Some considerations related to the use of the Scherrer equation in powder X-ray diffraction as applied to heterogeneous catalysts

Abstract

This short overview summarises some of the basic considerations which should be undertaken when the Scherrer equation is applied to reflection widths in X-ray diffraction patterns of heterogeneous catalysts in order to extract meaningful information. Frequently, little account has been taken of the apparent complications arising from the presence of microstructural strain and disorder such as that which can be introduced upon doping or of anisotropic effects and such considerations are highlighted. Graphical abstract Scanning electron micrograph showing the highly anisotropic nature of biogenic iron oxide found in a natural iron ochre source.

Catalytic oxidation of SO2 by novel Mn/copper slag nanocatalyst and optimization by Box-Behnken design

“…This indicates that the structure of copper slag is unaltered during the impregnation process. The average crystallite size of the Mn/CS was calculated applying the Debye-Scherer equation [18,19]:…”

High Performance Inverted Planar MAPbI3 Perovskite Solar Cells with a Simple Annealing Process

“…According to the Scherrer equation:FWHM ¼ kl ð Þ=ðDcosq), in which k is a shape constant, λ is the wavelength of the X-ray source, D is the crystallite size and θ is the Bragg angle, the smaller FWHM indicates the better crystalline quality of the perovskite layer. [56,57] So the MAPbI 3 perovskite layers annealing at 90°C or 100°C present the best morphology and crystalline quality. This result is consistent with the phenomenon of grain size shown in the Figure 2 (a-f).…”

Qualitative Approaches Towards Useful Photocatalytic Materials

“…X-ray diffraction (XRD) is the most common core technique for phase identification and structural information of materials. Several issues have been raised with regards to the limitations of XRD analysis and the interpretation of XRD patterns (Ohtani, 2010 ; Hargreaves, 2016 ). The consideration of a material as crystalline from inspection of diffraction patterns—based on the sharpness of diffraction peaks—is venturous, and account of amorphous parts and density of crystalline defects is largely excluded.…”