Axial divergence in a conventional X-ray powder diffractometer. II. Realization and evaluation in a fundamental-parameter profile fitting procedure

An accurate model for the axial divergence aberration function has been imp lemented within a fundamental-parameters fitting procedure for diffraction profiles from a conventional X-ray powder diffractometer. The aberration fu nction for axial divergence is derived from the geometrical dimensions of t he diffractometer in the axial plane and the angular apertures of any Selle r slits in the beam path. This function is then convoluted with other instr ument and specimen aberration functions to form the final profile shape. As this process only requires a modest amount of computational effort, it has been incorporated into both a fundamental-parameters profile-analysis fitt ing program and a Rietveld refinement program. In these programs, the refin able parameters for the axial divergence contribution to the profile shape are the axial X-ray source length, the sample length, the receiving-slit le ngth and the aperture angles of the primary and secondary Seller slits. The procedure developed has been evaluated by fitting diffraction patterns col lected using two different X-ray diffractometers and a variety of Soller sl its and sample configurations to introduce varying degrees of axial diverge nce in the incident and diffracted beams. The reference materials used for this work included Y2O3, LaB6 (SRM 660), Cr2O3 (SRM 674a) and CeO2 (SRM 674 a). In all cases, the refined instrumental parameters defining the axial di vergence were in good agreement with the directly measured values. Rietveld refinement using the present axial divergence model resulted in R-wp value s that are significantly lower than those based on currently available mode ls for this aberration function.