Remarkable precision of the 90-year-old dynamic diffraction theories of Darwin and Ewald

The reflectivity functions calculated by Bonse and Hart for a multi-bounce channel-cut single crystal, following the 90-year-old theories of Darwin and Ewald, exhibit extremely narrow nearly rectangular profiles. This feature provides ultra-high angular resolution and sensitivity for the double-crystal diffractometers now widely used for the observation of large-scale structures in condensed matter. However, the experimental results are several orders of magnitude poorer than the theoretical prediction, the `wings problem'. The reason for this discrepancy has remained unidentified for more than 40 years, creating problems for both theory and practice. A solution to this problem for neutron diffraction in Si channel-cut crystals is presented here. The results enable nearly theoretical functions of multiple reflectivity to be obtained, demonstrate the remarkable precision of the Darwin and Ewald theories in the range of the wings, and give rise to much improved sensitivity for the next generation of Bonse-Hart double-crystal diffractometers.