A practical approach to the direct-derivation method for QPA: use of observed powder patterns of individual components without background subtraction in whole-powder-pattern fitting

The direct-derivation (DD) method for quantitative phase analysis (QPA) can be used to derive weight fractions of individual phases in a mixture from the sums of observed intensities along with the chemical composition data [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. The whole-powder-pattern fitting (WPPF) technique can be used as one of the tools for deriving the observed intensities of individual phases. In WPPF, the observed powder pattern of a single-phase sample after background (BG) subtraction can be used as the fitting function in combination with the fitting functions widely used in Pawley and Rietveld refinements. The direct fitting of the observed pattern is a very useful technique when the target component is a low-crystallinity or amorphous material [Toraya (2018). J. Appl. Cryst. 51, 446–455]. Technical problems in utilizing the BG-subtracted pattern are the uncertainty associated with the determination of BG height and the parameter interaction between the BG function (BGF) and the BG-subtracted pattern in the least-squares fit. In this study, a practical approach in which single-phase observed patterns are used for the direct fitting without subtracting their BG intensities is proposed. In QPA, the contribution of BG intensities can be neutralized by converting the sum of BG-included intensities into the sum of BG-subtracted intensities by multiplying by a conversion factor. When the magnitudes of the conversion factors are almost identical for all components, they can be canceled out under the normalization condition in deriving weight fractions, and they are not required in QPA. The magnitude of the conversion factor for each component can be determined by one of two experimental techniques: using a single-phase powder of the target component or a mixture containing the target component in a known weight ratio. The theoretical basis of the present procedure is given, and the procedure is experimentally verified. In this procedure, the interaction between the BGF and the BG-included observed pattern is negligibly small. Least-squares fitting with a few adjustable parameters is very fast and stable. Accurate QPA could be conducted, as indicated by the average deviation of 0.05% from weighed values in QPA of α-Al2O3 + γ-Al2O3 mixtures with five different weight ratios and 0.4% in QPA of an α-SiO2 + SiO2 glass mixture