Analytical Transmission Electron Microscopy: An Introduction for Operators

357 Pages·2014·10.57 MB·English

by  Jürgen Thomas, Thomas Gemming (auth.)

Analytical Transmission Electron Microscopy
Jürgen Thomas • Thomas Gemming
Analytical Transmission
Electron Microscopy
An Introduction for Operators
1 3
Jürgen Thomas Thomas Gemming
Leibniz Institute for Solid State and Leibniz Institute for Solid State and
Materials Research (IFW) Dresden Materials Research (IFW) Dresden
Germany Germany
This book is the revised and slightly expanded translation of the German book edition by
Jürgen Thomas and Thomas Gemming: “Analytische Transmissionselektronenmikroskopie—
Eine Einführung für den Praktiker”, Springer-Verlag, Wien 2013, ISBN 978-3-7091-1439-1.
ISBN 978-94-017-8600-3 ISBN 978-94-017-8601-0 (eBook)
DOI 10.1007/978-94-017-8601-0
Springer Dordrecht Heidelberg New York London
Library of Congress Control Number: 2014932544
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Preface
What is the goal of a transmission electron microscope (TEM)? It is expensive and
causes large running costs. The understanding of the results is sometimes difficult
and they can be wrongly interpreted. It needs specialists and, connected with that,
causes additional labour costs.
On the other hand, it is a microscope, i.e. its results are magnified pictures and
everybody is able to understand pictures. Apparently, there are no problems under-
standing them. Why do we need an additional textbook about this topic?
Goethe: „Mikroskope und Fernrohre verwirren eigentlich den reinen Men-
schensinn.“ [1] (Microscopes and telescopes confuse the human mind.)
However, analytical transmission electron microscopy does not only include the
microscopic imaging. Electron diffraction and compositional analysis by spectrom-
eters for X-rays and energy losses of the electrons complement it. The analytical
transmission electron microscope covers four challenging methods: electron micro-
scopic imaging, electron diffraction, analysis of characteristic X-rays, and electron
energy loss spectroscopy. There are specialists for each of these methods; neverthe-
less the operator at the microscope should hold an overview about the possibilities
of analytical transmission electron microscopy. He should be able to handle them
and should be familiar with the basics of the interpretation of the measured results.
It is the goal of this textbook to give such an overview. The idea to write this book
was arising during the work in our electron microscopic laboratory of the Leibniz
Institute for Solid State and Materials Research (IFW) Dresden. While teaching the
students of materials science in lectures and practical courses about analytical trans-
mission electron microscopy as well as while instructing graduate students, Ph.D.
students, and technicians at the microscope we have attained experiences regarding
frequently asked questions by the beginners and the didactical procedure to explain
the function and the practical handling of a transmission electron microscope.
These experiences are integrated in this book. It addresses people who want
or have to work at a transmission electron microscope and have not yet a further
knowledge about this topic. The book should also be helpful for service engineers
to ensure an overview of the basic knowledge about the microscopes maintained by
them. Additionally, the book should be also a little bit amusing to receive interest in
electron microscopy from non-experts, too.
v
vi Preface
The focus lies on explanations with the help of simple models and on hints for the
practical electron microscopic work. The headlines of the chapters already indicate
this matter. This is the difference to other introductions into electron microscopy.
As far as practicable, we tried to avoid explanations based only on mathematical
formalisms.
In this context we would like to give a comment on the model assumptions in
physics: On the one hand, we speak about electrons as particles, on the other hand as
waves. Or the position of the specimen within the electron microscope: Sometimes
we draw the specimen outside of the objective lens, sometimes within the magnetic
field of the lens. One or two of the readers will see a discrepancy here. However, it
is not a discrepancy but a property of models in physics suitable to explain special
features in nature. Dependent on the experimental setup we observe sometimes the
particle and otherwise the wave character of the electrons. Or: To explain the multi-
stage imaging of the electron microscope we draw the specimen outside of the mag-
netic field since the beam path within the lens does not play any role in this case.
Only the beam path outside of the lens is important. On the other hand, when we
discuss the imaging of magnetic samples the direct interaction between the sample
and the magnetic lens field is essential and we have to use another model. In other
words: The physical models used in this book are chosen to be as simple as possible
to explain a specific outcome.
Despite the attempt of plausible explanations some correlations can be better
understood with the help of mathematics. Formulas are necessary to obtain quanti-
tative values. Especially the last chapter 10 considers this. There are some special
basics explained in more detail, where it is applicable we point to such detailed
explanations within the text. Here and there equations are also listed in the ear-
lier chapters containing elements of the infinitesimal mathematics like differentials
and integrals. Describing definitions and physical basics sometimes it is absolutely
necessary. This should be no reason to stop reading the book even if the reader has
problems with this kind of mathematics.
For specialists the chapter 10 cannot substitute textbooks about special topics of
electron microscopy. We suggest some of such books in the hints for further reading
at the end of this book.
Finally, we would like to thank: our academic teachers, friends and colleagues
who introduced us into the topics of electron microscopy or had facilitated the work
at modern instruments later on. Some names we would like to mention: Prof. Alfred
Recknagel, Dr. Hans-Dietrich Bauer, and Prof. Klaus Wetzig in Dresden as well
as Prof. Manfred Rühle, Prof. Frank Ernst, Dr. Günter Möbus, and Prof. Joachim
Mayer working at the “Max-Planck-Institut für Metallforschung” in Stuttgart in the
relevant time.
Electron microscopic investigations are only possible using suitably prepared
thin samples. Many of the electron microscopic images could be only presented
in this book because of the careful specimen preparation by Dipl.-Ing. (FH) Birgit
Arnold and Dina Lohse.
In an early state of our book project we spoke with Prof. Josef Zweck from
Regensburg and Prof. Klaus Wetzig from Dresden about our concept. They had
Preface vii
encouraged us in our project and contributed by their advocacy essentially to the
publication of the book by the Springer Verlag.
Stephen Soehnlen B.S., Wil Bruins, and Annelies Kersbergen were our nego-
tiants of the Springer Verlag in Dordrecht. Without their benignity this book had not
been published.
Nora Thomas M.A. was so kind to help us finding Goethe’s citations with her
special knowledge.
We are indebted to the persons mentioned here, as well as to those electron mi-
croscopists from Dresden who had been reading the German book manuscript or
parts of it, as well as this English version later on, and gave helpful hints for its
improvement but also to the colleagues, friends, and students who inspired us by
questions and comments to think about facts and circumstances which seemed to
be “completely clear”.
Goethe: „Alles Gescheite ist schon mal gedacht worden, man muß nur ver-
suchen, es noch einmal zu denken.“ [2] (All the prudent things have been already
thought. One just has to try to think about them once more.)
Dresden October 2013 Jürgen Thomas
Thomas Gemming
References
1. von Goethe, J. W.: Wilhelm Meisters Wanderjahre, ed. Erich Trunz, Goethes Werke—
Hamburger Ausgabe Bd. 8, Romane und Novellen III, 12. Aufl. München, II/Betrachtungen im
Sinne der Wanderer (1989), p. 293
2. von Goethe, J. W.: ibidem, p. 283
Common remark: Biographic Data: Wikipedia—the free encyclopedia, http://de.wikipedia.org/
wiki/Wikipedia
Contents
1 W hy Such an Effort? ............................................................................... 1
1.1 The Problem with the Magnification ................................................ 1
1.2 The Limitation of Resolution ............................................................ 2
1.3 Electron Waves .................................................................................. 6
1.4 The Role of Magnification ................................................................ 8
2 What Should we Know about Electron Optics and the
Construction of an Electron Microscope? ............................................. 11
2.1 The Principle of Multistage Imaging ................................................ 11
2.2 Rotational-Symmetric Magnetic Fields as Electron Lenses ............. 12
2.3 Lens Aberrations ............................................................................... 15
2.4 Resolution Limit Considering the Spherical Aberration ................... 19
2.5 Electron Gun ..................................................................................... 20
2.6 “Richtstrahlwert” (Brightness) .......................................................... 24
2.7 We Construct an Electron Microscope .............................................. 27
2.7.1 Illumination System .............................................................. 27
2.7.2 Imaging System .................................................................... 29
2.7.3 Specimen Stage ..................................................................... 30
2.7.4 Acquiring the Images ............................................................ 32
2.7.5 V acuum System..................................................................... 34
2.7.6 Miscellaneous ....................................................................... 37
References .................................................................................................. 39
3 We Prepare Electron-Transparent Samples .......................................... 41
3.1 What is the Challenge? ...................................................................... 41
3.2 “Classical” Methods .......................................................................... 43
3.3 Cutting, Grinding, and Ion Milling ................................................... 47
3.4 Focussed Ion Beam (“FIB”) Techniques ........................................... 51
References .................................................................................................. 56
ix
x Contents
4 Let us Start with Practical Microscopy.................................................. 57
4.1 What do We Peripherally Need? ....................................................... 58
4.2 We Put the Specimen into the Holder and Insert
it into the Microscope ........................................................................ 59
4.3 We Check the (alignment) State of the Microscope .......................... 61
4.4 Focussing the Image—Sharpness and Contrast ................................ 69
4.5 Contamination and Sample Damaging .............................................. 70
References .................................................................................................. 73
5 Let us Switch to Electron Diffraction ..................................................... 75
5.1 Why Diffraction Reflections? ........................................................... 75
5.2 Crystal Lattices and Lattice Planes ................................................... 78
5.3 Selected Area and Convergent Beam Electron Diffraction ............... 84
5.4 What Can We Learn from Selected Area Diffraction Patterns? ........ 90
5.4.1 Radii in Ring Diagrams ........................................................ 90
5.4.2 Rules for Forbidden Reflections ........................................... 93
5.4.3 Intensities of the Diffraction Reflections .............................. 98
5.4.4 Positions of Diffraction Reflections in Point Diagrams ....... 99
5.4.5 Indexing of Diffraction Reflections ...................................... 103
5.5 Kikuchi- and HOLZ-lines ................................................................. 106
5.6 Amorphous Samples.......................................................................... 110
References .................................................................................................. 112
6 Why Do We See Any Contrast in the Images? ...................................... 115
6.1 Elastic Scattering of Electrons Within the Sample ........................... 115
6.2 Mass Thickness and Diffraction Contrast ......................................... 116
6.3 Brightfield and Darkfield Imaging .................................................... 120
6.4 Bending Contours, Dislocations, and Semicoherent Particles .......... 123
6.5 Thickness Contours, Stacking Faults, and Twins .............................. 128
6.6 Moiré Patterns ................................................................................... 132
6.7 Magnetic Domains: Lorentz Microscopy .......................................... 133
References .................................................................................................. 136
7 We Increase the Magnification ............................................................... 137
7.1 Imaging of Atomic Columns in Crystals: Phase Contrast ................. 137
7.2 Contrast Transfer by the Objective Lens ........................................... 142
7.3 W ave-optical Interpretation of the Resolution Limit ........................ 145
7.4 Periodic Distribution of Brightness in Pictures: Fourier Analysis .... 147
7.5 Mass Thickness and Phase Contrast.................................................. 150
7.6 Contrast of Amorphous Samples ....................................................... 152
7.7 Correction of Astigmatism ................................................................ 154
7.8 Measurement of the Resolution Limit ............................................... 156
7.9 Correction of Spherical and Chromatic Aberration .......................... 158
7.10 Interpretation of High Resolution TEM Images ............................. 161
References .................................................................................................. 162
Contents xi
8 Let Us Switch to Scanning Transmission Electron Microscopy .......... 163
8.1 What Happens Electron-Optically? ................................................... 163
8.2 Resolution or: What is the Smallest Diameter
of the Electron Probe? ......................................................................... 165
8.3 Contrast in the Scanning Transmission
Electron Microscopic Image ............................................................... 170
8.4 Speciality: High Angle Annular Darkfield Detector ........................... 173
References .................................................................................................... 174
9 Let us Use the Analytical Possibilities ...................................................... 177
9.1 Analytical Signals by Inelastic Interaction ......................................... 177
9.1.1 Emission of X-rays ................................................................. 178
9.1.2 Electron Energy Losses .......................................................... 182
9.2 Energy Dispersive Spectroscopy of Characteristic
X-rays (“EDXS”) ..................................................................................185
9.2.1 X-ray Spectrometers and Spectra ........................................... 186
9.2.2 Qualitative Interpretation of X-ray Spectra ............................ 190
9.2.3 Quantifying X-ray Spectra ...................................................... 194
9.2.4 Line Profiles and Elemental Mappings ................................... 202
9.3 Electron Energy Loss Spectroscopy (“EELS”) .....................................204
9.3.1 Electron Energy Spectrometer ................................................ 205
9.3.2 Low-Loss and Core-Loss Regions of the Spectra .................. 206
9.3.3 Qualitative Elemental Analysis ............................................... 209
9.3.4 Background and Multiple Scattering: Requirements
to the Sample .......................................................................... 210
9.3.5 Measurement of the Specimen Thickness .............................. 213
9.3.6 Edge Fine Structure: Bonding Analysis .................................. 216
9.3.7 Quantifying Energy Loss Spectra ........................................... 219
9.4 Energy Filtered Imaging...................................................................... 221
9.5 Comparison Between EDXS and EELS ............................................. 224
References .................................................................................................... 225
10 Basics Explained in More Detail (with a Bit More Mathematics) ....... 227
10.1 Diffraction at an Edge (Huygens’ Principle) ................................... 227
10.2 W ave Function for Electrons ........................................................... 228
10.3 Electron Wavelength Relativistically Calculated ............................ 233
10.4 Electron Beam Paths in Rotational-Symmetric Magnetic Fields .... 234
10.5 Resolution Limit Considering Spherical Aberration ....................... 243
10.6 Schottky Effect ................................................................................ 244
10.7 Electric Potential in Rotational-Symmetric Arrangements
of Electrodes .................................................................................... 247
10.8 Laue Equations and Reciprocal Lattice, Ewald Construction ......... 249
10.9 Kinematical Model: Lattice Factor and Structure Factor ................ 261
10.10 Debye Scattering ........................................................................... 268
10.11 Electrons Within a Field of a Central Force .................................. 272