Study the Lattice Distortion and Particle Size of One Phase of MnO by Using Fourier Analysis of X-ray Diffraction Lines

Abstract

In this study, the Fourier analysis method was used for the analysis of the X-ray diffraction pattern of MnO (111), (200), (220), (311) and (222). The particle size of each X-ray line was calculated, the particle size of the manganese oxide was then calculated. The Fourier method was also used to calculate the mean square lattice strain of the manganese oxide and the results were as follows, where the particle size is equal to 7.9563 nm and the mean square strain equal to 0.3566 × 10^-4. In order to determine the accuracy of the results of this method, other methods of analysis were used, such as the Debye - Scherrer method and Williamson–Hall method of analysis, and Modified Scherrer equation for calculating the particle size. The value of particle size and strain of these four methods was compared with the value of particle size and mean square strain of the Fourier method.

Keywords: Lattice Distortion, Particle Size, Fourier analysis, X-ray Diffraction Lines