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  • 1
    Electronic Resource
    Electronic Resource
    Computer-aided derivation of theoretical joint probability distributions of normalized structure factors (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 513-522 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general theoretical and practical procedure is presented for deriving joint probability distributions of any number of structure factors in any space group. The distributions include all higher-order terms up to a present order of N and thus may be used at any approximation. The procedure combines and extends the two different methods introduced by Naya, Nitta & Oda [Acta Cryst. (1964). 17, 421-433; Acta Cryst. (1965). 19, 734-747] for deriving joint probability distributions of phase-restricted and not-phase-restricted normalized structure factors respectively. The general algorithm for deriving joint probability distributions of structure factors has been implemented in a computer program, thus resulting in the possibility of computer-aided derivations of probabilistic relations for any set of structure factors. Optionally, the program transforms the resulting series-expansion form of the joint probability distribution into an exponential expression. In low-order approximation these exponential expressions usually turn out to be identical to expressions known from the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387099094
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  • 2
    Electronic Resource
    Electronic Resource
    A new joint probability distribution for the triplet phase sum. Inclusion of higher-order terms (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 309-317 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new joint probability distribution of three normalized structure factors is derived for the case of N equal atoms in the space group P1. The distribution appears in a series expansion. Convergence of the series is obtained by inclusion of higher-order terms up to order N-5, although with the exception of terms up to order N-1/2 the distribution does not contain all possible terms. Test results show improved estimates of the absolute value of the triplet phase sum when compared with the Cochran distribution. In particular, the systematic errors are reduced appreciably.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099191
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  • 3
    Electronic Resource
    Electronic Resource
    Estimation of quartet phase sums from a new joint probability distribution of normalized structure factors (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 84-92 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new joint probability distribution of normalized structure factors is derived for equal-atom structures in space group P1. From this general distribution, a series expansion, the conditional joint probability distribution of the quartet phase sum is obtained, when restrictive conditions among the reciprocal vectors are imposed. The main difference from existing quartet distributions is the possibility of enclosing higher-order terms to any given order of N, although an approximation employed in the derivation limits the number of them considerably. The higher-order terms present are easily employed in the series since the determination of their explicit appearance has been automated: a computer program derives the terms up to a desired order and stores them in a coded form. In general, the incorporation of selective terms up to order N-3 appears to yield sufficient convergence. Only high |E| values or a low N value may necessitate the use of higher-order terms. Test results show that, in contrast to results from the quartet distributions of Hauptman and Giacovazzo, systematic estimation errors are hardly present, while absolute estimation errors are reduced as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387099823
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  • 4
    Electronic Resource
    Electronic Resource
    Optimal symbolic phase determination (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 751-763 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A systematic method of phase determination is presented inspired by the dynamic-programming principle. In this new procedure the starting set and the best phasing sequence are determined while executing the symbolic phase determination itself. Special attention is given to the way in which statistical weights for symbolic phase indications can be calculated. Test results show that the new procedure leads to considerable improvements over the phase-determination procedures based on the convergence procedure currently available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387098568
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  • 5
    Electronic Resource
    Electronic Resource
    Ab initio structure determination from powder data using direct methods (1994)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 578-582 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876819400306X
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  • 6
    Electronic Resource
    Electronic Resource
    On the determination of accurate intensities from powder diffraction data. II. Estimation of intensities of overlapping reflections (1992)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 25 (1992), S. 237-243 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Even the best least-squares algorithm to extract intensities from a powder diagram will not be able to determine the separate intensities of completely overlapping peaks. In this paper a new method (DOREES) is presented to determine these intensities more accurately by applying relations between structure factors derived from direct methods and the Patterson function. The intensities obtained from the least-squares fit are used as a starting set for DOREES. Comparative tests on both artificially generated and real data show that DOREES improves the intensity set considerably.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889891012128
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  • 7
    Electronic Resource
    Electronic Resource
    Geometrical aspects of real-time powder diffraction using a normal generator and a linear diode-array detector (1994)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 27 (1994), S. 302-315 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A real-time powder diffractometer has been constructed, with which it is possible to follow structural changes taking place in a specimen in min or even seconds. Arrangements are available to control and change the temperature of the sample in the diffractometer. A formula describing the line width resulting from the non-conventional geometry has been derived. This formula can be used for tuning the equipment to meet practical requirements. Experiments to assess this formula are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889893009823
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  • 8
    Electronic Resource
    Electronic Resource
    Preferred-Orientation Correction and Normalization Procedure for Ab Initio Structure Determination from Powder Data (1995)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 28 (1995), S. 127-140 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A preferred-orientation analysis for powder diffraction data is proposed, based upon an extension of the Wilson-plot intensity analysis, in order to correct the integrated intensities before the structure determination is started. The technique is based on an empirical exponential model for preferred orientation proposed earlier in the literature, of which a formal derivation is now given. Prerequisites are disc-shaped behaviour of the crystallites and spinning of the specimen. Furthermore, the indexed powder pattern and the unit-cell contents are required, but neither a structural model nor pole-figure observations are necessary. The influence of preferred orientation on the statistics of the normalized structure factor are assessed. It is shown that preferred orientation diminishes the quality of the triplet-phase-sum statistics. Improvements of the normalization procedure for powder diffraction intensities are proposed. Finally, it is shown by means of simulated powder data under which conditions the (most likely) preferred-orientation direction and corresponding strength can be established. Test results indicate that a reconstruction of the preferred-orientation model imposed is feasible provided the maximum individual intensity enhancement (or decrease) as a result of imposed preferred orientation is at least 70%, when compared with data in which preferred orientation is absent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889894010629
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  • 9
    Electronic Resource
    Electronic Resource
    On the determination of accurate intensities from powder diffraction data. I. Whole-pattern fitting with a least-squares procedure (1992)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 25 (1992), S. 231-236 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new algorithm, direct intensity fitting, has been developed which performs a whole-pattern fitting for powder data. The algorithm is related to the fitting technique of Pawley [J. Appl. Cryst. 14, 357–361] but does not require start values for the intensities of the individual reflections. Comparative tests show that direct intensity fitting extracts more accurate intensities from a powder diffractogram and reduces the minimum peak distance for accurate data to half of the half-widths. The structure of the superconductor Ba2YCu3O8−x can be solved in a default direct-methods run with direct-intensity-fitting intensities extracted from a normal laboratory powder diffractogram.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889891012104
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  • 10
    Electronic Resource
    Electronic Resource
    Partial multiplicity factors for texture correction of cubic structures in the disc-shaped crystallite model (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 26 (1993), S. 449-452 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The correction of integrated intensities for preferred orientation in the disc-shaped crystallite model is analyzed. The partial multiplicity factors have been derived to describe the relationships between the prominent – preferentially oriented – HKL pole density PH(α) and the total pole density PTh(α = 0) for any set of symmetry-equivalent planes {hkl}. (The angle α is referred to the sample-surface normal.) The analysis of partial multiplicity factors revealed, in all crystal systems, the preferentially oriented planes {HKL} for which the general and partial multiplicity factors are equal for all (hkl) and showed the {HKL} planes that require the introduction of partial multiplicity into the intensity formula. Present results enable the application of the disc-shaped crystallite model with a simple texture correction for all kinds of preferentially oriented planes {HKL} in all crystal systems, which is especially useful for cubic structures, where the special multiplicity factors have to be used for every {HKL}.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889893000810
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