Simultaneous four-beam Borrmann diffraction

A general procedure is described for the calculation of n-beam Borrmann diffraction effects. These include the coordinates of points on the sheets of the dispersion surface, absorption coefficients, excitation of modes of propagation and transmitted intensities. The procedure has been used to calculate four-beam effects involved in the simultaneous transmission of the 000, 11, 3 and 20 reflections through essentially perfect germanium crystals. Emphasis has been placed on calculations which illustrate the transitions from four-beam interactions to one or two-beam cases. The minimum value of the absorption coefficients for Cu Kα₁ at the exact four-beam setting is 6.2 cm^-1, compared with the 'normal' coefficient of 352 cm^-1. The effects of several relevant variables on transmitted intensities and on the effective absorption coefficients, are described. High-resolution divergent-beam photographs, utilizing a microbeam X- ray source and an evacuated path of 160 cm from crystal to film, reveal a number of previously unreported anomalies in the transmitted intensities. The calculated values of the corresponding reflection intensities agree well with these observations.