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Material Characterization using Electron Holography
Exploration of a unique technique that offers exciting possibilities to analyze electromagnetic behavior of materials
Material Characterization using Electron Holography addresses how the electromagnetic field can be directly visualized and precisely interpreted based on Maxwell’s equations formulated by special relativity, leading to the understanding of electromagnetic properties of advanced materials and devices. In doing so, it delivers a unique route to imaging materials in higher resolution.
The focus of the book is on in situ observation of electromagnetic fields of diverse functional materials. Furthermore, an extension of electron holographic techniques, such as direct observation of accumulation and collective motions of electrons around the charged insulators, is also explained. This approach enables the reader to develop a deeper understanding of functionalities of advanced materials.
Written by two highly qualified authors with extensive first-hand experience in the field, Material Characterization using Electron Holography covers topics such as:
- Importance of electromagnetic fields and their visualization, Maxwell’s equations formulated by special relativity, and de Broglie waves and wave functions
- Outlines of general relativity and Einstein’s equations, principles of electron holography, and related techniques
- Simulation of holograms and visualized electromagnetic fields, electric field analysis, and in situ observation of electric fields
- Interaction between electrons and charged specimen surfaces and interpretation of visualization of collective motions of electrons
For materials scientists, analytical chemists, structural chemists, analytical research institutes, applied physicists, physicists, semiconductor physicists, and libraries looking to be on the cutting edge of methods to analyze electromagnetic behavior of materials, Material Characterization using Electron Holography offers comprehensive coverage of the subject from authoritative and forward-thinking topical experts.
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Veröffentlichungsjahr: 2022
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Table of Contents
Cover
Title Page
Copyright
Preface
List of Specimens
Part I: Introduction
1 Importance of Electromagnetic Field and Its Visualization
References
2 Maxwell's Equations and Special Relativity
2.1 Maxwell's Equations and Electromagnetic Potentials
2.2 Maxwell's Equations Formulated Using Special Relativity
References
3 Basis of Transmission Electron Microscopy
References
Part II: Principles and Practice
4 Principles of Electron Holography
4.1 Types of Electron Holography
4.2 Outline of Electron Holography
4.3 Comparison of Phase Shifts Due to Scalar and Vector Potentials
4.4 Analysis of Reconstructed Phase Images by Computer Simulation
References
5 Microscope Constitution and Hologram Formation
5.1 Basic Constitution of Transmission Electron Microscope
5.2 Biprism System
5.3 Coherence Lengths
5.4 Formation of Interference Fringes
5.5 Simulation of Interference Fringes
References
6 Related Techniques and Specialized Instrumentation
6.1 Split‐Illumination Electron Holography
6.2 Dark‐Field Electron Holographic Interferometry
6.3 Lorentz Microscopy
6.4 Magnetically Shielded Lens and High‐Voltage Electron Microscope
6.5 Aberration‐Corrected Lens System
6.6 Multifunctional Specimen Holders with Piezodriving Probes
6.7 Specimen Preparation Techniques
6.8 High‐Resolution and Analytical Electron Microscopy
References
Part III: Application
7 Electric Field Analysis
7.1 Measurement of Inner Potential
7.2 Electric Field Analysis of Precipitates in Multilayer Ceramic Capacitor
7.3 Analysis of Spontaneous Polarization in Oxide Heterojunctions
7.4 Evaluation of Electric Charge with Laser Irradiation
7.5 Analysis of Conductivity with Microstructure Changes
7.6 Detection of Electric Field Variation Around Field Emitter
References
8 Magnetic Field Analysis
8.1 Quantitative Analysis of Magnetic Flux Distribution of Nanoparticles
8.2 Observation of Magnetization Processes
8.3 Observation of Magnetic Structure Change with Temperature
8.4 Analysis of Three‐Dimensional Magnetic Structures
References
Part IV: Visualization of Collective Motions of Electrons and Their Interpretation
9 Charging Effects and Secondary Electron Distribution of Biological Specimens
9.1 Visualization of Stationary Electron Orbits
9.2 Visualization of Accumulative and Collective Motions of Electrons
References
10 Collective Motions of Electrons Around Various Charged Insulators
10.1 Accumulation of Electrons on Cleaved Surfaces of BaTiO
3
10.2 Dependency of Electron Distribution on Surface Condition of Epoxy Resin and Kidney
10.3 Electron Distribution Between Epoxy Resin and Kidney
10.4 Control of Electron Distribution Around Cellulose Nanofibers by Applying External Electric Field
References
11 Extension of Analysis of Collective Motions of Electrons
11.1 Electron Spin Polarization
11.2 Accumulation of Electrons on Bulk Insulator Surface
References
12 Theoretical Consideration on Visualizing Collective Motions of Electrons
12.1 De Broglie's Matter Wave and Wave Function
12.2 Disturbance‐Free Observation
12.3 Electron Interference and General Relativity
12.4 Spinning Linear Wave Model
12.5 Electron Interference Formulated with Spinning Linear Wave
12.6 Interpretation of Wave–Particle Dualism
References
A Physical Constants, Conversion Factors, and Electron Wavelength
Index
End User License Agreement
List of Tables
Chapter 4
Table 4.1 Characteristics of various 200‐kV electron guns.
Chapter 5
Table 5.1 Parameters used for hologram simulation.
Chapter 6
Table 6.1 Aberrations of objective, intermediate, and projector lenses.
Chapter 8
Table 8.1 Magnetic properties and compositions of Alnico 5 and Alnico 8.
List of Illustrations
Chapter 1
Figure 1.1 (a) U‐shaped magnet. (b) Simulated magnetic field around magnet. ...
Figure 1.2 (a) TEM image showing two pieces of Co–Zr–O magnetic specimen. (b...
Chapter 3
Figure 3.1 (a) Schematic showing electron scattering in a specimen. (b) Diag...
Chapter 4
Figure 4.1 Two types of electron holography: (a) in‐line electron holography...
Figure 4.2 Illustration showing geometric configuration of electron holograp...
Figure 4.3 Formation of interference fringes with increasing biprism voltage...
Figure 4.4 Illustration of phase shift due to (a) scalar and (b–d) vector po...
Figure 4.5 (a) Hologram and (b) reconstructed phase image of quenched Fe
73.5
Figure 4.6 (a) Model specimen used for simulation of phase image reconstruct...
Figure 4.7 Diagram illustrating process of separating electric and magnetic ...
Figure 4.8 Flow chart for determining magnetization distribution by electron...
Figure 4.9 (a) Reconstructed phase image of Nd
4.5
Fe
74
B
18.5
Cr
3
nanocomposite ...
Chapter 5
Figure 5.1 Cross section of column in transmission electron microscope (JEM‐...
Figure 5.2 Principle of double‐deflection system for beam tilt. DEF1: first‐...
Figure 5.3 Quarter cross section of objective lens system comprising lens co...
Figure 5.4 Cross section of standard objective pole piece showing position o...
Figure 5.5 Electron path in pole pieces, showing principle of action in elec...
Figure 5.6 Configuration of slow‐scan CCD camera. CCD is designed to be cool...
Figure 5.7 Block diagram showing main components of transmission electron mi...
Figure 5.8 Biprism wire holder and power connection. (a) Outline of biprism ...
Figure 5.9 Wire voltage vs. fringes with accelerating voltage of 300 kV. Acc...
Figure 5.10 Ray paths of electron beam passing through specimen, biprism wir...
Figure 5.11 (a) Main beam path in hologram mode and (b) corresponding column...
Figure 5.12 Schematic illustration showing average distance between incident...
Figure 5.13 Illumination angle and vertical component of electron momentum r...
Figure 5.14 Calculated beam current density vs. spatial coherence length at ...
Figure 5.15 Schematic showing how main beam is split into two parts by bipri...
Figure 5.16 Illustration showing interference fringe formation based on wave...
Figure 5.17 Electric potential as function of distance from center of bipris...
Figure 5.18 Illustration showing ray paths from electron source to observati...
Figure 5.19 Spaces and interfaces defined for discussion of Green's integral...
Figure 5.20 Geometrical configuration for discussion of Green's half‐space f...
Figure 5.21 Geometry for calculation of interference fringe intensity.
Figure 5.22 Comparison of profiles of observed and simulated interference fr...
Figure 5.23 Process of interference fringe formation with increase in incide...
Chapter 6
Figure 6.1 (a) Ray path for (single‐biprism) split‐illumination electron hol...
Figure 6.2 Observation of magnetic flux in electrical steel sheet with sub‐m...
Figure 6.3 Ray path diagram for (a) conventional electron holography and (b)...
Figure 6.4 (a)
g
‐reflection ray path diagram and (b)
‐reflection ray path d...
Figure 6.5 Strain map determined by DFEH. (a) Strain map representing elonga...
Figure 6.6 (a) Trajectory of electron passing through magnetized specimen. (...
Figure 6.7 Lorentz microscopy images of as‐quenched Fe
73.5
Cu
1
Nb
3
Si
13.5
B
9
spe...
Figure 6.8 Lorentz microscopy images of as‐sintered Sm–Co magnet observed us...
Figure 6.9 (a) Schematic illustration of 180° domain wall in film with uniax...
Figure 6.10 Lorentz microscopy images of as‐sintered Sm–Co magnet for series...
Figure 6.11 FWHM of wall image measured as function of defocus value.
Figure 6.12 Observed (squares) and theoretical (curves) intensity distributi...
Figure 6.13 Schematic illustration of Lorentz microscopy in Foucault mode.
Figure 6.14 (a) Electron diffraction pattern of sintered Nd
2
Fe
14
B magnet. (b...
Figure 6.15 Lorentz microscopy images of step‐aged Sm–Co magnet observed in ...
Figure 6.16 Geometric configuration of electron gun and quadrant detector in...
Figure 6.17 Geometric configuration of quadrant detector and image processin...
Figure 6.18 Images of Co polycrystal captured by (a) DPC Lorentz STEM and (b...
Figure 6.19 Example of phase reconstruction using TIE equation for Fe
18.8
Co
6
...
Figure 6.20 Schematic illustrations (cross‐sectional views) of magnetically ...
Figure 6.21 (a) Simulated magnetic field around specimen and lens gap obtain...
Figure 6.22 Schematic illustration of magnetic field distribution of objecti...
Figure 6.23 TEM image (left) and magnetic flux distribution (right) of CoFeB...
Figure 6.24 Schematic illustration of effect of lens aberration on path of s...
Figure 6.25 (a) With convex lens, electron beam spreads over spherical aberr...
Figure 6.26 (a) 200‐kV transmission electron microscope with spherical aberr...
Figure 6.27 Spherical aberration correction process. (a) Highly magnified im...
Figure 6.28 (a) Schematic representation of double‐probe piezodriving holder...
Figure 6.29 (a) Electron holography imaging process. (b) Shielding technique...
Figure 6.30 Reconstructed phase images showing triboelectricity of toner par...
Figure 6.31 (a) Schematic of optical system for observing and analyzing elec...
Figure 6.32 (a) Geometric configuration of incident Ga‐ion beam and Co–CoO t...
Figure 6.33 Hologram (above) and reconstructed phase images (below) of Co–Co...
Figure 6.34 Geometric configuration of ultramicrotomy.
Figure 6.35 Cross‐sectional view of Co–CoO magnetic tape prepared by ultrami...
Figure 6.36 Three observation modes in electron microscopy using an objectiv...
Figure 6.37 High‐resolution images of Co
71.5
Zr
9.2
O
19.3
(a), Co
59.9
Zr
10.3
O
29.
...
Figure 6.38 Principle of HAADF microscopy.
Figure 6.39 (a) HAADF–STEM image of Sm
2
(Fe
0.95
, Mn
0.05
)
17
N
4.2
. (b and c) One...
Figure 6.40 (a) Inner‐shell electron excitation. (b) Resultant electron ener...
Figure 6.41 Electron energy‐loss spectra of YBa
2
Cu
3
O
y
for energy ranges of (...
Figure 6.42 Characteristic X‐ray spectrum of YBa
2
Cu
3
O
y
.
Figure 6.43 Elemental mapping images of Sm–Co magnet. (a) Isothermal aging. ...
Chapter 7
Figure 7.1 (a) Cross‐sectional view of a DLC film. (b) Electron hologram of ...
Figure 7.2 (a) Electron hologram of an amorphous SiO
2
particle. (b) Conventi...
Figure 7.3 Phase shift evaluated from the interference fringes at lines
X
an...
Figure 7.4 Hologram of an amorphous SiO
2
particle of 250 nm diameter (a) and...
Figure 7.5 (a) Schematic of a thin‐foil specimen of a multilayer ceramic cap...
Figure 7.6 (a) Elemental distribution mappings for a TiO
2
junction (upper pa...
Figure 7.7 (a–c) Schematic of the process of charging through mechanical fri...
Figure 7.8 (a) Laser irradiation‐induced change in the electric potential di...
Figure 7.9 Nonlinear
I
–
V
curve measured for an initial state of cured bulk A...
Figure 7.10 (a) Experimental setup for electric field analysis of a Ag‐based...
Figure 7.11 (a) TEM image corresponding to area indicated by dotted lines in...
Figure 7.12 Bright‐field images of the specimen (a) before and (b) after a 1...
Figure 7.13 (a) Current–voltage (
I
–
V
) curves observed in a model specimen wi...
Figure 7.14 Simulations of local electric field of model specimen. (a) Struc...
Figure 7.15 (a and c) Electron hologram and reconstructed phase image obtain...
Figure 7.16 (a)
I
–
V
curve showing field emission from a TaSi
2
nanowire, obse...
Figure 7.17 (a) Reconstructed phase image obtained from a TaSi
2
nanowire at ...
Chapter 8
Figure 8.1 Magnetic microstructure of a chain composed of core–shell Co–CoO ...
Figure 8.2 (a) Reconstructed phase image of the nanocrystal indicated in Fig...
Figure 8.3 (a) Reconstructed phase image showing magnetic information of a r...
Figure 8.4 Illustration showing introduction of residual magnetic field of o...
Figure 8.5 Change with increasing tilt angle in reconstructed phase images o...
Figure 8.6 Schematic of head of a magnetizing stage: (a) a plane view and (b...
Figure 8.7 (a–i) Change with increasing magnetic field in reconstructed phas...
Figure 8.8 Lorentz micrograph of a doubly oriented electrical steel sheet in...
Figure 8.9 Lorentz micrographs of a non‐oriented electrical steel sheet obse...
Figure 8.10 Reconstructed phase images of (a–d) anisotropic and (e–h) isotro...
Figure 8.11 (a) Bright‐field image, (b) Lorentz microscope image, and (c) re...
Figure 8.12 Schematic of part of a specimen holder equipped with a sharp mag...
Figure 8.13 (a–c) Lorentz microscope images and (d–f) reconstructed phase im...
Figure 8.14 (a) Dark‐field image and (b) Lorentz microscope image of demagne...
Figure 8.15 (a) and (b) Enlarged Lorentz microscope images of Alnico 5, as c...
Figure 8.16 (a) Reconstructed phase image of demagnetized Alnico 8. (b) Reco...
Figure 8.17 Lorentz microscope images captured from a videotape, showing nuc...
Figure 8.18 Simulated reconstructed phase image of a recorded Co–CoO tape (r...
Figure 8.19 Magnetization distribution inside the recorded tape. This area c...
Figure 8.20 Change of magnetic flux distribution in remanent states of a rec...
Figure 8.21 Reconstructed phase images show magnetization process of a CoNiF...
Figure 8.22 Hologram of a TMR spin‐valve head, which was cut from original h...
Figure 8.23 Magnetization distribution of a TMR spin‐valve head. The reconst...
Figure 8.24 Change in magnetization distribution with applied field. (a) Rec...
Figure 8.25 Image and schematic of a thin Fe
0.5
Co
0.5
Si specimen produced usi...
Figure 8.26 Two‐dimensional phase maps and three‐dimensional structure of th...
Figure 8.27 (a) Lorentz microscope image and (b) reconstructed phase image r...
Figure 8.28 Magnetization process of a Ni
50
Mn
25
Al
12.5
Ga
12.5
alloy in parent ...
Figure 8.29 Reconstructed phase images of La
0.44
Sr
0.56
MnO
3
as a function of ...
Figure 8.30 Reconstructed phase images of La
0.46
Sr
0.54
MnO
3
as a function of ...
Figure 8.31 (a) Reconstructed phase image of separated ferromagnetic domains...
Figure 8.32 Direct imaging of magnetization distribution in APB region Fe
70
A...
Figure 8.33 Determination of the magnetic flux density in APB region. (a–c) ...
Figure 8.34 Reconstructed phase images of Fe
84
Nb
7
B
9
annealed at 773 K as a f...
Figure 8.35 (left) Schematic of experimental setting. Specimen was fixed on ...
Figure 8.36 SIM and reconstructed phase images of a square‐column‐shaped Y–B...
Figure 8.37 Schematic configuration of magnetization vectors near the vortex...
Figure 8.38 Reconstructed phase images of amorphous FeSiB with an amplificat...
Figure 8.39 Schematics of stacked ferromagnetic disks and axes used for 360°...
Figure 8.40 Typical magnetic phase shifts
ϕ
M
obtained by rotating speci...
Figure 8.41 Three‐dimensional view of reconstructed magnetic vortex cores.
z
Chapter 9
Figure 9.1 Schematic illustrations showing effect of charging on biological ...
Figure 9.2 TEM images of microfibril of sciatic nerve tissue observed under ...
Figure 9.3 (a) Electron hologram of tangled microfibrils of sciatic nerve ti...
Figure 9.4 (a) Bright‐field image of single microfibril of sciatic nerve tis...
Figure 9.5 (a) Electron hologram of microfibril of sciatic nerve tissue. (b ...
Figure 9.6 Simulated orbits (red lines) of secondary electrons as function o...
Figure 9.7 (a) Hologram superimposed on its reconstructed amplitude image. R...
Figure 9.8 Schematic illustration of amplitude reconstruction process for el...
Figure 9.9 (a) Simple model for part of electron orbits projected along inci...
Figure 9.10 Reconstructed amplitude images showing change in electric circui...
Figure 9.11 (a) HAADF‐STEM image of microfibril. (b) Os (Mα) mapping image o...
Figure 9.12 (a) Electron micrograph and (b) hologram of microfibril of sciat...
Figure 9.13 (a) Reconstructed amplitude images obtained from hologram of mic...
Figure 9.14 Simulation results showing trajectories of secondary electrons e...
Chapter 10
Figure 10.1 Charging effect and secondary electron distribution of BaTiO
3
. (...
Figure 10.2 Distribution of secondary electrons around cleaved BaTiO
3
rod ti...
Figure 10.3 (a) Reconstructed phase image of ultramicrotomed epoxy resin. (b...
Figure 10.4 (a) Reconstructed phase image of kidney flake prepared by microt...
Figure 10.5 (a) Reconstructed phase images when square pillar of epoxy resin...
Figure 10.6 (Left) Hologram indicating location of CNF and probe. (Right) Re...
Chapter 11
Figure 11.1 (a) Geometric configuration of mica needle fabricated using FIB ...
Figure 11.2 Experimental setup in which “e
−
” pattern was drawn on insu...
Figure 11.3 Successively recorded SIM images of “e
−
” characters prepar...
Chapter 12
Figure 12.1 Schematic illustration of experimental setup used to form hologr...
Figure 12.2 (a) Illustration showing electron consisting of one‐dimensional ...
Figure 12.3 (a) Illustration showing motion of linear wave with length
L
LW
. ...
Figure 12.4 Geometrical configuration of transmission electron microscope wi...
Figure 12.5 (a) Illustration showing geometrical configuration of incident a...
Figure 12.6 Illustration showing geometrical configuration of incident elect...
Figure 12.7 Principle of interference fringe formation with two‐dimensional ...
Figure 12.8 Simulated intensity profiles of interference fringes. (a) Line t...
Part IV
Figure 1 (a) TEM image of microfibril of sciatic nerve tissue with energy di...
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
List of Specimens
Begin Reading
A Physical Constants, Conversion Factors, and Electron Wavelength
Index
End User License Agreement
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Material Characterization using Electron Holography
Daisuke Shindo
Takeshi Tomita
Authors
Dr. Daisuke ShindoRIKENCenter for Emergent Matter Science2‐1 Hirosawa, Wako351‐0198 SaitamaJapan
Mr. Takeshi Tomita242‐12 Fuchigami197‐0833 Akiruno‐city, TokyoJapan
Cover Image: © Daisuke Shindo, Zentaro Akase, Direct observation of electric and magnetic fields of functional materials, Mater. Sci. & Eng. R 142 (2020) 100564, with permission from Elsevier
All books published by WILEY‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing‐in‐Publication DataA catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2023 WILEY‐VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978‐3‐527‐34804‐6
ePDF ISBN: 978‐3‐527‐82969‐9
ePub ISBN: 978‐3‐527‐82970‐5
oBook ISBN: 978‐3‐527‐82971‐2
Preface
Transmission electron microscopy (TEM) is widely utilized to clarify the microstructures of various functional materials. To comprehensively understand a material's functionality coupling electric and magnetic properties, it is necessary to characterize the electromagnetic fields in and around the material. Among the various TEM techniques, electron holography is unique in its ability to visualize electric and magnetic fields by utilizing the electron interference effect. This book presents the basis, various applications, and the latest developments of electron holography in four parts.
Part I Introduction emphasizes the importance of the field concept, which is closely related to the theory of relativity. It also briefly explains the basic constitution of transmission electron microscopes along with their mathematical formulation, which is utilized in subsequent parts.
Part II Principles and Practice explains the basic principles of electron holography and the utilization of transmission electron microscopes with special instrumentation. In addition to explaining Maxwell's equations and electromagnetic potentials, it presents the simulation procedures for reconstructing phase images and interference fringes.
Part III Application describes the visualization of electromagnetic fields in and around various functional materials as a means to identify their functional electromagnetic properties. It also describes the clarification and interpretation of the electromagnetic functionalities of a wide variety of materials based on extensive in situ observations of electromagnetic fields created by applying electric or magnetic field at various temperatures.
Part IV Visualization of Collective Electron Motions and Their Interpretation describes the extension of electron holography to the visualization of the collective motions of electrons. Theoretical considerations on the point‐charge behavior and interference effect of electrons are presented along with a discussion of the relevant quantum mechanics and the general theory of relativity.
We are grateful to the late Akira Tonomura, the late Shinji Aizawa, Yoshinori Tokura, Toshiaki Tanigaki, Joong J. Kim, Hyun S. Park, Tsuyoshi Matsuda, Xiuzhen Yu, Yasukazu Murakami, Akira Taniyama, Zentaro Akase, Yoichi Ikematsu, Hideyuki Magara, Naoyuki Kawamoto, Yoshimasa A. Ono, Nobuhiko Ohno, Shinichi Ohno, Mitsuru Morita, Hiromitsu Kawase, Kei Hirata, Takafumi Sato, Akira Yasuhara, Masao Inoue, Yoshitaka Aoyama, Tetsuo Oikawa, Katsushige Tsuno, Gyeong S. Park, Jun‐Mo Yang, Young‐Gil Park, Jung H. Yoo, Ki H. Kim, Ken Harda, Yoh Iwasaki, Keiko Shimada, Chiari Itonaga, Satoko Takahashi, Kodai Niitsu, Zheng Liu, Weixing Xia, Youhui Gao, Tetsuya Akashi, Hiroto Kasai, Kimi Matsuyama, Hiroyuki Shinada, and Nobuyuki Osakabe for their generous support and invaluable collaboration.
Wako, Japan, 14 December 2021 Daisuke Shindo and Takeshi Tomita
RIKEN
List of Specimens
Part
Specimen
Fig. no.
Page
Part II
Quenched Fe
73.5
Cu
1
Nb
3
Si
13.5
B
9
4.5
Nd
4.5
Fe
74
B
18.5
Cr
3
nanocomposite magnet
4.9
nMOSFET
6.1
Nd
2
Fe
14
B including α‐Nd precipitates
6.5
Quenched Fe
73.5
Cu
1
Nb
3
Si
13.5
B
9
6.7
Sintered Sm‐Co
6.10
Sintered Nd
2
Fe
14
B
6.14
Step‐aged SmCo
5
6.15
Co polycrystal
6.18
Fe
18.8
Co
60
Cu
0.6
Nb
2.6
Si
9
B
9
nanocrystalline soft magnetic material
6.19
CoFeB/Ta multilayer
6.23
Toner particle with Mo shield
6.30
Toner and carrier particles
6.31
Co–CoO tape prepared by FIB
6.32
Co–CoO thin film
6.33
Co–CoO tape prepared by ultramicrotomy
6.35
Co
71.5
Zr
9.2
O
19.3
, Co
59.9
Zr
10.3
O
29.8
, Co
52.9
Zr
12.0
O
35.1
6.37
Sm
2
(Fe
0.95
, Mn
0.05
)
17
N
4.2
6.39
YBa
2
Cu
3
O
y
6.41
Sm–Co magnet with additives
6.43
Part III
DLC film
7.1
Amorphous SiO
2
particle
7.2
BaTiO
3
matrix multilayer ceramic capacitor
7.5
Oxide heterojunctions
7.6
Organic photoconductor
7.7
Ag‐based conductive adhesive
7.10
Epoxy and silver
7.13
Unused and used Schottky emitters
7.15
TaSi
2
nanowire
7.16
Core–shell Co‐CoO nanocrystals
8.1
Fe
3
O
4
nanoparticles
8.3
Fe
73.5
Cu
1
Nb
3
Si
13.5
B
9
8.5
Mn–Zn ferrite
8.7
Anisotropic and isotropic Ba ferrites
8.10
Sm(Co
0.720
Fe
0.200
Cu
0.055
Zr
0.025
)
7.5
8.11
Sintered Nd
2
Fe
14
B
8.13
Alnico 5
8.15
Alnico 8
8.16
Nd
2
Fe
14
B
8.17
Recorded Co‐CoO tape
8.20
Magnetization process of CoNiFe pole tip
8.21
TMR spin‐valve head
8.23
Skyrmion lattices in Fe
0.5
Co
0.5
Si
8.26
Ni
50
Mn
25
Al
12.5
Ga
12.5
8.28
La
0.44
Sr
0.56
MnO
3
8.29
La
0.46
Sr
0.54
MnO
3
8.30
Fe
84
Nb
7
B
9
8.34
Y–Ba–Cu–O with external magnetic field
8.35
Y–Ba–Cu–O without external magnetic field
8.36
Amorphous FeSiB
8.38
Stacked ferromagnetic disks
8.40
Part IV
Tangled microfibrils of nerve tissue
9.3
Single microfibril of nerve tissue
9.4
Tangled microfibrils with W probe
9.10
Microfibril wedge shape (two branches)
9.13
BaTiO
3
(two branches)
10.1
BaTiO
3
(creaved)
10.2
Epoxy resin prepared by ultramicrotomy and FIB
10.3
Kidney prepared by ultramicrotomy and FIB
10.4
Epoxy resin and kidney
10.5
Cellulose nanofiber and probe (Pt‐Ir)
10.6
Mica needle with external magnetic field
11.1
Part IIntroduction
1Importance of Electromagnetic Field and Its Visualization
Transmission electron microscopy (TEM) has been widely utilized to clarify the microstructures of various functional materials. In addition to bright‐field and dark‐field imaging methods for observing various lattice defects [1–5], high‐resolution TEM [6–10] has been used for direct observation of atomic arrangements projected along the incident electron beam direction. Such detailed atomic arrangements can now be observed with a resolution of less than 0.1 nm.
Scanning transmission electron microscopy (STEM) is commonly used for elemental mapping at the atomic level with a microprobe (diameter, less than 0.1 nm) and a beam scanning system [11–14]. Analytical electron microscopy with energy‐dispersive X‐ray spectroscopy (EDS) and electron energy‐loss spectroscopy (EELS) have also been used for composition and electronic state analyses [15–19]. EELS studies can now be performed with an energy resolution of less than 0.1 eV by using monochromators.
To comprehensively understand a material's functionality based on coupling electric and magnetic properties, the electromagnetic fields should be characterized inside and around the material. Among the various TEM techniques, electron holography is unique in its ability to quantitatively visualize electromagnetic fields on the nanometer scale. Here, in relation to visualizing electromagnetic fields, we highlight the importance of the field concept in reference to Einstein and Infeld [20]:
A new concept appears in physics, the most important invention since Newton's time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and particles which is essential for the description of physical phenomena. The field concept proves…
…………
The theory of relativity arises from the field problems…
From “The Evolution of Physics” by A. Einstein and L. Infeld, Cambridge University Press, Cambridge, 2nd ed. (1978) p. 244.
If we bring a magnetic material near a U‐shaped magnet, as in Figure 1.1a, we will feel a force between the material and the magnet. This phenomenon can be explained by the existence of a magnetic field, which can be simulated as shown in Figure 1.1b.
Figure 1.1 (a) U‐shaped magnet. (b) Simulated magnetic field around magnet. Arrows indicate the direction of a magnetic flux.
Though a magnetic field cannot be observed with the naked eye or even with conventional microscopy techniques, it can be visualized using electron holography. Figure 1.2a shows a TEM image of a Co–Zr–O magnetic material [22]. The magnetic information can be recorded by first creating a hologram through the interference effect of incident electrons (Figure 1.2b). Then, by processing the hologram with a Fourier transformation, the magnetic fields both inside and outside the material can be directly visualized (Figure 1.2c). The importance of visualizing electric fields is discussed in Section 6.6.
Electron holography is thus a useful technique for directly visualizing electromagnetic fields. This book addresses the theory and application of electron holography, including the fundamental formulations of electromagnetic fields and relativity. The basic formulations of Maxwell's equations in relation to the special theory of relativity are presented in order to understand the formulation of electromagnetic visualization. The last section of this chapter covers the basic principles of TEM for the specific and detailed explanations of electron microscope hardware in the following chapters.
On the basis of these formulations and explanations, outlines of electron holography and the basic constitution of electron microscopes are explained in the former of Part II. Further detailed explanations of the hardware of transmission electron microscopes for electron holography with special instrumentation are presented in the latter of Part II.
Part III describes the extensive application of electron holography to various functional materials with respect to the principles and instrumentation of electron holography presented in Parts I and II. Techniques for visualizing and interpretating electromagnetic fields in and around materials are introduced for a wide variety of functional materials using a computer simulation. Part III also discusses the effectiveness of using advanced special attachments for in situ observation of electromagnetic fields in order to understand the electromagnetic properties of functional materials.
Figure 1.2 (a) TEM image showing two pieces of Co–Zr–O magnetic specimen. (b) Hologram obtained through interference effect of incident electrons. (c) Reconstructed phase image showing detailed magnetic fields both inside and outside the material. Image in (a) was observed under slightly defocused condition. Domain wall contrast (see Section 6.3.1) and absorption contrast due to thickness change appear.
Source: Shindo and Akase [21], with permission from ELSEVIER.
Part IV focuses on one of the most interesting applications of electron holography to visualize the motion of electrons. The stationary orbital formation and accumulation of secondary electrons around insulating materials, which depend on the material's surface morphology, can be visualized by detecting the fluctuations of the electric fields due to the motions of the secondary electrons. Furthermore, the magnetic flux due to electron spin polarization can be detected by applying an external magnetic field to the secondary electrons. Finally, on the basis of the theory of relativity, electron interference is interpreted using a “spinning linear wave” model proposed by the authors. With this model, the formation of electron interference fringes is successfully reproduced by simulation as a function of the number of incident electrons.
References
1
Hirsch, P.S., Howie, A., Nicholson, R.B. et al. (1977).
Electron Microscopy of Thin Crystals
. New York, FL: Robert E. Krieger Publishing Co. Inc.
2
Amelinckx, D.D.S., Landuyt, J., and Tenderloo, G. (1997).
Handbook of Microscopy
. Weinheim: VCH.
3
Cockayne, D.J.H., Ray, I.L.F., and Whelan, M.J. (1968).
Proceedings. 4 th European.Regional.Conference.Electron Microscopy
, 129. Vaticana, Roma: Tipografia Poliglotta Vaticana.
4
Howie, A. and Basinski, Z.S. (1968).
Philos. Mag. A
17: 1039.
5
Cockayne, D.J.H., Ray, I.L.F., and Whelan, M.J. (1969).
Philos. Mag. A
20: 1265.
6
Cowley, J.M. (1990).
Diffraction Physics
. New York: North‐Holland.
7
Horiuchi, S. (1994).
Fundamentals of HREM
. Amsterdam: North‐Holland.
8
Spence, J.C.H. (1988).
Experimental High Resolution Electron Microscopy
. New York: Oxford University Press.
9
Shindo, D. and Hiraga, K. (1998).
High Resolution Electron Microscopy For Materials Science
. Tokyo: Springer.
10
Spence, J.C.H. (1999).
Mater. Sci. Eng., R
26: 1.
11
Pennycook, S.J., Berger, S.D., and Culbertson, R.J. (1986).
J. Microsc.
144: 229.
12
Morishita, S., Ishikawa, R., Kohno, Y. et al. (2018).
Microscopy
67: 46.
13
Shibata, N., Seki, T., Sánchez‐Santolino, G. et al. (2017).
Nat. Commun.
8: 15631.
14
Shibata, N., Kohno, Y., Nakamura, A. et al. (2019).
Nat. Commun.
10: 2308.
15
Joy, D.C., Roming, A.D., and Goldstein, J. (1986).
Principles of Analytical Electron Microscopy
. Springer Science & Business Media.
16
Reimer, L. (1984).
Transmission Electron Microscopy: Physics of Image Formation and Microanalysis
. Springer.
17
Egerton, R.F. (1996).
Electron Energy‐Loss Spectroscopy in the Electron Microscope
, 2e. New York: Plenum.
18
Williams, D.B. and Carter, C.B. (1996).
Transmission Electron Microscopy: A Textbook For Materials Science
. Springer.
19
Shindo, D. and Oikawa, T. (2002).
Analytical Electron Microscopy for Materials Science
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20
Einstein, A. and Infeld, L. (1978).
The Evolution of Physics
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21
Shindo, D. and Akase, Z. (2020).
Mater. Sci. Eng. R Reports
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22
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262: 308.
2Maxwell's Equations and Special Relativity
As the basis for understanding the description of electromagnetic field visualization by using electron holography in Part II, the relationship between electromagnetic fields and electromagnetic potentials is presented through Maxwell's equations (Section 2.1). As a basis for understanding the discussion of the gravitational field in relation to electron coherency in the framework of the general theory of relativity in Part IV, Maxwell's equations are reformulated in the framework of the special theory of relativity (Section 2.2).
2.1 Maxwell's Equations and Electromagnetic Potentials
In this section, we sort out Maxwell's equations and their relationships with electromagnetic potentials. This is important for understanding the principles of electron holography on the basis of scalar and vector potentials discussed in Part II. We also reformulate Maxwell's equations in accordance with the special theory of relativity. This reformulation is fundamentally important to understanding the Lorentz covariance and extending it to the discussion of the general theory of relativity in Section 12.3.
Here, Maxwell's equations with electric charge density ρ and electric current density in SI units (Système International d'Unités) are written as
where and are the electric flux density and electric field, respectively, and and are the magnetic flux density and magnetic field, respectively. Their relationships are expressed as
where ε0 and μ0 are, respectively, the dielectric constant and magnetic permeability for vacuum:
According to Eqs. (2.1) and (2.2), and are given by scalar and vector potentials φ and :
By inserting Eqs. (2.7) and (2.8) into Eqs. (2.3) and (2.4), we obtain
Equations (2.9) and (2.10) are equivalent to Eqs. (2.3) and (2.4) under the Lorenz condition [1]; i.e.
This is because, from Eqs. (2.9) and (2.10),
where the right side is zero due to the charge conservation law.
2.2 Maxwell's Equations Formulated Using Special Relativity
On the basis of Maxwell's equations (Eqs. (2.1)–(2.4)), the field around a charged particle at rest, e.g. the electric field, can be evaluated using Eq. (2.3). When the particle or observer moves, the magnetic field formed has to be taken into account using Eq. (2.4).
In the special theory of relativity, the physical laws hold in their simplest forms for any coordinate system subjected to a uniform translational motion relative to another coordinate system (Lorentz covariance). Under this condition and with the same light velocity for both systems, Maxwell's equations are rewritten as follows.
To specify a point in the space–time of physics, we use a four‐coordinate representation xμ(μ = 0, 1, 2, 3):
A quantity with the suffix written in the upper position is called a “contravariant element.”
Let us take a point close to the point xμ, and let the coordinates of the point be x + dxμ. The four coordinates forming the displac
3Basis of Transmission Electron Microscopy
In this chapter, we formulate the scattering of incident electrons. This is important to understand the basis of transmission electron microscopy (TEM) and for mathematical treatments of electron holography data.
The plane wave of an incident electron is generally given by exp[i], where k and ω are the wave number and angular frequency given by 2π/λ and 2πν (λ: wavelength, ν: frequency), respectively. For a specimen in the stationary condition, the phase and amplitude changes of the plane wave are independent of time. Thus, the plane wave of an incident electron is simply given by exp(i). If the effect of the specimen on the plane wave is given by q(x, y), the scattering amplitude at the observation point (s, t) shown in Figure 3.1a is given by
where C is a constant and r is given as
When the first term in the square root is much larger than the sum of the second and third terms, the binomial theorem is applied to r:
Part IIPrinciples and Practice
4Principles of Electron Holography
In this chapter, we first explain two types of electron holography and then describe the visualization process of electromagnetic fields. Finally, we outline the computer simulation of reconstructed phase images of the electromagnetic field.
4.1 Types of Electron Holography
The concept of holography was introduced by Gabor in 1948 [1]. Using an interference microscope and a method for reconstructing wavefronts, Gabor aimed to improve the resolution of electron microscopes by recording the amplitude distribution of interference fringes resulting from the interaction of an object and a coherent reference wave.
He used in‐line holography, which is the simplest way of producing a hologram. An example of geometrical configurations of in‐line holography using a transmission electron microscope is illustrated in Figure 4.1a. The transmitted plane wave acts as a reference wave. The object wave indicated by dark region and the reference wave propagate parallel to the optical axis. However, at the time, this approach was problematic because, first, the spatial or lateral coherence length (Section 5.3
