The approximation of symmetric X-ray peaks by Pearson type VII distributions

Abstract

Some symmetric X-ray diffraction peaks can be approximated in shape by Pearson type VII distributions: y(x) = y_0[1 + (x - \bar x)^{2}/ma^2]^{-m}.This distribution is Cauchy for m = 1, modified Lorentzian for m = 2, and Gaussian for m = ∞. Some properties of the distribution and some illustrative applications are presented.