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  • 1
    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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  • 2
    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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    Paper (German National Licenses)
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  • 3
    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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  • 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
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    On the doublet phase sums of isomorphous data sets (1993)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 359-369 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The role of the doublet phase sum present among isomorphous data sets is investigated in connection with the triplet-phase-sum statistics. Several probabilistic and algebraic techniques are discussed to estimate the doublets. The combination of an algebraic estimation technique and a new difference Patterson synthesis, the maxima of which are used to improve iteratively the doublet phase sums, is shown to be successful. Test results for large model structures and idealized protein data show that this technique reduces the triplet-phase-sum errors to a level small enough for ab initio direct-methods applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767392009851
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  • 8
    Electronic Resource
    Electronic Resource
    On the relation between the diffraction ratio, the doublet values and the reliability of the triplet estimates (1993)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 350-358 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A diffraction ratio is proposed that predicts the differences to be expected between the intensities of two-isomorphous data sets. This ratio is important for the ab initio structure determination of isomorphously related structures by means of direct methods. The diffraction ratio is shown to be linearly related to the average doublet phase sum of the isomorphous data. It is argued that the doublets are essential for correct triplet-phase-sum estimates. The diffraction ratio and the idealized average triplet-phase-sum error, as calculated from a recent probabilistic theory, turn out to be related. A minimum diffraction ratio is required to obtain a triplet-phase-sum-error level comparable with that of small structures that are solved routinely by conventional direct methods. The diffraction ratio can be used to maximize the triplet-phase-sum reliability before collecting the data by choosing the optimal wavelength in a single anomalous-scattering experiment, selecting the most suitable heavy-atom derivative in a single-isomorphous-replacement experiment or selecting the optimal wavelengths in a multiwavelength experiment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767392009863
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  • 9
    Electronic Resource
    Electronic Resource
    The Estimation of Four-Phase Structure Invariants Using the Single Difference of Isomorphous Structure Factors (1996)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 77-87 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The recently introduced approach of using the difference between isomorphous structure factors as a random variable in the derivation of joint probability distributions of isomorphous structure factors has been extended to secure the conditional joint probability distribution of the quartet phase sums present among isomorphous structure factors. It is shown for calculated data sets (native and heavy-atom derivative) of the proteins avian pancreatic polypeptide and cytochrome c that, with single-wavelength anomalous-scattering data, reliable estimates can be obtained for the quartet phase sums, even if the estimates are based on the structure-factor differences of the four quartet main-term reflections only.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767395011226
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  • 10
    Electronic Resource
    Electronic Resource
    The joint probability distribution of structure factors incorporating anomalous-scattering and isomorphous-replacement data (1991)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 47 (1991), S. 428-440 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method to derive joint probability distributions of structure factors is presented which incorporates anomalous-scattering and isomorphous-replacement data in a unified procedure. The structure factors FH and F−H, whose magnitudes are different due to anomalous scattering, are shown to be isomorphously related. This leads to a definition of isomorphism by means of which isomorphous-replacement and anomalous-scattering data can be handled simultaneously. The definition and calculation of the general term of the joint probability distribution for isomorphous structure factors turns out to be crucial. Its analytical form leads to an algorithm by means of which any particular joint probability distribution of structure factors can be constructed. The calculation of the general term is discussed for the case of four isomorphous structure factors in P1, assuming the atoms to be independently and uniformly distributed. A main result is the construction of the probability distribution of the 64 triplet phase sums present in space group P1 amongst four isomorphous structure factors FH, four isomorphous FK and four isomorphous F−H−K. The procedure is readily generalized in the case where an arbitrary number of isomorphous structure factors are available for FH, FK and F−H−K.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767391002441
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