Total reflection x ray fluorescence analysis and related methods

Chemical Analysis: A Series of Monographs on
Analytical Chemistry and Its Applications
Mark F. Vitha, Series Editor

Total-Relection X-ray
Fluorescence Analysis
and Related Methods
SECOND EDITION

REINHOLD KLOCKENKÄMPER
ALEX VON BOHLEN


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Total-Reflection X-Ray
Fluorescence Analysis
and Related Methods


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CHEMICAL ANALYSIS
A SERIES OF MONOGRAPHS ON ANALYTICAL CHEMISTRY
AND ITS APPLICATIONS

Series Editor
MARK F. VITHA

Volume 181

A complete list of the titles in this series appears at the end of this volume.


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Total-Reflection X-Ray
Fluorescence Analysis
and Related Methods
Second Edition

Reinhold Klockenkämper
Alex von Bohlen
Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V.
Dortmund and Berlin, Germany


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Copyright  2015 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Klockenkämper, Reinhold, 1937- author.
Total-reflection X-ray fluorescence analysis and related methods.—Second edition / Reinhold
Klockenkämper, Alex von Bohlen, Leibniz-Institut für Analytische Wissenschaften-ISAS-e.V.,
Dortmund und Berlin, Germany.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-46027-6 (hardback)
1. X-ray spectroscopy. 2. Fluorescence spectroscopy. I. Bohlen, Alex von, 1954- author.
II. Title.
QD96.X2K58 2014
543'.62–dc23
2014022279

Printed in the United States of America
10 9 8

7 6 5 4

3 2 1


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CONTENTS

FOREWORD

xiii

ACKNOWLEDGMENTS

xv

LIST OF ACRONYMS

xvii

LIST OF PHYSICAL UNITS AND SUBUNITS

xxii

LIST OF SYMBOLS

xxiii

CHAPTER 1

FUNDAMENTALS OF X-RAY FLUORESCENCE
1.1 A Short History of XRF
1.2 The New Variant TXRF
1.2.1 Retrospect on its Development
1.2.2 Relationship of XRF and TXRF
1.3 Nature and Production of X-Rays
1.3.1 The Nature of X-Rays
1.3.2 X-Ray Tubes as X-Ray Sources
1.3.2.1 The Line Spectrum
1.3.2.2 The Continuous Spectrum
1.3.3 Polarization of X-Rays
1.3.4 Synchrotron Radiation as X-Ray Source
1.3.4.1 Electrons in Fields of Bending
Magnets
1.3.4.2 Radiation Power of a Single
Electron
1.3.4.3 Angular and Spectral
Distribution of SR
1.3.4.4 Comparison with Black-Body
Radiation
1.4 Attenuation of X-Rays
1.4.1 Photoelectric Absorption
1.4.2 X-Ray Scatter
1.4.3 Total Attenuation

v

1
2
8
8
13
15
15
17
19
27
29
30
32
35
36
42
44
46
49
51


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CHAPTER 2

CHAPTER 3

CONTENTS

1.5

Deflection of X-Rays
1.5.1 Reflection and Refraction
1.5.2 Diffraction and Bragg’s Law
1.5.3 Total External Reflection
1.5.3.1 Reflectivity
1.5.3.2 Penetration Depth
1.5.4 Refraction and Dispersion
References

53
53
59
62
66
67
71
74

PRINCIPLES OF TOTAL REFLECTION XRF
2.1 Interference of X-Rays
2.1.1 Double-Beam Interference
2.1.2 Multiple-Beam Interference
2.2 X-Ray Standing Wave Fields
2.2.1 Standing Waves in Front of a Thick

Substrate
2.2.2 Standing Wave Fields Within a Thin Layer
2.2.3 Standing Waves Within a Multilayer
or Crystal
2.3 Intensity of Fluorescence Signals
2.3.1 Infinitely Thick and Flat Substrates
2.3.2 Granular Residues on a Substrate
2.3.3 Buried Layers in a Substrate
2.3.4 Reflecting Layers on Substrates
2.3.5 Periodic Multilayers and Crystals
2.4 Formalism For Intensity Calculations
2.4.1 A Thick and Flat Substrate
2.4.2 A Thin Homogeneous Layer
on a Substrate
2.4.3 A Stratified Medium of Several Layers
References

79
80
80
84
88

INSTRUMENTATION FOR TXRF AND GI-XRF
3.1 Basic Instrumental Setup
3.2 High and Low-Power X-Ray Sources
3.2.1 Fine-Focus X-Ray Tubes
3.2.2 Rotating Anode Tubes
3.2.3 Air-Cooled X-Ray Tubes
3.3 Synchrotron Facilities

3.3.1 Basic Setup with Bending Magnets
3.3.2 Undulators, Wigglers, and FELs
3.3.3 Facilities Worldwide

88
94
100
100
102
104
106
108
110
112
113
116
120
123
126
128
130
131
132
133
134
136
137
139

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CONTENTS

3.4

The Beam Adapting Unit
3.4.1 Low-Pass Filters
3.4.2 Simple Monochromators
3.4.3 Double-Crystal Monochromators
3.5 Sample Positioning
3.5.1 Sample Carriers
3.5.2 Fixed Angle Adjustment for TXRF
(“Angle Cut”)
3.5.3 Stepwise-Angle Variation for GI-XRF
(“Angle Scan”)
3.6 Energy-Dispersive Detection of X-Rays
3.6.1 The Semiconductor Detector
3.6.2 The Silicon Drift Detector
3.6.3 Position Sensitive Detectors
3.7 Wavelength-Dispersive Detection of X-Rays
3.7.1 Dispersing Crystals with Soller
Collimators
3.7.2 Gas-Filled Detectors
3.7.3 Scintillation Detectors
3.8 Spectra Registration and Evaluation
3.8.1 The Registration Unit
3.8.2 Performance Characteristics
3.8.2.1 Detector Efficiency
3.8.2.2 Spectral Resolution

3.8.2.3 Input–Output Yield
3.8.2.4 The Escape-Peak
Phenomenon
References
CHAPTER 4

PERFORMANCE OF TXRF AND GI-XRF
ANALYSES
4.1 Preparations for Measurement
4.1.1 Cleaning Procedures
4.1.2 Preparation of Samples
4.1.3 Presentation of a Specimen
4.1.3.1 Microliter Sampling by Pipettes
4.1.3.2 Nanoliter Droplets by Capillaries
4.1.3.3 Picoliter-Sized Droplets by Inkjet
Printing
4.1.3.4 Microdispensing of Liquids
by Triple-Jet Technology
4.1.3.5 Solid Matter of Different Kinds

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150
150
155
157
160
161
162
162
164

165
167
169
173
176
178
182
183
183
185
185
188
194
197
200

205
207
207
211
215
216
217
218
220
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CONTENTS

4.2

4.3

4.4

4.5

4.6

Acquisition of Spectra
4.2.1 The Setup for Excitation with X-Ray
Tubes
4.2.2 Excitation by Synchrotron Radiation
4.2.3 Recording the Spectrograms
4.2.3.1 Energy-Dispersive Variant
4.2.3.2 Wavelength-Dispersive Mode
Qualitative Analysis
4.3.1 Shortcomings of Spectra
4.3.1.1 Strong Spectral Interferences
4.3.1.2 Regard of Sum Peaks
4.3.1.3 Dealing with Escape Peaks
4.3.2 Unambiguous Element Detection
4.3.3 Fingerprint Analysis
Quantitative Micro- and Trace Analyses
4.4.1 Prerequisites for Quantification

4.4.1.1 Determination of Net Intensities
4.4.1.2 Determination of Relative
Sensitivities
4.4.2 Quantification by Internal Standardization
4.4.2.1 Standard Addition for a Single
Element
4.4.2.2 Multielement Determinations
4.4.3 Conditions and Limitations
4.4.3.1 Mass and Thickness of Thin
Layers
4.4.3.2 Residues of Microliter Droplets
4.4.3.3 Coherence Length of Radiation
Quantitative Surface and Thin-Layer Analyses
by TXRF
4.5.1 Distinguishing Between Types
of Contamination
4.5.1.1 Bulk-Type Impurities
4.5.1.2 Particulate Contamination
4.5.1.3 Thin-Layer Covering
4.5.1.4 Mixture of Contaminations
4.5.2 Characterization of Thin Layers by TXRF
4.5.2.1 Multifold Repeated Chemical
Etching
4.5.2.2 Stepwise Repeated Planar Sputter
Etching
Quantitative Surface and Thin-Layer
Analyses by GI-XRF

222
222

225
226
227
227
228
228
229
235
235
236
237
238
240
240
241
244
245
246
248
249
251
252
257
257
257
258
259
259
262
262

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CONTENTS

4.6.1
4.6.2
4.6.3
4.6.4
4.6.5
References
CHAPTER 5

Recording Angle-Dependent Intensity
Profiles
Considering the Footprint Effect
Regarding the Coherence Length
Depth Profiling at Grazing Incidence
Including the Surface Roughness

DIFFERENT FIELDS OF APPLICATIONS
5.1 Environmental and Geological Applications
5.1.1 Natural Water Samples
5.1.2 Airborne Particulates
5.1.3 Biomonitoring
5.1.4 Geological Samples
5.2 Biological and Biochemical Applications

5.2.1 Beverages: Water, Tea, Coffee, Must,
and Wine
5.2.2 Vegetable and Essential Oils
5.2.3 Plant Materials and Extracts
5.2.4 Unicellular Organisms and Biomolecules
5.3 Medical, Clinical, and Pharmaceutical
Applications
5.3.1 Blood, Plasma, and Serum
5.3.2 Urine, Cerebrospinal, and Amniotic Fluid
5.3.3 Tissue Samples
5.3.3.1 Freeze-Cutting of Organs
by a Microtome
5.3.3.2 Healthy and Cancerous Tissue
Samples
5.3.4 Medicines and Remedies
5.4 Industrial or Chemical Applications
5.4.1 Ultrapure Reagents
5.4.2 High-Purity Silicon and Silica
5.4.3 Ultrapure Aluminum
5.4.4 High-Purity Ceramic Powders
5.4.5 Impurities in Nuclear Materials
5.4.6 Hydrocarbons and Their Polymers
5.4.7 Contamination-Free Wafer Surfaces
5.4.7.1 Wafers Controlled by Direct
TXRF

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268
270
272

274
283
284
291
292
292
297
302
306
307
308
312
312
315
317
317
320
322
322
324
327
329
330
331
332
334
336
336
338
340

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CONTENTS

5.4.7.2 Contaminations Determined
by VPD-TXRF
5.4.8 Characterization of Nanostructured
Samples
5.4.8.1 Shallow Layers by Sputter
Etching and TXRF
5.4.8.2 Thin-Layer Structures by Direct
GI-XRF
5.4.8.3 Nanoparticles by TXRF
and GI-XRF
5.5 Art Historical and Forensic Applications
5.5.1 Pigments, Inks, and Varnishes
5.5.2 Metals and Alloys
5.5.3 Textile Fibers and Glass Splinters
5.5.4 Drug Abuse and Poisoning
References
CHAPTER 6

CHAPTER 7

342
346

346
347
354
357
357
361
363
365
367

EFFICIENCY AND EVALUATION
6.1 Analytical Considerations
6.1.1 General Costs of Installation and Upkeep
6.1.2 Detection Power for Elements
6.1.3 Reliability of Determinations
6.1.4 The Great Variety of Suitable Samples
6.1.5 Round-Robin Tests
6.2 Utility and Competitiveness of TXRF
and GI-XRF
6.2.1 Advantages and Limitations
6.2.2 Comparison of TXRF with Competitors
6.2.3 GI-XRF and Competing Methods
6.3 Perception and Propagation of TXRF Methods
6.3.1 Commercially Available Instruments
6.3.2 Support by the International Atomic
Energy Agency
6.3.3 Worldwide Distribution of TXRF and
Related Methods
6.3.4 Standardization by ISO and DIN
6.3.5 International Cooperation and Activity

References

383
384
384
385
388
391
393

413
417
420
424

TRENDS AND FUTURE PROSPECTS
7.1 Instrumental Developments
7.1.1 Excitation by Synchrotron Radiation
7.1.2 New Variants of X-Ray Sources

433
434
434
436

397
398
400
409
410

410
413


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CONTENTS

Capillaries and Waveguides for Beam
Adapting
7.1.4 New Types of X-Ray Detectors
7.2 Methodical Developments
7.2.1 Detection of Light Elements
7.2.2 Ablation and Deposition Techniques
7.2.3 Grazing Exit X-Ray Fluorescence
7.2.4 Reference-Free Quantification
7.2.5 Time-Resolved In Situ Analysis
7.3 Future Prospects by Combinations
7.3.1 Combination with X-Ray Reflectometry
7.3.2 EXAFS and Total Reflection Geometry
7.3.3 Combination with XANES or NEXAFS
7.3.4 X-Ray Diffractometry at Total Reflection
7.3.5 Total Reflection and X-Ray
Photoelectron Spectrometry
References

xi

7.1.3

INDEX

438
442
445
445
449
452
459
462
463
464
466
468
480
486
491
501


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FOREWORD

This second edition of the first and only monograph on total reflection X-ray
fluorescence (TXRF) is thoroughly revised and updated with important developments of the last 15 years. TXRF is a universal and economic multielement
method suitable for extreme micro- and trace analyses. Its unique and inherent

features are elaborated in detail in this excellent monograph. TXRF represents
an individual method with its own history and special peculiarities in comparison
to other XRF techniques, and is well established within the community of
elemental spectroscopy. In particular, TXRF has been realized and understood
as a complementary rather than competitive instrument within the orchestra of
ultramicro and ultratrace analytical instrumentation. In different round-robin
tests, TXRF demonstrated its performance quite well in comparison with
methods such as ET-AAS, ICP-OES, ICP-MS, RBS, and INAA.
Total reflection XRF is widely used in the analysis of flat sample surfaces
and near-surface layers. Here, it may be applied as a nondestructive method
especially suitable for the quality control of wafers in the semiconductor
industry. It can be used for the determination of impurities at the ultratrace
level and for mapping of the element distribution on flat surfaces. In addition to
the composition, the nanometer-thickness of thin layers can be determined by
tilting the sample at grazing incidence. Direct density measurements are a
special and unique feature of TXRF after sputter-etching.
The authors have built a successful and well established team in the field of
TXRF for about 25 years. In the first edition of this book, R. Klockenkämper
described the principles and fundamentals of TXRF, the performance of
analyses, and its applications. After his retirement, he cooperated with A.
von Bohlen in order to examine the latest developments and to place TXRF in
a leading position of analytical atomic spectrometry.
Several new sections of this second edition demonstrate the essential progress of TXRF. The new generation of silicon drift detectors, which are cooled
thermo-electrically, is highlighted. About 80 synchrotron facilities around the
whole world are listed—with work places that are dedicated solely to TXRF
offering an extremely brilliant and tunable radiation. The previous fields of
applications are enumerated and diversified, contamination control of wafers is
shown to be standardized, and many new fields are represented especially in
the life sciences. Combinations of different methods of spectrometry, such as
NEXAFS and XANES, with excitation under total reflection build a trend and

xiii


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xiv

FOREWORD

have been presented as future prospects. The worldwide distribution of
TXRF’s instrumentation and its different fields of applications are evaluated
statistically.
This articulate monograph on TXRF with several color pictures provides
fundamental and valuable help for present and future users in the analytical
community. Many disciplines, such as geo-, bio-, material-, and environmental
sciences, medicine, toxicology, forensics, and archaeometry can profit from the
method in general and from this outstanding monograph in particular.
Geesthacht, May 2014

PROF. DR. ANDREAS PRANGE
Helmholtz-Zentrum Geesthacht
Institute for Coastal Research
Head of the Department for
Marine Bioanalytical Chemistry


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ACKNOWLEDGMENTS

The authors are grateful to all the colleagues of our TXRF community for their
laborious and important investigations and for manifold publications that build
the basis of this monograph. Special thanks go to the attendees of the last
conference on TXRF, who took part in the survey described in Chapter 6.
We also wish to thank Mrs. Maria Becker for carefully adapting the first
edition in a readable word document, and for the diligent compilation of all
references and all the data of synchrotron beamlines. Furthermore, we thank
our former colleague Prof. Dr. Joachim Buddrus for proofreading chemical
terms and formulas. Scientific and technical assistance of the Leibniz-Institut
für Analytische Wissenschaften – ISAS – e.V., represented by members of the
Executive Board, Prof. Dr. Albert Sickmann and Jürgen Bethke, is gratefully
acknowledged. ISAS in Dortmund is supported by the Bundesministerium für
Bildung und Forschung (BMBF) of Germany, by the Ministerium für Innovation, Wissenschaft und Forschung of North Rhine-Westphalia, and by the
Senatsverwaltung für Wirtschaft, Technologie und Forschung, Berlin.
It is a pleasure for the authors to thank our friend Prof. Dr. Andreas Prange
for providing a felicitous and penetrative foreword. The authors are also
obliged to the publishers John Wiley and particularly to Bob Esposito and
Michael Leventhal for their reliable assistance, and to Dr. Mark Vitha for his
great care in editing the manuscript. We also pay tribute to the printers for the
excellence of their printing, especially to our project manager, Ms. Shikha
Pahuja, for the diligent organization.

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LIST OF ACRONYMS

AC
ADC
AFM
AITR
ALS
AMC
ANNA
APS
ASTM
ATI
AXIL
BB
BCR
BESSY
BRM
CAS
CCD
CHA
CHESS
CMA
CMOS
CMOS
CRM
CVD
CXRO
DC

Alternating current

Analog-to-digital converter
Atomic force microscopy
Attenuated internal total reflection
Amyotrophic Lateral Sclerosis
Adiabatic microcalorimeter
Activity of Excellence and Networking for Nanoand Microelectronics Analysis
Advanced photon source or American Physical Society
American society for testing and materials
Atom institute
Analytical X-ray analysis by iterative least squares
Black body
Breakpoint cluster region (protein or gene) or
British Chemical Standard - Certified reference material
Berliner Elektronen Speicherring Gesellschaft
für Synchrotronstrahlung
Blank reference material
Chemical Abstracts Services
Charge-coupled device
Concentric hemispherical analyzer
Cornell high-energy synchrotron source
Cylindrical mirror analyzer
Complementary metal oxides
Complementary metal oxides semiconductor
Certified reference material
Chemical vapor deposition
Center for X-ray Optics and Advanced Light Source
Direct current
xvii

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xviii
DCM
DESY
DIN
DMM
DORIS
EDS
EDTA
EPMA
ESCA
ET-AAS
EXAFS
FAAS
FCM
FEL
FET
FPS
FT-IR
FWHM
GC-MS
GeLi
GE-XRF
GF-AAS
GI-XRD
GI-XRF
GIE-XRF
GLP
HASYLAB

HOPG
HPGe
HPLC
HS
IAEA
IC
ICDD
ICP
ICP-MS
ICP-OES
IDMS

LIST OF ACRONYMS

Double-crystal monochromator
Deutsches Elektronen Synchrotron
Deutsches Institut für Normung
Double multilayer monochromator
Doppel Ring Speicher
Energy-dispersive spectrometry or spectrometer
Ethylene-diaminetetraceticacid
Electron probe microanalysis
Electron spectroscopy for chemical analysis
Electrothermal atomic absorption spectrometry
Extended X-ray absorption fine structure
Flame atomic absorption spectrometry
Four-crystal monochromator
Free-electron laser
Field effect transistor
Flat panel sensor

Fourier transform-infra red
Full width at half maximum
Gas chromatography-mass spectrometry
Ge(Li) detector; Germanium drifted with Lithium ions
Grazing exit X-ray fluorescence
Graphite furnace-atomic absorption spectrometry
Grazing incidence X-ray diffractometry
Grazing incidence X-ray fluorescence
Grazing incidence/exit X-ray fluorescence
Good laboratory practice
Hamburger Synchrotron Strahlungslabor
Highly ordered (oriented) pyrolytic graphite
HPGe detector; high-purity Germanium
High-performance liquid chromatography
Humic substances
International Atomic Energy Agency
Integrated circuit
International Centre for Diffraction Data
Inductively coupled plasma
Inductively coupled plasma-mass spectrometry
Inductively coupled plasma-optical emission spectrometry
Isotope dilution-mass spectrometry


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LIST OF ACRONYMS

IEEE
IFG

IMEC
INAA
IR
IRMM
ISO
ITRS
IUPAC
JCPDS
JFET
KFA
LED
LINAC
MBI
MCA
MRI
MRT
NEXAFS
NIES
NIST
NSF
NSLS
PES
PGM
PIN
PIXE
PMM
PTB
PVD
QM
QXAS

RBS
RMS
ROI
RSD
SAXS
SD

Institute of Electrical and Electronics Engineers
Institut für Geräteentwicklung
Interuniversity Microelectronics Center
Instrumental neutron activation analysis
Infrared
Institute of Reference Materials and Measurements
International Standard Organization
International Technology Roadmap for Semiconductors
International Union for Applied Chemistry
Joint Committee on Powder Diffraction Standards
Junction Gate FET
Kernforschungsanlage
Light emitting diode
Linear accelerator
Max-Born Institut
Multichannel analyzer
Magnetic resonance imaging
Magnetic resonance tomography
Near extended X-ray absorption fine structure
National Institute for Environmental Studies
National Institute of Standards and Technology
Nephrogenic Systemic Fibrosis
National Synchrotron Light Source

Photoelectron spectrometry
Plane grating monochromator
Positive-intrinsic-negative
Proton or particle induced X-ray emission
Primary methods of measurement
Physikalisch-Technische Bundesanstalt
Physical vapor deposition
Quality management
Quantitative X-ray analysis system
Rutherford backscattering spectrometry
Root mean square (of the mean squared deviations)
Region of interest
Relative standard deviation
Small angle X-ray scattering
Standard deviation, absolute value

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xx
SDD
SDi
SEM
SGM
SiLi
SIMS
SOP
SPM

SQUID
SR
SRM
SSD
SSRL
STJ
STM
SW
TDS
TES
TR
TRIM
TR-XPS
TR-XRD
TR-XRR
TXRF
UCS
UHV
ULSI
UPS
USB
UV
VAMAS
VLSI
VPD
WDS
XAFS
XANES
XPS
XRD

LIST OF ACRONYMS

Silicon drift detector
Strategic Directions International
Scanning electron microscopy
Spherical grating monochromator
Si(Li) detector; Silicium drifted with Lithium ions
Secondary ion mass spectrometry
Standard operating procedure
Suspended particulate matter
Superconducting quantum interference device
Synchrotron radiation
Standard reference material
Solid-state detector
Stanford Synchrotron Radiation Laboratory
Superconducting tunnel junction
Scanning tunneling microscope or microscopy
Standing wave
Total dissolved solids
Transition edge sensor
Total reflection
Transport and range of ions in matter
Total reflection XPS
Total reflection XRD
Total reflection XRR
Total reflection X-ray Fluorescence
Ultra-Clean Society
Ultra-high-vacuum
Ultra-large-scale integration

Ultraviolet photoelectron spectrometry
Universal serial bus
Ultraviolet
Versailles Project on Advanced Materials and Standards
Very-large-scale integration
Vapor-phase decomposition
Wavelength-dispersive spectrometry or spectrometer
X-ray absorption fine structure
X-ray absorption near-edge structure
X-ray photoelectron spectrometry
X-ray diffractometry


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LIST OF ACRONYMS

XRF
XRR
XSW

X-Ray fluorescence
X-ray reflectometry
X-ray standing waves

Chemical Compounds
APDC
DNA
h-BN
HMDTC

mQC
MIBK
NaDBDTC
PEDOT:PSS
PEG
PFA
PEI
PEO
PP
PTFE
PMMA
RNA
ROS
TEAB
TMAB
TMB

Ammonium pyrrolidine dithiocarbamate
Deoxyribonucleic acid
hexagonal form of boron-nitride
Hexamethylene-dithiocarbamate
murine Glutaminyl cyclase
Methyl isobutyl ketone
Sodium dibutyldithiocarbamate
Polyethylenedioxythiophene: Polystyrene sulfonate
Polyethylene glycol
Polyfluoroalkoxy (polymers)
Polyethylenimine
Polyethylene oxide
Polypropylenes

Polytetrafluoro-ethylenes
Polymethyl methacrylate
Ribonucleic acid
Reactive oxygen species
Triethylamine borane
Trimethylamine borane
Trimethylborazine

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LIST OF PHYSICAL UNITS AND SUBUNITS

A
a
°C
C
cm
d
eV
F
ft
GHz
GeV
g
h
hPa
Hz

in
J
K
keV
kg
km
kPa
kV
kW
l
m
mA

ampere
year (annum)
°Celsius or centigrade
coulomb
centimeter
day
electronvolt
farad
foot
gigahertz
giga-electronvolt
gram
hour or hecto
hectopascal
hertz
inch
joule

kelvin
kilo-electronvolt
kilogram
kilometer
kilopascal
kilovolt
kilowatt
liter
meter or milli
milliampere

MeV
min
ml
mm
mol
mrad
N
nl
nm
Pa
pl
rad
rpm
s
sr
T
V
W
kΩ

μl
μrad
Ω
%
‰
ppm
ppb
ppt

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mega-electronvolt
minute
milliliter
millimeter
mole
milliradian
newton
nanoliter
nanometer
pascal
picoliter
radian
revolutions per minute
second
steradian (squared radian)
tesla
volt
watt
kiloohm

microliter
microradian
ohm
per cent (10 2)
per mill (10 3)
parts per million (10 6)
parts per billion (10 9)
parts per trillion (10 12)


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LIST OF SYMBOLS

Symbols for Physical Quantities (in general they are unambiguous; in exceptional cases their meaning becomes clear by their individual context; for a
detailed definition and distinction they can have indices)
α
αcrit
αd
αf
αk
β

γ
δ
Δ
ε
ζ
η
θ

Θ
λ
λC
λcut
μ/ρ
ν
ξ
ρ
ρm

Glancing angle of incident primary beam
Critical angle of total reflection
glancing angle determined by the detector’s field of vision
Sommerfeld’s fine structure constant or glancing angle determined
by the footprint
glancing angles of Kiessig maxima
Imaginary component of refractive index or ratio of electron
velocity and light velocity or take-off angle of the fluorescence
radiation
Lorentz factor
Decrement or real component of refractive index (or sometimes
difference)
Path difference or interval
Efficiency of a detector
Vertical coherence length
Efficiency
Polar angle of an electron’s position (in plane of the orbit)
Tilt angle around horizontal x-axis (corresponds to α)
Wavelength
Compton wavelength

Longest wavelength of radiation refracted at a given angle
Total mass-absorption coefficient
Frequency or index
Horizontal coherence length
Density of an element or material
Radius of curvature of the circular electron orbit

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