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.