errors in analysis of rich samples...errors in analysis of sulphide rich samples by x-ray...

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

National Libraiy u * l ofCanada Biiothèque nationale du Canach

Acquisitions and Acquisitions et Bibliographie Services services bibliographiques 395 Wellington Street 395. rue Wellington OltawaON KlAON4 OüawaûN K 1 A W Canada Canada

The author has granted a non- exclusive licence dowing the National Library of Canada to reproduce, loan, disîribute or seil copies of this thesis in microfom, paper or electronic formats.

The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial exûacts fiom it may be printed or otherwise reproduced without the author's permission.

L'auteur a accordé une licence non exclusive permettant a la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfichelfilm, de reproduction sur papier ou sur format électronique.

L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.

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


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.


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.


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.


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


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.


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.


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.


-

-

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


infinite thickness. The sarne approach was adopted to check for vertical heterogeneity due

to segregation in chapter 6, Figure 12.


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.


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.


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


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:


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 ,,.


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-


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.


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.


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


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,


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.


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


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


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.


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


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


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


gives the smallest error (0-30 weight % pyrite) compared with the other S lines in the

corrected graphs.


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


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.


- 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.


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 rich samples...errors in analysis of sulphide rich samples by x-ray...

Documents