Experimental determination of triplet phases and enantiomorphs of non-centrosymmetric structures

Abstract

The X-ray standing wave technique for the localization of surface atoms has been used so far with crystals in the Bragg-case geometry. Since the standing wave intensity is modulated along the diffracting vector h, the Laue-case geometry with h nearly parallel to the surface is more preferable for the studies of lateral structures of the surface.For this purpose total exter~al reflection at grazing incidence angles is used to create a standing wave extending on both sides of the boundary surface (P. L. Cowan, 1985, Phys. Rev., 32, 5437-5439). Dynamical X-ray diffraction in thisgeometry _ involves two angles that can be controlled independently: the angle of incidence ¢o and the deviation angle 68 from the exact Laue incidence. The geometry is best inspected using a three-dimensional dispersion surface. It can be sgown that the sectioned reciprocal space is divided into four regions, I to IV, where there are zero, one or two standing waves.For P 0 ' located in region I simple specular reflection occurs with no standing wave formed even when the Laue condition is exactly met.In region II the external diffracted wave is evanescent and the standing wave is confined in shallow depths of a few tens Angstrom on the both sides of the interface (P. L. Cowan, ibid.).Here the real part of the external wave vector ;em8ins parallel to the crystal surface. Calculations show that an abrupt change occurs in the specularly reflected beam intensity whenever P 0 ' traverses the sectioned dispersion surface.The ¢ 0 angles where the change occurs define critical angles of total reflection for the two wave fields associated with the two branches of the dispersion surface. A 100% specular reflectivity is expected from non-absorbing crystals only when P 0 ' is located in region I. Otherwise the incident energy is partly spent in exciting the crystal fields.We have confirmed some of the above predictions in experiments using a germanium or gallium arsenide crystal at a synchrotron radiation source, where secondary fluorescent X-rays were measured from the specimen together with the specular and diffracted beams.

Direct measurements of triplet phase relationships of organic non-centrosymmetric structures using synchrotron radiation

“…The special ~b-(six-)circle diffractometer described earlier (HiJmmer, Bondza & Weckert, 1987) was installed at the DORIS II storage ring at HASY-LAB/DESY, Hamburg. The angular resolution of the crystal circles was improved to 2 x 10 -4° The radiation was taken from a bending magnet at 3.65 GeV.…”

“…The special ~b-(six-)circle diffractometer described earlier (HiJmmer, Bondza & Weckert, 1987) The fractional atomic coordinates were taken from: (1) Kartha & De Vries (1961); (2) Brown & Sadanaga (1965); (3) Hvoslef (1968) [warning: in this paper a left-handed coordinate system is used]; (4) Berman (1970); (5) Lehmann & Nunes (1980); (6) Burzlaff (1988); (7) Paulus (1988); (8) Weckert (1990a); (9) Weckert (1990b); (10) Weckert (1990c).…”

Resonant Scattering of Light Atoms - Measuring Methods and Applications

“…Primary reports indicate "chiral sensitivity with still too low confidence levee" [21]. As a promising but exclusive, due to unique instrumentation, alternative to the diffraction experiments described above, may be considered SR high resolution azimuthal scan [25].…”

<title>Phase-sensitive data collection in x-ray crystallography using reference-beam diffraction</title>

“…Early works also included those by Hart and Lang on three-beam Pendellosung fringes [15] and by Ewald and Heno on theoretical aspects of three-beam dispersion surfaces [16]. The method was further developed in the 1980's by several groups [17][18][19][20] to show that the technique can be applied not only to perfect crystals but also to real, mosaic crystals. Furthermore, it was shown that the use of circularly polarized x-rays in a multiple-beam experiment can lead to additional phase information, especially for noncentrosymmetric systems [2 1,22].…”

“…The two diffracted waves interfere with each other and produce an asymmetric intensity profile in an azimuthal (psi) scan around one of the Bragg reflections. This intensity interference pattern depends directly on the relative phase of the two reflected waves, which can be shown equal to the triplet phase [15,[17][18][19][20] in crystallography. Therefore by measuring the three-beam interference patterns the triplet phases can be obtained directly in a diffraction experiment.…”