Advanced Transmission Electron Microscopy Imaging and Diffraction in Nanoscience

by Jian Min Zuo, John C.H. Spence

Advanced Transmission Electron Microscopy Imaging and Diffraction in Nanoscience This volume expands and updates the coverage in the authors popular 1992 book Electron Microdiffraction As the title implies the focus of the book has changed from electron microdiffraction and convergent beam electron diffraction to all forms of advanced transmission electron microscopy Special attention is given to electron diffraction and imaging including high resolution TEM and STEM imaging and the application of these methods to crystals their defects and nanostructures The autho

Publisher : Springer Verlag New York

Author : Jian Min Zuo, John C.H. Spence

ISBN : 9781493966059

Year : 2017

Language: en

File Size : 26.71 MB

Category : Engineering Transportation

Jian Min Zuo
John C.H. Spence

Advanced
Transmission
Electron
Microscopy
Imaging and Diffraction in Nanoscience

Advanced Transmission Electron Microscopy

Jian Min Zuo John C.H. Spence


Advanced Transmission
Electron Microscopy
Imaging and Diffraction in Nanoscience

123

Jian Min Zuo
Frederick-Seitz Materials Research
Laboratory, Department of Materials
Science and Engineering
University of Illinois, Urbana-Champaign
Urbana, IL
USA

ISBN 978-1-4939-6605-9
DOI 10.1007/978-1-4939-6607-3

John C.H. Spence
Department of Physics
Arizona State University
Tempe, AZ
USA

ISBN 978-1-4939-6607-3

(eBook)

Library of Congress Control Number: 2016947937
© Springer Science+Business Media New York 2017
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
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The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this
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for any errors or omissions that may have been made.
Printed on acid-free paper
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The registered company address is: 233 Spring Street, New York, NY 10013, U.S.A.

To my family, Xiurong, Yuan and Ling,
and in memory of my parents,
Yijun and Qiaozhen
—Jian Min Zuo
To my family, in gratitude
—John C.H. Spence

Preface

This book is written and organized around three topics: electron diffraction, electron
optics, and electron crystallography. It is intended as an advanced undergraduateor graduate-level text in support of course materials in materials science, physics, or
chemistry departments. High-resolution transmission electron microscope imaging
and scanning transmission electron microscopy are treated as major applications of
electron optics, as well as powerful electron crystallographic techniques for structure determination. The emphasis here is on the fundamentals and applications of
electron diffraction and imaging in materials research, especially in the study of
nanoscience. For this purpose, we have included theory for electron wave propagation, electron diffraction and imaging, and a detailed treatment of electron optics,
aberration correction, and instrument techniques, on a level that can be followed by
a materials science or physics graduate student. For crystallography, we have
emphasized the fundamentals of symmetry, structure and bonding, diffuse scattering, imaging of defects, strain measurement, and determination of nanostructures.
Structure determination of large crystals, including polymeric and biological samples, is not discussed specifically in this book, although the electron diffraction and
imaging theories presented here and instrumental techniques apply equally to these
topics.
Transmission electron microscopy (TEM) traditionally refers to electron
diffraction and imaging techniques that are enabled by a transmission electron
microscope (with the same TEM acronym). Scanning transmission electron
microscopy (STEM) embodies a separate set of techniques. The development of
modern TEMs that function as both TEM and STEM has brought them together, as
complementary techniques, often abbreviated as S/TEM. For this reason, we have
simply used TEM in the book’s title. STEM, more than TEM, is associated with
powerful analytical techniques, such as electron energy loss spectroscopy and
energy-dispersive X-ray spectroscopy. This aspect of TEM is not covered here, and
readers are referred to the excellent books on these subjects by Egerton (2011),
Hawkes and Spence (2007), and Pennycook and Nellist (2011).

vii

viii

Preface

The materials included here come from multiple sources. Firstly, we have
updated our previous book on “Electron Microdiffraction” (Plenum, New York,
1992, by J.C.H. Spence and J.M. Zuo). The previous Chaps. 2–4, 7, and 9 are now
parts of Chaps. 3, 5, 12, 13, and 10, respectively. The new Chap. 10 on instrumental
techniques also incorporates the previous Chap. 6. The previous Chap. 8 is now
separated into Chap. 14, which discusses atomic-resolution imaging and Chap. 15 on
the characterization of defects. Secondly, we have incorporated much new teaching
material throughout the book, such as waves and wave properties (Chap. 2), kinematical theory of electron diffraction (Chap. 4), electron optics (Chaps. 6 and 7),
diffuse scattering (Chap. 13), and electron imaging (Chaps. 14 and 15). This material
is based on the lectures given to graduate students at University of Illinois,
Urbana-Champaign in two courses: diffraction physics and advanced electron
microscopy. The writing of Chaps. 6 and 7 has benefitted from the special invited
lectures given by Prof. Harald Rose in 2011 to the advanced electron microscopy
class.
In writing this book, we have also relied on the original research work by many
graduate students, post-docs, and our collaborators. To them, we owe special
thanks, especially to Profs. Michael O’Keeffe, Ragnvald Hoier (1938–2009),
Miyoung Kim, Randi Holmestad, Jerome Pacuad, Jean-Paul Morniroli, Syo
Matsumura, Yoshitsugu Tomokiyo and Drs. Bin Jiang, Weijie Huang, Jing Tao,
Jiong Zhang, Min Gao, Celik Ayten, Shankar Sivaramakrishnan, Amish Shah,
Ke Ran, Wenpei Gao, and Honggyu Kim. The work at University of Illinois was
funded by the Department of Energy, Basics Science and Division of Materials
Research, National Science Foundation. Especially, JMZ wishes to thank Dr. Jane
Zhu at the Department of Energy for the support of the electron nanocrystallography project.
On reading the literature, one is struck by the enormous variety of applications of
TEM/STEM. These include studies of various defects, grain boundaries and
interfaces in a broad range of materials, analyses of the symmetry changes which
accompany phase transitions, polarization and charge ordering including
charge-density waves in layered structures, accurate mapping of the distribution of
valence electrons in crystals, phase identification and strain measurement around
defects, precipitates and interfaces in alloys or semiconductors, in addition to the
characterization of all sorts of nanostructures. To review all this work, published in
a vast number of papers, and draw out its implications for materials physics would
be a Herculean task. Our aim has been a limited one, to explain the principles of
TEM, to provide the theory in a consistent format and to convey enough understanding to students and researchers to let them get started with modern TEM for
materials characterization. Thus, to experts in the field, some examples in this book
may seem somewhat oversimplified. Also, we have cited references that are directly
related to our discussions. We offer our apologies to many of our colleagues whose
works were not covered or cited here. With regret, for reasons of space, we have not
been able to include the topics of structure determination (see Zou et al. 2011),
electron tomography, or coherent diffractive imaging.

Preface

ix

Several chapters were written during the sabbatical stay of JMZ at CEA,
Grenoble, France, in the fall of 2014. He is therefore grateful to Drs. Jean-Luc
Rouviere and Alain Fontaine for their hospitality and also to the Nanoscience
Foundation, Grenoble, for the Chair of Excellence position which made his visit
possible.
The study of electron diffraction and imaging can be significantly helped by
computer simulations. For this purpose, we have made available of computer
programs listed in the “Electron Microdiffraction” book on the website http://cbed.
matse.illinois.edu/, as well as links to other online resources.
Urbana, USA
Tempe, USA

Jian Min Zuo
John C.H. Spence
ForMemRS

References
Egerton, R.F.: Electron Energy-Loss Spectroscopy in the Electron Microscope, 2nd edn. Springer,
New York (2011)
Pennycook, S., Nellist, P. (eds.): Scanning Transmission Electron Microscopy, Imaging and
Analysis. Springer, New York (2011)
Rose, H.: Electron Optics. University of Illinois, Urbana-Champaign (2011) http://cbed.matse.
illinois.edu/download/Rose_optics_of_magnetic_lenses.pdf
Hawkes, P.W. and Spence, J.C.H. (eds) Science of Microscopy. Springer, New York (2007) , and
Springer Handbook of Microscopy, (2017) to follow.
Spence, J.C.H., Zuo, J.M.: Electron Microdiffraction. Plenum, New York (1992)
Zou, X., Hovmöller, S., Oleynikov, P.: Electron crystallography, electron microscopy and electron
diffraction. Oxford University Press (2011)

Preface to “Electron Microdiffraction,”
Plenum, New York, 1992

Much of this book was written during a sabbatical visit by J.C.H.S. to the Max
Planck Institute in Stuttgart during 1991. We are therefore grateful to Profs.
M. Ruhle and A. Seeger for acting as hosts during this time and to the Alexander
von Humboldt Foundation for the Senior Scientist Award which made this visit
possible. The Ph.D. work of one of us (J.M.Z.) has also provided much of the
background to the book, together with our recent papers with various collaborators.
Of these, perhaps the most important stimulus to our work on convergent beam
electron diffraction resulted from a visit to the National Science Foundation’s
Electron Microscopy Facility at Arizona State University by Prof. R. Hoier in 1988
and from a return visit to Trondheim by J.C.H.S. in 1990. We are therefore particularly grateful to Prof. R. Hoier and his students and coworkers for their
encouragement and collaboration. At ASU, we owe a particular debt of gratitude to
Prof. M. O’Keeffe for his encouragement. The depth of his understanding of crystal
structures and his role as passionate skeptic have frequently been invaluable.
Professor John Cowley has also been an invaluable sounding board for ideas and
was responsible for much of the experimental and theoretical work on coherent
nanodiffraction. The sections on this topic derive mainly from collaborations by
J.C.H.S. with him in the seventies. Apart from that, we have tried to review the
literature as impartially as possibly and at the same time bring out the underlying
concepts in a clear and unified manner, so that the book will be useful for graduate
students. We are particularly grateful to Dr. J.A. Eades for his critical review of
Chap. 7. We apologize to those authors whose work may have been overlooked
among the many hundreds of papers. In order to make the book more practically
useful, we have included some FORTRAN source listings, together with
POSTSCRIPT code which allows the direct printing of Kikuchi and HOLZ line

xi

xii

Preface to “Electron Microdiffraction,” Plenum, New York, 1992

patterns on modern laser printers from the programs. Support from NSF award
DMR-9015867 (“Electron Crystallography”) and the facilities of the NSF-ASU
National Center for High Resolution Electron Microscopy is gratefully
acknowledged.
Tempe, USA

John C.H. Spence
Jian Min Zuo

Contents

1

Introduction and Historical Background . . . . . . . . .
1.1
Electrons and the Electron Wavelength . . . . . .
1.2
Electron and Sample Interaction . . . . . . . . . . .
1.3
Transmission Electron Microscope . . . . . . . . .
1.4
Electron Microdiffraction and STEM . . . . . . .
1.5
Analytical TEM . . . . . . . . . . . . . . . . . . . . . . .
1.6
A Brief History of Electron Microdiffraction .
1.7
A Note to Students and Lecturers . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1
1
2
5
7
9
12
16
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2

Electron Waves and Wave Propagation . . . . . . . . . . . . . . . . . . . . . .
2.1
Wave Functions and the Wave Equation . . . . . . . . . . . . . . . . .
2.2
Quantum Mechanical Wave of Electrons and Schrődinger
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
The Principle of Wave Superposition . . . . . . . . . . . . . . . . . . . .
2.4
Amplitude and Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . .
2.5
Coherence and Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6
Wave Packets and the Uncertainty Principle . . . . . . . . . . . . . . .
2.7
The Gaussian Wave Packet and Its Propagation . . . . . . . . . . . .
2.8
Temporal Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9
Spatial Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Electron Refraction and the Refractive Index . . . . . . . . . . . . . .
2.11 Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.1 Huygens–Fresnel Principle. . . . . . . . . . . . . . . . . . . . . .
2.11.2 Propagation of Plane Wave and Fresnel Zones . . . . . .
2.11.3 Fresnel Diffraction—The Near-Field Small-Angle
Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11.4 Fraunhofer Diffraction—Far-Field Forward
Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19
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3

Contents

The Geometry of Electron Diffraction Patterns . . . . . . . .
3.1
Bragg’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Laue Diffraction Condition . . . . . . . . . . . . . . . . . . .
3.3
Lattice d-Spacing and Crystal, Real,
and Reciprocal Lattices . . . . . . . . . . . . . . . . . . . . . .
3.4
Transmission Electron Diffraction Patterns . . . . . . .
3.5
Excitation Error . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6
Kikuchi Lines and Their Geometry (Kinematic) . . .
3.7
Diffraction Pattern Indexing . . . . . . . . . . . . . . . . . .
3.8
One-Dimensional (Systematics) CBED . . . . . . . . . .
3.9
Two-Dimensional CBED . . . . . . . . . . . . . . . . . . . .
3.10 High-Order Laue Zone (HOLZ) Lines . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.........
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4

Kinematical Theory of Electron Diffraction . . . . . . . . . . . . . . . . . . . 77
4.1
First-Order Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2
Weak-Phase-Object Approximation. . . . . . . . . . . . . . . . . . . . . . 80
4.3
Electron Atomic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4
Kinematical Electron Scattering from a Monoatomic Small
Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5
Electron Crystal Structure Factors and the Diffracted Intensity
from a Small Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.6
Integrated Diffraction Intensity of a Rotating Crystal . . . . . . . . 90
4.7
Atomic Thermal Vibrations and Effect on Electron
Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.8
Electron Structure Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.9
Electron-Optical Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5

Dynamical Theory of Electron Diffraction for Perfect Crystals . . . .
5.1
Many-Beam Theory, Wave-Mechanical Approach . . . . . . . . . .
5.2
Howie–Whelan Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3
Two-Beam Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4
The Concept of the Dispersion Surface . . . . . . . . . . . . . . . . . . .
5.5
Absorption and Its Effects in a First-Order Approximation . . . .
5.6
Many-Beam Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Three-Beam Theory and Particular Solutions
for Centrosymmetric Crystals . . . . . . . . . . . . . . . . . . .
5.6.2 Two-Beam Theory with Weak-Beam Effects . . . . . . . .
5.6.3 Three-Beam Theory—Noncentrosymmetric Crystals
and the Phase Problem . . . . . . . . . . . . . . . . . . . . . . . .
5.6.4 Dynamic HOLZ Intensities and Positions.
Dispersion Surfaces for HOLZ Lines.
How the Bragg Law Depends
on Local Composition . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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159
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7

Lens Aberrations and Aberration Correction . . . . . . . . .
7.1
Lens Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2
Aberration Coefficients . . . . . . . . . . . . . . . . . . . . . .
7.3
Multipole Fields and Quadrupole Focal Properties .
7.4
Aberrations of Hexapole Fields . . . . . . . . . . . . . . . .
7.5
Cs Correctors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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165
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8

Electron Sources . . . . . . . . . . . . . . . .
8.1
Source Properties . . . . . . . . . .
8.2
Thermionic Emission Source .
8.3
Schottky Emission Source. . . .
8.4
Cold-Field Emission Source . .
References . . . . . . . . . . . . . . . . . . . . . .

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9

Electron Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1
Scintillator–Photomultiplier Detectors . . . . . . .
9.2
Characteristics of Point Detectors . . . . . . . . . .
9.3
Characteristics of ADF Detectors . . . . . . . . . .
9.4
CCD Cameras . . . . . . . . . . . . . . . . . . . . . . . . .
9.5
Detector Characteristics of CCD Cameras . . . .
9.6
Direct Detection Cameras . . . . . . . . . . . . . . . .
9.7
Film and Image Plates . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10 Instrumentation and Experimental Techniques . . . . . . . . . . . . . . . . .
10.1 Electron Beam Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.1 Illumination Using Two Condenser Lenses . . . . . . . . .
10.1.2 The Use of Condenser Minilens . . . . . . . . . . . . . . . . .
10.1.3 A Third Condenser Lens and Kohler Illumination . . . .
10.1.4 Beam Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.5 Coherence and Coherent Current . . . . . . . . . . . . . . . . .

231
232
232
234
235
236
237

6

Electron Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1
Magnetic Lenses . . . . . . . . . . . . . . . . . . . . . . .
6.2
Fundamental Rays and Conjugate Planes . . . .
6.3
Thin Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4
Thick Lenses. . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Glaser’s Bell-Shaped Model . . . . . . .
6.4.2 Cardinal Points and Planes . . . . . . . .
6.4.3 Lens Equation . . . . . . . . . . . . . . . . . .
6.4.4 Determination of Cardinal Points
from the Electron Path . . . . . . . . . . . .
6.5
The Objective Lens . . . . . . . . . . . . . . . . . . . . .
6.6
The Objective Prefield . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xvi

Contents

10.2
10.3
10.4

Probe Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beam Deflectors and Scanning . . . . . . . . . . . . . . . . . . . . . . . . .
Electron Diffraction Techniques . . . . . . . . . . . . . . . . . . . . . . . .
10.4.1 Selected Area Electron Diffraction (SAED) . . . . . . . . .
10.4.2 Nanoarea Electron Diffraction (NAED)
and Nanobeam Diffraction (NBD) . . . . . . . . . . . . . . . .
10.4.3 Convergent-Beam Electron Diffraction (CBED). . . . . .
10.4.4 Large-Angle Methods . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.5 Precession Electron Diffraction . . . . . . . . . . . . . . . . . .
10.4.6 Selected Area Diffraction in STEM . . . . . . . . . . . . . . .
10.4.7 Scanning Electron Nanodiffraction . . . . . . . . . . . . . . . .
10.5 Specimen Holders and Rotation . . . . . . . . . . . . . . . . . . . . . . . .
10.6 Energy Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6.1 First-Order Focusing by Magnetic Sectors . . . . . . . . . .
10.6.2 Energy Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6.3 Vertical Focusing Using Fringing Fields . . . . . . . . . . .
10.6.4 Sector Fields, Paraxial Equations,
and Second-Order Aberrations . . . . . . . . . . . . . . . . . . .
10.6.5 In-Column Energy Filters . . . . . . . . . . . . . . . . . . . . . .
10.6.6 Post-Column Imaging Filters . . . . . . . . . . . . . . . . . . . .
10.6.7 Isochromaticity, Filter Acceptance, and Distortion . . . .
10.7 Radiation Effects and Low-Dose Techniques . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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250
250

11 Crystal Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1 Symmetry Operations and Symmetry Groups . . . . . . . . . . . . . .
11.2 Point Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3 Lattice and Space Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4 Symmetry Operation in Real and Reciprocal Spaces . . . . . . . .
11.5 Symmetry Determination Using Kinematic Diffraction
Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6 Symmetry Determination by CBED . . . . . . . . . . . . . . . . . . . . .
11.6.1 Point Symmetry in Dynamic Diffraction . . . . . . . . . . .
11.6.2 Point Group Determination by CBED . . . . . . . . . . . . .
11.7 Bravais Lattice Determination . . . . . . . . . . . . . . . . . . . . . . . . . .
11.8 Space Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.9 Quantification of CBED Pattern Symmetry and Symmetry
Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.10 Symmetry and Polarization in Ferroelectric Crystals . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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297
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Contents

xvii

12 Crystal Structure and Bonding . . . . . . . . . . . . . . . . . . . . . . . . .
12.1 Description of Crystal Structure . . . . . . . . . . . . . . . . . . . .
12.2 Common Structure Types . . . . . . . . . . . . . . . . . . . . . . . . .
12.3 Chemical Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.1 Bonding of a Diatomic Molecule. . . . . . . . . . . . .
12.3.2 Atomic Sizes and Electronegativity . . . . . . . . . . .
12.3.3 Bonding in Infinite Crystals . . . . . . . . . . . . . . . . .
12.3.4 Types of Bonds . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.5 Characteristics of Bonds . . . . . . . . . . . . . . . . . . .
12.3.6 Charge Density as the Ground-State Property
in Density Functional Theory . . . . . . . . . . . . . . .
12.4 Experimental Measurement of Charge Density . . . . . . . . .
12.4.1 X-Ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . .
12.4.2 Electron Diffraction . . . . . . . . . . . . . . . . . . . . . . .
12.4.3 Combined Electron and X-Ray Analysis . . . . . . .
12.4.4 Multipole Expansion of Electron Density . . . . . .
12.5 Crystal Electron Density and Bonding . . . . . . . . . . . . . . .
12.5.1 Covalent Bonding in Diamond Structure . . . . . . .
12.5.2 Ionic Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.5.3 Metallic Bonding . . . . . . . . . . . . . . . . . . . . . . . . .
12.5.4 Transition Metal Oxides . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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398

13 Diffuse Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.1 Electron Diffuse Scattering . . . . . . . . . . . . . . . . . . .
13.2 Thermal Diffuse Scattering . . . . . . . . . . . . . . . . . . .
13.3 Diffuse Scattering from Small Lattice Defects . . . .
13.4 Scattering by Solid Solutions . . . . . . . . . . . . . . . . .
13.5 Modulated Structures . . . . . . . . . . . . . . . . . . . . . . .
13.6 Multiple Scattering Effects in Diffuse Scattering . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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403
404
406
411
418
425
430
438

14 Atomic Resolution Electron Imaging . . . . . . . . . . . . . . . . . . . . .
14.1 Introduction and a Brief History . . . . . . . . . . . . . . . . . . . .
14.2 Abbe’s Theory of Coherent Imaging. . . . . . . . . . . . . . . . .
14.3 Coherent Imaging in an Ideal Lens . . . . . . . . . . . . . . . . . .
14.4 Coherent Imaging in a Real Lens . . . . . . . . . . . . . . . . . . .
14.5 Linear Imaging Theory and Contrast Transfer Function
(CTF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.6 The Effects of Electron Energy Spread
and Partial Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.7 Electron Probes for High-Resolution STEM and Analysis
14.8 Probe Size and Resolution in Bright-Field STEM . . . . . . .
14.9 Ronchigrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.10 Coherence in STEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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