Step size, scanning speed and shape of X-ray diffraction peak

Abstract

The influences of step size and scanning speed on the shape of a single X-ray diffraction (XRD) peak are analyzed quantitatively. For this purpose, it is assumed that XRD peak shapes are a mixture of Cauchy and Gauss curves. Six equations are established for the calculation of position, maximum intensity and full width at half-maximum (FWHM) errors caused by step size and two for the FWHM errors caused by counting statistics. The ratio of step size to FWHM is proposed as the shape-perfect coefficient of the XRD peak. From these equations and the relationship between the FWHM and the integral width of a peak based on the pseudo-Voigt function or Voigt function, three basic elements of a single symmetric XRD peak (peak position, maximum intensity and FWHM) can be refined. The optimum step size and scanning time can also be set from them.