Bent crystal optics for high energy synchrotron radiation

Abstract

The use of elastically bent perfect crystals as optical elements of high energy synchrotron radiation beamlines is reviewed. The geometrical principles of focusing are described, and formulas for focal lengths and energy band-passes are given for transmission (Laue) and reflection (Bragg) cases. The effects of bending on the reflectivity of the crystal are discussed within models that combine trajectories of the beam inside the crystal with the conditions of dynamical diffraction. It is shown that the reflectivity of the crystal can be tailored for a given application by changing the bending radius, asymmetric cut, and thickness. Slightly different x-ray energies are reflected at different depths, so that the reflectivity curve is broadened. At high energies, where the crystals become almost transparent, large gains of intensity are achieved. This is important and very useful for x-ray spectroscopy of weak scattering, where the resolution and efficiency of the crystal spectrometer must be optimized. The integrated reflectivity can reach the kinematical limit. In the Laue case the reflectivity curve is almost flat-topped, and the maximum reflectivity may be close to unity. Calculations based on the Penning-Polder model agree well with the measured reflectivity curves. In the Bragg case the reflectivity curve is calculated using a layer-crystal model, and also these results are substantiated by experimental results. The above ideas are used in several constructions of crystal monochromators and analyzers at the ESRF. These include focusing single-bounce Bragg-type monochromators for inelastic scattering experiments, thick asymmetrically cut Laue-type monochromators for scattering studies above 200 keV, and tuneable Laue-Bragg monochromators with fixed exit beam and focal length for energies between 50 keV and 120 keV. A Laue-type monochromator has been built for the beamline dedicated for dispersive EXAFS, and a scanning spectrometer with Rowland circle focusing is used for high-resolution Compton profile measurements. The solutions for dynamical bending and cooling of the crystals are described and performances of the various instruments are given.