Computer simulations of X-ray spherical wave dynamical diffraction in one and two crystals in the Laue case

Abstract

This article reports computer simulations of X‐ray spherical wave dynamical diffraction in one and two single crystals in the Laue case. An X‐ray compound refractive lens (CRL) as a secondary radiation source of spherical waves was considered for the first time and in contrast to previous simulations with the assumption of the use of a slit. The main properties of the CRL as a secondary source are discussed and two focusing phenomena are analysed. The first one is the diffraction focusing effect for one single crystal in the reflected beam and in the case of a large source‐to‐detector distance. The second one is the same but for two single crystals and for the twice‐reflected beam in the case of a short distance between the source and detector. The first effect is well pronounced in the case of strong absorption. However, it may also be used as an element of an energy spectrometer in the medium and even weak absorption case. The second effect will appear in the case of weak absorption. It is shown that it is not effective to use it in an energy spectrometer. In the case of weak absorption the transverse size of the diffraction focused beam will oscillate together with the reflected beam integral intensity. The oscillation period is close to the extinction length.

Theory of the Laue Diffraction of X Rays in a Thick Single Crystal with an Inclined Step on the Exit Surface. I: Numerical Solution

“…The average reflected-beam intensity at the lower boundary (i.e., at the thickness t 1 ) is assumed to be unity. Note that the diffraction-focusing thickness [12,36] for the distance under consideration is t df = L|χ h |F = 60.8 μm, where F = 1/(sin θ B sin 2θ B ). Therefore, a part of radiation with weak absorption is maximally compressed at this thickness, then it diverges again, and exhibits an almost uniform intensity distribution over the x axis (along the surface) in the step region.…”