X-ray diffraction with a four-reflection monochromator

A formula is derived for simulating rocking-curve measurements made with an X-ray diffractometer fitted with a four-reflection monochromator. The derivation is carried out both graphically and algebraically. Results of a simulation using this formula are then compared with experimentally obtained rocking curves. The rocking curves were obtained using a diffractometer with a four-reflection monochromator that uses 440 reflections from two channel-cut germanium crystals. The experimental data comprise 200, 400, 600, 511, 711, 622, 422 and 444 reflections from thick single-crystal indium phosphide grown by the vertical-gradient freeze technique. The simulated data correlate well with the experimental data, although the simulations consistently show somewhat higher reflectivities and narrower linewidths than the experiment, indicating the existence of broadening mechanisms not included in the simulation that are affecting the experiment.