The resolution function of a triple-crystal diffractometer for high-energy synchrotron radiation in nondispersive Laue geometry

The k-space resolution function of a triple-crystal diffractometer is calculated for an arrangement of three perfect silicon single crystals Bragg diffracting in nondispersive Laue geometry. A comparison is made with the results of measurements using synchrotron radiation in the energy range from 80 to 150 keV. In this case, absorption is very weak and according to dynamical theory the width of the diffraction pattern of thick perfect single crystals is proportional to the wavelength λ, whereas its Lorentzian tails are proportional to λ². Together with the fact that the Bragg angles are only of the order of 2°, this leads to a concentration of the starlike k-space resolution function into a narrow band parallel to the reciprocal-lattice vector G. For diffraction of 80 keV synchrotron radiation at the silicon 111 reflection, the full width at half-maximum (FWHM) of the intensity distribution in the scattering plane is 1.1 × 10⁻⁵ Å⁻¹ perpendicular to G and 2.2 × 10⁻⁴ Å⁻¹ parallel to G. The observed differences in the contributions from monochromator and analyzer crystal to the resolution function are explained by the finite width of the electronic window of the detector counting chain and the non-Bragg scattering contribution from the crystals. If annealed Czochralski-grown silicon single crystals with a mosaicity of ~3′′ are used as monochromator and analyzer, the resolution is reduced by one order of magnitude, but for studies of imperfect samples or of diffuse scattering large gains in intensity can be accomplished this way.