Variance and centroid optimization in X-ray powder diffraction analysis

Line profiles of a powder diffraction pattern and the aberrations which affect the centroid and the variances of the peaks have been analyzed using the visualization in scientific computing (ViSC) systems. The constrained optimization of those aberrations has been derived from the theory developed by Wilson (1963). It allows the determination of systematic instrumental effects and gives indication of other diffraction effects related to the samples. The CuKβradiation was used to process the experimental data directly as it is comprised of only one single wavelength.