Improvement of deconvolution–convolution treatment of axial-divergence aberration in Bragg–Brentano geometry

An improved method to correct observed shift and asymmetric deformation of diffraction peak profile caused by the axial-divergence aberration in Bragg–Brentano geometry is proposed. The method is based on deconvolution–convolution treatment applying scale transform of abscissa, Fourier transform, and cumulant analysis of an analytical model for the axial-divergence aberration. The method has been applied to the powder diffraction data of a standard LaB6 powder (NIST SRM660a) sample, collected with a one-dimensional Si strip detector. The locations, widths and shape of the peaks in the deconvolved–convolved powder diffraction data have been analyzed. The finally obtained whole powder diffraction pattern ranging from 10° to 145° in diffraction angle has been simulated by the Pawley method applying a symmetric Pearson VII peak profile model to each peak with ten background, two peak-shift, three line-width, and two peak-shape parameters, and the Rp value of the best fit has been estimated at 4.4%.