A deconvolutional method for preprocessing powder diffraction data has been improved. The cumulants of instrumental aberration functions of Bragg-Brentano (Parrish) diffractometer calculated up to the fourth order are presented. The treatments of axial-divergence aberration and the effective spectroscopic profile of the source X-ray have been simplified from those used in previous methods. The current method has been applied to powder diffraction data collected with a Cu-target X-ray tube, used over 20 years, and a Ni-foil Kβ filter.

Four series of small parasite peaks observed in powder diffraction data recorded with a Cu-target X-ray tube and a Ni filter on the diffracted beam side in Bragg–Brentano geometry are investigated. One series of the parasite peaks is assigned to the tungsten Lα-emission. Other three types of the parasite peak series are likely to be caused by the K-emissions of Ni, but the peak locations are deviated from those predicted by the Bragg's law. An empirical formula to locate the parasite peaks and a method to remove them from observed powder diffraction data are proposed. The method is based on the whole-pattern deconvolution–convolution treatment on the transformed scale of abscissa. The parameters optimized for the diffraction data measured for Si powder has been applied on treatment of the data of LaB6 powder recorded under the same experimental conditions. It has been confirmed that the parasite peaks in the observed data can effectively be removed by the deconvolution treatment with parameters determined by a reference measurement.