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  • International Union of Crystallography (IUCr)  (52,383)
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  • 1
    Journal cover
    Wiley-Blackwell - STM | International Union of Crystallography (IUCr)
    Online: 1.1994 – 17.2010
    Publisher: Wiley-Blackwell - STM , International Union of Crystallography (IUCr)
    Print ISSN: 0909-0495
    Electronic ISSN: 1600-5775
    Topics: Geosciences , Physics
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  • 2
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    International Union of Crystallography (IUCr) | Wiley-Blackwell - STM
    Online: 53.1997 – 66.2010
    Publisher: International Union of Crystallography (IUCr) , Wiley-Blackwell - STM
    Corporation: International Union of Crystallography, IUCr
    Print ISSN: 0907-4449
    Electronic ISSN: 1399-0047 , 2059-7983
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 3
    Journal cover
    International Union of Crystallography (IUCr) | Wiley-Blackwell - STM
    Online: 53.1997 – 66.2010
    Formerly as: Acta Crystallographica  (1948–1967)
    Publisher: International Union of Crystallography (IUCr) , Wiley-Blackwell - STM
    Corporation: International Union of Crystallography, IUCr
    Print ISSN: 0108-7681 , 0567-7408 , 2052-5192
    Electronic ISSN: 1600-5740 , 1600-8650 , 2052-5206
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 4
    Journal cover
    International Union of Crystallography (IUCr)
    Online: 1.1948 – 23.1967
    Publisher: International Union of Crystallography (IUCr)
    Print ISSN: 0365-110X
    Electronic ISSN: 1600-8642
    Topics: Geosciences
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  • 5
    Journal cover
    International Union of Crystallography (IUCr) | Wiley-Blackwell - STM
    Online: 53.1997 – 66.2010
    Formerly as: Crystal Structure Communications  (1972–1982)
    Publisher: International Union of Crystallography (IUCr) , Wiley-Blackwell - STM
    Corporation: International Union of Crystallography, IUCr
    Print ISSN: 0108-2701 , 2053-2296
    Electronic ISSN: 1600-5759 , 2053-2296
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 6
    Journal cover
    International Union of Crystallography (IUCr)
    Online: 64.2008 –
    Publisher: International Union of Crystallography (IUCr)
    Corporation: International Union of Crystallography, IUCr
    Electronic ISSN: 1600-5368 , 2056-9890
    Topics: Chemistry and Pharmacology , Geosciences
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  • 7
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    International Union of Crystallography (IUCr) | Wiley-Blackwell
    Online: 57.2001 – 63.2007
    Publisher: International Union of Crystallography (IUCr) , Wiley-Blackwell
    Corporation: International Union of Crystallography, IUCr
    Electronic ISSN: 1600-5368
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 8
    Journal cover
    International Union of Crystallography (IUCr)
    Online: 61.2005 –
    Publisher: International Union of Crystallography (IUCr)
    Electronic ISSN: 1744-3091
    Topics: Chemistry and Pharmacology , Physics
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  • 9
    Journal cover
    International Union of Crystallography (IUCr) | Wiley-Blackwell - STM
    Online: 61.2005 – 66.2010
    Publisher: International Union of Crystallography (IUCr) , Wiley-Blackwell - STM
    Print ISSN: 1744-3091
    Electronic ISSN: 2053-230X
    Topics: Biology , Chemistry and Pharmacology , Geosciences , Physics
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  • 10
    Formerly as: Acta Crystallographica  (1948–1967)
    Publisher: International Union of Crystallography (IUCr) , Wiley-Blackwell - STM
    Corporation: International Union of Crystallography, IUCr
    Print ISSN: 0108-7673 , 0567-7394
    Electronic ISSN: 1600-5724 , 1600-8596 , 2053-2733
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 11
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    International Union of Crystallography (IUCr)
    Online: 4.1996 –
    Publisher: International Union of Crystallography (IUCr)
    Print ISSN: 1067-0696
    Electronic ISSN: 1945-0834
    Topics: Geosciences , Physics
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  • 12
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    International Union of Crystallography (IUCr)
    Online: 1(1).2014 –
    Publisher: International Union of Crystallography (IUCr)
    Electronic ISSN: 2052-2525
    Topics: Geosciences , Physics
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  • 13
    Journal cover
    Wiley-Blackwell - STM | International Union of Crystallography (IUCr)
    Online: 1.1968 – 42.2009
    Print: 26.1993 – 30.1997 (Location: A17, Archiv, Magazin, 30/5)
    Publisher: Wiley-Blackwell - STM , International Union of Crystallography (IUCr)
    Print ISSN: 0021-8898
    Electronic ISSN: 1600-5767
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  • 14
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 515-532 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Through the reformulation of crystallography that treats periodic and quasiperiodic structures on an equal footing in three-dimensional Fourier space, a novel computation is given of the Bravais classes for the simplest kinds of incommensurately modulated crystals: (3 + 3) Bravais classes in the cubic system and (3 + 1) Bravais classes in any of the other six crystal systems. The contents of a Bravais class are taken to be sets of ordinary three-dimensional wave vectors inferred from a diffraction pattern. Because no finer distinctions are made based on the intensities of the associated Bragg peaks, a significantly simpler set of Bravais classes is found than Janner, Janssen & de Wolff [Acta Cryst. (1983). A39, 658–666] find by defining their Bravais classes in higher-dimensional superspace. In our scheme, the Janner, Janssen & de Wolff categories appear as different ways to describe identical sets of three-dimensional wave vectors when those sets contain crystallographic (3 + 0) sublattices belonging to more than a single crystallographic Bravais class. While such further discriminations are important to make when the diffraction pattern is well described by a strong lattice of main reflections and weaker satellite peaks, by not making them at the fundamental level of the Bravais class, the crystallographic description of all quasiperiodic materials is placed on a single unified foundation.
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  • 15
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 533-541 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A description is given of three new distinct quasiperiodic tilings that exhibit tenfold symmetry. Related to each other by decomposition, these tilings are most easily generated from their respective Fibonacci pentagrid dual tilings. The latter, one of which is singular, are based on the property that there are three principle Fibonacci quasiperiodic sequences that possess mirror symmetry. The resulting tilings, while somewhat analogous to the Penrose tilings, are more complex in that they contain inequivalent tiles of the same shape. Associated with each of these decagonal tilings, which belong to different local isomorphism classes, are one twofold and two different fivefold tilings. Twelve inflations or deflations are necessary before each of the latter reoccurs with the same orientation.
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  • 16
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 541-544 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The scaling scheme in the quantitative phase-determination procedure proposed by Chang & Tang [Acta Cryst. (1988), A44, 1065–1072] is corrected by taking the average peak intensity of two centrosymmetrically related three-beam diffractions as the maximum kinematical intensity for the reconstruction of the phase-independent intensity profiles. By subtraction of these phase-independent profiles from the measured intensity distributions, more reliable information about phases can be obtained. This procedure is applied to the three-beam diffraction profiles of several organic crystals, reported by Hiimmer, Weckert & Bondza [Acta Cryst. (1990), A46, 393–402], for quantitative phase analysis. The determined phase values are in good agreement with those calculated from the known structures.
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  • 17
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 545-554 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent consolidation by Cummings & Hart [Aust. J. Phys. (1988), 41, 423–431] of five measured data sets of high-precision Si structure factors and subsequent analysis by Deutsch [Phys. Lett. A (1991), 153, 368–372] produced information on the charge density of Si with precision that is unmatched by any other system. A detailed comparison with newly performed ab initio electronic structure calculation within the local density formalism (LDF) is presented here. The convergence of the calculation is extended to the limit at which the results reflect the predictions of the underlying LDF, unobscured by computational uncertainties. Excellent agreement (e.g. R = 0.21% which is three to five times better than previous calculations) is found. This allows the effects of high-index structure factors to be assessed (currently beyond the reach of high-precision measurements) on both static and dynamic deformation charge densities.
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  • 18
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 555-562 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The problem of recovering the structure factors that contribute to a zone-axis convergent-beam diffraction pattern is discussed. It is shown that an automated matching procedure that minimizes the sum-of-squares difference between experimental and simulated patterns is effective whether one is refining accurate structure factors in a known crystal or attempting ab initio structure determination. The details of the minimization method are analysed and it is shown that a quasi-Newton method that uses analytically derived gradients is particularly effective when several structure factors are varied. The inversion method for ab initio structure determination is tested on the [110] axis of GaP, using simulated patterns as ideal 'experimental' data.
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  • 19
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Electron diffraction intensity data were collected at 1200 kV from thin epitaxically oriented crystals of copper perbromophthalocyanine (C32Br16CuN8) in a projection down molecular columns. Measured cell constants for the projection with cmm symmetry are d100 = 17.88 (9), b = 26.46 (15) Å. The structure was determined by Fourier refinement after three heavy-atom positions were identified in an initial potential map. In addition to the copper and halogens, all light-atom positions were found. Although the final R value for all data is 0.41, n-beam dynamical calculations for crystal thicknesses corresponding to the estimated sample dimension account for the observed amplitudes that deviate most from their kinematical values.
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  • 20
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 112-115 
    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.
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  • 21
    ISSN: 1600-5724
    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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  • 22
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 1099-1101 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The photon flux generated by the six-pole wiggler at CHESS combined with a focusing mirror and a focusing monochromator allowed diffraction experiments at 1.56 Å, wavelength with a 2.2 (5) μm3 CaF2 single crystal. The crystal was oriented by means of a multiwire proportional area counter. Reflection profiles and Bragg intensities were collected with a scintillation counter. The Bragg intensities were used for a structure refinement. The results demonstrate that crystals composed of light elements with volumes down to only 0.5 μm3 can be mounted and used for single-crystal X-ray diffraction experiments. Until now such crystals have been considered as powder grains. Besides the possibility of applying single-crystal methods to materials of which larger crystals are not available the essentially extinction-free data from microcrystals allow a high- precision determination of electron densities and vibrational amplitudes.
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  • 23
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 169-174 
    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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  • 24
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    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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  • 25
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 203-208 
    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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  • 26
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 210-210 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 27
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 211-212 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 28
    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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  • 29
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 234-238 
    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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  • 30
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 193-199 
    ISSN: 1600-5724
    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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  • 31
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 208-210 
    ISSN: 1600-5724
    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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  • 32
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 210-210 
    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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  • 33
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 264-268 
    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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  • 34
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 268-274 
    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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  • 35
    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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  • 36
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 308-308 
    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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  • 37
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 314-319 
    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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  • 38
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 320-325 
    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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  • 39
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 325-333 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The modified multislice theory [Wang (1989). Acta Cryst. A45, 193-199] has been employed to calculate the electron reflection intensity with and without considering the plasmon diffuse scattering in the geometry of reflection high-energy electron diffraction (RHEED). It has been shown that the inelastic scattering can greatly enhance the reflectance of a surface, depending critically on the incident conditions of the electrons. At some incidences, the inelastic resonance reflection is enhanced, which is considered as the 'true' surface resonance state. This happens within a very narrow angular range (<1 mrad). For 'true' resonance states, the inelastic intensity is much stronger than for other conditions as shown both theoretically and experimentally. The enhancement of the reflection intensity may not be the proper criterion for identifying the 'true' surface resonance. Besides the surface plasmon peaks, an 'extra' peak, located at 4.5 eV, is observed in the reflection electron energy-loss spectroscopy (REELS) study of the 'true' resonance of GaAs (110) surface. This is considered as a characteristic of the resonance propagations of the electrons along the surface and may result from the generation of resonance radiation.
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  • 40
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: There are two errors in the paper by Velmurugan & Hauptman [Acta Cryst. (1989), A45, 158-163]. In equation (3.3), A should read: A = 8RR^2_{\bf K}{\bar R}^2_{\bf K}[C_2(C_{12} + C_{{\bar 1}2}) + S_2(S_{12} + S_{{\bar 1}2})],and in Table 1, the third row and second column should read: R_1 = |E_{{\bar h}{\bar k}l}|.
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  • 41
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 357-361 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An iteration method is presented for calculation of the gross physical properties of polycrystals in terms of the physical properties of the crystals. No assumptions are made concerning the shape or behaviour of the crystallites. The only mathematical condition to be fulfilled is that the product of the matrix of a gross physical property with its inverse must give a unit matrix if the same is valid for the crystals. The method is demonstrated by the calculation of the effective elastic tensor of a hypothetical texturized polycrystal consisting of Cu crystallites. The calculated upper and lower bounds of the Young modulus are extremely close to each other.
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  • 42
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The conditional probability density function of a three-phase invariant is computed from exact expressions derived and discussed in the first paper of this series [Shmueli, Rabinovich & Weiss (1989). Acta Cryst. A45, 361-367] and comparisons are presented of these computations with the approximate conditional density due to Cochran [Acta Cryst. (1955), 8, 473-478]. Conditional variances computed from the exact and approximate expressions are also compared. The computations are carried out for the space group P1. This is the first numerical comparison of conditional phase-invariant statistics evaluated from exact and approximate expressions. The discrepancy between these two kinds of statistics appears to be negligible if the E values involved are small and the number of atoms in the cell is moderately large. Very significant discrepancies are observed when the number of the atoms in the unit cell is small, as well as in the case of the presence of an outstandingly heavy atom. For a given triplet of magnitudes of E values or a fixed atomic composition of the unit cell the exact conditional density functions tend to have sharper peaks than the approximate ones.
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  • 43
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 409-415 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A lattice-dynamical calculation of thermal parameters is performed for naphthalene and anthracene in the external Born-von Karman formalism using 6-exp potential functions and electrostatic interactions in the form of an atomic point-charge model. Phonon dispersion curves and density-of-states functions are calculated with and without charges. In general, the effect of the Coulombic forces is small and sensibly affects optical branches linked to the Bu mode in both compounds, improving the agreement with the experimental data. The effect on thermal parameters is roughly opposite to that of molecular non-rigidity.
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  • 44
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 422-427 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The effect of dislocations in a silicon single crystal on the zeroth-order Laue-zone (ZOLZ) pattern in large-angle convergent-beam electron diffraction (LACBED) has been studied experimentally. It is found that edge dislocations cause the ZOLZ pattern to be compressed or elongated and screw dislocations cause it to be dislocated. This phenomenon is the consequence of opposite shifts of the two halves of the Tanaka pattern, separated by the shadow image of the dislocation line along directions b and -b of the Burgers vector. The shift direction of each half of the pattern depends on the dislocation characteristics and the position of the incident-beam crossover. The pattern on the side, pointed to by the vector u × c (or -u × c) from the shadow image of the dislocation line is shifted along b (or -b), where u is the direction of the dislocation-line vector and c is a vector pointing to the beam crossover from the dislocation line. This phenomenon can be used to determine the Burgers vector (both its direction and sense) of a dislocation.
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  • 45
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Figures of merit based on PSIO and on strong triplets are often unreliable for structures with superstructure effects. Prior information on pseudotranslational symmetry is used in order to estimate one-phase seminvariants. These are used, together with quartet invariants, for finding the correct solution in a multisolution process.
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  • 46
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 445-453 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure is described for the determination of the phases of waves scattered by a multilayer structure using interference between surface reflections and structure diffraction. The applicability of the method to Langmuir-Blodgett and metallic sputtered multilayers is discussed.
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  • 47
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two methods are discussed in detail. In the first method the triplet relationship is treated using the first neighborhood, and the quartet relationship using its second neighborhood. For the triplet relationship it is found that the reliability φh +φk - φh+k ∼ 0 is enhanced when Rh ∼ Rk ∼ Rh+k and large. This conclusion is drawn from formula (16) giving the conditional probability of φh + φk - φh+k using an asymptotic development up to and including terms of order N-1/2. For the quartet relationship it is found that the reliability that φh + φk + φl - φh+k+l ∼ π given Rh+k ∼ Rh+l ∼ Rk+l ∼ 0 is diminished when Rh ∼ Rk ∼ Rl ∼ Rh+k+l and large. This conclusion is drawn from formula (19) using similar calculations for the triplet relationship. A heuristic theoretical discussion of this last result trying to explain this difference with the usual theories is given. In the second method the triplet relationship is treated using its first neighborhood. These calculations have been done using a 'normal' asymptotic development up to and including terms of order N-1/2. As a result a formula (28) is obtained that is (at least theoretically) able to predict negative cosine values. A third method that is proposed where one uses the ideas of Patterson superposition will be discussed in detail in a forthcoming paper.
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  • 48
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Compton profiles of NaF and CaO single crystals were measured along the [100] and [110] directions using 60 key gamma rays. A theoretical analysis based on Compton profiles and autocorrelation functions was performed by application of the augmented plane wave (APW) and linear combination of atomic orbitals (LCAO) methods. In the case of NaF both theories agree well with each other but their results differ in a characteristic manner from the experiment. For CaO a good agreement of the APW results and experiment especially for the difference quantities is found whereas the LCAO model yields less satisfying results in this case.
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  • 49
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The statistical theory of X-ray scattering from a crystal that is disordered in one dimension is discussed. The state of disorder is characterized by probabilities that different types of scattering elements occupy specified positions. The effect this disorder has on the corresponding ensemble average axial reflections is determined. Finite size is explicitly accounted for. Motivated by recent experiments on water intercalation into thin, lyotropic multilayers, special consideration is given to systems whose components differ with respect to size, but not with respect to their scattering factors. Focusing on this case of pure displacement disorder in a binary mixture, a representation of the scattering function in closed form is derived. The case of a random binary mixture leads to the results of Hendricks & Teller [J. Chem. Phys. (1942), 10, 147- 167], and Méring [Acta Cryst. (1949), 2, 371-377], while in the presence of nearest-neighbor correlations, a connection is established with the theory of Kakinoki & Komura [J. Phys. Soc. Jpn (1952), 7, 30-35]. In extension of their treatment, systems with non-stationary transition probabilities are investigated. The effects on the scattering function of constraining composition fluctuations are also studied. Particular characteristics of the scattering function are displayed and discussed.
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  • 50
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The resolution function of an X-ray triple-crystal diffractometer on a rotating-anode source has been studied both experimentally and theoretically. Three different experimental configurations were used, with perfect germanium, distorted germanium and pyrolytic graphite as monochromator and analyser, leading to changes in the resolution of two orders of magnitude. The results are compared with a Gaussian description of the resolution function and it is found that this describes the width of the central part with an accuracy of better than 25%. The wings of the resolution in the high-resolution mode show the effect of the non-Gaussian resolution elements but these are reproduced by a full numerical convolution theory of the resolution function.
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  • 51
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    Acta crystallographica 45 (1989), S. 428-431 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The effect of the depth z0 of a stacking fault and the specimen thickness t on the displacement and splitting of higher-order diffraction fringes has been observed experimentally by means of large-angle convergent-beam electron diffraction and simulated theoretically under the two-beam dynamical approximation. Moreover, a quantitative relationship between the displacement and splitting of a diffraction fringe on the one hand and the displacement vector R of the stacking fault, the specimen thickness t, and the diffraction-vector amplitude g on the other hand, was deduced in the thin-specimen approximation when the fault lies at the midpoint of the specimen (z0 = t/2).
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  • 52
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 53
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The influence of an electric field on the X-ray scattering of the nonlinear optical organic crystal MNA (2-methyl-4-nitroaniline) has been studied, using a three-step pulsed alternating electric field. The field changes are synchronized with the gating to three different counting chains (the three-step modulation method). A field strength of 39 kV cm-1 induces 0.2% maximum variation in the integrated intensity and a small shift in Bragg angles (an inverse piezoelectric effect). A special electron density refinement method, which uses the differences between the zero- and applied-field intensities as observations, has been developed and applied in the interpretation of the results.
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  • 54
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 456-463 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new direct method (called TRYMIN) for phase-problem solution is described. At first a methodical procedure is presented for the construction of a direct method. The aim of the calculation is formulated as a consistency between theoretical and calculated distributions of invariants. A minimized function is obtained and an algorithm for its minimization is proposed. The algorithm is based on the partial decomposition of phases into three subsets and on the cyclical improvement of the estimate of local minima. The efficiency of the method has been tested on 23 structures and a short evaluation of the results of computer experiments with test structures is presented.
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  • 55
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 471-477 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Crystallographic refinement based on molecular dynamics (MD) has been applied to a 2.5 Å resolution X-ray structure of the pore-forming fragment of colicin A. The crystallographic R factor was reduced from 48 to 23% with a concomitant improvement in stereochemical parameters. The method considerably speeded up the refinement process but was associated with some pitfalls. In particular, some badly fitted segments of the structure required manual rebuilding, even after MD refinement and some problems with weighting schemes were encountered. Analysis of the effects of the refinement and ideas for improvements are presented.
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  • 56
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 485-490 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two new families of minimal balance surfaces are described. Their surface patches are not finite but have the shape of infinite strips. Such a strip is bounded by two congruent zigzag lines in one case or by a zigzag line and a meander line in the other case. In addition, certain minimal balance surfaces derived before with the aid of finite surface patches can also be generated from infinite strip-like surface patches.
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  • 57
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 490-494 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new phase refinement function that makes explicit use of the well resolved nature of the atomic peaks is presented. This function is first deduced for the one-dimensional case and then extended to the three-dimensional one. A new modified tangent formula can be derived from it. The effectiveness of this modified tangent formula is illustrated on the basis of some test structures. This function also seems to provide the XMY function of Debaerdemaeker & Woolfson [Acta Cryst. (1983), A39, 193-196] with a possible rational explanation.
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  • 58
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 686-698 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An extension of the maximum-entropy (ME) data- restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases with various types of added noise and in examples of normal and high-resolution electron-microscopy images, dramatic improvement can be obtained from two to four stages of iteration, even in cases where traditional ME restoration provides little improvement. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated.
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  • 59
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 628-635 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Comparisons between structures with similar atomic skeletons are made by mathematically deforming one over the other using inhomogeneous transformations. Removal of shallow bending and twisting distortions between the structures reveals local differences that are masked by comparisons using homogeneous transformations. Inhomogenous deformations are restrained to prevent unrealistic changes in local atomic bonding geometry by the addition of penalty functions similar in form to the potentials used in empirical molecular mechanics calculations.
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  • 60
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 645-654 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a new approach to helical diffraction a helix generating function is defined, and thence an expression for the autocorrelation function (a.c.f.) for a helix is obtained. The Fourier transform of this a.c.f. gives a new expression for the diffracted intensity, which is shown to be equivalent formally to the classical expression of Cochran, Crick & Vand [Acta Cryst. (1952), 5, 581-586] and A. R. Stokes (unpublished). The new expression allows straightforward examination of the effects of helical disorders on the diffracted intensity. The thermal and paracrystalline effects of disorders with cylindrical symmetry are shown, and examples are given from the diffraction of a model of the actin helix. The general case, disorder with no symmetry, is derived and the effects of axial and radial disorder, separately and together, are computed, again for the model actin helix. Translational disorder is also included, and its effects are explained. The new results are compared with existing accounts of the effects of helical disorders on fibre diffraction.
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  • 61
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    Acta crystallographica 45 (1989), S. 658-658 
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  • 62
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. fc29-fc32 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An orthorhombic strain is shown to transform a f.c.c. lattice into itself. A related transformation takes the b.c.c. lattice into itself. The energy barriers for two f.c.c. systems are found to be of the order of the melting temperature. Possible connections with melting, liquid structure and crystal growth are discussed.
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  • 63
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 661-671 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Convex polyhedra with regular faces were used for developing the crystal-chemical model of atomic interactions. Some examples of inorganic crystal structures with coordination polyhedra belonging to convex polyhedra with regular faces are considered. Only four polyhedra - tetrahedron, octahedron, trigonal bipyramid and cube (without due regard for displacement of some atomic groups as a whole) - are shown to be stable at any value of the atomic interaction potential.
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  • 64
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    Acta crystallographica 45 (1989), S. 636-644 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A multislice theory is proposed to solve Yoshioka's coupling equations for elastic and inelastic scattered high-energy electrons in a solid. This method is capable, in principle, of including the non-periodic crystal structures and the electron multiple scattering among all the excited states in the calculations. It is proved that the proposed theory for calculating the energy-filtered inelastic images [Wang (1989). Acta Cryst. A45, 193-199], based on the physical optics approach, is equivalent to the quantum-mechanical theory under some approximations. The basic theory of simulating the energy-filtered inelastic image of core-shell losses and thermal diffuse scattering is outlined.
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  • 65
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    Acta crystallographica 45 (1989), S. 654-656 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that Shen & Colella [Acta Cryst. (1986). A42, 533-538; Nature (London). (1987). 329, 232-233; Acta Cryst. (1988). A44, 17-21] are in error in asserting that 'irrespective of instrumental resolution' asymmetric n-beam benzil interactions can be recorded only if incident-beam wavelengths equal to, or greater than, 3.5 Å are used. Such interactions are clearly displayed in our Cu Kα1 and Cr Kα1 n-beam patterns of organic crystals, such as benzil, and that useful phase information can be readily extracted from such data.
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  • 66
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    Acta crystallographica 45 (1989), S. 657-657 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Solutions to the rotational superposition problem published recently by Diamond [Acta Cryst. (1988), A44, 211-216] Kearsley [Acta Cryst. (1989), A45, 208-210] and MacKay [Acta Cryst. (1984), A40, 165-166] are compared. It is shown that the first two of these are identical and that MacKay's solution underestimates the rotation unless the initial orientation is optimal or perfect fitting is possible, or the residual vectors after optimal fitting are all parallel to the corresponding rotation axis.
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  • 67
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    Acta crystallographica 45 (1989), S. 659-659 
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  • 68
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 659-660 
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  • 69
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    Acta crystallographica 45 (1989), S. 671-678 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The idea of structural ensembles is introduced in the framework of the crystal-chemical model of atomic interactions (CCMAI). The atomic ensemble is treated as a minimal portion of atoms, which predetermines the crystal structure. Inorganic crystal structures such as graphite, white tin, PbO are considered. It is supposed that both atoms and localized electron pairs form these structures. On the basis of CCMAI the hypothetical structure of icosahedral quasicrystals is worked out. In accordance with this hypothesis the initial cluster (or simply cluster) of the quasicrystal has a double-shell structure and each shell has an icosahedral form; the thickness of a shell is equal to the diameter of one atom; the number of atoms in one shell is 10n2 + 2, where n is the number of the shell. The quasicrystal has two subsystems of atoms. One of them consists of the central atoms of clusters and the atoms included in the first shells of clusters. The 13-atom icosahedral bodies form a crystal lattice with space group Fd3. All icosahedra of this atomic subsystem have a perfect form and all of them are perfectly oriented with respective to each other. The first atomic subsystem is responsible for the diffraction of electrons and X-rays. The second atomic subsystem includes atoms of the second shells of clusters. This subsystem has no translational symmetry, but it is partially ordered.
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  • 70
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    Acta crystallographica 48 (1992), S. 872-879 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A model of crystal defects is developed to describe the diffraction of X-rays from imperfect crystals containing defect surfaces and crystal grains. The model, which is based on continuum theory for an isotropic homogeneous elastic medium, leads to a stochastic first-order differential equation, known as a Langevin equation. The solution of this equation is used to derive a correlation function for the strain-dependent term in the formula for the crystal reflectance. A consequence of the model is that the kinematic reflectivity of an imperfect crystal is given by the convolution between the perfect-crystal reflectivity and a function that transforms between a Gaussian and a Lorentzian depending on a correlation length in the crystal.
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  • 71
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    Acta crystallographica 48 (1992), S. 884-901 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: General ideas about symmetries of quasicrystals based on simple self-similar tiling models and their mathematical formulation in terms of higher-dimensional multimetrical space groups find extensive confirmation in the structure of the decagonal Al78Mn22 quasicrystal phase. There is an incredible richness and variety of symmetries involving, in addition to mirror, rotation, translation and screw-rotation symmetries, planar and linear scalings as well, together with involutions generating those scalings, with and without associated nonprimitive, translations. The linear parts of these symmetries generate a point group of infinite order, not yet fully investigated but, up to now, consistent with the symmetry of a self-similar decagram. The applicability of these symmetries to the atomic structure of the quasicrystal Al78Mn22 observed in nature requires the concept of higher-dimensional crystal forms and their projections in the physical space and in the internal space, respectively.
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  • 72
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Conditional joint probability distribution functions P(φ1, ..., φn| R1, ..., Rn, ..., Rp) of any set of n phases given any set of p diffraction moduli are calculated. The distributions include terms up to order 1/N and involve both triplet and quartet contributions. Two types of formulae are derived, which may be considered as developments of two mathematical approaches described by Hauptman [Acta Cryst. (1975). A31, 680–687] and by Giacovazzo [Acta Cryst. (1975). A31, 252–259; Acta Cryst. (1976). A32, 91–99] for the estimation of the quartet invariants.
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  • 73
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the first paper in this series [Giacovazzo, Burla & Cascarano (1992). Acta Cryst. A48, 901–906], the conditional joint probability distribution function of n phases given p ≥ n moduli was derived. The properties of the concluding formulae are checked here. It is found that the distribution is not maximized by the correct phases, mostly because of bias in the formulae. If the triplets are estimated via the P10 formula [Cascarano, Giacovazzo, Camalli, Spagna, Burla, Nunzi & Polidori (1984). Acta Cryst. A40, 278–283] instead of being estimated by the Cochran relationship [Cochran (1952). Acta Cryst. 5, 65–67], the situation is remarkably improved but further improvements are needed. A practical procedure is also described that successfully uses phase relationships to solve difficult structures.
    Type of Medium: Electronic Resource