Application of Numerical Method and Statistical Analysis in the Integrated Intensity Calculation of the Peaks from the X-Ray Diffraction (XRD) Pattern of α-Iron

Abstract

The aim of this work is to analyze the error of the calculated integrated intensity of the x-ray peaks of a-iron (BCC-Fe) powder from x-ray diffraction (XRD) pattern by using the numerical method and the statistical analysis. The a-Fe powder was characterized by the x-ray diffractometer using step scan mode, step sizes 0.03o 2q and 0.05o 2q, and preset times from 0.1 to 3.5 s. The integrated intensity () of an x-ray peak and its error () were calculated using numerical method. The correlation between the relative error () and the preset time or step size were analyzed by the statistical analysis methods which are linear regression and statistical hypothesis testing. The results from the statistical analysis at significance level of 0.05 show that the relative error () correlate with x = preset time or integrated intensity by when a1 and a2 are the positive constants. From the mathematical model, for this work, the step size does not affect the relative error. However, the increasing of preset time reduces relative error on integrated intensity calculation. To minimize the error on XRD analysis, the preset time should be greater than one second. Moreover, on a XRD pattern, the lower integrated intensity peak has the higher relative error.