A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases

Abstract

A new method for the quantitative phase analysis of multi-component polycrystalline materials using the X-ray powder diffraction technique is proposed. A formula for calculating weight fractions of individual crystalline phases has been derived from the intensity formula for powder diffraction in Bragg–Brentano geometry. The integrated intensity of a diffraction line is proportional to the volume fraction of a relevant crystalline phase in an irradiated sample, and the volume fraction, when it is multiplied with the chemical formula weight, can be related to the weight fraction. The structure-factor-related quantity in the intensity formula, when it is summed in an adequate 2θ range, can be replaced with the sum of squared numbers of electrons belonging to composing atoms in the chemical formula. Unit-cell volumes and the number of chemical formula units are all cancelled out in the formula. Therefore, the formula requires only single-measurement integrated intensity datasets for the individual phases and their chemical compositions. No standard reference material, reference intensity ratio or crystal structure parameter is required. A new procedure for partitioning the intensities of unresolved overlapped diffraction lines has also been proposed. It is an iterative procedure which starts from derived weight fractions, converts the weight fractions to volume fractions by utilizing additional information on material densities, and then partitions the intensities in proportion to the volume fractions. Use of the Pawley pattern decomposition method provides more accurate intensity datasets than the individual profile fitting technique, and it expands the applicability of the present method to more complex powder diffraction patterns. Test results using weighed mixture samples showed that the accuracy, evaluated by the root-mean-square error, is comparable to that obtained by Rietveld quantitative phase analysis.