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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 779-789 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 27 (1994), S. 411-417 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A procedure is presented for the automatic solution of composite (misfit) layer compounds, for the case when the composite crystal structure consists of two types of layer, each of which can be approximately described as a three-dimensional periodic structure with, however, mutually incommensurate lattices and hence mutually induced incommensurate modulations. The composite structure can be described as a periodic structure in four-dimensional superspace [van Smaalen (1992), Mater. Sci. Forum, 100&101, 173–222]. From reflection data indexed with four integer indices HKLM, the phase problem is solved as follows. The basic structures of layers 1 and 2 are solved by routine application of automated Patterson interpretation and Fourier recycling using the main reflections only and ignoring the modulation effects. The two layers are brought to a common origin by a shift function based on correlating Fobs and Fcalc using the main reflections common to both layers. All other reflections, which are the (usually weaker) satellite reflections, are phased from the known phases of the main reflections of either layer by application of the Sayre equation in four-dimensional superspace [Hao, Liu & Fan (1987), Acta Cryst. A43, 820–824; Fan, van Smaalen, Lam & Beurskens (1993), Acta Cryst. A49, 704–708]. The procedure is performed by the program MISFIT, which is embedded in the DIRDIF system.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 704-708 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A direct method is proposed for the determination of the modulation in incommensurate intergrowth compounds. The method is based on a new type of Sayre equation that relates the phase of a satellite reflection to the sum of structure-factor products of pairs of main reflections. Phases of satellite reflections are thus uniquely determined by the phases of main reflections. This reflects the fact that the modulation in intergrowth structures is the result of the interaction of all of the subsystems that form the basic structure. Test calculations were done with experimental data of two known composite structures of the inorganic misfit layer compounds (LaS)1.14NbS2 and (PbS)1.18TiS2. The results showed that the method is accurate and efficient and is fully independent of any preliminary assumption of the model of modulation.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 709-721 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An analytical expression is derived for the probability density function (p.d.f.) of X-ray structure-factor amplitudes of a crystal with an incommensurate one-dimensional modulation. The influence of the (3+1)-dimensional superspace symmetry is taken into account. It is shown that, in first-order approximation, this p.d.f. has the same functional form as the p.d.f. for a nonmodulated crystal, with a suitable modification of the atomic form factor. For main reflections and satellite reflections, an expression for the average intensity is derived. This leads to a definition of normalized structure factors for a crystal with an incommensurate one-dimensional modulation. In the same first-order approximation, the p.d.f. for the amplitudes of these normalized structure factors is identical to the p.d.f, for a nonmodulated crystal and does not distinguish between main reflections and satellite reflections. The theoretical p.d.f.s are compared to p.d.f.s obtained from X-ray diffraction data of some incommensurate one-dimensionally modulated crystals.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 511-515 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A modified Sayre equation for incommensurate intergrowth compounds is presented. With this equation, both magnitude and phase for structure factors of satellite reflections can be estimated quantitatively through the observed intensities of main reflections, provided their phases are already known. Modulation functions can then be revealed by the Fourier synthesis calculated using the observed main reflections and the estimated satellites. The method has been tested with the known structures of two inorganic misfit layer compounds, (LaS)1.14NbS2 and (PbS)1.18TiS2. Satisfactory results were obtained.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 690-703 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Statistical methods are used to derive an expression for the average X-ray diffraction intensity, as a function of (sinθ)/λ, of crystals with an incommensurate one-dimensional modulation. Displacive and density modulations are considered, as well as a combination of these two. The atomic modulation functions are given by truncated Fourier series that may contain higher-order harmonics. The resulting expression for the average X-ray diffraction intensity is valid for main reflections and low-order satellite reflections. The modulation of individual atoms is taken into account by the introduction of overall modulation amplitudes. The accuracy of this expression for the average X-ray diffraction intensity is illustrated by comparison with model structures. A definition is presented for normalized structure factors of crystals with an incommensurate one-dimensional modulation that can be used in direct-methods procedures for solving the phase problem in X-ray crystallography. A numerical fitting procedure is described that can extract a scale factor, an overall temperature parameter and overall modulation amplitudes from experimental reflection intensities.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 640-644 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A multidimensional direct method is proposed for ab initio phasing of the main reflections of incommensurate intergrowth compounds. This method represents an objective procedure for solving the average structure of composite crystals in multidimensional space. The `normalized structure factors' are calculated separately for different subsets of main reflections. The derivation of phase information of the reflections and the refinement are performed in multidimensional space. The proposed procedure is tested with known structures of the inorganic misfit layer compounds (LaS)1.14NbS2 and (PbS)1.18TiS2. The results show that the phases of the reflections thus obtained are sufficiently accurate to reveal the average structures of these composite crystals.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 947-954 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The recently defined normalized structure factors for incommensurately modulated structures [Lam, Beurskens & van Smaalen (1993). Acta Cryst. A49, 709–721] have been subjected to extensive tests regarding their applicability in direct methods for phase determination. It is shown that the probability distribution associated with the structure invariants E(−H)E(H′)E(H − H′), where H and H′ are reciprocal vectors of main and/or satellite reflections, approximately has the same functional form as the Cochran distribution but triplet phase relations are relatively less reliable when satellites are involved. The use of the multidimensional Sayre equation for the determination of phases of satellite reflections [Hao, Liu & Fan (1987). Acta Cryst. A43, 820–824; Fu & Fan (1994). J. Appl. Cryst. 27, 124–127] is not improved by using normalized structure factors instead of ordinary structure factors.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of chemical crystallography 21 (1991), S. 667-672 
    ISSN: 1572-8854
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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