Modified Scherrer equation to calculate crystal size by XRD with high accuracy, examples Fe2O3, TiO2 and V2O5

Abstract

A key parameter in the analysis of compounds and the study of their physical, chemical, and mechanical properties is the knowledge of the crystal size. There are two common techniques for determining this size: transmission electron microscopy (TEM) and Brunauer-Emmett-Teller theory (BET). These methods are time-consuming and expensive; thus, the calculation of this size by X-ray diffraction (XRD) is proposed. There are several methods for calculating the crystal size by X-ray diffraction, but not all peaks were considered and the errors were very large. In this study, the Modified Scherrer method is practically explained, and three important rules for obtaining crystal size values with high accuracy are introduced and applied. For better understanding, this study explains the Modified Scherrer method for iron oxide (Fe₂O₃), titanium oxide (TiO₂) and vanadium oxide (V₂O₅) powders as examples. Crystal size values were calculated using the modified Scherrer method for Fe₂O₃, TiO₂, and V₂O₅ as 30.94, 16.57, and 24.30 nm, respectively. Furthermore, the extracted crystal size values of ∼ 31, 18 and 30 nm for Fe₂O₃, TiO₂, and V₂O₅ were tandemly recorded by TEM. Moreover, the crystal size values for Fe₂O₃, TiO₂, and V₂O₅ were calculated to 32.96, 15.87 and 16.66 nm by BET tandemly. The results show that the Modified Scherrer method has high accuracy and agreement with the analyses of TEM and BET. Thus, this method is proposed for calculating each crystalline compound as it has high accuracy and XRD analysis is available and cheaper.