Metrological characterization of X-ray diffraction methods at different acquisition geometries for determination of crystallite size in nano-scale materials

Crystallite size values were determined by X-ray diffraction methods for 183 powder samples. The tested size range was from a few to about several hundred nanometers. Crystallite size was calculated with direct use of the Scherrer equation, the Williamson–Hall method and the Rietveld procedure via the application of a series of commercial and free software. The results were statistically treated to estimate the significance of the difference in size resulting from these methods. We also estimated effect of acquisition conditions (Bragg–Brentano, parallel-beam geometry, step size, counting time) and data processing on the calculated crystallite size values. On the basis of the obtained results it is possible to conclude that direct use of the Scherrer equation, Williamson–Hall method and the Rietveld refinement employed by a series of software (EVA, PCW and TOPAS respectively) yield very close results for crystallite sizes less than 60 nm for parallel beam geometry and less than 100 nm for Bragg–Brentano geometry. However, we found that despite the fact that the differences between the crystallite sizes, which were calculated by various methods, are small by absolute values, they are statistically significant in some cases. The values of crystallite size determined from XRD were compared with those obtained by imaging in a transmission (TEM) and scanning electron microscopes (SEM). It was found that there was a good correlation in size only for crystallites smaller than 50 – 60 nm.