Exact and approximate mathematical models for the effects of sample transparency on the powder diffraction intensity data are examined. Application of the formula based on the first-order approximation about the deviation angle is justified for realistic measurement and computing systems. The effects of sample transparency are expressed by double convolution formulas applying two different scale transforms, including three parameters, goniometer radius R, penetration depth μ−1, and thickness of the sample t. The deconvolutional treatment automatically recovers the lost intensity and corrects the peak shift and asymmetric deformation of peak profile caused by the sample transparency.

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.

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%.

A simple procedure was devised for the preparation of a standard KCl powder to be used for the experimental determination of the instrumental profile in the Bragg–Brentano geometry. The standard was tested on several diffractometers, and narrow Bragg reflections in the range 28°–132° were recorded adopting various experimental conditions. Profiles were modeled with analytical functions, to describe the trend of width and shape of the instrumental profile as a function of the diffraction angle. Some indications were given to perform reliable profile fitting and line broadening analysis; a high resolution setup, obtained by employing narrow slits, large goniometer radius, and a monochromator in the diffracted beam, gives narrow reflections, even though the intensity of the diffracted beam is considerably reduced. The choice of these experimental conditions, which can be achieved using the majority of the commercial instruments, leads to symmetrical profiles, even at relatively low angle (2Θ=28°), which are highly recommended for reliable profile fitting and line broadening analysis.