Determination of Crystallite Size with the X-Ray Spectrometer

TLDR

The Scherrer crystallite size equation’s accuracy is limited by uncertainty in β, and existing methods for estimating β from Debye‑Scherrer line breadths are not generally applicable to the x‑ray spectrometer. The study develops a correction curve for β by applying convolution analysis to account for geometrical broadening effects on the pure diffraction contour. The correction procedure’s reliability is verified using Stokes’ direct Fourier transform to recover the pure diffraction contour, and the authors outline procedures for size determination across different ranges. The paper presents suggestive procedures for crystallite size determination with the x‑ray spectrometer, supported by several illustrative examples.

Abstract

The accuracy of the Scherrer crystallite size equation is limited in part by the uncertainty in β, the experimentally deduced pure diffraction broadening. Currently used procedures for estimating β from the observed breadth of a Debye-Scherrer line are not, in general, applicable to the x-ray spectrometer. By making use of a scheme of convolution analysis for analyzing the effect of geometrical factors in broadening the pure diffraction contour, a correction curve is developed for determining β from the experimentally measured line breadths b and B (Jones' notation). The degree of reliability of this correction procedure is ascertained by applying Stokes' direct Fourier transform procedure for determining the form of the pure diffraction contour free of instrumental effects. Suggestive procedures are given for crystallite size determination with the x-ray spectrometer in different size ranges, and several examples are described.