Accurate and time-saving quantification of a component present in a very small amount in a mixture by the direct derivation method

Abstract

In quantitative phase analysis (QPA) using the direct derivation (DD) method, total sums of diffracted/scattered intensities for individual components are used as observed quantities. Fluctuation in their relative intensity ratios induces errors in derived weight fractions, and it ought to be suppressed for improving the accuracy in QPA, in particular, of a component that is present in a small amount. The fluctuation is primarily caused by the termination in summing/integrating diffracted/scattered intensities on the high-angle side. It is usually associated with changing the 2θ range in whole-powder-pattern fitting (WPPF) used to decompose the mixture pattern into individual component patterns. In this study, calculated patterns for individual components, fitted in WPPF, are normalized so as to give the unit area when they are separately integrated over their definition ranges in 2θ. The termination effect could effectively be reduced by extending the definition range to a certain high-angle limit. Scale parameters for adjusting the calculated patterns become non-fluctuating against the change of the 2θ range in WPPF. Thus, the time spent for intensity data collection of mixture patterns can be reduced by shortening the scan range. The present procedure has been tested with binary mixtures containing small amounts of crystalline phases of 0.02–0.4 wt%. QPA could be conducted with errors of 0.01–0.03 wt% for both inorganic materials chosen as ideal samples and pharmaceutical materials as practical ones. QPA of an amorphous component present in a small amount is also discussed.

Review of the direct derivation method: quantitative phase analysis with observed intensities and chemical composition data

“…The QPA of crystalline phases present in a very small amount, say <0.5 wt%, in mixtures is a very important issue in quality control of industrial products as well as in the research and development. The last example is the QPA of mixtures of (a) α-SiO 2 + α-Al 2 O 3 (SA) and (b) glass-SiO 2 + α-SiO 2 (GS) in five different weight ratios (Table VII), where the second components represent minor phases (Toraya, 2020). As shown in Figure 4, the presence of crystalline phases as minor components can be discerned as tiny peaks in both mixtures.…”

“…As was described above, the constant optical setting should be kept in measuring powder diffraction patterns of both target mixtures and single-phase components to be used as the type-C and/or the type-C 2 functions. When the type-C/C 2 functions were used, the shift of a whole pattern, y(2u) ′ k or y(2u) S k , along the 2θ-axis, associated primarily with the shift in the height of a specimen surface, can be corrected by adjusting the parameter, Δ2θ k (Toraya, 2018) [δ 2θk is a different symbol (Toraya, 2019(Toraya, , 2020]. Regarding the 2θ-range for scanning, [2θ L , 2θ H ], the 2θ L should include the reflection at the lowest angle.…”

“…The results of QPA are given in Table VI, giving errors of just 1.2 wt% in their average. (Toraya, 2020).…”

“…As will be described later, the DD method itself is based on a simple principle. There are, however, various ways to obtain the total sums of diffracted/scattered intensities from the target mixture pattern, and they have been reported in several papers (Toraya, 2016(Toraya, , 2017(Toraya, , 2018(Toraya, , 2019(Toraya, , 2020. In this report, it is tried to review comprehensively the theoretical background of the DD method and the techniques for the pattern decomposition.…”

“…If we define the normalized fitting function by extending the [2θ L , 2θ H ] to the high-angle limit such as 100 • or 120 • (for CuKα radiation), the 2θ-range in WPPF for target mixture patterns can be much shortened to, say, 60 • . Therefore, we can save the time spent for intensity data collection without losing the accuracy in derived weight fractions (Toraya, 2020).…”