X-ray diffraction characteristics of curved monochromators for synchrotron radiation

A theoretical study is presented concerning the diffraction characteristics of curved monochromators for X-ray synchrotron radiation used at the laboratories of Hamburg, Orsay and Stanford. The investigation was performed by extending to the X-ray case a simple model recently developed and fruitfully employed to describe the neutron diffraction properties of curved monochromators. Several diffraction patterns were obtained corresponding to different monochromator materials (Ge, Si) used by the different laboratories, for different reflecting planes (111), (220). asymmetry angles, X-ray wavelengths (Mo Kα, Cu Kα, Cr Kα) and curvature radii. The results are discussed in physical terms and their implications on the design of curved monochromators for synchrotron radiation are presented. In particular, the study shows that all the monochromators used in the different laboratories should behave practically as perfect crystals and therefore should have a very low integrated reflectivity corresponding to an optimized wavelength passband Δλ/λ ≃10⁻⁴. The gain that can be obtained by increasing the curvature, by introducing a gradient in the lattice spacing or by any other kind of imperfection is quite limited and much lower than the desirable value. The adopted model can help in obtaining a possible moderate gain in intensity by also taking into consideration other parameters, such as crystal material, reflecting plane, asymmetry of the reflection and X-ray wavelength.