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ERRORS IN ANALYSIS OF SULPHIDE RiCH SAMPLES
BY X-RAY FLUORESCENCE SPECTROMETRY
Mirela P. Saraci
A thesis submitted in confonnity with the requirernents
for the degree of Masfer- ofScience
Graduate Department of Geofog?
University of Toronto
O Copyright by Mirela P. Saraci, 2001
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ERRORS IN ANALYSE OF SULPHIDE RICH SAMPLES
BY X-RAY FLUORESCENCE SPECTROMETRY
Mirela SARACI, M-Sc., Department o f Geology, University of Toronto, 200 1
Abstract:
XRF analyses of sulphide bearing sarnples using pressed powder pellets are
subject to large errors. Large errors, due to inhomogeneity and segregation, were found
in two-component mixtures and were most severe in mixtures with low sulphide
concentrations (up to 30%). Grain size is also a source of intensity errors if it is larger
than the average penetration depth of the fluorescent x-rays.
Fundamental parameters cannot handle the wide range o f composition in
sulphides without using the non-standard corrections. Accurate results may be obtained
if silicate and sulphide mixtures are used for calibration or if different calibration curves
are used to cover difierent concentration ranges.
In multi component mixtures, total S analyses were correct whereas chalcophile
elements were too low and lithophile elements, too high. The magnitude o f errors in Cu,
Zn and Fe are similar whereas those for Pb are much larger.
Acknowledgements
My first special thanks go to my supervisor Dr. Mike Gorton for his invaluable
help, guidance and support. 1 thank him for giving me the chance to continue the
scientitic path which started with simple ideas that lead to a complex probiem which 1
hope have helped to give answers.
1 would also like to thank my thesis cornmittee members Dr. G. Henderson and Dr
J.M. Brenan for their review of this rescarch and comments for its improvement.
Special thanks go to Mr. and Mrs. McRae for their generosity in providinç the
financial support and their extraordinary help in overcoming difficuities while completing
my program.
1 wish also to thank Dr. J. J. Fawcett for his continuous support and
encouragement during these years and Dr. C. Cennignani, Dr. D.S. Smith and G.
Kretschmann for their help with other techniques used in this project.
Finally, 1 am most grateful to my son, Armir and my husband Arben for showing
patience, understanding and giving me unconditional love and support during these years.
TABLE OF CONTENTS
Abstrac t
Acknowledgements
Table of contents
List of tables
List of figures
Introduction
Analytical conditions
Sample considerations
2.1. Sample preparation procedure
2.2. Pellet preparation
2.3. Penetration depths
2.4. Grain size effects
2.5. Segregatior, effects
Inter element effects (Matrix effects)
Quantitative analysis-Fundamental parameters method
Calibration procedure
Results
Concf usions
References
List of Tables
Table I : Operating conditions in sulphide application 7
Table 2: Pellet formation precision 8
Table 3: Analysis depth and mass absorption coefticients of sulphide minerals 19
Table 4: Emission and absorption x-ray energies 34
Table 5: Cali bration reference materials 45
Table 6: Sulphide rich mixtures analyzed by X-ray Spectrometer
Table 7: Control results for mixture containing 50% Galena
Table 8: General table of quantitative results
a) concentration and
b) raw intensities.
List of Figures
Figure 1 Penetration depths of different elements in sulphide minerais. 18
Figure 2 Grain size effects on Sr Ku intensity (Claisse and Samson. 1962) 24
Figures 3&4 SEM images of grain size distribution for pyrite, CuS, sphalerite and
galena. 25-26
Figures 5,6 &7 Grain size et'fects on intensities of pyrite, sphalerite and galena. 27-29
Figure 8 Absorption and fluorescence effects on constituent elements of
sulphide minerais. 35
Figures 9 & 10 Effect of y factor on the Fe calibration curve. 49-50
Figures 1 1-20 Binary mixtures- uncorrected and FP corrected 58-67
Figures 2 1-25 Multi component mixtures FP corrected. 73-77
1. Introduction
X-ray fluorescence spectrometry (XRF) is one of the most commonly used
techniques for the analysis of geological samples and is ideal for the measurement of major
and minor elements in rocks. The main advantages of the technique are that it can perform
multi- elemental analysis measuring a wide range of concentrations, ofien with a precision
of better than 1%, requires relatively simple preparation techniques and analyses solid
sarnples. Moreover, modem XRF spectrometers have high long-term stability and
automated spectrometers allow for extended operations and faster throughput of sarnples.
The traditional techniques that are employed in analyzing sarnples rich in suiphides
require digestion of the sarnples by strong acids (aqua regia, KN03, HC104, HF, HCl) and
analysis by Atomic Absorption (AA) or Inductively Coupled Plasma Atomic Emission
Spectrometer (ICP-AES). This digestion rnethod works weli for sulphides but is less
satisfactory for silicates. Reliable whole rock analyses require pre-fusion with lithium
metaborate or tetraborate. However, the presence of even small arnounts of sulphides causes
problems because the released sulphur attack the platinum crucibles used for tùsion.
Sulphide bearing samples can be fiised in graphite crucibles or pre-roasted in air, although it
can lead to formation of sulphates. Fusion is also subject to the loss of volatile heavy
metals. Thus, simultaneous, accurate analysis of both the sulphide and silicate component,
are dificult to achieve.
However, x-ray fluorescence analysis of sulphide rich sarnples has also been
considered a challenging problem (Nomsh & Thomson, 1990; Spanenberg, Fontbote &
Errors in anafysis of sulphide rich samples by x-ray fluorescence spectrometry
Pemicka, 1994). The primary dificulties associated with obtaining accurate elemental
determinations of elements cornprising sulphides mise fiom their broad variable modal
abundances, up to tens of percent. Matrix effects are also particularly problematic because
of the wide range of the absorption coefficients of the transition elements and the common
occurrence of secondary fluorescence. Another problem in anaiyzing base metals in
sulphides is the scarcity of well-characterized reference samples.
Very little previous work has been done on this subject. Most studies on sulphide
and ore samples have reduced the matrix effects and eliminated particle size effects by using
fused Li tetraborate glass discs, which however, presents the already described problems.
The use of pressed powder pellets for the analysis of zinc ore concentrates is described by de
Gyves, et al., (1939) where they study a limited compositional range in which Zn, only
varied over to 40-65%, Pb O. 1 - 10% and Fe 0.5- 1 1 %.
The main objective in this research was to investigate the application of XRF to the
analysis of sulphide rich samples using pressed powder pellets, what problems anse and
what c m be done to eliminate or at least to minimize them as much as possible.
A secondary objective was to investigate the application of the Fundarnental
Parameters data reduction software. The Fundarnental Parameters method permits
determination of the composition of a sarnple directly fiom the measured intensities by using
the primary spectral distribution from X-ray tube and the absorption and fluorescent yield of
matrix elements by using mathematical equations. Since these influence parameters are
Errors in analysis of sulphide rich samples by x-ray fluorescence spectromeby
calculated fkom theory they can apply to any kind of matrix and no empirical correction
coefficients are required (Rousseau,. 199 1 ).
If the application of this method were satisfactory in sulphide rich materials, it would
facilitate rapid, quantitative analysis on a routine basis. This powerfiil method has great
potential to yield improved results and combines the theoretical exactness of fundamental
parameters with its innovative calibration procedure. Theoretically, it c m be applied to the
analysis of any sample type and offers maximum accuracy limited only by the quality of
sample preparation and standards used.
A third objective concerns the evaluation of analyses for Cu. Researchers from other
laboratories have reported unreliable results when analyzing Cu in Cu- bearing sulphide
minerals and similar problems have arisen fiom different commercial labs (usually results
are too low). For those who deal with Ni sulphides and Pt group elements, accurate
concentrations of Cu are important as Cu interferes with the Ni sulphide assay (Chusi Li. p.
comm.).
The new XRF spectrometer, PW 2404 and the built-in software c m , with some
effort, handle the corrections for matrix effects by using the tùndamental parameters data
reduction. However, the results are still affected by errors fiom sample preparation and
inhomogeneity on the scale of the penetration depths, as described in this study.
Errors in analysis of sulphide nch samples by x-ray fluorescence spectromeûy
Chapter 1. Analytical conditions
X-ray fluorescence analyses for major elements in sulphide rich sarnples were
performed by wavelength dispersive x-ray fluorescence spectrometry (WD-XRF). The
instrument used is a fùlly automated, Philips PW 2404 sequential spectrometer equipped
with an automated sample changer. An end-window rhodium anode tube with a 4 KV
power supply was used for irradiating the sarnples. Operating parameters for the
determination of major elements on pressed powder pellets are listed in Table 1.
In the sulphide application package, a combination of crystals and collimators are
used to achieve the optimum resolution and sensitivity. The standard crystal LiF200 is used
with the 300 pm collimator to give the maximum sensitivity for elements expected to be
present in trace concentrations like Ag, Cd, As, Mn. AI1 major elements are analyzed using
the combination of the LiF220 with the fine 150 pm collimator, which increases the
resolution, but reduces the sensitivity in order to avoid overloading the detectors. Sulphur is
measured using the Ge I l 1-C crystal and the fine collimator. This method has a high
sensitivity for sulphur, since the Rh L a l line with an energy of 2.7 keV eficiently excites
the S Ka line used in S determination (S K,b = 2.470 keV).
For accurate x-ray fluorescence analysis it is necessary to obtain clear peak
intensities corrected for background and spectral overlaps, before any corrections for matnx
effects are made. Corrections for spectral overlaps are applied when the neighbouring line
in the spectrum causes line overlaps, which are not completely resolved, by the spectral
resolution of the spectrometer or the energy resolution of the detector. Line overlaps are
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
usually corrected using the intensities of the interfenng element. However, corrections for
overlaps of Mo L a and Pb M a on sulphur cannot be made directly because their intensities
are not been measured (Mo L a = 2.293 keV and Pb Ma = 2.346 keV). Instezd, corrections
must be made using intensities calculated fiom concentrations. This is less reliable because
of the uncertainties in the concentrations caused by matrix factors and uncertainties in the
calculated intensities fiom the calibration.
For major elements, spectral interferences are usually minor and the determinations
of their concentrations are made using the intensities of Ka emission Iines. However, in the
first transition metals, the choice of backgrounds requires care to avoid interference from the
KP line of the preceding element in the periodic table. Corrections for the Kj3 interference to
the background, peak or both were made from Mn to Ni. Overlap corrections are applied to
the background of Cd Ka for As K a and Ag Ka for Cd Kai (Table 1).
The most severe line overlap occurs if the sarnple composition is expected to contain
Pb and As. Since these two elements are most likely to be expected in sulphide samples, a
carefiil choice of lines is made in the sulphide application. The As K a is the strongest line
in the As spectrum but it has the sarne emission energy as the strongest Pb line (As K a =
10.543 keV and Pb La = 10.549 keV). Thus, in the sulphide application, As is measured
using As KPi (15%) and Pb using Pb Lpi (80%).
Precision and accuracy: The precision of an x-ray fluorescence intensity
measurement is a function of the total number of counts registered. The XRF instrument
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
used in the research, PW 2404 model, given the proper selection of operating conditions,
offers high sensitivity and stability. Even with the lowest counting time chosen, 2 seconds
on the peak and 2 seconds on the each background, the sensitivity is more than adequate to
give acceptable precision. The worst cases would be in mixtures with low concentrations of
elements i.e. 5 % galena where S Ka has the lowest counts possible 5.2255 * 0.036 kcps,
giving a relative error of 0.4 %. Similady, Zn in the mixture of 5 % sphalerite yields the
lowest counts for a transition element with a counting statistics of 42.693 * 0.103 kcps and a
relative error of 0.24 %. In the mixture, where SiOz is the least abundant compound, the
counting statistics are 304.74 0.276 kcps and a relative error of 0.09 1 %.
Another factor, which could affect the precision of the measurements, is randorn
variations introduced by the pellet formation procedure, which was investigated by making
five identicaI pellets for pyrite and galena (Table 2). The five replicates were prepared from
the same sample powder for each mineral and using the sarne pressure in the press. The
precision of pellet preparation b a s d on the eiemental concentration results are as follows:
S,, = 53.57*0.25; S, =14.M 0.089; Fe = 46.0M0.053 and Pb = 87.56* 0.042. The relative
errors are the largest for S (=: OS%), lower for Fe (-0.1%) and the lowest for Pb (~0.05%).
The fact that sulphur, with the least penetrating x-rays, has the largest error, suggests that
these variations are due to the roughness of the pellet surface.
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
A ? , a m m m ~ ~ 0 aJ c a E Z
Chapter 2. Sample considerations
X ray spectrometry is probably the most flexible of al1 the instrumental analytical
methods with respect to the variety of.physica1 specimen f o m s that can be presented to the
spectrometer for x-ray irradiation. The basis of quantitative x-ray fluorescence spectrometry
is the measurement of the intensity of one of the characteristic lines, which is then used to
calculate the concentration of the element. In an ideal situation, where neither grain size nor
the inter-element effects affect the intensity of the x-rays, the intensity of the characteristic
line would be linearly proportional to the concentration of the element. However, in general
and especially in sulphide rich samples, this is not the case becaüse of the influence of other
factors such as physical effects of the sample and elemental interactions (Chapter 3).
This chapter considers problems in the quantitative analysis of sulphides, which are
directly connected with sample preparation. In particular, this involves the effect of grain
size on the intensities of the fluorescent x-rays of the major elements in sulphide minerals.
As stated in Jenkins, et al. (1995), the dependence of x-ray intensities upon the physical state
of the specimen is well known since the fluorescent radiation is coming fiom shallow depth.
Thus, the surface and the grain size of the particles become very important factors in x-ray
fluorescence analysis. In addition, segregation during pellet formation, also influences the
accuracy of the results.
Therefore, specimen preparation is one of the largest sources of emrs in x-ray
fluorescence analysis and the choice of the sample preparation method is very important.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
The goal of a suitable specimen preparation procedure is to prepare the specirnen in such a
manner that the physical properties (apart fiom the composition), which influence the
emitted intensity of charactenstic lines, wi 11 be minimised. Therefore, at the beginning of
this research, with the purpose of getting accurate and reliable analysis, it was important to
consider what kind of sample preparation method is the most suitable one for sulphide rich
sarnples.
2.1 Sample preparation proccdure
In analyzing geological samples by XRF, the most commonly used sample
preparation methods are: fised glass disks and pressed powdcr peliets.
For whole rock analysis, fused glass discs are the method of choice for major
elements. The hsion technique eliminates particle size effects, and reduces matrix effects
significantly. This is a very effective method, where fusion with sodium or lithium
tetraborate transforms the sample into a homogenous glass. Although this method is ideal
for most whole rock analysis, its application to sulphide rich samples is practically
impossible.
The first problem is that sulphides even at Iow concentrations (few %), melt and
dissolve the expensive Pt-Au fusion crucibles, destmying them.
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
The second problem with sulphides is the loss of volatile elements dunng the fusion
and heating. Sulphur has a boiling point of 444" C, while the boiling points for other
elements are as follow: Zn of 907' C, Cd of 765' C, As of 6 14.0° C, Se of 685" C and Hg of
365' C. There are different approaches to the fusion procedure that try to retain these
elements but even when oxidants are used or samples are oxidized by preheating in air,
some elements like Pb and As form volatile compounds which will evaporate readily.
Furthemore, some of the gaseous species produced during evaporation are poisonous, such
as As, Pb, Cd and Hg. This becomes a serious problem when a great number of samples are
required to be fùsed.
These restrictions and limitations lead to the consideration of pressed powder pellets
as an alternative sample preparation method. The pressed powder method is a rapid and
convenient technique, which allows the preparation of both permanent standards and
unknown samples. When using the pressed powder pellet method in sample preparation it is
essential that al1 samples and standards have the same average particle size and particle size
distribution in order for al1 the effects to cancel out. Therefore, al1 samples and standards
were prepared in precisely the same way.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
2.2 Pellet preparation
In quantitative analysis, it is important to ensure that the sample is thick enough for
the analysis depth of the characteristic line that is going to be used in the determination of
the composition (see next section). The mass of powder cm vaiy, depending on the energy
of line that is going to be used. The most energetic lines (Ka), which have high penetrating
power, require a higher effective volume of sample, and the mass needed to prepare the
pressed powder pellets can be calculated. The minimum mass of powder that can give
infinite thickness can be calculated for each element (analyte line) that we are interested in
according to the formula:
Sample mass = Volume * p
= Thickness * Area * p
where p is the density of the material.
Philips sample holders have a circula aperture of diarneter 28 mm, which is the
diameter of the powder, exposed to the primary x rays. The thickness is the analysis depth
(penetration depth) for sample to be considered "infinitely thick". For the 28 mm sample
holders, the penetration depth (P.D.) formulae is:
P.D. = 2-96 / (p*p)
Errors in analysis o f sulphide rich samples by x-ray fluorescence spectrometry
where, p is the mass absorption coefficient of the sample, and
2.96 is a constant that incorporates the area of the sarnple, the sine of the take off
angle and -in(O.O 1 ).
Sample mass = (2.96 1 p*p) * Area* p =
= 18.23 / p (g)
Before the sample preparation procedure, al1 the masses required for infinite
thickness are calculated and for two extreme minerals in the sulphide series, the mass for Fe
Ku and Pb LP (the least and rnost energetic lines) Vary between 0.14 and 0.28 grams. In the
case of S, it releases low energy x-rays, which are the least penetrating x-rays arnong al1 the
elements of sulphide minerals. Since they corne from a very shallow depth, the effective
volume for S Ku is very small compare to the volume of the high energy s-rays.
Consequently, for S it was not necessary to calculate the infinitely thick mass of the sarnple.
In practice, the minimum mass required for sulphide minerals is too small to make a
layer of reliably uniform thickness; therefore, a mass of 2 g. is used in each pellet of pure
sulphide specimen, creating an infinitely thick pellet for each anal yte line. When sulphides
are in the mixtures with silicate rock powder, the lower density and mass absorption
coefficient requires 4 g., for an infinitely thick pellet.
Al1 samples are prepared by grinding and using the -400 mesh fraction in al1
standards and mixtures except for the synthetic compounds which proved to be rnuch finer
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrornetry
grained. Grinding is an extremely quick and effective means of reducing the particle size
effects but it does not eliminate them. Natural sulphide samples like pyrite, galena,
sphalerite, Fe rich-sphalerite, and pyrrhotite are ground for 10 -1 5 minutes in the alumina
mil1 and the powder is sieved to obtain 400 mesh (Iess than 38 pm) material.
The calculated mass of the powdered material is briquetted into pellets under 5
ton/inch2. In order to make the pellets easy to handle, powdered boric acid is used to encase
and make a backing for the pellet. The pressed powder pellet in this form is rigid and easy
to use in the x-ray fluorescence spectrometer.
Al1 mixtures are prepared using the 4 0 0 mesh fraction of each sulphide of interest
with fine rock powder. They are mixed mechanically using a Spcs MixerMill 8000 for
about 4-5 minutes. Attempts to mix them for a longer time failcd becausc aggregation
causes caking of the material on the sides of the miII.
2.3 Penetration depth
In x-ray spectrometry, it is the intensity of the fluoresced, characteristic x-rays from
the specimen, which provides the analytical signal for quantitative analysis. When the
sample is irradiated with x-rays, the primary beam is attenuated exponentially as it
penetrates the sample and the characteristic x-rays that are produced from elements present
in the sample are similarly attenuated as they escape (Jenkins and De Vries, 1973). Thus the
Errors in analysis of sulphide rich samples by x-my fluorescence spectromew
fluorescent x-rays, which are detected, have originated mostly fkom the surface of the
sample with progressively fewer from greater depths, consequently the contribution of the
outer layers of the sarnple will be much greater than that of the inner layers.
Theoretically, XRF spectrometry is concemed with the penetration depth, which is
not the depth of penetration of the primary x-rays into the sample but the depth fkom which
the secondary fluorescent x rays escape from the sarnple. The analysis depth (P.D.) is the
thickness, which gives 99 % of the maximum possible intensity and is calculated from the
following equation:
* *d / sin (y2)) Id& = 0.01 = e ('
This can be reamnsed to give d, the analysis depth,
d = - In (0.01)* sin ( v t ) / p *p
Where:
Id Intensity of x-ray at depth d
10 Intensity of the x-ray at the surface of the sample
P Mass absorption coefficient (cm2 / g)
P Specific density of the material (g / cm')
d Penetration depth (cm)
VI2 Take off angle of the spectrometer
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
For a given x ray energy, 99% of the x-rays corne fiom the volume of sarnple defined
by this equation, and this means that beyond this volume, secondary x-rays cannot emerge to
the surface. Therefore, the maximum intensity can be obtained for the thickness that
corresponds to 99% yield of intensity and sarnples that exceed this thickness are termed
"infinitely thick".
Penetration depth is dependant on the energy of the photons, the mass attenuation
coefficient (average atomic number) of the sampte matrix and the density of the sarnple. In
samples that consist of different elements, the absorption coefficients of the matrix are
different for each characteristic line; therefore, the infinite thiclcness is different for each
element. In order to obiain satisfactory analysis, it is necessary that the specimen be
infinitely tliick, calculated from the equation (2), for the highest energy of line to be
mcasured. Al! the prcsscd powder pellets are prcparcd aftcr thc pcnctratiori dcptlls arc
calculated, witli sufficient sarnple to create infinitely thick pellets for every element analysed
(see previous section).
The calculated analysis depths for most common elements in sulphide minerals, S,
Fe, Pb, Cu and Zn, are plotted in the graph in Figure 1, and are calculated from the pure
sulphide of each element. Al1 curves in the graph are calculated fiom equation (2) and
cumulative intensities are plotted against peneiration depths. Penetration depth for S is
calculated fiom CuS and al1 calculated penetration depths for each component in sulphide
are shown in Table 3.
Errors in analysis of sulphide nch sampfes by x-ray fluorescence spectrometry
The analysis of light elements like S, as s h o w in the graph of x- ray attenuation with
depth (Figure 1) is a surface phenomenon and most of the S x-rays are coming from the
upper few microns of the sample. From the graph, in order for light elements like S to give
their 99 % intensity, their penetration depth is in the range 4-9 pm (Table 3) whereas for
other elements with higher energy x rays the penetration depths are much higher, ranging
from Fe K a at 45.7 pm to Zn K a at 128.8 Pm. The graph in Figure 1 also shows that for S,
only the surface of the grains will be analyzed in the commonly used fraction of -200 mesh
(less than 75 pm). But, even in the fiaction 400 mesh with an average 15 pm grain size we
are not measuring the volume of the grain.
FurtIierinore, bccause of the exyoiiciitiüi naturi: of s-ray atteiiuatioii, tIic figures for
pençtration depths are misleading arid the dominant part of the s-rays corne fronl the
shallowest layers of the sarnple. Table 3 includes depths for 50 % yield, equivalent to
"average penetration depths", whicli are a factor of 6.6 less than the penetration depths for
99 % yield. This fùrther emphasizes the very surface-related nature of x-ray spectrometry.
Surface area to volume ratio is a strong function of grain size. As we further reduce
grain size, we increase the surface area and consequently increase the intensity of the low
energy x-rayç, which are mostly coming from the surface of grains. Considering, the first 50
% yield of x-rays are the most dominant x-rays in the intensity measurements, in order to
achieve the maximum expected intensity, the grain size is required to be far less than the
penetration depth of 50 % yield.
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
2.4 Grain size effects
In penetration depth section, it was concluded that grain size could also affect the
measured intensities. Several studies have investigated grain size effects on spectral line
intensities for specific situations, and for the most part in compound mixtures. Various
authors give different grain sizes that would not affect the intensities of the fluorescent
radiation depending on the specific nature of the sarnple. Jenkins and de Vries (1977)
indicate that grinding the matenal to a size of less than 20 pm cm eliminate grain size
effects while others (Bertin, 1975) consider the size fraction 400 mesh (less than 38 pm )
free fiom these effects.
Claisse and Sampson, (1962) have studied the effect of particle size in synthetic
mixtures of compounds and have shown that for any x-ray wavelength, a sample gives
fluorescent intensities that are independent of particle size orily for very fine (less than 5
pm) or very coarse particles ( 1 mm). In between tliese extremes, there is a transition zone
where intensities depend in a complex way on the phases present in the mixture and the
shape of their particle-sire distribution curves, and quantitative analysis become very
difficult. Theoretically calculated, the intensity curve as a function of grain size has a
sigmoid form, which reaches a plateau when the grain size is less than the average
penetration depth of the wavelength (Figure 2). According to the Claisse and Samson's
study, the grain size effects are larger for concentrations of fluorescent compounds less than
60%, smdler for high concentrations (40-go%), while for pure compounds there is no
reliance of intensity on the grain size.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
However, for pure compounds, Bertin (1975) has shown that the intensity of the line
initially remains constant for very coarse grain sizes, and then increases as the particie size
in the sarnple approaches the penetration depth of the measured wavelength. They
suggested that this effect happens in the surface of the specimen where coarse grains (larger
than the penetration depth of the line) have a shielding effect on the fluorescence x-rays.
Having considered al1 the information from the Iiterature, and before starting the
calibration of the XRF machine, it was necessary to know what grain size could be
practically attained and at what grain size intensities for metals and S would rernain
constant. It was also important to investigate if the finest fraction in the routine sample
preparation is good enough for quantitative analysis of sulphide minerals.
For this reason, pure sulphide samples have been investiçated including pyrite
(containing Fe the lowest atornic nurnbtlr transition element) sphalerite and galena (Pb, the
largest atomic number, chaikophile element). Samples were ground and then sieved,
creating six different fractions -635, 635-300, 400-325, 325-200, 200- 120 and the coarser
100- 120 mesh with the mean average sizes of 10 Pm, 19 Pm, 4 1.5 Pm, 60 Pm, 100 Fm, and
137.5 pm respectively. In order to assess the distribution of the grain sizes, pellets with the
finest material used (-400 mesh), were inspected under SEM (Figure 3 and 4). The two
finest fractions of -635 mesh and 635-400 mesh were later prepared to investigate the
effects of srnaller grain sizes on intensity.
Errors in anaiysis of sulphide rich sample; by x-ray fluorescence spectrometxy
The pyrite,
distribution of 15
sphalerite and galena -400 mesh fiactions have an average grain size
microns, but also include very fine material (down to 2-3 pm) and
consequently the packing eficiency is higher than the other hctions. The packing
,efficiency is higher stili for CuS pellet which contains grains of size less than -1000 mesh
(less than 1 pm) and al1 the surface of the pellet is covered with CUS grains. The apparently
coarse texture in Figure 3b is due to agglomeration of the powder before pressing as
concluded fiom the SEM backscattered image of this pellet.
X-ray fluorescence intensities for the major constituent elements Fe, Zn, Pb and S
are plotted against the mean average size of the ?actions for each minera1 (Figures 5, 6 and
7). Contrary to Claisse & Samson (1962), these diagrams show that even for homogenous
samples like pyrite, galena and sphalerite, the intensity is very grain size dependent. The
highest intensities are obtained with the tinest fraction, which is -635 rnesh (less than 10 pm)
and al1 graphs show that intensities increase as the grain sizes decrease. Al1 the metals, Fe,
Zn and Pb, show the trend to increase until the grain size reaches the penetration depth for
50% yield. Beyond this point, the intensities tend to remain constant (plateau zone). The
grain size of the - 400 mesh fraction that is used in a11 synthetic mixtures is on the plateau
zone for al1 the metals. Sulphur x-rays have very shallow penetration depths, therefore, the
grain size that would satisw the 99% or even 50 % yield is impossible to achieve. Thus, it is
expected that intensities of S x-rays would suffer tiom grain size effects more than metals in
the sulphide samples.
The shapes of the curves and the increase in intensity for the three major elements in
the suIphides are different. Pb and Fe, with penetration depths of around 50 p, lie mostly
Errors in analysis of su1 phide nch samples by x-ray fluorescence spectrometry
in the transition zone and show decreases of 18% and 13% respectively. Zn with a
penetration depth of 128 prn lies mostly on the plateau and shows a decrease of only 5%.
The grain size is not the only factor that might affect the fluorescence, otherwise we would
expect the three curves to have the same shape. The other factor that might affect the
fluorescent intensity is the packing eficiency. As the grain size increases, the pore space
between grains is larger than the pore space in the finer material, therefore in the coarser
material fewer grains are represented in the measured fluorescent intensity.
In order to be completely free from intensity errors caused by changes in grain size,
it is desirable. in the pressed-powder method, to work outside the transition zone, however,
practical coiisiderations may make tliis impossible. Thc position of the transition zonc will
be different for different elements and the dope of the line in this zone controls the
magnitude of errors in fluorescent intensities.
When using pressed powder pellets, errors introduced due to grain sizr: effects can be
minimizcd or climinated by grinding the s m p l e to a grain size Icss tlian the penetration
depth. In addition, grinding al1 unknowns and standards to the same grain size will serve to
cancel out errors.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
-
-
1 1 , 1 1 , , , , L 1 1 , , 1 1 1 , 1 1 L 1 . 1
1
, , , d i , ,
1 O 1 O0 1 O00
Grain size " 1" in microns
FIG. 2. Grain-size effects on SrKa in 9% SrCl2 iii CaC03 sliowing a close fit between the data and theoretical curve. Primary radiation Mo Ku. (From Claisse aiid Samson, 1962)
SEM image of the Pyrite and CuS pellets
FIG. 3. Back scattered electron image of the surface of a) pyrite and b) CuS pellets prepared from the -400 mesh fraction of each powder.
SEM image of the Sphalerite and Photomicrograph of Galena pellet
FIG 4. a) Back scattered electron image of the surface of sphalerite pellet prepared fiom the powder used in mixtures. b) Photomicrograph using reflected light of the galena pellet prepared fiom -400 mesh fraction.
Grain size effects in Pyrite
Grain size in micron
FIG. 5. Grain size effects on S and Fe x-ray intensities in pyrite measured in this study. The x symbols represent the penetration depths for 99% and 50 % intensity yield.
Grain size effects in Sphalerite
Grain s i x in micron
FIG. 6. Grain size effects on S and Zn x-ray intensities in splialeritc measured in tliis study. The x symbol represent the penetration depths for 99% and 50% intcnsity yicld.
Grain size effects in Galena
1 O0 Grain size in micron
FIG. 7. Grain size effects on S and Pb x-ray intensities in galeiia iiieasured in this study. The x symbol represcnt the penetration depths for 99% and 50% iiiieiisity yield.
2.5 Sample segregation
The use of pressed powder pellets for the analysis of sulphide rich rock sarnples
faces another source of error due to heterogeneity of the sarnples. A rather special problem
arises when analyzing samples that are of different phases and different grain sizes. During
grinding, differential particle size reduction may occur because the various hardness of
constituents of the sarnple creating reduction in size at different rates. Therefore, in
powders, which have different grain sizes, segregation may occur during preparation of
pellets. It occurs when pouring of the powder into the pellet die or while pressing it. This
rnay occur either due to different grain sizes, differences in density and differences in
surface properties of the minerals present in the sample (Boutreux, 1998). Segregation
effects are to be expected in the synthetic mixtures, because of the differences in density of
sulphide and silicate minerals.
As mentioned before, x-rays penetrate a very thin layer on the sudace of the pellet. It
is important that the surface is a representative layer of the bulk sample and thus vertical
segregation is a potentially significant source of error. Inhomogeneity due to lateral
segregation would automatically be averaged out because of the use of a sample spinner to
rotate the sarnple in horizontal plane. Furthemore, diameter of the pellet is large relative to
the small distance over which segregation appears to occur.
The occurrence of segregation has been checked using L lines as they are rnuch
lower in energy than K lines, consequently much less penetrating. Thus comparing results
between the K line and L line of the same element is a cornmonly used way to check for
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrornetry
infinite thickness. The sarne approach was adopted to check for vertical heterogeneity due
to segregation in chapter 6, Figure 12.
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
Chapter 3. M a t h effects
The intensity of fluorescent x-rays, in addition to being proportional to the
concentration of the element of interest, is also affected by interaction with other elements in
the sample. This interaction is known under the general term of "matrix eflects" and creates
the main disadvantages in using the XRF technique. This chapter deals with compositional
matrix effects that are important in the analysis of sulphide samples.
Matrix elements may cause either absorption or enhancement to the line of interest.
Enhancement occurs when a matrix elernent releases x-rays sufficiently high in energy to
displace inncr electrons in the element of the interest, thereby increasing the yield of
fluorescent x-rays. This effect is known as "secondary fluorescence" and the correction is
called "fl~iorcscencc correction" and is proportional to the concentration of the ~iiatrix
element.
In sulphidcs, the effect is most pronounccd for ~natrix clcments t\fro positions to thc
right of the element of interest in the periodic table (Z+2 , see Figure 8), and dies away for
elements further away. Absorption occurs when matrix elements absorb x-rays fiom the
element of interest. A particular problem occurs if the x-rays are able to displace an inner
electron fkom the matrix element, because this is accornpanied by a sharp increase in the
absorption coefficient. These increases are known as "absorption edges". In sulphides, this
effect is most pronounced for elements two positions to the lefi in the periodic table (2-2,
see Figure 8), again dying away for elements further to the lefi.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
The diagram in Figure 8 shows the part of the periodic table, with the major elements
common to sulphide minerals and the principal sources of fluorescence and absorption. This
combination of relative positions of transition metals is very cornmon in sulphide samples
and along with high concentrations causes severe matrix effects. In general, absorption-
enhancement effects become more severe, the deeper the effective layer thickness is. That
is, the greater the depth fkom which analyte-line radiation can emerge or, the shorter the
wavelength of the analyte-line radiation.
One of the advantages of XRF is that these effects are predictable because of the
re~wlar variation of x-ray ener_gy and absorption edzes with atomic number. Thus. in NiS
the matrix factor for Fe (a strong absorber) is 0.56, the factors for Co, Ni aiid Cu (which
neither absorb nor fluorescence Ni) are about 0.57 and the factor for Zn (which sti-ongly
fluorcsccs Ni) is about 2.5. Thus, therc is a 51.c-îbld range in matris factors o \u - this part of
periodic table, compared with matrix factors for silicates, whicli typically range from 0.8 to
1.2.
The magnitude of these effects is dependent on the concentrations of each element,
and in quantitative determinations by XRF, fiindamental parameters corrects for these
effects. Knowledge of the complete sample matrix is thus essential to allow the prediction
and correction of the absorption and enhancement effects that will occur. Relationships
among the K Iines and absorption edges of adjacent elements are given in Table 4.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
Absorption and Fluorescence Effects on Sulphide Elements
Figure 8. Absorption and fluorescence effects on constituent clements of sulphide minerais. In each horizontal raw, the green colour shows the elements of interest while in blue and rcd are shown elements that will cause absorption and fluorescence effects respectively.
Errors iii aiialysis of sulphidc rich süiiiples by x-ray fluorcscciice spccironietry
Chapter 4. Quantitative Analysis - (Fundamental Parameters Method)
In quantitative spectrometry, the ideal situation would be a homogenous sarnple with
the intensity of the measured x-ray proportional to the concentration of the element of the
interest.
This situation is practically impossible to achieve in the case of the sulphide rich
samples, due to the grain size and the nature of inter-element effects as noted previously.
Measured s-ray intensities from a given element in a sample are not linearly related to
composition because of the matrix effects. While the sample preparation effects can be
minimized by grinding, the inter element effects are much more difficult to correct for.
Simple data rcduction schetnes wlierc cmpiricnl calibration cunrcs arc sct up o\.cr a
certain range of compositions by using standards of similar matrises and compositions, rire
very limited and can be used only for unknown samples witliin the range of the standards
uscd for calibratioii. In the case of naturd sulphidc-rich samplcs, this is difficult bccause of
the very wide range of compositions of base metals and the lack of suitable sulphide
standards.
A second problem arises fiom the large matnx correction factors associated with
sulphides. These factors are higher in sulphides than in silicate minerals, almost twice as
high as oxides, because of the high atomic number of elements comprising sulphides and
because silicate (oxide) minerals contain -50% oxygen, which reduces the magnitudes and
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
variations of matrix factors fiom one type of rock to another. Moreover, O mass absorption
coefficients are smaller than those of S in sulphides. Typical matrix factors in rocks are 0.8
-1.2 (1.6 at high Fe concentrations) whereas sulphides may range from 0.1 to 30. In
addition, the presence o f adjacent transition metals allows for high variations in matrix
factors. Compounds with high concentrations of these metals such as steels etc., suffer fiom
the same variations in these factors, too.
To solve the problems associated with empirical data reduction methods an
alternative method has been developed, known as the fundamental parameters (FP) method.
In contrast to empirically based schemes, this is a theoretically based calcuIation. The
f~indamental parameter method was proposed first by Criss and Birks (1969) and it is an
application of the basic èquations relating the x-ray intensitics from a sarnple to its
composition. which \vas first derived by Sherman in 1955.
One of the major advantages of the FP method is tliat it avoids the limited
conipositioii ranges of cnipiricnl mctliods, and tlius sliould bc cspccinlly uscful for tlic \\.idc
variations of elemental composition in sulphide rich samples.
The FP method employs a mathematical relationship between the measured intensity
of the characteristic x-ray wavelength and chernical composition. Like the other quantitative
methods, it assumes that the specimen is homogenous and infinitely thick and it has a plane
surface presented to the primary X rays. The general formulation for quantitative analysis
can be expressed as:
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
C is the concentration
K is the calibration factor
1 is the intensity of characteristic l ine emitted by the specirnen
M is the matrix factor that allows for correction of the rnatrix factors and is simply the summation of
each individual matrix effect correction in form of M = C (influence coeflicient) * Concentration
In detail, this equation requires the use of many terms to correct for al1 the possible effects.
[ ~ i + ( i ~ m r i I = i Ci p i ( Di. p i i r i r i A - r i 1 ri CSC @ + (JI/p)bl,
i . ~ CsC ) * ( l+ 1 1 Z(p/~)i.~ri x[ Dj. i-pri CjKj ()ilp)i, i-1 (~lp)~.i.~ril * [(l ( l t / i /~)~~,~ri C s c *) *
log, ( 1 + (p/p)~i,~ri csc / (I~/P).\I. i-i ) f (1 / (I'/P)AI, ;-L CSC \v) logc(l + (P/P)M, ;.L csc ~1
(F/P).\I. ;-1 1 l 1)
is the concentration of anrilyte elenlent i
is the conccriirntion o f nnnlytr elcmcnt j
has the value 1 if A ,,, is short enough to excite, AL: it has the value O for longer wavslenpths.
has the value 1 if A ,,, is short enough to excite, Aj: it has the value O for longer wavelengths.
is a function of absolute intensity of AL from element i; g cancels if a relative intensity
fiinction is used.
is [ l-(Ih)] O for the particular spectral line of element j that excites AL of element i.
is intensity of analyte line of element i.
is intensity of analyte line excited by primary spectrum.
is intensity of analyte line excited by spectral lines of matrix elernent. j in the specirnen.
is intensity of the primary bearn in the wavelength interval M ,,.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
is the analyte element
is a matrix element.
is the specimen matrix, including the analyte i.
is the absorption edge jump ratio.
is a wavelength interval into' which the prirnary spectrurn is arbitrarily divided for summation
purposes.
is the wavelength of a spectral line of elernent j capable of exciting AL.
is the wavelength of a spectral line of elernent i.
is the wavelength of the prirnary beam.
are the mass absorption coefficients o!':inaiyte i. matrix element j and matrix M. respectively.
J
AL
Apri
de ph. (Pmj.
( N P h
(@p)Il. LI,
(*ph. i.1.
( l d ~ h . >.pri are m a s absorption coefficients of matrix M for. A,. . AL and . &-
u> is the angle betwzen the central ray of the prinial cone and the specinien.
W is the ansle betwsrn the centra1 rays ~ F ~ l i t . secoiidary coiie and the speciiiieti. tnkc orf angle.
w is the fluorescent yield.
This mathematical relationship ailows the correction of mütrix effects using a series
of theoretical correction factors, wliicli are called u factors. These factors art: calculüted
using three fundamental parameters:
a) prirnary spectral distribution,
b) absorption coefficient,
c) and fluorescent yield which influence x-ray intensities.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectromeuy
The prirnary spectral distribution fiom the x-ray tube, is the most diff~cult to quantifi
because it varies with the type of tube, the choice of target material, and the operating
conditions (especially accelerating voltage and age of the tube). Al1 these parameters are
included in theoretically calculations.
Fundamental parameters that correct for absorption and fluorescence have been
theoretically calculated and are used by the data reduction routine. The accuracy of the
calculated concentrations is very dependant on the accuracy of the fundamental constants
that are in use in the quantitative model. The early use of fundamental parameters was
limited by the accuracy of these constants. Over the years, improved values for the
constants, additional corrcction terms and more powcrfi~l comp~iters have 3l!owcd accurate
(+ 1 %) calculations of cc-factors (Rousseau, 199 1).
However, in diffiçult matrixes it still niay not providç a lincar calibration ovcr a
range of compositions of more than a fcw tens of percctit. Gyves ct al. (1989) obtained good
rcsults usirig tlic FP ~netliod in analysiiig sulphidcs in tlic Iiniitcd rangc of coriccnti-atio~i (Zn
40-65 %, Pb 0.1-10% and Fe 0.5-1 1%). However, Bilbrey et al. (1988) show that the
method does not work well for Ni alloys, which had much larger ranges in composition,
similar to sulphides and errors are much larger (up to 30%) for Ni concentrations of 0- 100%.
In this research, the Philips x-ray spectrometer is attached to a computer equipped
with SuperQ software, which offers fundamental parameters. The conversion of intensities
to concentrations obtained after the corrections using FP coeficients used a concentration-
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrornetry
based regression model: C= D+E*R*M where D, E are both calibration constants and are
instrument dependent -D is the intercept and E is the slope, while R is the count rate and M
is the matrix factor. It can be seen that this regression model separates parameter D from the
matrix dependent parameters allowing a linear relationship to be derived between the
corrected net intensity and concentration. M is the matrix model used in superQ and is o f the
form:
where, Z and C are count rates and concentrations for element i, which is the element of
interest, and elements j and k are interfering elements in the sample, N is the ntimher of
clcmcnts prescnt, and a, a, S and y arc factors tliat corrcct for matrix cffccts. In the
regression, al1 thcse correction factors c m bc L I S C ~ and npplic'd to obtnin n bcttcr corrclation
but only alpha (a) factors can be calculated tIieorctically.
Alplia (u) fiçtors corrcct for tlic etfcct of losscs of iiitciisity duc ro tlis prcsciicc of
elements that absorb this wavelength in the matrix, for the enhancement that occurs due to
secondary fluorescence caused by absorption of x-rays fiom matrix elements and for the
efficiency of excitation attributable to instrumental factors.
Beta correction factors (p) are an alternative to alpha factors, but are used in the
Rasberry-Heinrich calibration model, which is not used in this research. The use of this
Errors in analysis o f sulphide rich sarnples by x-ray fluorescence spectrometry
mode1 was considered inconvenient, because f3 factors are detennined empirically and a
large number of standards are required to calculate them.
Delta factors (6) are additional factors, which are intended to be used when
concentration ranges are too large to give satisfactory results with a factors alone. In
reality, the sarnple composition and their concentrations Vary from sarnple to sarnple and the
use of delta factors could be very important especially in the sulphide rich samples.
The gamma factor (y) is called a secondary alpha factor and it corrects for a chain
process of enhancements during excitement of elements in the matrix. Because gamma
correction is a secondary effect, it is more likely to givc improvements if the clcments
concerned have relatively large concentration ranges about 10% or more.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
Chapter 5. Calibration procedure
The main goal of this research is to evaluate results over the compositional range and
element associations commonly found in sulphide rich ores. This required calibration for
the expected major elements in such sarnples, like Fe, Pb, Cu, Zn, Ni, Co, and S and proved
unexpectedly challenging. A list of reference materials used for calibration is given in Table
5.
Acquisition of standards and the accuracy of their composition were the first major
factors to be considered in the calibration and creation of the sulphide analysis package.
Alt!ioug!l tlicrc arc a nunibcr of ixitcrnationa! standards, n.liicli arc si il pli id^ coiiîcntrritcs,
they L I S L ~ ; ~ I I ~ coiitain significant silicatc inipriritics, n.liic!i complicatc tlic cdibrritioii
proccdrii-c. F~rtlicrriiorc. nonc of tficni lias ri coiiiplctc major cTc~ncnt ;111;1I>,sis. \i.hich is
nccdcd for a coniplcte miltri'c corrcctioii. TIi~is, a ~iiirnbcr of additional standards nrcrc
prcpared.
Initially, naturally occurring sulphides were chosen as standards for calibration to
cover the elemental concentration range of interest, from O wt % to about 70 wt % of each
element. We chose pyrite, galena, sphalerite (Zn and Fe ric h), chalcopyrite, bomite and
pyrrhotite and later, during the process of calibration, synthetic CuS, NiS and COS were
obtained fiom Alfa Aesar. However, the compositions of the synthetic sulphides were
uncertain as the manufacturer provided only a range of values, and in the extreme it was
found that the composition of COS does not even appear to be within the stated range.
Errors in analysis o f sulphide rich sampies by x-ray fluorescence spectrometry
In x-ray spectrometry, standards must have the sarne physical form as al1 the
unknown sarnples, in order to eliminate or minimise emors due to sample preparation. As
such, al1 the standards developed for the sulphide package were prepared as pressed powder
pellets using the smallest size fraction (-400 mesh) obtained through selective sieving.
In order for al1 the prepared standards to be reliable, we needed accurate
concentrations for major elements. For this reason, al1 natural sulphide standards were first
analyzed by electron microprobe. Electron microprobe analyses were carried out on
polished mounts using a CAMECA SX50 instrument. Standard operating conditions were
as follows: accelerating voltage of 20 kV and beam ciirrent of 25nA for major elements and
thc sccond sct of conditions of ZOKV and 100 11A for tracc elcments. A focuscd beam spot
\vas L I S C ~ in a!! analyses. Count timc at pcnk positions for iiiajor clcmcrits (k, Zn, Cu. Pb
and S ) nm 10 sccands niid for tracc clcn~cnts (Co. AS. Yi. A g Sb. Bi. and Cd) i\.:is 60
scconds; count timr on background positions nfas h d f of the timc on tlic pcak and dope
1.000. Spectromctcr crystals uscd werc LIF (Fc, Zn, Cu, Pb, As, Co) and PET (S, Cd and
Mo). Nat~iral and synthctic standards were used for calibrntion.
However, most of the natural minerds contained impurities, which made it difficult
to apply the microprobe results to the XRF calibration. For pyrite and galena, which were
uncontaminated, the point analysis of microprobe and average analysis fkom XRF were in
good agreement but al1 the other sulphides were contaminated with silicates and we had to
tum to other techniques in an attempt to obtain accurate concentrations for major elements.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
The impurities found in the sulphides (1 3- 15% silicates) reduced the reliability of
these standards to be used in calibration.
The next technique was Inductively Coupled Plasma Optical Emission Spectrometer
(ICP-OES), which gave reproducible results for the synthetic Cu, Ni and Co sulphides both
when they were dissolved in nitric acid and in aqua regia. We used a Perkin-Elrner Optima
3300 ICP-OES capable of operating in both radial and axial modes at ultraviolet and visible
wavelengths. The RF power was 1300 W and the samples were introduced using a
concentric Meinhard nebulizer and a Scott spray charnber. The measurements were made
with the instrument set in radial mode. The instrument was calibrated using 1, 10 and 100
m 3 2 standards prcpared by dilution of rnixcd standard QC 1. The blank used riras 2:: nitric
acid, whicli is tlic sainc indium uscd to dilutc staildards. For C X I I malytc i i ~ a s u ~ * c ~ l \\.c
~iscd thscc diffcrci~t n~n~-clc~igtIis sclcctcd from thc n1m~:facturcrs sccon~n-ieiidatioi~s. Tlic
results for al1 three wavelengths were calculatcd and wlien at Ieast two wa\.elengtlis agrcc
(witliin 5%) then the wavelength with the higher prefercnce, according to manufacturci-
specificat ions, was selected.
Although results were reasonably satisfactory for synthetic sulphides, natural
sulphides containing silicate impurities yielded poor results as indicated by disagreement
amongst triplicate analyses. Attempts to re-calculate the concentrations allowing for
impurities did not help in providing usable XRF calibration curves (initials w/s -with silicate
components; wols- without silicate components). Later in the research, it was found that the
presence of significant silicate irnpurities in sulphides produce large non-linear effects due
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
to particle size and matrix factor interaction. Thus, sulphides contaminated with silicate
material were deemed to be of little use for calibration purposes.
The final analytical technique used to characterize standards was INAA. This
technique also yielded poor results because of its extreme sensitivity, thus requiring small
sarnple sizes. These small samples weights were probably not representative of the whole
sarnple, consequently the INAA results were not satisfactory either to be used in XRF
calibration.
Thus, the initial calibrations were based on the synthetic sulphides and
uncontarninated sulphides like pyrite, galena and Zn-ricti sphalerite and at low
concentrations - normal silicate rock standards. These calibrations yicldcd rcasonably
straight lines, in terms of intensities versus concentrations, for concentrations up to about
40%. Above that however, the lines curved markedly upward. This trend was confirmed
for many elements by measuring both oxides and the pure metal, which gave spurious
concentrations up to 140%. This problem is most clearly illustrated by Fe (Figure 9 and 10)
because rock standards can be used to define a very reliable curve up to about 12%. The
misfit at low concentrations can be seen in the enlarged box in the Fe calibration curve
without use of y factor.
A review of the literature revealed that this curvature was caused by failure of the a-
factors to apply over the full concentration range (Jenkins et al., 1995). This posed a serious
calibration problem. Firstly, the Philips software did not permit a curved calibration line,
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
and secondly for al1 metals except Fe, the only standards with concentrations of more than a
few thousand ppm were the pure sulphides. These sulphides, with metal concentrations of
65 - 85 % were well within the non-linear part of the calibration curve. Theoretically, this
problem should be dealt with by the use of 6 factors. In practice this failed because the
software: a) calculated factors of the wrong sign - making the problem worse, and b)
blocked the manual use of sufficiently large factors of the correct sign.
Finally, secondary fluorescence factors, y factors were used, to artificially straighten
the curve and the results are seen in figure 10. This was achieved by specifying that the
element was fluoresciiig itself. which is physically impossible. The resulting y factor is
effectively applying a quadratic terrn (i.e. proportional to concentration'), which thus acts
preferentially on the higher concentrations, attempting to fit them to thc curve defined by the
low concentrations standards. Because this correction is strongly progressive, it tends to
overcorrect very high concentrations (such as pure metals), but fortunately, this was not a
serious limitation over the concentration range in sulphides (up to 70% elemental
concentration). However, the reliability of this approach is strongly dependent on having a
well-defined calibration at low concentrations. This can be difficult for lcss common
elements such as Co because al1 the International Reference Standards contain less than 200
ppm Co. Thus, it is difficult to create linear calibration for low concentrations.
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
Chapter 6. Results
The fundamental parameters method is the best general method for analyzing
samples that suffer fiom very large matrix effects. To find out how this method works for
sulphides and what kinds o f errors arise in natural samples, two different mixture sets with
known compositions, of sulphide minerals and silicate rock were prepared (Table 6). The
first set of mixtures cover the simplest situation where only one sulphide is present (binary
mixtures), and contain a wide range of 5-75% sulphides (range of elemental concentrations
of less than 1% up to 70%). The second set of mixtures are more complex (multi
component mixtures), containing three different sulphides totalling 10, 20 and 30% total
sulphides, and were created to be similar to naturally occurring concentrates. Al1 data used
in plotting the graphs are given in Table 8a and 8b.
Al1 mixtures were prepared using, natural galena, pyrite, sphalerite and syntlietic NiS,
COS and CuS. The - 400 mesh fraction of each sulphide was thoroughly mixed with rock
powder in a ball-mixer for 4-5 minutes to obtain a homogenous mixture and prepared as
pressed powder pellets. Al1 pellets made up of these mixtures were run using the quantitative
program and the calibration curves established in the suiphide package, and al1 the results
are plotted in the graphs shown in the Figures 1 1 - 19.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectromety
Binary mixtures.
In order to evaluate the results that the fundamental parameters method provides for the
sulphide bearing minerals, graphs (Figure 16-19) labelled "FP corrected" have been ploned
using data corrected with the fundamental parameters. These are the plots of expected
proportions of the sulphide mineral and the silicate component in each mixture against the
apparent proportion calculated independently for SiOz, S and the transition metal. Because
the silicate component is a multi-element mixture, for convenience Si02 normalized to
100% has been used to represent the rock. The data for pyrite have been corrected for the Fe
contribution from the silicate rock. The straight black lines represent 1 : 1 agreement.
The results for binary mixtures are plotted in graphs (Figure 11-15) labelled
"Uncorrected pyrite, CUS, sphalerite, galena" and are constructed using raw intensities
without making any correction for matrix effects. The straight, diagonal linç is based on the
sensitivity (kcpsl %) of pure sulphide minera1 or pure silicate rock (represented by SiO2) and
again shows the ideal linear relationship between the calculated concentrations and the tme
values.
The graphs of the FP corrected data have surprisingly large errors in accuracy. It is now
clear that these errors are typical of what can be expecîed from most labs using XRF to
measure sulphide- bearing samples with pressed powder pellets. The errors have a number
of common features:
Errors in analysis of sulphide rich samples by x-ray fluorescence spectromeûy
rn Cations in the sulphide component are too low.
Elements in the silicate component are too high.
Errors are worst at sulphide: rock ratios of 5050 by W..
= Totals may be high because the positive errors in the silicate component are ofien
larger than the negntive errors in the sulphide component.
Despite these common features, there is a surprising diversity of results among the
different sulphides. Plots for pyrite illustrate the simplest case. The penetration depths for
50% attenuation (average penetration depth) for both S and Si x-rays in pyrite and the
silicate rock are about 1 Pm, whereas the average grain size in -400 mesh samples is about
15 Fm. Thus. essentially S x-rays might be expected to escape only from the surface of
pyrite grains. Similarly, Si x-rays would escape onIy from the surtàce of silicate grains, and
there would be no interaction with sulphide grains. This is supported by the plot of
uncorrected data (Figure I I ) in which the concentrations for S and Si are in surprising
agreement with the expected values, despite the lack of matrix corrections. In the case of
Fe, however, the 50% penetration depth in the rock is about 20 pm and this allows Fe x-rays
to cscape not only from the pyrite, but also through some silicate grains. Because the
absorption coefficient of the silicate is about 35% less than pyrite (Table 3) for Fe Ku. this
explains the resulting increase in the apparent pyrite concentration evident in Figure 1 1.
The application of the fiindamental parameters matrix correction to pyrite does not
yield satisfactory results as shown in Figure 16. This is because the software assumes that
the sample is completely homogenous (Le. glas). Thus, Si intensities are corrected for the
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
40% higher absorption coefficient of the pyrite component and apparent SiOz concentrations
are therefore increased, making them too hi&. Meanwhile, Fe is corrected initially,
appropriately for the increase yield due to the lower absorption coefficient of the silicate
component. However, the overestimation of the rock (Si@) eventually results in the Fe
being overcorrected and thus apparent pyrite concentrations become too Iow. In tliis case,
sulphur is Iittle changed because the increase in the silicate component is balanced by the
decrease in the pyrite component. The errors in Si02 and Fe reach about 10 % relative in the
5050 mixture.
Because the uncorrected data gives better results, it might at first appear that the use
of fundamental parameters is unnecessary. However, it must be remembered that the data
has been normalized to the pure silicate and sulphide end-members. Changes in
composition of either end-member cannot be accommodated and thus these curves are not
valid for any other samples.
Despite some minor differences, the data for CuS and sphalerite (Figure 13 and 14)
are genêrally similar to tliat for pyritc and can rcadily bc intcrpretcd in tlic samc nrriy. Tlicsc
similarities are in contrast to reports from other commercial labs that claim unrelioble results
when analyzing Cu. However, initially quite different results, with large errors were
obtained for CUS (Figure 12). These samples appear to have suffered segregation in which
the surface of the pellet has become depleted in sulphide and e ~ c h e d in silicate. As a
result, SiOz is much too high and S much too Iow, and fundamental parameters only make
the problem worse. Cu, however, is only slightly too low, relative to Figure I l . This could
Errors in analysis of sulphide rich sarnples by x-ray fluorescence spectrometry
be explained if the sulphide depletion was confined to the surface of the pellet, whereas Cu
Ka, with an average penetration depth of 20 Pm, samples a much larger volume, which on
average is only slightly depleted. This is confinned by the data for Cu La (Figure 12), which
has an average penetration depth of only about 0.5 Pm, and is even more depleted than S.
Relative errors (Figure 20) show that segregation is roughly constant up to 30% CuS and
thereafter declines steadily. CuS is a synthetic compound supplied as a very fine powder
(less than I Pm)? whereas pyrite and sphalerite are natural suiphides sieved to 400 mesh
(less than 38 pm). Thus, the very fine-grained nature of the CuS must be partly responsible
for its tendency to segregate.
However, it appears that surface charactsi-istics of the grains also play a role.
Attempts to study segregation fùrther were defeated when new pellets, prepared in the same
way, showed little or no sign of segregation (Figure 13). Apparently, in the intemening
three months, the CuS has reacted with the atrnosphere, perhaps suffering surface oxidation
or absorption of moisture, which has modified its surface properties. Experiments were
made to investigate the effect of changing the surface properties of the grains by drying CuS
yowdcr for 4 hours and 24 Iiours. Ttircc pellcts coritaiiiing 30% CUS wcrc made ~ising
untreated CuS powder, CuS dried powder for 4 hours and CUS dried for 21 hours. Results
showed a moderate increase in segregation with Cu La raw intensities of 1 1.484 kcps,
10.579 kcps and 8.152 kcps respectively, compared with 4.42 kcps from the original, highly
segregated pellet.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
The diagram for galena (Figure 15) also shows large deviations fiom the expected
results. Pb is strongly enhanced, but this is to be expected, because the absorption coefficient
of the rock is much lower than galena and no matrix correction is being applied to
compensate for this. However, SiO2 is also too high, and this cannot be explained by the
absence of the matrix corrections. Penetration depths for Si K a are much too srnall to
penetrate galena grains. and in any case, galena absorbs Si Ka more strongly than the rock
and thus, should have reduced SiO?. The presence of complementary depletion in sulphur,
suggests that the SiO2 enrichment is in fact again due to segregation at the surface.
Fundamental parameters correct the Pb for the presence of the silicate matrix, but
because SiO2 is too high, once again the Pb is overcorrected (Figure 19). This effect was
investigated by manually entering the correct silicate concentrations for 50% galena -50%
rock mixture and recalculating Pb and S (Table 7). The results are plotted as two coloured
dots on Figure 19 showing that the Pb concentration is now almost correct, but sulphur is
still much too low. This confirms that the errors in Pb are introduced by the matrix
corrections as a result of the errors in SiO?, whereas the errors in suiphur are unchanged and
thus arc probably due to segregation at the surface.
Segregation requires differential movement of the rock or sulphide grains during the
pellet making process. The fact that galena is especially susceptible suggests that the
sofiness of galena may be a contnbuting factor. The absence of significant segregation in
pyrite and sphalerite suggests that in natural samples, where sulphide and rock have similar
Errors in analysis o f sulphide rich samples by x-ray fluorescence spectrometry
grain sizes, segregation may not be a serious problem, except for sulphides such as galena
and molybdenite.
It is clear that overestimation of SiOl consistently results in the underestimation of
sulphides. This suggests that much better results could be obtained using a range of
sulphide-silicate mixtures for calibration. Because of the curvature in Figures 16- 19, these
calibrations are unlikely to be linear over a range of more than 3096 - 40% sulphides, thus
requiring several different calibration curves to cover the entire concentration range. Gyves
et al., 1989 showed that in zinc concentrates, this method works very well over the limited
range for Zn 40-65%, Pb 0.1-1 0% and Fe 0.5- 1 1 %, but it is impossible to extrapolate to
wider range of compositions or other elements. Their study did not cover the investigation
of possible sources of errors except for precision of pellet formation. In this study, the
evaluation of reproducibility in pressed powdcr pellet formation seemed to be the least
possible source of error.
Errors in analysis of suiphide rich samples by x-ray fluorescence spectnimetry
Pyrite uncorrected
O 1 O 20 30 40 50 60 70 80 90 1 O0
Expected wt.% of Pyrite & Rock
FIG. 1 1 . The observed and expected coiicentratioiis for pyrite and rock usiiig Fe, S aiid Si02 intensities before FP correction.
CuS uncorrected
Expected wt.% of CuS & Rock
FIG. 12. The observed and expected concentrations for CuS and rock using Cu, S and Si02 intensities before FP correction. CuLa is used to confirm the effects of segrcgation in the initial pellets.
CuS uncorrected-New mixtures
O 10 20 30 40 50 60 70 80 90 1 O0 Expected wt. U/u of CuS &Rock
FIG. 1 3. The observed and expected coiicentratioiis for CuS oiid rock usi iig Cu, S and Si02 intensities before FP correction. CuLa is used to coiifirm the absence of scgregation in tlic pellets.
Spalerite uncorrected
O 10 20 30 40 50 60 70 80 90 1 O0
Expected wt. %, of Splialeritc & Rock
FIG. 14. The observed aiid expected concentrations for Sphalcritc and rock using Zn, S and Si02 intensities before FP correction. ZnLa line used to test the segregation cffccts on the pellets.
Sphalerite corrected
Expected wt.% of Sphalerite&Rock
FIG. 18. The observed and expected concentrations for splialcritc aiid rock usiiig Zn, S and Si02 FP- corrected quantitative data.
Calena- FP corrected 66
Expected wt.% of Galeiia & Rock
FIG. 19. The observed and expected conceiitratioiis for galeiia and rock usiiig Pb, S and Si02 FP-corrected quantitative data.The two dots represent apparent galcna coiiceiitratioii giveii froiii Pb aiid S (sec text).
Segregation errors in CuS
FIG.20. Errors in Cu, S and Si02 x-ray intensities caused hy segregation iii CuS: silicate rock mixtures.
Kesults oSXKF aiialysis on sulphide ricli mixtures
Table 6
Mixture label Components in wt. % Ga 5-Rck pwd Ga IO-i(ck pwd
- Ga 20- Rck pwd Ga 30- Rck pwd Ga 50- Rck pwd Ga 75- Rck pwd
Py 5-Rck pwd - - - - -- - -
Py I O-Rck pwd -*- - - -- -- - *. Py 20- Rck pwd
- ~ y 30- ~ c k pwd - - -.
Py 50; - - Rck pwd Py 75- ~ c k pwd
Expected elernent concentration Pb ! S
4.28 0.6 15 8.56 1.33 17.13 3.46 25.68 3.69 43.8 6.15 64.3 9.235
P
Fe S 2.63
1 l 5.37 4
I 10.53 1 15.8
26.33 39.5 i
m
-- Zli S ~ p h i n 5-Rck pwd 3.34 1.69 sphzn 10-Rck pwd 6.675 3.396 ~ p h ~ n 20- Rck pwd 13.35 6.792 SphZn 30- Rck pwd 20.03 10.19 SphZn 50- Rck pwd 33.35 16.98
- . - CUS 5-Rck pwd 3.35 1.59 CuS 10-Rck pwd 6.68 3.19 cus 20- Rck pwd 13.37 6.37 CuS 30- Rck pwd 20.05
I 9.56 CuS 50- Rck pwd i 33.42 15.93 CuS 75- Rck pwd I 50.12 33.895
Measured element concentration 1
- . . . - -
Pb I s 2.440 0.309 4.570 0.565 8.398 1.130 12.935 1.906 24.007 3.715 46.135 1 7.122
Fc S
Zii S
Errors in niirilysis of sulphide ricli saiiiplcs by x-ray fluoresceiicc specironietry
Com~onents in wt. %
- -- (P~+&&s) I O-Rckpwd 1.5 i 2.85 2.23 3.22
- ( P ~ + G ~ + C U S ) 20-Ück pwd 3.0 5.7 4.46 6.47
Ni S
(Py+Ga+NiS) 1 O-Rck pwd 1.5 1 2.85 2.17 3.22 ( P ~ + G ~ + N ~ s ) 20-Rck pwd 3.0 5.7 4.34 6.42 (Py+Ga+NiS) 30-Rck pwd 4.5 1 8.56 6.5 1 9.62
, Fe Pb Co S
(P~+G~+c&) 1 O-Rck pwd 1.5 2.85 2.04 3.43 ( P ~ ~ G ~ ~ c o s ) - - 70-Rck pwd 3.0 5.7 4.08 6.84 (P~+G~+cos) 30-Rck pwd 4.51 , 8.56 6.1 12 10.25
' Pb - h l
4
Fe , l S i
(Py+Ga+Sph) 1 O - ~ c k pwd l
-- 1.5 ! 2.85 , 2.22 3.29 (py+~a+sph) - - 50-Rck pwd 3.0 5.7 , 4.45 6.6 1 (Py+Ga+Sph) 3 0 - ~ c k pwd 4.51 1 8.56 6.68 0.9
Cu Ni Zii S
(CuS+NiS+Sph) 1 O-Rck pwd 2.23 3.17 2.32 3.33 ( c u s ~ N ~ s + s ~ ~ ) 20-Rck pwd 1 4.46 4.34 4.45 6.48 ( ~ Ü s + ~ i ~ t ~ p h ) 30-Rck pwd j 6.68 6.51 6.68 9.7 1
Table 6 continues
Measured element concentration
Fe* ' Pb Cu S 1.028 i 1.647 : 1.847 1 2.883 2.434 i 3.237 ' 3.772 1 6.009 3.981 1 4.643 5.771 1 9.073
w
Fe* Pb Ni S 1
Fe* ' Pb Co S
1 .O85 1.761 1.536 ' 3.365 2.586 ' 3.309 3.09 6.445 4.258 5.046 4.831 i 9.819
*Fe corrected for contributioii of rock as Sollows: 90 % rock = 3.73%; Y0 O/b rock = 3.3%; 70 % rock = 2.898%.
Errors iii aiialysis of sulpliidc ricli saiiiplcs by x-ray tluorcsceiicc spcctrcitiietry
Composition of the mixture galena 50%-rock 50% afier manually changing silicate
composition.
Table 7
Before manually edited I After manually edited
Concentration Concentration Com~ound S tatus Status
S Measured 3.735 Measured 4.177
- - Cao
-,- -- - ---- . - .- ---. - . -- O Man. 0.88
. ---- . ...
CO, 0.000 ..... -. - .....
HIO Man. 5.25
Errors in analysis o f sulphide rich samples by x-ray fluorescence spectrometry
Multi component mixtures.
In the more cornplex mixtures (Figures 21-25), as mentioned before, three different
sulphide minerals are mixed with rock powder so that the sum of three sulphide rninerals
varies from 10-30 weight O h . Again as expected, al1 errors have constituent features where
the high absorber element, Pb, gives the largest errors and al1 other transition elements give
et-rors that are smaller than Pb.
Mixtures, that contain synthetic materials COS and NiS, show large errors compared
with i~atural pyrite and sphaIerite. Tliese crrors may also bc duc to segrcgation as sliowii in
thc CuS binary mixtures. The small concentrations of each sulphide (up to 30 wcight O/u
total sulphide) in these mixtures, increases the chances of segregation as shown in Figure 20.
Thus the Co and Ni data can be discounted and not applied to natural samples.
Once again considering Cu results, there is no evidence that Cu results differ
signitïcantly from the results from Fe and Zn. They al1 show the same fsatures and
development when analysed by XRF.
SiO, concentration is again overestimated while S gives the right answer for most of
mixtures. The reason for that is probably bccause the pyrite is always 1/3 of the mixture
composition and it has much higher S intensity than the other sulphides and thus dominates
the S behaviour of the total mixture. According to the FP corrected pyrite (Figure 14), S line
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrornetry
gives the smallest error (0-30 weight % pyrite) compared with the other S lines in the
corrected graphs.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
Mixture of Pyrite, Galena, COS and Rock I;'P r-
I O 20 Expected total concentration of sulphides
Fig. 2 1 . The observed and expected total weiglit percent concentrations for sulpides and rock (Si02) using elemental concentrations analyzed by XRF in the mixture of pyrite, galena and COS. Data used in the graph taken from Table 8a.
Mixture of Pyrite, Calena, NiS and Rock FP corrected
Expected total of sulpliide
Fig. 22. The observed and expected total concentratioris foi sulpides and rock (Si02) using elemental concentrations analyzed by XRF in the mixture of pyrite, galena aiid NiS. Data used in the graph taken froni Table 8a.
Expeçted total coiiceiitibatioii of sulpliides
Mixture of Pyrite, Galena, CuS and Rock FP corrected
Fig. 23. The observed and expected total coiiceiitrations for sulpides and rock (Si02) using elemental concentrations analyzed by XRF in the mixture of pyrite, galena and CuS. Data used in the graph taken from Table 8a.
Mixture of Pyrite, Galena, Sphalerite and Rock FP corrected
Expected total sulphide conceiitratioii
FIG.24.T he observed and expected total concetitratioiis for sulyides and rock (Si02) iising elemental concentrations analyzed by XRF in the mixture of pyrite, galetia, sphalerite and rock. Data used in the graph taken from Table 8a.
Mixture of CuS, NiS, Sphalerite and Rock FP corrected
O 5 10 15 20 25 30
Expected total sulphide concentration
Fig. 25. The obscrved and expected total concentratioiis for sulpides and rock (Si021 using elemental concentrations aiialyzed by XRF in the iiiixturc of pyritegalena and CuS.Data used in the graph takcn froin Table 8a.
Chapter 7. Conclusions
1. Fundamental parameters cannot handle the wide range in compositions found in sulphides.
However, satisfactory results were obtained for pure sulphides by using non-standard
modifications (y factor). Contrary to the theory of fundamental parameters that no
intermediate standards are required for any matrix, it is necessary to have standards with
intermediate concentrations in order to create linear calibration curves and allow the y
factor modifications.
2. Both surphide and rock components in the binary mixtures give significant errors due to
inhomogeneity on the scale of x-ray penetration deptti. This inhomogeneity is
unavoidable in pressed powdcr pellets and although particle size reduction reduces this
problem, it does not completely eliminate it. These errors invariably result in rock
components too high (shallow analysis depth) and sulphides too low. Much more accurate
results can be obtained if sulphide + rock standard mixtures are used for the calibration of
al1 elements and if different calibrations are used h r different concentration ranges.
3. In the multi component mixtures (10-30 wt. %), which are closer to a natural sulphide rich
sample, S analyses are usually correct. Pb gives the largest errors while the errors in other
elements (Fe, Co, Ni, Cu and Zn) are smaller.
4. Large errors c m also be caused by segregation in preparing mixtures, apparently due to
grain size and/or grain surface characteristics. This may not be a problem for most natural
samples but it presents a potential problem in the preparation of standards used in
calibration. The largest errors in segregation occur at low sulphide concentrations (up to
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
30%). In natural samples this may be a serious problem for galena and molybdenite rich
rocks where the high density and surface properties may favour segregation.
5. Grain size does affect intensities. Again, this is especially a problem for making
standards. Consequently, standards and unknowns must have the same size distribution.
For greatest convenience and precision it is preferable to g h d and mix the standard
mixtures to a grain size that is below the 50% penetration depth of the element of interest
and mix for no l e s than 10 minutes.
6. It appears that there is no evidence to suggest that Cu results should be any less reliable
than Zn and Fe and al1 the errors have similar features.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
'fi.
- 2 9 o m o
- .- - -- .- -
- m o r n e O O O C O XX?Xg
in Cr)
X
C A , , z = C O - =? " X 8 q O 2
c O r? m '? 9 - cri
8 O N ç -E CL P
'CA ;v,
O QC F Oc r? ici OC
I I I
O o o i n c. . - m ' n e % m m = & U o " & U u z ~ ~
REFERENCES
Bertin, E.P., (1975) Principles and Practice of X-ray Spectrometric Analysis, Plenum
Press, New York
Bilbrey D.B., Bogart GR., Leyden D.E. and Harding A.R. (1988) Cornparison of
Fundarnental Parameters Programs for Quantitative X-Ray Fluorescence
Spectrometry, X- Ray Spectr.ontetry, v. 17. 63- 73.
Boutreux T., (1998) Surface Flow o f Granular Mixtures: II. Segregation with Grains
of Different S ize, Eur. Phys. J.B 6 ,4 1 9-424
Claisse F., and Samson C., (1962) Heterogeneity effects in X-ray analysis, d4rlrwr1. X-r-e.
Anal. v. 5, 335-54
Criss J.W., and Birks S.L., (1969) Calculation Methods for Fluorescent X-Ray
Spectrometry-Empirical coefficients vs. Fundarnental Parameters, Anal. Clicni. 1.. 40,
1080-6.
De Gyves J., Baucells M., Cardellach E. and Brianso J.L., (1989) Direct Determination
of Zinc, Lead, Iron And Total Sulphur In Zinc Ore Concentrates by X-Ray
Fluorescence Spectrometry, rltta[vsr, t.. 114, 559
Jenkins R., and De Vries, (1973) "An Introduction to X-Ray Spectrornetry", Heyden,
London".
Jenkins R., and De Vries, (1977) "Practical X-Ray Spectrometry" Springler-Verlag, New
York Inc.
Jenkins R, Gould R.W. and Gedcke D., (1995) Quantitative X-Ray Spectrometry, 2nd ed.,
Dekker: New York, 484 pp.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
Norrish K. and Thomson G.M. (1990) XRS Analysis of Sufphides by fusion methods, X-
Ra-v Spectrometr y, v. 19,67-7 1
Rousseau R.M., (1991) Quantitative XRF Analysis Using Fundamental Algorithm,
Advances in X- Ray A~lal-vsis, v.34, 1 57.
Sherman, J., (1958) Advances in X-Rav Analisis, Plenum, New York, v. 1. 23 1.
Spanenberg J., Fontbote L., and Pernicka E., (1994) X-Ray Fluorescence Analysis of
Base Meta1 Sulphide and Iron-Manganese Oxide Ore Sarnples in Fused Glass Disc,
X-Rav Spêctrornetr?~. v. 23.
Errors in analysis of sulphide rich samples by x-ray fluorescence spectrometry
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