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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 810-820 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The joint probability distribution of six structure factors for a pair of isomorphous structures [Hauptman (1982). Acta Cryst. A38, 289-294] is used for probability calculations in which doublet invariant phase information (i.e. phase-difference information) is employed as conditional information together with intensity data. This information is obtained from the structure-factor magnitudes of the structure formed by the replacement atoms (assumed to be known) and the two isomorphous structures. First, conditional probability distributions of the triplet invariants of the native structure are derived. An alternative to the approach of Fortier, Moore & Fraser [Acta Cryst. (1985), A41,571-577] is presented, based on a new enantiomorph-sensitive distribution. It is argued that application of enantiomorph-sensitive distributions obtained by restriction of phase invariants can be widened by using various enantiomorph-defining invariants. Second, the ambiguity in single isomorphous replacement is resolved by calculating the probability of the two possible solutions as was proposed by Fan Hai-fu, Han Fu-son, Qian Jin-zi & Yao Jia-xing [Acta Cryst. (1984), A40, 489-495], but using a different probabilistic basis. It turns out that the formulae of the latter authors are a special case of formulae derived in the present paper.
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  • 2
    Electronic Resource
    Electronic Resource
    [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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  • 3
    Electronic Resource
    Electronic Resource
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 1817-1819 
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 517-520 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The procedure adopted by Heinerman [Acta Cryst. (1977). A33, 100-106] to incorporate structural information in phase determination is combined with that of Giacovazzo [Acta Cryst. (1983). A39, 685-692]. The resulting joint probability distribution of three structure factors is a generalization of the corresponding distributions of the previous authors. This distribution is used (i) to calculate the phase of a triple product given a priori structural information, (ii) to resolve the sign ambiguity in single isomorphous replacement if the replacement structure is known. The latter application for the incorporation of partial structure information is more general than that proposed by Fan Hai-fu & Gu Yuan-xin [Acta Cryst. (1985). A41, 280-284].
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 521-526 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The two-step procedure for estimating triplet invariants from two-wavelength data [Klop, Krabbendam & Kroon (1989). Acta Cryst. A45, 203-208] is applied to artificial data from the protein ferredoxin. Two different probability distributions for the estimation of triplet invariants are compared. The possibility of estimating triplet phase invariants for which one or more reflections have a small heavy-atom contribution is demonstrated. The estimated triplet invariants are used in a convergence procedure and a generalized tangent formula. It is shown that accurate phase determination is possible even at low resolution.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 609-613 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A generalization and extension is given of the two-wavelength ratio technique for phase determination [e.g. Cascarano, Giacovazzo, Peerdeman & Kroon (1982). Acta Cryst. A38, 710-720 and references therein]. It is shown that the phase-determining formula of the ratio technique for acentric reflections merely depends on Bijvoet ratios and dispersion terms even if there are no restrictions on these dispersion terms. The system of equations which forms the basis for both the ratio technique and the Bijvoet difference method of Singh & Ramaseshan [Acta Cryst. (1968), B24, 35-40] (S&R) permits the derivation of a relationship between the scale factors of data collected at different wavelengths for acentric reflections. If this relationship is used as scaling scheme, the S&R method is algebraically equivalent to the ratio technique. For centric reflections the two methods are equivalent provided that the same scaling is applied.
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  • 7
    Electronic Resource
    Electronic Resource
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 51-53 
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 8
    Electronic Resource
    Electronic Resource
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 1342-1344 
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 9
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 31 (1993), S. 1319-1330 
    ISSN: 0887-6266
    Keywords: alternating ethylene carbon monoxide copolymer crystal structure melting ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The perfectly alternating ethylene carbon monoxide copolymer (polyketone; POK) has been studied by means of 1H nuclear magnetic resonance and thermal analysis, and the crystal structure, determined by wide angle x-ray scattering methods, is presented. The crystal structure of this polymer in well-oriented fibers (POK-α) is as follows: Space group Pbnm, α = 6.91 (2) Aå, b = 5.12 (2) Aå, c = 7.60 (3) Aå (fiber axis), pc = 1383 kg/m3. This differs from the structure reported earlier by Chatani et al. (POK-β). The very dense packing in the POK-α structure is a result of the arrangement of the dipoles in the crystal lattice, giving rise to strong lateral forces between the polymer chains. Owing to the all-trans conformation of the polymer chain in the crystal lattice, high moduli can be achieved for well-oriented fibers. A first approximation results in a value of 360 GPa for the theoretical modulus. From the melting data for a series of low molecular weight polyketone homologs, a first, estimate is derived for the crystalline heat of fusion (215-330 J/g) for infinite chain length. As a result of the strong lateral forces, this polymer shows a (very) high crystalline heat of fusion, whereas creep and compressive strength of oriented fibers are expected to be superior to those of high-modulus polyethylene fibers. © 1993 John Wiley & Sons, Inc.
    Additional Material: 12 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 33 (1995), S. 315-326 
    ISSN: 0887-6266
    Keywords: alternating ethylene-carbon monoxide copolymer ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Differential scanning calorimetry and high temperature x-ray diffraction were used to study the perfectly alternating copolymer of ethene and carbon monoxide (polyketone; POKC2). It was found that oriented POK-C2 fibers show a crystalline phase transition at a temperature between 110-125°C with a 10% change in crystalline density. At this temperature, the crystal structure reported recently (POK-α) is transformed to a crystal structure that was reported in the past for room temperature imperfectly alternating polyketone. The latter structure will be designated as POK-β. The influence of chain defects on the crystal structure was studied by synthesizing terpolymers (POK-C2/C3), in which small amounts of propylene-CO units are incorporated into the polymer backbone. The resulting terpolymers differ from the copolymer by the presence of methyl groups randomly distributed along the polyketone backbone chain. Evidence is presented that indicates that the methyl groups are built into the crystal lattice as defects. With more than 5 mole-% propene the terpolymer fibers crystallize exclusively in the β-modification. Below this level the α/β ratio (at room temperature) increases with decreasing amounts of propene. Both as-synthesized and as-spun POK-C2 were found to consist of both POK-α and POK-β; the α/β ratio depends on the method of preparation. Because the drawn POK-C2 fibers studied here consist exclusively of POK-α, the process of spinning and drawing leads to the transformation of unoriented β-rich material into oriented POK-α. © 1995 John Wiley & Sons, Inc.
    Additional Material: 9 Ill.
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