Data smoothing and distortion of X-ray diffraction peaks. II. Application

Based on the analysis of geometric relations, it is found that the amplitude of the distortion of the full width at half-maximum (FWHM) of a peak after smoothing is the largest among the distortions of the seven parameters of a peak: maximum intensity, FWHM, shape, asymmetry, integral intensity, peak position and integral width. Hence the FWHM distortion is used as a criterion of smoothing. The 1% and 5% error limits of smoothing are calculated. Quadratic and quartic polynomial Savitzky-Golay filters are compared. Aberrations of an X-ray diffraction (XRD) peak caused by using double, matched, 1.5 and 0.7 FWHM filters are described in more detail by means of the analyses of internal and external factors. It is found that the smoothing-induced distortions of an actual XRD peak trend towards those of ideal curves. The distortions are classified according to three types of peak. A possible method to obtain the actual peak parameters, called `system smoothing refinement', is presented.