Simultaneous Diffraction of X Rays and the Borrmann Effect

Abstract

The Borrmann effect (the anomalous transmission of x rays through thick perfect crystals) has been used as the primary diffraction in a study of simultaneous diffraction. The major part of the work is an analysis of multiple diffraction using the dynamical theory of x-ray diffraction. In the analysis we have utilized the concept of normal modes in describing the propagation of the x-ray wave field. We have determined these modes when the Bragg condition is exactly and simultaneously satisfied for all the diffracting planes. The particular configuration studied was one in which only three noncoplanar waves have appreciable amplitudes. We have shown that at least one of the proper modes of any three-field case of the type considered is a nonabsorbing mode of propagation (i.e., having nodes of the electric field at the atomic planes). This indicates that the primary anomalous transmission will persist with little or no change in intensity when a third reciprocal lattice point enters the Ewald sphere. In particular, when the third reciprocal lattice point is of the same family as the primary, simultaneous anomalous transmission is predicted. For this case, a relatively small change in the primary reflected beam and a twofold enhancement of the forward beam is calculated which are seen to be due to a superposition of two degenerate Borrmann effects having a common forward diffraction direction. Experimental results using polarized and unpolarized incident radiation are presented and discussed. 9 E. J. Saccocio and A. Zajac, Acta Cryst. 18, 478 (1965). 10 E. J. Saccocio, Ph.D. thesis, Polytechnic Institute of Brooklyn, 1964 (unpublished).

Multiple diffraction of X-rays and the phase problem. Computational procedures and comparison with experiment

“…In recent years numerous treatments of multibeam cases have appeared in the literature* (Saccocio & Zajac, 1965;Hildebrandt, 1967;Joko & Fukuhara, 1967;Ewald & H6no, 1968;H6no & Ewald, 1968;Penning, 1968;Penning & Polder, 1968;Dalisa, Zajac & Ng, 1968;Balter, Feldman & Post, 1971, and many others). In all these papers only the Laue case of diffraction was considered, because the authors' attention was concentrated on the enhancement of anomalous transmission occurring in some multi-beam cases (double Borrmann effect).…”

Simultaneous bright- and dark-field X-ray microscopy at X-ray free electron lasers

“…In both cases, the beam is translated from its initial position due to these multiple scattering events. This effect, termed the Borrmann effect 40 , makes the TXM line beam spread out laterally, as ghost-fringes appear next to the primary beam. Information about the extent of dynamical diffraction can be helpful in understanding how to interpret image features with DFXM, as they also complicate signal in DFXM images.…”

Simultaneous diffraction:Umweganregungpeaks in the case of a vibrating single crystal

“…After the famous experimental work of Borrmann & Hartwig (1965), the dynamical theory, which has no restrictions on the numbe? of excited reflections, has usually been applied to multiple diffraction so that the situations in which more than one set of atomic planes are in position to transmit X-rays anomalously could be investigated (Saccocio & Zajac, 1965;Hildebrand, 1967;Joko & Fukuhara, 1967;Penning, 1968;Iveronova, Katsnelson & Runova, 1977;Post, Chang & Huang, 1977). In the paper of Ewaid & H6no (1968), there is also discussed the problem of direct Umweganregung phenomena.…”