Error Estimation in XRD Crystallite Size Measurements

Abstract

Th effect of diffraction peak broadening is commonly used as a convenient tool for the grain size determination of fine crystalline powders. Quantitative analysis of the peak profile also allows the size distribution to be determined, providing complete Grain Size Distribution (GSD) curve. Among other things, the accuracy of the crystallite size (or GSD) measurements depends on the level of noise present in the experimental diffraction patterns. Particularly, GSD analysis relies on the resolution of two strongly correlated parameters: the average grain size and the dispersion of grain sizes σ. Both influence the diffraction profile being fitted in a similar way. Resolution of these quantities is then a very demanding task in terms of quality of the the experimental data. In this paper possible errors in GSD analysis arising from experimental noise present in diffraction patterns are estimated. It will be shown, that the dispersion of grain sizes a is more sensitive to the noise than the size . Photon flux (X-ray tube/synchrotron) needed for reliable evaluation of GSD will be estimated and a practical directions on optimal experimental setup given. A simple experssion for the standard deviations of the GSD parameters (i.e. dispersion of average grain size and dispersion of dispersion of the grain sizes) will be given as a function of the experimental noise level.