Rietveld quantification of amorphous portions with an internal standard—Mathematical consequences of the experimental approach

Abstract

The Rietveld method is increasingly used for amorphous portion determination. This article describes the quantification of amorphous portions using an internal standard in a formal mathematical way. From a set of basic assumptions and postulations, equations for the amorphous portion quantification, the optimum amount of internal standard, and the slope of the amorphous portion calculation formula were derived. With this tool set, the influence of the method principle on the analytical uncertainty is discussed. It is shown that the amount of internal standard has a strong influence on the precision of the amorphous portion determination. A poor choice can make the determination impossible, while a clever choice can enhance the precision compared to the precision of the Rietveld refinement.

Amorphous determination in calcium sulfoaluminate materials by external and internal methods

“…These were the highest values measured in this study and these are typical numbers for fly ash. Moreover, ACn deviations obtained by using the internal standard methodology are intrinsically minimised when these values are very high (Westphal et al, 2009). …”

Rietveld quantitative phase analysis of Yeelimite-containing cements

“…All details for these calculations have been already reported [32]. Furthermore, the errors associated to this approach and the optimum amount of standard has been recently discussed [61].…”

Rietveld Quantitative Phase Analysis of OPC Clinkers, Cements and Hydration Products

“…Under these conditions, the overall ACn content is derived and this is applied to the weight fractions determined in the first fit to place them in an absolute scale. The errors associated to this approach and the optimum amount of standard has been recently discussed (Westphal et al 2009). Finally, NIST standard reference material (SRM) 676a, corundum (a-Al 2 O 3 ) powder, has been certified to have a phase purity of 99.02% ± 1.11% (95% confidence interval) by RQPA against a suitable primary standard (powder silicon carefully prepared from a single crystal).…”