Prototype grooved and spherically bent Si backscattering crystal analyzer for meV resolution inelastic x-ray scattering

The high-order backscattering reflections from single crystals of silicon have mrad rocking curve widths that can be exploited to produce meV energy-resolution focusing analyzer crystals for use in inelastic x-ray scattering experiments at third-generation synchrotron sources. The first generation of these analyzers has been limited in efficiency principally by slope and/or figure errors. We calculate the effect of slope errors on the theoretical energy resolution and focus spot size of a typical analyzer design using a ray-tracing code to ensure that there are no unforeseen contributions to the energy resolution and efficiency. We also present measurements of the slope errors of the atomic planes for a prototype, spherically bent, strain-relief grooved analyzer as proof that it is in principle possible to obtain the slope and figure error limits required for a high efficiency meV resolution backscattering crystal