Effect of divergence and receiving slit dimensions on peak profile parameters in Rietveld analysis of X-ray diffractometer data

A range of `normal' divergence (0.25, 1.0°) and receiving (0.1, 0.2, 0.4 mm) slit dimensions has been used to determine their effect on the peak profile parameters obtained by Rietveld analysis of X-ray powder diffraction data from a conventional X-ray source. The instrument is a standard Bragg-Brentano diffractometer equipped with a diffracted-beam monochromator and Soller slits. The instrumental profile characteristics are provided by a sample of coarsely crystalline Si, and the effects of small particle size and isotropic strain by fluorite, CaF₂. Results are discussed for refinements of the full diffraction patterns (24 to 140°), and of the individual peaks at 28, 47 and 88° in each pattern. The use of a wide receiving slit aperture (i.e. 0.4 vs 0.1 mm) provides (i) increased peak intensities, (ii) much improved values of the Rietveld agreement indices (especially at low angles), (iii) slightly more Gaussian peak shapes, and (iv) slightly wider peaks. A wider divergence slit (i.e. 1.0 vs 0.25°) has only a small effect on the refinement results. The Voigt and pseudo-Voigt peak shape models are seriously deficient for low-angle peaks when axial divergence is larger than about 2°, but are otherwise satisfactory. The CaF₂ peaks are wider and more Lorentzian in character (at high angles) than those obtained for Si, owing to the presence of very small (350 Å) and strained crystals; in this case, the peak shape/width characteristics can be adequately modelled at all diffraction angles, regardless of axial divergence. Quantitative information about crystal size and strain can be extracted from the CaF₂ pattern by direct incorporation of the instrumental profile into the parameters of the Voigt function during Rietveld refinement.