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. 365

Section 3.9.10.3.1. Crystallite-size issues

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

3.9.10.3.1. Crystallite-size issues

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Crystallite size is considered here as the length of a coherent scattering domain and should not be confused with the terms grain or particle size used frequently in powder diffraction to describe the macroscopic size of the components in the sample. The macroscopic size of the particle is somewhat irrelevant (as in ceramics or other solid pieces of samples) as long as the crystallites (or domains) that comprise the particle are (i) sufficiently small to ensure that there are enough crystallites contributing to the diffraction process (Smith, 1992[link]) and (ii) randomly oriented, thus ensuring a true powder-average representation of intensities. However, for large domains or crystallites this assumption is usually not fulfilled and therefore it is necessary to reduce the crystallite size by reducing the size of the particles or grains that constitute the macroscopic objects of a powder.

Most issues in sample preparation are related to crystallite size and preferred orientation of the particles in the sample holder. For QPA a representative sampling of all possible orientations of crystallites with respect to the diffraction geometry is required. Rotation of the sample improves the particle statistics, since more crystallites can satisfy the diffraction condition (Elton & Salt, 1996[link]).

Large-crystallite issues are easily detected using two-dimensional (2D) detectors, where the Debye rings show a `spotty' intensity distribution. However, most QPA measurements are performed using 0D (point) or 1D (strip) detectors. The effect of large crystallites in a 1D pattern is that a few crystallites may contribute to irregularly high intensities for selected reflections. In the diffraction pattern, this situation is usually identified by intense reflections having a sharp peak profile compared with the surrounding peaks in the pattern. Furthermore, in a Rietveld refinement this situation is manifested by large intensity differences between the observed and calculated pattern that may not be associated with a particular crystallographic direction and hence to preferred orientation. Another way of detecting inhomogeneous crystallite distributions is to measure a series of scans from the same specimen at various rotation angles and comparing the relative peak intensities. It is worth noting that the push towards ever higher resolution in both laboratory and synchrotron instruments serves to further exacerbate the crystallite-size issue. This arises from the use of beams with decreased divergence, resulting in fewer crystallites likely to satisfy the diffraction condition.

There is no simple mathematical correction for large-crystallite issues and the effect is often misinterpreted in Rietveld refinement as preferred orientation. In this case, the correction would typically involve use of several directions for March–Dollase-type functions (Dollase, 1986[link]) or an increasing order of spherical-harmonics coefficients (Ahtee et al., 1989[link]). In any case, this is an improper use of these corrections and the necessity to do so clearly points to deficiencies in the sample preparation and data-collection regime.

The best way to minimize the large-crystallite issue is to reduce the crystallite size through grinding of the sample. However, size-reduction methods need to be carefully assessed, since overgrinding can cause peak broadening due to (i) a decrease of long-range order and hence crystallite size and (ii) the introduction of microstrain (Hill & Madsen, 2002[link]). The practical effect of peak broadening is increasing peak overlap, which may complicate the phase identification. For whole-pattern-based QPA, overgrinding is not as serious as long as it does not yield nanometre-sized particles or amorphous materials. This is because the integral intensity of the peaks is preserved. It should be noted that some phases can undergo transformation to other polymorphs or decompose to other phases during grinding (Hill & Madsen, 2002[link]).

In practice, there is no generally applicable comminution strategy. For each material, a suitable milling device and grinding strategy needs to be identified. Inhomogeneous materials such as ores, concentrates and other mineralogical materials may have very different comminution properties for their constituents, leading to size fractionation during grinding. Large-crystallite issues are frequently observed for hard minerals (e.g. quartz, feldspar) while the grain size of soft minerals (e.g. talc) is reduced more rapidly.

A practical way of finding a best compromise for the milling conditions of a mixture may be the analysis of a series of samples of the same material where, for example, the grinding time is successively increased and the quantification results are compared. Fig. 3.9.17[link] shows the variation of analysed wt% with grinding time for two minerals: a stable result is eventually obtained.

[Figure 3.9.17]

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Variation of the magnetite (filled diamonds) and quartz (open squares) concentration of an iron-ore sample with grinding time. Stable conditions are obtained after about 180 s. Data courtesy ThyssenKrupp – Resource Technologies (Knorr & Bornefeld, 2013[link]).

There is a more extensive discussion of the impact of large-crystallite size on observed diffraction data (Smith, 1992[link]) and ways to minimize its effect (Elton & Salt, 1996[link]) in the published literature.

References

Ahtee, M., Nurmela, M., Suortti, P. & Järvinen, M. (1989). Correction for preferred orientation in Rietveld refinement. J. Appl. Cryst. 22, 261–268.Google Scholar
Dollase, W. A. (1986). Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Cryst. 19, 267–272.Google Scholar
Elton, N. J. & Salt, P. D. (1996). Particle statistics in quantitative X-ray diffractometry. Powder Diffr. 11, 218–229.Google Scholar
Hill, R. J. & Madsen, I. C. (2002). Structure Determination from Powder Diffraction Data, edited by W. David, K. Shankland, L. McCusker & C. Baerlocher, ch. 6, pp. 98–116. Oxford University Press.Google Scholar
Smith, D. K. (1992). Particle statistics and whole pattern methods in quantitative x-ray powder diffraction analysis. Adv. X-ray Anal. 35, 1–15.Google Scholar








































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