# Methodology of quantitative phase analysis

• Lev S. Zevin
• Giora Kimmel
• Inez Mureinik
Chapter

## Abstract

The basic equations of quantitative phase analysis, which relate the X-ray intensity to the abundance of a phase in a specimen, were derived in Chapter 2 for various diffractometric schemes. In the forthcoming discussion, we will concentrate on Bragg-Brentano reflection focusing, since this is the most widely used diffractometric arrangement. This approach has general application, because the results and conclusions obtained can be applied to other schemes using corresponding intensity-weight fraction relationships. The relationship for the Bragg-Brentano scheme, as was first derived by Alexander and Klug (1948) [see the derivation of equation (3.11)], takes the form:
$${{I}_{{ij}}} = \frac{{{{K}_{{ij}}}\prime {{c}_{j}}}}{{{{\rho }_{j}}\mu *}} = \frac{{{{K}_{{ij}}}\prime {{c}_{j}}}}{{{{\rho }_{j}}\sum\limits_{{k = 1}}^{n} {{{\mu }_{k}}*{{c}_{k}}} }}$$
(4.1)
where cj is the weight fraction of phase j in the specimen, ρj is the density of phase j, µ* is the mass absorption coefficient of the specimen, and ck, µk* are the weight fractions and absorption coefficients, respectively, of the phases abundant in the specimen. Kij′ is a calibration constant, which is a product of several phase-related, instrument-related, and scattering-angle-related terms discussed in detail in Section 3.2. The subscripts i and j in Kij′ refer to phase j and diffraction peak i. The density of phase j, i.e., ρj—(as a constant for given phase)—may be included in the calibration constant; equation (4.1) is then simplified to:
$${{I}_{{ij}}} = \frac{{{{K}_{{ij}}}{{c}_{j}}}}{{\mu *}} = \frac{{{{K}_{{ij}}}{{c}_{j}}}}{{\sum\limits_{{k = 1}}^{n} {{{\mu }_{k}}*{{c}_{k}}} }}$$
(4.2)
where Kij = Kij′/ρj.

## Keywords

Weight Fraction Pure Phase Dope Sample Calibration Constant Powder Diffraction File
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag New York, Inc. 1995

## Authors and Affiliations

• Lev S. Zevin
• 1
• Giora Kimmel
• 2
• Inez Mureinik
• 3
1. 1.The Institutes for Applied Research and Department of Materials EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael
2. 2.Department of Materials EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael
3. 3.The Institutes for Applied ResearchBen-Gurion University of the NegevBeer-ShevaIsrael