Experimental determination of triplet phases and enantiomorphs of non-centrosymmetric structures. I. Theoretical considerations

Hümmer, K.; Billy, H.

doi:10.1107/s0108767386099749

Cited by 60 publications

(14 citation statements)

References 8 publications

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“…All the ideal ψ-scan profiles are depicted schematically in Fig. 4a-d. Hummer and Billy [5] explained the ideal ψ-scan profiles due to three-beam interference effects by means of phase-vector diagrams.…”

Section: Ideal Profilesmentioning

confidence: 99%

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Experimental Determination of Reflection Phases by Three-Beam Diffraction and its Applications

1992

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Information on phase relationships between Bragg reflections can be obtained by the interference of Bragg waves. In the three-beam case, phase difference is given by a structure invariant triplet phase relationship. The intensity variation due to the three-beam interaction can be best measured by a ψ-scan experiment. The resulting ψ-scan diffraction proflles scanning through a three-beam position uniquely depend on the triplet phase relationship involved. In principle each three-beam profile is given by a superposition of a symmetrical phase-independent and a phase-dependent profile. Thus, triplet phases can be determined experimentally with an accuracy of about 45 degrees. The ψ-scan method is discussed and some examples of applications to the determination of the absolute structure as well as to the structure determination by combination of measured triplet phases with direct methods are given.

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Section: Ideal Profilesmentioning

confidence: 99%

“…Therefore, we neglect the coupling between the π and σ polarization components of each wave field [5] and we are left with the following simplified system of equations for the three-beam case:…”

Section: Three-beam Dynamical Theorymentioning

confidence: 99%

Experimental Determination of Reflection Phases by Three-Beam Diffraction and its Applications

1992

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“…It has been known that the interference effect in a multiple-beam diffraction process can be used to extract lost crystallographic phase information from diffraction intensities (Colella, 1974; Post, 1977;Chapman, Yoder & Colella, 1981;Chang, 1982;Juretschke, 1982;Shen, 1986;Shen & Colella, 1986;Hummer & Billy, 1986;Shen & Colella, 1987, 1988Chang & Tang, 1988;Hummer, Weckert & Bondza, 1989;Shen & Finkelstein, 1990). As realized by several authors, when linearly polarized or unpolarized X-rays are used as the incident beam, the multibeam interference effect on the wings of a multiple reflection peak contains information on only the cosine of the relative phase or the real part of the phase factor.…”

Section: Gaas 442: Solving Acentric Phase Problem~mentioning

confidence: 99%

“…The information on the sine of the relative phase, which is directly related to the noncentrosymmetry of a crystal, is still missing in such an experiment. Although such phase information may exist at the center of a multiple-reflection peak (Hummer & Billy, 1986;Chang & Tang, 1988;Hummer, Weckert & Bondza, 1989), it is usually affected by the kinematic effect if one uses the dynamical theory or the extinction effect if one uses the kinematic theory. Recently it has been demonstrated by Shen & Finkelstein (1990) that another way to obtain the noncentrosymmetric phase information is to utilize circularly polarized X-rays as the incident beam in a multiple-beam diffraction experiment.…”

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confidence: 99%

Effects of a general X-ray polarization in multiple-beam Bragg diffraction

Shen¹

1993

Acta Cryst Sect A

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The formalism of the N-beam dynamical theory of X-ray diffraction is extended to include all possible incident and diffracted polarizations. With this new formalism it is shown that the intensity of a simultaneously excited Bragg reflection can be described through a polarization density matrix that involves the Stokes-Poincar6 parameters. In particular, the multibeam diffracted intensity is sensitive to the circularly polarized component in the incident beam and the structure-factor phases of the diffracting crystal. Experimental results on the GaAs 442 and Ge 333 reflections confirm the theoretical calculations. © 1993 International Union of Crystallography Printed in Great Britain -all rights reservedThis kind of measurement can provide useful acentric phase information and can also be used for circular X-ray polarimetry. Another feature of N-beam diffraction is its ability to turn a linear polarization into an elliptical polarization, which means it can be used as an X-ray phase plate. IntroductionX-ray polarization plays an important role in every scattering and diffraction experiment. In crystallography, one needs to use the polarization-factor correction in order to obtain structure factors from diffracted intensities (Warren, 1969). In X-ray physics and Acta Crystallographica Section A ISSN 0108-7673 ©1993 606 X-RAY POLARIZATION IN MULTIPLE-BEAM BRAGG DIFFRACTION material science, polarization analysis can often reveal interesting features of the magnetic properties and atomic-site symmetries of the diffracting material (Templeton & Templeton, 1985;Blume & Gibbs, 1988;Belyakov & Dmitrienko, 1989;Kirfel, Petcov & Eichhorn, 1991;Finkelstein, Shen & Shastri, 1992). The increasingly available energy and polarization tunabilities of many intense synchrotron sources promise to provide experimenters with an extra dimension in the analysis of X-ray polarization in future diffraction experiments. It is, therefore, worthwhile to re-examine and extend some of the well established fields in X-ray diffraction. One such field is that of multiple-beam Bragg diffraction.Because of the co-existing effects of multibeam interference and polarization mixing (Shen, 1991), some new and interesting features in multibeam diffraction can emerge if one includes general elliptically polarized X-rays in the incident beam. These new features include phase determination on noncentrosymmetric crystals (Shen & Finkelstein, 1990), complete characterization of an elliptical polarization of an X-ray beam and utilization of multibeam diffraction as an X-ray circular phase plate.Multiple-beam diffraction occurs in a crystal when two or more atomic planes satisfy the Bragg conditions simultaneously. The process usually gives rise to a secondary peak (Renninger peak) in the intensity of a Bragg reflection, H, when the diffraction crystal is rotated around the scattering vector H (Renninger, 1937;Cole, Chambers & Dunn, 1962). The reflection H is usually termed the main reflection and the rotation is described by an azimuthal angle, ~o...

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“…The use of three-beam diffraction for experimental phase determination, first suggested by Lipscomb [13] in 1949, elaborated by Post [14], was further developed by hummer and Billy [15,16]. The use of synchrotron beam allowed Tischler and Batterman in 1984 [17] to measure the absolute structure factor of (622) reflection in germanium.…”

Section: Introductionmentioning

confidence: 99%

Absolute Structure Determination in Absence of Heavy Scatterers

Grochowski

1997

Acta Phys. Pol. A

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Experimental determination of triplet phases and enantiomorphs of non-centrosymmetric structures. I. Theoretical considerations

Cited by 60 publications

References 8 publications

Experimental Determination of Reflection Phases by Three-Beam Diffraction and its Applications

Experimental Determination of Reflection Phases by Three-Beam Diffraction and its Applications

Effects of a general X-ray polarization in multiple-beam Bragg diffraction

Absolute Structure Determination in Absence of Heavy Scatterers

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