X-ray multislice computation using the Moodie–Wagenfeld equations: divergent-beam pattern simulation in three-beam and six-beam Laue cases

Abstract

Pattern simulations for three-beam and six-beam X-ray diffraction are presented using multislice calculations based on Moodie & Wagenfeld's formulation of the X-ray equations, which factorize Maxwell's equations into Dirac format, using circular-polarization bases. The results are presented in three forms: one-dimensional rocking curves, Pendellösung thickness fringes, and convergent/divergent-beam patterns of single-diffraction orders, using experience gained from CBED (convergent-beam electron diffraction) and LACBED (large-angle CBED) techniques developed for high-voltage electron diffraction transmission patterns. This latter and quite new technique displays the results in the most compact form. The acronym DBXRAD (divergent-beam X-ray diffraction) is used for these patterns. The optics required for these patterns has only recently become available for radiations up to Mo Kα1 in energy and for limited angular divergences, but with capillary focusing currently undergoing rapid development these limits are likely to be extended. However, these simulations define critical angular ranges within reach of current designs. Simulations for light- and heavy-atom structures belonging to the enantiomorphic space-group pair P3121 and P3221 provide clear evidence of chiral interaction between radiation and structure, highlighting divergences from the use in structure analysis of the well studied CBED pattern symmetries. Mo Kα1 and Ta Kα1 wavelengths were used to minimize absorption for the two structures studied, an important factor owing to the large thicknesses (up to 20 mm) required.