X-ray convergent beam pattern simulation using the Moodie-Wagenfeld equations: 3-beam Laue case

Pattern simulations for 3-beam X-ray diffraction are presented, by multi-slice calculations based on Moodie and Wagenfeld's formulation of the X-ray equations, which factorise Maxwell's equations into Dirac format, using circular-polarisation bases. The results are presented in the form of convergent-beam patterns for each diffraction order, using experience gained from CBED (convergent beam electron diffraction) and LACBED (large-angle CBED), since this displays the results in the most compact form. The acronym CBXRAD (convergent-beam X-ray-diffraction) is used for these patterns. Although optics required for the complete patterns is not currently available, capillary focussing is undergoing rapid development, and our simulations define critical angular ranges within reach of current designs. Simulations for light and heavy-atoms 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 well studied CBED pattern symmetries. MoKα1 and TaKα1 wavelengths were used to minimise absorption for the two structures respectively, although 'anomalous absorption' is always important due to the large thicknesses required (up to 20 mm)