potential V(ω) that is experienced by a C60 molecule in the cubic surrounding at 295 K has been obtained. f(ω) shows strong deviations from the uniform orientational probability density function that would result from isotropic rotation. Accordingly, V(ω) exhibits well developed minima. The absolute potential minimum is found at an Euler-angle set ω1 and a second set of minima at slightly higher energy at ω2. The potential difference between V(ω1) and V(ω2) is 313 K, whereas the overall rotational potential barrier height amounts to 522 K. ω1 and ω2 are comparable with the major and minor orientations that are adopted by the molecules in their low-temperature arrangement. The angles ω1 and ω2 are fixed by the intrinsic geometry of the Euler-angle space (α, β, γ) under the combined action of the cubic site and the icosahedral molecular point group.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 189-197 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Accurate density data yield the primary information required for a thermodynamic model of molecular disorder. A detailed analysis of the structure from neutron Bragg data shows that the protons of the ammonia groups perform nearly unhindered rotations at room temperature as well as at 30 K. The nuclear density distribution is derived from a combination of conventional crystallographic split-atom density interpolation and maximum-entropy density reconstruction. The crystallographic density interpolation allows unique phases to be determined, i.e. phases that are independent of details of the model, for the measured Fourier components. MaxEnt reconstruction eliminates series-termination effects and provides for higher quality in the spatial resolution compared with standard Fourier maps. The proton density obtained in [Co(NH3)6](PF6)2 at both temperatures is concentrated on a plane perpendicular to the fourfold crystal axis and is found to be nearly circular, with a weak tetragonal contribution superimposed. This is a strong indication of nearly free uniaxial rotation in this compound. The proton density is analysed in terms of an anharmonic orientational potential, which couples rotational and translational motion. The nearly unhindered rotation in this compound is a consequence of the quasi-eightfold symmetry built up by the next-neighbour F atoms surrounding the NH3 groups in their plane of rotation.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 397-407 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A two-channel maximum-entropy method (MEM), first used to enhance magnetization densities from phased polarized neutron data by Papoular & Gillon [(1990). Europhys. Lett. 13, 429–434], has been applied to the electron deformation density. The resulting entropic densities are compared with standard deformation densities and with dynamic and static deformation maps obtained from multipole refinements. The procedure is illustrated with simulated and real single-crystal X-ray data sets on the molecular crystal of α-glycine. Both a uniform prior and a prior equal to the MEM-enhanced dynamic model deformation density are used in the MEM procedure, the result of which does not depend on the starting density. The method is judged by the appearance of the resulting maps and the values of the molecular dipole moment before and after the MEM. Compared with the conventional deformation density, the MEM procedure sharpens the peaks in the bond but flattens the weaker features, especially when a uniform prior is used. The dipole-moment criterion shows the non-uniform prior to be preferable to the uniform prior in reproducing electrostatic properties. The usefulness of the MEM in charge-density analysis remains open to discussion.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 739-746 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The maximum-entropy method (MEM) for structure determination is applied on the plastically crystalline phases of KOH and KOD characterized by delocalized H+ or D+ ions in a simple rock salt structure. The structure factors measured by neutron diffraction already give a consistent picture of the hydrogen distribution by conventional Fourier and modelling methods, which helps to understand the merit of the MEM. Owing to the negative sign of the scattering length of hydrogen, the MEM can, in a limited sense `model free', separate off the hydrogen density distribution. It is found, however, that the MEM cannot be applied naively for these compounds and reasons are given why the uniform density as a priori information has to be given up in the present case. The a priori information procedure to be used is discussed. In addition, and perhaps unexpectedly, the deuterium density is also obtained.
    Type of Medium: Electronic Resource
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