International
Tables for
Crystallography
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, p. 344

Section 3.9.1. Introduction

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:  ian.madsen@csiro.au

3.9.1. Introduction

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The field of quantitative phase analysis (QPA) from powder diffraction data is almost as old powder diffraction itself. Debye and Scherrer first developed the method around 1916 (Debye & Scherrer, 1916[link], 1917[link]) and between 1917 and 1925 Hull (1917[link], 1919[link]) and Navias (1925[link]) were reporting studies of QPA related to the new technique. However, further developments in QPA were relatively slow, as much of the activity in X-ray diffraction (XRD) at the time was dedicated to the solution of crystal structures rather than the extraction of other information present in a powder diffraction pattern. While a small number of QPA applications continued to be published in the intervening years, it was not until the advent of scanning diffractometers around 1947 (Langford, 2004[link], Parrish, 1965[link]) and the work of Alexander and Klug in 1948 (Alexander & Klug, 1948[link]), which provided the formal methodology and a practical approach, that the field began to expand.

Since those original developments, which utilized the intensity of individual peaks or a small group of peaks in the diffraction pattern, there have been extensions to the methodology that use whole-pattern approaches. These methods operate via the summation of either (i) patterns collected from pure components or (ii) component contributions calculated from their crystal structures. There are a number of benefits accruing from the whole-pattern approaches since all reflections in the pattern, which may number in the hundreds or thousands, now contribute to the final analysis.

The mathematical basis of QPA is well established and, ideally, QPA should be a relatively straightforward science. However, there are a significant number of factors, many of them experimental, that serve to decrease the accuracy that can be obtained (Chung & Smith, 2000[link]). Some of these, such as accuracy and precision in measurement of peak position and intensity, resolution of overlapping peaks and counting statistics, relate to instrument geometry and data-collection conditions. Other sources of error derive from sample-related issues and include effects such as (i) preferred orientation (which distorts the observed relative intensities from those expected for a randomly oriented powder); (ii) crystallite size and strain broadening (leading to increased peak width and hence overlap); (iii) the grain-size effect (where there may be too few crystallites contributing to the diffraction process to ensure that a representative powder pattern can be measured);1 and (iv) microabsorption (where phases that strongly absorb the incident and diffracted beams are underestimated with respect to weakly absorbing phases). Of these, microabsorption remains the largest impediment to accurate QPA and is more pronounced in X-ray diffraction than in neutron-based studies.

While there is a very broad scope for the application of diffraction-based estimation of phase abundance, the perceived difficulty involved in developing and using these methods often deters non-specialist users. Consequently, they may resort to other, non-diffraction, material characterization techniques that are more readily implemented.

Analytical techniques for most of the 92 naturally occurring elements are generally well established and, in many cases, the subject of internationally accepted standards. However, the physical properties of minerals and materials formed by these elements, and the manner in which they react, is not solely dependent on their chemical composition but also on how the constituent elements are arranged; that is, their crystal structures. This finite number of known elements combines in an almost infinite array within the 230 crystallographic space groups. Further variability is induced by factors such as solid solution, degree of crystallinity and morphology, thus making QPA by diffraction methods considerably more difficult to implement.

In industry, many manufacturing or processing lines are controlled by measurement of elemental composition alone, simply because these values can be readily obtained to a high degree of accuracy and precision. For example, a plant extracting Cu from an ore body might measure the Cu content of the feed ore and the concentrate, and the plant conditions are optimized based on efficiency of extraction. However, if the mineralogical form of the Cu changes in the feed, then it may not behave in the same manner during grinding, flotation and density separation, and this will affect the recovery. Frequently, where knowledge of the mineralogy or phase abundance is actually used in plant optimization and control, it is derived from bulk or micro-compositional analysis rather than being measured directly. This is often achieved by normative calculation, where the results of element composition analysis are assigned to specific phases based on an assumed knowledge of individual phase composition. Further details of this approach can be found in Chapter 7.7[link] .

In materials science, new compounds are being synthesized at a rapidly increasing rate with techniques such as high-throughput synthesis capable of generating hundreds of new variants in a single experiment. Such techniques are being used in fields ranging from drug discovery, catalyst synthesis and new metal alloy design. The properties of these materials, and their suitability for their designed purpose, are not only dependent on their structural form but, for multiphase materials, on the amount of each component present. In this case, accurate, or at the very least reproducible, QPA is crucial to the screening process.

This chapter focuses on the application of QPA techniques for the extraction of phase abundance from diffraction data. While there is extensive coverage of the QPA methodology in other texts (Klug & Alexander, 1974[link]; Smith et al., 1987[link]; Snyder & Bish, 1989[link]; Zevin & Kimmel, 1995[link]), some of the more commonly used approaches will be described here along with examples of their use in practical applications.

References

Alexander, L. E. & Klug, H. P. (1948). Basic aspects of X-ray absorption in quantitative diffraction analysis of powder mixtures. Anal. Chem. 20, 886–889.Google Scholar
Chung, F. H. & Smith, D. K. (2000). Industrial Applications of X-ray Diffraction, edited by F. H. Chung & D. K. Smith, ch. 1, pp. 3–10, and ch. 2, pp. 13–32. New York: Marcel Dekker.Google Scholar
Debye, P. & Scherrer, P. (1916). Interferenzen an regellos orientierten Teilchen im Röntgenlicht Phys. Z. 17, 277–283.Google Scholar
Debye, P. & Scherrer, P. (1917). X-ray interference produced by irregularly oriented particles: Constitution of graphite and amorphous C. Phys. Z. 18, 291–301.Google Scholar
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Navias, L. (1925). Quantitative determination of the development of mullite in fired clays by an X-ray method. J. Am. Ceram. Soc. 8, 296–302.Google Scholar
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Smith, D. K., Johnson, G. G., Scheible, A., Wims, A. M., Johnson, J. L. & Ullmann, G. (1987). Quantitative X-ray powder diffraction method using the full diffraction pattern. Powder Diffr. 2, 73–77.Google Scholar
Snyder, R. L. & Bish, D. L. (1989). In Modern Powder Diffraction, edited by D. L. Bish & J. E. Post, pp. 101–142. Washington DC: Mineralogical Society of America.Google Scholar
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