Limitations of asymmetric parallel-beam geometry

Bragg diffraction peak profiles and intensities in asymmetric (Ω–2θ) diffraction using a mirror-based parallel-beam geometry were compared with symmetric parallel-beam (θ–2θ) and conventional Bragg–Brentano (θ–2θ) diffraction for a powdered quartz sample and the NIST standard reference material (SRM) 660a (LaB₆, lanthanum hexaboride). A comparison of the intensities and line widths (full width at half-maximum, FWHM) of these techniques demonstrated that low incident angles (Ω < 5°) are preferable for the parallel-beam setup. For higher Ω values, if 2θ < 2Ω, mass absorption reduces the intensities significantly compared with the Bragg–Brentano setup. The diffraction peak shapes for the mirror geometry are more asymmetric and have larger FWHM values than corresponding peaks recorded with a Bragg–Brentano geometry. An asymmetric mirror-based parallel-beam geometry offers some advantages in respect of intensity when compared with symmetric geometries, and hence may be well suited to quantitative studies, such as those involving Rietveld analysis. A trial Rietveld refinement of a 50% quartz–50% corundum mixture was performed and produced adequate results.