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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 825-826 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the course of a discussion of the nature of an ambiguity in the indexing of Renninger peaks the possibility was discovered of distinguishing some opposite directions in a cubic crystal without recourse to anomalous scattering. A multiple-diffraction experiment performed on a (111) Ge plate rotated about [222] enabled distinction between the [1{\bar 1}0] and [0{\bar 1}1] directions to be made. The azimuthal angles counted from alternative zero meridians containing [1{\bar 1}0] or [0{\bar 1}1] are the same, but give rise to peaks indexed hkl and 2 - l,2 - h,2 - k respectively. However, dynamically equivalent situations 222, hkl/(2 - h,2 - k,2 - l) and 222, (2 - l,2 - h,2 - k)/lhk are geometrically different, being distinguished as Bragg-Laue and Bragg-Bragg, respectively, or vice versa.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 876-889 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Multiple simultaneous Bragg diffraction effects of X-rays in quaternary III-V liquid-phase epitaxial thin layers are investigated with both photographic and counter detection methods. For the photographic investigation, a divergent source is used. The geometric aspects of this type of diffraction, affected by lattice mismatch between epitaxial layers and substrates, are discussed for cases involving five-, six- and eight-beam reflections. The lattice mismatches in directions parallel and perpendicular to the interface normal of InGaAsP/ InP, determined from a single divergent-beam photograph, are obtained. For the counter detection study, a collimated incident beam and several single and double heterojunction samples, with large lattice mismatches are used. A kinematical treatment for a general n-beam diffraction, from double- and triple-layer systems, is derived to account for the measured intensities.
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 41-48 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The use of exponential functions as an approximation for reflection powers leads the intensity problem of n-beam kinematical diffraction to an eigenvalue problem. It is solved in the way similar to an n-beam Borrmann dynamical diffraction problem. Besides the intensities of Bragg-reflected beams, the excitation of modes concerning the intensity attenuation is also calculated for highly absorbing infinitely thick crystals. Experiments of multiple reflection from GaAs, InAs and InP single crystals for Cu Kα radiation were carried out. Comparison between the experimental and calculated reflected intensities for several 2-, 3-, 4-, 5- and 8-beam cases are given and discussed.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 870-878 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The method proposed by Chang & Tang [Acta Cryst. (1988), A44, 1065-1072] for quantitative determination of phases of X-ray reflection from three-beam diffraction profiles is applied to an organic crystal of (2R, 3 R)-3-acetoxy-5,7-dihydroxy-6-methylflavanone, with a mosaic spread of 0.08°. The expression for the kinematical diffraction intensities is modified according to the kinematical theory of X-ray diffraction in the multibeam regime. Three-beam Umweganregung and Aufhellung diffraction profiles are analyzed. With the help of the modified intensity expression, the crystal symmetry imposed by the space group and the three-beam diffraction geometry, four acentric phases and fourteen centric phases of structure-factor triplets are determined.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 98-101 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The relation Sp = SL SR between the signs of the triplet phase products Sp, the multiple diffraction line profiles SL and the crystal lattice rotations SR is applied to the structure determination of a centrosymmetric Cs10Ga6Se14 crystal [space group C2/m, a = 18.233 (7), b = 12.889 (5), c = 9.668 (3) Å, β = 108.2°, z = 2]. This structure could not be solved by the ordinary MULTAN program, including MUL TAN-80. From the profile analysis of the multiple diffraction pattern of 311 using a four-circle single-crystal diffractometer with Cu Kα radiation, 12 phase relations among closely linked reflections are determined. Four possible sets of 14 reflection phases are deduced. Using these four sets as the starting phases for MULTAN-74, 225 correct phases are developed. The final E map shows all the atomic positions of Cs, Ga and Se. The structure refinement gives R = 0.047, Rw = 0.053 [1907 reflections with I 〉 2σ(I)]. Details about the procedure are given.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 1073-1078 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The method proposed by Chang & Tang [Acta Cryst. (1988). A44, 1065-1072] of quantitative determination of X-ray reflection phases from multiple diffraction profiles is applied to nearly perfect crystals of gallium arsenide. The detailed intensity-profile-analysis procedures are given. Multiple diffraction profiles obtained with a conventional X-ray source and synchrotron radiation are subjected to this analysis. It is found that, for this particular diffraction example, errors as small as 15° in phase determination are achieved. Errors due to the theoretical approximation, peak position measurement and scaling factor are also discussed.
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 832-835 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Multiple diffraction patterns of a single crystal of GaAs have been recorded with Cu Kα1 radiation. Calculations indicated that 19 peaks, all involving reflections with odd indices, should be observed in the 45° asymmetric angular range of the multiple diffraction pattern. All these were observed and indexed. In addition, six sharp but barely detectable intensity minima, were observed in the background. These result from one eight-beam, one six-beam, and four four-beam interactions, all involving reflections with even indices. The geometry of these interactions is discussed and their integrated intensities have been calculated. These show fair agreement with the corresponding measured intensities.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 543-547 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that the real part of the root of the dispersion equation for the permitted modes of propagation is always positive for two-beam Laue and Bragg reflections at the exact diffraction position. Based on this, a general rule is proposed to determine the number, Np, of permitted modes of propagation for N-beam dynamical diffraction, where no extremely asymmetric reflections are involved. In other words, for both σ- and π-polarized wavefields, Np= 2(N- NBragg), where NBragg is the number of Bragg reflections involved. This conclusion is supported by calculations for three-, four-, six- and eight-beam cases.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 414-417 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The experimental method for the direct determination of phases, proposed by Chang [Appl. Phys. (1981), A26, 221-226; Phys. Rev. Lett. (1982), 48, 163-166], utilizing the coherent interaction of diffracted X-ray beams according to the dynamical theory in a three-beam multiple Bragg reflection, is applied to the crystal structure of diamond by using an irregularly shaped crystal on a conventional four-circle single-crystal diffractometer. The phases of three reflections can be derived from the signs of three triplet-phase products which are obtained experimentally from three multiple-reflection line profiles. Using these phases as a starting set for the direct method, the phases of other reflections are obtained. The computing time for the MULTAN program is therefore drastically reduced.
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 348-352 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The polyhedron which confines the Poynting vectors of N-beam transmissions in crystal space is referred to as the Borrmann pyramid. The observation of this Borrmann pyramid is realized from the diffraction images of the four-beam, (000)(220)(2\bar 20)(400), transmission case of silicon single crystals for Mo Kα. The directions of the Poynting vectors for the eight modes of wave propagation involved and the diffraction images are calculated. These calculations confirm the experimental observations. The variation of the direction of the Poynting vector for each mode is also reported.
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