Data smoothing and distortion of X-ray diffraction peaks. I. Theory

A general model of smoothing-induced distortions of an X-ray diffraction (XRD) peak is derived from theoretical analyses by convoluting a Savitzky-Golay (S.-G.) polynomial filter with the Gaussian, Lorentzian and pseudo-Voigt curves. This is based on the assumption that an XRD peak consists of five basic parameters and two additional parameters. Flattening and broadening are the general effects of smoothing. No change in peak area after smoothing is a new feature revealed by this analysis. An unusual change (sharpening with narrowing first, then flattening with broadening as usual) of the peak in a short smoothing range is found for an asymmetric peak. This phenomenon is variable, being governed mainly by the degree of asymmetry of the peak and factors such as peak shifting, curve type, state of the peak top and smoothing range. Formulae describing the smoothing changes of all parameters of a peak are derived. Constants used to link these formulae are set and their properties are analysed with different functions, different states of the peak top, coefficients of shape perfection (`shape-perfect coefficients'), degrees of asymmetry and smoothing ranges.