Progress in mineralogical quantitative analysis of rock samples application

TECHNICAL ARTICLE
Progress in mineralogical quantitative analysis of rock samples: application
to quartzites from Denali National Park, Alaska Range (USA)
Mă rgă rit M. Nistor,1 Nicolae Har,2 Simona Marchetti Dori,1 Simona Bigi,1 and Alessandro F. Gualtieri1
1
Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via S. Eufemia 19, I-41121 Modena,
Italy
2
Department of Geology, University of Babeş-Bolyai, Kogălniceanu Street 1, 400084 Cluj-Napoca, Romania
(Received 9 September 2015; accepted 29 October 2015)
This work deals with the determination of the mineralogical composition of three quartzite samples,
selected as case study to verify the viability and accuracy of various experimental techniques commonly used in geometallurgy and petrography for the determination of the mineralogical composition
of rock samples. The investigated samples are from the North-Eastern side of the Denali National Park
(Alaska Range, USA). The mineralogical phase abundance of the samples was determined by digitally assisted optical modal point counting, scanning electron microscopy (SEM) + energy dispersive
spectroscopy (EDS) modal and digital image analysis, normative calculation from bulk chemistry
calculation, and modal Rietveld X-ray powder diffraction. The results of our study indicate that the
results provided by modal optical and SEM digitalized counting seem less accurate than the others.
The determination with EDS mapping was found to be inaccurate only for one sample. Agreement
was found between the X-ray diffraction estimates and bulk chemistry calculation. For both modal
optical and SEM digitalized counting, the statistics was probably insufficient to provide accurate
results. The estimates obtained from the various methods are compared with each other in the
attempt to attain general indications on the precision, accuracy, advantages/disadvantages of each
method. © 2016 International Centre for Diffraction Data. [doi:10.1017/S0885715615000871]
Key words: Rietveld method, Denali quartzite, optical counting, SEM, EDS, bulk chemistry
calculation
I. INTRODUCTION
The samples investigated in this study are from the
North-Eastern side of the Denali National Park (Alaska
Range, USA). The Alaska Range represents a tectonically active zone, where Pacific Plate is subducted under North
America Plate. The study area is located in the central part
of Alaska, and precisely in the external curvature of Alaska
Range. The entire region of Central and South Alaska is
crossed by a complicated system of faults and thrusts
(Csejtey et al., 1982; Singh et al., 2007). The most important
is the Denali Faults Systems whose length is around 2000 km
long (Hickman et al., 1978).
The occurrence of the samples used for the present investigation is from the North-Eastern side of Denali National
Park. Denali National Park occupies a large sector of Alaska
Range, including Mount McKinley and its surroundings.
This park is the oldest preserved area in Alaska (about 24
500 km2) as it was instituted in 1917. The investigated area
(see Figure 1) included the Southern part of Mount
Margaret and Savage River (between 63°30′ –63°50′ N and
149°00′ –149°30′ W). Savage River is characterized by a
large valley, modelled by glaciers in Pleistocene and forms
the canyon between Mount Margaret and Mount Healy. The
geology of the area shows metamorphic and magmatic complexes alternated with sedimentary rocks. The low lands and
valleys are covered by gravels and unconsolidated deposits.
Overall, Mount Margaret is constituted by sedimentary
rocks dating from Cambrian to Devonian, with a great variety
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Powder Diffraction 31 (1), March 2016
of rock types. Under the microscope, collected samples 602,
607, and 608 represent sericite-rich quartzites. These rocks
display quartz as major component and have inhomogeneous
structure with porphyry texture. For the present study, we have
focused exclusively on the quartzite rocks with the aim of presenting an accurate mineralogical characterization of these
samples. This investigation is preparatory for a more general
project in progress about the petrology and petrogenesis of
these rock-types which is part of the PhD thesis of the first author M. N. M.
Mineralogical quantitative phase determination of rock
samples is a method used since more than 60 years in mineralogy, petrography, geometallurgy, archeometry, materials
science, and other scientific applicative disciplines. Until the
end of the last century, the mineralogical phase composition
or phase abundance (modal composition) was typically determined by three methods:
(i) point-counting techniques using optical microscopy
(optical modal analysis). The optical mode is determined
by direct observation and can be assigned a measure of
precision (Chayes, 1956). Generally, this method is inappropriate for fine-grained and/or very altered rocks with a
grain size usually lower than 10 µm. Besides that, determination suffers from rock heterogeneity, some components can be misidentified, and errors can arise from the
conversion from two-dimensional to three-dimensional
data;
0885-7156/2016/31(1)/31/9/$18.00
© 2016 JCPDS-ICDD
31
Figure 1. (Colour online) Location of the samples on the Alaska map and Margaret Mount surroundings. Maps source: UAF-GINA/SDMI http://alaskamapped.
org/bdl.
(ii) normative calculation from bulk chemical data (Barth,
1959). Norms are theoretical mineral abundances calculated from a bulk chemical analysis. This technique is chosen in place of optical microscopy for fine-grained rock
samples although not all rock types are adequately modelled by the standard calculation procedures and, because
ideal compositions are assumed for the minerals, small
variations in bulk chemistry that can strongly affect the resultant mode (Hill et al., 1993). In general, it is not expected that norms will match the mode, except for simple rock
compositions. The use of multicomponent chemical mass
balancing in solving mineral quantities from chemical
analysis [e.g. X-ray fluorescence (XRF)] has been successfully used for decades by a number of researchers
and laboratories (see for example Lamberg, 2011; Lund
et al., 2013). Normative calculations used by geologists
for classification purposes, for example Cross, Iddings,
Pirsson, and Washington (CIPW) (Cross et al., 1902), differ from mass balancing method by calculating hypothetical and not actual mineral composition for samples, using
stoichiometric compositions for minerals (e.g. CIPW uses
volatile free minerals) and reporting mineral grades as
normative per cent, not as weight proportions. In this
paper, we will refer to this method as “bulk chemistry
calculations”;
(iii) modal X-ray powder diffraction (XRPD) (including the
Rietveld method: Hill et al., 1993). The Rietveld method
has been used to obtain reliable modal quantitative phase
analysis (QPA) estimates (Rietveld, 1969; Hill and
Howard, 1987; Bish and Howard, 1988; Bish and Post,
1993; Madsen and Scarlett, 2008) since about 25 years.
In this method, the mass fraction (wi) of each ith
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Powder Diffr., Vol. 31, No. 1, March 2016
crystalline component in a mixture can be calculated
from the following equation:
w
S (Z M V )
i = i i i i
wj
Sj (Zj Mj Vj )
j
(1)
j
where Si is the refined scale factor, Zi is the number of formula
units in the unit cell, Mi is the mass of the unit formula and Vi
is the elementary cell volume. QPA using the Rietveld method
relies upon the normalization condition (Σi wi = 1).
In the last 15 years, a significant progress has been made
in this field because of both the advent of image digitalization
and analysis and the application of electron microscopy techniques. Image analysis with optical microscopy makes the
modal method faster but still positive identification of minerals is not always easy especially if a process sample comprised
of very fine-grained particles. Scanning electron microscopy
(SEM)-based image analysis (Quantitative Evaluation of
Minerals by SCANning electron microscopy (QEMSCAN®),
mineral liberation analyzer (MLA), pressure transient analysis
(PTA), IncaMineral) provides more rapid modal quantitative
analysis of mineral grades and textures (Gu, 2003; Moen,
2006; Liipo et al., 2012). The drawbacks of the method are:
(i) it is standardless; (ii) for accurate analysis from particulate
materials, the sample should have a narrow size distribution to
avoid classification in sample preparation and to eliminate the
need for changing magnification during image collection
(Kwitko-Ribeiro, 2011); there are limitations on the particle
size. For sound statistics one needs to analyse thousands of particles; for very fine particle and mineral grain sizes (<5 µm), the
Mă rgă rit M. Nistor et al.
32
resolution starts to be a problem in mineral identification as the
electron beam diameter approaches the size of individual
grains; minerals with very similar chemical composition are
difficult to identify in SEM-based image analysis (Lund
et al., 2013). For these reasons this method is widely used in
geometallurgy but less in other research fields.
In this work, we have selected three quartzite samples from
Denali National Park as case study to apply the various experimental techniques from geometallurgy and petrography used
for the determination of the mineralogical quantitative analysis
of rock samples. It was not possible to collect more than three
samples during the field expedition because of the hard environmental conditions. Hence, this work should be considered
a preliminary methodological investigation which calls for additional investigations using a larger statistically meaningful
number of samples. The mineralogical phase abundance of
the samples has been calculated with modal optical microscopy
and digital image analysis, modal SEM + energy dispersive
spectroscopy (EDS) and digital image analysis, XRF bulk
chemistry calculation, and modal Rietveld QPA. Results
from the various methods are compared with each other and
general indications on the precision, accuracy, advantages/disadvantages of each method are outlined.
607 and 608) the first terrace and the left bank of river, that
stretch between 760 and 800 m. Samples 607 and 608 represent sericite-rich schists and quartzites (Figure 1).
In the laboratory, raw samples were quartered to obtain
about 10 g of homogeneous representative material and subsequently dried at 105 °C for 2 h.
B. Digitally assisted optical point counting
An optical microscopy study of samples 602, 607, and 608,
aimed at determining the modal composition was conducted on
thin sections obtained from selected representative fragments.
Using polarized light microscopy and a camera, representative
images at 50× were obtained. Visual observation was supported
by statistical analysis on three selected pictures for each sample
using the ImageJ open source software (version 1.42q, Wayne
Rasband National Institute of Health, USA: Schneider et al.,
2012). Each observation was conducted with the automatic particle analyse procedure available in the software. The obtained
figures allowed determination of an independent mineralogical
determination of the crystalline components.
C. SEM/EDS
II. EXPERIMENTAL
A. Sample collection
A representative amount of each sample (around 2 kg)
was collected from the southern slope of Mount Margaret
and from Savage River Valley, upstream of the Savage
Canyon. The outcrops of Mount Margaret show the presence
of igneous and metamorphic rocks. Sample 602 is from Mount
Margaret (Figure 1) composed of gabbroic rocks, quartzites,
and schists. The specimens were sampled at 1000–1200 m altitude. Even if the bottom of Savage Valley is constituted by
rewashed gravels deposited in the river suspension, the characteristics of samples taken from Savage Valley (Figure 1)
do not differ greatly from the samples from Mount
Margaret. In Savage Valley we have outcropped (samples
TABLE I.
Results of the mineralogical quantitative determination of the investigated samples.
Phase (wt%)
Sample 602
Chlorite
Mica
Quartz
Others
Sample 607
Chlorite
Mica
Quartz
Others
Sample 608
Chlorite
Micac
Quartz
Others
The modal quantitative determinations using the combined
SEM/EDS analysis was conducted using a FEI Quanta 200 environmental scanning electron microscopy (ESEM) instrument
equipped with an energy dispersive XRF X-EDS Oxford
INCA-350 spectrometer. For the observations, the thin sections
of samples 602, 607, and 608 used for the optical microscopy
were loaded on aluminium stubs. Measurements were performed in low vacuum mode without coating. Micrographs of
each sample were collected in triplicate at 500 and 1000× magnifications using back-scattered electrons.
The obtained images were digitalized and analysed through
using both ArcGIS ESRI version 10.1 and ImageJ open source
version 1.42q (Wayne Rasband National Institute of Health,
USA) software to determine the phase fraction of each mineral
phase on the basis of the crystal habit/morphology. In ArcGIS,
QPA Rietvelda
Optical counting
EDS mappingb
Chemistry bulk calculation
0.7(2)
13.7(2)
85.6(1)
–
–
10.1
89.9
–
–
5.4
89.6
5.0
–
13.0
84.6
2.4
2.5
14.1
83.4
–
–
6.7(2)
93.3(2)
–
–
9.0
91.0
–
–
11.3
88.3
0.4
–
11.3
88.7
–
1.1
4.3
94.6
–
2.3(2)
11.7(1)
86.0(1)
–
–
9.6
90.4
–
–
13.5
86.2
0.3
–
13.5
83.9
2.6
4.7
10.0
85.3
–
SEM
The agreement factors of the refinements are: 602 Rwp = 15.33%, Rp = 12.22%, and χ2 = 7.723; 607 Rwp = 16.11%, Rp = 12.18%, and χ2 = 12.0; 608 Rwp =
15.67%, Rp = 11.63%, and χ2 = 11.53.
b
Merge of both 500 and 1000×.
c
The term mica includes both muscovite and biotite.
a
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Powder Diffr., Vol. 31, No. 1, March 2016
Quantitative analysis of quartzites from Alaska Range (USA)
33
mineral phase. To do that, morphological inputs and data of
the chemical spot analysis were used. The fraction of each coloured area was calculated using ImageJ by automatic decomposition of each RGB channel and using the particle analyse
function. With this procedure, it was possible to accomplish
the fraction of each coloured fraction of each image and the
final composition was obtained by merging all the single
image data.
The mineralogical quantitative determination was also attempted using an automatic elaboration of elemental X-EDS
distribution maps for samples 602 and 607. The software
ImageJ was used again for the data analysis. In the first step,
the K-map and Al-maps were subtracted from the Si-map so
as to enhance the areas where Si concentrates (white areas, related to quartz) with respect to the areas where the other elements
such as K, Al, and Fe concentrate (dark areas corresponding to
mica and accessory minerals). The next step was to apply a 6–10
pixel wide filter to render the image more homogeneous.
Contrast and lightness were optimized to isolate the white
areas form the dark areas. The obtained image was digitalized
to binary format and analysed with the tool particle analyse.
Figure 2. SEM image and relative EDS scan of a well-defined crystal of
presumably goethite found inside sample 602.
the high capacity of raster data analysis, allowed us to quantify
the minerals in two ways: manual vectorization applied to each
mineral phase and histogram analysis. Prior to the analysis
using ImageJ, the images were digitalized using the free vector
graphics editor Inkscape version 0.48.5 and images were decomposed into different colours related to each observed
D. XRF
XRF data of the major oxides on samples 602, 607, and 608
for the bulk chemistry calculation were collected using a
Philips PW 1480 spectrometer. The content of the structure volatiles was independently determined by Thermogravimetric
(TG analysis) using a SEIKO SSC 5200 instrument in the temperature range 20–1100 °C and a heating rate of 10 °Cmin−1.
Given the very simple mineralogical assemblage, the
Figure 3. (Colour online) Selection of optical micrographs. Legend: (a) section of 602 sample (10×); (b) section of 607 sample (10×); (c) section of 608 sample
(10×); and (d) section of 602 sample (10×) showing an example of the digitalization procedure of the mineral selection using ArcGIS.
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Powder Diffr., Vol. 31, No. 1, March 2016
Mă rgă rit M. Nistor et al.
34
Figure 4. (Colour online) Gallery of SEM micrographs. Legend: (a) sample 602, 500× (the marker is 300 µm wide); (b) sample 607, 500× (the marker is 300 µm
wide); (c) sample 608, 500× (the marker is 300 µm wide); (d) sample 602, 1000× (the marker is 300 µm wide); (e) sample 607, 1000× (the marker is 300 µm wide);
(f) sample 608, 500× (the marker is 300 µm wide); (g) section of 602 sample (500×) showing an example of the digitalization procedure of the mineral selection
using ArcGIS.
calculation of the mica muscovite weight fraction was determined as: wt% muscovite = (determined wt%K2O × 100)/
10.01. The value of 10.01 corresponding to the wt% K2O of
pure muscovite [KAl2(OH)2Si3AlO10], was calculated from
experimental data (the average of 23 chemical compositions
of muscovite samples from Volk, 1939). In turn, all MgO wt
% has been assigned to ideal clinochlore [Mg5Al
(OH)8Si3AlO10] (Brown and Bailey, 1963). The difference
with respect to 100 wt% is the wt% fraction of quartz.
Fragments of the original rock samples were manually
crushed and pre-ground using an agate mortar. The rather
coarse material was dry-milled for 20 min using an agate
mill. Final milling was performed for 40 min using a micromill with SiC balls as grinding media at low speed, to produce
a fine powder but not to overgrind it with the risk to produce
amorphous silica or amorphous phases (this procedure has
been tested in our laboratory using standard sample powders).
XRPD data for both qualitative and quantitative analyses
were collected using a Bragg–Brentano θ–2θ diffractometer
(Philips PW 1710 with PW 1729 goniometer, PANalytical,
The Netherlands) equipped with a gas proportional detector.
The experimental set-up accomplished: a ½° divergence slit,
0.04 rad soller slits, and a ½° anti-scatter slit on the incident
beam pathway, a 0.2 mm receiving slit, 0.04 rad soller slits
and a curved graphite monochromator on the diffracted
beam. The radiation source was an X-ray tube with copper radiation (λCuKα1,Kα2 = 1.540 59, 1.544 39 Å) and the anode
tube load was 40 kV and 30 mA. The samples were sideloaded on a quartz flat zero background holder. XRPD patterns were collected at room temperature in the 5°–80°2θ
range, with a scanning rate of 0.004°s−1 and a step size of
0.02°2θ.
Preliminary qualitative phase analyses were performed
using the X’Pert High Score Plus software (PANalytical,
The Netherlands). Rietveld QPAs were performed using the
GSAS package (Larson and Von Dreele, 1999) and its graphical interface EXPGUI (Toby, 2000). The starting atomic coordinates for all phases in the investigated systems were
taken from the literature: chlorite (clinochlore: Zanazzi
et al., 2009), muscovite (Guggenheim et al., 1987), and quartz
(Gualtieri, 2000). The background profile was fitted with a
Chebyshev polynomial function with 8–12 coefficients. The
profile of the diffraction peaks was modelled using a
35
Quantitative analysis of quartzites from Alaska Range (USA)
E. Rietveld QPA
Powder Diffr., Vol. 31, No. 1, March 2016
35
Figure 5. An example of back-scattered electrons image of sample 602 (a) and the relative elemental distribution map of silicon (b), and iron (c). The map
digitalization using an automated procedure using the ImageJ software is shown for silicon (d), and for iron (e).
pseudo-Voigt function with one Gaussian and two Lorentzian
coefficients in addition to an instrumental peak asymmetry
component set to be equal for all phases.
III. RESULTS AND DISCUSSION
Table I reports the mineralogical quantitative determination from different methods for the three investigated samples
602, 607, and 608. Quartz is obviously the major phase with
subordinate mica (muscovite), and minor chlorite in 602 and
608. The SEM investigation also revealed traces of other impurities such as amorphous of poorly-crystalline iron oxides/
hydroxides, present as alteration products (Figure 2 with the
image of a well-defined crystal and its EDS chemical composition), rutile and zircon. Such impurities are below the detection limit of X-ray diffraction.
Figure 3 reports a gallery of optical images for the investigated samples 602 (a), 607 (b), and 608 (c) at 10× magnification. For sample 602 at 10× magnification, Figure 3(d)
shows an example of the digitalization procedure of the mineral selection using ArcGIS (ESRI, 2011). Figure 4 is a selection of SEM micrographs for the investigated samples 602 at
500× magnification (a), sample 607 at 500× magnification (b),
sample 608 at 500× magnification (c), sample 602 at 1000×
magnification (d), sample 607 at 1000× magnification (e),
and sample 608 at 1000× magnification (f). For 602 sample (500×), an example of the image digitalization procedure
of the mineral selection using ArcGIS is portrayed in
Figure 4(g).
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Powder Diffr., Vol. 31, No. 1, March 2016
Table I reports the results of the determinations for the three
samples using the various experimental techniques. The first
column reports the results of the XRPD QPA using the
Rietveld method. The second column reports the software assisted counting of grains of different mineral species from optical
microscopy in transmission mode. The third column reports the
software assisted counting of grains of different mineral species
from SEM imaging. Results from the analysis of images at 500
and 1000× magnification, and using two different programs
(ArcGIS and ImageJ) were merged. Insignificant differences
were detected with respect to the magnification and software
used. The fourth column is relative to the results obtained
from the digitalization of the EDS elemental maps using
ImageJ. Figure 5 reports an example of back-scattered electrons
image of sample 602 (a) and the relative elemental distribution
map of silicon (b) and iron (c). The map digitalization using an
automated procedure in ImageJ is shown in Figure 5(d) for silicon and (e) for iron. The last column of Table I reports the
phase fractions calculated from the bulk XRF chemical analysis. Table I reports the Rietveld quantitative phase composition
of the samples with the relative agreement factors (as defined in
Larson and Von Dreele, 1999). The Rietveld graphical outputs
are shown in Figures 6(a–c).
Figures 7(a–c) are histogram plots for the three samples of
the fractions of quartz, mica, and other accessory minerals
(chlorite) determined with the various experimental techniques. The horizontal full line is the calculated mean and
the broken lines are relative to the standard deviation. With
the aid of the standard deviation, the numbers which greatly
depart from the mean value can be appreciated.
Mă rgă rit M. Nistor et al.
36
Figure 6. (Colour online) The Rietveld graphical outputs for sample 602 (a),
607 (b), and 608 (c). Markers relative to the reflections of the crystalline phases
present in the systems in the selected 2θ range are also shown together with the
difference curve between the observed and calculated pattern.
In Figure 7(a), the mean value for quartz is 86.6 (2.6) wt%.
Both EDS mapping and bulk chemistry calculation are in line
with the results from the Rietveld method. On the other hand,
both optical and SEM counting appear to be overestimated.
The same applies to mica. The mean value for mica is 11.3
(3.4) wt%. The quantitative determination with the Rietveld
method shows results similar to the EDS mapping and bulk
chemistry calculation. They are all close to the mean value
[Figure 7(a)]. The optical counting is instead underestimated
and the SEM counting is grossly underestimated. This may indicate that the statistics used of the SEM method was probably
not satisfactory and that during the measurements, areas with
abundance of quartz grains with respect to mica were presumably observed.
For sample 607, Figure 7(b) shows that the mean value for
quartz is 91.2 (3.1) wt%. The modal optical counting and bulk
chemistry calculation are close to the values from the Rietveld
method and also close to the mean value. Both modal SEM
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Powder Diffr., Vol. 31, No. 1, March 2016
Figure 7. Histogram plots showing the fractions of quartz, mica, and chlorite
(others) determined with the various experimental techniques. The horizontal
full line is the calculated mean and the broken lines are relative to the standard
deviation. Legend: (a) sample 602; (b) sample 607; and (c) sample 608.
counting and EDS mapping are underestimated although rather close to the standard deviation. The same applies to the results observed for muscovite. The mean value for mica
muscovite is 8.5 (3.1) wt%. Although the quantitative determination of all the methods except the bulk chemistry calculation is close to the mean value [Figure 7(b)], SEM and
EDS mapping determinations are fairly different from the results of the Rietveld method. The determination of the other
phases is statistically not significant.
In Figure 7(c) (sample 608), the mean value for quartz is
86.2 (2.5) wt%. The quantitative determinations are all within
the limits of the standard deviation. SEM and bulk chemistry
calculation convey results close to those determined with the
Rietveld method. Instead, the determination with the modal
optical counting is instead strikingly overestimated. The
Quantitative analysis of quartzites from Alaska Range (USA)
37
mean value for mica is 11.7 (2.3) wt%. All the quantitative determinations are within the limits of the standard deviation and
close to the results from the Rietveld method. The few observations for the other phases prevent any statistically significant
consideration.
In the section Introduction, we have reported that it was
not possible to collect more than three samples during the
field expedition because of the hard environmental conditions
and that this work should be considered a preliminary methodological investigation. Notwithstanding, despite the small
number of observations (samples), it is possible to highlight
that the results which apparently show major scatter and larger
departure from the Rietveld estimates are from modal optical
and SEM counting. Good agreement is found between the
X-ray diffraction estimates and bulk chemistry calculation as
they are both bulk methods with high statistics significance.
Although we have analysed a number of sections for both
the optical and SEM digitalized counting, the statistics is probably insufficient to provide accurate results comparable with
those accomplished with bulk methods. A protocol of analysis
should be drawn by defining the minimum number of fields to
be analysed for both modal optical and SEM counting to obtain statistically meaningful accurate data.
Our findings are in line with those reported for the case of
heavy minerals in sandstones for which Webster et al. (2003)
reported that the optical/SEM area observations should be
considered preliminary especially for epidote, augite, feldspars, and talc. More confidence could be placed in the
optical-SEM/EDS results if they included microanalysis of
all questionable grains present in each of the three size fractions. Although Webster et al. (2003) claimed that there is reasonable agreement between mineral abundances determined
from the optical/SEM work and Rietveld refinements, significant difference between the two methods was found in the
paper concerning the abundance of the dominant phase diopside: Rietveld refinements yielded 46 wt% whereas optical/
SEM work yielded 56–57 wt%. This difference was probably
greater than uncertainty in optical identifications or the limited
number of refinements can explain and was likely because of
the effects of preferred orientation not properly accounted for
in the Rietveld refinements. On the same line, such discrepancies have also been recently observed in a different more complex system, e.g. cement–asbestos (Croce et al., 2014).
There is certainly a dependence of the accuracy of the results upon the nature of the sample as other authors (Gonzalez
et al., 2003) reported that despite uncertainties, the results of
the Rietveld QPA of volcanic rocks (dacite) compare quite
well with optical/SEM results. Le Saoût et al. (2011) observed
a good agreement between SEM and Rietveld data as far as the
alite/belite ratio in anhydrous cements is concerned.
It should be remarked that the accuracy of the estimates
from bulk chemistry calculation are favoured by the simple
mineralogical assemblage displayed by our samples but
cases of more complex systems such as ultramafic rocks
which display accurate results are also reported in the literature
(Hill et al., 1993). As a matter of fact, determinations with
bulk chemistry calculation can be affected by large discrepancies as the chemical composition of the mineral phases in the
system is not well defined. If the choice of the chemical composition is correct, it is found that model-derived bulk analysis
and optical modes may display comparable results. Although
normative mineralogy is based on complete equilibrium
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Powder Diffr., Vol. 31, No. 1, March 2016
crystallization and may not exactly represent the volumetric
proportions in the mode, it at least provides a basis for comparison, and indicates that the optical modes are reasonable
(McBirney, 1993; Hamilton and Christensen 2000).
IV. CONCLUSIONS
In the present work, three quartzite samples from Alaska
were selected as case study to test the various experimental
techniques commonly used for the determination of the mineralogical quantitative analysis of rock samples (modal optical
counting, modal SEM + EDS counting, bulk chemistry calculation, and Rietveld QPA). The findings of this work may be
of help to select the best non Rietveld method to perform
quantitative-/semi-QPA on natural (rock) or industrial samples
such as cements and clinkers.
Despite the limited relevance of our statistical analysis, it
was found that the less accurate results are apparently obtained
from modal optical and SEM digitalized counting. The determination with EDS mapping was found to be inaccurate only
for sample 607. Agreement was found between Rietveld QPA
estimates and bulk chemistry calculation. For both optical and
SEM digitalized counting, the statistics was probably insufficient to provide accurate results comparable with those accomplished with bulk methods. A protocol of analysis should be
outlined by defining the minimum number of fields to be analysed for both optical and SEM counting to obtain statistically
meaningful accurate data, accepting a compromise between
accuracy and time of analysis.
The analytical plan used hereby should be applied to more
complex natural and synthetic systems in the attempt to generalize the findings of this work and assess the precision and accuracy of each experimental method even when biasing
factors such as the presence of amorphous phase.
ACKNOWLEDGEMENTS
G. Urso of the Centro Interdipartimentale Grandi Strumenti
(CIGS) of the University of Modena and Reggio Emilia is
kindly acknowledged for help with the SEM analyses.
SUPPLEMENTARY MATERIALS
To view supplementary material for this article, please
visit http://dx.doi.org/10.1017/S0885715615000871
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metamorphic rocks,” J. Geol. 67(2), 135–152.
Bish, D. L. and Howard, S. A. (1988). “Quantitative phase analysis using the
Rietveld method,” J. Appl. Crystallogr. 21, 86–91.
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Quantitative analysis of quartzites from Alaska Range (USA)
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