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

Powder Diffraction ◽

10.1017/s0885715621000373 ◽

2021 ◽

pp. 1-10

Author(s):

Hideo Toraya

Keyword(s):

Chemical Composition ◽

Phase Analysis ◽

Technical Problem ◽

Theoretical Background ◽

Unit Weight ◽

Quantitative Phase Analysis ◽

Scattered Intensity ◽

Direct Derivation ◽

Quantitative Phase ◽

Composition Data

The direct derivation (DD) method is a technique for quantitative phase analysis (QPA). It can be characterized by the use of the total sums of scattered/diffracted intensities from individual components as the observed data. The crystal structure parameters are required when we calculate the intensities of reflections or diffraction patterns. Intensity can, however, be calculated only with the chemical composition data if it is not of individual reflections but of a total sum of diffracted/scattered intensities for that material. Furthermore, it can be given in a form of the scattered intensity per unit weight. Therefore, we can calculate the weight proportion of a component material by dividing the total sum of observed scattered/diffracted intensities by the scattered intensity per unit weight. The chemical composition data of samples under investigation are known in almost all cases at the stage of QPA. Thus, a technical problem is how to separate the observed diffraction pattern of a mixture into individual component patterns. Various pattern decomposition techniques currently available can be used for separating the pattern of a mixture. In this report, the theoretical background of the DD method and various techniques for pattern decompositions are reviewed along with the examples of applications.

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Quantitative phase analysis of amorphous components in mixtures by using the direct-derivation method

Journal of Applied Crystallography ◽

10.1107/s1600576718016394 ◽

2019 ◽

Vol 52 (1) ◽

pp. 13-22 ◽

Cited By ~ 4

Author(s):

Hideo Toraya ◽

Kazuhiko Omote

Keyword(s):

Phase Analysis ◽

Periodic Structures ◽

Amorphous Material ◽

Peak Height ◽

Quantitative Phase Analysis ◽

Chemical Formula ◽

Direct Derivation ◽

Patterson Function ◽

Formula One ◽

Quantitative Phase

The direct-derivation (DD) method is a new technique for quantitative phase analysis (QPA) [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. A simple equation, called the intensity–composition (IC) formula, is used to derive weight fractions of individual components (w k ; k = 1–K) in a mixture. Two kinds of parameters are required as input data of the formula. One is the parameter S k , which is the sum of observed powder diffraction intensities for each component, measured in a wide 2θ range and corrected for the Lorentz–polarization factor. The other is the parameter a k −1, defined by a k −1 = M k −1∑nik 2, where M k is the chemical formula weight and n ik is the number of electrons belonging to the ith atom in the chemical formula unit. The parameter a k −1 was originally derived by using the relationship between the peak height and the integrated value of the peak at the origin of the Patterson function, implicitly assuming the presence of periodic structures like crystals. In this study, the formula has been derived theoretically from a general assemblage of atoms resembling amorphous material, and the same expression as the original formula has been obtained. The physical meaning of a k −1, which represents `the total scattering power per chemical formula weight', has been reconfirmed in the present formulation. The IC formula has been tested experimentally by using two-, three- and four-component mixtures containing SiO2 or GeO2 glass powder. In the whole-powder-pattern fitting (WPPF) procedure, incorporated into the DD method, a background-subtracted halo pattern is directly fitted as one of the components in the mixture, together with profile models for crystalline components. In the WPPF, an interaction was observed between the parameters of the background function (BGF) and the parameter for scaling the halo pattern, and this resulted in systematic deviations of w k from weighed values. The deviations were ≤0.7% in the case of binary mixtures when the BGF was fixed at the correct background height, supporting the hypothesis that the DD method is applicable to the QPA of amorphous components.

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A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases. Corrigendum

Journal of Applied Crystallography ◽

10.1107/s160057671700365x ◽

2017 ◽

Vol 50 (2) ◽

pp. 665-665 ◽

Cited By ~ 3

Author(s):

Hideo Toraya

Keyword(s):

Phase Analysis ◽

Powder Diffraction ◽

New Method ◽

Quantitative Phase Analysis ◽

Chemical Compositions ◽

Direct Derivation ◽

X Ray ◽

Quantitative Phase ◽

Integrated Intensities

Erroneous equations in the paper by Toraya [J. Appl. Cryst. (2016), 49, 1508–1516] are corrected.

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Quantitative phase analysis using observed integrated intensities and chemical composition data of individual crystalline phases: quantification of materials with indefinite chemical compositions

Journal of Applied Crystallography ◽

10.1107/s1600576717005052 ◽

2017 ◽

Vol 50 (3) ◽

pp. 820-829 ◽

Cited By ~ 5

Author(s):

Hideo Toraya

Keyword(s):

Chemical Composition ◽

Phase Analysis ◽

Target Component ◽

Quantitative Phase Analysis ◽

Chemical Compositions ◽

Chemical Formula ◽

Crystalline Phases ◽

Quantitative Phase ◽

Two Parameters ◽

Integrated Intensities

In a previous report, a new method for quantitative phase analysis (QPA) of multi-component mixtures using a conventional X-ray powder diffractometer was proposed. The formula for deriving weight fractions of individual crystalline phases presented therein includes sets of observed integrated intensities measured in a wide 2\theta range, chemical formula weights and sums of squared numbers of electrons belonging to atoms in respective chemical formula units [Toraya (2016).J. Appl. Cryst.49, 1508–1516]. The latter two parameters required to perform QPA could be calculated from only the information of chemical formulae of individual phases. In the present study, these two parameters are replaced with a single parameter in the form new parameter = (chemical formula weight)/(sum of squared numbers of electrons). As will be expected from this definition, the parameter has nearly equal values for groups of materials consisting of similar kinds of atoms, and its value becomes identical for polytypes or polymorphs having the same chemical composition. That characteristic of this parameter makes it possible to estimate the parameter value not only directly from the chemical composition of the target material itself but also from database-stored chemical analysis data sorted on the basis of mineral or chemical composition. The parameter value is also hardly changed as a result of small compositional variations of the target component material. Therefore, the present method can be applied to QPA of materials not only of definite chemical compositions but also of indefinite chemical compositions without degrading the accuracy of the analysis. This is expected to widen the application to QPA of, for example, natural products containing many kinds of trace elements, industrial materials with complex substitutional replacement of atoms, nonstoichiometric compoundsetc. The theory and some examples of applications are presented. A procedure for quantifying unknown material is also proposed.

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