Fundamentals of Crystallography, Powder X-ray Diffraction, and Transmission Electron Microscopy for Materials Scientists

287 Pages·2022·41.731 MB·English

by  Dong ZhiLi

Fundamentals of
Crystallography, Powder
X-ray Diffraction, and
Transmission Electron
Microscopy for
Materials Scientists
Advances in Materials Science and Engineering
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Fundamentals of Crystallography, Powder X-ray Diffraction, and
Transmission Electron Microscopy for Materials Scientists
Dong ZhiLi
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Fundamentals of
Crystallography, Powder
X-ray Diffraction, and
Transmission Electron
Microscopy for
Materials Scientists
Dong ZhiLi
First edition published 2022
by CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Dong, ZhiLi, author.
Title: Fundamentals of crystallography, powder X-ray diffraction, and transmission electron microscopy
for materials scientists / Dong ZhiLi.
Description: First edition. | Boca Raton, FL : CRC Press, 2022. | Series: Advances in materials science
and engineering | Includes bibliographical references and index. | Summary: “The goal of this textbook
is to effectively equip readers with an in-depth understanding of crystallography, x-ray diffraction, and
transmission electron microscopy theories as well as applications. Written as an introduction to the topic
with minimal reliance on advanced mathematics, the book will appeal to a broad spectrum of readers,
including students, engineers, and researchers in materials science and engineering, applied physics,
and chemical engineering. It can be used in XRD and TEM lab training”– Provided by publisher.
Identifiers: LCCN 2021056285 (print) | LCCN 2021056286 (ebook) | ISBN 9780367357948 (hbk) | ISBN
9781032246802 (pbk) | ISBN 9780429351662 (ebk)
Subjects: LCSH: Materials--Analysis. | Crystallography. | X-ray diffraction imaging. | Transmission
electron microscopy.
Classification: LCC QD131 .D66 2022 (print) | LCC QD131 (ebook) | DDC 543–dc23/eng20220207
LC record available at https://lccn.loc.gov/2021056285
LC ebook record available at https://lccn.loc.gov/2021056286
ISBN: 978-0-367-35794-8 (hbk)
ISBN: 978-1-032-24680-2 (pbk)
ISBN: 978-0-429-35166-2 (ebk)
DOI: 10.1201/9780429351662
Typeset in Times
by SPi Technologies India Pvt Ltd (Straive)
Contents
Acknowledgments .....................................................................................................ix
Preface .......................................................................................................................xi
Author ......................................................................................................................xv
Symbols Used in This Book ..................................................................................xvii
Introduction ................................................................................................................1
PART I Introduction to Crystallography
Chapter 1 Periodicity of Crystals and Bravais Lattices ......................................17
1.1 Crystals, Lattices and Basis .....................................................17
1.2 Unit Cell Types, Crystal Systems and Bravais Lattices ...........18
1.3 Rhombohedral Cells and Non-rhombohedral Cells in
Trigonal Systems .....................................................................21
1.4 Miller–Bravais Indices in Hexagonal Systems ........................24
Summary ............................................................................................28
References ..........................................................................................28
Chapter 2 Symmetry of Crystals, Point Groups and Space Groups....................29
2.1 Symmetry Elements and Representations ...............................29
2.2 Combinations of Symmetry Elements .....................................35
2.3 Point Groups for Cubic System ...............................................38
2.4 Thirty Two Crystallographic Point Groups and
230 Space Groups ....................................................................42
Summary ............................................................................................47
References ..........................................................................................48
Chapter 3 Reciprocal Lattices .............................................................................49
3.1 Definition and Lattice Parameter Relationships ......................49
3.2 Some Important Properties of the Reciprocal Lattice
and Associated Calculations ....................................................55
Summary ............................................................................................69
References ..........................................................................................69
Chapter 4 Examples of Crystal Structure Representation ...................................71
Summary ............................................................................................72
References ..........................................................................................73
v
vi Contents
PART II X-ray Diffraction of Materials
Chapter 5 Geometry of X-ray Diffraction ...........................................................79
5.1 Bragg’s Equation .....................................................................79
5.2 Ewald Sphere Construction and the Vector form of
Bragg’s Law .............................................................................80
Summary ............................................................................................83
Reference ............................................................................................83
Chapter 6 The Intensity of Diffracted X-ray Beams ...........................................85
6.1 Scattering of an X-ray by an Electron .....................................85
6.2 Scattering by an Atom .............................................................87
6.3 Scattering by a Unit Cell .........................................................92
6.4 Further Discussion on Structure Factor .................................106
6.5 Diffraction by a Small Crystal ...............................................110
Summary ..........................................................................................119
References ........................................................................................119
Chapter 7 Experimental Methods and the Powder X-ray Diffractometer .........121
Summary ..........................................................................................136
References ........................................................................................137
Chapter 8 Rietveld Refinement of Powder X-ray Diffraction Patterns .............139
Summary ..........................................................................................145
References ........................................................................................146
PART III Transmission Electron Microscopy
of Materials
Chapter 9 Atomic Scattering Factors for Electrons and X-rays ........................155
9.1 Atomic Scattering Factor for an Electron ..............................155
9.2 Relationships Between the Atomic Scattering Factor for
X-rays and Electrons .............................................................161
Summary ..........................................................................................163
References ........................................................................................164
Contents vii
Chapter 10 Electron Diffraction in Transmission Electron Microscopes ...........165
10.1 Geometry of Electron Diffraction in TEMs ...........................165
10.2 Intensity of Diffracted Beam .................................................174
Summary ..........................................................................................191
References ........................................................................................191
Chapter 11 Diffraction Contrast ..........................................................................193
11.1 Two-beam Dynamical Theory ...............................................197
11.2 Discussion of Diffraction Contrast ........................................203
11.2.1 Amplitude of the Diffracted Beam and
the Formation of Thickness Fringes and
Bend Contours ..........................................................203
11.2.2 Discussion of the Two Bloch Waves ........................207
11.2.3 Discussion on the Contrast of the Crystal Defects .....208
Summary ..........................................................................................209
References ........................................................................................209
Chapter 12 Phase Contrast ..................................................................................211
12.1 Interference of Two Beams ....................................................211
12.2 Projected Potential of Thin Crystals and HRTEM Images .....212
12.3 HRTEM Image Simulation ....................................................217
12.4 Lens Aberrations and Aberration Corrections .......................220
12.5 Example of Application of HRTEM to Materials Research ....226
Summary ..........................................................................................229
References ........................................................................................229
Appendix 1: Fourier Series, Fourier Transforms, and
Associated Equations ......................................................................231
Appendix 2: Nearly Free Electron Approximation and the
Band Structure of Crystals ..............................................................241
Index ......................................................................................................................255

Acknowledgments
I would like to take this opportunity to express my thanks to those who have shared
with me their experiences in crystallography, X- ray diffraction, the Rietveld method,
transmission electron microscopy and the HRTEM image simulations. I am deeply
grateful to my teachers from Tsinghua University. I learned mathematical techniques
for reciprocal lattice calculations as well as X- ray diffraction theories for crystal
structure examination from Professor Lin Zi Wei. I further learned X- ray crystallog-
raphy, experimental X-r ay diffraction techniques and transmission electron micros-
copy from Professor Tao Kun and Professor Zhu Bao Liang. I received much help
from my Ph.D. supervisor, Professor Hori Shigenori, and from Dr. Zhang Di and Mr.
Fujitani Wataru while I was doing TEM experiments for my Ph.D. project at Osaka
University during 1987 and 1988.
I am indebted to Professor Nutting who shared his invaluable experience on the
interpretation of electron diffraction and the diffraction contrast formation in metal-
lic and ceramic materials when I was a visiting professor at the University of
Barcelona from June 1993 to November 1996. I would like to thank Dr. Tim White,
who shared his Rietveld refinement, HRTEM multi- slice simulation experiences and
helped our collaborative research projects on synthetic apatites when I was a senior
industrial research scientist at the Environmental Technology Institute of Singapore.
I also want to express my special thanks to the following TEM experts. While I
was preparing my lecture notes on transmission electron microscopy, many discus-
sions with Dr. Pan Ming, of Gatan Inc., were very helpful. I learnt from Professor
Andrew Johnson and Professor Ray Withers how to conduct CBED in a modern
TEM during their visits to our TEM labs and during my visit to Andrew for further
discussions at the University of Western Australia. I wish to thank Professor Lumin
Wang and Dr. Kai Sun from the University of Michigan, Dr. Liu Binghai from
Wintech Nano- Technology Services Pte Ltd, and Professor Jie Lian from Rensselaer
Polytechnic Institute for their help in interpreting electron-b eam- induced structure
modification during TEM observations. I also wish to thank the following experts.
For the Cs-c orrected TEM analysis in some research projects, I received much help
from Dr. Zhang Zaoli from the Erich Schmid Institute of Materials Science, from Dr.
Christopher Brian Boothroyd and Dr. András Kovács from Forschungszentrum Julich
GmbH in the Helmholtz Association. During the IAMNano Workshop 2015 at
Hamburg, Professor Harald Rose shared a very encouraging message in his TEM
research, and his experience of training scientists. I truly benefited from the excellent
EELS analysis by Dr. Michel Bosmann from the Singapore Institute of Materials
Research and Engineering when we were supervising a Ph.D. research project
together.
In addition, tremendous thanks must go to my former research advisors Professor
Chen Nanping and Professor Tang Xiangyun for their guidance on metallic materials
research, to my previous research group directors, Professor Jose Maria Guilemany
and Professor Khor Khiam Aik for giving me the opportunity to investigate the coat-
ing structures for their thermal spray projects, and to my former School Chair
ix