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

Abstract

Errors in the quantitative phase analysis (QPA) ofand -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 À 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 re¯ections 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 in¯uence on the QPA, whereas the choice of the pro®le function had a large in¯uence. Truncation errors in pro®le function calculations and the 2 range of the observed data are below AE0.1 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 -phase re¯ections 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 9 the Rietveld method.

Atomic-scale assessment of the crystallization onset in silicon carbonitride

“…[31][32][33][34] To our best knowledge, the observed ␣-Si 3 N 4 -like nanoclusters are the smallest in size reported so far for silicon nitride-based materials. Thus, a volume of the nano-clusters with a diameter of 0.8 nm corresponds to that of one unit cell of ␣-Si 3 N 4 or Si 12 N 18 , 35,36 i.e. they contain only 12 Si atoms; the larger clusters (1.5 and 2.1 nm) consist consequently of 6 and 19 unit cells, respectively (i.e., Si 72 N 108 and Si 228 N 342 , respectively).…”

Quantitative phase analysis of α- and β-silicon nitrides. II. Round robins

“…During the three-year investigation, a theoretical study was required in order to evaluate the various kinds of errors involved in the QPA of silicon nitrides using the MNI method and the Rietveld method. Its results are described in part I (Toraya, 1999). The RR results are reported in this paper (part II).…”

“…Therefore, a ranking of the methods with respect to the dif®culty of these methods was in the order of the MNI method using peak-height intensities, the MNI method using integrated intensities obtained by pro®le ®tting, followed by the Rietveld method. The accuracy and the precision of these methods were, however, found to follow the reverse order (Toraya, 1999).…”

Total oxidation of methane over Pd catalysts supported on silicon nitrideInfluence of support nature

“…This straight forward method was preferred to more accurate methods than the mean normalized intensity method or the Rietveld full pattern fitting [21] because it is easier to implement. The ratio of concentrations of two phases ␣ and ␤ is proportional to the ratio of diffracted intensities…”