Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.9, pp. 344-345

Section 3.9.2. Phase analysis

I. C. Madsen,a* N. V. Y. Scarlett,a R. Kleebergb and K. Knorrc

aCSIRO Mineral Resources, Private Bag 10, Clayton South 3169, Victoria, Australia,bTU Bergakademie Freiberg, Institut für Mineralogie, Brennhausgasse 14, Freiberg, D-09596, Germany, and cBruker AXS GmbH, Oestliche Rheinbrückenstr. 49, 76187 Karlsruhe, Germany
Correspondence e-mail:

3.9.2. Phase analysis

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There are a number of traditional methods for the estimation of phase abundance in multiphase materials (Zevin & Kimmel, 1995[link]). In summary, these can be divided into two groups:

  • (1) Indirect methods – these are usually based on the measurement of total chemical composition, which is then apportioned according to an assumed composition for each phase. A very widely used form of this normative calculation approach is the Bogue method (Bogue, 1929[link]) for the quant­itative estimation of Portland cement phases. The limitations in this approach arise when the actual compositions of in­dividual phases vary from those assumed in the calculation. This frequently occurs in the cement industry, where variance in local materials and production conditions can affect detailed phase compositions. Normative calculation has the potential to be unstable when a number of phases in the mixture have similar chemical composition and it cannot be used at all for the limiting case of polymorphs that have identical chemical composition.

  • (2) Direct methods – these are based on a property that is specific to phases of interest in the sample. These methods are often not generally applicable to the entire sample, but are useful in estimating abundances of selected components. Examples include:

    • (a) Magnetic susceptibility – this is applicable to samples in which component phases have different magnetic properties. The magnetic component can be separated and weighed to determine its weight fraction in the starting material. This approach assumes that the magnetic phase is well separated from non-magnetic phases and accuracy will be reduced when there is a fine inseparable intergrowth of magnetic and non-magnetic components.

    • (b) Selective dissolution – where the rate and extent of dissolution can be phase dependent, and the weight fraction of the residue is used to determine the fractions of soluble and insoluble components.

    • (c) Density – involves the physical separation of phases with different densities. As with magnetic separation, this approach assumes that the phase of interest is well separated from other phases.

    • (d) Image analysis – optical microscopy using thin sections is still frequently used for the analysis of mineralogical samples. Thin sections can be time consuming to prepare and analyse, and the observations can be highly subjective depending on the analyst's experience. While automated image analysis of optical and electron-beam images brings more consistency to the estimation of phase abundance, issues in stereology may still affect the determined phase abundances.

    • (e) Thermal analysis – where the magnitude of endo- and exothermic features during phase transitions are proportional to the amount of the phases present. This can be effective for well known and characterized phases, but is less useful for new phases or complex multiphase samples where there may be significant overlap in the features in the observed patterns. There may also be difficulty in distinguishing features related to individual minerals, for example H2O evolution from co-existing hydrated minerals.

    • (f) Infrared (IR) techniques – these are gaining in popularity, especially in mineral exploration environments because of their portability, speed and ability to measure directly from a cleaned drill core or section. However, because the IR beam only penetrates 1–2 µm into the sample, it is a surface-analysis technique providing a semi-quantitative analysis at best. To work effectively, the method needs to be calibrated using other techniques such as diffraction-based phase analysis.

    • (g) Powder diffraction may be included in the direct-methods category, as it distinguishes and quantifies phases on the basis of their unique crystal structures, giving the technique broad applicability for crystalline materials.

Quantification from powder diffraction data is reliant on determination of the contribution to the final pattern of each component phase in a mixture. Commonly used methods can be divided into two distinct groups:

  • (1) The traditional `single-peak' methods, which rely on the measurement of the intensity of a peak, or group of peaks, for each phase of interest and assumes that the intensity of these peaks is representative of the abundance of the individual phases. This is often not the case because of peak overlap and phase-dependent factors, such as preferred orientation and microabsorption, which affect the relative observed intensities.

  • (2) Whole-pattern methods, which rely on the comparison of observed diffraction data over a wide range of 2θ with a calculated pattern formed from the summation of individual phase components which have either been (i) measured from pure phase samples, or (ii) calculated from crystal-structure information.


Bogue, R. H. (1929). Calculation of the compounds in Portland cement. Ind. Eng. Chem. Anal. Ed. 1, 192–197.Google Scholar
Zevin, L. S. & Kimmel, G. (1995). Quantitative X-ray Diffractometry. Springer-Verlag New York, Inc.Google Scholar

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