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  • 1
    Electronic Resource
    Electronic Resource
    Generalized extinction in bipyramidal crystals (2001)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 201-211 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The generalized extinction factors for a set of strong reflections as a function of wavelength are obtained by indirect measurements. The experiments are performed on a crystalline system that satisfies the geometrical requirements imposed by theoretical models developed for a finite perfect crystal. With increased perfection, represented by a reduction in the width of the mosaic distribution function from three to one thousandth of a degree, the experiments give results that approach the predictions from the theory. The present procedure utilizes measurements of the integrated diffracted power of a weak reflection for scaling the strong reflections, hence non-measurable wavelength-dependent factors are assumed to be eliminated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767300018572
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  • 2
    Electronic Resource
    Electronic Resource
    Three-beam interference measurements with a six-circle κ diffractometer (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 49-51 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A procedure for calculating the correct angle setting for a specific three-beam situation on a six-circle κ diffractometer is outlined. It is experimentally shown that interference profiles can be recorded using this approach. Limitations owing to mechanical constraints, with particular emphasis on the ability to measure Friedel-related triplets, are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889899012029
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  • 3
    Electronic Resource
    Electronic Resource
    Three-Beam Diffraction in Finite Perfect Crystals. I. Exploring Laue–Laue and Bragg–Laue Scattering Using a Series-Expansion Approach for the Solution of the Takagi–Taupin Equations (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 120-128 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Using the boundary-value Green-function technique, analytical expressions in the form of finite series expansions are obtained for the relative change in the integrated power of the primary reflection due to the gradual excitation of a secondary reciprocal-lattice point on the Ewald sphere. Solutions are found for both a Laue–Laue and a Bragg–Laue case in finite shaped crystals confined by the scattering vectors. When the crystal sizes do not exceed the Pendellösung length of the involved reflections, the \psi profiles exhibit the same qualitative features in the two cases. The solutions do however indicate a strong dependence on the outer crystal dimensions – which add a geometrical aspect to the interpretation of the Aufhellung and Umweganregung concepts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397010362
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  • 4
    Electronic Resource
    Electronic Resource
    Existence of Two Crystal Structures of the Complex α-D-Glucose·NaCl·H2O(2:1:1) Verified by Three-Beam Diffraction Experiments (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 338-347 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Triplet phases from three-beam interference measurements have been used to resolve a case of apparent structural ambiguity. 13 crystals, all cut from one large single crystal of the complex α-D-glucose · NaCl · H2O (2:1:1) were subjected to physical measurements of triplet phases, which involved studies of a set of model-sensitive triplets being particularly sensitive to the differences in structure between the two models. From 8 to 43 triplets were examined for each crystal specimen. The estimated phases have been compared with the corresponding quantities calculated for the refined structure models. A statistical analysis of the results provides highly significant evidence that both structure models are present, but do not coexist in the same crystal. One possible explanation for this apparent anomaly is that a phase transition may be induced by the mechanical stress applied during cutting of the hard and nearly perfect crystals. Triplet phases for structure verification and discrimination between similar structure models, as demonstrated in the present work, appears to be a novel and potentially powerful application of three-beam interference measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397018849
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  • 5
    Electronic Resource
    Electronic Resource
    Symmetrical X-ray Diffraction in a Perfect Rectangular × l Crystal. Extinction and Absorption (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 416-429 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The boundary-value Green function technique has been used with the Takagi–Taupin equations to explore analytically the diffraction in a perfect rectangular t\times l crystal for a symmetrical coplanar scattering mode. The important contribution is the development of the integration structure over the entrance and exit surfaces of the crystal. A single parameter, \zeta = (t/l)\tan\theta_{oh}, maps the different crystals and the scattering geometries. In the limits \zeta\rightarrow 0 and \zeta\rightarrow \infty, the well known functions for the primary extinction factors for perfect semi-infinite crystals in the case of Laue and Bragg scattering are retrieved. Numerical integrations extend the range of applicability of the method. Both ordinary absorption and generalized extinction, i.e. the joint effect on the kinematical integrated power due to multiple scattering and resonant scattering, are addressed. Germanium is used as a model system for some of the calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397020278
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  • 6
    Electronic Resource
    Electronic Resource
    An exact analytical expression for the primary extinction factor for a perfect spherical crystal in the limit θ oh → π/2 (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 511-512 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Based on the boundary-value Green-function technique, an analytical expression for the primary extinction factor for a perfect non-absorbing spherical crystal has been found in the Bragg limit, \theta_{oh}\rightarrow \pi/2. The asymptotic behaviour is also outlined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767398002657
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  • 7
    Electronic Resource
    Electronic Resource
    Absorption and Weighted Path Lengths in Cylinders and Spheres (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 186-190 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By using the boundary-value Green-function technique for the Takagi equations, it is possible to calculate the normal absorption factor and weighted path length in cylinders and spheres as double integrals in angular coordinates of well defined functions. The results are easy to implement for numerical computations. Exact analytical expressions for both crystal geometries are found in the limits of the Bragg angle \theta_{oh}\rightarrow 0^{\circ} and \theta_{oh}\rightarrow 90^{\circ}.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397012531
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  • 8
    Electronic Resource
    Electronic Resource
    Primary Extinction in Cylinders and Spheres (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 172-185 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By transforming the Takagi equations into a representation using angular coordinates, it is in principle possible to obtain analytical expressions for the coefficients in a series expansion for the primary extinction factor in perfect crystals with a circular diffraction plane. In practice, it has been possible to obtain the first five terms in the expansion. This involves establishing recurrence relations for the families of Bragg and Laue boundary-value Green functions combined with integrations over the entrance and exit surfaces. The calculations, which cover the whole range of values for the scattering angle, \theta_{oh}, are performed using the mathematical software systems Mathematica and Maple.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876739701252X
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  • 9
    Electronic Resource
    Electronic Resource
    Three-Beam Diffraction in Finite Perfect Crystals. II. Influence of Absorption, Resonant Scattering and Polarization (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 129-136 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By using the boundary-value Green-function technique, effects of absorption, resonant scattering and polarization are incorporated in the solution of the Takagi–Taupin equations for three-beam diffraction in finite perfect crystals. It is shown how such features may influence the dynamical interactions. The potential of three-beam interference acting as a phase-sensitive probe for resonant scattering is demonstrated. Depending on the applied model used for the calculations of the corrections to the atomic scattering factor, profile asymmetry reversal is theoretically predicted to occur near the photoelectric threshold in a finite germanium crystal. Significant distortions of the three-beam profiles are found for polarized incident radiation, especially for reflection triplets having an invariant phase sum near 90°.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767397010659
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  • 10
    Electronic Resource
    Electronic Resource
    Three-Beam Diffraction in Finite Imperfect Crystals. An Analysis of Coherent Wavefield Interactions Using Statistical Dynamical Theory (1998)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 137-145 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By applying the concepts of statistical dynamical theory and the boundary-value Green-function technique, an analytical expression in the form of a series expansion has been obtained for the coherent contribution to the integrated power in a finite crystal geometry. The solution suggests that three-beam interference is likely to cause observable perturbations also in crystals with a high degree of imperfection. Owing to a first-order dependence on the invariant triplet phase sum, profile reversal may occur in cases where this sum is close to 90°. The result may serve as an experimental check on statistical dynamical parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876739701088X
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