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 (Si 3 N 4 ) 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.