ADVANCES IN QUANTITATIVE X-RAY MINERALOGY – MIXED
CRYSTALS IN BAUXITE
Karsten Knorr1*, Reiner Neumann2
1Bruker
2CETEM
AXS GmbH, Östliche Rheinbrückenstraße 49, 76187 Karlsruhe, Germany
Centre for Mineral Technology, Ministry of Science and Technology, Av. Pedro Calmon, 900 Cidade Universitária, 21941-908 Rio de Janeiro, Brazil
Abstract
Comparing results of quantitative Rietveld refinement to chemical analysis may be difficult due to the
presence of crystals with variable stoichiometry. In principle, variations in composition could be determined
by refining site occupancy parameters in the Rietveld software. Unfortunately, in quantitative phase analysis
the measured data usually do not permit one to do so. However, from these kinds of data the lattice
parameter may be obtained very precisely. Linking the lattice parameters to site occupancy factors in the
TOPAS software package improves quantitative phase analysis. The example of Al substitution in goethite,
FeOOH, for iron-rich bauxite is discussed. The quantitative mineralogy of 11 CETEM-certified reference
bauxites was determined using Rietveld refinement of XRD data. For a highly substituted material, agreement
within 1% compared to XRF data may be achieved.
Keywords: XRD, quantitative mineralogy, bauxite, mixed crystals, Rietveld TOPAS
1
INTRODUCTION
In the past few years, the Rietveld method [1] has emerged as a routine tool for quantitative phase
analysis (QPA) from X-ray diffraction data. Fast and reliable results became possible by combining modern
computer technology and optimized mathematical algorithms with the fundamental parameters approach in
the Bruker AXS TOPAS software [2].
QPA from X-ray powder diffraction (XRD) data is used in mineral industries for the characterization
of raw materials and for process control. Traditional XRD QPA is based on single peak analysis and the
determination of calibration curves. This method has inherent difficulties for multiphase problems with
strong reflection overlap. In the past few years, the Rietveld method emerged as a routine tool for QPA from
XRD data. Rietveld QPA is based on the calculation of the full powder pattern from crystal structure
information. Therefore, single peak deconvolution or fitting is not necessary; it does not rely on calibration
curves and also tube ageing does not need consideration.
QPA in the TOPAS software is based on the method first described by Hill and Howard in 1987 [3].
This method is based on the assumption that (i) all phases in the specimen are identified, (ii) all phases are
crystalline and (iii) the crystal structures of all phases are known. The wt%, wu, of a phase u in a mixture of n
phases is
n
wu # S u ZMV !u / "k #1 S k ZMV !k
with S being the scale factor of the Rietveld calculation, Z the number of formula units in the unit cell,
M the mass of one formula unit, and V the unit cell volume. The factor (ZMV) is a phase-specific scaling
parameter that is solely defined by the crystal structure of the mineral. This factor can also be obtained by
*Correspondence to: [email protected]
Broekmans, MATM (editor)
Proceedings, 10th International Congress for Applied Mineralogy (ICAM)
1-5 August 2011, TRONDHEIM, Norway
ISBN-13: 978-82-7385-139-0
377
calibration with a reference material in the cases of unknown crystal structures, and unindexed or amorphous
materials; this is also known as the PONKCS method in TOPAS [4].
The precise knowledge of all crystal structures is crucial for high accuracy quantification. One issue
with quantifying minerals is the substitution of different kinds of atoms at the same position of the crystal
structure. While standard crystal structure refinement by the Rietveld method may determine site occupancy
parameters, this is difficult in QPA. Usually, there is only limited measurement time available in process
control and a range of about 80° 2$ is sufficient for Rietveld QPA. However, such short measurement ranges
typically do not permit site occupancy refinement.
The linear relation between lattice parameters and concentration of binary alloys is well known as
Vegard’s law [5]. It is used for obtaining concentrations in binary mixtures from the measurement of lattice
parameters. Also, minerals with a variable stoichiometry show variations of the individual lattice parameters
with composition that may be nonlinear and also different for the different lattice directions. However, there
is usually still a clear relation between lattice parameters and stoichiometry. In the cases where this relation is
known, it can be used to improve the accuracy of a quantitative analysis, taking into account the variable
chemistry of a given mineral.
This article describes how to apply a lattice parameter as a constraint for site occupancies in the
TOPAS software. The method is applied to bauxite from Brazil, which may show high levels of aluminum to
iron substitution.
2
2.1
MATERIALS AND METHODS
Materials
Eleven samples of bauxite certified reference materials from CETEM, Brazil, were analyzed by XRD.
As with CRMs prepared for the aluminum industry, all the material was previously characterised [6] in an
inter-laboratory program with respect to chemical composition and degree of recovery of alumina at
conditions similar to those of the industrial Bayer process. The material predominantly consists of Al2O3,
Fe2O3, SiO2 and TiO2. Most samples are “washed”, meaning fines were removed, but not all of them.
Relevant data are reproduced in Table 1. According to the certificates, samples were oven-dried at 378 K,
crushed and ground to 100% <150 µm, and then blended to assure homogeneity.
2.2
X-ray powder diffraction
About 4 g of each sample was ground in a McCrone Micronizer mill with agate grinding elements, by
adding 10 ml of distilled and deionised water as a grinding agent. All samples were ground for 10 minutes,
discharged into a PTFE Petri dish, and dried overnight at 323 K in a vacuum oven. The dry powder was
gently reground with agate pestle and mortar and stored in a polypropylene vial.
Pulverized sample material was back-loaded into sample holders. Operating conditions of the Bruker
D4 ENDEAVOR diffractometer were set to 40 kV and 40 mA, using Fe-filtered CoK radiation. Co
radiation was selected in order to minimize micro-absorption. Diffractograms were recorded from 4° to 80°
2 , in 0.02° 2 increments. A LYNXEYE linear Si-strip-type detector was used with an opening of 3.8° 2 ,
being equivalent to 188 active channels. A counting time of 1.0 s per increment and channel was used,
resulting in a total measurement time per scan of about 1 h.
2.3
Data analysis
QPA was performed utilizing the Rietveld method implemented in TOPAS, version 3. The
background was calculated with a fifth order Chebychev polynomial. A seven-line source emission profile was
used to model the emission of the Fe-filtered CoK% radiation as well as remnants of K& radiation in the
order of about 0.5% of the related K% peaks. An intensity level of 0.001% of the main peak amplitude was
used as the cut-off criterion for the intensity calculations. The fundamental parameters approach [7] was used
for describing the peak profile as a convolution of the Bragg–Brentano geometry based instrument resolution
function and peak broadening related to sample effects. The crystallite size of the individual phases was
considered as a Lorentzian contribution to the peak width, but for a coarse gibbsite fraction a Gaussian part
was also added. The major advantage of this approach is the minimal number of parameters needed to
378
individually model the line shape of all phases, thus reducing parameter correlations and adding numerical
stability to the refinement [8].
The intensity contributions of the individual phases to the total diffractogram were calculated based
on the tabulated crystal structures of the minerals. A scale factor, all lattice parameters, and the peak width
parameters related to crystallite size were simultaneously refined for all phases. Preferred orientation was
corrected whenever necessary using the March–Dollase algorithm [9].
Each refinable parameter in the calculation is identified by a unique keyword. These identifiers may be
used for formulating numerical dependencies by applying the macro language that is an integral part of the
TOPAS package. A straightforward application of the macro language is to constrain the site occupancy
parameters, which define the degree of substitution of different kinds of atoms at a given crystallographic site
in a crystal structure, to values between 0 and 1.0 with the actual magnitude depending on the length of a
lattice parameter.
Here, the substitution of Al in goethite is shown. Aluminum may replace up to about 36% of iron in
the crystal structure of natural goethite [10] and creates a linear variation of the lattice parameters with the b
lattice parameter, showing the largest variation and the best correlation with the aluminum content [11].
Figure 1 displays the linear equations used to formulate the aluminum and iron concentration as a function of
the lattice parameter b and how to implement this within the TOPAS graphical user interface. Furthermore,
the sum over the Fe and Al occupancies is forced to be 1.0.
3
RESULTS
The typical result of a Rietveld quantitative phase analysis is shown in Figure 2 for the sample BXMG3. The major phases are gibbsite (Al(OH)3), goethite (FeOOH), and hematite (Fe2O3). Gibbsite shows a
bimodal size distribution, which was considered by refining two phases having different crystallite size
parameters. Furthermore, small amounts of rutile and anatase (TiO2), quartz (SiO2), and kaolinite
(Al2Si2O5(OH)4) were found. The refined b lattice parameter of goethite is 2.9750(7) Å, thus indicating a
highly substituted Al-goethite with the occupancy of Al at the Fe site of 0.283(4).
The numerical agreement parameters of the refinement, Rwp = 2.96 and GOF = 1.71, are indicative
of a good fit. This is also represented in the difference curve between the observed and calculated intensities,
shown in Figure 2. The intensity axis is shown using a sqrt(I) scale. Owing to the sqrt-representation, the
noise corresponds to the statistical error of the measured intensities. The differences between the
measurement and the calculated model are in the order of the noise of the difference curve or measurement
errors, respectively. Thus, no statistically relevant deficiencies of the evaluation are present. All refinements
show a similar picture as presented in Figure 2. Table 2 reports the concentrations as well as the occupancy
parameter of Al at the Fe site for all samples investigated.
4
DISCUSSION
Figure 3 compares the certified chemical analysis for the bauxite standards with the chemical
composition calculated from XRD/Rietveld refinement. The top graph considers regular chemical
composition of all minerals, but for the bottom graph the Al content in goethite has been considered in the
calculations. Although the direct result is already good, there is a slight improvement in the conciliation when
Al-for-Fe substitution is considered.
The real advantage of tracing back elements to their carrier minerals, including aluminum in the
goethite structure, can be observed in Figure 4, where information from XRD/Rietveld (bold markers) and
chemical composition are compared. The upper part of the graph (between 80% and 100%) is a comparison
of the percentage alumina calculated from XRD that is due to gibbsite against the proportion of total alumina
analyzed as available to the Bayer process. For most samples, both match closely. However, for the BXPA
samples (7 to 10, numbers matching the order of entries in Tables 1 and 2), gibbsitic alumina is higher than
the chemically available one.
The second group of data, which plot from 30% to 65%, comprises the grades, total and available
alumina by chemistry, and total and gibbsitic alumina by XRD/Rietveld. There is a high level of agreement
for both datasets. As for the four BXPA samples (numbers 7 to 10), these values are very similar. Therefore,
this is no explanation for the amount of chemically available alumina being lower than that of the gibbsitic
379
alumina from the grades. Most probably, the leaching procedure that simulates the Bayer process is not able
to extract all the gibbsitic—and therefore supposedly available—alumina from the samples.
The data at the bottom of the graph refer to the proportions of kaolinitic and goethitic aluminum.
Kaolinite and goethite account for the not-available and non-gibbsitic aluminum. From the 11 measured
samples, kaolinite is the main non-gibbsitic aluminum carrier for seven samples, goethite for two, and for
other two both are equivalent. For all samples where goethite is the main non-gibbsitic aluminum carrier
(mainly for BXMG-1 and 3), process prediction based on not-available alumina, that is supposed to be
kaolinitic and therefore related to reactive silica, could lead to miscalculations.
5
CONCLUSIONS
The quantitative mineralogy of CETEM-certified reference bauxites was determined using Rietveld
refinement of XRD data. The method is considered accurate as the main chemistry figures derived from the
XRD results agree well (better 1–2 wt %) with bulk chemical analysis from the certificates. In addition, not
only total chemistry but also knowledge on element partitioning into different minerals is obtained. This
directly supports the process mineralogy in general. Gibbsite is identified as the main source of recoverable
alumina in Brazilian bauxite, and both kaolinite and goethite account for the not-available alumina.
Differences between gibbsitic alumina from XRD and available alumina from chemical analysis could mean
that there is potential for improvement in the extraction process.
Lattice and site occupancy parameters are correlated in substitutional mixed crystals. The
consideration of their ratio in TOPAS Rietveld quantification is possible via the built-in macro language and
improves the accuracy of the quantitative X-ray mineralogy results. Aluminum not available to processing can
be locked in goethite.
The particular example of Al-bearing goethite is of importance for the benefication of bauxite during
alumina or refractories production. There are several other potential applications to be targeted, such as the
Al content of goethite-rich iron ore or dolomite composition in limestones.
6
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
380
REFERENCES
Rietveld, H.M. (1969): A profile refinement method for nuclear and magnetic structures. Journal of
Applied Crystallography (2): 65–71. Also see Young, R.A. (1993): The Rietveld method. IUCr
Monographs on Crystallography, Vol. 5 Oxford University Press, Oxford.
TOPAS: Total Pattern Analysis Solution, Bruker AXS GmbH, Karlsruhe, Germany, (2003 – 2009).
Hill, R.J. and Howard, C.J. (1987): Quantitative phase analysis from neutron powder diffraction data
using the Rietveld method. Journal of Applied Crystallography (20): 467–474.
Scarlett, N.V.Y. and Madsen, I.C. (2006): Quantification of phases with partial or no known crystal
structures. Powder Diffraction (21/4): 278–284
Vegard, L. (1921): Die Konstitution der Mischkristalle und die Raumfüllung der Atome. Zeitschrift für
Physik (5): 17.
http://www.cetem.gov.br/mrc/ing/available_crms.htm
Cheary, R. and Coelho, A.A. (1992): A fundamental parameters approach to X-ray line-profile fitting.
Journal of Applied Crystallography (25): 109–121.
Kern, A. (2008): Profile analysis. In: Clearfield, A (editors): Principles and Applications of Powder
Diffraction, Blackwell, Oxford: 158–199 .
March, A. (1932): Mathematische Theorie der Regelung nach der Korngestalt bei affiner Deformation.
Zeitschrift für Kristallographie (81): 285–297.
Schwertmann, U. and Carlson, L. (1994): Aluminum influence on iron oxides: XVII. Unit-cell
parameters and aluminum substitution of natural goethites. Soil Science Society of America Journal
(58): 256–261.
Schulze, D.G. (1983): The influence of aluminum on iron oxides. VIII. Unit-cell dimensions of Alsubstituted goethites and estimation of Al from them. Clays and Clay Minerals (32/1): 36–44.
TABLE 1: Certified mass fraction (m/m%) and loss of ignition (LOI) for the analyzed bauxite samples. Refer to [6] for
additional information.
Bauxite
Al2O3
BXGO-1†
BXMG-1
BXMG-2
BXMG-3
BXMG-4†
BXMG-5†
BXPA-1
BXPA-2
BXPA-3
BXPA-4
BXSP-1†
†not washed.
total
60.7
50.1
50.4
37.9
50.4
50.5
52.8
55.4
53.7
57.3
50.1
available
59.3
44.1
45.5
33.2
40.7
39.7
49.0
50.6
49.8
52.7
40.0
SiO2
Fe2O3
TiO2
LOI
0.6
3.1
6.4
2.3
9.5
10.7
4.9
4.9
4.2
4.7
14.7
4.6
17.4
13.7
35.3
9.9
9.2
12.8
9.2
11.6
6.9
6.7
0.5
2.1
1.6
2.0
1.8
1.3
1.4
1.4
1.9
1.3
1.2
33.1
26.9
27.6
22.2
26.4
26.8
27.5
29.1
28.3
29.8
26.1
TABLE 2: Rietveld quantitative phase analysis results of CETEM reference material bauxite samples (wt%). Symbols
according to IMA list of rock- and ore-forming minerals.
Bauxite
BXGO-1
BXMG-1
BXMG-2
BXMG-3
BXMG-4
BXMG-5
BXPA-1
BXPA-2
BXPA-3
BXPA-4
BXSP-1
Gbs
coarse
13.1
14.6
10.6
5.3
5.2
6.1
11.4
10.3
9.1
11.3
8.0
fine
80.6
56.9
62.1
46.1
60.4
59.0
67.1
71.0
70.2
73.7
56.1
Hem
Gt
Kln
Ant
Qtz
Bhm
Rt
Ms
Al in Gt
0.8
5.4
2.5
18.3
2.3
1.4
10.7
5.9
8.8
5.0
2.1
constr.
4.3
16.5
14.7
24.9
7.5
8.5
2.1
3.8
3.8
2.2
6.2
—
2.8
4.7
1.9
13.0
16.0
6.1
6.6
5.9
6.0
13.9
0.3
0.2
0.4
1.1
1.6
1.0
1.3
1.1
1.1
0.8
1.5
0.3
2.1
5.0
1.6
1.1
1.0
1.4
1.3
1.1
1.0
5.3
—
1.4
—
—
—
—
—
—
—
—
—
—
—
—
0.9
—
0.6
—
—
—
—
—
—
—
—
—
8.9
6.4
—
—
—
—
6.9
(%at)
0.327
0.322
0.304
0.283
0.283
0.280
0.001
0.102
0.119
0.212
0.208
Figure 1: Definition of site occupancy (Occ.) constraints for goethite in the TOPAS
graphical user interface.
381
Figure 2: TOPAS quantification result of Bauxite BXMG-3. The upper curves show the measured XRD
data and the calculated Rietveld fit. The bottom of the graph presents the position of all peaks from all
different minerals according to their order in the top right corner list of concentrations. The
difference between measured and calculated curve is given above the peak markers,
the individual goethite pattern is highlighted above.
382
70.0
60.0
Chemical analysis
50.0
40.0
30.0
SiO2
20.0
Fe2O3
TiO2
10.0
LOI
Al2O3
0.0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Rietveld (not constrained)
(A)
70.0
60.0
Chemical analysis
50.0
40.0
30.0
SiO2
20.0
Fe2O3
TiO2
10.0
LOI
Al2O3
0.0
0.0
(B)
10.0
20.0
30.0
40.0
50.0
60.0
70.0
Rietveld (constrained)
Figure 3: Comparison of chemical analysis of the bauxite standards against composition calculated from
mineral quantification through Rietveld analysis (A—regular mineral composition, B—considering Al-for-Fe
substitution in goethite).
383
100
Concentration %
80
60
40
20
0
0
1
2
3
4
5
6
7
Sample number
8
9
10
11
Al2O3 total
% available Al2O3
Available alumina (wt%)
Al2O3 total XRD (wt%)
% gibbsitic/total
% goethitic/total
12
Figure 4: Plot comparing results derived from mineral quantification through XRD/Rietveld analysis
(including Al in goethite) and chemical analysis. Data from XRD are presented with filled symbols.
384