XXXIV. The theory of X-ray reflexion

Abstract

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Coherent convergent-beam time-resolved X-ray diffraction

“…Equation (5.2) does, however, predict correctly a ninety degree phase shift between direct and scattered X-rays, which is not present in the Born approximation, owing to differing treatments of boundary conditions. We note that Darwin's formula for Bragg diffraction from a bulk crystal [18], when integrated across the rocking curve, predicts a stronger l 3 -dependence of scattered intensity on beam energy because it treats a bulk crystal, does not make the projection approximation made above, and treats full rather than partial reflections. In decisions concerning the maximum beam energy for future XFEL designs, this rapid fall-off in scattered intensity with increasing beam energy must be combined with the dependence of the incident XFEL fluence per shot on beam energy (often decreasing), together with cost estimates to determine a cost/benefit ratio for scattering experiments.…”

Laue diffraction lenses for astrophysics: Theoretical concepts

“…Actually, the angular (or energy) acceptance can be relatively large (up to a few degrees), and the integrated reflectivity is much higher than expected from a perfect crystal with a thickness T 0 t ext . Darwin (see [13,14,15,10]) proposed that a macroscopic crystal is actually an agglomerate of small, perfect crystals. The angular orientation of these small crystals is randomly distributed (see fig.…”

“…(37) 13 Formula 37, along with equation 33, is of constant use to estimate the diffraction efficiency of a mosaic crystal, and by extension, the efficiency of a Laue lens.…”

Perfect crystal propagator for physical optics simulations with Synchrotron Radiation Workshop

“…Dynamical diffraction of plane waves from perfect crystals was treated at length in the early twentieth century by Darwin, 1 Prins, 2 Ewald 3 and von Laue 4 ; reviews of their theory have been provided by Zachariasen 5 and by Batterman and Cole 6 among others. Dynamical diffraction of spherical waves from absorbing perfect crystals was subsequently treated by Kato 7,8 in the Laue case and by Saka, Katagawa and Kato 9 in the Bragg case.…”