Theoretical considerations on the design of three-beam X-ray monochromators for synchrotron radiation
Double-crystal X-ray monochromators utilizing three-beam multiple diffraction are proposed for synchrotron radiation. An analytical formalism is derived, with the two-beam approximation, for the wavelength resolution, the wavelength tunability, and the angular widths of acceptance and of divergence in Bragg's angle and in azimuthal rotation. Calculations of these beam parameters are performed for asymmetrically cut germanium double-crystals at the three-beam, (000)(222)(113) and (000)(222)( overline1overline11), diffraction positions, respectively. It is found that the degree of parallelism of the monochromatic beam from the three-beam monochromators is better than the one from the ordinary two-beam double-crystal monochromator. Besides, the energy resolution and angular width can be tuned by adjusting the azimuthal angle of the two crystals involved. The disadvantage of this kind of monochromator is, however, the tradeoff of the intensity for the angular width of acceptance.