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  • International Union of Crystallography (IUCr)
  • 1985-1989  (6,250)
  • 1955-1959  (1,463)
  • 1950-1954  (1,308)
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Publisher
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Crystallographic refinement by simulated annealing: application to crambin (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 50-61 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A detailed description of the method of crystallographic refinement by simulated annealing is presented. To test the method, it has been applied to a 1.5 Å resolution X-ray structure of crambin. The dependence of the success of the simulated annealing protocol with respect to the temperature of the heating stage is discussed. Optimal success is achieved at relatively high temperatures. Regardless of the protocol used, the molecular-dynamics refined structure always yields an improved R factor compared with restrained least-squares refinement without manual re-fitting. The differences between the various refined structures and the corresponding electron density maps are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009195
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  • 2
    Electronic Resource
    Electronic Resource
    Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 63-75 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Subcommittee has attempted to elucidate the nature of problems encountered in the definition and use of statistical descriptors as applied to crystallography and to propose procedural improvements. The report contains (a) a dictionary of statistical terms established for use by experimentalists; (b) a description of the statistical basis for refinement procedures; (c) sections dealing with defects in the physical model used for refinement, and with the choice and significance of weighting schemes; and (d) recommendations, some of which may be readily implemented, whilst others may require a long-term effort to bring them into general use.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009596
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  • 3
    Electronic Resource
    Electronic Resource
    Two-dimensional intensity distributions obtained with crystal-monchromated X-radiation and a small specimen crystal (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 75-85 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two-dimensional (Δω, Δ2θ) intensity distributions in the plane of diffraction are calculated for the case of crystal-monochromated X-radiation incident on a small specimen. The calculations are based on ray tracing and take into account the mosaic spread of the monochromator, depth of penetration into the monochromator, source emissivity distribution, wavelength distribution, broadening due to the detector aperture, and various aspects of the experimental arrangement involved. The general form of the Δω, Δ2θ distributions for the case of a monochromator and small specimen crystal is considered. Some calculations are compared with experimental results and reveal excellent agreement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009250
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  • 4
    Electronic Resource
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    Phase dependence of Kikuchi patterns. I. Theory (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 104-109 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Thermal diffuse scattering in high-energy electron diffraction is analysed using the Einstein model of lattice vibrations. An expression for the intensity distribution in the Kikuchi pattern is obtained which includes thickness-dependent terms (i.e. a dependent-Bloch-wave theory is used) and the effects of a general crystal structure. The corresponding two-beam limit is shown to consist of four distinct terms, two of which depend on the phase of the structure factor. One of these is found to be non-zero only for non-centrosymmetric crystals and for relatively thin crystals. It leads to an asymmetric Kikuchi band, even in a symmetrical scattering geometry. This asymmetry may be used to determine the polarity of non-centrosymmetric crystals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009304
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  • 5
    Electronic Resource
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    The possible translational parts of (3+d) superspace symmetry operations (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 109-111 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A necessary condition for possible translational parts of (3 + d) superspace symmetry operations is derived. The general conditions are discussed especially for (3 + 1) superspace symmetry operations and some examples illustrate the application.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009663
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  • 6
    Electronic Resource
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    Electron density in the alkali halide crystals (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 112-115 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Structure factors at room temperature are computed for LiF, NaF, NaCl and KCl by means of theoretical ionic form factors and theoretical Debye-Waller factors. The values obtained are compared with the best available experimental data. For LiF, KCl and NaF - for which good experimental data are available - there is generally very good agreement, with only a few sizeable discrepancies for NaF that can be attributed to deficiencies of the experimental data. It is concluded that there is no apparent need to question the validity of the Debye-Waller theory as recently proposed in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009523
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  • 7
    Electronic Resource
    Electronic Resource
    X-ray attenuation coefficients of beryllium in the energy range 5 to 20 keV (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 1-3 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Mass attenuation coefficients for beryllium have been determined by an X-ray energy-dispersive method with a relative experimental error of 1-2%. Results are given for Cr, Fe, Co, Cu and Mo Kα lines and compared with recent experimental and theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388008347
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  • 8
    Electronic Resource
    Electronic Resource
    Application of the Ps-function method to macromolecular structure determination (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 794-797 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Ps function derived from anomalous-dispersion data [Okaya, Saito, & Pepinsky (1955). Phys. Rev. 98, 1857-1858] has been tested with observed data for an Hg derivative of a small protein, avian pancreatic polypeptide [Glover, Moss, Tickle, Pitts, Haneef, Wood & Blundell (1985). Adv. Biophys. 20, 1-12]. The Ps map was superimposed on the four Hg sites via a sum function and negative densities were eliminated from the resultant map. This map, with appropriate density inserted at Hg sites, closely resembles a map calculated with true phases; the two maps have a correlation coefficient of 0-67. For 2109 reflexions the unweighted mean phase error is 39.9° but with |FoFc| weighting this reduces to 29.5°.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389007646
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  • 9
    Electronic Resource
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    R factors in X-ray fiber diffraction. I. Largest likely R factors for N overlapping terms (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 258-260 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Simple expressions are obtained for the largest likely R factor in X-ray fiber diffraction recently derived by Stubbs [Acta Cryst. (1989), A45, 254-258]. These generalize the largest likely R factors obtained by Wilson [Acta Cryst. (1950), 3, 397-399] for centric and acentric crystals. Expressions are obtained in terms of special functions and as finite series that simplify the calculation of R factors. These may be useful for further analysis and understanding of the effects of particle diameter and symmetry and diffraction data resolution on the reliability of structure determinations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388011079
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  • 10
    Electronic Resource
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    Three-beam and many-beam theory in electron diffraction and its use for structure-factor phase determination in non-centrosymmetric crystal structures (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 839-851 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Closed-form expressions for three-beam dynamical transmission electron diffraction are compared. These are used as a guide to determine the best experimental conditions for the determination of structure-factor phases by convergent-beam electron diffraction in the general non-systematic case. The validity domains of Kambe's [J. Phys. Soc. Jpn (1957), 12, 1-13] 'strong coupling' approximation and Bethe's [Ann. Phys. (Leipzig) (1928), 87, 55-129] second approximation are compared, and these approximations reconciled. A comparison of many-beam calculations with experimental non-systematic CBED patterns is used to determine a three-phase invariant for CdS with an accuracy of ±5° in the electron structure-factor phase. If it is assumed that two of the phases are known exactly, the error in the third (00\bar 2) X-ray structure-factor phase would be ±0.75°. The accuracy of the method for determining phases, atomic position parameters and bonding charge distributions is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876738900913X
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  • 11
    Electronic Resource
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    On the calculation of small-angle diffraction patterns from distorted lattices (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 861-870 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is presented for the calculation of the diffraction properties of distorted lattices. An isotropic correlation field is used and the influence of finite crystal size is taken into account. An approximate model is described which is based on a fit of the correlation function to a sum of Gaussians. This method, which is applicable to more complex structures than simple lattices, simplifies the calculation of complicated convolution integrals. The method is illustrated with the calculation of the diffraction properties of 2D hexagonal lattices and exponential correlation. Various aspects, such as variations in peak intensity, line width and line shifts, are discussed.
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    URL: http://dx.doi.org/10.1107/S0108767389009220
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  • 12
    Electronic Resource
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    Segmented anisotropic refinement of bovine ribonuclease A by the application of the rigid-body TLS model (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 851-861 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The anisotropic displacements of selected rigid groups in bovine ribonuclease A have been refined from X-ray diffraction data by the application of the rigid-body TLS model. The rigid groups chosen were the side chains of tyrosine, histidine and phenylalanine and the planar side chains of aspartic acid, glutamic acid, glutamine, asparagine and arginine. The method has also been applied to the co-crystallizing active-site sulfate anion. This has enabled the description of the motion of the above-mentioned side-chain atoms by anisotropic displacement ellipsoids from a 1.45 Å refinement. The hydrophobic side groups in the protein core show mainly translational motion, with mean-square librations of 20 deg2 which are similar to those found in some close-packed crystals of small organic molecules. Librational displacements are much more significant in the hydrophilic side groups where their magnitudes can be correlated with solvent accessibility. Large liberations of some solvent exposed side chains correspond with the breakdown of a simple TLS model and the existence of multiple orientations of the side groups. The TLS model has also been applied to the whole protein molecule and shows that the average motion is approximately isotropic with little librational character.
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    URL: http://dx.doi.org/10.1107/S0108767389009177
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  • 13
    Electronic Resource
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    Prices of Acta Crystallographica and Journal of Applied Crystallography (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 882-884 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    URL: http://dx.doi.org/10.1107/S0108767389010536
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  • 14
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    A structural model for a quasicrystalline material (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc33-fc36 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A structural model for a quasicrystalline material of approximate composition Al65Cu20Fe15 is presented. The validity of the model was tested by comparing the optical diffraction of projections of the model with experimental electron diffraction patterns of crystal fragments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389012018
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  • 15
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    Character table of the hypercubic point group in six dimensions (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 879-882 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By application of a modified Burnside method, based on the explicit determination of class multiplication coefficients hijk, the character table of the hypercubic point group in six dimensions B6 - a group of order 46 080 - is obtained. This point group is used in the study of quasicrystals through a projection from six to three dimensions.
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    URL: http://dx.doi.org/10.1107/S0108767389007348
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  • 16
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    Quantitative determination of phases of X-ray reflection from three-beam diffraction. III. Experiments on mosaic crystals (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 870-878 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The method proposed by Chang & Tang [Acta Cryst. (1988), A44, 1065-1072] for quantitative determination of phases of X-ray reflection from three-beam diffraction profiles is applied to an organic crystal of (2R, 3 R)-3-acetoxy-5,7-dihydroxy-6-methylflavanone, with a mosaic spread of 0.08°. The expression for the kinematical diffraction intensities is modified according to the kinematical theory of X-ray diffraction in the multibeam regime. Three-beam Umweganregung and Aufhellung diffraction profiles are analyzed. With the help of the modified intensity expression, the crystal symmetry imposed by the space group and the three-beam diffraction geometry, four acentric phases and fourteen centric phases of structure-factor triplets are determined.
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    URL: http://dx.doi.org/10.1107/S0108767389009293
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  • 17
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    A reconsideration of the role of two-phase seminvariants. V. Basic results (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 99-104 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A basic obstacle to the widespread use of two-phase seminvariants of first rank in direct methods is often the large amount of computing time needed for their probabilistic estimation. A new very fast algorithm for identifying such seminvariants and a modified probabilistic formula for their estimation are described. Contrary to common belief, practical tests show that the amount of information contained in two-phase seminvariants is in general not negligible compared with information provided by triplets.
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    URL: http://dx.doi.org/10.1107/S0108767388009298
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  • 18
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    Particle shapes and oscillatory deviations from the Porod law: the hyperbolic contact point case (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 86-99 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The leading term in the asymptotic expansion of the isotropic component of the X-ray intensity scattered by a homogeneous right circular cylindrical particle (of height H and diameter D) can be written as: {\cal ch-4[ST-2SB cos (hH)- SL sin (hD)]. Here SL, SB and ST denote respectively the lateral, the base and the total surface area of the cylinder, while {\cal c is a normalization factor. From this expression one is led to conjecture that the oscillatory deviations from the Porod law, originated by the two interface subsets which have the same normal and are separated by δ, are proportional to cos (hδ) or to sin (hδ) depending on whether the tangency points between one of the interphase subsets and the spheres of radius δ centred on the opposite subset are elliptical or hyperbolic respectively. It is proved that the conjecture is true and general expressions for the coefficients in front of the two oscillatory functions are obtained.
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    URL: http://dx.doi.org/10.1107/S0108767388009286
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  • 19
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    The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 115-123 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The anomalous high-index faces (hkl) of the mineral calaverite (Au1 - xAgxTe2) measured goniometrically in the year 1931 by Goldschmidt, Palache & Peacock [Neues Jahrb. Mineral (1931), 63, 1-58] are re-interpreted and related to the wave vector q of the displacive incommensurate modulation which was recently found in the crystal structure. All crystal faces (including the high-index ones) can be given four low indices (hklm), using q as a fourth basis vector. From this an almost hundred-year-old anomaly in crystal morphology is in principle solved.
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    URL: http://dx.doi.org/10.1107/S010876738800981X
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  • 20
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    Electron microscope analyses of domains and discommensurations in ferroelectric Rb2ZnCl4. Erratum (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 146-146 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The following corrections should be made in Tsuda, Yamamoto & Yagi [Acta Cryst. (1988). A44, 864-870]. (1) 'only two kinds of domain boundaries' in the Abstract should be changed to 'two kinds of image contrast of domain boundaries'. (2) The expressions for h2, h4, h6 in § 4.1 should be replaced by h2: -x -y -z + h4: -x -y -z (inversion) h6: -x -y -z + (3) "two kinds of DC's showing different contrast' in the second paragraph in § 4.1 should be changed to 'two kinds of DC contrast'.
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    URL: http://dx.doi.org/10.1107/S0108767388012395
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  • 21
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    XV International Congress of Crystallography, Bordeaux, France, 19-28 July 1990. Call for programme proposals (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 146-148 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    URL: http://dx.doi.org/10.1107/S0108767389099988
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  • 22
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    Correlation between occupancy and temperature factors of solvent molecules in crystal structures of proteins (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 145-146 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Correlation between occupancy and temperature factors during the refinement of a disordered molecule is discussed on the basis of their effects on an atomic scattering factor curve. When the resolution of the data is limited, occupancy and temperature factors affect scattering-factor curves in a similar fashion, and therefore they are correlated. An examination of this correlation suggests that small deviations (0.1) of occupancy factors from their tentative values may be compensated by suitable changes in temperature factors when the data are limited to medium (2.5 Å) resolution.
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    URL: http://dx.doi.org/10.1107/S0108767388008967
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  • 23
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    Report on the IUCr Logo Design Contest (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 148-148 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    URL: http://dx.doi.org/10.1107/S0108767388010852
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  • 24
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    Comments on an asymmetric domain for intercrystalline misorientation in cubic materials in the space of Euler angles (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc1-fc2 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The following comments are made on a paper by Zhao & Adams [Acta Cryst. (1988), A44, 326-336]. An asymmetric domain for intercrystalline misorientation in cubic materials has also been published for the parametrization of rotations by a rotation vector instead of Euler angles. The former parametrization minimizes discontinuities in contrast to the latter. The value 1152/m of distinct equivalent rotations has not been determined correctly for a number of CSL (coincident site lattice) boundaries; the correct values are available in earlier publications.
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    URL: http://dx.doi.org/10.1107/S0108767388011031
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  • 25
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    Limits of the Patterson method for the determination of one-dimensionally modulated structures (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc5-fc8 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Patterson function can reveal the modulation of a basic structure if its summation terms include only satellite reflections. Examples of Patterson summations for various types of modulated structures illustrate the difficulties of interpretation and the bias occurring in the determination of the amplitudes and phases of the modulation. The opportunity to use the Patterson function to determine modulated structure is discussed.
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    URL: http://dx.doi.org/10.1107/S0108767388013844
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  • 26
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    Comments on The phases of forbidden reflections, by Post & Ladell (1987) (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc3-fc4 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The observations of Post & Ladell [Acta Cryst. (1987), A43, 173-1791 of the asymmetry of the strong primary reflection 311 in germanium in the neighborhood of weak reflections such as {222} are shown to be in good quantitative agreement with the predictions of this asymmetry based on first-order perturbation theory of such interactions [Juretschke (1986). Acta Cryst. A42, 405-406]. Since the theory accounting for these data is insensitive to the phases entering in these many-beam interactions, the asymmetries observed in this experimental configuration do not allow any inferences about the phases of forbidden reflections.
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    Theoretical study of X-ray diffraction in homogeneously bent crystals – the Bragg case (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 732-738 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray dynamical diffraction in homogeneously bent crystals is studied theoretically in the Bragg case. The study starts from the Green function given previously by Chukhovskii, Gabrielyan & Petrashen' [Acta Cryst. (1978), A34, 610-620] as an inverse Laplace transform and which can be viewed as an integral over all incident plane waves. The integrand is developed by means of an asymptotic representation of parabolic cylinder functions. Integration by the stationary- phase method leads to the evidence of curved X-ray paths and, in the case of large values of strain gradient, to the creation of a new wave field. The intensity of the new wave field is shown to be a fraction exp (-2π|v|) of the incident beam where |v| is the inverse of the strain gradient expressed in reduced units.
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    The minimization of errors in the molecular replacement structure solution; the effect of the errors on the least-squares refinement progress (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 227-234 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The molecular replacement method (MR) is likely to cause significant systematic errors in the analysed structure. These errors are not always corrected automatically during least-squares refinement. It is therefore crucial that both the orientation and translation parameters are optimized before refinement is undertaken. The techniques used to achieve this depend either on the rigid-body refinement concept or on a six-dimensional R-factor minimization and all are expensive and time consuming. A simple procedure to refine the molecular replacement structure solution parameters is shown. It uses the existing restrained least-squares method, requires no new software, and is shown to be very effective.
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    On the use of the term `absolute' in crystallography (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 234-238 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The concept of 'absolute structure' as introduced by Jones [Acta Cryst. (1984), A40, 660-662] is discussed, and the term 'absolute' is extended to cases where the structure has been related to some external macroscopic physical property. The non-centrosymmetric crystal classes are divided into seven distinct categories for which specific terms are proposed: structural chirality, when the 'absolute structure' is determined for crystals in classes 1, 2, 3, 4, 6, 222, 422, 32, 622, 23 and 432; absolute chirality, when the 'absolute structure' is linked to a chiral property such as optical rotation; absolute polarity, when the 'absolute structure' is linked to a polar property such as pyroelectricity; absolute morphology, when the 'absolute structure' is linked to the crystal habit: in this case there may be two further subdivisions - absolute chiral morphology (or absolute enantiomorphism) to describe a link to the hand of the habit, and absolute polar morphology to describe a link to the polar nature of the habit. It is further recommended that the term absolute configuration should be reserved only for molecular species and not for crystal structures.
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    On integrated intensities in Kato's statistical diffraction theory (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 241-244 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new approach to Kato's [Acta Cryst. (1980), A36, 763-769, 770-778] calculations in the Laue case is presented, giving a clearer and simpler derivation of the mixed terms of the integrated intensities (Bragg- and forward-diffracted beams). The results are in agreement with calculations by Al Haddad & Becker [Acta Cryst. (1988), A44, 262-270] showing the necessity of correcting two errors in the original treatment of Kato.
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    Bragg's law with refraction (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 238-241 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Expressions for Bragg's law have been derived for the general case of Bragg diffraction in which an incident beam strikes a crystal surface at an angle α, is then diffracted by planes inclined to the surface by φ and leaves the same surface at an angle β. The crystal is assumed to have a refractive index n = 1 - δ and λ is the X-ray wavelength in air or vacuum. Under these conditions Bragg's law can be written as λ = 2d(1 - δ)[cos φ sin (α - δ/tan α) + sin φ cos (α - δ/tan α) cos σ] and λ = 2d(1 - δ)[cos φ sin (β - δ/tan β) + sin φ cos (β - δ/tan β) cos τ]. σ and τ are dihedral angles defined in terms of N, the normal to the crystal surface; d*, the normal to the diffracting planes; -s0, a ray in air antiparallel to the incident beam and s, the diffracted ray in the air. σ is the angle between (-s0, N) and (d*, N) and τ the angle between (s, N) and (d*, N). When the plane of diffraction contains N, σ and τ are either 0 or 180° and Bragg's law takes the form λ = 2d(1 - δ) sin (α - δ/tan α ± φ) + φ for σ = 0° - φ for σ = 180° λ = 2d(1 - δ) sin (β- δ/tan β ± φ) + φ for τ = 0° - φ for τ = 180°. The magnitude of the refraction effect varies primarily with X-ray wavelength, electron density, and beam-to-crystal angle. Because of refraction the beam-to-crystal-surface angle required to satisfy Bragg's law can change by 10-4 to 10-1 degrees.
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    A time-of-flight neutron diffraction study of anharmonic thermal vibrations in SrF2, at the spallation neutron source ISIS (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 244-247 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Measurements have been made, at wavelengths in the range 0.3-6.2 Å, of hhl reflections of SrF2 on the single-crystal diffractometer (SXD) at the ISIS Spallation Neutron Source. After application of a variable-wavelength extinction correction to the derived |Fhkl| values, a refinement of the anharmonicity parameter βF of the fluorine atoms was carried out, yielding a value of -4.19 (30) × 10-19 J Å-3.
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    On the probabilistic theory of isomophous data sets: general joint distributions for the SIR, SAS and partial/complete structure cases (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 247-254 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By characterizing isomorphism in reciprocal space [i.e. diffraction data sets are isomorphous if they have the same geometry (the same reciprocal-lattice unit cell) and the same symmetry] it is shown that the diffraction data of a native protein and of its heavy-atom derivatives, the calculated data of a partial structure and the observed data of its associated complete structure, and the Friedel-pair data of an anomalously scattering crystal structure all belong to the more general class of isomorphous data sets. Their joint probability distributions for two- and three- phase structure invariants are shown to be isomorphous: they have the same functional form and differ only in individual atomic scattering factors. General joint probability distributions, which can be used for any isomorphous data pairs, are presented.
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    Benzene crystals at low temperature: a harmonic lattice-dynamical calculation (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 261-263 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A harmonic lattice-dynamical model has been used to calculate vibrational frequencies and crystallographic atomic displacement parameters (a.d.p.) for benzene crystals at 15 and 123 K. The agreement of the frequencies with the experiment is good; the a.d.p.'s are in excellent agreement with data derived from neutron diffraction only at very low temperature. At 15 K, the zero-point contribution is about 90% of the a.d.p.'s, and so further cooling will produce little change. A bond-length correction according to the general-motion formula leads to an average of 1.401 Å for the C-C bonds, which is higher than expected.
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    Full-matrix inversion procedure for minimum-variance Fourier coefficient (MVFC) refinement (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 308-308 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A fast matrix inversion procedure is suggested for matrices containing a large diagonal block as is the case in minimum- variance Fourier coefficient refinement.
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    Commission on Powder Diffraction. Newsletter No. 2 (Extracts) (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc19-fc23 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Simultaneous search for symmetry-related molecules in cross-rotation functions (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 309-314 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a typical cross-rotation function, the Patterson function of a single search molecule is compared with an observed Patterson function, which contains a set of symmetry-related intramolecular vector sets. In principle, it is better to search for the symmetry- related molecules simultaneously, and Nordman [Am. Crystallogr. Assoc. (1986), Hamilton, Ontario, Program Abstr. p. 36] has reported success with an algorithm of this type. In this paper, the differences between the ordinary search and a simultaneous search are investigated, and it is shown that the combined presence of crystallographic symmetry and approximate symmetry of a search model may lead to significant bias in conventional rotation functions. The nature and magnitude of this symmetry bias are discussed. An efficient algorithm is derived for generating a modified unbiased cross-rotation function map from conventional rotation functions. Two examples are described that demonstrate improvement in the quality of the rotation function maps and the ability to obtain physically meaningful correlation coefficients.
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    Minimization of cross entropy: a tool for solving crystal structures (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 4-10 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new algorithm for the solution of crystal structures via the principle of minimum cross entropy is described. This method is an extension of direct methods. Conventional direct methods are used to find an initial set of phases which are extended and refined by a search for the minimum-cross-entropy solution. This search is done directly in terms of the phases rather than the Lagrange multipliers used in most other approaches. It was tested by solving two structures, a small molecule and a macromolecule of 610 atoms in the asymmetric unit.
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    Crystal elasticity and inner strain: a computational model (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 20-25 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The internal strain induced in a crystal structure by lattice deformation was considered. A suitable rotationally invariant representation was introduced and the corresponding contribution to the elastic constants was calculated. The method is based on the use of crystallographic rather than Cartesian atomic coordinates as variables of energy derivatives, with full exploitation of space-group symmetry and no constraint on the lattice geometry. A two-body Born interatomic potential was assumed, for both ionic and molecular crystals; energy derivatives of electrostatic lattice sums were calculated with the Ewald series. Molecular groups are treated within a rigid-body scheme based on Eulerian angles and translations as inner strain variables. Results of computations of Mg2SiO4 (forsterite) are reported, and the importance of optimizing the potential parameters against experimental data is discussed.
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    Infinite periodic minimal surfaces and their crystallography in the hyperbolic plane (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 10-20 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Infinite periodic minimal surfaces are now being introduced to describe some complex structures with large cells, formed by inorganic and organic materials, which can be considered as crystals of surfaces or films. Among them are the spectacular cubic crystalline structures built by amphiphilic molecules in the presence of water. The crystallographic properties of these surfaces are studied from an intrinsic point of view, using operations of groups of symmetry defined by displacements on their surface. This approach takes advantage of the relation existing between these groups and those characterizing the tilings of the hyperbolic plane. First, the general bases of the particular crystallography of the hyperbolic plane are presented. Then the translation subgroups of the hyperbolic plane are determined in one particular case, that of the tiling involved in the problem of cubic structures of liquid crystals. Finally, it is shown that the infinite periodic minimal surfaces used to describe these structures can be obtained from the hyperbolic plane when some translations are forced to identity. This is indeed formally analogous to the simple process of transformation of a Euclidean plane into a cylinder, when a translation of the plane is forced to identity by rolling the plane onto itself. Thus, this approach transforms the 3D problem of infinite periodic minimal surfaces into a 2D problem and, although the latter is to be treated in a non-Euclidean space, provides a relatively simple formalism for the investigation of infinite periodic surfaces in general and the study of the geometrical transformations relating them.
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    Bounding a molecule in a noisy synthesis (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 34-39 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method of bounding a protein molecule in a very noisy synthesis is considered. It consists of two steps. In the first step ('nonlinear filtration') basic points are chosen that are most likely to belong to the region of the molecule. In the second step ('linear filtration') a compact region with the maximal concentration of these points is searched. Various modifications of the method are analysed. It is shown that the molecular region in a finite-resolution synthesis contains not only the highest positive maxima of the density distribution but also the deepest negative minima.
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    Quelques propriétés des représentations induites principales illustrées par les groupes ponctuels cristallographiques (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 26-34 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A point group representation spanned by a set of equivalent positions is a peculiar principal induced representation (PIR) associated with the stabilizer subgroup of the generating position. The characters, the irreducible components and the kernels of the PIR are determined by means of classical methods. The PIR properties are specially studied in connection with subgroup relations. There is a mapping from the ordered set of conjugate subgroups to the ordered set of non-equivalent PIR. The PIR direct products may always be split into a sum of PIR; in special cases the product reduces to one PIR. The intersection of PIR is not always a PIR; this depends on relative properties of their associated subgroups. When the point group is commutative the set of non-equivalent PIR may be erected into a modular lattice (in the mathematical sense). It is isomorphic to the modular lattice of subgroups. The study is illustrated by numerous examples built on point groups \bar 42m, 23 and 4/m.
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    Polarization anisotropy of anomalous scattering in lithium iodate and effect of K-level width (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 39-42 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The anomalous scattering tensor, measured using synchrotron radiation with lithium iodate near the iodine K absorption edge, shows polarization anisotropy similar to that in the bromate ion, but lesser in magnitude: about 1 electron/atom at most. The reduction is explained by a greater natural width of the K level. Equally small or smaller anisotropy is predicted for any other absorption edge above 33 keV.
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    A memory-efficient fast Fourier transformation algorithm for crystallographic refinement on supercomputers (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 42-50 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A vectorizable algorithm for fast computation of structure factors and derivatives during refinement of macromolecular structures is presented. It is based on fast Fourier transformations on subgrids that cover the unit cell of the crystal. The use of subgrids allows reduction of the total memory requirements for the computations without producing large overheads. The algorithm is applicable to all space groups. The performance of the algorithm on a conventional scalar computer as well as on supercomputers is discussed.
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    An alternative convention for solving the ambiguity problem of (3+1) superspace group symbols (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 61-63 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An alternative convention is proposed for solving the ambiguity problem of (3 + 1) superspace group symbols described by Yamamoto, Janssen, Janner & de Wolff [Acta Cryst. (1985), A41, 528-530] based on the requirement that the condition for equivalence of modulation vectors to be independent on a selection of basis vectors is satisfied.
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    Direct methods in protein crystallography (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 765-781 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is pointed out that the 'direct methods' of phase determination for small-structure crystallography do not have immediate applicability to macromolecular structures. The term 'direct methods in macromolecular crystallography' is suggested to categorize a spectrum of approaches to macromolecular structure determination in which the analyses are characterized by the use of two-phase and higher-order-phase invariants. The evaluation of the invariants is generally obtained by the use of heavy-atom techniques. The results of a number of the more recent algebraic and probabilistic studies involving isomorphous replacement and anomalous dispersion thus become valid subjects for discussion here. These studies are described and suggestions are also presented concerning future applicability. Additional discussion concerns the special techniques of filtering, the use of non-crystallographic symmetry, some features of maximum entropy and attempts to apply phase-determining formulas to the refinement of macromolecular structure. It is noted that, in addition to the continuing remarkable progress in macromolecular crystallography based on the traditional applications of isomorphous replacement and anomalous dispersion, recent valuable advances have been made in the application of non-crystallographic symmetry, in particular, to virus structures and in applications of filtering. Good progress has also been reported in the application of exact linear algebra to multiple-wavelength anomalous-dispersion investigations of structures containing anomalous scatterers of only moderate scattering power.
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    Nominations sought for the Patterson Award for 1990 (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 802-803 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Solids and surfaces: a chemist's view of bonding in extended surfaces by R. Hoffmann (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 803-804 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    The Monte Carlo simulation of random stacking faults in close-packed structures (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 797-801 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new approach to the estimation of the concentration of random stacking faults in close-packed structures (and also multilayers) is presented. It is based on the Monte Carlo computer simulation of the arrangement of stacking faults in a crystal, given by an appropriate h-k sequence. Thus the corresponding intensity (structure-factor) distribution along the streaked reciprocal-lattice rows may be calculated from nearly the same expression as for a perfect multilayer structure. In particular, good agreement is observed with the computations on the basis of the intensity equations derived for several particular cases. Some peculiarities in the diffracted intensity distribution of crystals with multilayer structures containing random stacking faults of different types, or having different dimensions of the hexagonal unit cell, are pointed out.
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    The coset and double coset decomposition of the 32 crystallographic point groups (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 801-802 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The coset and double coset decompositions of the 32 crystallographic point groups with respect to each of their subgroups are tabulated.
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    The probability distributions of X-ray intensities in fiber diffraction: largest likely values for fiber diffraction R factors (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 254-258 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: R factors in fiber diffraction are generally lower than in conventional crystallography, because of the cylindrical averaging of fiber diffraction data. The probability distributions for fiber diffraction intensities, analogous to Wilson's distributions for crystal diffraction intensities, are derived, and from these the largest likely values of R are estimated. These values depend on the size and symmetry of the diffracting particle and on the resolution of the analysis, and range from 0.586 for systems for very high symmetry (as in crystal diffraction) to much lower values for systems of low symmetry.
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    A HREM study of the intergrowth of magnetite and coulsonite (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 264-268 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The microstructures of magnetite containing vanadium and titanium, found in Sichuam province, China, have been studied by high-resolution electron microscopy (HREM). The [110] structural images showed a multiply intimate intergrowth of magnetite and coulsonite as a result of exsolution along the [110] direction instead of the [111] direction as reported previously. The detectable different contrast of the two phases was confirmed by image simulation. The antiphase domain and various stacking faults related to the nonstoichiometry of the transitionmetal oxide in the same direction were also observed in magnetite and coulsonite, respectively. The possible genetic aspect and formation of these defects on exsolution are also considered.
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    Description of hexagonal Frank–Kasper phases by a projection method (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 268-274 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure of hexagonal Frank-Kasper (FK) phases can be described by the projection of the seven-dimensional (7D) Cr3Si and Zr4Al3 cubes in a suitable projection subspace onto a 3D hyperplane. The close relationship between hexagonal FK phases and the dodecagonal quasicrystal with 12-fold rotational symmetry is discussed.
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    Symmetry properties of grain boundary junctions (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 297-303 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The symmetry group of the coincidence site lattice (CSL) is used for the study of the properties of triple junctions formed by plane boundaries. The experimental evidence that there are junctions with an obviously symmetrical relationship among the adjacent planes is analysed systematically. The analysis concerns the triple junctions in which the grain boundaries (GBs) are described by 180° CSL rotations. For these triple junctions the common intersection is a CSL rotation axis of the three GBs. Two cases need to be distinguished. In the first case the common intersection is a symmetry axis of the three CSLs, while in the second case the common intersection is a general direction. Thus in the first case the corresponding symmetry element is a common symmetry element of the three CSLs participating in the junction.
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    Linear algebraic analyses of structures with one predominant type of anomalous scatterer (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 303-307 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Further studies have been made of the information content of the exact linear equations for analyzing anomalous dispersion data in one-wavelength experiments. The case of interest concerns structures containing atoms that essentially do not scatter anomalously and one type of anomalously scattering atoms. For this case, there are three alternative ways of writing the equations. The alternative sets of equations and the transformations for transforming one set into the other are given explicitly. Comparison calculations were made with different sets of equations. Isomorphous replacement information is readily introduced into the calculations and the advantage of doing so is clearly illustrated by the results. Another aspect of the potential of the exact linear algebraic theory is its application to multiple-wavelength experiments. Successful applications of the latter have been made by several collaborative groups of investigators.
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    Cauchy distribution, intensity statistics and phases of reflections from crystal planes (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 314-319 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recently near-Gaussian distributions have been of much interest in the field of crystallographic statistics. In the present work, expressions for a truncated Cauchy distribution corresponding to acentric and centric cases have been derived. Expressions for P+, the probability of sign relations for centric crystals, and for Pφ, the probability of the tangent relationship for acentric crystals, have been derived on the basis of the Cauchy distribution of structure factor components. Theoretical N(Z) curves for centric and acentric Cauchy distributions have been compared with those for acentric, centric and bicentric Gaussian distributions. The N(Z) curve for the Cauchy acentric distribution follows closely that for the Gaussian acentric up to Z = 0.5. It then takes an upward turn and surpasses the Gaussian bicentric curve at high Z values. A similar trend is shown by the N(Z) curve for the Cauchy centric distribution after being approximately intermediate between the Gaussian centric and bicentric cases up to Z = 0.5. The results of P+ and Pφ have been compared with some known crystal data and the agreement is quite satisfactory for the cases studied.
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    Systematic determination of coincidence orientations for all hexagonal lattices with axial ratio c/a in a given interval (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 320-325 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two neighbouring grains of the same phase with a lattice of hexagonal Bravais type are considered which have a three-dimensional lattice of symmetry translations in common, called the coincidence site lattice or CSL. The volume ratio of unit cells for the CSL and the original lattice is called the multiplicity Σ. The Σ-hex theorem gives Σ in terms of four integral parameters that describe the axis and angle of the rotation connecting the hexagonal lattices of the two neighbouring grains and in terms of their axial ratio c/a. Two types of rotations generating CSL's may be distinguished, viz common rotations, which generate CSL's with the same Σ; for every value of c/a, and specific rotations, which generate CSL's with a low value of Σ only for a few values of the axial ratio. The Σ-hex theorem makes it possible to determine a lower and an upper bound for Σmin, the minimum value of the multiplicity of specific rotations for a given axial ratio. The lower bound can serve to determine systematically all specific rotations with c/a in a given interval and Σ not larger than some given value Σc. The bound is used to complete published tables. The upper bound is stronger than a similar bound given by Delavignette.
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    Reduced cells based on extremal principles (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 123-131 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is known that the Buerger cell, a + b + c = abs min, is ambiguous. Uniqueness is usually achieved by an additional system of inequalities which leads to the generally accepted Niggli cell. However, this system is rather unusual and does not suggest any geometrical meaning for the Niggli cell. In this paper four types of unique cells originating from the Buerger cell are introduced by means of simple conditions which have an extremal character. Any of these cells may stand for a reduced cell and has an express geometrical property. One of the four types coincides with the Niggli cell, which is thus given a geometrical interpretation. Systems of inequalities are shown that allow recognition of the cell of any type and algorithms are presented for achieving it. An algorithm for obtaining all Buerger cells of a lattice is included. The use of the reciprocal lattice enables the definition of four further unique cells which, however, need not be Buerger cells and are not discussed in detail. The mathematics must deal with a number of inequalities which often contain square roots, and sometimes rather intricate technical tricks are required.
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    A new von Mises probabilistic formula for quartet invariants (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 141-143 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Von Mises formulas for quartet invariants [Giacovazzo (1976). Acta Cryst. A32, 91-99], even if useful in most cases of practical interest, suffer from some systematic errors. A new von Mises formula is suggested with better theoretical features.
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    An alternative approach to the Hauptman–Karle determinantal inequalities (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 144-144 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure is described for constructing a series of progressively stronger restrictions on the magnitudes and phases of individual structure factors in terms of sets of other structure factors. The existence of the Cholesky factors of Hauptman-Karle matrices is used to ensure that the electron density is everywhere positive.
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    Grazing-incidence Bragg–Laue X-ray diffraction (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 132-141 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Internal waves excited by the dynamical diffraction of X-rays from a single set of crystal planes perpendicular to the incidence surface can produce both Bragg diffracted and reflected beams and Laue diffracted and transmitted beams for crystal slabs of finite thickness. The excitation of Bragg and Laue beams for grazing-incidence diffraction geometries is investigated experimentally and theoretically. The traditional dispersion surface picture for describing allowed internal and external wave vectors is developed to illustrate how the Bragg and Laue beams arise. Experiments performed on a thin silicon wafer demonstrate the evolution of the Laue beams from the back surface into Bragg beams at the front surface of the crystal. The results are in good agreement with calculated curves obtained from the 'n-beam' diffraction theory of Colella [Acta Cryst. (1974), A30, 413- 423]. This theory is shown to be very useful for grazing-incidence excitations because of its completely general treatment of Bragg and Laue beams, and the exact numerical nature eliminates the need for approximations. Experiments also reveal how the presence of a 40 Å AuPd layer on the incidence surface suppresses the Bragg-diffracted beam but not the specular and Laue beams.
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    Non-conventional unit cells (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc9-fc9 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Stepan Alekseevich Semiletov, 1925-1988 (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 149-149 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    On integrating the techniques of direct methods with anomalous dispersion: the one-phase structure seminvariants in the monoclinic and orthorhombic systems. II. Applications (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 163-165 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Applications are considered of the conditional probability distributions of the one-phase structure seminvariants in the monoclinic and orthorhombic systems when anomalous scatterers are present. Test results with error-free data show accurate estimates of seminvariants, the accuracy varying with the complexity of the structure and with the number and strength of the anomalous scatterers.
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    Concerning phase relationships which are not structure invariants or seminvariants (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 150-157 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Often some primitive random variables (e.g. the atomic coordinates) are non-uniformly distributed over the unit cell. Prior information about such distributions is often available but not always used in current direct-methods procedures. Examples are described according to which primitive random variables are restricted to some domains (attended domains) or, in an equivalent way, are prevented from frequenting some domains (forbidden domains). Emphasis has been put on the fact that non-uniform distributions generate phase relationships which are not structure invariants or seminvariants, but it is also anticipated that formulas for estimating phase invariants and seminvariants are deeply affected by such prior information.
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    On integrating the techniques of direct methods with anomalous dispersion: the one-phase structure seminvariants in the monoclinic and orthorhombic systems. I. Theoretical background (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 158-163 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Conditional probability distributions are derived for the one-phase structure seminvariant in the presence of anomalous scattering for the monoclinic and orthorhombic systems. The results are presented in a compact tabular form. The applications of these results are discussed in the following paper [Velmurugan, Hauptman & Potter (1989). Acta Cryst. A45, 163-165].
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    New surface patches for minimal balance surfaces. I. Branched catenoids (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 166-169 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Three new families of minimal balance surfaces have been derived. For this a new kind of surface patch, i.e. branched catenoid, has been used. A concave polygon with one point of self-contact and a convex polygon are the two generating circuits of such a minimal balance surface.
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    New surface patches for minimal balance surfaces. II. Multiple catenoids (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 169-174 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Eight new families of minimal balance surfaces are described. Their surface patches belong to a new kind, called multiple catenoids. The generating circuits of such a minimal surface are two congruent concave polygons with one point of self-contact each. The new minimal balance surfaces are complementary to other minimal balance surfaces which are built up from catenoid-like surface patches and have been known before.
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    Direct determination of triplet phases and enantiomorphs of non-centrosymmetric structures. II. Experimental results (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 182-187 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Direct measurements of triplet phase relationships for non-centrosymmetric light-atom organic structures with medium-size unit cells are reported. The phase information can be extracted from the three- beam profiles of a Renninger ψ-scan experiment. The measurements were carried out with a special ψ-circle diffractometer installed on a rotating Cu-anode generator. The incident-beam divergence is reduced to 0.02°. The experimental results confirm the theoretical considerations of paper I of this work [Hümmer & Billy (1986). Acta Cryst. A42, 127-133]. As triplet phases of +90° can be distinguished, the absolute structure can be determined unambiguously. The measurements show that the triplet-phase-dependent interference effects may be superposed on phase-independent Umweganregung or Aufhellung effects. By a comparison of the ψ-scan profiles of two centrosymmetrically related three-beam cases, the triplet phases of which have opposite signs, it is possible to evaluate the phase-independent effects and to determine the value of the triplet phase with an accuracy of at least 90°.
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    Crystallography, geometry and physics in higher dimensions. V. Polar and mono-incommensurate point groups in the four-dimensional space %E4 (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 187-193 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystallographic point groups of the four-dimensional Euclidean space {\bb E}4 are a convenient means of studying some crystallized solids of physical space, for instance the groups of magnetic structures and the groups of mono-incommensurate structures, as is demonstrated by a simple example. The concept of polar crystallographic point groups defined here in {\bb E}4, and also in {\bb E}n enables the list and the WPV notation {geometric symbol of Weigel, Phan & Veysseyre [Acta Cryst. (1987), A43, 294-304]} of these special structures to be stated in a more precise way. This paper is especially concerned with the mono-incommensurate structures while a discussion on magnetic structures will be published later.
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    Bloch-wave solution in the Bragg case (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 174-182 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Bloch-wave method for reflection diffraction problems, primarily electron diffraction as in reflection high-energy electron diffraction (RHEED) and reflection electron microscopy (REM), is developed. The basic Bloch-wave approach for surfaces is reviewed, introducing the current flow concept which plays a major role both in understanding reflection diffraction and determining the allowed Bloch waves. This is followed by a brief description of the numerical methods for obtaining the results including specific results for GaAs near to the [010] zone axis. A number of other Bloch-wave phenomena are also discussed, namely resonance diffraction and its relationship to internal and external reflection and variations in the boundary conditions and Bloch-wave character, splitting of diffraction spots due to stepped surfaces, which can be completely explained, and the reflection equivalent of thickness fringes.
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    Modified multislice theory for calculating the energy-filtered inelastic images in REM and HREM (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 193-199 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Inelastic plasmon diffuse scattering (PDS) is treated as an effective position-dependent potential perturbing the incident electron wavelength in a solid surface, resulting in an extra phase grating term in the slice transmission function. This potential is derived for the geometry of reflection electron microscopy (REM) and high-resolution electron microscopy (HREM). The energy-filtered inelastic images can be calculated following the routine image simulation procedures by using different slice transmission functions for the elastic and inelastic waves, by considering the 'transitions' of the elastic scattered electrons to the inelastic scattered electrons. It is predicted that the inelastic scattering could modify the electron intensity distribution at a surface. It is possible to take high-resolution energy-filtered inelastic images of crystals, the resolution of which is about the same as that taken from the elastic scattered electrons.
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    The maximum entropy distribution consistent with observed structure amplitudes (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 200-203 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that an electron density distribution of the form ρk = exp [Σfj(rk)xj] has maximum entropy under the constraint that the expected values of a set of functions, fj(r), are constant. For a Fourier map the functions fj(r) are the magnitudes of the structure factors for a set of reflections hj including F(000). The values of the parameters xj for which [(exp (2πihj . r))] = [Fobs(hj)[ for an arbitrarily large set of reflections may be found by an iterative algorithm in which xi + 1 = xi + Hi-1Δi, where the matrix H is positive definite. Because the distribution ρ(r) is everywhere positive, if non-negativity of electron density is sufficient information to determine a unique structure by direct methods, it follows that the maximum entropy procedure must lead to the same unique structure. Maximum entropy is thus an efficient way of expressing the phase implications of a large set of structure amplitudes.
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    On the orthogonal transformation used for structural comparisons (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 208-210 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Rotation matrices that minimize or maximize the sum of the squared distances between corresponding atoms for two structures are found using a constrained least-squares procedure solved analytically as an eigenvalue problem in quaternion parameters.
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    The estimation of triplet invariants from multi-wavelength data (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 203-208 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A two-step procedure is presented for the estimation of triplet invariants from multi-wavelength data. In the first step wavelength-independent structure-factor magnitudes of both the total structure and the light-atom substructure, together with associated structure-factor phase differences, are calculated explicitly via a modified Singh & Ramaseshan [Acta Cryst. (1968), B24, 35-40] procedure. In the second step these quantities are employed as conditional information in the probability distribution of a triplet invariant which can be derived from Hauptman's [Acta Cryst. (1982), A38, 289-294] joint probability distribution for an isomorphous pair of structures. Test calculations on the structure of the iron-containing protein ferredoxin show the feasibility of the procedure.
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    Space groups rare for organic structures. Erratum (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 210-210 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: There is an error in the Appendix of the paper by Wilson [Acta Cryst. (1988), A44, 715-724]. Equation (A3) should read (p) = I/(N + 2) = N-1. (A3)
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    Nominations for the Ewald Prize (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 210-210 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    European Microbeam Analysis Society (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 210-211 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Nobel Prize for Chemistry (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 211-211 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Morphology of crystals: Part A (Series in materials science of minerals and rocks) edited by I. Sunagawa (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 211-212 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Search for satellite reflections and low-temperature study of the 1223 and 2212 Tl–Ba–Ca–Cu–O superconductors (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc11-fc14 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structures of the 1223 and 2212 phases of the T1-Ba-Ca-Cu-O system have been determined at 125 K. No satellite reflections were observed in extensive searches at both room and low temperature. The temperature dependence of the thermal parameters of the thallium atoms confirms the presence of a static disorder beyond that already incorporated in the refinements.
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    Commission on Charge, Spin and Momentum Densities. Newsletter No. 1 (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc15-fc17 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Géométrie des relations d'orientation dans la symétrie hexagonale. Dimension de la coïncidence (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 217-227 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The main characteristics of the orientation relationship between two hexagonal lattices are simply denoted by four parameters (M, U, V, W). In the case of a tridimensional coincidence orientation relationship, for a rational value of (c/a)2, these four parameters become four prime integers (m, un, vn, wn). The equivalence class of the orientation relationship may be represented by 12 equivalent descriptions for which the indices of the rotation axes are noted on the basis of one crystal. This original representation can lead to the concept of spatial distribution of the equivalent rotation axes, a distribution which is strongly related to the c/a ratio. In real materials (c/a irrational), bidimensional coincidence orientation relationships can describe a large number of grain boundaries.
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    Explicit Fourier representations of non–ideal hypercentric P.D.F.'s of E (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 213-217 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Explicit non-ideal hypercentric distributions of the magnitude of the normalized structure factor have been derived and investigated for the space group P\bar 1. One of the distribution types investigated arises when the asymmetric unit of P\bar 1 consists of several identical centrosymmetric motifs, interrelated by additional non-crystallographic centres of symmetry. The ideal version of such distributions was studied by Rogers & Wilson [Acta Cryst. (1953), 6, 439-449]. The other distribution type studied originates from atomic arrangements in which the asymmetric unit is composed of several unrelated centrosymmetric fragments that may differ in their sizes and chemical compositions. Explicit non-ideal probability density functions (p.d.f.'s) of the magnitude of the normalized structure factor were formulated for both above types of distribution as Fourier series, were evaluated numerically and were compared with appropriately simulated distributions of |E|. The computations were carried out for a range of atomic compositions, and numbers of unrelated centrosymmetric fragments that comprise the asymmetric unit; both of these factors have a significant influence on the deviation of the hypercentric p.d.f.'s from the values predicted on the basis of the central-limit theorem approximation.
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    Relativistic Hartree–Fock X-ray and electron atomic scattering factors at high angles (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 786-793 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An enlarged set (atomic number Z = 2 to 98) of free-atom X-ray atomic scattering (form) factors for high angles [2 ≤ (sin θ)/λ ≤ 6Å-1] has been calculated based on those of Doyle & Turner [Acta Cryst. (1968). A24, 390-397]. Four-parameter 'exponential polynomial' fits for these are presented which give far more accurate estimates of the scattering factors at high angles than the Gaussian fits normally used. The use of the Mott formula in conjunction with these new high-angle X-ray form factors allows the calculation of improved-accuracy high-angle electron scattering factors. The use of these high-accuracy high-angle scattering factors for important applications such as Fourier charge-density analysis and computer simulation of high-resolution electron microscope (HREM) images is discussed.
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    From a partial to the complete crystal structure. III. A new procedure and its applications (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 781-786 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The procedure described in the first two papers of this series [Giacovazzo (1983). Acta Cryst. A39, 685- 692; Camalli, Giacovazzo & Spagna (1985). Acta Cryst. A41, 605-613] for recovering from a partial crystal structure the complete one has been reconsidered. Several modifications have been introduced which make the procedure more efficient. Furthermore, a new method is described which is able to combine prior information on a located fragment with the second representation formula P10. Experimental tests show that very small fragments are sufficient to recover the complete crystal structure.
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    Patterson and Pattersons. Fifty years of the Patterson function. (IUCr crystallographic symposia, Vol. 1) edited by J. P. Glusker, B. K. Patterson and M. Rossi (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 804-804 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Symmetries in physics. Springer series in solid state physics. Vol. 64 by W. Ludwig and C. Falter (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 804-804 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Subperiodic classes of reducible space groups (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 815-823 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Classification of reducible space groups into pairs of complementary subperiodic classes with respect to various reductions is introduced and analysed. This classification is finer than the classification into geometric classes and it intersects with the classification into arithmetic classes. It is proved that an intersection theorem holds for those classes which correspond to Z decomposition of the translation subgroups of the reducible space groups and then symmorphic representatives of subperiodic classes of reducible space groups are introduced in analogy with the ordinary concept of symmorphic space groups. In particular, it is shown that the symmorphic space group is a symmorphic representative of subperiodic classes, defined by complementary symmorphic subperiodic groups. In cases of Z reductions it is shown that the pair of complementary subperiodic classes may define none, one or several space groups; if one such group belongs to these classes, then also a set of groups which differ by shifts in space does. These shifts are determined with translation normalizers. Further ramifications and possible use of the theory are discussed.
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    Subperiodic groups as factor groups of reducible space groups (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 805-815 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Reducible space groups are introduced as those for which the point groups G are Q-reducible. The splitting of the rational space V(T, Q), spanned by the translation subgroup T of the reducible space group, into two G-invariant components is considered. First, it is shown that cases of orthogonal and inclined reductions have to be distinguished. Further, reductions which lead to Z decomposition are distinguished from those which lead to Z reduction. The central point of the paper is the 'factorization theorem' which asserts that factor groups of reducible space groups by their partial G-invariant translation subgroups have the structure of subperiodic groups. The homomorphisms which map the space group onto respective subperiodic groups are analogous to homomorphisms, which map space groups onto respective site-point groups. In analogy with point groups, subperiodic groups are introduced which do not act on the Euclidean space but on a Cartesian product of Euclidean space spanned by their translation subgroup with the vector space spanned by missing translations; it is suggested that these groups are called the contracted subperiodic groups and a formalism is developed in which these groups are geometrically natural representatives of factor groups of reducible space groups.
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    Theoretical considerations on two-beam and multi-beam grazing-incidence X-ray diffraction: nonabsorbing cases (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 823-833 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two-beam and symmetric three- and four-beam grazing-incidence X-ray diffraction (GIXD) by crystals without absorption are studied based on the dynamical theory of X-ray diffraction. For two-beam cases, a new geometrical scheme is given to reveal graphically the excitation of the dispersion surface. For symmetric three- and four-beam cases, the expressions for specularly reflected and forward diffracted intensities are derived analytically. Results from the numerical calculations for the diffracted intensities, the penetration depths, the coordinates of the dispersion surface and the mode excitations are also presented for two-, three- and four-beam GIXD.
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    Determination of crystal structures from poor-quality data using Patterson methods (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 833-839 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is found to be possible to solve the structures of fairly simple materials from very poor-quality diffraction data by the use of reciprocal-space Patterson methods. Data sets assessed include those from a high-resolution neutron powder diffractometer, data sets with inaccurate randomized |Fh| values, very small data sets (as few as ten reflections) and data sets with no estimates of |Fh| values given. While refinement is not always feasible from such data it is found possible to obtain atomic positions and consequent structural information with reasonable accuracy. Reasons for using Patterson rather than direct methods in such cases are discussed.
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    Pendellö/sung fringes in stroboscopic X-ray section topography of weakly excited quartz resonators (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 275-285 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The theory for slightly distorted crystals [Kato (1963). J. Phys. Soc. Jpn, 18, 1785-1791] is applied to the case of quartz AT-cut resonators to interpret stroboscopic section topographs. Features in the diffraction process such as ray trajectories, phase changes and intensities of diffracted waves are drawn from this theory. Furthermore, it is shown that extra Pendellö/sung fringes appearing on section topographs with increasing acoustic vibration can be directly related to the vibration amplitude within a precision of about 0-3 Å. Experimental images are compared with Kato's theoretical profiles and simulated images obtained by solving Takagi's [Acta Cryst. (1962), 15, 1311-1312] equations. The results lead to the conclusion that stroboscopic X-ray topography is a precise method to measure the vibration amplitude in weakly excited resonators.
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    The incommensurate misfit layer structure of (SnS)1.17NbS2, `SnNbS3'. II. A study by means of electron microscopy (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 291-296 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Electron diffraction and high-resolution imaging are used to study the remarkable incommensurable misfit layer compound (SnS)1.17NbS2, 'SnNbS3'. Electron diffraction patterns along the zone axis perpendicular to the layer planes are analysed in detail based on the mixed-layer assumption proposed in paper I [Meetsma, Wiegers, Haange & de Boer (1989). Acta Cryst. A45, 285-291]. The relative intensities of the hk0 reflections due to the two types of constituent layers are strongly influenced by the foil thickness. Stacking variants along the c axis are frequently observed and strongly complicate the diffraction patterns. Under particular conditions of thickness and defocus, high-resolution images are shown to reflect the varying degree of coincidence of the atom columns in the misfit layers and thus they directly reveal the incommensurate misfit.
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    The incommensurate misfit layer structure of (SnS)1.17NbS2, `SnNbS3'. I. A study by means of X-ray diffraction (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 285-291 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: (SnS)1.17NbS2, Mr = 334.92, is a compound with misfit layer structure consisting of two-atom-thick layers of SnS and three-atom-thick sandwiches of NbS2 which alternate along the c axis. The lattices of SnS and NbS2 both have C-centered orthorhombic unit cells which match along the b and c axes but not along the a axes. The unit cells and space groups are a = 5.673 (1), b = 5.750 (1), c = 11.760 (1) Å, space group C2mb (no. 39), Z = 4, for SnS; a = 3.321 (1), b = 5.752 (1), c = 11.763 (1) Å, space group Cm2m (no. 38), Z = 2, for NbS2. From the ratio of the lengths of the a axes of the two parts of the complete structure (5.673/3.321 = 1.708 being irrational) one obtains a composition (SnS)1.17NbS2. The structure determination consisted of three parts: the structures of the SnS and NbS2 parts separately and their relative position. Intensities were measured with Mo K{\bar \alpha} radiation (λ = 0.71073 Å) at T = 293 K, μ = 102.3 cm-1. For the SnS part RF = 0.088 for 306 unique reflections; for the NbS2 part RF = 0.031 for 329 unique reflections (for both cases 0kl reflections excluded). The relative position of these two lattices was determined from the common reflections 0kl: RF = 0.072 for 98 reflections. The SnS part of the structure consists of deformed slices of SnS with a thickness of half the cell edge of (hypothetical) NaC1-type SnS. Each Sn atom is in this way coordinated by five sulfur atoms; four sulfur atoms are in a plane perpendicular to the c axis with SnS distances 2.74 (1) (1×), 2.913 (1) (2×) and 3.01 (1) Å (1×), whereas the fifth Sn-S bond with length 2.695 (9) Å is approximately along the c axis. The NbS2 part of the structure is that of NbS2-2H with Nb in trigonal prisms of sulfur; the Nb-S distances are 2.473 (1) Å. From refinement of the common 0kl reflections the relative y and z positions of the two sublattices were found; along the common a direction the lattices of SnS and NbS2 are incommensurate.
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    α-N-tert-Butyloxycarbonyl-L-amino-(N-methyl)succinimide (Boc-L-Asu-NMe) (1989)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 83-85 
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    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    The structure of octamethyltetraoxaquaterene (1989)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 137-140 
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    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Structure of a tricyclic lactone – an important intermediate for the total synthesis of dihydromevinolin (1989)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 145-148 
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    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Structure of dilithium selenate(VI) (1989)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 158-159 
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    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Structure of the hydrogensulfate salt of a diazaadamantanone, 5,7-diphenyl-1,3-diazatricyclo[3.3.1.13,7]decane-6-one (1989)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 114-116 
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    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    URL: http://dx.doi.org/10.1107/S0108270188010340
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