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

Crystallite size values were determined by X-ray diffraction methods for 210 TiO2 (anatase) nanocrystalline powders with crystallite size from 3 nm to 35 nm. Each X-ray diffraction pattern was processed using different free and commercial software. The crystallite size calculations were performed using Scherrer equation and Warren–Averbach method. Statistical treatment and comparative assessment of the obtained results were performed for the purpose of an ascertainment of statistical significance of the obtained differences. The average absolute divergence between results obtained with using Scherrer equation does not exceed 0.36 nm for the crystallites smaller than 10 nm, 0.54 nm for the range 10–15 nm and 2.4 nm for the range > 15 nm. We have also found that increasing the analysis time improves statistics, however does not affect the calculated crystallite sizes. The values of crystallite size determined from X-ray data were in good agreement with those obtained by imaging in a transmission electron microscope.