Mineralogical Analysis of Bayer Materials - Rietveld or Not Rietveld

Gerald Roach and Nicholas Pearson

Research and Development

Alcoa of Australia Limited

Kwinana, Western Australia


Quantitative Rietveld x-ray diffraction analysis of Bayer materials is fraught with complications that preclude its use as a "black box" tool. The advent of fast and powerful personal computers has made the method widely available. The Rietveld method was originally developed for refinement of crystal structures using neutron diffraction data, but has been extended to quantitative analysis and x-ray powder diffraction data. This has raised many new problems. Equipment suppliers and others were quick to promote the technique without recognising and acknowledging its limitations. Bayer materials such as bauxite and smelter grade alumina present many issues that must be carefully dealt with to ensure that sensible results are obtained. Careful selection of analytical conditions is essential. Analysis of bauxites requires absorption effects to be eliminated. Other complications include minerals prone to preferred orientation, and the presence of alumina substituted iron oxides for which good crystallographic data is not readily available. In smelter grade alumina the poorly crystalline intermediate aluminas suffer from extremely large peak widths, and a lack of good quality crystallographic data. Examples of many of these issues are presented. Currently the combined use of chemical analysis with XRD data is the method preferred by Alcoa for mineralogical analysis of Bayer materials.


Mineralogical Analysis of Bayer Materials - Rietveld or Not Rietveld

Gerald Roach and Nicholas Pearson

1.0 Introduction

Mineralogical analysis of bauxite is required to assist in the operation and control of the milling, digestion and clarification areas in a Bayer refinery. The mineral content of bauxite can affect extraction, grinding efficiency, desilication, settling in thickeners, and filtration. Conventional XRD analysis, using single or multiple peaks and comparison to standard materials, cannot alone provide complete quantitative mineralogical analysis of bauxite. (XRD in this paper refers to x-ray powder diffraction using a diffractometer with Bragg-Brentano geometry.) Problems arise with obtaining suitable standard materials, preferred orientation, peak overlap, and poorly crystalline materials (eg. iron oxides/hydroxides). Similar issues exist in the mineralogical analysis of red mud residue, and smelter grade alumina. Generally, it is necessary to combine wet chemical and x-ray fluorescence data with XRD data to obtain a complete mineralogical analysis.

Rietveld XRD analysis is a full profile least squares refinement technique that has been expounded as being able to provide a complete quantitative mineralogical analysis of bauxites from a single analytical technique. The technique was originally developed for and applied very successfully to the refinement of crystal structures from neutron diffraction data. Alcoa has had a long association with this technique as applied to XRD analysis. In past because Professor Rietveld studied at the University of Western Australia and is a frequent visitor to Perth, but also because the technique has been championed very much by Professor O’Connor at Curtin University, Department of Applied Physics. Both he and Associate Professor Li are heavily involved in the development of XRD as a quantitative tool. However, while the Rietveld method addresses many of the problems associated with conventional XRD analysis, Rietveld application to XRD data and quantitative analysis presents a complete new suite of problems. Some suppliers and XRD practitioners have been over-zealous in promoting the technique as a "black box" method of analysis, without paying consideration to the need for an intimate knowledge of crystallography and diffraction principles. Without these, inaccurate and unreliable results will almost certainly be obtained.

2.0 Problems in Rietveld XRD Analysis of BAUXITE

2.1 Absorption

Linear absorption coefficients (m ) for x-rays vary significantly with the x-ray wavelength, and with the physical properties and elemental composition of each mineral. This is illustrated in Table 1.

Table 1

Linear absorption coefficients for the major components of Darling Range bauxite for CuKa (1.5418) and CoKa (1.7902) radiations (Pearson, 1990)








m CuKa (cm-1)







m CoKa (cm-1)







When there are large differences in linear absorption coefficients between phases for a given radiation, "absorption contrast" is said to exist. This is the case for all bauxites containing more than about 5% Fe2O3 analysed using CuKa radiation. In strongly absorbing phases x-rays may be absorbed by individual particles, in which case diffraction is no longer a "volume" process and peak intensities are biased. Rietveld software packages contain facilities for correcting absorption effects using a "microabsorption correction factor" that requires the operator to input particle sizes for each phase. However, the particle size for each phase in a bauxite is impossible to determine for several reasons:

  • most of the convenient sizing techniques cannot provide size analyses for the individual minerals present in the mixture,
  • individual phases will have a range of particle sizes (the median size not necessarily the best to use for microabsorption corrections (Zydek and O’Connor,1990)),
  • particles may be multi-phase,
  • particles may be irregular in shape.

Table 2 illustrates the effect on quantitative results if incorrect particle sizes are used for microabsorption corrections.

Table 2

Quantitative Rietveld XRD analysis of Darling Range bauxites against the particle size used for microabsorption correction. Diffractogram obtained using CuKa radiation (Pearson, 1990)

Assumed Particle Size (m m)







(CuKa ) Uncorrected







(CuKa ) 3m m







(CuKa ) 5m m







(CuKa ) 8m m







Particle sizes could be input to obtain almost any result desired! Surprisingly this has been the procedure recommended by some software suppliers and Rietveld practitioners. Alternatively it has been suggested that particle sizes that produce correct results on a sample of known composition are determined, and that these sizes are used for analysis of samples of unknown composition. Such a procedure may be acceptable provided that the compositions of the unknown samples do not differ significantly from the sample used to determine the sizes. If compositions do vary significantly, inaccurate results will be obtained. Furthermore, the sizes determined to produce accurate results on the sample of known composition do not necessarily bear any physical resemblance to the particle size that can be estimated by sizing techniques. An "agglomeration factor" has been used to relate the measured particle size to that which gives the desired quantitative result. Generally, such factors have no physical significance, and are merely a correction factor to obtain a desired result. Accurate Rietveld XRD analysis of bauxite is not possible using CuKa radiation. Despite this, papers in the literature persist with the use of CuKa radiation and particle size corrections to obtain a perceived correct result.

For Rietveld XRD analysis of bauxite absorption effects need to be eliminated. This can be achieved in two ways, as given in G.W. Brindley’s 1945 paper (Brindley, 1945). First, the radiation used should be selected such that large absorption coefficients, and in particular contrasts in absorption, are not present. Table 1 shows that CoKa radiation meets these requirements for the analysis of bauxites. When CoKa radiation is used for bauxites particle size corrections are unnecessary. Second, the sample should be ground to a fine particle size (eg. by using a McCrone Micronising Mill). Only when absorption effects are eliminated can accurate Rietveld XRD analysis of bauxite be undertaken (Pearson, 1994; Pearson and Roach, 1992). The considerations for absorption effects for bauxite apply equally to the analysis of red mud residues.

2.2 Preferred Orientation

Preferred orientation is the tendency for particles with either "plate-like" or "needle-like" morphologies to assume a specific orientation when the sample is packed into a sample holder for XRD analysis. Reflection from the plane of preferred orientation is enhanced for plate-like morphologies, and suppressed for needle-like morphologies. This has been used to advantage with a "morphology ratio" for hydrate to describe particle morphologies (Roach and Cornell, 1988), and has been used as a process monitoring tool for calcination (Loughlin, 1990) . Pressing samples for XRD analysis using a pneumatic or mechanical press improves the repeatability between operators but tends to enhance preferred orientation effects. Rietveld software contains a "preferred orientation" parameter to correct the bias caused by preferred orientation. For randomly oriented particles, the preferred orientation parameter is equal to 1.0. For plate-like morphologies the parameter is less than 1.0, and for needle-like morphologies the parameter is greater than 1.0.

In Rietveld refinements, corrections for the bias caused by preferred orientation are generally reliable provided the preferred orientation parameter does not differ excessively from 1.0. However, for materials in which the deviations from 1.0 are significant, the corrections for preferred orientation are less reliable, and may even lead to unstable refinements. In the case of platey materials such as kaolinite and muscovite, the preferred orientation correction may be beyond the capability of the software, especially when such phases are only a minor component of the sample.

The crystal morphology of gibbsite varies significantly with the source of the bauxite. Gibbsite in Jamaican bauxite has a morphology ratio (intensity (002) / intensity (110)(200)) of 2, suggesting crystallites with a low aspect ratio, i.e. no preferred orientation. However, gibbsite in Trombetas bauxite (Brazil) has a morphology ratio of 27, suggesting very platy crystallites. The corresponding preferred orientation parameters in Rietveld refinement are 0.97 and 0.54, which are consistent with the morphologies suggested by the morphology ratio. Furthermore, in a mixture containing 50% Jamaican bauxite and 50% Trombetas bauxite, the gibbsite morphology ratio is 10, and the Rietveld preferred orientation parameter is 0.64, both intermediate to the values in the parent materials. This supports the preferred orientation parameter in Rietveld analysis of bauxite as providing an adequate indication of morphology, and thus the potential for sensible results.

However for red mud residues, in which the gibbsite content is low, Rietveld software will be less able to deal with gibbsite preferred orientation, due to the low intensity signal (see Figure 1). For minor phases, it is often impossible to sensibly refine any parameters other than the scale factor (from which the weight percent is determined). Failure to refine other parameters leads to inaccuracy in the scale factor, and thus the quantitative results. In cases of significant preferred orientation, the errors will be enhanced. For residues, the problem will be complicated by the presence of gibbsite from autoprecipitation.


Figure 1

X-ray Diffractogram of Red Mud Residue from Darling Range Bauxite

2.3 Iron Oxides/Hydroxides

Goethite and hematite in bauxite tend to have very fine crystallite sizes that produce broad, low intensity diffraction peaks. Slow scan rates are preferable to ensure that the diffraction signal from such peaks is not degraded by background noise. However, slow scan rates are undesirable in Bayer plant XRD laboratories having a high throughput of samples. Background modelling (either manually or using polynomial functions) and/or background subtraction procedures must be implemented with great care to ensure that the data in broad peaks is not rejected as background.

Goethite and hematite in bauxite generally have alumina substitution that affects many of the parameters used in quantitative Rietveld refinements. Crystallographic data for the alumina substituted iron phases will need to be entered as a new phase into the software or crystal databank as the case may be. Such data may not be available in the literature, and will have to be determined by the operator. The alumina substitution will have to be estimated from peak shifts. Alumina substitution in iron oxides/hydroxides affects unit cell dimensions. Atomic scattering factors and thermal vibration parameters for the aluminium atoms must be included. The density and mass absorption coefficient of the material will also be affected. Without these considerations the quantitative results will be inaccurate. Compilation of such data requires a good understanding of crystallography.

Goethite and hematite in bauxite may contain two or more different levels of alumina substitution, or even a continuous range of alumina substitution. The broad, low intensity peaks for these phases means that it is a non-trivial task to determine the levels of substitution present, and input the required data into Rietveld software. The potential for Rietveld analysis to improve goethite/hematite ratio determinations hinges on the ability of the analyst to correctly deal with alumina substitution in these phases. As discussed earlier, Cu Ka radiation will result in unreliable goethite/hematite determinations due to absorption issues.

2.4 Amorphous Phases

Materials with very short range order, or completely disordered structures, do not produce diffraction peaks, but contribute to the background or produce very broad humps in the background. Some bauxites contain such "amorphous" materials. If these are not considered in Rietveld analysis, the quantitative results for the crystalline phases will all be overestimated. This was an oversight in all of the original Rietveld programmes where amorphous phases were ignored and the analysis normalised to 100%. This issue was pointed out (Pearson and Roach, 1992), and alterations made to the software to quantify amorphous phases using internal standards. As XRD cannot indicate the nature of an amorphous phase, other techniques such as x-ray fluorescence will be required to determine its nature.

An example of the effect of amorphous material is shown in Figure 2. The diffractogram for a hydrate sample heated to 300 C shows only boehmite peaks to be present, and the sample appears to be 100% boehmite. The chemical analysis was consistent with the formula Al2O3.H2O. This is the result obtained if Rietveld analysis is undertaken without an internal standard, as the result is normalised. However, when an internal standard is added to the sample, it is found that the material is only 30% boehmite, the remaining 70% being amorphous. That was confirmed by a caustic digest which removed the 70% of amorphous hydrated alumina.

Figure 2

X-ray Diffractogram of a Sample Apparently Containing 100% Boehmite

2.5 Minor Phases

Minor phases in bauxites produce low intensity diffraction peaks. Slow scan rates are preferable to ensure that the diffraction signals from minor phases are not lost in the background noise. Slow scan rates are not always possible in XRD laboratories having a high throughput of samples. Again, treatment of the background must not reject the diffraction peaks from minor phases. Because of the low signal-to-noise ratio for minor phases, it is often only possible to refine a limited number of parameters, otherwise nonsensical refined parameters will be obtained that bear no real physical significance, and results may be biased.

3.0 Problems in Rietveld XRD Analysis OF Smelter Grade Alumina

Smelter grade alumina (SGA) is composed in the main part by poorly crystalline intermediate aluminas, with a small proportion of alpha alumina and occasionally gibbsite, see Figure 3. The x-ray diffraction pattern is dominated by broad, severely overlapping, low intensity diffraction peaks from the intermediate aluminas, while both alpha alumina and gibbsite suffer from preferred orientation (Roach et al., 1990). Such extremes of peak width are not handled well by Rietveld software. Furthermore, the crystallographic data available for some of the intermediate alumina phases is of low quality. Data for some of the materials are incomplete, and the structures of some phases are still being determined and improved upon. Two separate structures for gamma alumina have been demonstrated to exist (Gan, 1996). Any crystallographic data used should be from a reputable source, and supported by documentation indicating any issues.

Figure 3

X-ray Diffractogram of Smelter Grade Alumina

4.0 Other Considerations

As indicated above, Rietveld analysis requires a thorough understanding of crystallography and diffraction theory if quality results are to be obtained. An overview of the method is given by Young, 1993. Rietveld software is notoriously complex and difficult to use. The practitioner must understand refinement strategies and the significance of the parameters used in the software, otherwise meaningless results will be obtained. Low "R" values are often considered to constitute a high quality analysis. This is quite erroneous, as poor results can be obtained from a good pattern fit, if incorrect assumptions or procedures have been used.

Some early commercial versions of Rietveld software failed to compensate for anomalous dispersion, a resonant effect that can lead to grossly inaccurate quantitative results, and incorrect predictions of amorphous content. Software is now widely available on the Internet. Software should only be obtained from reputable sources that provide supporting documentation on its use features, and any considerations necessary in its use.

5.0 Conclusion

Quantitative Rietveld analysis of Bayer materials is extremely complex, and requires expert knowledge of crystallography and diffraction theory. If used as a "black box" procedure, nonsensical results are likely. After 15 years of being involved in Rietveld XRD analysis, Alcoa still undertakes mineralogical analysis of bauxite and residues using a combination of reference intensity ratio XRD and chemical analyses. These and a knowledge of both bauxites in general and the process itself enable reliable information to be obtained on the myriad of Bayer materials analysed. Rietveld analysis as a stand-alone technique for mineralogical analysis is still an area for experts in crystallography and diffraction theory.


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Gan, B.K. (1996). Crystallographic Transformations Involved in the Decomposition of Gibbsite to Alpha-Alumina. Thesis (Ph.D) Curtin University of Technology, Western Australia.

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