Laboratory X-ray powder diffraction: a comparison of different geometries with special attention to the usage of the Cu Kα doublet

In a laboratory X-ray powder diffraction study, the evaluation of the patterns of three Bragg–Brentano powder diffractometers with different monochromator geometries has been undertaken. For the measurements on each diffractometer, the standard reference material SRM 640 (silicon) and the corundum samples SRM 674a and SRM 1976 have been used. In each case, the peak profiles were fitted with a split Pearson VII function and the FWHM (full width at half-maximum) parameters and exponent m were determined for the left (lower 2θ) and the right (higher 2θ) sides of the Bragg peaks. It was found that there is a strong dependence of both the FWHM and the exponent m on the diffraction angle for the two configurations that included monochromators, whereas nearly constant values of m were found for the geometrically simplest diffractometer working without a monochromator. Finally, the two components of the Cu Kα doublet show systematically different peak profiles. There is a clear difference not only concerning the FWHM, which becomes more obvious at higher 2θ values, but also in the course of m with respect to the diffraction angle for the left and the right tails of the powder reflections. This is the main reason for the difficulties in Kα₂ stripping and also in single-line-profile analysis when using the Kα doublet. Therefore, it is not surprising that this phenomenon, which can be explained by Heisenberg's uncertainty principle, does affect the reliability (represented by standard R values) of structure refinement by the Rietveld method.