MONTE CARLO ERROR SIMULATION APPLIED TO CALIBRATON-FREE X-RAY DIFFRACTION PHASE ANALYSIS.

A series of linear equations relating diffracted X-ray intensities, weight fractions and quantitation factors coupled with mass balance relationships can be solved for the unknown weight fractions and factors. Uncertainties associated with the measured X-ray intensities, owing to counting of random X-ray quanta, are used to estimate the errors in the calculated parameters utilizing a Monte Carlo simulation. The Monte Carlo approach can be generalized and applied to any quantitative X-ray diffraction phase analysis method. Two examples utilizing mixtures of CaCO//3, Fe//2O//3 and CaF//2 with an alpha - SiO//2 (quartz) internal standard illustrate the quantitative method and corresponding error analysis.