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 implemented within a fundamental-parameters fitting procedure for diffraction profiles from a conventional X-ray powder diffractometer. The aberration function for axial divergence is derived from the geometrical dimensions of the diffractometer in the axial plane and the angular apertures of any Soller slits in the beam path. This function is then convoluted with other instrument 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 fitting program and a Rietveld refinement program. In these programs, the refinable parameters for the axial divergence contribution to the profile shape are the axial X-ray source length, the sample length, the receiving-slit length and the aperture angles of the primary and secondary Soller slits. The procedure developed has been evaluated by fitting diffraction patterns collected using two different X-ray diffractometers and a variety of Soller slits and sample configurations to introduce varying degrees of axial divergence in the incident and diffracted beams. The reference materials used for this work included Y₂O₃, LaB₆ (SRM 660), Cr₂O₃ (SRM 674a) and CeO₂ (SRM 674a). In all cases, the refined instrumental parameters defining the axial divergence were in good agreement with the directly measured values. Rietveld refinement using the present axial divergence model resulted in R_wp values that are significantly lower than those based on currently available models for this aberration function.