Spectrochemical Analysis by X-Ray Fluorescence

327 Pages·1972·8.814 MB·English

by  Rudolf O. Müller (auth.)

SPECTROCHEMICAL
ANALYSIS BY
X-RAY FLUORESCENCE
SPECTROCHEMICAL
ANALYSIS BY
X-RAY FLUORESCENCE
Rudolf O. Muller
CIBA-GEIGYAG ..
Basel, Switzerland
Translated from German by
Klaus Keil
Director, Institute of Meteoritics
Department ot Geology
University ot New Mexico
Albuquerque, New Mexico
~PLENUM
PRESS • NEW YORK • 1972
Rudolf O. Muller, after completing his studies at the Eidgenossische Tech
nlsche Hochschule in Zurich and at the University of Bern, became a staff
scientist in 1959 at the CIBA-GEIGY AG, Basel. He is in charge of the X-ray fluo
rescence laboratory for spectrochemical analysis and production control as well
as of the laboratory for X-ray diffraction and X-ray structure analysis. Dr. MOiler
is particularly known for his work on basic theoretical aspects of quantitative X
ray fluorescence analysis and its application to spectrochemical determination.
The original German text, published by R. Oldenbourg, Munich and Vienna, in
1967, as Spektrochemische Analysen mit Rontgenfluoreszenz, has been cor
rected by the author for the present edition.
Library of Congress Catalog Card Number 70-107540
ISBN-I3: 978-1-4684-1799-9 e-ISBN-13: 978-1-4684-1797-5
DOl: 10.1007/978-1-4684-1797-5
© 1972 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1972
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
All rights reserved
No part of this publication may be reproduced in any form
without written permission from the publisher
Preface
In recent years the x-ray fluorescence technique has become increasingly
important in modern analysis and production control; it can be classified
as a spectroscopical method for the determination of the elemental com
position. Many articles treat this method; however, there exists no modern
textbook suitable for the beginner as well as the practician and theoretician.
In this monograph the author intends to fill this need to present the prin
ciples of x-ray fluorescence analysis and to develop a theoretical under
standing of the technique. Both principles and theory w.ill be treated exten
sively, for they are the basis for successful practical application of the
method. X-ray fluorescence, on the other hand, is often carried out
exclusively because of its practical usefulness. For this reason theoretical
investigations are used exclusively as a basis for practical work and the
multitude of applications, which constitute the value of the x-ray fluores
cence method, will be explained on the basis of simple theory.
The idea to write this monograph originated and developed when
efforts to train coworkers required a more complete treatise. I would like
to thank the elBA Aktiengesellschaft in Basel, where this work originated,
for generous support and permission to publish the book. The head of
the Physics Department, Dr. E. Ganz, and my colleagues have contributed
to this book by providing a stimulating working atmosphere. I am grateful
to my associates, in particular Messrs. E. Eng, S. Gasser, and H. R.
Walter, for assistance in setting up the x-ray fluorescence laboratory over
the past seven years. H. O. Meyer read part of the manuscript.
Basel, May 1966 RUDOLF MULLER
v
Contents
Introduction 1
Part I
Principles and Qualitative Analysis
1. Absorption and Scattering of X-Rays . 11
2. Characteristic Emission Spectra . 19
3. Photoelectrons, Fluorescent Yields, and Auger Electrons 34
4. Qualitative Analysis . 36
4.1. General Remarks 36
4.2. Anomalous Intensities of Lines in a Spectrum 39
5. Fluorescent Intensity of a Pure Element 47
5.1. Derivation of the Intensity Formula 47
5.2. Dependence of Fluorescent Intensity on the Anode Material
of the Tube 52
6. Fluorescent Intensity of an Element in Two- and Multicom-
ponent Mixtures . 57
6.1. Derivation of the Intensity Formula 57
6.2. Intensity Formula for Low Concentrations 62
6.3. Effects of Associated Elements on the Fluorescent Intensity 62
6.4. Example for the Numerical Calculation and the Term
Weighted-Average Wavelength 64
7. Interelemental or Secondary Excitation. 67
8. Grain-Size and Surface Roughness Effects 72
8.1. Introduction 72
8.2. Homogeneous Powders 73
8.3. Heterogeneous Powders 74
8.4. Effects of Surface Roughness 79
9. Intensity Formula for a Divergent Primary Beam 84
10. Apparatus 87
10.1. Instrumentation of X-Ray Fluorescence Units 87
vii
viii Contents
10.2. Generators 88
10.3. X-Ray Tubes 88
10.4. Spectrometers 91
10.5. Collimators 94
10.6. Crystals 95
10.7. Counters . 98
10.8. Pulse-Height Analysis and Discrimination 101
10.9. Filters 103
11. Measurement Techniques 106
11.1. Principles of Statistics 106
11.2. Counting Statistics and Counting Loss 113
11.3. Background Correction 117
11.4. Optimal Conditions of Analysis . 120
11.5. Short-Term Drift and Variations From Measurement to
Measurement 125
11.6. Long-Term Drift 126
11.7. Errors Due to Sample Preparation and Calibration 126
11.8. Detection Limits 128
Part II
Quantitative Analysis
12. Calibration Curves and Regression Coefficients 133
13. Determination of Low Concentrations . 139
13.1. Effects of the Matrix on Fluorescent Intensity 140
13.2. Quantitative Trace Element Determination . 144
13.3. Use of Diffusely Scattered X-Ray Radiation. 145
14. Determination of Thin Film Thicknesses 152
14.1. Determination of Mass Density 152
14.2. Semiquantitative Determination of Mass Density 154
14.3. Determination of Thin Film Thicknesses via Absorption. 155
15. Determination of High Concentrations with Calibration Curves 159
15.1. Curves for Constant Admixture of a Third Component. 160
15.2. Curves for Constant Mixing Ratios of Associated Com-
ponents 162
15.3. Presentation in a Concentration Triangle 164
15.4. Correction for Effects of a Third Component by Correc-
tion Factors 165
16. Determination of Concentration, Formulated as a Linear
System of Equations . 171
16.1. Derivation of the Linear System of Equations 171
16.2. Formulation According to Sherman 174
Contents ix
16.3. Formulation According to Beattie and Brissey 174
16.4. System of Equations According to Marti 175
16.5. Formulation According to Traill and Lachance 176
16.6. Determination of the Interaction Coefficients 177
17. Analysis of Multicomponent Mixtures and Solutions for the
Linear System of Equations 181
17.1. Separation into Subsystems 181
17.2. Decomposition and Dilution 182
17.3. Admixture of a Strongly Absorbing Substance 186
17.4. Internal Standard Method . 187
17.5. External Standard Method. 190
17.6. Double Dilution Method 194
17.7. Effects of Certain Minor Components 196
17.8. Semiquantitative Determination of Concentration . 197
17.9. Direct Mathematical Solution 199
17.10. Mathematical Determination of Concentration of a
Single Component in a Multicomponent Mixture. 202
17.11. Appendix 206
Part III
Examples of Applications and Abstracts
18. Analysis of MixturesWhich Are Difficult to Separate Chemically 215
18.1. Zirconium-Hafnium . 216
18.2. Niobium-Tantalum . 218
18.3. Molybdenum-Tungsten 222
18.4. Scandium-Yttrium-Rare Earths 222
18.5. Thorium-Uranium-Plutonium 224
19. Steel and Iron Industry 230
19.1. Steel and Iron . 231
19.2. Slags 239
20. Base Metals and Ores 242
20.1. Alloys and Industrial Materials 242
20.2. Ores 246
21. Light-Metal Industry 250
22. Determination of Thicknesses of Thin Films 254
23. Cement Industry and Silicate and Rock Chemistry. 260
23.1. Cement and Clay 261
23.2. Silicates and Rocks 263
23.3. Determination of Coordination Number 271
24. Petroleum and Coal Industry 273
24.1. Trace Element Determination in Petroleum Products 273
Contents
24.2. Trace Element Determination in Catalysts 278
24.3. Determination of Admixtures in Fuels. 279
24.4. Determination of Additives in Lubricating Oils 281
24.5. Trace Element Determination in Coals 284
25. Chemical Industry 286
25.1. Determination of Trace Elements. 286
25.2. Determination of Major Elements 289
25.3. Determination of Organic Substances via X-Ray Analysis
of an Associated Element 291
26. Medicine and Biology. 293
26.1. Medicine . 294
26.2. Analysis of Plants, Animal Feed, Water, and Air 299
27. Analysis of Small Amounts of Substance and of Small Areas 303
Text References and Articles Abstracted in Part III 309
Index 325
Introduction
In recent years x-ray fluorescence analysis, together with other analytical
techniques, has been applied in industry to research as well as con
tinuous production control. Hardly any other analytical technique is so
universally suited for qualitative and quantitative determinations as is
x-ray fluorescence analysis. This is largely due to the fact that analysis is
independent of composition and chemical bond of the sample. Solid,
powdered, and liquid samples can be analyzed. On the basis of x-ray
spectra, Coster and Hevesy (1923) discovered element hafnium (Z = 72)
and have detected its occurrence in natural zircons; and Noddack, Tacke,
and Berg (1925) discovered the element rhenium (Z = 75) in columbite
concentrates.
In 1895 W. C. Rontgen, while working with cathode-ray tubes, dis
covered an hitherto unknown and invisible radiation which occurs together
with the cathode rays; because of its unknown nature he named it
x-radiation. The physical properties of these rays were described, in a
complete and qualitatively correct manner, by Rontgen in the first two
Sitzungsberichte der Wiirzburger Physikalischen-M edicinischen Gesellschaft.
After Rontgen's discovery, x-rays were the subject of numerous investi
gations by various researchers. In particular, C. G. Barkla proved indirectly
that the radiation emitted from a sample consists of several spectra of
different wavelengths, which he named K and L spectra. In the summer of
1912 M. Laue, together with M. Friedrich and P. Knipping, made the
fundamental discovery of the interference of x-rays which occurs when the
rays are scattered by a three-dimensional ordered crystal lattice. This experi
ment shows that x-rays are electromagnetic waves of a wavelength on the
order of 10-8 cm. In England, W. H. and W. L. Bragg used monochromatic
x-rays for diffraction by crystal plates. In 1913 they interpreted diffraction
as a reflection on selected net planes in the crystal according to the equation
2d sin 8 = nA. Shortly thereafter, Laue showed that diffraction and reflection
are two different interpretations of one and the same phenomenon, and that
1
2 Introduction
1111
1
T; ••
Viii
Crill
Mnlll
II.
.llto Fe
II.cu
IIIII
Brass
Fig. 1.1. X-ray spectra of the elements calcium (Z = 20) to
zinc (Z = 30) as a function of wavelength. Every spectrum
consists of an intense <X line (always to the right) and a
weaker f3 line of shorter wavelength. The orderly decrease
of wavelength with increasing atomic number is clearly
visible. Recorded photographically. Original after Moseley
(1913).
the Bragg equation can be derived directly from the Laue equation for inter
ference on three-dimensional lattices. In 1913 N. Bohr published two papers
on the constitution of atoms and molecules. Spectral lines were interpreted
as electron transitions between the various energy levels of the electrical
field around the nucleus and were documented numerically for the light
elements. Stimulated by this work and by Bragg's experiments, H. G. J.
Moseley, in the same year, systematically studied the x-ray spectra of the
elements calcium through zinc. He found that the frequency of emission
lines is proportional to the square of the charge of the nucleus. This regu
larity can be understood on the basis of Bohr's atom theory extended to the
heavy nuclei. Moseley had already shown that the spectrum of brass con
tains the spectra of the elements copper and zinc and, hence, that the chemi-