The influence of X-ray diffraction pattern angular range on Rietveld refinement results used for quantitative analysis, crystallite size calculation and unit-cell parameter refinement

Abstract

This article reports a detailed examination of the effect of the magnitude of the angular range of an X-ray diffraction (XRD) pattern on the Rietveld refinement results used in quantitative phase analysis and quality assurance/quality control applications. XRD patterns from 14 different samples (artificial mixtures, and inorganic and organic materials with nano- and submicrometre crystallite sizes) were recorded in 2θ interval from 5–10 to 120°. All XRD patterns were processed using Rietveld refinement. The magnitude of the workable angular range was gradually increased, and thereby the number of peaks used in Rietveld refinement was also increased, step by step. Three XRD patterns simulated using CIFs were processed in the same way. Analysis of the results obtained indicated that the magnitude of the angular range chosen for Rietveld refinement does not significantly affect the calculated values of unit-cell parameters, crystallite sizes and percentage of phases. The values of unit-cell parameters obtained for different angular ranges diverge by 10−4 Å (rarely by 10−3 Å), that is about 10−2% in relative numbers. The average difference between the calculated and actual phase percentage in artificial mixtures was 1.2%. The maximal difference for the crystallite size did not exceed 0.47, 5.2 and 7.7 nm at crystallite sizes lower than 20, 50 and 120 nm, respectively. It has been established that these differences are statistically insignificant.