Optimization of quantitative X-ray phase analysis by Monte Carlo methods

Abstract

Present methods for quantitative X-ray phase analysis make extensive use of multilinear regression. Practical application of these methods compels workers to make a choice among many different sets of experimental conditions such as the number, identity and relative concentration of the phases in the synthetic mixtures used for the solution of the regression problem; the number and extent of the angular regions within which X-ray intensities are to be measured; and so on. There are as yet no general criteria for this selection, and classical statistical experimental methods, even such effective ones as SIMPLEX, are very time consuming. In the present work a Monte Carlo method is proposed for optimization of the reproducibility and detection limit for a completely general quantitative X-ray phase analysis. A system of three computer programs to this end is developed and applied to X-ray phase analysis of laterites, illustrating the choice of a set of performing conditions among 20 of them.