Detectability of two overlapping Pearson VII peaks in simulated X-ray diffraction patterns

This article presents mathematical methods for calculating the shoulder limit and detection limit for two merging Pearson VII functions. Results are given for the particular case of the modified Lorentzian (n = 2). The modified Marquardt algorithm of the data reduction program used by the authors is briefly discussed. Synthetic diffraction patterns are used to determine a practical detection limit for this program that compares favourably with the theoretical detection limit.