Simulation of diffraction profiles for sagittally bent Laue crystals

The diffraction profiles (or rocking curves) of sagittally bent Laue crystals are known to be significantly wider than those of perfect crystals as a result of the lattice distortion introduced by the sagittal bending. The existing analytical model explains the rocking curve broadening as well as the reflectivity observed. Many theoretical methods were developed for calculating diffraction profiles of meridionally (in the diffraction plane) bent crystals. In this work, we extend these methods to accommodate sagittally bent crystals. The total lattice distortion angle for anisotropic crystals under sagittal bending is adapted into the multi-lamellar approximation using the rotating crystal method, in which the incident angle changes through each lamella. The Penning-Polder theory is examined for bent crystals with the uniform strain gradient. In addition, the Takagi-Taupin equations are solved numerically for sagittally bent Laue crystals. Finally, examples of these simulation results are presented and the merit of each method is discussed.