Quantitative phase analysis of α- and β-silicon nitrides. I. Estimation of errors

Errors in the quantitative phase analysis (QPA) of α- and β-silicon nitrides (Si₃N₄) using the mean normalized intensity (MNI) method and the Rietveld method have been estimated by theory and experiments. A total error for a weight fraction (w) in a binary system can be expressed in the form E(w) = w(1 − w)S, where S is the quadratic sum of statistical and systematic errors. Random errors associated with counting statistics for integrated intensities in the MNI method are below 0.1∼0.2 wt% if the studied reflections have average peak heights of more than ∼1000 counts. Such errors will become approximately twice as large if peak-height intensities are used. The error associated with particle statistics in the studied samples was smaller than the counting-statistics error. Among various sources of systematic errors examined, incorrect choice of constrained/unconstrained full width at half-maximum (FWHM) parameters gave the largest error. The choice of the background function had little influence on the QPA, whereas the choice of the profile function had a large influence. Truncation errors in profile function calculations and the 2θ range of the observed data are below ±0.1 wt% when appropriate criteria are applied. Systematic errors in the measurement of peak-height intensity arise primarily from the overestimation of intensities of weak peaks that overlap the tails of strong peaks, as well as from line broadening of β-phase reflections in the studied samples. Errors caused by ignoring the difference in density between the two phases were negligibly small. Estimated errors of the methods followed the order: the MNI method using peak-height intensities < the MNI method using integrated intensities ≃ the Rietveld method.