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  • 1
    Electronic Resource
    Electronic Resource
    Theoretical considerations on phase determination by three-beam interference (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 841-848 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For φ-scan experiments rotating the crystal through a three-beam case the rocking-curve: profiles have been calculated on the basis of the dynamical theory of X-ray diffraction. Divergence and wavelength spread of the incident beam have been taken into account. It is shown that for centrosymmetric crystal structures the asymmetry of the profiles is related to the sign of the triple product of the structure factors F({\bar {\bf h}})F(g)F(h - g) which are involved in a three-beam case. If anomalous absorption ('double Borrmann' effect) can be neglected the typical asymmetry is independent of the diffraction geometry (Laue or Bragg case). For Laue geometry and thick crystals (μ0 t 〉 1) corrections are necessary. For centrosymmetric structures it may be possible to determine the phase sum of a triplet by inspection of the rocking curve without computer calculations. The general features of the rocking curve are discussed and a physical interpretation is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482001727
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  • 2
    Electronic Resource
    Electronic Resource
    On the quantitative determination of triplet phases by X-ray three-beam diffraction (1990)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 387-393 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Calculations of the integrated diffracted intensity for Renninger experiments, i.e. calculations of ψ-scan profiles scanning through three-beam positions, are reported. The fundamental equations of the dynamical theory are solved by means of an eigenvalue procedure and boundary conditions consistent with the diffraction geometry. It is shown that for noncentrosymmetric structures the three-beam ψ-scan profiles bear information on both the magnitude, defined in the range 0 ≤ |φ| ≤ 180°, and the sign of the triplet phase involved in the three-beam interference. In general, the ψ-scan profiles can be separated into two parts: a phase-dependent part ('ideal' profile) due to the interference effect and a symmetric phase-independent Umweganregung or Aufhellung profile due to the mean energy flow in a three-beam case. Both parts can be calculated by summing up the ψ-scan profiles for + φ and -φ, one profile being reversed with respect to the three-beam point. As a result, the experimentally best suited three-beam cases for triplet phase determination should involve structure factors of nearly equal magnitude.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389013863
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  • 3
    Electronic Resource
    Electronic Resource
    Direct measurements of triplet phase relationships of organic non-centrosymmetric structures using synchrotron radiation (1990)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 393-402 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent progress in experimental triplet phase determination by the method of three-beam diffraction for non-centrosymmetric light-atom structures is reported. The measurements were carried out with a special ψ-circle diffractometer installed at the DORIS II storage ring in Hamburg. Experimental results confirm the theoretical considerations. In general, the ψ-scan profiles consist of a phase-independent Umweganregung or Aufhellung part superimposed on a phase-dependent part due to the three-beam interference, which contains the phase information. Experimentally, Umweganregung and Aufhellung effects can be evaluated by comparison of the two centrosymmetrically related three-beam cases. It is shown that with moderate phase-independent effects the triplet phase can be determined with an accuracy of about 45°.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389013875
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  • 4
    Electronic Resource
    Electronic Resource
    On the ambiguities in merohedral crystal structures (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 506-508 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The ambiguities in merohedral crystal classes are discussed from the group-theoretical point of view. A classification of merohedral point groups and the extension of these terms to space groups and crystal structures is proposed. Similarities and differences for special types of merohedries are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388002703
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  • 5
    Electronic Resource
    Electronic Resource
    Experimental determination of triplet phases and enantiomorphs of non-centrosymmetric structures. I. Theoretical considerations (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 127-133 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Information on the triplet phase sum ΦΣ of the structure factor product F(-h)F(h - g)F(g) can be deduced from the rocking curve of a ψ-scan experiment scanning through a three-beam position. For non-centrosymmetric structures, four typical profiles can be observed. For ΦΣ = 0, 180°, asymmetric profiles result, whereas a nearly symmetrical decrease or increase of the two-beam intensity appears for ΦΣ = ±90°. In a first approximation this behaviour can be explained by the interference between the directly diffracted wave of h and the 'Renninger Umweg' wave of g and h - g. Their phase relationship and the amplitudes are governed by a spatial resonance term, which causes a phase shift of 180° and a continuously turning on and off of the Umweg wave amplitude scanning through the three-beam position. This interference can be displayed by a phase-vector diagram which outlines the main features of the ψ-scan profiles. The semi-quantitative results are confirmed by calculation based on the dynamical theory. The distinction between ΦΣ = ±90° allows the experimental determination of enantiomorphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099749
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  • 6
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 1600-5724
    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°.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388011067
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  • 7
    Electronic Resource
    Electronic Resource
    The absolute configuration of (+)-2-benzyl-2-[N-(α-phenylethyl)amino]cyclohexanone hydrochloride (1993)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 307-310 
    Details
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108270192008965
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  • 8
    Electronic Resource
    Electronic Resource
    A feasibility study of experimental triplet-phase determination in small proteins (1991)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 47 (1991), S. 60-62 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown for the first time that the measurement of triplet phases of three-beam cases where strong structure factors are involved is possible in small protein structures, for example myoglobin. The exploitation of the triplet phase from the interference profile is not affected as long as the structure factors of unavoidable overlapping three-beam cases are small.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767390013150
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  • 9
    Electronic Resource
    Electronic Resource
    Enantiomorphism and three-beam X-ray diffraction: determination of the absolute structure (1995)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 431-438 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that three-beam X-ray diffraction provides a means of resolving the enantiomorphism problem. It is based on the fact that three-beam interference leads to significantly different ψ-scan profiles for triplet phases close to +90 or −90°, which are selectors between enantiomorphs. Since this method works without the need of anomalous scattering, it is particularly suitable for resolving the absolute structure of light-atom compounds. The application of this method is discussed in detail. Its capability of distinguishing between enantiomorphs has been rejected in a recent paper by Colella [Acta Cryst. (1994), A50, 55–57]. Detailed comments on the invalid arguments of Colella's analysis are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767394013644
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  • 10
    Electronic Resource
    Electronic Resource
    Comments on papers on quantitative phase determination from three-beam diffraction by Chang and Tang (1988) (1990)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 534-536 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In two papers [Chang & Tang (1988). Acta Cryst. A44, 1065-1072 and Tang & Chang (1988). Acta Cryst. A44, 1073-1078] the authors are confused with respect to the rotation sense of the crystal lattice during a Renninger ψ-scan experiment. This leads to wrong phase determination. We show that the definition of the triple phase sum involved in a three-beam case used by Chang & Tang is not valid if strong anomalous-dispersion effects must be taken into account.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767390000708
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