Structure Analysis of Advanced Nanomaterials: Nanoworld by High-Resolution Electron Microscopy 9783110305012, 9783110304725

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Takeo Oku Structure Analysis of Advanced Nanomaterials

Also of Interest Nanocarbon-Inorganic Hybrids. Next Generation Composites for Sustainable Energy Applications Dominik Eder, Robert Schlögl (Eds.), 2014 ISBN 978-3-11-026971-0, e-ISBN 978-3-11-026986-4 Inorganic Micro- and Nanomaterials. Synthesis and Characterization Angela Dibenedetto, Michele Aresta (Eds.), 2013 ISBN 978-3-11-030666-8, e-ISBN 978-3-11-030687-3 Nanocarbon-Inorganic Hybrids. For Energy, Sustainable Development and Biomedical Sciences Mario Leclerc, Robert Gauvin (Eds.), 2014 ISBN 978-3-11-030781-8, e-ISBN 978-3-11-030782-5 Polymer Surface Characterization Luigia Sabbatini (Ed.), 2014 ISBN 978-3-11-027508-7, e-ISBN 978-3-11-028811-7

Nanotechnology Reviews Challa Kumar (Editor-in-Chief) ISSN 2191-9089

Takeo Oku

Structure Analysis of Advanced Nanomaterials | Nanoworld by High-Resolution Electron Microscopy

Author Prof. Takeo Oku The University of Shiga, Prefecture Japan Department of Materials Science Hassaka 2500, Hikone SHIGA 522-8533, Japan E-Mail: [email protected]

ISBN 978-3-11-030472-5 e-ISBN (PDF) 978-3-11-030501-2 eISBN (EPUB) 978-3-11-038804-6

Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2014 Walter de Gruyter GmbH, Berlin/Boston Cover image: HREM image, © Takeo Oku Typesetting: le-tex publishing services GmbH, Leipzig Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen ♾ Printed on acid-free paper Printed in Germany www.degruyter.com

Preface Transmission electron microscopes (TEM) are a powerful apparatus for structural analysis. Although many research groups have their own electron microscopes recently, lots of researchers and PhD students are not able to operate the electron microscope and analyze the data efficiently and perfectly, which would be due to the complicated TEM operation and complicated analysis of the actual TEM data. Although various excellent specialized books for TEM have been published, yet there are not many books for TEM beginners. This book is for the TEM beginners who would like to operate TEM, overview the TEM, take pictures, and analyze the TEM data. When we see the specialized book for TEM, there are many mathematical equations and complicated imaging principles in the book, which is a little high hurdle for a TEM beginner. In this book, the complicated mathematical equations were reduced as little as possible, and the book is focused on the actual views of TEM data and analysis. This book would be helpful for beginners who would like to observe and analyze the samples in front of them. Recently, several companies can supply TEM photographs by their technique with a charge, and many researchers would make use of them. Sometimes, it is a good idea to ask the professional companies to prepare the TEM samples and to take TEM images with paying. If we ask the professional companies, the money, effort, and time can be saved, comparing with the money, effort, and time to purchase an electron microscope, to educate good TEM operators, and to obtain the TEM data. Such means can be suggested if the purpose and time are restricted and limited. However, it should be noted that the researchers should have clear eyes that can grasp the quality of the TEM data. It is important for them to see many examples of the actual TEM analysis, to analyze by themselves, and to distinguish the quality of the TEM data, in addition to learning the complicated principles of TEM. For them, necessary things would not be the complicated operation technique but understanding the analysis method of the TEM data. Of course, it is mandatory for researchers, who would like to obtain and analyze the TEM data perfectly, to understand the basic principles of TEM by reading many specialized good books. Reference books would be useful for the researchers who would like to understand and study the TEM in details. However, many students and researchers are under the pressure of necessity to understand their own TEM data and to extract necessary information for them as soon as possible instead of perfect understanding the TEM principles. It is much obliged for the author if this book is helpful for them.

vi | Preface The author would like to acknowledge K. Hiraga, D. Shindo, M. Hirabayashi, E. Aoyagi, S. Nakajima, A. Tokiwa, M. Kikuchi, Y. Syono, J.-O. Bovin, A. Carlsson, L. R. Wallenberg, J.-O. Malm, C. Svensson, M. Jansen, C. Linke, I. Higashi, T. Tanaka, Y. Ishizawa, O. Terasaki, X. D. Zou, S. Hovmöller, I. Narita, N. Koi, A. Nishiwaki, T. Hirano, K. Suganuma, T. Kajitani, H. Yamane, K. Takagi, T. Hirai, T. Matsuda, M. Murakami, H. Kawata, H. Wakimoto, H. Ishikawa, E. Bruneel, S. Hoste, M. Nishijima, Y. Osawa, Y. Tamou, N. Kikuchi, R. V. Belosludov, Y. Kawazoe, Y. Tokura, K. Osamura, T. Kizu, K. Kosuge, N. Kobayashi, Y. Hirotsu, T. Kusunose, K. Niihara, H. Nakae, and S. Hosoya for excellent collaborative works, useful discussion, providing samples and experimental help. It is a great pleasure to publish this book in the international year of crystallography. March 2014, Takeo Oku

Contents Preface | v Table for physical constants | ix 1 1.1 1.2 1.3

Introduction | 1 Characteristic of electron microscopy | 1 What information can be obtained by electron microscopy? | 2 Various types of electron microscopy | 5

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

Structure and principle of electron microscopes | 8 Structure of transmission electron microscope | 8 Observation mechanism of atoms by electrons | 10 Information from electron diffraction pattern | 13 High-resolution electron microscopy | 15 Scanning electron microscope | 17 Electron energy-loss spectroscopy | 19 Energy dispersive X-ray spectroscopy | 22 High-angle annular dark-field scanning TEM | 23 Electron holography and Lorentz microscopy | 24 Image simulation | 26

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10

Practice of HREM | 28 Sample preparation | 28 Specimen preparation methods | 28 Structure analysis by X-ray diffraction | 31 TEM observation | 33 HREM observation | 38 Fourier filtering | 41 Resolution of HREM images | 42 Prevention of damage and contamination | 43 Taking images and reading data | 44 Mental attitude for TEM | 45

4 4.1 4.2 4.3 4.4 4.5

Characterization by HREM | 46 What information can be obtained? | 46 Direct atomic observation | 46 Crystallographic image processing | 51 Comparison of HREM image with calculated images | 53 Atomic coordinates from HREM image | 54

viii | Contents 4.6 4.7 4.8 4.9 4.10 4.11 4.12

Combination of HREM and electron diffraction | 56 Quantitative HREM analysis with residual indices | 61 Detection of atomic disordering by difference image | 64 Combination of diffraction amplitudes and phases | 70 Structural optimization by molecular orbital calculation | 72 Three-dimensional high-resolution imaging | 74 Detection of doping atoms in C60 solid clusters | 77

5 5.1 5.2 5.3 5.4 5.5

Electron diffraction analysis of nanostructured materials | 87 Modulated superstructures of Tl-based copper oxides | 87 Modulate structures of lanthanoid-based copper oxides | 91 Oxygen ordering in YBa2 Cu3 O7−x | 94 Structures of Bi-based copper oxides | 98 Twin structures in BN nanoparticles | 100

6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13

HREM analysis of nanostructured materials | 110 Defect structures | 110 Interfaces and surface structures | 113 GaAs-based semiconductor devices | 116 Zeolite materials | 119 Solid clusters and doping atoms | 120 Surface structure with light elements | 122 Crystal structures of Pb-based copper oxides | 124 Structures of Sm-based copper oxides | 129 Y-based copper oxides with high Jc | 131 BN nanotubes | 134 BN nanotubes with cup-stacked structures | 140 BN nanotubes encaging Fe nanowires | 145 Nanoparticles with 5-fold symmetry | 149

A A.1 A.2 A.3

Appendix | 158 7 crystal systems and 14 Bravais lattices in three dimensions | 158 Miller indices and direction in the crystals | 159 Distances dhkl and angles 𝜙 of lattice planes | 160

Index | 163

Table for physical constants

Physical constants Velocity of light Planck constant Dirac constant Gravitational constant Electron charge Electron mass Proton mass Neutron mass Electron energy Compton wavelength Boltzmann constant Magnetic permeability Dielectric constant Avogadro constant Gas constant

Symbol c h ℏ = h/2𝜋 G e me , m0 mp mn me c2 𝜆c k, kB 𝜇0 = 4𝜋 × 10−7 𝜀0 = 1/𝜇0 c2 NA R = kNA

Physical constants Ångström Electron volt Wavelength of 1 eV photon Standard atmosphere

Values

SI units

2.99792458 × 10 ms−1 −34 6.62607 × 10 Js 1.05457 × 10−34 Js 6.67384 × 10−11 m3 s−2 kg−1 1.60218 × 10−19 As (C) 9.10938 × 10−31 kg 1.67262 × 10−27 kg 1.67493 × 10−27 kg 0.5110 MeV 2.4263 × 10−12 m 1.38065 × 10−23 JK−1 1.25664 × 10−6 Hm−1 (NA−2 ) 8.85419 × 10−12 Fm−1 (NV−2 ) 6.02214 × 1023 mol−1 −1 8.31446 JK mol−1 8

Symbol

Values and units

Å eV 𝜆 atm

0.1 nm = 10−10 m 1.60218 × 10−19 J 1239.84 nm 1.01325 × 105 Pa

1 Introduction 1.1 Characteristic of electron microscopy Each matter around us consists of atoms. The atoms consist of atomic nuclei and electrons. Electrons were discovered by Joseph John Thomson in 1897. It is believed that electrons are elementary particles which cannot be decomposed further. The size of electron is below 10−18 m. Ernest Rutherford discovered atomic nucleus and proton in 1911 and 1919, respectively. After that, neutrons were discovered by James Chadwick in 1932, and a basic model of atom is established. The size of atomic nucleus is 10−15 m. Murray Gell-Mann proposed the quark model in which protons and neutrons consist of up quark and down quark. In this book, main topics are to observe “atoms” which are atomic nucleus with electrons around the nucleus. Electrons exist as electronic cloud around the atomic nucleus, as shown in Figure 1.1. A size of atom is ∼ 0.2 nm which is the average size of electron cloud with high existing probability. How can we observe such atoms? At first, we can think about optical microscopes which are often used in the lessons in elementary schools. For the optical microscopy, images of objects are magnified by optical lens and light. However, wavelengths of the visible light are in the range of 400 and 700 nm, and it is difficult to observe the atoms with the smaller size. Is there anything with shorter wavelengths compared to visible light? One of the candidates is electrons. For example, the wavelength of electron is 0.000736 nm when the accelerating voltage is 1250 kV. Electrons have very short wavelengths, and they seem to be used for the observation of atoms. Electron microscopes are apparatuses which enlarge the images of matter in atomic scale by electrons. Although optical microscopes are small devices, electron microscopes are larger scale apparatus compared to optical microscopes. Figure 1.2 shows a high-voltage, high-resolution electron microscope with an accelerating voltage of 1300 kV and a point resolution of 0.1 nm. Each atom can be observed by this electron microscope. The size of this electron microscope is over 10 m, and the special building is needed for it. To investigate atomic arrangements, other methods such as X-ray diffraction and neutron diffraction are used, and especially, X-ray diffraction is widely used in many research laboratories. For these diffraction methods, X-ray or neutron beam are irradiated to specimens, and diffracted beams are analyzed. However, atomic arrangements are not observed directly, and information on atomic arrangements can be obtained by detailed analysis of the diffracted beams. A difference between these diffraction methods and electron microscopy is that we can observe the atoms “directly” by electrons transmitted through the specimens. Figure 1.3 is a high-resolution electron microscope image of thallium-based superconducting oxides. Each

2 | 1 Introduction

Atomic nucleus 앑 10 –15 m

Proton

2 쎹 10 –10 m Electron cloud

Meson Neutron

Electron 쏝 10 –18 m

Gluon

u

u

d Proton

u

d

Quark 쏝 10 –17 m

d Neutron

Fig. 1.1: Structure of atom.

dark dot corresponds to metal atoms, and thallium (Tl), barium (Ba), and copper (Cu) atoms are clearly observed. Since atoms can be directly observed by electron microscopes, the electron microscopy is a very useful tool for structural analysis.

1.2 What information can be obtained by electron microscopy? Information obtained by transmission electron microscopy is as follows: – – – – – –

Outline of sample: size, shape, etc. Crystal structure: atomic arrangement, space group, etc. Disordering of atomic arrangement: defect, dislocation, surface, interface, etc. Electronic state: binding state between atoms Composition: atomic composition ratio of sample Magnetic flux: lines of magnetic force

1.2 What information can be obtained by electron microscopy?

| 3

Fig. 1.2: High-voltage, high-resolution electron microscope (JEOL, www.jeol.co.jp/en/).

Cu

Cu Ba

Tl

Ba Tl

Tl Ba

Tl Ba

Cu

Cu

300 pm

Fig. 1.3: High-resolution image of Tl2 Ba2 CuO6 superconducting oxide.

In the nanotechnology field, structure analysis in atomic scale is mandatory. X-ray and neutron diffraction are also used for the analysis, and they are summarized as listed in Table 1.1. Characteristics for high-resolution electron microscopy (HREM) are as follows. (1) Since atomic and unit cell arrangements can be observed by the HREM directly, complicated, unknown structures, which cannot be analyzed by X-ray and neutron diffraction, can be analyzed directly. (2) X-ray and neutron diffraction methods are suitable to obtain information on averaged atomic arrangements since they are information measured on reciprocal

4 | 1 Introduction Table 1.1: Methods for structure analysis. Method

Radiation rays

Interaction

Wavelength Measurement (nm)

X-ray diffraction

Electromagnetic wave

Electron cloud

HREM & electron diffraction Neutron diffraction

Electron

Electric field

Neutron

Atomic nucleus

0.15418 (40 kV) 0.000736 (1250 kV) 0.2 (0.02 eV)

Reciprocal lattice Real space and reciprocal lattice Reciprocal lattice

space. However, HREM is more suitable to obtain information on local atomic arrangements such as defect, surface, interface, cluster, and nanostructure with 5fold symmetry. (3) Atomic structures can be solved in the crystallographic way using intensities and phases of the structure factors. Only intensity data of structure factors (square of amplitudes) can be obtained by diffraction methods using X-ray, neutron and electron, and phase information is not included in the data. On the other hands, phase information can be extracted from Fourier transform of HREM images. Fields for interaction are also different. As listed in Table 1.1, X-ray, neutrons and electrons interact with electron cloud, atomic nucleus and electric field (potential), respectively. Methods for structure analysis can be selected in proportion to the purpose. Since electrons interact with matter millions times stronger than X-ray, crystals with extremely small size of nanometer scale can be analyzed, and a small amount of sample is enough for the structure analysis. Many of recent important materials have nanostructures, and electron beam is very effective for the structure analysis of these nanomaterials. By the development of electron gun, lens, detectors, and software, various information of nanodiffraction, electron energy loss spectroscopy (EELS), energy dispersive X-ray spectroscopy (EDX), and holography are combined together to elucidate atomic arrangements, composition, electronic states, and magnetic structure, simultaneously. Although various information on materials can be obtained simultaneously by electron microscopy, there are some weak points. Since specimens are set in vacuum in electron microscopes to irradiate electron beam on the specimens, it is difficult to observe liquid and vapor, and living things cannot be observed as it is. Since the electron beam has high energy, sensitive samples such as organic materials are damaged by the electron beam. In addition, elements with small atomic number such as hydrogen have weak interaction with electron beam, and it is difficult to detect the atoms directly. In spite of these weak points, electron microscopy is very attractive apparatus to give us various atomic information in nanoworld. Details of the transmission electron microscopy (TEM) are described in Refs. [1–9].

1.3 Various types of electron microscopy

|

5

1.3 Various types of electron microscopy Various types of electron microscopy are used according to the purpose. Here, various types of electron microscopes and microscopy methods are introduced. The electron microscopy means a method for observation and analysis of various signals coming out from the sample when electron beams are irradiated.

1.3.1 Transmission electron microscope Transmission electron microscope (TEM) is a most widely used electron microscope. Electron beams are irradiated on a sample, and transmitted electrons through the sample are focused and imaged under the sample. Since the image can be enlarged over several 10,000 times, microstructures can be directly observed. The word “TEM” seems to acquire citizenship among material scientists.

1.3.2 Electron diffraction One of the important characteristics of electron microscopes is that it is possible to obtain electron diffraction (ED) showing averaged atomic arrangements at the same nanoscopic scale view.

1.3.3 High-resolution electron microscope High-resolution electron microscope (HREM) is an apparatus that the resolution of TEM is enhanced up to ∼ 0.2 nm. Atomic arrangements and nanostructures can be directly observed by the HREM, and the HREM is a main subject in this book.

1.3.4 Energy dispersive X-ray spectroscopy Energy dispersive X-ray spectroscopy (EDX or EDS) is a method for composition analysis. By measuring energies of characteristic X-rays radiating from the observed region, the element can be identified and the atomic composition of the sample can be clarified.

6 | 1 Introduction 1.3.5 Electron energy-loss spectroscopy (EELS) The element and atomic composition of the sample can be identified by measuring the loss energies of inelastic scattered electrons at the observed regions. In addition, information on electronic states can be obtained.

1.3.6 Energy filtering TEM (EF-TEM) Two-dimensional distribution of elements and binding states can be directly observed by electron energy-loss spectroscopy (EELS) using the energy difference of transmitted electrons.

1.3.7 Lorentz microscopy Lorentz microscopy is a method to observe magnetic domains in ferromagnetic samples by TEM. The magnetization of the sample affect electron beams to generate Lorentz force, which results in changing the image contrast in the sample.

1.3.8 Electron holography Magnetic and electric fields around the sample can be directly observed by reconstructing the interfered electron beams utilizing the coherency of electron waves.

1.3.9 Cs corrected TEM A negative spherical aberration coefficient (Cs ) to cancel positive Cs of the magnetic lenses of the microscope is produced by the Cs corrector, which achieves higher resolution TEM images.

1.3.10 In-situ observation Change of the sample can be observed continuously at nanoscale, during cooling (−269°C) or annealing (∼1000°C), reaction with various vapor, and addition of electricity or physical stress in the electron microscope.

Bibliography

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7

1.3.11 Convergent beam electron diffraction (CBED) Space groups (crystal symmetry), thickness, and strain of the sample can be determined by analyzing electron diffraction pattern obtained by converging electron beams on the sample.

1.3.12 High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) The image is obtained by detecting only elastic scattered transmitted electrons scanning on the sample. The image is called as “Z contrast image” which shows white contrast for a larger atomic number.

1.3.13 Scanning electron microscope The image is obtained by reflected electrons at the sample surface. The scanning electron microscope (SEM) image provide information on the surface structure and shape. By combining various electron microscopes and microscopy techniques, not only atomic arrangements of the samples but also various information such as electronic and magnetic structures can be obtained simultaneously. Other techniques are extraction of information by image processing using Fourier transform, structure determination by comparing image simulation and observation, and structural optimization by molecular orbital calculation.

Bibliography [1] Williams DB, Carter CB. Transmission Electron Microscopy: A Textbook for Materials Science. Springer, Berlin, 2009. [2] Shindo D, Hiraga K. High-Resolution Electron Microscopy for Materials Science. Springer, Tokyo, 2013. [3] Shindo D, Oikawa T. Analytical Electron Microscopy for Materials Science, Springer, Tokyo, 2002. [4] Spence JCH. High-Resolution Electron Microscopy. Oxford University Press, Oxford, UK, 2013. [5] Fultz B, Howe J. Transmission Electron Microscopy and Diffractometry of Materials. Springer, Berlin, 2013. [6] Reimer L, Kohl H. Transmission Electron Microscopy: Physics of Image Formation. Springer, Berlin, 2010. [7] Zou XD, Hovmöller S, Oleynikov P. Electron Crystallography: Electron Microscopy and Electron Diffraction. Oxford University Press, Oxford, UK, 2011. [8] De Graef M. Introduction to Conventional Transmission Electron Microscopy. Cambridge University Press, Cambridge, UK, 2003. [9] Kirkland EJ. Advanced Computing in Electron Microscopy. Springer, Berlin, 2010.

2 Structure and principle of electron microscopes 2.1 Structure of transmission electron microscope A photograph of a 300 kV field emission transmission electron microscope is shown in Figure 2.1 (Jeol. Ltd., JEM-3000F). A transmission electron microscope (TEM) mainly consists of irradiation system (electron gun and magnetic lens), specimen holder, recording system (film, imaging plate, and CCD camera), and vacuum system (ion pump). High vacuum is kept at ∼ 10−5 Pa in the microscope. A specimen for observation with the diameter of 3 mm and the thickness of ∼ 1 μm is introduced in the column. Electron beams are irradiated on the specimen, and transmitted through the specimen. An image can be seen under the sample at the observation screen using the transmitted electron beams. Since the electrons are very light (9.1094 × 10−28 g) and interact strongly with atoms in the specimen, the specimen should be thinned as thin as possible. In order to take high-resolution images, very thin specimen, below ∼ 10 nm, is needed. Such thin specimens can be prepared by various methods such as argon ion milling, sample crushing method, microtome, and focused ion beam method. Various kinds of materials such as metals, semiconductors, ceramics, organic materials, and biological materials can be observed. Electrons are emitted from an electron gun (electron source) at the upper part of the column shown in Figure 2.1. A small size of electron source is needed to emit a large number of electrons and to be in phase of electron waves. Therefore, electron microscopes with a field emission gun which is a point source of electrons with high brightness, and W(100) is used for the source. The (100) is Miller index which indicates crystal planes and is usually represented as hkl. (100), (010), and (001) are equivalent for cubic structures such as tungsten (W), and can be also summarized as {100}. The details of crystal planes and directions are described in appendix. LaB6 crystal is also used for normal electron microscopes. Electrons are accelerated at an accelerator under the electron gun. Electrons pass through condenser lens and condenser aperture, and the condenser lens control brightness of electron beams roughly. The condenser aperture is used for brightness control of electron beams, and the balance of brightness and electron beam damage should be adjusted by the aperture. The electron beams are irradiated on the specimen, and transmitted through the specimen, objective aperture, objective lens, selected area aperture, middle lens, projective lens to fluorescent screen, and an electron microscope image is obtained. The objective aperture is used to select the needed diffraction spots during diffraction observation, and TEM images with high contrast can be obtained by using the smaller aperture, but the resolution is lowered. The selected area aperture is used to select the observation region during TEM observation, and the electron diffraction pattern can be obtained from

2.1 Structure of transmission electron microscope

|

9

Electron gun Condenser aperture Liquid N2 holder Objective aperture Electron biprism Binocular microscope

Goniometer Specimen holder EDX detector Selected area aperture Display Operating panel

Track ball Camera room EELS detector Double-tilt controller

Observation window Fluorescent screen

Fig. 2.1: 300 kV field emission transmission electron microscope.

the selected area. The image on the fluorescent screen can be observed by binocular microscope or CCD camera under the screen to view on the display. A goniometer set at the specimen holder is tilting device of the specimen, and the tilting angle is controlled by the double-tilt controller at the feet. Tilting angles are normally 20–30°, which depends on the microscope. The specimen position is controlled by a track ball. (The diffraction phenomenon is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings. Diffraction from a three dimensional periodic structure such as atoms in a crystal is called Bragg diffraction or reflection.) Most of operations are carried out on the operation panel of the both sides. The electron microscope in Figure 2.1 has energy a dispersive X-ray spectroscopy (EDX) detector at upper right side, an electron biprism for electron holography at the column, an electron energy loss spectroscopy (EELS) detector under the camera room. In addition to the high-resolution observation in atomic scale, analyses on elemental composition and electronic structure of the specimen are possible by using this electron microscope, and the direct observation magnification is 1.5 million times. Various types of electron microscopes corresponding its purpose are obtainable, which can be seen at the web sites of several industries that produce transmission electron microscopes. – FEI, www.fei.com/ – Hitachi High-Tech, www.hitachi-hitec.com/global/index.html – JEOL, www.jeol.co.jp/en/

10 | 2 Structure and principle of electron microscopes

2.2 Observation mechanism of atoms by electrons How can we observe atoms by electrons? Since interpretations by details and mathematical equations are described in Refs. [1–8], an outline of the whole mechanism of atomic observation is described here. Schematic illustration of interaction between irradiated electron beams and atoms is shown in Figure 2.2. Two kinds of electrons pass through the atoms when electron beams (waves) are irradiated over the specimen. One is transmitted electrons, which have no information on atomic arrangements. Another is scattered electrons, and there are two types of scattered electrons. One is elastic-scattered electrons, which interact with electric field (potential) in atoms consisting of atomic nucleus (plus charge) and electron (minus charge). Another is inelastic-scattered electrons which are emitted after giving energy to electron in atoms. The elastic-scattered electrons are used for usual TEM observation. The inelastic electrons are used for analytical microscopy such as EELS. Averaged potential for atoms have a tendency to be larger for larger atomic number, and is also dependent on atomic densities. Although potential distribution depends on atomic arrangement in the crystal, the averaged potential in the inorganic materials are about 10–30 V by neglecting the detailed potential distribution. A factor representing the degree of electron scattering by the atom is an atomic scattering factor (f ). The atomic scattering factor depends on the difference of atomic nucleus and electrons. The atomic scattering factor increases for larger atomic number, and decreases for larger scattering angle. The values of f are determined from theElectron beam (wave) e앥

Atom

e앥

Atom

Atomic Nucleus

Electric field potential Electron cloud

Transmitted electron

Scattered electron

Fig. 2.2: Schematic illustration of interaction between electrons and atoms. Sizes of the electrons and nucleus are actually smaller by far compared with the real sizes.

2.2 Observation mechanism of atoms by electrons

| 11

Electron beam (wave) e앥 e앥 e앥 e앥

Real space Specimen for observation

Transmitted electron

Scattered electron Electronic lens

A Reciprocal space

B Diffraction pattern

Real space Image

Fig. 2.3: Electron diffraction pattern and TEM image formed from electron beams transmitting through the specimen.

oretical calculation for X-ray scattering, which depend on electrons around the atoms. On the other hand, electron beams are more scattered by electric field (potential) consisting of atomic nucleus and electrons. The atomic scattering factors f are calculated from those of X-ray scattering. Atomic scattering factors of electrons depends on the elements, and are ∼ 104 larger compared to X-rays. Information can be obtained by large interaction of electrons with atoms even in the small amount of the specimen. An electron diffraction pattern and a TEM image formed from irradiated electron beams transmitting through the specimen are schematically illustrated in Figure 2.3. Electron beams are emitted from the electron gun, and irradiated on the very thin specimen. Electrons have characteristics of both particles and waves, and they are divided in transmitted electrons and scattered electrons. If the specimen is a crystal, scattered electrons show a diffraction phenomenon. Intensities (amplitudes) of diffracted waves by scattered electrons have information on kinds of atoms, and phases of the waves have information on atomic positions. (Electrons are detected as particles with existence probability of |𝜓|2 just when the electrons are observed.) After electron waves are transmitted through the specimen and pass through electron lens consisting of electric magnet, directions of electrons are focused at the electron lens. In actual electron

12 | 2 Structure and principle of electron microscopes microscopes, there are some more electron lens upper and lower the specimen. Transmitted and scattered electrons go forward, and the electron waves show brightness by amplifying the waves at the position with integer times of wavelength of electrons (same phase). This bright region is diffraction spots, and a diffraction pattern can be observed as shown in Figure 2.3, which is called reciprocal space. Such phenomenon that electron waves are changed from the specimen in real space to reciprocal space through the electron lens corresponds to Fourier transform in mathematics. The diffraction spots are white spots observed in the electron diffraction patterns, and each spot is due to diffracted spots by the crystal. If the crystal structure is known, the diffraction spots can be indexed. The Fourier transform is used for the transformation of real space to reciprocal lattice. Diffraction patterns can be obtained by Fourier transform of periodic atomic arrangement. The Fourier transform is also used to obtain frequency distribution from waves of light or sound. Transmitted and scattered electrons pass thorough two diffraction spots in the reciprocal space, and go down. Since routes of electrons are different, distances of the course is different. Therefore, two waves interfere one another at a certain position, and an image is formed by the phase difference. This image is transmission electron microscope image, and this contrast is called as phase contrast which corresponds to the real space. The transform from the reciprocal space to the real space also corresponds to the Fourier transform. Note that the phase contrast shows no contrast when the focus of the objective lens is adjusted at the atomic position. The reason is that a shift of the phases of the waves of transmitted and scattered electrons is just 𝜋, and the intensities of the waves are canceled and the image shows no phase contrast. When the focus is shifted to under the just focus, phase contrast can be observed by the phase difference of electron waves. Atomic arrangements can be observed in the weak phase contrast taken by a high-resolution electron microscope. Note that much more electrons are necessary to take such atomic-resolution image. Various conditions such as control of electron lens and others are needed to obtain the high-resolutions images. The atomic-resolution image is a phase contrast using the phase of the electron waves, and the intensities are very weak. The high-resolution images are commonly taken at ∼ 1 million magnifications. Note that no high-resolution lattice image can be taken even at the high magnification if the resolution of the electron microscope is not high. When images are observed at low magnifications, the following two types of contrasts are main ones. The main contrast at several thousand magnifications is an absorption contrast. Thick region in the specimen or region consisting of atoms with large atomic number shows dark contrast. Another is diffraction contrast which is contrast due to different type of electron diffraction phenomenon compared with an ideal crystal at region with distorted lattice such as precipitates, interfaces, and defects. The magnetic field is changed by controlling electric current of electron lens, and the focus distance can be controlled. Therefore, the required observation magnification can be easily obtained.

2.3 Information from electron diffraction pattern | 13

2.3 Information from electron diffraction pattern Many materials consist of crystals that atoms are arranged regularly. As described in the previous section, electron waves scattered by regularly arranged atoms are interfered and form electron diffraction pattern, as shown in Figure 2.4. Phases of scattered electron waves are determined by atomic position, and amplitudes are determined by kinds of atoms. Electron diffraction patterns commonly show bright dot patterns, and the brightness (intensity) of the spots are related to the amplitudes of the diffracted waves. However, information on the phases is lost in the diffraction patterns, and the information on the absolute atomic positions cannot be obtained. Only relative atomic positions can be obtained from the arrangements of diffraction spots. The intensity I of the electron diffraction pattern is given by the following equation: I = D|F|2 Here, D is the dynamical diffraction effect, and F is the structure factor. Information on atomic species and atomic position in the crystal is included in the electron diffraction intensity. The F is called crystal structure factor, which corresponds to a factor obtained by Fourier transform of distribution of potential (atoms) in the crystal. The crystal structure factor F includes information on atomic species and relative atomic position in the crystal unit cell, and depends on the distribution of atomic scattering factor f in the unit cell. The unit cell means basic parallel hexahedron lattice of the crystal, and represented with three vectors (a, b, and c) and three angles (𝛼, 𝛽, and 𝛾) (see Appendix A.3). The crystal is three-dimensionally stacked lattice of the unit cell. An actual value of F is measured as diffraction intensities (brightness of the diffraction spot), and the value is different for the each diffraction spot. In addition, dynamical diffraction effect D is important, which is the effect by the crystal thickness. In Figure 2.3, the electrons are scattered only once by the atoms in the specimen. However, the electrons are commonly scattered more than twice in the actual specimen with crystal thickness, and often cause complicated diffraction effects. It is important to reduce the dynamical diffraction effect as small as possible in order to analyze the data simply. An example of crystal structure and electron diffraction patterns is shown in Figure 2.4. Atomic structure models of silicon with a diamond structure and calculated electron diffraction patterns along the [100], [110], and [111] are shown. These electron diffraction patterns were calculated along three different directions of silicon. Intensities of Bragg reflection (bright dots) correspond to the amplitudes of diffracted waves, and include information on atomic species and relative atomic sites in the crystal unit cell. An outline of the atomic arrangements can be known by analyzing the electron diffraction patterns. The dynamical diffraction effect is large for the actual crystal, and it is difficult to determine the atomic species and positions directly although a size of the unit cell can be investigated. Under very severe conditions such as the least dynamical diffraction effect for the very thin crys-

14 | 2 Structure and principle of electron microscopes

022

022 000

[100]

004

111 000

[110]

220 202 000

[111] Fig. 2.4: Atomic structure models (left) of silicon with a diamond structure observed along [100], [110] and [111]. Calculated electron diffraction patterns (right) along [100], [110], and [111].

tal and many diffraction spots from various crystal directions, it is possible to analyze the atomic species and atomic sites in the crystal unit cell to a certain level. A detailed structure model can be obtained from the high-resolution images and the electron diffraction patterns by satisfying the severe conditions. Identification of known compounds is one of the most used methods for electron diffraction patterns. Crystal structures and lattice constants can be obtained from the electron diffraction patterns. If the sample is a material which has already been determined from X-ray diffraction (XRD), each electron diffraction spots can be indexed by comparing with diffraction intensities of each reflection in XRD database, and can be identified as the objective structure or not.

2.4 High-resolution electron microscopy

|

15

2.4 High-resolution electron microscopy As shown in Figure 2.3, electron waves go down from the diffraction spots in the electron diffraction pattern, and a high-resolution electron microscopy (HREM) image is formed from phase contrast by phase difference of the electron waves. Here, the observed specimen is thin enough to neglect the dynamical diffraction effects D. Then, the image intensity I of the HREM image is given by the following equation: I ≈ 1 − 2𝜎V where 𝜎 is the interaction constant, and V is the projected potential. This is called weak-phase-objective approximation. The interaction constant 𝜎 is determined by accelerating voltage E (V). As the accelerating voltage increases, the 𝜎 decreases, and image intensity I increases. V is the projected potential in the crystal along the observation direction. The potential is distributed three-dimensionally in the crystal. The HREM image is projected two-dimensional image of the three-dimensional potential distribution observed from a certain direction of the crystal, and this is represented as potential V. An HREM image is Fourier transform of an electron diffraction pattern, and the potential distribution V in the real space appears again. From the above equation, positions with large potential V (ex. metal atom position) show dark black contrast. Positions with small potential V are the position without atom, and they show bright white contrast. HREM images are taken intentionally by defocusing from the phase difference 𝜋 which shows 0 intensity by interference of transmitted and diffracted waves. Information on phases is included in the HREM image in addition to the amplitudes of diffracted waves. Therefore, information on the absolute atomic position can be obtained, which is very important advantage of the HREM image. Information obtained by HREM images is summarized as follows, and the details will be described in Chapter 4.

2.4.1 Atomic species Atomic species can be recognized, when HREM images are taken under the severe conditions such as crystal structure, observation direction, crystal thickness, imaging conditions, and atomic composition. The atomic composition of the specimen is determined from the starting compositions and EDX analysis. If the image is taken under the optimum conditions, atoms with large atomic numbers are imaged as darker black dots.

16 | 2 Structure and principle of electron microscopes 2.4.2 Atomic position Central positions of dark dots observed in structural image indicate atomic positions, and coordinates of metal atom positions can be determined. Comparing the atomic positions with the results of X-ray and neutron diffraction experiments, absolute atomic positions of metals can be determined with a precision of ∼ 0.01 nm.

2.4.3 Number of atoms Number of atoms in the observed region can be determined by comparing HREM images with simulation under the limited conditions. An example of HREM image is shown in Figure 2.5, which is an HREM image of high transition temperature (Tc ) superconductor Tl2 Ba2 CaCu2 O8 taken along the aaxis [9]. In the early stage of the superconducting oxide research, isolation of a single phase from mixed phases was difficult, and high-resolution electron microscopy was a powerful method for atomic structure analysis instead of X-ray diffraction. This HREM image was taken for the very thin specimen (∼ 2 nm) at the Scherzer focus which is an optimum defocus value, and image processing was performed. The HREM image exactly shows distribution of the projected potential, and positions of cations show dark black dots. From the HREM image and composition of the superconductor, the atomic structure model can be proposed as shown in Figure 2.5. Heavy atoms such as Tl (atomic number Z = 81) and Ba (Z = 56) show dark black contrast. Cu (Z = 29) and Ca (Z = 20) atoms show smaller dark dots. Although oxygen atom positions cannot

Ca Ov Ca Cu Ba Ba Tl Tl Tl Ba Cu Cu Ca Cu Cu

Ba

Ca

Tl

O Tl CuO Ov

CuO

Tl Tl

Ba Ca

c

Ba Cu Ca

Ov

1 nm

a Fig. 2.5: HREM image of Tl2 Ba2 CaCu2O8 taken along the a-axis.

2.5 Scanning electron microscope | 17

be observed directly in this image, white brighter contrast is observed in the Ca layer as indicated by Ov , which are oxygen vacancies. It is believed that oxygen atoms are located at other white regions. Although each dark black dot (Tl, Ba, Cu, and Ca) in the HREM image of Figure 2.5 seems to be each single atom, there are actually several atoms along the observation direction. By comparing the observed HREM image with simulated images, number of atoms can be estimated at the dark positions.

2.5 Scanning electron microscope Scanning electron microscopes (SEM) are used for observation of surface of the specimen. Comparing with optical microscopes, a three-dimensional image can be obtained since the optimum focus is on wide region due to the deep focus depth. The specimens are not needed to be thinned, which is different from TEM. Since the specimen can be observed as it is in the microscope, the SEM is widely used for surface observation. A field emission SEM is shown in Figure 2.6, which is a more compact apparatus compared with TEM because of lower accelerating voltage. Various operations such as focusing, taking images and observation can be done on the computer screen recently. Elemental analysis is also possible with EDX detector, which is similar to TEM. In SEM, electron beams are emitted from electron gun, and they are adjusted by electron lens, and irradiated on the specimen, which is the same as TEM. A different point from the TEM is recording secondary electrons from the specimen surface by scanning electron beams on the specimen. Incidence depth of electron beams is ∼ 10 nm, which depends on the accelerating voltage and materials, and secondary electrons emitted from the specimen surface are detected by a SEM detector. Electrons in the specimen are excited from core electronic state to the higher energy level than that of vacuum,

Fig. 2.6: Scanning electron microscope (www.zeiss.com/SEM).

18 | 2 Structure and principle of electron microscopes

200 nm Fig. 2.7: SEM image of boron nitride synthesized by chemical vapor deposition.

and are emitted from the surface, which are the secondary electrons. Although reflected electrons are also detected, the secondary electrons are mainly used for the SEM image. Since the secondary electrons are emitted from surface region of the specimen within the depth of ∼ 10 nm, inner information is included in addition to the surface information. If an accelerating voltage is increased (ex. more than ∼ 10 kV), surface image may be vague a little because of the strong inner information. When the accelerating voltage is below several kilovolts, the microstructure can be observed clearly, and a phenomenon of vague image due to charge up of insulator specimen can be suppressed. If the accelerating voltage is decreased, the resolution is lowered, and it is necessary to control the accelerating voltage. Figure 2.7 is a SEM image of boron nitride (BN) synthesized by a chemically vapor deposition (CVD) method [10]. Bright white region in the image shows the region with emitted secondary electrons. Much secondary electrons are emitted at the edges of crystals, as observed at bright white regions in the image. For the surface of the BN, pentagonal pyramidal-shaped structures are observed, as indicated by black solid lines. A detailed pentagonal structure will be described in Chapter 6. For the SEM observation, electron beams are sometimes diffracted at the surface of crystal specimen, and show diffraction pattern, which is called electron channeling pattern. An analysis method of the crystal surface by the diffraction phenomenon is electron backscatter diffraction (EBSD). Irradiated electrons on the crystal specimen are scattered in the specimen, and emitted from the specimen as reflected electrons. Then, the electrons are diffracted, and the electron diffraction pattern is detected by

2.6 Electron energy-loss spectroscopy

| 19

a detector, and crystal directions are analyzed from the obtained diffraction pattern. Since the EBSD occurs at the depth of several tens nm from the specimen surface, the specimen surface should be clean and smooth to obtain precise data. Crystal directions of bulk sample can be investigated by the EBSD without very thin specimen like TEM. Although a resolution of SEM increased to 0.5 nm, it is impossible to identify each atom. To obtain information on atomic arrangements of surface, scanning tunneling microscope (STM) and atomic force microscope (AFM) may be suitable. Low vacuum SEMs were also developed, and a living body including water can be observed by cooling. In addition, insulator materials which have a phenomenon of electron charge-up can be observed directly with the low vacuum SEM by suppressing the charge-up at the specimen surface by positive ionization of remained gas in the SEM. There are various types of SEM like TEM, and please refer to the websites of the companies. – FEI, www.fei.com/ – Hitachi High-Technologies Corporation, www.hitachi-hitec.com/global/index.html – JEOL, www.jeol.co.jp/en/ – Shimadzu, www.shimadzu.com/an/index.html

2.6 Electron energy-loss spectroscopy An important merit of TEM is simultaneous acquisition of HREM image in the real space and electron diffraction pattern in reciprocal space at the same place. Furthermore, information on atomic composition and electronic bonding state can also be obtained. Electron energy-loss spectroscopy (EELS) and energy dispersive X-ray spectroscopy (EDX or EDS) are analysis methods for elemental composition and bonding state. The EELS is a method to investigate atomic composition and electronic state by measuring electron energy at the observation region. The EDX is a method to investigate atomic composition by measuring energy of characteristic X-ray emitted from the observation region. At first, the principle of EELS is described here. A schematic illustration of electrons and X-ray emitted by electron incidence on atoms is shown in Figure 2.8. As described in Figure 2.2, main electrons to obtain TEM images are transmitted electrons without interaction with the specimen and elastic-scattered electrons by electric field (potential) in the specimen consisting of atomic nucleus and electron cloud. Incident electrons sometimes lose energy by interacting with electrons in the specimen. As shown in Figure 2.8, there are core-loss electrons under the specimen, and the electrons in which the energy was lost are called inelastic-scattered electrons. Since the loss energy depends on the types of elements, density of states, and atomic distances can be identified by measuring the loss energy. Electrons captured by the detector

20 | 2 Structure and principle of electron microscopes Electron beam (wave) e앥 Characteristic X-ray Kb Ka

e앥 Free electron cloud e앥

Atomic nucleus K L M La

Core-loss electron Transmitted electron Inelastic scattered electron

Elastic scattered electron

Fig. 2.8: Schematic illustration of electrons and X-ray emitted by incidence of electrons on atoms. Actual sizes of nucleus and electron are far smaller from the illustration.

are mixture of elastic-scattered electrons keeping the original energy and inelasticscattered electrons with loss energy. When magnetic field is applied on the mixture electrons by electromagnet (spectrometer), the Lorentz force functions on the electrons, and the loci of electrons are curved. Electrons with less energy have lower energy and are curved, and energy distribution of electrons can be obtained by setting a detector on the electron pass. The energy spectrometers are set under the fluorescence screen and the TEM column. Electrons with various energies are introduced, and the energies of electrons can be detected in the energy spectrometer. An example of EELS is shown in Figure 2.9, which is an EELS spectrum of BN nanotubes and nanocapsules. Two distinct absorption features are observed at 188 and 401 eV, which correspond to boron (B) K-edge and nitrogen (N) K-edge onsets, respectively. Spectrum peaks in the EELS is called edge, and peaks due to excited K-shell (1s electrons) is called K-edge. When the atomic number is large, M-edge and L-edge are also observed. As observed in the spectrum, small peaks due to the elements are observed in the background noise, and peaks due to nitrogen are very small. Since the background noise is large for the thick specimen, the specimen should be thin as thin as possible. BN has a hexagonal structure as shown in Figure 2.9. The 𝜎-bonding is a strong covalent bond in the hexagonal rings, and 𝜋-bonding is a weak van der Waals bond along the c-axis perpendicular to the hexagonal rings. Two sharp peaks are observed for the B, and the left and right ones correspond to 𝜋∗ and 𝜎∗ , respectively. These 𝜋∗ (2Pz orbital of B and N) and 𝜎∗ (2Px,y orbital of B and N) are unoccupied antibonding orbital which have higher energies compared with 𝜋- and 𝜎-bonding orbital,

2.6 Electron energy-loss spectroscopy

Intensity [A.U.]

Boron K (188 eV)

p*

N/B = 1.0 앧 0.2

s*

Nitrogen K (401 eV) s* p*

ELNES EXELFS A B

200

| 21

300

400

500

Energy loss [eV]

C

2 nm Fig. 2.9: EELS, TEM image, and structure model of BN.

and the 𝜋∗ and 𝜎∗ are used for the indication of 𝜋- and 𝜎-bonding. A composition of elements can be estimated from the EELS data by removing the background, and the atomic composition of N/B = 1.0 ± 0.2 was obtained for this specimen. Since the EELS peaks are weak for elements with larger atomic number as observed in Figure 2.9, materials containing light elements are suitable for the EELS analysis. For the EELS spectrum, unoccupied density of states is reflected as the energy loss near edge structure (ELNES) from the peak edge to 50 eV, and information on atomic distance is reflected as extended energy loss fine structure (EXELFS) at the higher energy regions. Information on interband transition and radical distribution function can be obtained by the detailed analysis. Electrons interacting with only free electrons are called plasmonloss electrons, and are used for measurements of specimen thickness. When a peak corresponding to a certain element such as boron in Figure 2.9 is obtained, a TEM image where the region element exists is imaged as bright contrast only by using electrons with the peak energy can be obtained, which is called elemental mapping. A quantitative diffraction analysis is difficult for background due to inelastic-scattered electrons. However, experiments with the reduced background using elastic-scattered electrons can be done by using the energy filtering to remove the inelastic-scattered electrons.

22 | 2 Structure and principle of electron microscopes

2.7 Energy dispersive X-ray spectroscopy The EDX is a method to investigate atomic composition by measuring energy of characteristic X-ray emitted from the observation region. In Figure 2.8, positions of core electrons knocked-on by inelastic-scattered electrons become vacancies, and electrons fall down from outer electron orbitals. Then, extra energies are emitted as characteristic X-ray such as K𝛼, K𝛽, and L𝛼 in Figure 2.8. Since the characteristic X-rays indicate the specific energy values for each element, kinds of elements can be identified by measuring the characteristic X-rays. X-rays emitted by transition from L shell to K shell, M shell to K shell, and M shell to K shell are called K𝛼, K𝛽, and L𝛼, respectively. When the detection range of the EDX detector is in the range of 0–40 keV, K𝛼 peaks from Be (Z = 4) to La (Z = 57) are often used for the EDX analysis. L𝛼 peaks are also used for heavier elements than Cu (Z = 29). Energy peak positions corresponding to the elements can be analyzed by the attached software, and composition analysis of the specimens can be investigated by the intensities of peaks. An example of EDX analysis is shown in Figure 2.10, which is an EDX spectrum of BN nanocapsules with Ag nanoparticles [10]. K𝛼 peaks corresponding to boron (B), nitrogen (N), and oxygen (O) are observed, and the intensity of B and N is almost same. Although K𝛼 peaks corresponding to Cu (8.0 keV) and Ag (22 keV) are not observed in Figure 2.10, L𝛼 peaks with lower energies are observed, and an L𝛽 peak is also observed for Ag. Peaks corresponding to Cu and O arise from the TEM grid and starting materials of BN. It should be noted that peaks outside from the observed area can be sometimes detected. Energy resolutions of EDX and EELS are 150 and 1 eV, respectively. Therefore, information of electronic structures can be obtained only by the EELS, and cannot be obtained by the EDX because of low-energy resolution. On the other hand, background noise is small for the EDX, which is suitable for composition analysis with heavy elements. EELS and EDX can be used for the purpose and expected elements in the specimen.

BN 2 nm

N Ka

Intensity [A. U.]

B Ka

Ag

O Ka

Ag La Ag Lb

Cu La

0

0.5

1.0

1.5

2.0

Energy [KeV]

2.5

3.0

3.5

Fig. 2.10: EDX spectrum of BN nanocapsules with Ag nanoparticles.

2.8 High-angle annular dark-field scanning TEM |

23

2.8 High-angle annular dark-field scanning TEM In addition to the HREM method, high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) is widely noticed. The HAADF-STEM is a method to obtain two-dimensional elemental mapping image by scanning the specimen using conversed electron beams (∼ 0.2 nm). Elastic scattered electrons with angles higher than 70 mrad is important for this method when the electron beam is irradiated on the specimen. The elastic-scattered electrons with higher angles have no diffraction effects, and the image can be analyzed more easily compared to the conventional HREM image. Inelastic-scattered electrons which are unsuitable for the structure analysis have lower scattering angles, and they can be excluded by the detector. A schematic illustration is shown in Figure 2.11 (a). The transmitted electrons at the center do not contribute for the imaging, which is different from the usual bright field TEM image, and this is called dark field image. The bright field image is taken with only transmitted electrons (000 index in the electron diffraction pattern) by using an objective aperture on the electron diffraction pattern. On the other hand, the dark field image is taken only with diffracted electrons, and is used for observation of precipitates and defects with high contrast (absorption contrast and diffracted contrast). The elastic-scattered electrons with high scattered angles have no diffraction effect on the detector, and inelastic-scattered electrons provide comparatively low scattered angles. To increase efficiencies of detection of the scattered electrons, an annular detector is used since electron scattering by an atom is anisotropic in principle. For the HAADF, elastic-scattered electrons with higher angles are collected by the annular detector, and the electron intensity is recorded as two-dimensional mapping. The detected electron-beam intensity I is represented as I ∝ Z 2 (Z: atomic number), and the image contrast is proportional to Z 2 . Therefore, the observed image is called Z contrast. The Z contrast has little dynamical effect even for thick specimens, and provides white contrast at the atomic positions for larger atomic number. (On the other hands, dark black contrast is observed at the atomic positions for the optimal HREM observation.) Since the white dots can be regarded as atomic positions for the Z contrast image, the image can be analyzed more easily compared with the phase contrast image for the HREM. An example of HAADF-STEM image is shown in Figure 2.11 (b) [11]. Fourier noise filtering was applied on the image to increase the image quality. A circle indicated by a white line with a size of ∼ 2 nm corresponds to an atomic cluster consisting of ∼ 500 atoms. White dots in the image correspond to atomic positions of Ni and Ru. Since Al atoms (Z = 13) have smaller atomic number compared with Ni (Z = 28) and Ru (Z = 44), no image contrast due to the Al is observed, and only Ni and Ru are imaged as white dots.

24 | 2 Structure and principle of electron microscopes Electron beam (wave) e앥 e앥

Real space Specimen

Scattered electron Real space Transmitted electron (a)

High-angle annular dark field detector

(b)

1 nm

Fig. 2.11: (a) Schematic illustration of HAADF-STEM. (b) HAADF-STEM image of Al70 Ni20 Ru10 decagonal quasicrystal (Courtesy of Prof. K. Hiraga, Tohoku University).

The resolution of HAADF-STEM depends on the size of the electron beam, and field-emission electron microscopes with convergent electron beams provide the high resolution. Combination of the HREM and HAADF-STEM, more detailed nanostructures can be analyzed.

2.9 Electron holography and Lorentz microscopy Magnetic and electric fields can be directly observed by using interference of electron waves, which is called electron holography. Since electron beams by field emission electron gun have high interference, magnetic and electric fields inside and outside of the specimen can be observed by recording and reproducing the interference fringes (hologram). The electron holography consists of two steps. The first step is to record phase information of electrons by taking a hologram image using transmission electron microscopy. A schematic illustration of electron hologram recording is shown in Figure 2.12 (a). Electron waves with high interference are irradiated at the edge of the specimen by using field emission electron gun. Transmitted electrons through the specimen are affected by electric field (potential) and magnetic field, and the phases of transmitted electrons are more progressed compared with those of electron caves through the vacuum. Object waves (diagonal lines in Figure 2.12 (a)) transmitted through the specimen and reference waves transmitted through the vacuum are polarized by an electron biprism of the TEM, and a superposition image of the objective and reference waves is formed at the image plane. The interference image of the electron wave is hologram, which is recorded by using photographic films, imaging plates and slow scan charge coupled devices (CCD).

2.9 Electron holography and Lorentz microscopy

(a)

e앥

e앥

Electron beam (wave)

|

25

(b)

Specimen

Electron lens

1 μm Electron biprism

(c) h/e

Hologram Fig. 2.12: (a) Schematic illustration of electron holography. (b) Lorentz microscopy image. (c) Electron hologram recording images of Sm–Co-based magnet (Courtesy of Prof. D. Shindo, Tohoku University).

The second step is to reproduce recorded phase information by image processing of digital data. The hologram recorded as digital data in the first step is input in the computer, and is Fourier transformed. One of the sideband is filtered by aperture, and the origin is moved. Then, objective waves obtained by inverse Fourier transform are interfered with reference waves, and the final interference image (phase image) is reproduces. The phase information can be analyzed by Fourier phase analysis software (ex. image-sense.co.jp/). A Lorentz electron micrograph of Sm–Co magnet is shown in Figure 2.12 (b) [12]. Electron beams are affected with Lorentz force by magnetization of the specimen, and magnetic domains of magnetic materials can be directly observed as black and white bands by large defocus of the objective lens. White and black lines in Figure 2.12 (b) are the domain walls, and the magnetic domain exists between the domain walls. An interference micrograph (hologram) of the same region is shown in Figure 2.12 (c). Lines of magnetic force are observed as black lines inside and outside of the specimen. Magnetic domain walls and lines of magnetic force are indicated by white lines and arrows, respectively. The magnetic flux for every h/e (h: Planck constant, e: elementary charge) has phase difference of 2𝜋, and the distance of the magnetic flux corresponds to h/e. Equivalent potential lines can be observed for electric field, and the electric charge for local regions can be estimated. The nanoscopic region can be measured quantitatively by using the electron holography, which is expected as the characterization method for nanomaterials.

26 | 2 Structure and principle of electron microscopes

2.10 Image simulation When atomic structures are discussed from HREM images, the actual HREM data should be compared with calculated images based on the electron microscope. Based on the atomic structure models, HREM images are calculated by computers, considering electron scattering in the specimen, aberration of electron lens, and other observation parameters. Software for image and diffraction calculations is available, and it is better to understand the principle of the image calculation. MacTempasX (www.totalresolution.com/) To calculate a crystal structure, various information such as space groups, lattice constant, atomic coordinate, occupancy, temperature factor, parameters of the electron microscope is needed. If the specimen is the known materials, values of database and published papers can be used for calculation. If the crystal structure is unknown, a structure model should be proposed from the assumed space group, lattice constant and other parameters, and trials and errors are necessary to coincide the experimental results and the assumed structure model. If no space group can be assumed for isolated structures (ex. molecule, cluster, and others), the space group can be set as 1, and all atomic positions should be introduced. Other important parameters are focus values of electron microscope and crystal thickness, which should be varied for comparison with the experimental data. An example of image calculation on Si crystal used in solar cells is shown in Figure 2.13, as functions of crystal thickness and defocus values of the objective lens of a 200 kV TEM. Actual examples of image calculation analysis with HREM images will be described in Chapter 4.

–10

–20

–30

Defocus values [nm] –40 –50 –60 –70

–80

–90

1 2 3

Thickness [nm]

4 5 6 7 8 9 10

Fig. 2.13: Calculated HREM images of Si along [011] as functions of crystal thickness and defocus values of objective lens.

Bibliography

|

27

Bibliography [1]

Williams DB, Carter CB. Transmission Electron Microscopy: A Textbook for Materials Science. Springer, 2009. [2] Shindo D, Hiraga K. High-Resolution Electron Microscopy for Materials Science. Springer, Tokyo, 2013. [3] Spence JCH. High-Resolution Electron Microscopy. Oxford University Press, Oxford, UK, 2013. [4] Fultz B, Howe J. Transmission Electron Microscopy and Diffractometry of Materials. Springer, 2013. [5] Reimer L, Kohl H. Transmission Electron Microscopy: Physics of Image Formation. Springer, 2010. [6] Zou XD, Hovmöller S, Oleynikov P. Electron Crystallography: Electron Microscopy and Electron Diffraction. Oxford University Press, Oxford, UK, 2011. [7] De Graef M. Introduction to Conventional Transmission Electron Microscopy. Cambridge University Press, Cambridge, 2003. [8] Kirkland EJ. Advanced Computing in Electron Microscopy. Springer, 2010. [9] Oku T, Direct structure analysis of advanced nanomaterials by high-resolution electron microscopy. Nanotechnol. Rev. 2012, 1, 389–425. [10] Oku T, Kusunose T, Niihara K, Suganuma K. Chemical synthesis of silver nanoparticles encapsulated in boron nitride nanocages. J. Mater. Chem. 2000, 10, 255–258. [11] Hiraga K, Ohsuna T, Sun W, Sugiyama K. The structural characteristics of Al–Co–Ni decagonal quasicrystals and crystalline approximants. J. Alloys Comp. 2002, 342, 110–114. [12] Shindo D, Park YG. Lorentz microscopy and holography characterization of magnetic materials. In: Yi Liu Y, Sellmyer DJ, Shindo D (eds). Handbook of Advanced Magnetic Materials. Springer, 2006, 397–438.

3 Practice of HREM 3.1 Sample preparation Sample preparation is an important point to obtain good TEM data. The TEM results often strongly depend on the sample preparation, as shown in Figure 3.1. No good TEM image can be taken for bad samples. Conditions for TEM samples are as follows: (1) (2) (3) (4)

Thin thickness. Below ∼ 10 nm for especially high-resolution observation. Small damage against electron beam irradiation. High stability in vacuum. Electronic conductivity.

The specimen should be as thin as possible. Very thin specimen less than ∼ 10 nm is necessary for high-resolution observation in atomic scale. Such specimen can be prepared by argon ion beam milling and crashing method. Various types of samples such as metals, semiconductors, ceramics, and life materials can be observed. Note that stability against electron beams is strongly dependent on the specimens during observation. For electron beam irradiation, high vacuum of ∼ 10−5 Pa is needed inside of the electron microscope. The specimens should be set in the microscope after stability processing even in the vacuum. Living materials containing water should be frozen or observed at low temperatures. Electron beam irradiation is continued during the observation, and electrons are piled up in the specimen. If the specimen is an insulator, charge-up phenomenon occurs by accumulated electrons. Then, irradiated electrons are scattered by the charged up electrons, and cause image disturbance and specimen vibration. Sometimes the specimens should be coated with carbon or metal thin films by vacuum evaporation. For inorganic, organic and metal materials and life materials, methods for specimen preparation are different seriously.

3.2 Specimen preparation methods Specimen preparation methods for TEM and their merits are summarized in Table 3.1. Common sizes of specimens are 3 mm in diameter and thin disks (< ∼ 0.1 μm), which depends on the size of the specimen holder of each maker of electron microscope.

3.2 Specimen preparation methods | 29

Electron beam e앥

e앥

Thick region

Thin region

Fig. 3.1: Specimen for electron microscope.

Transmitted electron Table 3.1: Specimen preparation methods for TEM. Preparation methods

Samples

Merit

Demerit

Crushing, powder

Ceramics, powders

Easy fabrication, clear surface, thin region

Only cleavage sample, mechanical damage by crushing, small observation region

Ion milling

Semiconductor thin films, ceramics, metals

Wide view and thin specimen

Small damage of surface

Electropolishing

Metals and alloys

Comparatively simple

Oxide formation at the surface

Focused ion beam

Semiconductor devices

Cross section of interfaces consisting of different materials

Surface damage by ion beam

Ultra microtome

Living and organic materials

Sample slicing by chemical and frozen methods

Sample distortion by slicing and difficult slicing method

3.2.1 Crushing and powder Solid samples are crushed by an agate mortar. Strong crushing destroys thin regions, and soft crushing is necessary. Fine powders can be observed as it is. The powders and thin layers are dispersed in organic solvent such as ethanol, butanol, and acetone, which are agitated and absorbed by tweezers or pipettes. Then, the suspension is dropped on the holey carbon microgrid for TEM on the filter papers. Extra solutions are absorbed by the filter papers, and the powder samples remain on the microgrids as dispersed, which are used as TEM specimens.

30 | 3 Practice of HREM This method is widely used for ceramics and oxides with high cleavage characteristics, and also used for micropowders. This method is very simple and has small contamination at the specimen surface. Very thin regions less than several nanometers sometimes can be observed. However, this crushing method can be only used for cleavage sample, and ductile materials such as metals are difficult to use. Various structures such as grain boundaries, defects, and precipitates are often lost by the crushing.

3.2.2 Ion milling Thin specimens are prepared by ion beam sputtering atoms at the specimen surface. The ion beams using argon gas are accelerated at several kilovolts, and irradiated on the specimen. This preparation method is widely used for TEM specimen such as semiconductors, ceramics, and multilayered thin films. Before ion milling, the sample is cut and thinned down to 0.1 mm by a diamond cutter and emery papers. The sample is processed as a disk 3 mm in diameter by a supersonic wave cutter. Sometimes the sample is strengthened by a copper ring. The center of the sample is thinned down to 20 μm by a dimple grinder. Then, the sample is set in the ion milling apparatus. Argon is usually used for ion source, and iodine or neutral atoms are sometimes used to reduce the sample damage. The ions are irradiated at the center of the sample disk with angles of 5–30° against the sample. A hole is processed by the ion milling at the center of the sample, which is used for very thin TEM specimen. This method is also used to remove impurity layers at the surface of electropolished specimen. Sputtering rates depends on the elements, and it is difficult to process thin, uniform specimen for samples containing elements with largely different atomic numbers. The specimen surface is often damaged by the ion bombardment, and amorphous layers with thicknesses of several nanometers are formed. To reduce the damage, low accelerating voltage, small angle irradiation, and liquid nitrogen cooling are applied.

3.2.3 Electropolising Electropolishing is used for conducting materials such as metals and alloys. The anode and cathode are the sample plate and platinum, respectively. Direct current is applied on the electrodes in electrolysis solutions, and the sample is polished. A sample plate less than 0.5 mm is cut from the bulk sample, and mechanically polished down to 0.1 mm. This plate is set as the cathode, and platinum or stainless steel is set as the anode. Then, direct current is applied on the electrodes in electrolysis solutions to polish the sample. After electropolishing, the sample is rinsed by

3.3 Structure analysis by X-ray diffraction

| 31

methanol to obtain a TEM specimen. Types, temperatures of electrolysis solutions, and suitable voltages depend on the materials. When the methanol rinsing is unsuitable, impurity layers such as oxides may be formed. Ion milling may be required to remove the impurity layers. A similar method is chemical polishing, which is a method that semiconductor materials such as silicon are dissolved by polishing solutions.

3.2.4 Focused ion beam method Thin specimens can be obtained by processing local regions of the sample using focused ion beams such as gallium. The sample surface is observed by secondary electrons occurred from the surface, which are caused by ion beam irradiation. After selecting the region for processing, the sample is processed by sputter etching irradiating focused ion beams. For the sample with hetero-interface or optional region, TEM specimens with uniform thickness can be obtained by this method. It is necessary to be careful for gallium ion damage and injected gallium ion in the sample.

3.2.5 Ultra microtome Ultra microtome is used to process soft materials and life materials. For life materials, the sample was quickly frozen and dried, embedded in resins, cut by diamond knife, dyeing, and mounted on the microgrid with holey carbon films. Resins for embedding are acrylic and epoxy resin, which are processed easily, soluble in organic solution, stiffened in short time, and comparatively stable against electron beams. Although the principle of cutting is simple, inorganic materials are easily distorted. Note that the microstructures are often distorted, and proficiency is needed for specimen preparation.

3.3 Structure analysis by X-ray diffraction When the sample amount is larger than 10–100 mg, rough structure can be investigated by X-ray diffraction (XRD). The XRD will indicate that the sample is a single phase or mixed phase. If the sample consists of nanoparticles or nanocrystals, the crystallite size can be estimated. From the XRD data, analyses of HREM image and electron diffraction will become easier. If the sample is a known material, plane distances (d) and indices can be clarified from the diffraction peaks of XRD. An example of XRD pattern on silicon with a diamond structure is calculated, as shown in Figure 3.2 and Table 3.2. When the sample has an unknown structure, the values of plane distances (d) can be obtained by the XRD, which will effectively stimulate the structure analysis by transmission electron microscopy.

32 | 3 Practice of HREM 111 Intensity counts

5000 4000 2 20 3000 3 11

2000 1000

400 10

30

50

3 31

70

422 3 3 3 511 90

440 110

2q [°]

Fig. 3.2: Calculated X-ray diffraction pattern of silicon with a diamond structure. ̄ a = 0.54307 nm = Table 3.2: Calculated X-ray diffraction parameters of silicon. Space group Fd3m. 5.4307 Å. Index

2𝜃 (°)

d-spacing (Å)

|F|

Relative intensity (%)

Multiplicity

111 220 311 400 331 422 511 333 440

28.4430 47.3038 56.1237 69.1317 76.3782 88.0326 94.9552 94.9552 106.7118

3.1354 1.9200 1.6374 1.3577 1.2459 1.1085 1.0451 1.0451 0.9600

58.8691 67.4859 44.1701 56.2748 37.6093 48.6258 32.6341 32.6341 42.3846

100.00 64.40 37.40 9.61 14.19 19.47 8.35 2.78 7.23

8 12 24 6 24 24 24 8 12

When the sample amount is smaller than ∼ 5 mg, it is difficult to obtain the necessary diffraction amplitude by XRD. Since the amount is enough for the TEM observation, only TEM observation may be applied to obtain the structure data. To obtain the information on the fundamental atomic arrangements, electron diffraction patterns should be taken along the various directions of the crystal, and the fundamental crystal system and lattice constants may be estimated. Then, HREM observation and composition analysis by EDX are performed, and the approximate atomic structure model is constructed. Most of the materials have similar structures to the known materials, and the structures will be estimated if the database on the known structures is available. For example, lots of new structures were found for high-Tc superconducting oxides, which have basic perovskite structures, and the approximate atomic structure models can be constructed from the HREM images, electron diffraction patterns, and composition analysis of the elements.

3.4 TEM observation

| 33

3.4 TEM observation Obtained TEM specimen with a disk shape 3 mm in diameter is set in the TEM sample holder. Side-entry and top-entry type sample holders are used. The top-entry type holder is set in the center of column, and is stable for high-resolution observation. However, the space is small around the holder, and difficult to attach analytical system. A part of the side-entry-type holder is outside the column, and it is necessary to be careful for the mechanical vibration. Analytical system such as EDX can be attached, and composition analysis and HREM observation can be performed simultaneously. TEM specimens are set in the sample holder, evacuated in the column, and irradiated with electron beams to form TEM images on the fluorescent screen (Figure 2.1).

220 020

022 111 002

002 000

000

[100]

[110]

022

220

111

202

022

000

000

[111]

[211]

131

131

131

002 000

[310] Fig. 3.3: Face-centered cubic (fcc) structure (Au, Al, Ag, Cu, etc.).

34 | 3 Practice of HREM The TEM specimen is set in the column, and electron beams are irradiated on the specimen. Electron beams are usually aligned and observed on the fluorescent screen, and electron beam alignment is sometimes necessary. Beam alignment can be adjusted to neutral position by computer for the recent electron microscope. TEM observation is performed on the fluorescent screen or computer monitor. Three basic observations are low magnification observation (5–100k magnifications), high-resolution structural observation (200k–1M magnifications) and electron diffraction pattern. If a structure of the TEM specimen is known, observation direction of the crystal should be selected, and electron diffraction pattern along the direction should be

011

020

110

112

000

011

000

002

[100]

[110] 121

110

121

011

002

101 000

000

[111]

[210]

130

000

132

002

[310] Fig. 3.4: Body-centered cubic (bcc) structure (Fe, Nb, W, etc.).

3.4 TEM observation

| 35

estimated. The electron diffraction patterns can be drawn by yourself or commercial software¹ from the structural data such as space group, lattice constants and atomic coordinates. Atomic structure models of basic materials and calculated electron diffraction patterns along the several basic directions are shown in Figures 3.3–3.7. Any regions selected by the selected area aperture can be observed in electron diffraction patterns, and the structure can be easily analyzed by comparing TEM images with electron diffraction patterns. When electron diffraction pattern is observed in the selected area, the diffraction pattern is often inclined from the aimed direction, which

022

004

220 111

022 000

000

[100]

[110]

220

004

022 111

131 022

000

202

[111]

000

[211]

260 131 131 133

000

004

[310] Fig. 3.5: Diamond structure (diamond, Si, Ge, etc.).

1 ex. www.totalresolution.com/ and www.crystalsoftcorp.com/

36 | 3 Practice of HREM

020

022 111 002 002

000

000 111

[100]

220

[110]

022 111

022

202 000

000

[111]

[211]

131

131

131

000

002

[310] Fig. 3.6: ZnS-type structure (ZnSe, GaAs, SiC, etc.).

is noticed from the asymmetry of the electron diffraction pattern. The sample holder can be usually tilted along two directions, and the specimen should be tilted as the diffraction pattern shows center symmetry. Control of the tilting is mandatory to take high-resolution electron microscope image in the atomic scale. After the tilting, the observation is changed from the diffraction mode to image mode. High-voltage alignment and astigmatism should be adjusted and corrected for high-resolution observation in the atomic scale. The control method is described in the TEM manual book, however, experience and practice are needed for the delicate control. After that, focus is adjusted for the high-resolution image. The high-resolution images are very sensitive to the TEM focus, and the details are described in the section of image condition of HREM image.

3.4 TEM observation

002 110

010

| 37

012 010

100

000

000

[001]

002

[100]

112

010

111

110 000

000

[110]

[101]

101

102

000

010

112

[201] Fig. 3.7: Hexagonal close-packed (hcp) structure (Ti, Mg, Zn, etc.).

Mechanical and electromagnetic vibrations should be careful during high-resolution observation. Mechanical vibrations are from trains, cars, vacuum pump, air conditioner, and human walking around the room. These vibrations should be avoided, and the high-resolution images sometimes should be observed during “midnight.” Moreover, the microscope column with a higher voltage than 300 kV vibrates even by human voice, and vibrations of atoms can be observed in the high-resolution images by the human voice.

38 | 3 Practice of HREM

3.5 HREM observation HREM images are phase contrast due to interference of electron waves, and direct information on atomic arrangements in crystals can be obtained. HREM images are sensitive to defocus values, crystal thickness, crystal tilting, and other parameters. HREM images of TlBa2 Ca3 Cu4 O11 superconductor which has the almost highest transition temperature of 123 K are shown in Figure 3.8 [1]. Although these three images were taken at the same magnification for the same sample, the image contrast is very different due to the imaging conditions. Figure 3.8 (a) is a one-dimensional lattice image taken perpendicular to the c-axis of the crystal by 200 kV TEM. Tl and Ba layers show dark contrast, and Ca layers together with oxygen vacancies (Ov) show white lines. Figure 3.8 (b) is a two-dimensional HREM image taken along the a-axis and perpendicular to the c-axis by 200 kV TEM. Although oxygen vacancy positions are imaged as bright dots due to dynamical diffraction effect, the image does not show the direct atomic arrangements. Figure 3.8 (c) is a structure image taken along the aaxis and perpendicular to the c-axis by 400 kV TEM. This HREM image is imaged by the interference of multielectron waves, and the potential in the crystal is clearly imaged. When the atomic arrangements of the superconducting oxides are discussed, structure images which show potential clearly in the crystal are needed, as shown in Figure 3.8 (c). On the other hand, lattice images like Figure 3.8 (a) and (b) are suitable for HREM observation in the unit cell scale such as defects, interface, and modulated structures. Necessary conditions to observe the structure images, which can be used to obtain information of crystal structures, are investigated by calculating high-resolution images with the multislice method. For the image calculations, a large-computer (ACOS2020) was used. Basic parameters used for the image calculations are as follows: accelerating voltage = 400 kV, radius of the objective aperture = 5.9 nm−1 , spherical aberration Cs = 1.0 mm, spread of focus 𝛥 = 8 nm, semiangle of convergence 𝛼 = 0.55 mrad, crystal thickness t = 1.9 nm, and defocus value of the objective lens 𝛥f = −49 nm (Scherzer defocus). Figure 3.9 (a) shows calculated images based on a structural model of TlBa2 Ca3 Cu4 O11 with the incident beam parallel to the a-axis. Structure parameters in the calculations were used with values determined by X-ray diffraction. In Figure 3.9 (a), the images calculated with various thicknesses under the Scherzer defocus condition (𝛥f = −45 nm) are shown, and the images of thinner crystals than 2 nm faithfully represent the projection of the crystal structure. The darkness or size of dark spots corresponding to Tl, Ba, Cu, and Ca positions can be identified to be nearly proportional to their atomic numbers. On the other hand, in the images of thicker than about 3 nm, the cation positions cannot be identified as dark spots. The calculations show that only images taken at nearly the Scherzer defocus (𝛥f = −45 nm) and from thinner crystals than 2 nm can be used for structure analysis. The structure images are formed by interference of many electron waves, and can be obtained for

3.5 HREM observation

Tl Ov

Ov

|

39

Tl

Tl O Cu Ca Ba

Tl

1 nm

(a)

1 nm

(b)

Tl

1 nm

(c)

Fig. 3.8: HREM images of TlBa2 Ca3 Cu4 O11 . (a) One-dimensional lattice image taken by 200 kV TEM. (b) Two-dimensional HREM image taken by 200 kV TEM. (c) Structure image taken by 400 kV TEM.

Tl O Cu Ca Ba

(a) t = 1.17

1.92

2.70

3.47 nm

Tl O Cu Ca Ba

(b) Df = 15

–15

–35

–55

–75 nm

Fig. 3.9: Calculated images of TlBa2 Ca3 Cu4 O11 with the a-axis incidence as functions of (a) crystal thickness (𝛥f = −45 nm) and (b) defocus value (t = 1.92 nm).

the thickness under the strongest wave show the maximum intensity. Thick regions in the specimen sometimes show periodic black and white contrasts, and can be used as lattice images for structure analysis.

40 | 3 Practice of HREM Another important factor for the structure image is defocus values of objective lens. As described in Section 2.2, the phase contrast shows no contrast when the focus of the objective lens is adjusted at the atomic position. A shift of the phases of the waves of transmitted and scattered electrons is just 𝜋, and the intensities of the waves are canceled and the image shows no phase contrast. When the focus is shifted to under the just focus, phase contrast can be observed by the phase difference of electron waves. From the various conditions of electron microscopes, structure image that the potential in the crystal are clearly projected can be theoretically calculated, and the defocus value is called Scherzer focus as indicated by the following equation: 𝜀s = 1.2Cs1/2 𝜆1/2

(Cs : spherical aberration coefficient, 𝜆: wavelength of electron)

When the accelerating voltage is 400 kV, the wavelength 𝜆 is 0.001644 nm. Then, the Scherzer focus 𝜀s is 48.7 nm for Cs = 1.0 mm. Actually, the defocus is shifted a little to just focus by the dynamical diffraction effect (crystal thickness effect), and observed materials and observation directions should also be considered. Figure 3.9 (b) shows HREM images of TlBa2 Ca3 Cu4 O11 calculated as a function of defocus value for a crystal thickness of 1.92 nm. A structure image clearly showing projected potential is obtained at the defocus of −35 nm. In Figure 3.9 (b), it is interesting to note that the image contrasts at 𝛥f = −75 and 15 nm are almost reversed to that of the Scherzer condition, and the cation positions appear as bright spots. Since these types of wrong images have been occasionally reported in some papers, one should keep it in mind. Other parameters are also needed for actual HREM observation as follows: – Perfect astigmatism correction: Magnetic lens are used for electron microscope, and the magnetic field is often out of center symmetry, which should be corrected. HREM images are affected by the astigmatism. – Electron beam incidence exactly along the crystal directions: When the crystal is tilted from the desired crystal axis, the exact projected images cannot be obtained. The specimen should be tilted by using electron diffraction pattern. Although commercial software for astigmatism correction, crystal tilting, and beam alignment to adjust are prepared, it is difficult for the observer to use it if he does not know the adjustment. Only HREM structure images obtained by keeping least beam irradiation, mechanical vibration, and other severe conditions can be used for crystal structure analysis.

3.6 Fourier filtering | 41

3.6 Fourier filtering If some methods for taking pictures are selected, the images are saved as digital image data in computers. Although digital image data sometimes can be used as is, the information for special purpose can be extracted by image processing. The Fourier filtering using Fourier and inverse Fourier transform is an effective method for removal of noise in the image. Commercial software such as DigitalMicrograph (Gatan; www.gatan.com/) can be obtained. An example of noise filtering by Fourier transform is shown in Figure 3.10. Figure 3.10 (a) shows an HREM image of (BiPb)2 Sr2 Ca2 Cu3 O10 [2], and an amorphous layer in 5 nm thickness is observed at the upper left side of the image, which is a surface damage layer by argon ion milling during the TEM specimen preparation. Although there seems to be the amorphous layer only at the upper left side, it is believed that there should be 5-nm-thick amorphous layers on both above or below the specimen in the present HREM image region, and therefore, clear HREM image cannot be obtained by the amorphous layers. Figure 3.10 (b) is a Fourier transform of Figure 3.10 (a). In addition to the fundamental diffraction spots, a diffuse noisy ring is observed, which is due to the amorphous layers produced by ion milling damage. Figure 3.10 (c) is a filtered Fourier transform of

0010

000

(a)

2 nm

220

(b)

0010

000

(c)

220

(d)

2 nm

Fig. 3.10: (a) HREM image of (BiPb)2 Sr2 Ca2 Cu3 O10 . (b) Fourier transform of (a). (c) Filtered image of (b). (d) Inverse Fourier transform of (c).

42 | 3 Practice of HREM Figure 3.10 (b). The diffuse noise was removed, and only fundamental diffraction spots are observed. Figure 3.10 (d) is an inverse Fourier transform of Figure 3.10 (c). The effect of the amorphous layer in the image was removed, and clear HREM image is obtained. The noise reduction by Fourier filtering is effective for the amorphous layer on the specimen as indicated above. Since fundamental reflections with high intensities are needed for the Fourier filtering, wide view and many numbers of the unit cell are mandatory.

3.7 Resolution of HREM images In Chapter 2, it is described that information on kinds, positions, and numbers of atoms can be obtained from the HREM images. The least distance that can be distinguished as each dot is called a point resolution (or point-to-point resolution). The point resolution is expressed as follows: d = 0.65Cs1/4 𝜆3/4 where Cs is the spherical aberration coefficient and 𝜆 is the wavelength of electron. When the accelerating voltage of the electron microscope is 1250 kV, the wavelength 𝜆 is 0.0007357 nm. If the Cs of the electron microscope is designed to be 1.65 mm, the point resolution d is calculated to be 0.104 nm. From this equation, it is effective for high-resolution to decrease the wavelength of electrons (i.e. to increase the accelerating voltage), in addition to the reduction of the Cs of electron microscope. When the accelerating voltage is high, the electron-beam transparency of the specimen increases. Then, clear images can be obtained even for the thick TEM specimen, which is applicable for three-dimensional observation. As described in Chapter 1, Cs corrected TEM are being used. A negative spherical to cancel positive Cs of the magnetic lenses of the microscope is produced by the Cs corrector, which achieves higher resolution TEM images. For actual electron microscopes, the resolution is lowered by chromatic aberration (Cc ) and divergence angle (𝛼) of incident electron beams. Cc is due to fluctuation of the electron-beam energy, which depends on the accelerating voltage of the electron microscope. The actual resolution of the electron microscope can be known by Fourier transform of the HREM images of amorphous thin films, etc. Although resolutions of SEM also depend on the accelerating voltages, the resolution also depends on the diameter of the electron beams. It is necessary to irradiate narrow, bright electron beams on the specimen during the SEM observation. HREM images are very sensitive to the defocus values, and suitable images can be obtained only for a narrow focus range. On the other hand, the SEM has deep focal depth, and the suitable image focus can be obtained for wide three-dimensional region, which is effective for threedimensional observation of the surface.

3.8 Prevention of damage and contamination

| 43

3.8 Prevention of damage and contamination Electron beam damage should be cared, which depends on specimens and electron microscopes. In spite of inorganic materials, zeolite, fullerene, and nanotubes are very sensitive to electron beams, and the structures change into amorphous structure even for the weak beams. Although the characteristic of the sample cannot be changed, the specimen damage sometimes depends on the sample preparation method. For example, superconducting oxides prepared by crushing are more stable than those by ion milling, which would be due to the damaged layers at the surface for the ion milled samples. The electron beam damage of the specimen also strongly depends on accelerating voltage and current density of the electron microscopes. When the accelerating voltage and current density are higher, the specimen is easily damaged. The accelerating voltage of the microscope is usually fixed, and the current density is the most important problem. Reduction of current density by spreading the electron beams during observation. In addition, expansion of electron beams increases the resolution for high-resolution observation. When the electron beams are too spread, the TEM view becomes too dark to observe the specimen, and “image drift” is observed because of the long exposure during taking the images. The most suitable exposure time is 1–4 s for negative films, and 0.1 s is also possible for imaging plates which are sensitive to the electron beams and have high linearity to electron beam intensity. When the exposure time is too short, background noise increases, and the “feeling” for suitable exposure time should be accustomed by taking many images. It should be dark during observation, and be bright for taking images by focusing the electron beams. It is important to take images as fast as possible avoiding the electron beam irradiation. Some specimens sensitive to the electron beams are damaged even in a second. When the region is selected to take images, the specimen sometimes drift mechanically because of the specimen holder, and several minutes are necessary for stability avoiding the electron beam irradiation. After stopping the specimen drift, images should be taken as soon as possible. The specimen drift depends on the sample holder and the maker of the electron microscopes. Since TEM observation of life and organic materials is difficult because of the electron beam damage, the specimen should be cooled down to liquid nitrogen or helium temperatures to avoid the damage. Commercial cooling TEM holders can be also used. Another problem is contamination of the specimen during observation, which is due to low vacuum of ∼ 10−4 Pa in the column of the electron microscope. When the electron beams are irradiated under the low vacuum, molecules in atmosphere form amorphous at the surface of the specimen, which affects the high-resolution observation. High vacuum should be kept by using liquid nitrogen trap.

44 | 3 Practice of HREM

3.9 Taking images and reading data To take TEM images and electron diffraction patterns, negative films, imaging plates (www.fujifilm.com/), TV camera and slow scan charge coupled device CCD camera (www.gatan.com/). The methods with various characteristics should be selected for the purpose. Digitalization of TEM camera is recently in progress, which is similar to the commercial digital cameras. It is easy to use digital methods for experiments on ordinary TEM images and electron diffraction patterns. Negative films with minute black and white contrast may be also used for HREM observation to take images in atomic scale. If the negative films are used, the data are digitalized by film scanners. Five to 10 negative films are needed for a through focus method adjusting the focus values, and the best films with the best focus should be selected from them. Suitable exposure time is usually shown on the TEM operating panel. Although pixels of imaging plates and slow-scan CCD camera are ∼ 24 μm, pixels of negative films using AgCl or AgBr are ∼ 0.3 μm, which are suitable for higher resolution imaging. However, the dynamic range of films is narrow, and development of films in a dark room is needed. Quality of the films depends on the development such as temperature and time. A standard order is as follows: development of films (5 min, 20°C), stopping (1 min), fixing (10 min), and washing (30 min). When the films are dried, it should be cared to avoid water drops using drywell. Stirring the solutions and flesh solutions are also needed for the development. Imaging plates can be used to record a two-dimensional image of the intensity short-wavelength electromagnetic radiations (X-ray and electron beams). The imaging plates are plastic plates coated with luminescence materials such as BaF(BrI):Eu2+ , and used in the same way as films in the film holder. The imaging plates can be used under the bright, and handling is easier. The dynamic range is very wide, and weak electron beams can be detected, which is suitable for easily damaged samples. In addition, electron intensity of the data has linearity, which is very effective quantitative analysis of TEM images and electron diffraction patterns. After taking images, the data are read by using laser beams and saved in computers. The imaging plates can be reused by irradiating strong light. Slow-scan CCD camera is a semiconductor recording device in which electron beam intensity is converted into light by yttrium aluminum garnet scintillator. Although the slow-scan CCD camera has almost the same resolution, sensitivity and linearity, obtained data are directly observed during the TEM observation. For films and imaging plates, the aimed data can be confirmed by developing or reading data after taking images. On the other hand, aimed data can be taken during the observation until the necessary data are obtained for the slow-scan CCD camera. Since the function of slow-scan CCD camera is out of order by strong beam irradiation during observation, it should be careful to take electron diffraction patterns. The digital recording media is useful for free when the apparatus is first set. Note that recent camera needs huge data storage.

Bibliography

| 45

3.10 Mental attitude for TEM It is also important to summarize and express the obtained data. For obtained data under the hardship, sometimes there are troubles such as small dust on the film, weak black and white contrast, too small magnification, and little obliquely. Although these are personal feeling of art, it may be better to make the data be clear for everyone to understand. Some people say, “Although it is difficult to see, there is one thing here!” Audiences and readers cannot see it, and it is not at all persuasive. It is necessary to present the clear data for the audiences and readers. The contrived data make an appeal to them, even if the data are completely same. The results also strongly depend on the experimental attitudes. Sometimes hundreds of images are taken only for one view, and only a few data can be used for presentation. The best image is severely selected from hundreds of images by adjusting the imaging conditions. The obtained data contain much information as it is, and more information can be extracted by image processing. The image analysis will be described in Chapter 4.

Bibliography [1] Oku T, High-resolution electron microscopy and electron diffraction of perovskite-type superconducting copper oxides. Nanotechnol. Rev. 2014, 3, in press. Available online: http://www.degruyter.com/view/j/ntrev.ahead-of-print/ntrev-2014-0003/ntrev-2014-0003.xml [2] Bruneel E, Oku T, Penneman G, Van Driessche I, Hoste S. Origin of the nanocrystalline interface in superconducting Bi-2223/Ag composites: a SEM/HREM study, Supercond. Sci. Technol. 2004, 17, 750–755.

4 Characterization by HREM 4.1 What information can be obtained? As described in the previous chapter, TEM samples are prepared with hardship, and then HREM data are obtained with various efforts. Although the experiments of HREM observation were finished, the structural analysis will just start. It is most important to obtain and extract information from the HREM data. Recently, several companies supply TEM photographs by their technique with a charge. Sometimes, it is a good idea to ask the professional companies to prepare the TEM samples and take TEM images by paying. If we ask the professional companies, the money, effort, and time can be saved, comparing with the money, effort, and time to purchase an electron microscope, to educate good TEM operators, and to obtain the perfect TEM data. However, it should be noted that detailed circumstances for the TEM data are sometimes unknown, when only the TEM data are obtained. For example, the temperature increase during the TEM specimen preparation, damage by ion milling, observation region, defocus of objective lens, inclination of electron beam, electron beam damage, and others should be cared. If the TEM data are taken by oneself or professional operators, extraction of structural information is the most important. To obtain the information, basic principles of electron microscopes, image processing, image calculation and other techniques are useful for the structural analysis. In this chapter, techniques to extract and obtain the atomic arrangement from the HREM images will be described.

4.2 Direct atomic observation Present electron microscopes have enough resolutions to observe atomic columns in simple crystal structures. Therefore, high-Tc superconductors based on the perovskite-type structure are suitable subjects for HREM, and a number of high-resolution studies of these materials have been carried out. Figure 4.1 (a) is an HREM image of TlBa2 Ca3 Cu4 O11 taken with the incident beam parallel to the a-axis together with a structure model, and the upper right side is the crystal edge. Figure 4.1 (b) is an HREM image modified by Fourier transform and crystallographic image processing. In Figure 4.1, the images of crystals thinner than ca. 2 nm faithfully represent the projection of the crystal structure. The darkness and size of dark spots corresponding to Tl, Ba, Cu, and Ca positions can be identified to be nearly proportional to their atomic numbers [1]. This type of high-resolution image is called structure images. However, in images thicker than about 3 nm, the cation positions cannot be identified as dark spots. Image calculations showed that only images taken at nearly the Scherzer defocus and from crystals thinner than 2 nm can be used for the structure analysis for high-Tc superconducting oxides.

4.2 Direct atomic observation

| 47

c a

2 nm

(a) Tl Ba Cu Ca

Tl

Tl O

Ba Cu

Ca

Cu

Ov Cu

Ca

Ov O

Ov Cu

Ba Tl

Ov O

Ov

Ca Cu

O O

Cu Cu

Cu

Ov O

O Tl

O

O

O O

c a

0.5 nm

(b) Fig. 4.1: (a) HREM image of TlBa2 Ca3 Cu4 O11 taken with the incident beam parallel to the a-axis. (b) HREM image after crystallographic image processing of (a), together with a structure model of TlBa2 Ca3 Cu4 O11 . Ov corresponds to oxygen vacant positions.

48 | 4 Characterization by HREM The dark spot positions corresponding to the cations in the structure images of Figure 4.1 (b) faithfully reflect their real atomic positions. The atomic coordinates of cations measured from the dark spot positions in Figure 4.1 are listed in Table 4.1, in comparison with the atomic coordinates determined by X-ray diffraction (XRD) [2]. As seen in Table 4.1, the dark spot positions in the observed structure image reflect the real positions of cations within an error of 0.01 nm, which may be within a measured error. This result shows that the cation positions can be determined with the precision of 0.01 nm from the structure images. Although oxygen atoms are not represented as dark spots in Figure 4.1 (b), the information on the oxygen atomic positions is contained in the structure image. It was also found that the observed images have valuable information not only on accurate coordinates of the cations but also on ordered arrangements of oxygen vacancies, as indicated by Ov in Figure 4.1 (b). The Tl-based superconductors have many types of layered structures with slightly different compositions, and the crystals often include intergrowth with various types of layered structures in addition to a well-ordered region. A typical example of such disordered region is shown in Figure 4.2, which is a structure image of the intergrowth of single and double Tl layers and various numbers of Cu–O layers. The upper and lower rectangles correspond to TlBa2 Ca3 Cu4 O11 and Tl2 Ba2 Ca3 Cu4 O12 , respectively. Figure 4.2 shows the 3-, 4-, and 5-fold Cu sequences between the Ba layers. In addition to the intergrowth of different numbers of Cu–O layers, an intergrowth structure with different numbers of Tl–O layers was observed in Figure 4.2. The various structures give rise to different transition temperatures Tc , and thus, steps or a tail in the resistivitytemperature curve was observed [3]. From the above comparison, it can be concluded that one can determine not only arrangements of cations but also accurate coordinates of cations from high-resolution images taken under severe experimental conditions. Unfortunately, oxygen atoms cannot be represented as dark spots in structure images taken with the present microscope. However, information on oxygen atom positions is contained in the structure images. Figure 4.3 has calculated images of TlBa2 Ca3 Cu4 Ox . Two types of models with oxygen vacancies and with oxygen atoms on the Ca layers are shown in Figure 4.3 (a) and (b), respectively. Image calculations were performed under the condition of a deTable 4.1: Structural parameters of cations in TlBa2 Ca3 Cu4 O11 , measured from the HREM images and X-ray diffraction (XRD) [2]. Space group P4/mmm. a = 0.3848 nm. c = 1.908 nm.

Tl Ba Cu Cu Ca Ca

x

y

z (HREM)

z (XRD)

0.0 0.5 0.0 0.0 0.5 0.5

0.0 0.5 0.0 0.0 0.5 0.5

0.0 0.140 0.245 0.413 0.330 0.5

0.0 0.147 0.250 0.417 0.334 0.5

4.2 Direct atomic observation

|

49

Tl1 Cu4 Tl1 Cu4 Tl1 Cu5

Tl2 Cu3 Tl2 Cu3 Tl2 Cu3 Tl2

1 nm

Fig. 4.2: Structure image of intergrowth of single and double Tl layers and various numbers of Cu–O layers. Upper and lower rectangles are TlBa2 Ca3 Cu4 O11 and Tl2 Ba2 Ca3 Cu4 O12 , respectively.

focus value of −45 nm and crystal thickness of 1.92 nm. Intensity profiles along the lines through Tl and Cu atoms parallel to the c-axis, are also shown at the right side of the calculated images. By comparing Figure 4.3 (a) and (b), one can notice that the oxygen vacant positions indicated by Ov show brighter contrast than the oxygen positions, and the intensity of the vacant positions shows higher peaks in the intensity profile. Another example to recognize the oxygen vacant positions from the structure images is shown in Figure 4.3 (c) and (d). Two models of TlBa2 Ca3 Cu4 Ox with oxygen atoms and with oxygen vacancies on the Tl layers, and their calculated images are shown in Figure 4.3 (c) and (d), respectively. Intensity profiles along the lines through Ba and Ca atoms are also shown at the right side of the calculated images. In the calculated image, the oxygen positions indicated by O in Figure 4.3 (c) show darker contrast than the oxygen vacant positions indicated by Ov in Figure 4.3 (d), and its intensity profile shows a small hollow at the oxygen position. The calculations above show that the ordered arrangements of oxygen atoms and oxygen vacancies can determined

50 | 4 Characterization by HREM

OV OV OV

Intensity

Tl O Cu Ca Ba

OV OV

1 Cu Cu

Cu Cu

Tl

0 c-axis (a)

Intensity

Tl O Cu Ca Ba

1 Cu Cu

Cu Cu

Tl

0 c-axis (b)

O

Intensity

Tl O Cu Ca Ba

1 O Ca Ca

Ba

Ba

Ca Ca

Ba

Ca Ca

0

O

c-axis

(c)

Ba

OV Intensity

Tl O Cu Ca

1 Ca Ca

Ba

0 c-axis (d) Fig. 4.3: Models and calculated images of TlBa2 Ca3 Cu4 O11 with oxygen vacancies on the Ca layers (a), and those of TlBa2 Ca3 Cu4 O14 with oxygen atoms on the Ca layers (b). Intensity profiles along the lines through Tl and Cu atoms parallel to the c-axis are also shown at the right side. Models and calculated images of TlBa2 Ca3 Cu4 O11 with oxygen vacancies on the Tl layers (c), and those of TlBa2 Ca3 Cu4 O10 with oxygen vacancies on the Tl layers (d). Intensity profiles along the lines through Ba and Ca atoms parallel to the c-axis are also shown at right side.

4.3 Crystallographic image processing

| 51

from the close examination of contrast of bright regions in the high-resolution structure images. In order to confirm the above results of image calculations, an observed structure image of TlBa2 Ca3 Cu4 O11 in Figure 4.1 (b) is examined. The observed image shows a good correspondence to the calculated image in Figure 4.3 (t = 1.92 nm, 𝛥f = −35 ∼ −45 nm). The darkness or size of dark spots corresponding to Tl, Ba, Cu, and Ca positions can be identified to be nearly proportional to their atomic numbers. In addition, positions of the dark spots corresponding to cations faithfully reflect the coordinates of the cations, determined with X-ray diffraction (Table 4.1). In the observed image, the oxygen vacant positions indicated by asterisks show brighter contrast than the other bright regions corresponding to oxygen positions. Therefore, the image clearly shows the existence of ordering of oxygen vacancies on the Ca layers. In addition, the positions between adjacent Tl atoms show darker contrast than the other oxygen positions, showing the existence of oxygen atoms on the Tl layers, as shown in the calculated image in Figure 4.3.

4.3 Crystallographic image processing Crystallographic image processing is an image processing technique with a higher level. As described above, HREM images strongly depend on various parameters such as defocus values, crystal thickness, and tilting of crystal, and the HREM images often do not agree with the true projected structure. To obtain HREM images with true projected structures, the projection direction should be adjusted precisely. The crystal should also be as thin as possible to satisfy the weak-phase-objective approximation. In addition, the objective lens should be adjusted to be Scherzer focus. When all of these conditions are satisfied, all information within the point resolution limit is transferred to the exact image contrast. Here, only the thin crystal satisfying the weakphase-objective approximation should be considered, and the crystallographic image processing will be described. To clarify the crystallographic structure, both the intensities and phases of the crystal structure factors are needed. Diffraction data obtained by X-ray, neutron, and electron diffraction contain only the intensity of the structure factor, which is the square of amplitude, and the phase information was lost. Fortunately, the phase information is included in the HREM image, and both the intensities and phases of the crystal structure factors can be directly obtained from the HREM images. For example, SEMPER (Synoptics) and CRISP (Calidris) can be used as software for crystallographic image processing based on the space group [4–6]. After Fourier transform of the original image, the phase information of each diffraction spot is extracted from lattice point of Fourier diffractogram. The intensities are obtained as sum of the diffracted spots (ex. sum of 3 × 3 pixels). Although the inverse Fourier transform calculated from all phases and intensities of diffraction spots

52 | 4 Characterization by HREM shows lattice-averaged image, the image is distorted by various distortion such as crystal tilting, electron beam tilting, and multiple scattering. To remove the distortions, the symmetry relation of phases and intensities extracted from the HREM image is corrected by applying the space group. There are 230 space groups in three-dimensional structures, and there are only 17 plane groups when the structure is projected two dimensionally. The phase information extracted from the HREM image is compared with the 17 plane groups, and the applicable plane group can be determined by selecting the agreed symmetry with the lowest averaged phase errors. Experimentally obtained phases are often in the range of 0–𝜋, and the phases of reflections can be corrected as 0 or 𝜋 when the appropriate plane group is applied. The intensities of the reflections are also corrected to satisfy the selected plane group. The inverse Fourier transform of these results is shown in Figure 4.4, which is a HREM image of (BiPb)2 Sr2 Ca2 Cu3 O10 after the crystallographic image processing [7].

Cu Cu Ca Cu Cu Sr Bi Bi

Ov

Bi Sr

Sr Cu Ca Ca Cu Ca Ca Cu Sr Sr Bi Bi Sr Cu Cu Ca Cu Cu

Ov

Bi

Ov

c 1 nm [110]

Fig. 4.4: HREM image of (Bi,Pb)2 Sr2 Ca2 Cu3 O10 . A structure model is inserted and oxygen vacancies are indicated by Ov . An overlay of a simulated image based on the structure model is enclosed by a white square.

4.4 Comparison of HREM image with calculated images

| 53

The HREM image clearly shows the metal atom arrangements in the crystal and the lines indicate the unit cell. The shading and size of the black spots corresponding to (Bi, Pb), Sr, Cu, and Ca positions can be identified as being nearly proportional to their atomic numbers. Although oxygen atoms are not represented as dark spots in Figure 4.4, information on the oxygen positions should be included in the image. In the Ca layers, oxygen positions indicated by Ov show a brighter contrast than the other white regions, which indicates the existence of an ordering of oxygen vacancies in the (Bi, Pb) layers. A structure model of Bi(Pb)-2223 determined by X-ray diffraction is inserted into Figure 4.4 and agrees well with the arrangements of the black dots.

4.4 Comparison of HREM image with calculated images HREM simulation is mandatory for HREM image analysis. Several calculated images have already been shown, and an example of comparison of a HREM image with simulated images. To investigate the observed HREM image in detail, HREM images were calculated based on the structure model for Bi-2223. Figure 4.5 shows calculated HREM ̄ direction. Image calculations were carried out for images for Bi-2223 along the [110]

1.2

Thickness [nm]

2.4

3.6

4.8

–10

–20

–30

–40

–50

–60

–70

–80

–90

Defocus [nm] Fig. 4.5: Calculated image of Bi2 Sr2 Ca2 Cu3 O10 as functions of crystal thickness and defocus values of the TEM objective lens.

54 | 4 Characterization by HREM various defocus values (under defocus) and crystal thickness to determine the imaging conditions of the observed images. The contrast changes of the images are very sensitive to both defocus value and crystal thickness, and (Bi, Pb) double layers are observed as dark dots around the defocus value of −30 nm. The simulation image calculated at the defocus value of −30 nm and crystal thickness of 2.7 nm inserted into Figure 4.4 and agrees well with the observed HREM image.

4.5 Atomic coordinates from HREM image Bulk samples of Tl-based copper oxides were prepared by reacting Tl2 O3 , CaO, BaO2 , CuO, and BaCuO2 [1, 8, 9]. The samples of Tl2 Ba2 CuO6 and TlBa2 CaCu2 O7 were reheated in the range 500–850°C, and then quenched in liquid nitrogen in order to control the oxygen content. The Tl2 Ba2 CuO6 , Tl2 Ba2 CaCu2 O8 , and TlBa2 CaCu2 O7 samples showed the superconductivity at transition temperatures. Samples for high-resolution observation were prepared by dispersing crushed materials on holey carbon films. Figure 4.6 (a) and (b) are high-resolution structure images of Tl2 Ba2 CuO6 (Tc = 80 K) taken with the incident beam parallel to the [100] and [110] directions, respect-

2 nm

2 nm

(a)

(b)

Cu Ba Tl Ba Cu

Cu Ba Tl Ba Cu

1 nm (c)

1 nm (d)

Fig. 4.6: High-resolution structure images of Tl2 Ba2 CuO6 (Tc = 80 K) taken with the incident beam parallel to the (a) [100] and (b) [110] directions. (c, d) HREM images after crystallographic image processing of (a) and (b), respectively.

4.5 Atomic coordinates from HREM image

|

55

Table 4.2: Structural parameters (z coordinates) of cations in Tl2 Ba2 CuO6 determined from the structure images of Figure 4.6, and diffraction methods. Tl2 Ba2 CuO6 Tl Ba Cu

z (HREM)

z (XRD) [10]

z (Neutron) [10]

0.206 0.084 0

0.20265 0.08301 0

0.2018 0.0822 0

ively. To observe the atomic arrangements clearly, a crystallographic image processing was carried out. The digital images were masked and fast Fourier transformed. The reciprocal lattice was indexed according to a unit cell, and the lattice parameters were determined using the positions of the strongest peaks in the analysis. The local background was subtracted, and the amplitudes and phases of the peaks were corrected using symmetrization [5, 6]. Before correcting the phases, the phase origin was determined by investigating the origin shift that gave the best accordance with the phase conditions for the two-dimensional plane group. Averaged symmetrized images were reconstructed from the corrected Fourier transforms. Crystallographic symmetrization based on the two-dimensional space group was used for the reconstruction of the Fourier transform, as shown in Figure 4.6 (c) and (d), respectively. Tl, Ba, and Cu atoms are clearly observed, and the darkness and size of the dark spots corresponding to the metal atom positions can be identified to be nearly proportional to their atomic numbers. In the images, a good correspondence between the arrangement of dark spots in the image and that of cations in the projected structure model proposed by X-ray diffraction is clearly observed. The larger black spots correspond to the Tl atoms and Ba atoms, and Cu and Ca atoms with smaller atomic numbers are represented as small dark spots. Oxygen atom positions are located on bright regions between the dark spots of the cations. In addition, positions of the dark spots corresponding to cations faithfully reflect the coordinates of the cations, determined with X-ray diffraction, as listed in Table 4.2. The z coordinates of cations, measured from the observed images, are listed in Table 4.2, together with values determined by diffraction methods [10]. Good correspondences between the z coordinates of cations determined from the observed high-resolution images and from diffraction methods. From Table 4.2, it can be seen that the dark spot positions in the structure images, reflect the real positions of cations within an error of 0.01 nm, which may be in a measured error. This result shows that the cation positions can be determined with the precision of 0.01 nm from the structure images. The oxygen vacant positions, which are located on the Ca layers, can be distinguished as brighter regions from the other bright regions corresponding to the oxygen sites.

56 | 4 Characterization by HREM

4.6 Combination of HREM and electron diffraction In this section, HREM imaging is described by referring to some of the compounds studied. Although HREM imaging is sensitive to many factors, the data presented here were obtained under optimum conditions of weak-phase object approximation [4, 11]. Ag2 SnO3 is a new compound with a modulated structure, whose crystals were prepared by a solid-state reaction of freshly prepared K2 Sn(OH)6 and Ag2 O at 430°C under an oxygen pressure of 35 MPa [12]. Electron diffraction patterns recorded along ̄ ̄ directions of the subcell of Ag2 SnO3 are shown in Figthe [001], [113], [010], and [110] ure 4.7 (a)–(d), respectively. Apart from the fundamental reflections, a large number of additional diffraction spots are observed in Figure 4.7 (b)–(d). Figure 4.7 (b) was recorded from the same region as Figure 4.7 (a) but after tilting (14.4°) [13]. Extra reflections appear around the fundamental reflections in Figure 4.7 (b) and are also visible in Figure 4.7 (c) and (d). Streaks were observed along the c∗ -axis in Figure 4.3 (c) and (d) because of stacking faults along the c-axis. In Figure 4.7 (c), the extra reflections are located with a separating distance of ∼ a∗ /6 along the a∗ direction, corresponding to a 3.1 nm period. However, the thirdorder satellites do not coincide. The modulation wave vector is determined as a∗ /6.4,

110

110

211

100 210 000 110

332

330

(a)

000

(b)

002

002 300

000

000

110

100

(c)

(d)

̄ ̄ direcFig. 4.7: Electron diffraction patterns recorded along (a) [001], (b) [113], (c) [010], and (d) [110] tions of Ag2 SnO3 . Indices according to cell determined by XRD.

4.6 Combination of HREM and electron diffraction

|

57

which indicates a disproportionately modulated structure. Figure 4.7 (b) also shows satellite reflections observed along the three directions. Figure 4.8 shows the HREM ̄ [113], ̄ and [001] directions [13]. HREM images of Ag2 SnO3 taken along the [010], [110], observations were performed with a 400 kV electron microscope (JEM-4000EX) with a resolution of 0.16 nm. The area of detection of a slow-scan CD camera (Gatan SSC model 694) is 1024 × 1024 pixels, with a pixel size of 24 × 24 μm, and the images were recorded at a magnification of 1 × 106 . For image processing of the recorded HREM images, Digital Micrograph (Gatan Inc., Pleasanton, CA, USA) and Semper (Synoptics Ltd., Cambridge, UK) software were used. Although the software had a normal Fourier transform function, crystallographic image processing and difference image calculation were carried out using original programs and manual operation. As a first step, the digital images were masked and fast Fourier transformed. The reciprocal lattice was indexed according to a 6-fold commensurate unit cell, and the lattice parameters were determined using the positions of the strongest peaks in the analysis. The local background was subtracted, and the amplitudes and phases of the peaks were corrected using symmetrization [4, 5]. Before correcting the phases, the phase origin was determined by investigating the origin shift that gave the best accordance with the phase conditions for the two-dimensional plane group. Averaged symmetrized images were reconstructed from the corrected Fourier transforms. The HREM images were calculated by the multislice method using MacTempas (Total Resolution, Berkeley, CA, USA) software and were compared with experimental images to verify the suggested model. The parameters used in the image calculations were as follows: accelerating voltage = 400 kV, radius of the objective aperture = 6.3 nm−1 , spherical aberration Cs = 1.0 mm, focus spread 𝛥 = 8 nm, and semiangle of convergence 𝛼 = 0.55 mrad. Structure models were also drawn using MacTempas and Crystal Kit (Total Resolution). Under optimal conditions, the atomic coordinates can be directly estimated from the HREM images. In Figure 4.4 (a) and (c), the large and small black dots correspond to tin and silver atoms, respectively. A sinusoidal displacement of the silver atoms along the hexagonal c-axis in both the tin oxide and the pure silver layers can be clearly observed. From this image, the coordinates of the silver atoms were directly estimated from the local image intensity minimum, and a model for the modulated structure was constructed (Figure 4.8 (e) and Table 4.3), in which the remaining Sn and O atoms were derived from the X-ray model [12]. Figure 4.8 (e) shows that a unit cell is orthorhombic with the cell parameters a = 6 ⋅ aH ⋅ cos 30° = 2.922 nm, b = cH = 1.267 nm, c = bH = 0.562 nm, where subscript H denotes the hexagonal subcell. From the relationships between the atomic coordinates of the superstructure model, the space group P21 21 21 could be derived. A list of atomic coordinates is given in Table 4.3. The atomic ratio of Ag/Sn was determined to be 2.1:1.0 by scanning electron microscopy with energy dispersive X-ray analysis, which is within the experimental error of the previous X-ray results. These results suggest that the modulation is not a compositional modulation but rather an atomic displacement modulation. In

58 | 4 Characterization by HREM

Ag Sn Ag Ag

b Sn Ag a

Ag

1 nm

(a)

Ag Sn

b

Ag

3 nm

Sn c

Ag 0.5 nm

(c)

(b) Sn Ag Ag Ag Sn Ag Ag Ag

Ag

c

a/2 (d)

O

b 0.5 nm

(e)

c a

̄ (c) [113], ̄ Fig. 4.8: HREM images of Ag2 SnO3 taken along the (a) [010], (b) [110], and (d) [001] directions. (e) Proposed model of the modulated structure.

4.6 Combination of HREM and electron diffraction

|

59

Table 4.3: Structural parameters for modulated structure of Ag2 SnO3 . Space group P21 21 21 , a = 2.922, b = 1.267, and c = 0.562 nm. All occupancy factors 1.0. B (isotropic displacement parameter) values for Ag(10–12) are a weighted average of the X-ray parameters. Atom Ag(1) Ag(2) Ag(3) Ag(4) Ag(5) Ag(6) Ag(7) Ag(8) Ag(9) Ag(10) Ag(11) Ag(12) Sn(1) Sn(2) Sn(3) Sn(4) Sn(5) Sn(6) O(1) O(2) O(3) O(4) O(5) O(6) O(7) O(8) O(9) O(10) O(11) O(12) O(13) O(14) O(15) O(16) O(17) O(18)

x

y

z

Occupancy

B (nm2 )

0.1667 0.3333 0.4457 0 0.0543 0.3877 0.2790 0.2210 0.1124 0.3889 0.2222 0.0556 0.3333 0 0.1667 0.2778 0.1111 0.4444 0.0557 0.3890 0.2223 0.2223 0.3891 0.0557 0.3248 0.1581 0.4915 0.2861 0.1195 0.4528 0.1582 0.3248 0.2861 0.4528 0.4915 0.1195

0.4925 0.0075 0.0140 0.4851 0.4860 0.0144 0.0026 0.4974 0.4886 0.2761 0.2239 0.1978 0.25 0.25 0.25 0.25 0.25 0.25 0.3379 0.3379 0.1621 0.3379 0.1621 0.1621 0.1621 0.3379 0.3379 0.3379 0.1621 0.1621 0.1621 0.3379 0.1621 0.3379 0.1621 0.3379

0.4241 0.5759 0.5871 0.9241 0.4130 0.0871 0.0871 0.9130 0.9130 0.75 0.25 0.75 0.25 0.25 0.75 0.75 0.25 0.25 0.3661 0.3661 0.6340 0.8661 0.1340 0.1340 0.5588 0.4413 0.4413 0.4427 0.5573 0.5573 0.0588 0.9413 0.0573 0.9427 0.0588 0.9427

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.031 0.031 0.031 0.031 0.031 0.031 0.031 0.031 0.031 0.030 0.030 0.030 0.017 0.017 0.017 0.014 0.014 0.014 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029

the present model, the sinusoidal displacements of silver atoms in the SnO2 and Ag layers have amplitudes along the c-axis of 0.0661 and 0.0189 nm, respectively [13]. The Ag atoms in the SnO2 layer occupy positions along the hexagonal c-axis, as revealed by the elongated electron density distribution in the X-ray results [12]. The minor displacements of Ag(1) found here could not be observed in the XRD.

60 | 4 Characterization by HREM Based on the suggested structure model, the electron diffraction patterns of the proposed model along four different directions were calculated, as shown in Figure 4.9. These directions correspond to those of Figure 4.7. In the calculated patterns in Figure 4.9 (b)–(d), the extra reflections due to the modulation of the structure are clearly observed. Extra reflections are not observed in Figure 4.9 (a) because the displacements of Ag atoms are only along the c-axis. The fundamental diffraction spots in the calculated and observed diffraction patterns agree well.

002

002 301 901 600

911 1800

1820

000

000 911

(a)

(b)

020 000

020

1820 1800

000

600

(c)

901

(d)

Ag Sn Ag

b Sn

Ag

a (e) ̄ Fig. 4.9: Calculated electron diffraction patterns along (a) [010], (b) [190], (c) [001], and (d) [109] directions of the superstructure of Ag2 SnO3 , based on the proposed structure model. (e) Simulated HREM image along [001] based on the proposed structure model of Figure 4.8 (e).

4.7 Quantitative HREM analysis with residual indices |

61

The calculated extra reflections due to the modulated structure also agree reasonably well with the experimental ones, with only minor discrepancies. The small difference for the satellite reflections in the diffraction patterns, recorded along [001] and [109], could be due to crystal thickness, stacking faults, and hexagonal twinning in the observed patterns. In Figure 4.7 (b) only, the three sets of extra reflections, which are due to the domain structure (Figure 4.8 (c)) along the three different directions, are simultaneously visible. The model corresponds to one of these directions, which resulted in extra reflections along only one direction in Figure 4.9 (b). The HREM images were also calculated along the [001] direction of the orthorhombic cell with a defocus value of −50 nm (optimum defocus) and a crystal thickness of 2.2 nm. The displacements of the Ag atoms in the SnO2 and Ag layers along the c-axis can be clearly observed. The simulated image of Figure 4.9 (e) agrees well with the experimental data of Figure 4.8 (a).

4.7 Quantitative HREM analysis with residual indices In this study, a slow-scan CCD camera with high linearity and electron sensitivity was used to record HREM images and electron diffraction patterns. Although ordinary negative films have no linearity for an electron beam, the digital data taken by the CCD camera can be used for quantitative analyses such as residual index and difference image calculations and detected intensities can be directly compared with calculated data. Figure 4.10 (a) is an HREM image (JEM-4000EX, 400 kV) of HgTlBa2 CuOx taken along the [100] direction. Darkness or sizes of dots corresponding to (Hg,Tl), Ba, and Cu positions can be identified as being nearly proportional to their atomic numbers [14]. Although oxygen atoms are not represented as dark spots in Figure 4.10 (a), information on the oxygen positions should be included in the image. In the (Hg,Tl) layers, oxygen positions indicated by Ov show a brighter contrast than those indicated by O. This result implies the existence of an ordering of oxygen vacancies in the (Hg,Tl) layers. Similar double-layer structures have been reported in PbBaSrCaCu3Ox and Pb(Ba,Sr)2 (Eu,Ce)2 Cu3 Ox , and these compounds have separated double-layer structures of (Pb–O)-(Cu–Ov ), as determined by HREM analysis (Ov = oxygen vacancy) [15]. This separated double-layer structure could not be observed by X-ray powder diffraction because of an alternate atomic arrangement in the double layers; it can be only observed by HREM analysis. From the above HREM results, the structure models for HgTlBa2 CuOx are constructed, as shown in Figure 4.10 (b) and (c). A structure model for HgTlBa2 CuO6 with a double layer of Hg and Tl atoms has been proposed in a previous work [16] and is shown in Figure 4.10 (b). In this study, a new model for HgTlBa2 CuO5 with an ordering of oxygen vacancies in the Hg layers is proposed, as shown in Figure 4.10 (c). In this model, the Hg and Tl layers are separated and the Hg atoms have straight bonding with two oxygen atoms, a reasonable coordination for

62 | 4 Characterization by HREM

Cu Ba

Cu

Cu Hg

Ba Hg

Hg

Hg

Hg Hg Tl Tl

O

Ba

Ba

O Hg Hg Tl Tl

Hg Tl Ba

Ba

Ba

Ba

Ba

Ba

Tl

Hg Hg Tl Tl

Ba

Ba

Ba Cu

Ba

Ba

Ba

Tl

Ba

Tl

Ba

Ba

O

Tl

Ba

Tl

Ba

Ba

Hg Tl

Hg

Ov

Hg

Cu

O Hg

Tl

Ov

Tl Ba

Hg

Cu Ba

Tl

Hg Hg Tl Tl

Ba

Ba

HgTlBa2CuO5

HgTlBa2CuO6

(b)

(c)

Cu

1 nm (a)

t = slices (1.542 nm) 0.26 HgTlBa2CuO6 HgTlBa2CuO5

2 0.24

Thickness [Slices]

4

RHREM

0.22

6

0.2

0.18 8 0.16 10 –10

(d)

–20

–30

–40

–50

Defocus values [nm]

–60

0.14 20 22 24 26 28 30 32 34 36 (e)

Defocus [nm]

Fig. 4.10: (a) HREM image of HgTlBa2 CuOx taken along the [100] direction. Black lines indicate unit cell. Structure models of (b) HgTlBa2 CuO5 and (c) HgTlBa2 CuO6 . (d) Calculated HREM images of HgTlBa2 CuO5 along the [100] direction. One slice is 0.386 nm. (e) RHREM values of observed HREM images as a function of defocus values.

Hg2+ cations [14]. The metal atom positions for HgTlBa2 CuO6 and HgTlBa2 CuO5 can be estimated from the observed HREM image as listed in Tables 4.4 and 4.5, respectively. The oxygen atom positions were assumed, and temperature factors were neglected.

4.7 Quantitative HREM analysis with residual indices

|

63

Table 4.4: Structural parameters used for image calculation of HgTlBa2 CuO6 . Space group I4/mmm. a = 0.3856 nm. c = 2.329 nm. Atom

x

y

z

Occupancy

Tl/Hg Ba Cu O(1) O(2) O(3)

0 0 0 0 0 0

0 0 0 0 0 0.5

0.201 0.413 0 0.299 0.117 0

0.5/0.5 1.0 1.0 1.0 1.0 1.0

Table 4.5: Structural parameters used for image calculation of HgTlBa2 CuO5 . Space group P4nc. a = 0.3856 nm. c = 2.329 nm. Atom

x

y

z

Occupancy

Hg Tl Ba(1) Ba(2) Cu O(1) O(2) O(3) O(3)

0.5 0 0.5 0 0 0.5 0.5 0 0

0.5 0 0.5 0 0 0.5 0.5 0 0.5

0.299 0.201 0.087 0.413 0 0.201 0.383 0.117 0

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

To investigate the observed HREM image in detail, HREM images were calculated based on the structure models for HgTlBa2 CuO6 and HgTlBa2 CuO5 . Figure 4.10 (d) are calculated HREM images for HgTlBa2 CuO5 along the [100] direction. Image calculations were carried out for various defocus values (under defocus) and crystal thickness to determine the imaging conditions of the observed images [17]. The contrast changes of the images are very sensitive to both defocus value and crystal thickness, and (Hg,Tl) double layers are observed as dark dots around the defocus value of 30 nm. The Hg layers show brighter contrast compared with Tl layers. To compare quantitatively the observed image of HgTlBa2 CuOx of Figure 4.10 (a) with the calculated images of Figure 4.10 (d), residual indices (RHREM = 𝛴|Iobs − Ical |/𝛴Iobs ) [18, 19] were calculated, as shown in Figure 4.8 (e). The minimum RHREM values of 0.153 and 0.177 were obtained at a defocus of 26 nm for HgTlBa2 CuO5 and HgTlBa2 CuO6 , respectively. This result indicates that the stability of the (Hg,Tl) double-layer structure is due to the formation of oxygen vacancies in the Hg layers. The present result indicates that the local atomic arrangement with light element oxygen can be determined by a combination of HREM and RHREM values. In this study, a residual index between the observed and the calculated images was used because of the simple form and the usefulness in the determination of de-

64 | 4 Characterization by HREM focus values and crystal thickness. The crystal structure of high-Tc superconductor of Tl2 Ba2 CuO6 was investigated by these RHREM values, and the Tl occupancy was determined after the determination of the crystal thickness and defocus values of the observed images. To analyze more clearly, through-focus imaging would be useful. In addition to the present RHREM values, various methods for the estimation of image agreement between experimental and simulated images exist, such as fractional mean absolute difference [18], cross-correlation function [20], mean relative difference [20], normalized Euclidean distance [21], and nonlinear least-square methods [22]. These are useful methods for structural evaluation by image matching. In this work, the observed image was fixed after processing in order to get information on the effects of thickness in the calculated images. It is believed that more accurate atomic positions can be determined by combining these RHREM values with the observed HREM images recorded under optimum experimental conditions with quantitative devices.

4.8 Detection of atomic disordering by difference image Recently, high-quality YB56 single crystals have been synthesized for use as high-resolution and synchrotron radiation-resistant monochromators. The YB56 has yttrium site occupancies of 0.575 from a single XRD [23], which suggests a peanut-shaped “Y-hole” (a pair of yttrium atoms). In actual local arrangement, a correction of the Y atom occupancy appears necessary [24]. Here, the information for the disordering of the atomic arrangements in YB56 was obtained from digital HREM images. The [100] direction of the YB56 crystals was selected to obtain the structural image of the Y atom arrangements in YB56 . To get an optimal resolution (< 0.016 nm/pixel), the digital images were recorded at microscope magnifications of 1.0 × 106 (JEM-4000EX, 400 kV). The images were recorded close to the Scherzer defocus condition (−49 nm). To observe the atomic arrangements more clearly, a crystallographic image processing was carried out for the Fourier transform. The reciprocal lattice was indexed, and the lattice distances were estimated using the positions of the strongest peaks in the transform. The local background and reflections below the resolution limit (0.17 nm) were subtracted, and the amplitudes and phases of the peaks were determined. A total of 23 independent reflections were obtained. Before the correction of the phases, the phase origin was determined by investigating the origin shift that gave the best accordance with the phase conditions for the two-dimensional space group. The corrected phases refined using crystallographic symmetrization based on the two-dimensional space group of p4mm were used for the reconstruction of the Fourier transform. Figure 4.11 (a) is one-unit cell of the reconstructed experimental HREM image [34]. Y atoms are clearly observed as indicated by arrows. Double rings with dark contrast are observed at the center and the corners of the marked unit cell in the image. Square-like rings with dark contrast are also observed around the

4.8 Detection of atomic disordering by difference image

Y

| 65

Y

(a)

(b)

Y Y

Y

B24

(c)

(d) B

B24 B24 Y

(e)

Y

Y

(f )

Fig. 4.11: (a) Observed image, (b) calculated image, (c) difference image of (a) and (b), and (d) structure model of YB56 projected along the [100] direction. Structure model of (e) Y-B24 clusters (Y-holes with B24 clusters). (f) Three-dimensional projection of Y-B24 clusters.

yttrium atom positions. These ring contrasts are due to (B12 )13 and B80 boron clusters, respectively. To investigate this averaged YB56 structure, the HREM images were calculated on the basis of the structure model of YB56 determined by XRD [23]. HREM images calculated along the [100] direction are shown in Figure 4.9 (b). As the unit cell parameter of YB56 is large, 2.346 nm (1608 atoms per unit cell), the unit cell was divided into four subslices. The image calculations were carried out for the image size of 512 × 512 pixels

66 | 4 Characterization by HREM

1

2

Thickness [slices]

3

4

6

8

10

12 –10

–20

(a)

–30

–40

–50

–70

Df = –50 nm

t = 4 slices (2.3 nm)

0.5

0.3

0.4

0.25 RHREM

0.35

RHREM

0.6

0.3

0.2

0.2

0.15

0.1

0.1 10 20 30 40 50 60 70

(b)

–60

Defocus values [nm]

–Df [nm]

0 (c)

2

4

6

8

10 12

t [slices]

Fig. 4.12: (a) HREM images of YB56 calculated along the [100] direction. One slice is 0.586 nm. RHREM values of [100] image as a function of (b) defocus value and (c) crystal thickness.

and an image depth of 0–255 gray scales. Calculations were carried out several times for the minimization of the RHREM values, as shown in Figure 4.12 (a). The cumulative distribution functions were also used to get the minimum RHREM values. The minimum

4.8 Detection of atomic disordering by difference image

| 67

RHREM value of 0.142 was obtained at a crystal thickness of four slices (2.346 nm) and defocus value of −50 nm, as shown in Figure 4.12 (b) and (c). Dark spots corresponding to the yttrium atom positions in the experimental images recorded at thin regions are weak compared with those of the calculated images. This result suggests that the yttrium atom is not fixed at only one position. The yttrium site occupancy of 0.575, which was determined by XRD, is merely a statistical value, and this implies that the “Y-hole” (the Y–Y pair with the shortest distance) should be occupied by only one yttrium atom. These results indicate that the alternating yttrium atom positions in the boron cluster from cell to cell. On the basis of this procedure, a local structural model for the Y-atom arrangement in YB56 has been proposed [24, 25]. The local Y atom arrangement was directly determined by digital HREM imaging. The boron atom, which has a fairly low atomic number (Z = 5) compared with the yttrium atom (Z = 39), still shows dark contrast in both observed and calculated HREM images. A differential image of Figure 4.11 (a) and (b) is shown in Figure 4.11 (c). The difference image is calculated as |Iobs − Ical | for each digital image pixel in the unit cell. Nonicosahedral B24 clusters around the Y-holes show white contrast, which indicates that the difference between the observed image (Figure 4.11 (a)) and the calculated image (Figure 4.11 (b)) is large at these positions. The supericosahedra (B12 )13 do not show a large difference. The regions that show white contrast in the difference images indicate a large difference between the observed and the calculated images on the basis of the X-ray data. A structure model of the Y-B24 clusters (Y-holes with B24 clusters) projected along the [100] direction is shown in Figure 4.11 (e). The perspective view of the Y-clusters is shown in Figure 4.9 (f). In a comparison of Figure 4.11 (e) and (f) with differential image (Figure 4.11 (d)), the positions with large difference of image intensity are the B24 clusters [26]. This result indicates the atomic arrangements of the Y-holes and nonicosahedral B24 clusters are disordered compared with that obtained by the X-ray data [27]. An HREM image of one unit cell, taken along [111], is shown in Figure 4.13 (a). Figure 4.13 (b) is a calculated image at a defocus of 45 nm and a crystal thickness of six slices (4.063 nm), which corresponds to a minimum RHREM value of 0.251. Along the [111] direction, the yttrium atom positions appear as dark spots in both the observed and the calculated images as indicated by arrows. The shortest distance of the yttrium atoms in the projected plane is 0.192 nm, which is clearly separated in both images. However, the darkness of the yttrium atom positions in the observed image of Figure 4.13 (a) is weaker compared with those in the calculated image of Figure 4.13 (b), and image calculations were carried out (Figure 4.14 (a)) to reduce the RHREM values on various defocus values and crystal thickness, as shown in Figure 4.14 (b) and (c). The supericosahedral (B12 )13 clusters appear dark in both Figure 4.13 (a) and (b), and the structure models of (B12 )13 clusters along the 3- and 5-fold axes are shown in Figure 4.13 (a) and (f), respectively. Figure 4.13 (c) is the difference image of Figure 4.13 (a) and (b). The yttrium atom positions and nonicosahedral B24 clusters (Figure 4.13 (e)) around the Y-holes show white contrast. This indicates the difference between the

68 | 4 Characterization by HREM

B156

(a)

B156

(b) Y

Y Y

B24

B

Y (c)

(d)

B

Y

B24

(e)

(f )

Fig. 4.13: (a) Observed HREM image, (b) simulated image, and (c) difference image of (a) and (b). Structure models of (d) YB56 and (e) Y-B24 clusters (Y-holes with nonicosahedral B24 clusters) projected along the [111] direction. (f) Structure model of supericosahedral (B12 )13 clusters projected along the 5-fold axis.

4.8 Detection of atomic disordering by difference image

| 69

1 2

Thickness [slices]

3 4 6 8 10 12 –10 (a)

–20

–30

–40

–50

–60

–70

Defocus values [nm] t = 6 slices (4.1 nm)

–Df = 45 nm 0.7

1 0.9

0.6 0.8 0.5 RHREM

RHREM

0.7 0.6

0.4

0.5 0.4

0.3 0.3 0.2

0.2 10 20 30 40 50 60 70 80

(b)

Defocus value [nm]

0 (c)

2

4

6

8

10 12

Thickness [slices]

Fig. 4.14: (a) HREM images of YB56 calculated along the [111] direction. One slice is 0.677 nm. RHREM values of [111] image as a function of (b) defocus value and (c) crystal thickness.

observed (Figure 4.13 (a)) and the calculated images (Figure 4.13 (b)) is large at these positions, which agree well with the results from the [100] observation. When the Yholes are formed, the cubic system would be destroyed locally around them. Although the B24 clusters have a 4-fold symmetry in the previous articles, another boron cluster should be proposed for a local structure model. However, it is difficult to determine directly the atomic arrangement of B around the Y-holes because of the low atomic number of boron. The B80 clusters around the Y-holes were proposed [23], which have the low occupancies (0.22–0.71) of boron atoms and large thermal parameters (0.017−0.058 nm2 ). In this boron cluster, the boron atoms of the B24 clusters have the

70 | 4 Characterization by HREM largest thermal parameter of 0.058 nm2 and a low occupancy of 0.64, which makes the determination more uncertain. In this work, the disordering of the boron atom positions was detected three dimensionally from the difference images. As there are various types of higher borides and fullerene compounds, this kind of disordering detection would be very useful for the evaluation of the disordering of light elements such as boron and carbon atoms.

4.9 Combination of diffraction amplitudes and phases The accurate atomic positions of the Y atoms in YB56 were determined by combining HREM imaging and electron diffraction [26]. Figure 4.15 (a) shows an HREM image of YB56 recorded along the [100] direction using the slow-scan CCD camera. The left side of the image is the thinnest region of the YB56 crystal. A unit cell of YB56 is indicated by white lines. The Fourier transform of Figure 4.15 (a) is shown in Figure 4.15 (b). An Table 4.6: Amplitudes and symmetrized phases of YB56 in Fourier transform derived by crystallographic image processing of HREM images, and amplitudes obtained from electron diffraction patterns. Plane group is p4mm. Indices hkl 020 040 060 080 0 10 0 0 12 0 220 240 260 280 2 10 0 2 12 0 440 460 480 4 10 0 4 12 0 660 680 6 10 0 6 12 0 880 8 10 0

Amplitudes and phases from Fourier transform 1199 5732 9249 3499 7116 1217 987 2768 562 931 258 166 2175 1028 1666 1071 398 957 2053 1122 82 1576 160

115 164 6 11 137 107 144 164 102 54 47 22 16 145 157 128 93 123 134 144 83 43 120

Symmetrized phases 180 180 0 0 180 180 180 180 180 0 0 0 0 180 180 180 180 180 180 180 0 0 180

Diffraction amplitudes 1277 1485 1703 1530 1712 896 680 720 841 909 308 266 1304 418 480 722 308 978 1049 536 193 476 272

4.9 Combination of diffraction amplitudes and phases | 71

0 10 0

10 0 0 000

2 nm

(a)

(b)

0 10 0 10 0 0 000

PR Y

(e)

Y*

Y 0.5 nm

(d) Intensity (A.U.)

(c)

Y*

Y*

Y

Y 0.2470 nm X axis

Fig. 4.15: (a) HREM image of the thin part of the YB56 crystals taken along the [100] direction. (b) Fourier transform of (a). (c) Electron diffraction pattern of YB56 observed along the [100] direction. (d) HREM image of YB56 reconstructed with amplitudes from electron diffraction patterns of (c). (e) Line profile of image intensity of white line (PR) in (d).

open circle indicates the resolution limit of the electron microscope of 0.16 nm. Figure 4.15 (c) is an electron diffraction pattern of YB56 recorded along the [100] direction, and 72 independent reflections were obtained. The amplitudes corresponding to 0.08 nm were also estimated, indicating a higher resolution than that of the HREM image. An HREM image of YB56 reconstructed with amplitudes from electron diffraction patterns of Figure 4.15 (c) is shown in Figure 4.15 (d). The symmetrized and corrected phases given in Table 4.6 are used for the inverse Fourier transformation. Y atoms are clearly observed as indicated by arrows. A line profile (trace along PR) of the reconstructed image is shown in Figure 4.15 (e). The dis-

72 | 4 Characterization by HREM tance between the Y-holes (Y∗ ) was measured to be 0.2740 nm. The distance between the Y atoms as determined by single XRD is 0.2716 nm. The difference between these values, from the reconstructed HREM image (Figure 4.15 (d)) and by XRD, is ∼ 0.002 nm, an error < 1% (0.0024 nm), which is small for HREM image analysis. This result indicates that the combination of phases extracted from the HREM images, corrected based on the crystallographic image processing and amplitudes extracted from electron diffraction, is useful for the determination of the atomic positions of heavy atoms such as Y in clusters of the light elements of boron. This type of method enables us to determine accurate atomic positions (error < 1%) by combining HREM images and electron diffraction in nanoscale (< 20 nm) regions. Some other useful methods for structural determination have also been developed [28–30].

4.10 Structural optimization by molecular orbital calculation Carbon was formed from polyvinyl alcohol after annealing at 400°C in Ar [31, 32], and the carbon matrix was found to have an amorphous structure from the HREM image, as shown in Figure 4.16 (a). The amorphous carbon was irradiated by an electron beam under a beam current of 100 μA/cm2 at 1250 kV (ARM-1250). This beam current is ∼ 20 times higher compared with that of the ordinary observation by the electron microscope [33–35]. A graphitization of amorphous carbon is observed, which is confirmed by the lattice fringes of carbon layers with a spacing of ∼ 0.34 nm, as shown in Figure 4.16 (b). Figure 4.16 (c) is an HREM image of the tetrahedral carbon onion produced from that of Figure 4.16 (b). Through electron beam irradiation for 10 min on the onions of Figure 4.16 (b), a carbon onion with a tetrahedral structure was formed, as shown in Figure 4.16 (c). At the center of the onion, there would be a tetrahedral carbon cluster, and the basic arrangements of carbon atoms are shown in Figure 4.16 (d). Each vertex consists of a hexagonal ring (as indicated by star marks), and three pentagonal rings exist around the vertex along the edge. Other parts are formed only by hexagonal rings. The atomic structure model of C84 @C276 for the tetrahedral onion at the center is proposed, as shown in Figure 4.16 (e). The edge lengths of the C84 and C276 are 0.78 and 1.42 nm, respectively. The total energies of the C84 and C276 were calculated to be 196 and 32 kcal/mol, respectively. The total numbers (N) of carbon atoms represented by the equation: N = 12(n + 2)2 − 24 (n = 1, 2, . . .). The smallest tetrahedral onion in the HREM image in Figure 4.16 (c) agrees well with the proposed structure model of C84 @C276 , as shown in the simulated image of Figure 4.16 (f). The energy levels of the C84 cluster are calculated, as shown in Figure 4.16 (g). The obtained energy gap is ∼ 1.5 eV, which is a little lower compared with 1.7 eV of the C60 cluster. The formation of onion structure had been reported and discussed intensively. Ugarte [36] reported that the onions had a spherical shape, and Ru et al. [37] reported that the onions had some vertices and 10-fold (icosahedral) symmetry.

4.10 Structural optimization by molecular orbital calculation |

2 nm

73

1 nm

(a) (b) 1 nm

C168 (d)

(c)

10

5

0

–5

–10 C84@C276 (e)

(f )

–15 (g) Energy (eV)

Fig. 4.16: (a) HREM image of as-prepared amorphous carbon. (b) Two carbon onions produced from amorphous carbon (a) by electron-beam irradiation for 20 min. (c) Tetrahedral carbon onion produced from (b) by electron-beam irradiation for 30 min. (d) Basic atomic structure of tetrahedral onion (C168 ) (e) Proposed atomic structure model of C84 @C276 . (f) HREM simulation of C84 @C276 . (g) Energy levels of C84 .

74 | 4 Characterization by HREM From the theoretical calculation of the giant fullerene (onion structure), the icosahedral symmetry with 5-fold axes is stable and the icosahedral symmetry has also 3-fold axes (with 6-fold shape). Although the tetrahedral carbon onions had been calculated to be unstable compared with the spherical onions due to rigidity, the tetrahedral carbon onion was successfully produced during the high-energy electron irradiation on amorphous carbon at 1250 kV. Although a similar structure consisting of C264 @C660 @C1248 was found and calculated [38], the size of the present tetrahedral carbon onion is smaller compared with the previous work. The present HREM and structural optimization results indicate that the carbon onions have a new tetrahedral structure. There are two important theorems of the Euler rule and the isolated pentagon rule (IPR) in the formation of the fullerene. According to the Euler rule, even if closed fullerene size becomes larger, the number of pentagonal rings is always 12. Based on the IPR rule, pentagonal rings do not adjoin to others when the size becomes bigger than C60 . There are 24 structural isomers in C84 , and C84 D2 and C84 D2d , with a ratio of 2:1, are the main structural isomers. The first inner shell of the tetrahedral carbon onion is equivalent to the C84 Td structural isomer. The heat of formation of C84 D2 and C84 D2d by the PM3 calculation is 4046 and 4050 kJ/mol, respectively. This means that the “isolated” spherical structure is more stable than the “isolated” tetrahedral C84 Td structure (heat of formations, 4159 kJ/mol) and the Stone–Wales transformation would be introduced during the growth of C84 Td , satisfying the Euler and IPR rules. The position of the pentagonal ring can be moved by this transformation, keeping the fullerene size. Although this tetrahedral structure (C84 Td ) might transform into a spherical structure (C84 D2 and C84 D2d ), the energy barrier between them would prevent the transformation. The barrier would be the van der Waals force from the outside shell and distortion due to the collision of the two onions.

4.11 Three-dimensional high-resolution imaging To get three-dimensional atomic arrangements, three-dimensional HREM observations were carried out using a slow-scan CCD camera [39]. The [100], [110], and [111] directions of the YB56 crystals were selected to obtain the three-dimensional potential map of YB56 . Forty-six independent reflections were obtained from the three HREM images [40]. The corrected phases, refined using crystallographic symmetrization, were used for the reconstruction of the Fourier transforms. Figure 4.17 (a) and (b) shows the perspective view of YB56 and the three-dimensional HREM image of YB56 obtained by inverse Fourier transformation of three-dimensional phases and amplitudes, respectively, which were taken from the 46 independent reflections in three HREM images (JEM-4000EX, 400 kV) along [100], [110], and [111]. The color shading is on an arbitrary scale for clear mapping. Flowchart of image processing for threedimensional imaging is shown in Figure 4.18. This three-dimensional HREM image is

4.11 Three-dimensional high-resolution imaging

Y

| 75

B

(a)

(b)

Y

Y

(c)

Y

(d)

Y

Y

(e)

(f )

Fig. 4.17: (a) Perspective view of YB56 . (b) Three-dimensional HREM image of YB56 obtained by inverse Fourier transformation of three-dimensional phases and amplitudes. Projected images of the three-dimensional image along (c,d) 100 and (e,f) 111 of YB56 , with different image intensities.

different from conventional two-dimensional HREM images, and it shows the threedimensional potential map of the crystal [41]. The three-dimensional image of YB56 in Figure 4.17 (b) shows a complicated potential arrangement, which is due to the complexity of the YB56 structure. As the crystal thickness is thin enough (< ∼ 5 nm) to satisfy the conditions of the weak-phase objective approximation, the dynamical effect is weak, and the image directly shows the potential distribution in YB56 , and they will be useful for three-dimensional structure analyses in the nanoscale regions.

76 | 4 Characterization by HREM

HREM images along several axes

Fourier transform

2 D plane group Crystal symmetry

Extraction of amplitudes (| F |) & phases ( f ) F(hk) = | F(hk) | exp[i (hk)]

Crystallographic image processing (CIP)

Proposed atomic structure model Molecular orbital calculation

Df, Minimization of RHREM

Difference image Correction of contrast transfer funcion 씮 Dfs

3 D data of corrected amplitudes & phases

Inverse Fourier transform

Reconstructed 3D HREM image

I(xyz) = l/s ·⌺F(hkl)exp[–2pi(hx+ky+lz)] Fig. 4.18: Flowchart of image processing for three-dimensional imaging.

The potential is high at the Y-atom positions and low around the boron atoms in Figure 4.17 (b). The boron atoms still show the potential distribution in the observed three-dimensional potential map of YB56 . Figure 4.17 (c)–(f) is projected image of the three-dimensional image of Figure 4.17 (b) with different image intensities. In Figure 4.17 (c), higher potential positions are emphasized and all Y atom positions and a part of (B12 )13 clusters are observed. All boron clusters are also imaged in Figure 4.17 (d). Figure 4.17 (e) shows the clear positions for the Y and (B12 )13 clusters. Most of the structure determinations by HREM have been carried out based on two-dimensional data recorded along a short-unit cell axis. The atomic positions along the short axis were estimated from geometries and chemical compositions. This twodimensional method is not suitable for crystals with long-unit cell axes, such as borides. The pore structures in mesoporous materials were evaluated by a three-dimensional method [42], and the porosity was directly estimated from three-dimensional images in mesoscale. The atomic positions of oxygen and phosphorous were also evaluated by the three-dimensional imaging [43, 44]. In this work, a full three-dimensional reconstruction in the nanoscale was successfully carried out from the HREM images using crystallographic image processing. Using the HREM method, the atomic structures of BN nanomaterials consisting of light elements were also investigated, as described in following sections.

4.12 Detection of doping atoms in C60 solid clusters

| 77

4.12 Detection of doping atoms in C60 solid clusters The disordering of yttrium atoms in YB56 crystal and mercury atoms in HgTlBa2 CuOx have been investigated by HREM quantitatively in the previous sections. In these works, the doping atoms of yttrium in the boron clusters and the mercury atoms in the oxide were directly detected by using difference images and residual indices for image analysis. Therefore, this method for structure analysis would be very useful for the evaluation of the doping atoms in the higher borides, fullerene, and zeolite materials with light elements such as boron, carbon, and oxygen. The possibility of direct detection of doping atoms in the C60 solid clusters from calculated HREM images was investigated. Since the discovery of the C60 clusters, various types of doped C60 clusters have been discovered and investigated. Metallofullerenes which have atoms (such as La, Y, Sc, Li, Na, N, and other lanthanoid) inside the C60 , C74 , C82 , C84 , and other giant fullerenes, are expected as superatoms with various structures and physical properties. In addition, C60 solid clusters with doping atoms (such as K, Rb, Cs, Na, Ca, Sr, Ba, and Yb) at the interstitial (tetrahedral and octahedral) sites are intriguing for both scientific research and future device applications as high-TC superconductors. Although electron paramagnetic resonance, mass spectrometry, and X-ray diffraction have been used for structure analysis of these fullerene materials with doping atoms, these are indirect methods. In addition, for the most part, metallofullerene are very few quantity and/or thin films, which makes it difficult to determine the crystal structure with doping atoms by X-ray diffraction. It is difficult to estimate the doping atoms in the fullerene materials only from HREM images, and a quantitative method should be developed for detection of doping atoms in C60 . The purpose is to investigate possibility of direct detection of doping atoms in the C60 solid clusters from calculated HREM images. Light element nitrogen (N: Z = 7) and heavy element rubidium (Rb: Z = 37) were selected as doping atoms in this work. It was reported that nitrogen atoms were included at the center of the C60 clusters, which was detected by electron paramagnetic resonance [9]. It was also reported that Rb atoms were doped at the octahedral sites of C60 solid clusters, which were determined by X-ray diffraction. Based on the crystal structure of C60 solid clusters, difference images between C60 and doped C60 were calculated for image analysis by using residual indices. This work will indicate a guideline for structure analysis of fullerene materials with doping atoms. Atomic coordinates of the N@C60 and RbC60 used in the image calculation were reported in the previous paper [45–47]. Atomic coordinates of carbon were assumed to be same as that of RbC60 . It was also assumed that nitrogen atoms exist at the center of C60 , which was detected by electron paramagnetic resonance. Although the crystal structure of C60 is represented as tetragonal lattice, the lattice parameters are equivalent to the cubic lattice. The Rb atoms exist at the octahedral sites of body-centered orthorhombic lattice. In this work, residual indices were calculated as

78 | 4 Characterization by HREM RHREM = 𝛴|Idoped-C60 − IC60 |/𝛴Idoped-C60 , and residual indices of local peaks at the doping positions were also calculated as RHREM-Peak = |I(Peak)doped-C60 − I(Peak)C60 |/I(Peak)doped-C60 . Since the image intensity is normalized in the whole image, the RHREM values should be in the range of 0–1. On the other hand, RHREM-Peak values could be in the range of 0-infinite. Structure models of C60 , N@C60 , and RbC60 solid clusters projected along the [100] directions of body-centered orthorhombic cell are shown in Figure 4.19. Doping atoms of nitrogen and rubidium exist at the center of C60 clusters and octahedral sites of body-centered orthorhombic lattice, as observed in Figure 4.19. Based on these projected structure models, image calculations were carried out for various accelerating voltages at the Scherzer defocus to investigate the imaging condition of the doping atoms of nitrogen and rubidium. Figure 4.20 (a) is HREM images of C60 , N@C60 , and RbC60 calculated along the [100] direction of orthorhombic cell as a function of accelerating voltage of electron microscopes. Crystal thickness is two slices, which is 2.00 and 1.83 nm for N@C60 , and RbC60 , respectively. This indicates that two nitrogen and two rubidium atoms exist along the [100] direction. For the C60 crystal calculated at 200 kV, a HREM image of C60 cluster show circle-like contrast. The HREM images of C60 cluster show clearer contrast as the accelerating voltage increases up to 1250 kV. For the N@C60 crystal, the dark dot due to the nitrogen atoms could be recognized at the accelerating voltage of 1250 kV, although it is difficult to distinguish the nitrogen atoms at the accelerating voltage of 200 and 400 kV. For the RbC60 crystal, dark contrast is observed at the Rb positions, and clear dots corresponding to the Rb atoms are recognized at 1250 kV. Difference images of C60 /N@C60 and C60 /RbC60 , calculated along the [100] direction as a function of accelerating voltage are shown in Figure 4.20 (b). Atomic positions of nitrogen and rubidium show white contrast, which indicates the difference between the nondoped and doped C60 clusters is large at these positions. For both N@C60 and RbC60 crystals, doping atoms of nitrogen and rubidium are clearly recognized at the higher accelerating voltage of 1250 kV. Rubidium atoms could be more easily recognized compared to the nitrogen, which is due to the larger atomic number C60

N@C60

RbC60 Rb

C60

N

Fig. 4.19: Structure models of C60 , N@C60 , and RbC60 solid clusters projected along the [100] directions of the orthorhombic cell.

4.12 Detection of doping atoms in C60 solid clusters

| 79

of rubidium. As observed in Figure 4.20 (b), contrast change of the images is sensitive to the accelerating voltage of the electron microscope. To estimate the difference between the nondoped and doped C60 clusters quantitatively, RHREM values were calculated as a function of accelerating voltage of electron microscope, as shown in Figure 4.20 (c). The crystal thickness and the defocus value are fixed at two slices and Scherzer defocus, respectively. For N@C60 crystals, small increase of RHREM values is observed at 1250 kV. On the other hand, RHREM values are reduced down to 0.03 as the accelerating voltage increases for RbC60 crystals. Since the RHREM values are calculated for all pixels, effects of doping atoms should be weak. RbC60

N@C60

N@C60 Accelerating voltage [kV] 1250 400 200

Accelerating voltage [kV] 1250 400 200

C60 C60

(a)

N

N

Rb

C60 N

C60

Rb

N Rb

N Rb

(b) 1

0.07 0.06

RbC60

N@C60 RbC60

N@C60 RbC60 0.8

RHREM-Peak

RHREM

0.05 0.04 0.03

0.6

0.4

0.02 0.2 0.01 0 (c)

0 Accelerating voltage [kV]

(d)

Accelerating voltage [kV]

Fig. 4.20: (a) HREM images of C60 , N@C60 , and RbC60 calculated along the [100] direction of the orthorhombic cell as a function of accelerating voltage of electron microscopes. The crystal thickness is two slices. (b) Difference images of C60 /N@C60 and C60 /RbC60, calculated along the [100] direction as a function of accelerating voltage. Image depth of 0–63 gray scale. (c) RHREM and (d) RHREM-Peak values of N@C60 and RbC60 as a function of accelerating voltage. The crystal thickness is two slices.

80 | 4 Characterization by HREM In order to detect the doping atoms more effectively, residual indices of local peaks at the doping positions were also calculated as shown in Figure 4.20 (d). Both clusters show higher RHREM-Peak values are observed compared to those of the ordinary RHREM values in Figure 4.20 (c). Highest RHREM-Peak values of 0.43 and 0.77 are obtained for N@C60 and RbC60 , respectively. Figure 4.21 (a) is HREM images of C60 , N@C60 , and RbC60 calculated as a function of crystal thickness. Since the HREM image calculated at 1250 kV showed clear contrast of doping atoms in the C60 clusters, the accelerating voltage was fixed at 1250 kV. The crystal thicknesses of one slice for N@C60 and RbC60 are 1.0001 and 0.9138 nm, respectively. For the C60 crystal, a HREM image of C60 cluster show darker contrast at the thicker crystal. For the N@C60 crystal, the dark dots due to the nitrogen atoms show clear contrast at crystal thickness of 10 slices. For the RbC60 crystal, clear dots corresponding to the Rb atoms are observed at crystal thickness of five slices. However, a HREM image of RbC60 at 10 slices showed different contrast from other images. Figure 4.21 (b) are difference images of C60 /N@C60 and C60 /RbC60 , calculated along the [100] direction as a function of crystal thickness. Accelerating voltage is 1250 kV. Atomic positions of nitrogen and rubidium show white contrast, which indicates the difference between the nondoped and doped C60 clusters is large at these positions. For both N@C60 and RbC60 crystals, doping atoms of nitrogen and rubidium are clearly recognized at the thick crystal of five slices. Rubidium atoms could be more easily recognized compared to the nitrogen, which is due to the larger atomic number of rubidium. A HREM image of RbC60 crystals at 10 slices shows large difference compared to the images at one slice and five slices. As observed in Figure 4.21 (b), contrast change of the images is sensitive to the crystal thickness. In order to estimate the difference between the nondoped and doped C60 clusters quantitatively, RHREM values were calculated as a function of crystal thickness, as shown in Figure 4.21 (c). For N@C60 crystals, RHREM value of 0.036 is observed at 10 slices. On the other hand, RHREM values increase up to 0.19 as the crystal thickness increases to 10 slices for RbC60 crystals. RHREM-Peak values for N and Rb atomic positions in N@C60 and RbC60 were also calculated as shown in Figure 4.21 (d). As the crystal thickness of N@C60 and RbC60 increases, the RHREM-Peak values increase up to 0.64 and 1.13, respectively. Figure 4.22 (a) is HREM images of C60 , N@C60 , and RbC60 calculated as a function of defocus values. Since the HREM image calculated at 1250 kV showed clear contrast of doping atoms in the C60 clusters, the accelerating voltage was fixed at 1250 kV. The crystal thicknesses of 2 slices for N@C60 and RbC60 are 2.00 nm and 1.83 nm, respectively. The defocus value of −40 nm is nearly Scherzer defocus, and the HREM images show the crystal structure clearly. However, for the defocus values of −10 and −70 nm, the HREM images show the different contrast from optimum conditions or vague contrast compared to that of −40 nm. RHREM values were calculated as a function of defocus values, as shown in Figure 4.22 (b). For both N@C60 and RbC60 crystals, the minimum RHREM values are observed at −40 nm, which is nearly the Scherzer defocus.

4.12 Detection of doping atoms in C60 solid clusters

C60

1

RbC60

N@C60

N@C60

C60

1

RbC60

C60

C60

Thickness [slices]

Thickness [slices]

N

5

10

| 81

Rb

N

5

Rb

N

10

Rb

(a)

N

N

Rb

(b)

0.2

1.2 N@C60 RbC60

1

0.15 RHREM-Peak

RHREM

0.8 0.1

0.6 0.4

0.05 N@C60 RbC60

0.2 0

0 0

(c)

2

4

6

8

10 12

Thickness [slices]

0 (d)

2

4

6

8

10 12

Thickness [slices]

Fig. 4.21: (a) HREM images of C60 , N@C60 , and RbC60 calculated along the [100] direction of the orthorhombic cell as a function of crystal thickness. The accelerating voltage of the microscope is 1250 kV. (b) Difference images of C60 /N@C60 and C60 /RbC60 , calculated along the [100] direction as a function of crystal thickness. Image depth of 0–63 gray scale. (c) RHREM and (d) RHREM-Peak values of N@C60 and RbC60 as a function of crystal thickness. The accelerating voltage of the microscope is 1250 kV.

RHREM-Peak values for N and Rb atomic positions in N@C60 and RbC60 were also calculated as shown in Figure 4.22 (c). The RHREM-Peak values show the maximum around the Scherzer defocus value of −41 nm for the both crystals. For both N@C60 and RbC60 crystals, it is believed that high accelerating voltage of 1250 kV, large thickness of 10 slices, and the Scherzer defocus values would be better for doping detection in this work. For the both crystals, calculated images at high accelerating voltage showed high contrast of doping atoms in HREM images and difference in the images, as shown in Figure 4.20 (a) and (b), respectively. For the N@C60 , RHREM of 1250 kV showed the highest value of 0.026, as shown in Figure 4.20 (c). On the

82 | 4 Characterization by HREM C60

RbC60

N@C60

–10

Defocus values [nm]

–25

–40

–55

–70

(a)

N

N 0.8

0.09 0.08

Rb

N@C60 RbC60

0.7 0.6 RHREM-Peak

RHREM

0.07 0.06 0.05

0.5 0.4 0.3

0.04 0.2 0.03

0.1

0.02

0 0 10 20 30 40 50 60 70 80

(b)

N@C60 RbC60

Defocus values [nm]

0 10 20 30 40 50 60 70 80 (c)

Defocus values [nm]

Fig. 4.22: (a) HREM images of C60 , N@C60 , and RbC60 calculated along the [100] direction of the orthorhombic cell as a function of the defocus value of electron microscopes. The accelerating voltage of the microscope is 1250 kV, and the crystal thickness is two slices. (b) RHREM and (c) RHREM-Peak values of N@C60 and RbC60 as a function of defocus. The accelerating voltage of the microscope is 1250 kV, and the crystal thickness is two slices.

Bibliography

|

83

other hand, for the RbC60 , RHREM of 200 kV showed the highest value, which would be due to dynamical diffraction effect (multiple scattering of electrons). Since the Rb atom (Z = 37) has larger atomic number compared to the carbon atom (Z = 6), the dynamical diffraction effect would be remarkable. RHREM-Peak values for N@C60 and RbC60 at 1250 kV showed highest values of 0.43 and 0.77, respectively. These high RHREM-Peak values could be easily detected by experimental observations. When the crystal thickness is one slice, the HREM images and difference images of N@C60 and RbC60 crystals, showed weak contrast for the doping atoms as shown in Figure 4.21 (a) and (b). As the thickness increases, the contrast for the doping atoms in the HREM and difference images showed strong and clear contrast. However, the dynamical diffraction effect is too much to estimate the structure properly as shown in the RbC60 images calculated at 10 slices in Figure 4.21 (a) and (b), and RHREM increase at 10 slices is observed in Figure 4.21 (c). In order to avoid the dynamical diffraction effect, it is better to select thin region as thin as possible. (In case of light doping element such as nitrogen, several slices might be better to observe the doping atom position.) These dynamical diffraction effects should be taken into account, when the low accelerating voltage and thick crystal thickness are used for image calculation. Even at the one slice (There is one doping atom along the observed direction.) for N@C60 and RbC60 , dark contrast due to these doping atoms is observed. This result indicates that only one doping N and Rb atoms in the C60 solid clusters could be detected by HREM with RHREM values of 0.02 and 0.03, and RHREM-Peak values of 0.31 and 0.71, respectively. As shown in Figure 4.20 (b) and 4.21 (b), the doping atoms in the difference images show clear white contrast, when the accelerating voltage and crystal thickness are high and thick, respectively. To detect only the positions of doping atoms, it would be better to select high accelerating voltage and thick crystal thickness. However, to estimate the structure more quantitatively, it is better to select high accelerating voltage and thin crystal thickness to avoid the dynamical diffraction effect. In this work, it was suggested that the RHREM values and difference images would be useful for doping detection in the C60 solid clusters, in order to evaluate dopant more quantitatively. In order to evaluate special atomic positions, RHREM-Peak values are also useful, as shown in Figures 4.20 (c) and 4.21 (c). It is believed that the more accurate atomic positions would be determined by combining the RHREM values with diffraction intensity, and the present structure analysis would be very useful for evaluation of doping atoms in the C60 solid clusters.

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[2]

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Nakajima S, Kikuchi M, Syono Y, Oku T, Shindo D, Hiraga K, Kobayashi N, Iwasaki H, Muto Y. Synthesis of bulk high Tc superconductors of TlBa2 Can − 1 Cun O2n + 3 (n = 2 − 5). Physica C 1989, 158, 471–476. Hovmöller S, Sjögren A, Farrants G, Sundberg M, Marinder BO. Accurate atomic positions from electron microscopy. Nature 1984, 311, 238–241. Weirich TE, Ramlau R, Simon A, Hovmöller S, Zou XD. A crystal structure determined to 0.02 Å accuracy by electron microscopy. Nature 1996, 382, 144–146. Zou XD, Hovmöller S. Electron crystallography: imaging and single-crystal diffraction from powders. Acta Cryst. A 2008, 64, 149–160. Bruneel E, Oku T, Penneman G, Van Driessche I, Hoste S. Origin of the nanocrystalline interface in superconducting Bi-2223/Ag composites: a SEM/HREM study, Supercond. Sci. Technol. 2004, 17, 750–755. Nakajima S, Kikuchi M, Oku T, Kobayashi N, Suzuki T, Nagase K, Hiraga K, Muto Y, Syono Y. Over-doping of Tl2 Ba2 CuO6 due to charge transfer Tl3 − t (Cu–O)p . Physica C 1989, 160, 458–460. Kikuchi M, Syono Y, Kobayashi N, Oku T, Aoyagi E, Hiraga K, Kusaba K, Atou T, Tokiwa A, Fukuoka K. Shock-induced superconductivity of Tl2 Ba2 CuO6 . Appl. Phys. Lett. 1990, 57, 813–815. Torardi CC, Subramanian MA, Calabrese JC, Gopalakrishnan I, McCarron EM, Morrissey KJ, Askew TR, Flippen RB, Chowdhry U, Sleight AW. Structures of superconducting oxides Tl2 Ba2 CuO6 and Bi2 Sr2 CuO6 . Phys. Rev. B 1988, 38, 225–231. De Rosier DJ, Klug A. Reconstruction of three dimensional structures from electron micrographs. Nature 1968, 217, 130–134. Linke C, Jansen M. Ag2 SnO3 , the first silver stannate. Z. Anorg. Allg. Chem. 1997, 623, 1441–1446. Oku T, Carlsson A, Bovin JO, Svensson C, Wallenberg LR, Linke C, Jansen M. Modulated structure of Ag2 SnO3 studied by high-resolution electron microscopy. Acta Crystallogr. B 2000, 56, 363–368. Oku T, Nakajima S. Crystal structure of HgTlBa2 CuOx studied by high-resolution electron microscopy. J. Mater. Res. 1998, 13, 1136–1140. Tokiwa A, Nagoshi M, Oku T, Kobayashi N, Kikuchi M, Hiraga K, Syono Y. Synthesis and superconductivity of PbBaSrY1 − x Cax Cu3 O7 . Physica C 1990, 168, 285–290. Nakajima S, Oku T, Nagase K, Syono Y. Superconductivity in over-doping state of (Hg,Tl)(Ba,La)CuOv and (Hg,Tl)2 Ba2 CuOv system. Physica C 1996, 262, 1–6. Oku T. Direct structure analysis of advanced nanomaterials by high-resolution electron microscopy. Nanotechnol. Rev. 2012, 1, 389–425. Smith AR, Eyring L. Calculation, display and comparison of electron microscopy images modelled and observed. Ultramicroscopy 1982, 8, 65–78. Shindo D, Oku T, Kudoh J, Oikawa T. Quantitative high-resolution electron microscopy of a high-Tc superconductor Tl2 Ba2 CuO6 with the imaging plate. Ultramicroscopy 1994, 54, 221–228. Möbus G, Rühle M. Structure determination of metal-ceramic interfaces by numerical contrast evaluation of HRTEM micrographs. Ultramicroscopy 1994, 56, 54–70. Hofmann D, Ernst F. Quantitative high-resolution transmission electron microscopy of the incoherent 𝛴3(211) boundary in Cu. Ultramicroscopy 1994, 53, 205–221. King WE, Cambell GH. Quantitative HREM using non-linear least-squares methods. Ultramicroscopy 1994, 56, 46–53. Higashi I, Kobayashi K, Tanaka T, Ishizawa Y. Structure refinement of YB62 and YB56 of the YB66 -type structure. J. Solid State Chem. 1997, 133, 16–20.

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[24] Oku T, Carlsson A, Wallenberg LR, Malm JO, Bovin JO, Higashi I, Tanaka T, Ishizawa Y. Digital HREM imaging of yttrium atoms in YB56 with YB66 structure. J. Solid State Chem.1998, 135, 182–193. [25] Oku T, Bovin JO. Atomic disordering in YB56 detected by high-resolution electron microscopy with residual indices. Philos. Mag. A 1999, 79, 821–834. [26] Oku T, Bovin JO, Higashi I, Tanaka T, Ishizawa Y. Atomic structures of YB56 studied by digital high-resolution electron microscopy and electron diffraction. J. Mater. Res. 2001, 16, 101–107. [27] Oku T. Digital high-resolution electron microscopy of atomic disordering in YB56 . J. Electron Microsc. 2000, 49, 41–52. [28] Dong W, Baird T, Fryer JR, Gilmore CJ, MacNicol DD, Bricogne G, Smith DJ, O’Keefe MA, Hovmöller S. Electron microscopy at 1-Å resolution by entropy maximization and likelihood ranking. Nature 1992, 355, 605–609. [29] Zuo JM, Kim M, O’Keefe MA, Spence JCH. Direct observation of d-orbital holes and Cu–Cu bonding in Cu2 O. Nature 1999, 401, 49–52. [30] Zandbergen HW, Jansen J, Cava RJ, Krajewski JJ, Peck WF Jr, Gyorgy EM. Structure of the 13-K superconductor La3 Ni2 B2 N3 and the related phase LaNiBN. Nature 1994, 372, 759–761. [31] Oku T, Hirano T, Nakajima S, Suganuma K. Formation and structure of carbon nanocage structures produced by polymer pyrolysis and electron-beam irradiation. J. Mater. Res. 1999, 14, 4266–4273. [32] Oku T, Niihara K, Suganuma K. Formation of carbon nanocapsules with SiC nanoparticles prepare by polymer pyrolysis. J. Mater. Chem. 1998, 8, 1323–1325. [33] Oku T, Narita I, Nishiwaki A. Formation, atomic structures and structural optimization of tetrahedral carbon onion. Diamond Relat. Mater. 2004, 13, 1337–1341. [34] Oku T, Hirano T, Kuno M, Kusunose T, Niihara K, Suganuma K. Synthesis, atomic structures and properties of carbon and boron nitride fullerene materials. Mater. Sci. Eng. B 2000, 74, 206–217. [35] Oku T, Kuno M, Kitahara H, Narita I. Formation, atomic structures and properties of boron nitride and carbon nanocage fullerene materials. Int. J. Inorg. Mater. 2001, 3, 597–612. [36] Ugarte D. Curling and closure of graphitic networks under electron-beam irradiation. Nature 1992, 359, 707–709. [37] Ru Q, Okamoto M, Kondo Y, Takayanagi K. Attraction and orientation phenomena of bucky onions formed in a transmission electron microscope. Chem. Phys. Lett. 1996, 259, 425–431. [38] Terrones H, Terrones M. The transformation of polyhedral particles into graphitic onions. J. Phys. Chem. Solids 1997, 58, 1789–1796. [39] Oku T. Three-dimensional imaging of YB56 by high-resolution electron microscopy. Chem. Commun. 2002, 302–303. [40] Oku T. Three-dimensional atomic imaging of Y and (B12 )13 clusters in YB56 by HREM and crystallographic image processing. Sci. Technol. Adv. Mater. 2004, 5, 657–661. [41] Oku T. Direct analysis of atomic structures of advanced ceramics by high-resolution electron microscopy. J. Ceram. Soc. Jpn. 2001, 109, S17–S24. [42] Sakamoto Y, Kaneda M, Terasaki O, Zhao D, Kim JM, Stucky GD, Shin HJ, Ryoo R. Direct imaging of the pores and cages of three-dimensional mesoporous materials. Nature 2000, 408, 449–453. [43] Downing KH, Meisheng H, Wenk HR, O’Keefe MA. Resolution of oxygen atoms in staurolite by three-dimensional transmission electron microscopy. Nature 1990, 348, 525–528. [44] Carlsson A, Oku T, Bovin JO, Wallenberg LR, Malm JO, Schmid G, Kubicki T. The first structure determination of nanosized colloidal particles of Pd3 P by high-resolution electron microscopy. Angew. Chem. Int. Edn. 1998, 37, 1217–1220.

86 | 4 Characterization by HREM [45] Almeida Murphy T, Pawlik T, Weidinger A, Höhne M, Alcala R and Spaeth JM. Observation of atomlike nitrogen in nitrogen implanted solid C60 . Phys. Rev. Lett. 1996, 77, 1075–1078. [46] Stephens PW, Bortel G, Faigel G, Tegze M, Jánossy A, Pekker S, Oszlanyi G, Forró L. Polymeric fullerene chains in RbC60 and KC60 . Nature 1994, 370, 636–639. [47] Oku, T, Kubota H, Ohgami T, Suganuma K. Possible detection of doping atoms in C 60 solid clusters by high-resolution electron microscopy. Carbon 1999, 37, 1299–1309.

5 Electron diffraction analysis of nanostructured materials 5.1 Modulated superstructures of Tl-based copper oxides In addition to the basic layer structures of Tl-based copper oxides, modulated structures accompanied with the satellite spots have been observed [1–4]. Figure 5.1 shows electron diffraction patterns of Tl2 Ba2 CuO6 taken along the various directions of the crystal [5]. In addition to the fundamental reflections, sharp satellite spots are observed in Figures 5.1 (a)–(c), which indicate the modulated superstructure. The electron diffraction pattern of Figure 5.8 (c) is obtained by 18° rotating Figure 5.1 (d) along the c-axis. The Tl2 Ba2 CuO6 has both tetragonal and orthorhombic structures, and the modulated structure is observed in the orthorhombic phase. The fundamental structure with the modulated structure is distorted a little, and the indices are those of an orthorhombic unit cell (a = 0.545 nm, b = 0.549 nm, c = 2.318 nm) as observed in the electron diffraction pattern of Figure 5.8 (a). The fundamental lattice has a twin

a*

a*

200

b*

220

220

b* 000

000

020

a*

b*

c*

c*

0010 311 000

620 000

220

Fig. 5.1: Electron diffraction patterns of Tl2 Ba2 CuO6 taken with the incident beam parallel to the ̄ ̄ directions. The electron diffraction pattern (b) showing the (a) [001], (b) [001], (c) [130], and (d) [110] modulated structure and its twinning.

88 | 5 Electron diffraction analysis of nanostructured materials structure with a twin plane of {110} as observed in Figure 5.1 (b). The superstructure reflections are observed along the [130], and the modulated wave vector was determined as q = [±0.07 0.22 1] = 1/6.2 ⟨1 3 0⟩, i.e. the modulation is incommensurate. Figure 5.2 (a) is an HREM image of Tl2 Ba2 CuO6 taken along c-axis. An enlarged image of Figure 5.2 (a) is shown in Figure 5.2 (b). In addition to the fundamental lattice fringes, dark and bright contrasts with a distance of ∼ 1.2 nm and their twin relations can be seen. This HREM images show that the direction of the modulated structure is near [130]. Although twinning of the modulated structure appears on both {110} and near {100} planes, the twinning of fundamental lattice appears only on {110} planes, as indicated by the arrows in Figures 5.2 (a) and (b). Figure 5.2 (c) is a high-resolution

1.2 nm

Tl 2.3 nm 2.4 nm (b)

(a)

(b)

c [130] Fig. 5.2: HREM image of Tl2 Ba2 CuO6 taken along c-axis. (b) Enlarged image of (a). (c) HREM image ̄ direction. with the incident beam parallel to the [310]

5.1 Modulated superstructures of Tl-based copper oxides

| 89

̄ incidence. Dark and bright contrasts image of Tl2 Ba2 CuO6 2201 taken with the [130] with a distance of ∼ 2.4 nm are observed, and the modulated region (a) and the nonmodulated region (b) are clearly distinguishable. By careful observation of the modulation contrast, changes in both the darkness and position of Tl atoms can be seen, as indicated by arrows in the region (a) of Figure 5.2 (c). This indicates that the origin of modulated structure would exist on the Tl–O planes. From detailed composition analysis of the Tl-2201 phase, the orthorhombic with modulated structure and the tetragonal without the modulation had the composition of Tl1.7 Ba2 CuO5.7 and Tl1.6 Ba2 CuO5.6 , respectively. The modulated structure has 0.3 oxygen and 0.3 Tl deficiencies per unit cell. The electron diffraction and high-resolution observation showed the 6.2 times superstructure along the [130] direction. These results indicated that the modulation would be due to the atomic ordering of oxygen and Tl in the Tl–O layers along the [130] with a period of 6.2 times. If the oxygen and Tl deficiencies are assumed along the [130] direction, the deficiencies are calculated as 0.36 per the unit cell, which agree well with the composition analysis. Therefore, the modulated superstructure is believed to be due to Tl and oxygen vacancies in the Tl– O layers along the [130] with a period of 6.2 times (∼ 2.4 nm). On the other hand, the tetragonal phase had more atomic deficiencies randomly, and did not show the modulated structure. Electron diffraction patterns of Tl2 BaSrCuO6 taken with the incident beam parallel to the [001] and [010] directions are shown in Figure 5.3 (a) and (b), respectively. When Sr atoms are doped at the Ba sites, the fundamental structure has a tetragonal structure. Satellite reflections due to a modulated structure are observed, which are weak and diffuse compared to the Tl-2201 phase. In addition, the modulation wave vector was changed as q = ⟨1/6 0 1⟩. For Tl2 Ba2 CaCu2 O8 (Tl-2212) [1, 2] and Tl2 Ba2 Ca2 Cu3 O10 (Tl-2223) [1], weak diffuse scatterings were also observed, and the modulation wave vector is determined to be q = ⟨1/6 0 1⟩ as observed in Figure 5.3 (c). This modulation shows twodimensional character, and the symmetry of the fundamental lattice remains tetragonal (a = 0.385 nm, c = 2.92 nm). An HREM image corresponding to Figure 5.10 (c) is shown in Figure 5.3 (d). Modulation contrast with a distance of ∼ 2.3 nm is observed in the Tl–O layer along the a-axis. Models for the modulated superstructures were reported as follows: short-range ordering due to displacements of Tl and O in the Tl–O planes [2], extra oxygen in the Tl–O planes [1], a partial substitution of Tl3+ by Tl+ [1, 3], and the mutual substitution of Tl and Ca atoms [4, 6]. The compositional analysis of the present samples showed that the Tl-2212 and Tl-2223 phases had compositions of Tl1.7 Ba2 Ca1.3 Cu2 O8 and Tl1.7 Ba2 Ca2.3 Cu3 O10 , respectively. This implies that the excess 0.3 Ca atoms are doped at the Tl sites per the unit cell. The electron diffraction and HREM observation showed six times superstructure along the a-axis. If the Tl atoms are substituted by Ca atoms with a period of six times along the axis, the substitution atoms are 0.33 per the unit cell, which agreed well with the measured composition of

90 | 5 Electron diffraction analysis of nanostructured materials c* a*

110

200

000

200

a*

000

c*

000

2.9 nm 2.3 nm

200

c a

020 010

000

100 000

200

Fig. 5.3: Electron diffraction patterns of Tl2 BaSrCuO6 taken with the incident beam parallel to the (a) [001] and (b) [010] directions. (c) Electron diffraction pattern and (d) HREM image of Tl2 Ba2 CaCu2O8 taken with the incident beam parallel to the [010] direction. Electron diffraction patterns of (e) TlBa2 CaCu2O7 and (f) TlBa2 Ca2 Cu3 O9 taken along the c-axis.

the samples. Therefore, the modulated superstructure is believed to be due to the Tl substitution by Ca atoms along the a-axis with a period of six times (∼ 2.3 nm). Figure 5.3 (e) and (f) are electron diffraction patterns of TlBa2CaCu2 O7 (Tl-1212) and TlBa2 Ca2 Cu3 O9 (Tl-1223) taken along the c-axis, respectively. Weak, diffuse satellite scatterings are observed as indicated by arrows, and the observed modulation wave vector is approximately q = ⟨0.28 0 0.5⟩ [5]. Almost the same incommensurate diffuse

| 91

5.2 Modulate structures of lanthanoid-based copper oxides

Table 5.1: Oxygen deficiencies 𝛿 of Tl-based superconductors calculated from electron diffractions of Figure 5.3 and iodimetric measurements of oxygen contents. Structure TlBa2 CaCu2 O7−𝛿 TlBa2 Ca2 Cu3 O9−𝛿 TlBa2 Ca3 Cu4 O11−𝛿

Reflection at x 0 0.5

Averaged 𝛿

Iodimetric measurement

Averaged 𝛿

0.24–0.29 0.26–0.31 0.25–0.32

0.27 0.29 0.29

0.279–0.309 0.277–0.311 0.254–0.326

0.29 0.29 0.29

scattering was observed for the TlBa2 Ca3 Cu4 O11 (Tl-1234) phase. As the modulation shows a two-dimensional character, the symmetry of the fundamental lattice remains tetragonal. The diffuse scattering becomes stronger as the oxygen loss is increased and also the Tc increases. Oxygen deficiencies 𝛿 of Tl-based superconductors calculated from electron diffractions of Figure 5.3 and iodimetric measurements of oxygen contents are summarized in Table 5.1. From the compositional analysis for the Tl-1212, 1223, and 1234 phases, the atomic ratios of Tl:Ba:Ca:Cu were determined to be 1:2:1:2, 1:2:2:3, and 1:2:3:4 (stoichiometry), respectively. However, 0.29 oxygen atoms are deficient per unit cell, as summarized in Table 5.1, which implies that the oxygen vacant positions are the same for these structures. In this work, oxygen atoms in the Tl–O layers would be deficient, and the measured modulation from the electron diffraction patterns are summarized in Table 5.1. As listed in Table 5.1, assumed oxygen vacancies in the Tl–O layers measured by electron diffraction agreed well with the measured oxygen vacancies by iodimetric measurements. Therefore, it is believed that the modulation superstructure would be due to oxygen vacancy ordering in the Tl–O layer along the a-axis with a period of 3.45 times (= 0.29−1 ) and two times along c-axis. The period of 3.45 times is incommensurate, which implies the mixture of 3- and 4-times superstructures. In fact, modulations with periods of 3.1–4.2 times (= 0.32−1 − 0.24−1 ) are observed for electron diffraction patterns, as listed in Table 5.1.

5.2 Modulate structures of lanthanoid-based copper oxides Various types of lanthanoid-based copper oxides have been reported, and electrondoped Nd2 − x Cex CuO4 superconductors were discovered [7, 8]. In order to clarify the microstructures, single crystals of Ln2 CuO4 prepared with various heat treatments are investigated by means of high-resolution electron microscopy and electron diffraction. Single crystals of Ln2 CuO4 (Ln = Pr, Nd, Sm) were grown by the traveling-solventfloating-zone technique using an infrared-heating furnace [9, 10]. To reduce oxygen content, parts of the Ln2 CuO4 (Ln = Pr, Nd, Sm) samples were annealed at 1100°C for 18 h in air and quenched in liquid nitrogen. The rests of the samples were annealed at 400°C in air for 38–140 h to saturate oxygen content in the crystals. SmLa0.75 Sr0.25 CuO4 was also synthesized from a mixture of La2 O3 , Sm2 O3 , CuO, and SrCO3 [11]. Mixed powder was first calcined at 950°C in air for 10 h, then pressed into pellets, and fi-

92 | 5 Electron diffraction analysis of nanostructured materials nally sintered at 1130°C in air for 15 h. The pellets were quenched to room temperature in air, and subsequently annealed at 550°C in the atmosphere with various oxygen pressures. Modulated superstructures are also observed in the lanthanoid-based copper oxides [12–14]. The domains of superlattice with sizes of 5–60 nm in diameter were observed, and the smaller domains (5–10 nm) are observed around a large one, and seem to grow into larger ones (40–60 nm). A representative superstructure domain in Nd2 CuO4 is shown in Figure 5.4 (a), and Figure 5.4 (b) is an electron diffraction pattern of Figure 5.4 (a). Sharp satellite reflections with a wave vector q = ⟨1/4 1/4 0⟩ are observed in Figure 5.4 (b). In Figure 5.4 (a), repeated dark and bright contrasts separated at a distance of 1.1 nm (≃ 2√2 × a) are observed in the [110] direction. The high-resolution image and the diffraction pattern reveal that the basic lattice spacing ̄ of the superlattice lengthen as much as 101.5% and 100.3% in the [110] and [110] directions, respectively, as compared with the fundamental lattice. Therefore, the contrast due to strain field is observed around the domain. Two-directional superlattice domain is also observed as shown in a HREM image in Figure 5.4 (c), and an

110

000

110

110

000

110

Fig. 5.4: (a) HREM image and (b) electron diffraction pattern of a single domain of the superlattice in Nd2 CuO4 , taken with the [001] incidence. (c) HREM image and (d) electron diffraction pattern of superlattice domains along two directions.

5.2 Modulate structures of lanthanoid-based copper oxides

|

93

electron diffraction pattern of the superlattice domains along two directions is shown in Figure 5.4 (d), which also indicates a modulation wave vector of q = ⟨1/4 1/4 0⟩. It can be considered that such domain structure is due to nonuniformity of oxygen content in the specimens. Various types of modulated superstructures were observed in the Ln2 CuO4 , as summarized in Table 5.2. Figures 5.5 (a)–(d) are electron diffraction patterns of ̄ direction. Nd2 CuO4 , Pr2 CuO4 , Pr1.85 Ce0.15 CuO4 , and Sm2 CuO4 , taken along the [110]

004

224

004

112 000

110

004

004 000

110

000

110

000

110

224

112 004 000

101 101

200

000

010

Fig. 5.5: Electron diffraction patterns of (a) Nd2 CuO4 , (b) Pr2 CuO4 , (c) Pr1.85 Ce0.15 CuO4 , and (d) ̄ incidence. Electron diffraction patterns of Pr2 CuO4 taken along the Sm2 CuO4 , taken with the [110] ̄ (e) [010] and (f) [111] directions.

94 | 5 Electron diffraction analysis of nanostructured materials Table 5.2: Summary of modulated structures of Ln2 CuO4 . Structure

Modulation wave vector q

Nd2 CuO4 Sm2 CuO4 Pr2 CuO4 Nd1.85 Ce0.15 CuO4 Sm1.85 Ce0.15 CuO4 Pr1.85 Ce0.15 CuO4

⟨1/4 1/4 0⟩ ⟨1/4 1/4 0⟩, ⟨1/2 1/2 1⟩ ⟨1/4.2 1/4.2 3/4.2⟩, ⟨1/4 1/4 1/2⟩, ⟨1/2 0 1/2⟩ ⟨1/4 1/4 0⟩ ⟨1/4 1/4 0⟩, ⟨1/2 1/2 1⟩ ⟨1/3 1/3 0⟩

For the Pr2 CuO4 , Pr1.85 Ce0.15 CuO4 and Sm2 CuO4 crystals, satellite reflections at 0.24 0.24 0.72, 1/3 1/3 0 and 1/2 1/2 1 are observed, as shown in Figure 5.5 (b), (c), and (d), respectively. Figures 5.5 (e) and (f) are electron diffraction patterns of Pr2 CuO4 taken ̄ directions, respectively, which also indicates weak diffuse along the [010] and [111] scattering and sharp satellite reflections at 1/2 0 1/2 and 1/4 1/4 1/2, respectively. A superstructure have been observed and characterized for Nd2 − x Cex CuO4 by a wave vector q = [1/4 1/4 0] [9], and was suggested that the modulation is due to ordering of oxygen vacancy and/or Ce. However, the satellite reflections were not observed in the diffraction patterns of Nd2 CuO4 and Pr2 CuO4 quenched from 1100°C. The result indicates that the appearance of superstructures is sensitive to the oxygen content and unrelated to ordering of Ce atoms. Since neutron diffraction study shows the deficiency of oxygen in Cu–O planes, it can be supposed that the superlattices are due to ordering of oxygen atoms in the Cu–O planes.

5.3 Oxygen ordering in YBa2 Cu3 O7−x The crystal structure of YBa2 Cu3 O7 is based on a triple perovskite structure and is characterized by the ordering of oxygen vacancies, that is, the oxygen positions on the Y atom layer and between two Ba atoms are vacant. In addition, oxygen orderings in the Cu–O basal planes were observed [15]. Bulk samples of YBa2 Cu3 O7−x superconductors were prepared by mixing BaCO3 , Y2 O3 , and CuO powders with the composition of YBa2 Cu3 O7−x phase. The mixture pellets were calcined at 930°C for 12 h in air and then cooled slowly in a furnace. After crushing the pellets to form powders, the process was repeated once more. The obtained pellets were reheated at 500–900°C and quenched into liquid nitrogen, and subsequently annealed at 500–300°C in the vacuum seal. The pellets were also annealed in a flowing N2 gas at various temperatures to control the oxygen contents. The oxygen contents were investigated by iodimetric measurements and mass change. As a consequence of the tetragonal-to-orthorhombic phase transition of YBa2 Cu3 O7−x at ∼ 600°C [16], twin boundaries are often observed. Figure 5.6 (a) and (b) are TEM image and lattice image of YBa2 Cu3 O7−x taken with the incident beam parallel

5.3 Oxygen ordering in YBa2 Cu3 O7−x

|

95

to the c-axis. Twin boundaries (TB) are coherent and indicated by arrows. The twin boundaries show distinct contrast in the TEM image, and the existence of boundaries is evident from kinks of the lattice fringes. In the oxygen-deficient YBa2 Cu3 O7−x compounds, oxygen vacancy ordering was observed. Figures 5.6 (c) and (d) are electron diffraction patterns of YBa2 Cu3 O6.68 taken with the incident beam parallel to the c-axis and b-axis, respectively. The electron diffraction pattern shows orthorhombic

TB

a*

b*

TB

TW

TB

003

110 000

100

b* 000 a*

a

b

b

a

TB

Fig. 5.6: (a) TEM image and (b) lattice image of YBa2 Cu3 O7−x taken with the incident beam parallel to the c-axis. Twin boundaries (TB) are indicated by arrows. Electron diffraction patterns of YBa2 Cu3 O6.68 taken with the incident beam parallel to the (c) c-axis and (d) b-axis. (e) Fourier transform of (b). (f) Filtered inverse Fourier transform of (e).

96 | 5 Electron diffraction analysis of nanostructured materials structure with a- and b-axes and a twin structure with a {110} twin plane. Both electron diffraction patterns in Figure 5.6 (c) and (d) show diffuse satellite reflections at 1/2 0 0 along the a-axis. This indicates the existence of modulated superstructure with a modulation wave vector q = ⟨1/2 0 0⟩, which would be due to ordering of oxygen vacancies on the basal Cu–O planes. Figure 5.6 (e) is a Fourier transform of HREM image of Figure 5.6 (b), and filtered inverse Fourier transform of Figure 5.6 (e) is shown in Figure 5.6 (f), in which linear bright stripes with the distance of 2a are observed

a*

b*

b* 010 b*

000

000

100

a*

a*

a*

b*

b*

010 b*

100 000

000 a*

a*

a*

b*

b* 000 a*

Fig. 5.7: Electron diffraction patterns of (a) YBa2 Cu3 O6.80 , (b) YBa2 Cu3 O6.47 , (c) YBa2 Cu3 O6.23 and (d) YBa2 Cu3 O6.29 taken along the c-axis. (e) HREM lattice image and (f) electron diffraction pattern of YBa2 Cu3 O6.47 taken along the c-axis.

5.3 Oxygen ordering in YBa2 Cu3 O7−x

| 97

Table 5.3: Summary of modulated structures of YBa2 Cu3 Oy . Quenched and annealed in a sealed tube y Tc / K Observed structure 6.80 6.68 6.60 6.47 6.29

86 49 48 4 –

Annealed in N2 Observed structure

y

Diffuse streaks along a-axis ⟨1/2 0 0⟩ Diffuse streaks along a-axis ⟨1/3 0 0⟩, ⟨1/2 0 0⟩ ⟨1/3 0 0⟩, ⟨1/4 0 0⟩

6.91 6.74 6.50 6.23 6.00

Perfect orthorhombic ⟨0 1/3 0⟩, ⟨1/2 0 0⟩ ⟨1/2 0 0⟩ ⟨1/2 0 0⟩, ⟨0 1/3 0⟩ Perfect tetragonal

along a-axis. The twin boundary can be clearly seen at a glancing view parallel to the a- or b-axis in Figure 5.6 (f). Electron diffraction patterns of oxygen deficient YBa2 Cu3 O6.80 , YBa2 Cu3 O6.47 , YBa2 Cu3 O6.23 and YBa2 Cu3 O6.29 taken along the c-axis are shown in Figure 5.7 (a)–(d), respectively. In Figure 5.7 (a), weak diffuse streaks are observed along a-axis, which would indicate short range ordering of oxygen atoms. In Figure 5.7 (b) and (c), superstructures with a modulation wave vector q = ⟨1/3 0 0⟩ and ⟨0 1/3 0⟩, which indicates the superstructures are formed along the a-axis and b-axis of orthorhombic cell, respectively. In addition, a superstructure with a modulation wave vector q = ⟨1/4 0 0⟩ is observed along the a-axis, as shown in Figure 5.7 (d). These modulated structures are summarized as listed in Table 5.3 [17]. Figure 5.7 (e) and (f) is a lattice image and an electron diffraction pattern of YBa2 Cu3 O6.47 taken with the [001] incidence. Satellite peaks with a modulation wave vector q = ⟨1/3 0 0⟩ are observed together with q = ⟨1/2 0 0⟩ in the diffraction pattern. Linear bright stripes with the distance of 3a are observed along the two principal lattice directions in the HREM image of Figure 5.7 (e). OV

Cu O

Cu O

O6

O7

O6.66 b O6.5 a O6.33 c b

O6.33 a

O6.25

OV (a)

(b)

Fig. 5.8: Models for ordered arrangement of oxygen vacancies in YBa2 Cu3 O7−x . (a) Two-times model along the a-axis. (b) Oxygen ordering models of basal planes (Cu–O) of the YBa2 Cu3 O7−x .

98 | 5 Electron diffraction analysis of nanostructured materials From these observations, a model for the ordered arrangement of oxygen vacancies is proposed, as shown in Figure 5.8 (a). The fundamental unit cell is orthorhombic, with a dimension of 2a × b × c. Other oxygen ordering models of basal planes (Cu–O) of the YBa2 Cu3 O7−x are also proposed as shown in Figure 5.8 (b), which depends on the oxygen content. These phases would correspond to the ortho-II phase and ortho-III phases [18–20], which results in the changes of Tc , and the control of oxygen atoms in the oxide crystals is important.

5.4 Structures of Bi-based copper oxides Bi-based copper oxides with Ag are expected for wire application. A spray-dried aqueous solution of nitrates with atomic ratio Bi1.5 Pb0.5 Sr2 Ca2 Cu3 was calcined at 650°C for 15 h, resulting in a mixture of oxides [21–23]. The resulting precursor powder with a grain size of 3 μm was mixed with 30 vol% Ag whiskers with a diameter of 20– 50 μm and a length of a few hundred micrometers. The Ag whiskers were synthesized via an electrochemical reduction of a Ag nitrate solution by a copper wire at pH 2. The mixture was pressed into bars and sintered at 853°C for 170 h in air to obtain the Bi-2223/Ag composites.

Ag

Bi2223

c b

220 111

000

0010

000

020

Fig. 5.9: (a) TEM image of (Bi,Pb)2 Sr2 Ca2 Cu3 Ox /Ag whisker interface in a sintered composite. Electron diffraction of (b) Ag and (c) (Bi,Pb)2 Sr2 Ca2 Cu3 Ox .

| 99

5.4 Structures of Bi-based copper oxides

Figure 5.9 (a) is a TEM image of the Bi-2223/Ag whisker interface in a sintered composite. A thin layer with a different contrast is observed at the Bi-2223/Ag interface. Electron diffractions of Ag and Bi-2223 phase are also shown in Figures 5.9 (b) and ̄ of the face-centered cubic (c), respectively. Figure 5.9 (b) is observed along the [110] Ag crystal. The diffraction pattern of Bi-2223 phase in Figure 5.9 (c) was taken along the a-axis, which indicates a modulated structure with a modulation wave vector of q ∼ ⟨0 1/4 0⟩. The origin of the modulated superstructure would be metal atom displacements in the crystal [24–26]. Figure 5.10 (a) is a TEM image of the Bi-2223/Ag whisker composite with the Agrich phase. Lattice fringes of c-planes of Bi-2223 phase are observed, and an amorphous/nanocrystalline (AM-NC) structure is observed at the Ag/Bi-2223 interface. The white areas are the result of preferential ion milling, probably of amorphous phases, which are more easily removed compared to Bi-2223. The superconducting phase is oriented with the c-axis perpendicular to the interface. An EDX spectrum of the AMNC phase in Figure 5.10 (a) is shown in Figure 5.10 (b), which indicates a composition of Ag2 Bi2.4 Pb0.6 Sr2 Ca0.8 Cu4.3 , and an increase of Ag, Bi, Pb, and Cu concentration in the amorphous phase. An enlarged HREM image and an electron diffraction pattern

AM-NC

AM-NC Cu

AM-NC

Bi2223

Bi

Intensity [A. U.]

Bi2223

O

Sr

Ag Ag Ca Ca

Bi2223

c

0

AM-NC

1

10 nm

[110]

2

3

4

5

Energy [keV] c*

c Bi2223 [110]

0010

Bi 000

220

AM-NC 10 nm

Fig. 5.10: (a) TEM image of the Bi-2223/Ag whisker composite with the Ag-rich phase. (b) EDX spectrum of the AM-NC phase in (a). (c) HREM and (d) electron diffraction pattern at the interface.

100 | 5 Electron diffraction analysis of nanostructured materials at the interface are shown in Figure 5.10 (c) and (d), respectively. The Bi-2223/AM-NC interface exhibits small steps of half or one unit cell of Bi-2223, and such intermediary phase was also observed [22]. The diffraction pattern exhibits [110] incident of the Bi-2223 crystal, and the observed streak along the c-axis indicates that there is a small amount of the Bi-2212 or Bi-2234 phase to form an intergrowth structure. A diffuse ring is also observed as indicated by arrows, which exhibits the amorphous-like structure of AM-NC phase. The influence of Ag on the yield in Bi-2223 synthesis can be explained in terms of the shift in the incongruent melting point.

5.5 Twin structures in BN nanoparticles Chemical vapor-deposited boron nitride (CVD-BN) has been used in various practical fields, such as crucibles for semiconductor materials, high-temperature jigs, and insulators, due to its high purity, high density, and chemical inertness. The effects of deposition temperature and total gas pressure on the crystal structure, density, and microstructure of CVD-BN have been studied. Structures of BN are hexagonal (h-BN, ABAB stacking), cubic (c-BN, ABCABC stacking), wurzite type (w-BN, ABAB stacking), amorphous (a-BN), turbostratic (t-BN), and rhombohedral (r-BN, ABCABC stack-

N

B

B N h-BN

r-BN

B N N c-BN w-BN Fig. 5.11: Structure models of h-BN, r-BN, w-BN, and c-BN.

B

5.5 Twin structures in BN nanoparticles

| 101

ing) was also reported [27, 28], as shown in Figure 5.11. The r-BN is expected as a starting material for c-BN, with high hardness and thermal conductivity next to diamond because of the same periodicity in the stacking ABCABC in crystallographic layers, and r-BN can be directly converted into c-BN by shock compression and high static pressure [29]. Formation and atomic structures of CVD-BN with rhombohedral

113

110

102

101 003 000

600 nm 113 102 111

011 000

70 nm c*

102

003 101 000

202 a*

200 nm Fig. 5.12: (a) TEM image of CVD-BN synthesized from BCl3 –NH3 –H2 gas system at a deposition temperature of 1600°C and a total gas pressure of 3 Torr. (c) TEM image of r-BN nanoparticle. (e) TEM image of r-BN nanoparticle perpendicular to the c-axis. (b, d, f) Electron diffraction patterns of (a, c, e), respectively. The diffraction patterns were taken in the large area (a), along (c) [211], and (e) [010] of r-BN nanoparticles.

102 | 5 Electron diffraction analysis of nanostructured materials and hexagonal structures were investigated, and the nanostructures of c-BN converted from r-BN were also investigated. CVD-BN plates with a rhombohedral structure were synthesized from BCl3 –NH3 –H2 gas system at 1600°C and a total gas pressure of 3–5 Torr on the graphite substrates in CVD apparatus (Tachibana Riko CVD-250T4) [30, 31]. BCl3 (purity, 99.9%) and NH3 (purity, 99.95%) gases were used as starting materials and H2 (99.999%) for dilution. These gases were introduced separately into the CVD reactor near the substrate. The gas-flow rates were kept constant at 90 sccm

N B NB

N B c

c

a

a c*

c*

003

104 101

000 c

a c*

c*

110 {000}

{003}

000

113

003

Fig. 5.13: (a) HREM image of r-BN. (b) Enlarged HREM image of r-BN after Fourier filtering. (c) HREM image of microtwin. (d) Electron diffraction pattern of twinned r-BN nanoparticle taken along [010]. (e) TEM image of twinned r-BN nanoparticle. (f) Electron diffraction pattern of (e), taken along [110].

5.5 Twin structures in BN nanoparticles |

103

for NH3 , 140 sccm for BCl3 , and 670 sccm for H2 . The growth rate was 1.7 mm/min. The lattice parameters of the deposited r-BN, as determined through XRD analysis, were a = 0.2506 ± 0.0004 nm and c = 1.003 ± 0.002 nm, which would indicate B/N 1:1. These BN plates were thinned to 0.1 mm with emery papers, and then punched to disks 2.3 mm in diameter with a supersonic wave cutter. The disks were polished with a dimple grinder to < 50 mm in thickness and thinned by argon ion milling at an accel-

c

b d {101}

a

113

101 101

012

012 111 000

111

000

113

101

012

101

111 000

000

012

111

Fig. 5.14: (a) TEM image of r-BN nanoparticle with twin structures. (b) HREM image of twin boundary at region d in (a) after Fourier filtering. (c–f) Electron diffraction pattern of twin boundary at regions a–d in (a), respectively, taken along [121].

104 | 5 Electron diffraction analysis of nanostructured materials erating voltage of 3–5 kV. c-BN powder was produced from r-BN at 1800–2200°C and 6–7 GPa in an octahedral anvil-type device. Figure 5.12 (a) is a TEM image of CVD-BN synthesized from BCl3 –NH3 –H2 gas system at a deposition temperature of 1600°C and a total gas pressure of 3 Torr. A considerable number of particles are observed in the sample. It should be noted that only those particles which satisfy certain diffraction conditions are visible in the image, which was confirmed by tilting the crystal. An electron diffraction pattern of Figure 5.12 (a), taken from the wide area (1 μm), is shown in Figure 5.12 (b). The electron diffraction pattern of Figure 5.12 (b) shows many diffraction spots attributed to the particles in addition to the Debye–Scherrer rings from the t-BN matrix. The rings are indexed as 003, 101, 102, 110, and 113 of r-BN. An enlarged image and an electron diffraction pattern of a r-BN nanoparticle is shown in Figure 5.12 (c) and (d), respectively. The reflections of Figure 5.12 (d) are indexed as r-BN along the [211] direction. A TEM image and an electron diffraction pattern of r-BN nanoparticle, taken along [010], are shown in Figure 5.12 (e) and (f), respectively. Streaks along the c∗ -axis are observed, which are due to the microtwin and stacking faults of {001}. A HREM image of r-BN in Figure 5.12 (e) is shown in Figure 5.13 (a). Figure 5.13 (b) is an enlarged HREM image of r-BN after Fourier filtering. White dots correspond to

311 220 111

000

111

200

111 000

Fig. 5.15: (a) TEM image and (b) electron diffraction pattern of c-BN nanoparticles synthesized from r-BN. (c) TEM image and (d) electron diffraction pattern of c-BN nanoparticle taken along [011].

5.5 Twin structures in BN nanoparticles |

105

BN atomic pair, as illustrated in Figure 5.13 (b). HREM image of microtwin is shown in Figure 5.13 (c), which agree with the streaks along c∗ -axis in electron diffraction pattern of Figure 5.12 (f). Figure 5.13 (d) is an electron diffraction pattern of twinned r-BN nanoparticle taken along [010], which indicates a {101} twin structure of r-BN. A TEM image of r-BN nanoparticle is shown in Figure 5.14 (e), and a twin boundary is indic-

{101}

{101}

{113}

{113}

{001}

{111}

Fig. 5.16: Atomic structure models of (a) {101}; (b) {101}; (c) {113}; (d) {113}; (e) {001} twin structures of r-BN along [010], [211], [110], [211], and [010], respectively. (f) Atomic structure model of {111} twin structure of c-BN along [011]. Circles indicate BN atomic columns along the projection model. Unit cells and twin boundaries are indicated by solid and dotted lines, respectively.

106 | 5 Electron diffraction analysis of nanostructured materials ̄ ated by arrows. An electron diffraction pattern of Figure 5.13 (e), taken along the [110] direction, is shown in Figure 5.13 (f), which indicates a {113} twin structure of r-BN. A TEM image of r-BN nanoparticle with twin structures is shown in Figure 5.14 (a), and three twin boundaries are indicated by arrows. A HREM image of twin boundary at region A in Figure 5.14 (a) is shown in Figure 5.14 (b), which indicates the mirror relation at the boundary. Figure 5.14 (c)–(f) shows electron diffraction pattern of twin boundary at regions A–D in Figure 5.14 (a), respectively. All diffraction patterns are taken along [211]. A {101} twin structure is observed in Figure 5.14 (d) and (f), and a c*

c* 111 003

012

104 101

101

000

000

c*

c* 111 012 110 113

000

000

003 101

101 111

200

003 111

000

000

102

Fig. 5.17: (a–f) Calculated electron diffraction patterns of twin structures of Figure 5.16 (a–f) of r-BN and c-BN, respectively.

Bibliography

|

107

{113} twin structure is observed in Figure 5.14 (e). These twin structures are often observed in the r-BN nanoparticles. A TEM image and an electron diffraction pattern of c-BN nanoparticles synthesized from r-BN are shown in Figure 5.15 (a) and (b), respectively. Debye–Scherrer rings indexed as 111, 220, and 311 of c-BN are observed in Figure 5.15 (b). A TEM image and electron diffraction pattern of c-BN nanoparticle taken along [011] are shown in Figure 5.15 (c) and (d), respectively. The electron diffraction pattern shows {111} twin structure of c-BN. Based on the above observation, atomic structure models of four kinds of twin structure are proposed, as shown in Figure 5.16. The structures have mirror relation at the twin boundaries. The {101} twin structures of Figure 5.16 (a) and (d) are completely the same model from different directions, and the {113} twin structures of Figure 5.16 (b) and (e) are also the same. Calculated electron diffraction patterns of twin structures of Figure 5.16 (a)–(f) are shown in Figure 5.17 (a)–(f), respectively. Figure 5.17 (a)–(d) and (f) agree well with observed diffraction patterns of Figure 5.13 (d), 5.14 (f), 5.13 (f), 5.14 (e), and 5.15 (d), respectively, which confirms the proposed atomic models of twin structures. The {001} twin structure of Figure 5.17 (e) does not agree well with Figure 5.12 (f), which is due to microtwins and stacking faults of h-BN and r-BN, as observed in Figure 5.13 (c) and streaks along the c∗ -axis in Figure 5.12 (f). Although only {112} twin plane was found in h-BN [27], three kinds of {101}, {113}, and {001} twin planes were found in r-BN [28]. The {113} plane is consistent with {112} planes of h-BN, and the {001} twins of r-BN is due to the crystallographic characteristics such as ABCABC stackings. The {101} twins were often observed in r-BN, which would be due to low interfacial energy in r-BN.

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[4]

[5]

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[17]

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Hiraga K, Shindo D, Hirabayashi M, Kikuchi M, Kobayashi N, Syono Y. Crystal structures of Tl–Ba-Ca–Cu–O superconducting phases studied by high-resolution electron microscopy. Jpn. J. Appl. Phys. 1988, 27, L1848–L1851. Tokura Y, Takagi H, Uchida S. A superconducting copper oxide compound with electrons as the charge carriers. Nature 1989, 337, 345–347. Takagi H, Uchida S, Tokura Y. Superconductivity produced by electron doping in CuO2 -layered compounds. Phys. Rev. Lett. 1989, 62, 1197–1200. Oku T, Kajitani T, Hiraga K, Hosoya S, Shindo D. High-resolution electron microscopy of Ln2 CuO4 (Ln=Pr,Nd,Sm). Physica C 1991, 185–189, 547–548. Kajitani T, Hiraga K, Hosoya S, Fukuda T, Oh-Ishi K, Kikuchi M, Syono Y, Tomiyoshi S, Takahashi M, Muto Y. Electric and structural changes in Nd2 − x Cex CuO4-y with x ≤ 0.2. Physica C 1990,169, 227–236. Tokura Y, Takagi H, Watabe H, Matsubara H, Uchida S, Hiraga K, Oku T, Mochiku T, Asano H. New family of layered copper oxide compounds with ordered cations: prospective hightemperature superconductors. Phys. Rev. B 1989, 40, 2568–2571. Chen CH, Werder DJ, James ACWP, Murphy DW, Zahurak S, Fleming RM, Batlogg B, Schneemeyer LF. Superlattice modulation and superconductivity in the electron-doped Nd2 CuO4 − x Fx and Nd2 − x Cex CuO4 systems. Physica C 1989, 160, 375–380. Williams T, Maeno Y, Mangelschots I, Reller A, Bednorz G. Oxygen vacancy ordering in superconducting Nd2 − x Cex CuO4-y . Physica C 1989, 161, 331–334. Van Aken PA, Muller WF. Superstructure formation in the electron-doped superconducting system Nd2 − x Cex CuO4-𝛿 : A transmission electron microscopical study. Physica C 1991, 174, 63–70. Hiraga K, Oku T, Shindo D and Hirabayashi M. High-resolution electron microscopy study on crystal structures of high-Tc superconductors. J. Electron Micros. Technique 1989, 12, 228–243. Kajitani T, Oh-ishi K, Kikuchi M, Syono Y, Hirabayashi M. Neutron diffraction study on orthorhombic YBa2 Cu3 O6.74 and tetragonal YBa2 Cu3 O6.05 . Jpn. J. Appl. Phys. 1987, 26, L1144–L1147. Oku T, High-resolution electron microscopy and electron diffraction of perovskite-type superconducting copper oxides. Nanotechnol. Rev. 2014, 3, in press. Available Online: http: //www.degruyter.com/view/j/ntrev.ahead-of-print/ntrev-2014-0003/ntrev-2014-0003.xml de Fontaine D, Ceder G, Asta M. Low-temperature long-range oxygen order in YBa2 Cu3 Oz . Nature 1990, 343, 544–546. Plakhty V, Stratilatov A, Chernenkov Y, Federov V, Sinha SK, Loong CK, Gaulin B, Vlasov M, Moshkin S. X-ray studies of the YBa2 Cu3 O6 + x superstructures in the range of 0.40(3) ≤ x ≤ 0.73(3). Solid State Commun. 1992, 84, 639–644. Stratilatov A, Plakhty V, Chernenkov Y, Fedorov V. The structure of the ortho-III phase of YBa2 Cu3 O6 + x by X-ray scattering. Phys. Lett. A 1993, 180, 137–140. Bruneel E, Oku T, Degrieck J, Van Driessche I, Hoste S. Structural and mechanical properties of particulate, whisker and unidirectional Bi-2223 Ag composites. Key Eng. Mater. 2002, 206, 637–640. Bruneel E, Oku T, Penneman G, Van Driessche I, Hoste S. TEM study on the alignation of BSCCO-2223 phase along Ag-whiskers in a bulk composite. Key Eng. Mater. 2002, 206, 1473–1476. Bruneel E, Oku T, Penneman G, Van Driessche I, Hoste S. Origin of the nanocrystalline interface in superconducting Bi-2223/Ag composites: a SEM/HREM study, Supercond. Sci. Technol. 2004, 17, 750–755. Shindo D, Hiraga K, Hirabayashi M, Kikuchi M, Syono, Y. Structure analysis of high-Tc superconductor Bi–Ca–Sr-Cu–O by processing of high-resolution electron microscope images. Jpn. J. Appl. Phys. 1988, 27, L1018-L1021.

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[25] Hirotsu Y, Tomioka O, Ohkubo T, Yamamoto N, Nakamura Y, Nagakura S, Komatsu T, Matsushita K. Modulated structure of high-Tc superconductor Bi–Ca–Sr–Cu–O studied by high-resolution electron microscopy and electron diffraction. Jpn. J. Appl. Phys. 1988, 27, L1869-L1872. [26] Eibl O. Displacive modulation and chemical composition of (Bi, Pb)2 Sr2 Can − 1 Cun O2n + 4 (n = 2, 3) high-Tc superconductors. Physica C 1991, 175, 419–434. [27] Oku T, Hiraga K, Matsuda T, Hirai T, Hirabayashi M. Formation and structures of multiplytwinned nanoparticles with fivefold symmetry in chemical vapor deposited boron nitride. Diamond Relat. Mater. 2003, 12, 1918–1926. [28] Oku T, Hiraga K, Matsuda T, Hirai T, Hirabayashi M. Twin structures of rhombohedral and cubic boron nitride prepared by chemical vapor deposition method, Diamond Relat. Mater. 2003, 12, 1138–1145. [29] Onodera A, Inoue K, Yoshihara H, Nakae H, Matsuda T, Hirai T. Synthesis of cubic boron nitride from rhombohedral form under high static pressure. J. Mater. Sci. 1990, 25, 4279–4284. [30] Matsuda T, Uno N, Nakae H, Hirai T. Synthesis and structure of chemically vapour-deposited boron nitride. J. Mater. Sci. 1986, 21, 649–658. [31] Matsuda T, Nakae H, Hirai T. Density and deposition rate of chemical-vapour-deposited boron nitride. J. Mater. Sci. 1988, 23, 509–514.

6 HREM analysis of nanostructured materials 6.1 Defect structures Perovskite-type superconducting copper oxides have many types of layer structures with slightly different compositions. Thus, their crystals always include high-density of intergrowth with various types of structures, in addition to well-ordered regions. A typical example of such disordered regions is shown in Figure 6.1 (a), which is a one-dimensional lattice image of TlBa2 Ca3 Cu4 O11 taken with the incident beam perpendicular to the c-axis. Although the image does not represent each atom, stacking sequence of the layered structure can be distinguished; that is, thick black lines correspond to Tl and Ba layers, and thin white lines correspond to Ca layers with oxygen vacancy. In Figure 6.1 (a), two, three, five, and sixfold-Cu sequences (white lines) between Tl and Ba layers (thick black lines) are observed in addition to the usual fourfold Cu sequences. This intergrowth gives rise to steps decreasing of electron conductivity near Tc , showing multiple transition temperatures [1], because the structures with different numbers of Cu–O layers show different transition temperatures. This defect is very sensitive to annealing condition of the sample. The lattice images such as Figure 6.1 (a) can be easily observed, and have enough information on the intergrowth of various layer structures. Figure 6.1 (b) is also an HREM image of TlBa2 Ca3 Cu4 O11 , which has a higher resolution than that of Figure 6.1 (a). Although the HREM image is a two-dimensional image, it is not a structure image. It is interesting that the periodic Tl1234 Cu4

Tl1234 Cu4 Cu5

Cu2 Cu3

Cu5 Cu5 Cu5

Cu5

Cu5 Cu5

Cu6

Cu5 Cu5 Cu5

Cu6 c

Cu5

c b

Fig. 6.1: High-resolution lattice images of TlBa2 Ca3 Cu4 O11 taken with the incident beam (a) perpendicular to the c-axis and (b) parallel to the a-axis.

6.1 Defect structures

c

| 111

c

Tl Tl *

* *

Fig. 6.2: (a) High-resolution lattice images taken with the incident beam perpendicular to the c-axis. (b) More Tl-vaporized region.

intergrowth forms a new ordered structure with a long period. It would be difficult to synthesize this type of crystal with a single phase. It is well known that Tl atoms in the Tl-based superconductors are easily vapored at high temperatures, and Tl content deceases by annealing at high temperatures. Figure 6.2 has one-dimensional lattice images of Tl-vaporized regions. Starting composition of the sample was Tl : Ba : Ca : Cu = 2 : 2 : 2 : 3, and was sintered at 890°C for 10 h. In the lattice image in Figure 6.2 (a), black strain contrasts are observed, which resulted from lattice deformation around the terminations of Tl–O layers, being about to disappear by the vaporization of Tl, as indicated by small arrows. In Figure 6.2 (b), the vaporization of Tl progressed furthermore. The regions of Cu–O layers were expanded, and the strain field contrasts become stronger. After Tl–O layers disappear, remained Ba–O layers are observed, as indicated by arrows in Figure 6.2 (b). Similar intergrowth structures were often observed in the Pb-based superconductors [2, 3]. An intergrowth of (Pb, Cu) layers is observed in PbBaSrYCu3O7 (Pb-2212), as shown in Figure 6.3 (a). In the image, the intergrowth of two types of units, (a) and (b), which have double (Pb, Cu) layers and stacks of two (Pb, Cu) and one Cu layers is observed. A high density intergrowth in PbBa0.7 Sr1.3 YCe3 Cu3 O13 is also shown in Figure 6.3 (b). In this image, the intergrowth of various numbers of (Y, Ce) layers was ob-

112 | 6 HREM analysis of nanostructured materials

(a)

(b)

Y Ba Sr Pb Cu O Cu

Fig. 6.3: HREM images of (a) PbBaSrYCu3 O7 and (b) PbBa0.7 Sr1.3 YCe3 Cu3 O13 taken with the incident beam parallel to the a-axis. Number of (Y,Ce) layers are shown in (b).

served, and disappearance of (Pb, Cu) layers is also observed as indicated by arrows, and extended regions of the (Y, Ce) layers can be seen. Observations of the intergrowth give us variable information on the possibility of appearance of new unknown structures and on the transitional structures to the equilibrium state. Lattice defects, particularly dislocations in the superconductors having complex structures is an interesting subject to study mechanical and electrical properties of these materials. Figure 6.4 (a) is an end-on view of a dislocation observed in the ̄ direction parallel to the incident Tl2 Ba2 CuO6 [4]. The dislocation is laid along the [110] beam direction. An extra plane by obliquely viewing Figure 6.4 (a) along the vertical direction. Figure 6.4 (b) is a Fourier transform of Figure 6.4 (a), and Figure 6.4 (c) is ̄ ̄ reflection in the Fourier diffractogram an image reconstructed by using 110 and 110 of Figure 6.4 (b). Figure 6.4 (d) is an enlarged image of Figure 6.4 (c). In the image of Figure 6.4 (d), a long range strain field over 4 nm in diameter is observed around the dislocation core. Although a Burgers vector of this dislocation cannot be determined from only this image, it would be [100] of the perovskite unit. The smallest Burgers vector in the perovskite unit is 1/2 [111] position, but the dislocation with the [100] Burgers vector is possibly stable in this structure, because a different type of atom is placed at the 1/2 [111] position. This dislocation would be considered to be formed during crystal growth, and it would be placed in the most stable state.

6.2 Interfaces and surface structures

110

000

| 113

110

c [110]

c [110]

Fig. 6.4: (a) High-resolution image of an end-on view of a dislocation in Tl2 Ba2 CuO6 , taken with the ̄ direction. (b) Fourier transform of (a). (c) Image reconstructed by incident beam parallel to the [110] ̄ ̄ reflection in the Fourier diffractogram in (b). (d) Enlarged image of (c). using 110 and 110

6.2 Interfaces and surface structures Understanding of interface and surface structures is important for application of the superconductors to electronic devices such as the Josephson junction and superconducting transistor, as illustrated in Figure 6.5 (a) and 6.5 (b), respectively. Recently, the surface structure has been widely studied with scanning tunneling microscopy in the atomic scale. High-resolution electron microscopy has also made possible to observe atomic structures of interfaces and surfaces in the superconductors. Figure 6.5 (c) shows one-dimensional lattice image of an antiphase boundary in Tl2 Ba2 CuO6 , which was observed perpendicular to the c-axis. Tl layers are indicated by arrows, and the phase displacement is 0.2c along the c-axis at the interface. This indicates that the displacement corresponds to one-block of the perovskite cell, and the Tl layers are connected with Cu layer at the interface. Figure 6.5 (d) is a structure image of an antiphase boundary in TlBa2 CaCu2 O7 taken along the a-axis. The interface is {103} of the TlBa2 CaCu2 O7 structure, and the phase displacement is 0.21c + 0.5a. This indicates that the displacement corresponds to half-block of the perovskite cell, and the Tl layers are connected with the Ba layers at the interface. Small disordering of atoms

114 | 6 HREM analysis of nanostructured materials Superconducting layer Interface Barrier layer Insulator Carrier Substrate (a) Base

Electrode

Emitter Barrier layer

Tl layer

Surface Carrier Electrode (b)

Collector

Superconducting layer

Fig. 6.5: Schematic illustration of (a) Josephson junction and (b) superconducting transistor. HREM images at the interfaces of (c) Tl2 Ba2 CuO6 and (d) TlBa2 CaCu2O7 .

is observed at the interface within ∼ 2 nm, which would work as insulator layers between two crystals. These interfacial structures with distances of a few nanometers are suitable for the Josephson junction devices as shown in Figure 6.5 (a). Surface structures were also observed, which is an important information on the superconducting transistors as illustrated in Figure 6.5 (b). Figure 6.6 (a) is an HREM

6.2 Interfaces and surface structures

| 115

Tl Ba Cu Ca O

a

c c

a

Eu, Ce Pb, Cu

Tl Pb

a

Sr CuO

c a

c Cu

Tl

Cu Tl

Tl Ba Cu Ca O

c a

Fig. 6.6: HREM images of (a) TlBa2 Ca3 Cu4 O11 , (b) Tl0.5 Pb0.5 Sr2 CuO5 , (c) Pb2 Sr2 Y0.5 Ca0.5 Cu3 O8 , (d) PbBa0.7 Sr1.3 EuCeCu3O9 , and (e) TlBa2 CaCu2O7 , taken along the a-axis together with projected structure models.

structure image of TlBa2 Ca3 Cu4 O11 taken with the incident beam parallel to the a-axis. The image is observed without any contamination layers at the sample edge, and an atomic arrangement can be directly observed at the crystal surface. High-resolution images were obtained from thin samples, which were selected from crushed materials dispersed in a solution of n-butanol and dropped on holely carbon films. A mixing of Tl, Ba, Ca, and Cu atoms near the surface is observed. Figure 6.6 (b) is an HREM structure image of Tl0.5 Pb0.5 Sr2 CuO5 taken along the a-axis together with projected structure model, which indicates no preferential surface structure. Figure 6.6 (c) is an HREM structure image of Pb2 Sr2 Y0.5 Cu3 O8 , and a characteristic surface structure with valleys at Pb layers and hills at between the Pb layers is observed. In the region of the hills, mixing of atoms appears to occur. An HREM structure image of PbBa0.7 Sr1.3 EuCeCu3 O9 taken along the a-axis is shown in Figure 6.6 (d), which indicates preferential atomic arrangements on the c-plane of the crystal. A HREM structure image of TlBa2 CaCu2 O7 is also shown in Figure 6.6 (e). At the crystal edge, preferential fracture occurs between Tl and Ba layers, as indicated by arrowheads, and the fracture surface has steps with Tl layers [5]. This result shows that the fracture surface parallel to the c-plane in the superconductor is stable and chemically unreactive to the solution and the atmosphere. On the other hand, the surface structures of the fracture nearly perpendicular to the c-axis show complex structures formed by rearrangement of atoms near the edge. However, Hg-based copper oxides showed stable surface, as will be described in Section 6.6. The characteristics of various surface structures should be taken into consideration, when the properties are sensitive to surface structures.

116 | 6 HREM analysis of nanostructured materials

6.3 GaAs-based semiconductor devices GaAs has high electron mobility and a wide direct band gap, and is attractive for specific electronic devices, such as high-frequency microwave and optoelectronic devices, which perform functions unattainable by Si devices. In addition, compared with the Si devices, the GaAs devices operate at lower power, and are more radiation tolerant. Despite these advantages, there are several technological hurdles to fabricate manufacturing GaAs devices. Development of low resistance, thermally stable ohmic contacts to n-type GaAs is one of the highest hurdles for the future very large scale integration (VLSI) metal-semiconductor field effect transistor (MESFET) devices. The purpose of this investigation is twofold. The first is to search a process window to reduce the contact resistance by adding a small amount of In or Au to the NiGe ohmic contacts. Indium is chosen as the third element, because In is expected to form an intermediate Inx Ga1 − x As layer with low-energy barrier between the metal and the GaAs substrate, leading to a reduction of the contact resistances. The Au was also chosen as the third element, because the formation of a small volume fraction of the AuGa phases would reduce the contact resistance without deteriorating the desirable properties of the NiGe contacts. The second purpose is to understand the ohmic contact formation mechanism of these contacts by analyzing the interfacial structure using a cross-sectional HREM. This microstructural study will indicate a key parameter which strongly influences the current transport at the metal and GaAs interface [6–8]. Prior to metal deposition, the GaAs wafers were cleaned by dipping in straight HCl for 1 min, following by a deionized water rinse and air blow dry. They were loaded into an electron beam evaporation system equipped with a cryopump. Ni and Ge were evaporated using an electron beam, and In was evaporated by a resistance heater. Samples with three-layered structure of GaAs/Ni/In/Ge were prepared, where the thicknesses of the Ni and In layers were changed, keeping Ge layers at 100 nm thick (a slash between two elements indicates deposition sequence). Contact resistances of previously developed NiGe ohmic contacts were reduced significantly by adding a small amount of In to the NiGe contacts without deteriorating the thermal stability, the surface smoothness, and the shallow diffusion depth. The optimum layer thicknesses to prepare the low resistance ohmic contacts were determined to be 60 nm for Ni, 100 nm for Ge, and 3 nm for In, and the contact resistances (Rc ) less than 0.3 Ωmm were obtained after annealing at temperatures in the range between 600°C and 700°C in a rapid thermal annealer filled with 5% H2 /N2 gas. Figure 6.7 (a) is an HREM image of the contact as prepared. During the TEM specimen preparation, the contact was annealed at ∼ 100°C, and Ni atoms diffused into the GaAs substrate through the native oxide layer at the GaAs surface, forming the Nix GaAs compound as observed in Figure 6.7 (a). The native GaAs oxide layer would block the carrier transport between the GaAs substrate and metal. The Ni layer on the top of the native oxide layer did not react at this temperature. The HREM image at the

6.3 GaAs-based semiconductor devices | 117

Ni

oxide

Gate

Source (metal) e앥

n

n쎵

NixGaAs

Drain (metal) e앥 n쎵

GaAs semi-insulating substrate (d)

NiGe O

a

EF EC

b

n쎵쎵-Ge n쎵쎵쎵 InGaAs n GaAs

Metal InGaAs

n쎵-GaAs

EV GaAs

(e)

NiGe

a O

EF EC GaAs Gel Metal

n쎵쎵GaAs

n쎵-GaAs

EV

GaAs (f )

Fig. 6.7: HREM images of (a) GaAs/Ni/Ge, (b) GaAs/InGaAs/NiGe, and (c) GaAs/NiGe interfaces. (d) Schematic illustration of GaAs MESFET. Energy band diagrams of the interfaces with (e) low barrier height and (f) heavy doping.

GaAs/Nix GaAs interface shows an epitaxial relation that the {102} plane of the Nix GaAs compound is parallel to the {110} plane of the GaAs substrate. Although weak contrast of a strain field due to the lattice mismatch is seen, the interface is almost coherent.

118 | 6 HREM analysis of nanostructured materials In order to directly observe the microstructure at the GaAs/metal interface, HREMs were performed for the Ni (60 nm)/In (3 nm)/Ge (100 nm) contacts which provided the lowest contact resistance. Figures 6.7 (b) is a high-resolution image of the contact annealed at 700°C for 5 s, which produced the low contact resistance (∼ 0.3 Ωmm). The GaAs/NiGe interface would be related to the main electron transport. Majority of Ni in the Nix GaAs layers reacted with Ge forming NiGe compounds, and the GaAs surface is covered by the NiGe compounds as shown in Figure 6.7 (b). A “regrown” GaAs layer was formed at the GaAs/NiGe interface by outdiffusing of Ni atoms from the Nix GaAs layer. The regrown GaAs and Inx Ga1 − x As layers are measured to be about 50 nm in thickness, and the {111} twin-related structure is observed in these layers. The In composition (x) of the Inx Ga1 − x As was measured to be about 0.4 from lattice spacings of the high-resolution images, which agrees with the value calculated from the diffraction spots. Figure 6.7 (d) is a schematic illustration of GaAs MESFET, and the GaAs/metal interfaces are indicated by circles. A transition from Schottky to ohmic behavior can be achieved by reducing the barrier height and/or by doping the GaAs heavily with donors at the GaAs/metal interface. There are two energy barriers for electron transportation through the n+− GaAs/regrown n++ -GaAs/n+ -Inx Ga1 − x As/NiGe interface; one is the energy barrier (𝜙a ) between n+ -Inx Ga1 − x As and NiGe and the other is the energy barrier (𝜙b ) between n++ -GaAs and n+ -Inx Ga1 − x As, as illustrated in Figure 6.7 (e). The Rc value at the GaAs/Inx Ga1 − x As/NiGe interface is determined by the serial resistances through these two barriers. Although absolute barrier heights of 𝜙a and 𝜙b are not known, it is likely that the barrier 𝜙a is higher than 𝜙b because the n+ -Inx Ga1 − x As layer is epitaxially grown on the regrown n++ -GaAs. Therefore, the Rc values of the present NiGe(In) contacts are believed to be controlled by the barrier height of 𝜙a . In order to justify the above assumption, the Rc was calculated using a 𝜙a value which was determined from the Inx Ga1 − x As layer [9]. The Rc values of the metal/Inx Ga1 − x As with x = 0.4 were calculated as a function of the doping levels and the barrier heights, where a barrier height 𝜙a , for the metal/Inx Ga1 − x As contacts was obtained by the relationship 𝜙a (eV) = 0.95 − 1.90x + 0.95x2 [10]. The Si doping level in the GaAs substrate used in the contact resistance measurement is close to 2×1018 cm−3 , and the doping level at the Inx Ga1 − x As layer was assumed to be this level. Using these values, the Rc value was calculated to be about 5 × 10−6 Ωcm2 . Typical Rc values obtained routinely in the present NiGe(In) contacts are about 5 × 10−6 Ωcm (∼ 0.3 Ωmm) and agree very well with the calculated value. This indicates that the 𝜙a value controls the Rc values of the NiGe(In) contacts. Therefore, the key parameter to determine the Rc value of this contacts is the total area of the regrown GaAs and the Inx Ga1 − x As layer covering the GaAs substrate. The microstructure of the Ni (40 nm)/Au (5 nm)/Ge (100 nm) contacts with low Rc was also investigated. At the initial stages of annealing at 300°C, most of the Ni react with the GaAs to form the ternary Nix GaAs compounds. It is believed that a small frac-

6.4 Zeolite materials |

119

tion of Ge may be contained in this Nix GaAs layer, because the Ni atoms attract the Ge atoms due to strong binding energy between Ni and Ge. At the later stages of annealing at 300°C, the Nix GaAs layer partially decomposes. The GaAs layer, which once formed the Nix GaAs layer, grows epitaxially on the GaAs substrate as observed in Figure 6.7 (c). It is believed that the Ge atoms remain in this regrown GaAs layer because of the slow diffusivity of Ge in GaAs. At this temperature, the Ni atoms in the Nix GaAs layer partially interact with Ge, forming NiGe compounds. During subsequent annealing at elevated temperatures above 300°C, a part of the Ga atoms in the Nix GaAs layer react with Au to form 𝛼-AuGa compounds. The exact current transport mechanism of this contact with low Rc is not clear at the moment. The first model is that the low contact resistance is due to heavy Ge doping in the regrown GaAs layer. When the Ga in the Nix GaAs layer react with Au, Ga vacancies would form in the regrown GaAs layer and the number of the Ge atoms which occupy the Ga vacancies is larger than that occupying the As sites, resulting in the formation of an n++ -GaAs layer doped heavily with Ge. The carriers would transport through the n+ -GaAs/n++ -GaAs/metal interface by the tunneling mechanism, as illustrated in Figure 6.7 (f). Another model to explain the low Rc values is that the Rc reduction is due to the reduction of the barrier height at the n-GaAs/metal interfaces by forming a thin n++ Ge layer, as illustrated in Figure 6.7 (e). In Figure 6.7 (c), a contrast of the regrown GaAs layer near the NiGe is different from that of the GaAs, which might be due to the existence of the epitaxially grown Ge layer. The barrier height at the n+-Ge/metal interface is in the range of 0.2–0.4 eV. This barrier height is lower than that at the n+GaAs/metal interface (∼ 0.8 eV), which results in the low contact resistance.

6.4 Zeolite materials Zeolite cage structures were investigated by the HREM method [11, 12]. The HREM images of [Na48 ][Al48 Si144 O384 ] along [110] and [111] recorded close to Scherzer defocus with a slow-scan CCD camera are shown in Figure 6.8 (a) and (b), respectively. The images were Fourier filtered and processed by crystallographic image processing. The projected structure models along [110] and [111] are also shown in Figure 6.8 (c) and (d). The iron atom positions inside the framework of zeolite [Na48 (Fe2 O3 )38 ][Al48 Si144 O384 ] were determined by means of electron crystallographic methods from high-resolution electron micrographs and selected area electron diffraction. The atom positions of the Si/Al network were found to coincide with those of the structure determined from single-crystal XRD methods. The iron-containing zeolite was also refined in the space group Fd3m (a = 2.47 nm) with 42 unique reflection amplitudes from electron diffraction [11]. The Fe6 O n molecule is situated in the sodalite cage with the iron atoms facing the square windows of the cage. The Fe–Fe distance is 0.36 nm and the Fe–O distances to the nearest oxygen atoms in the sodalite cage are close to 0.22 nm.

120 | 6 HREM analysis of nanostructured materials

Fig. 6.8: HREM images of [Na48 ][Al48 Si144 O384 ] along (a) [110] and (b) [111] recorded close to Scherzer defocus with a slow-scan CCD camera, after image processing. Projected structure models along (c) [110] and (d) [111].

6.5 Solid clusters and doping atoms Although the oxygen atoms are not resolved in Ag2 SnO3 in Figure 4.8 because of a smaller atomic number compared with Sn and Ag, a cluster structure with the light element boron is directly observed [13]. High-quality single crystals of Al2.6 Cu1.8 B105 were prepared using the solution growth technique [14, 15]. The purity of starting materials was as follows: Al, 99.99%; Cu, 99.999%; B, 99.5%. Each of the starting mixture with the required composition was placed in an Al2 O3 crucible and heated in an argon atmosphere using a vertical Al2 O3 tube furnace equipped with SiC resistors. The temperature of the furnace was increased to 1500°C, kept for 3 h, and then cooled to room temperature. The crystals grown in the solidified mixture were separated by dissolving the excess metal solvent Al or Cu with nitric acid. The chemical compositions of the Al–Cu–B crystals were determined using inductively coupled plasma atomic emission spectroscopy. Figure 6.9 (a) is an atomic structure model of a B84 cluster projected along the 5-, 3-, and 2-fold axis, which exists in B12 -based 𝛽-rhombohedral boron. An HREM image of Al2.6 Cu1.8 B105 taken along [211] is shown in Figure 6.9 (b). To observe the atomic

6.5 Solid clusters and doping atoms

5-fold

3-fold

|

121

2-fold

B 84

Al, Cu

Al, Cu

B12 B12 B12

Fig. 6.9: (a) Atomic structure models of a B84 cluster projected along the 5-, 3-, and 2-fold axes. (b) HREM image of Al2.6 Cu1.8 B105 after crystallographic image processing. (c) Structure models of Al2.6 Cu1.8 B105 with B12 -based 𝛽-rhombohedral boron structure, projected along [211]. (d) Simulated HREM image of Al2.6 Cu1.8 B105 .

122 | 6 HREM analysis of nanostructured materials arrangements clearly, a crystallographic image processing was carried out. Crystallographic symmetrization based on the two-dimensional space group of cmm was used for the reconstruction of the Fourier transform, as shown in Figure 6.9 (b). Al and Cu atoms are clearly observed at the doping positions, as indicated by arrows. The B12 icosahedra clearly show circular contrast. The present result indicates that it is possible to detect the arrangements of the doping element sites in B clusters that consist of light elements. The B84 clusters are directly observed in the image. A projected structure model of Al2.6 Cu1.8 B105 along [211] is shown in Figure 6.9 (c), and the doping atoms of Al and Cu atoms exist at the doping sites. The lattice parameters of Al2.6 Cu1.8 B105 used in this work is a = 1.1002 nm, c = 2.3976 [14]. The atomic coordinates and temperature factors of AlB31 [20] were used for Al2.6 Cu1.8 B105 , and metal occupancies were in the range of 0.60–0.05. It is assumed that each metal site is occupied by an Al/Cu ratio of 13/9 in the crystal. An HREM simulation image of Al2.6 Cu1.8 B105 is shown in Figure 6.9 (d) and agrees well with the experimental data of Figure 6.9 (b) [13].

6.6 Surface structure with light elements Although the B12 clusters were detected in the form of atomic clusters in Figure 6.9 (b), a description of the possibility of light element detection, in the form of a 1 atom in the plane of projection, follows. An HREM image of Hg0.5 Tl0.5 Ba2 CuO5 taken along the [010] direction (a-axis) is shown in Figure 6.10 (a), together with a projected structure model [5]. The Hg0.5 Tl0.5 Ba2 CuOx sample was prepared by a solid-state reaction using a wrapped gold foil and a sealed quartz tube technique from the starting materials of HgO (yellow), Tl2 O3 , BaO2 , and CuO. The upper side of the image is a vacuum in the electron microscope. There is no contamination layer at the sample edge, and the surface is stable and chemically inert to both the solution (n-butanol) and the atmosphere (air). The HREM image clearly shows the metal atom arrangements in the crystal, and the lines indicate the unit cell. The darkness and size of the black spots corresponding to (Hg,Tl), Ba, and Cu positions can be identified as being nearly proportional to their atomic numbers. A sharp flat crystal edge consisting of {100} (a planes) is observed at the surface in the atomic scale. An enlarged HREM image of the surface of Figure 6.10 (a) is shown in Figure 6.10 (b). A weak black contrast is observed outside the (Hg,Tl) layers, as indicated by arrows in Figure 6.10 (a) and (b). Each metal atom has an original atomic position, and there is no rearrangement of metal atoms. There is also no stable Cu–(Hg,Tl)– Cu layer at the surface. To observe the black contrast outside the (Hg,Tl) layers, the 200–255 gray scale was extracted from the original image (0–255) of Figure 6.10 (b), as shown in Figure 6.10 (c). Black dots are clearly observed outside the (Hg,Tl) layers as indicated by arrows and are believed to be oxygen atoms [16]. From the HREM observation, a surface structure model of Hg0.5 Tl0.5 Ba2 CuOx was proposed, as shown in Figure 6.10 (d). The atomic coordinates are based on the XRD analysis of HgBa2 CuOx .

6.6 Surface structure with light elements |

123

Hg Tl Ba Cu O

O

O

Ba HT

Ba Cu

O

Ba HT

O

Ba

Ba Cu

O

HT

Ba Cu

HT

Ba

Ba Cu

HT

O

(d)

O

O

HT

O

O Hg, Tl Ba Cu Ba HT

Ba Cu

Ba HT

Ba Cu

HT

Fig. 6.10: (a) HREM image of Hg0.5 Tl0.5 Ba2 CuO5 taken along the [010] direction. (b) Enlarged HREM image of Hg0.5 Tl0.5 Ba2 CuOx . HT indicates the Hg and Tl atoms. (c) Image depth of 200–255 gray scale. (d) Surface structure model of Hg0.5 Tl0.5 Ba2 CuOx . (e) Corresponding simulated HREM image.

The Hg, Tl, and oxygen occupancies of (Hg,Tl) layers were assumed to be 0.5. In Figure 6.10 (d), oxygen atoms exist 0.34 nm outside the Hg layers, as determined from the observed HREM image of Figure 6.10 (b). The simulated HREM image based on the proposed model agrees well with the experimental one, as shown in Figure 6.10 (e). To apply superconducting thin films to electronic nanoscale devices, the {100} plane (a-plane) should be flat and stable in the atomic scale because the carrier transport is parallel to the a-axis. Most high-Tc superconducting oxides have layered structures, with c-planes more stable than a-planes [5]. In this investigation, stable a-planes of Ba–O–Ba layers were observed outside the Hg layers in Hg0.5 Tl0.5 Ba2 CuO5 (1201-type structure). It is believed that the Hg layers are unstable because of the oxygen vacancies and that the oxygen atoms are effective for the stabilization of the {100} surface of Hg layers. The present result indicates that direct atomic determination of light elements such as oxygen is possible under special conditions.

124 | 6 HREM analysis of nanostructured materials

6.7 Crystal structures of Pb-based copper oxides Pb-based superconductors and related oxides have been discovered and investigated [17], and various new types of crystal structures of PbBaSrY1 − x Cax Cu3 O7 , Pb(Ba,Sr)2 (Ln,Ce)n Cu3 O5 + 2n (n = 1−5) and Pb2 Sr2 (Ln,Ce)n Cu3 O6 + 2n (n = 1−7) (Ln: lanthanoid) [18, 19] were determined by high-resolution electron microscopy, with the aid of electron and X-ray diffraction, and quantitative analysis of compositions of cations and oxygen. Some results of the determination of crystal structures are shown here. Samples were prepared from a mixture of PbO, BaO2 , Sr2 CuO3 , Y2 O3 , Eu2 O3 , CeO2 , and CuO by solid state reaction. After heating at 830°C in a 1% O2 –N2 mixed gas, the specimens were slowly cooled in a furnace, quenched into liquid nitrogen or annealed in a flowing O2 gas at 400°C. Electron probe microanalysis and iodide titration method are used for quantitative analysis of the element. Figure 6.11 (a) is a high-resolution structure image of PbBaSrYCu3O7 [2] taken with the incident beam parallel to the a-axis. The PbBaSrYCu3O7 shows superconductivity at 65 K by Ca substitution for Y sites [18]. An HREM image after crystallographic image processing of Figures 6.11 (a) is shown in Figure 6.11 (b). PC, BS, and Ov represent

OV Y

c

Y Cu BS BS PC PC PC BS Cu Cu OV Y Cu Cu BS PC PC PC BS BS Cu Y Y

c a

OV

a c*

110

000

110

000

110

Fig. 6.11: (a) HREM image of PbBaSrYCu3 O7 taken with the incident beam parallel to the a-axis. (b) HREM image after crystallographic image processing of (a). Electron diffraction patterns of PbBaSrY0.7 Ca0.3 Cu3 O7 taken with the incident beam parallel to the (c) [001] and (d) [110] directions.

6.7 Crystal structures of Pb-based copper oxides

| 125

(Pb,Cu), (Ba,Sr), and oxygen vacancy, respectively, and the image directly shows an arrangement of cations. The indicated atomic arrangements were proposed from the structure image, X-ray diffraction and energy dispersive spectroscopy (EDS) analysis. In Figure 6.11 (b), zigzag arrays consisting of larger black spots correspond to (Pb,Cu) layers, and on both sides of the (Pb,Cu) layers, there are layers of a mixture of Ba and Sr atoms. In this image, Cu and Y atoms, with smaller atomic numbers, are represented as small dark spots. Oxygen atom positions are located at bright regions between the cation sites of the dark spots. In addition, the oxygen vacant positions on the Y layers, indicated by Ov , can be distinguished as brighter regions from the other bright regions corresponding to the oxygen occupied sites in Figure 6.11 (b). Darkness of the spots in the double (Pb,Cu) layers in Figure 6.11 (a) suggests that the zigzag double layers contain some light element, Cu in addition to Pb. A random mixture of Pb and Cu in the double Pb layers is unlikely because of their different ionic radii and coordination schemes. Careful examination of contrast for the double Pb layers in a thin part near the crystal edges, as indicated by arrows in Figure 6.11 (a), suggests the pairwise distribution of Pb and Cu layers [3]. Some of these spots are large and dark, while some others are small and faint, which would correspond to Pb and Cu, respectively. The observed HREM image indicates that small domains of Pb and Cu layers alternate every several unit cells. This short range ordering seems to be twodimensional in the Pb and Cu layers, and Pb and Cu layers are not distinguishable due to an averaging effect in a thicker part of the specimen. Atomic coordinates of PbBaSrYCu3O7 determined from the high-resolution structure image of Figure 6.11 (b) are shown in Table 6.1. The z coordinates of oxygen atoms in (Pb,Cu) and Cu–O layers were assumed to be the same as those of cations, and oxygen positions in (Ba, Sr) layers were assumed to be shifted by 0.03 nm along the c-axis from the results of other Pb-based oxides [17]. Figure 6.11 (c) and (d) are electron diffraction patterns of PbBaSrY0.7Ca0.3 Cu3 O7 taken with the incident beam parallel to the [001] and [110] directions, respectively. Satellite reflections at 1/2 1/2 0 are observed, and weak reflections at 1/4 1/4 0 are also observed in Figure 6.11 (c), which indicates a modulated superstructure with a modulation wave vector of q = 1/4⟨1 1 0⟩, and the modulation would be due to oxygen ordering. Weak streaks at 1/2 1/2 0 along the c-axis are also observed in Figure 6.11 (d), which indicates stacking faults of the superstructure along the c-axis. The similar modulated superstructure with a modulation wave vector of q = 1/4⟨1 1 0⟩ was also observed in PbBa0.7 Sr1.3 EuCeCu3 O9 [19]. A high-resolution structure image of PbBa0.7 Sr1.3 EuCeCu3 O9 , which was taken with the incident beam parallel to the a-axis, is shown in Figure 6.12 (a). Here, the foil thickness increases from the top to the bottom in the picture. The image contrast of the thin region directly represents the projected potential. The structure model of PbBa0.7 Sr1.3 EuCeCu3 O9 was determined from the structure image by the aid of X-ray diffraction. The structure has a characteristic layer structure formed by alternate stacking of (Eu,Ce) double layers and (Pb,Cu) double layers, which are separated by

126 | 6 HREM analysis of nanostructured materials

Cu Eu Ce Sr Ba Pb Cu O

Cu O Sr Ce Y

c

c

a

a

Ce Y Cu O Pb Cu Sr Ba

Cu

Cu

Eu Ce Sr Ba Pb Cu O

Eu Ce Sr Ba Pb Cu O

Cu O Sr

Cu O Sr

Ce Y

Ce Y

Pb

Pb

c

a

Fig. 6.12: HREM images of (a) PbBa0.7 Sr1.3 EuCeCu3O9 , (b) PbBa0.7 Sr1.3 YCe2 Cu3 O11 and (c) Pb2 Sr2 (Y,Ce)5 Cu3 O16 taken with the incident beam parallel to the a-axis, together with projected structure models. Calculated images of two models of (d) PbBa0.7 Sr1.3 EuCeCu3 O9 and (e) Pb2 Sr2 (Y,Ce)5 Cu3 O16 with the a-axis incident, together with projected structure models.

6.7 Crystal structures of Pb-based copper oxides

| 127

Table 6.1: Structural parameters of cations and oxygen atoms in PbBaSrYCu3 O7 , determined from the high-resolution structure image of Figure 6.11 (b). See the text about the z coordinates of oxygen sites. Space group I4/mmm. a = 0.3847 nm and c = 2.748 nm. Atom

Site

x

y

z

Occupancy

Pb Ba Sr Y Cu(1) Cu(2) O(1) O(2) O(3)

4e 4e 4e 2a 4e 4e 8g 4e 4e

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0.5 0 0

0.283 0.130 0.130 0 0.283 0.438 0.062 0.359 0.217

0.5 0.5 0.5 1 0.5 1 1 1 0.5

(Ba,Sr) and Cu layers. In Figure 6.12 (a), (Eu,Ce) atoms are represented as the largest dark spots. The z coordinates were directly determined from the observed highresolution images. Figure 6.12 (b) is a high-resolution structure image of PbBa0.7 Sr1.3 YCe2 Cu3 O11 , which was taken with the incident beam parallel to the a-axis, together with a structure model. A good correspondence between the arrangement of dark spots in the image and that of cations in the projected structure model of PbBa0.7 Sr1.3 YCe2 Cu3 O11 is clearly observed. The image shows a layer structure with three (Y,Ce) layers between Cu–O layers. The atomic coordinates were directly determined from the observed high-resolution images as summarized in Table 6.2. Structure models of Table 6.2: Structural parameters of cations and oxygen atoms in PbBa0.7 Sr1.3 YCe2 Cu3 O11 , which were determined from the high-resolution image of Figure 6.12 (b). Oxygen sites were assumed. Space group I4/mmm. a = 0.385 nm. c = 3.80 nm. Atom

Site

x

y

z

Occupancy

Pb Ba Sr Ce(1) Ce(2) Y(1) Y(2) Cu(1) Cu(2) O(1) O(2) O(3) O(4)

4e 4e 4e 2a 4e 2a 4e 4e 4e 8g 8g 4e 4e

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0.5 0.5 0 0

0.225 0.337 0.337 0 0.434 0 0.434 0.225 0.111 0.033 0.111 0.171 0.275

0.5 0.35 0.65 0.67 0.67 0.33 0.33 0.5 1 1 1 1 0.5

128 | 6 HREM analysis of nanostructured materials

Ce Y Sr Ba Pb Cu

Y Ca

Cu O

2242

2222 2212

(a)

2232

c

2252

a a

Cu O Sr

Ce Y

c 2

c Y Ca

2

Pb

(b)

3212

3222

3232

3242

3252

Fig. 6.13: Structure models of (a) Pb(Ba,Sr)2 (Ln,Ce)n Cu3 O5+2n (n = 1−5) and (b) Pb2 Sr2 (Ln,Ce)n Cu3 O6+2n (n = 1−5) determined from high-resolution electron microscopy.

Pb(Ba,Sr)2 (Ln,Ce)n Cu3 O5 + 2n (n = 1–5) determined by this work are summarized in Figure 6.13 (a). In addition to the Pb(Ba,Sr)2 (Ln,Ce)n Cu3 O5 + 2n (n = 1–5) with double (Pb,Cu) layers, Pb2 Sr2 (Ln,Ce)n Cu3 O6 + 2n (n = 1–7) with triple (Pb,Cu) layers were investigated by high-resolution electron microscopy. Figure 6.12 (c) is an HREM image of the Pb2 Sr2 (Y, Ce)5 Cu3 O16 [20] taken with the incident beam parallel to the a-axis, together with a determined structure model, as listed in Table 6.3. This structure can be character-

6.8 Structures of Sm-based copper oxides

| 129

Table 6.3: Structural parameters of cations and oxygen atoms in Pb2 Sr2 YCe4 Cu3 O16 , which were determined from the high-resolution image of Figure 6.12 (c). Oxygen sites were assumed. Space group P4/mmm. a = 0.383 nm. c = 2.65 nm. Atom

Site

x

y

z

Occupancy

Pb Sr Ce(1) Ce(2) Ce(3) Y(1) Y(2) Y(3) Cu(1) Cu(2) O(1) O(2) O(3) O(4) O(5)

2h 2g 2g 2h 1b 2g 2h 1b 1a 2h 2g 2h 4i 4i 4i

0.5 0 0 0.5 0 0 0.5 0 0 0.5 0 0.5 0 0 0

0.5 0 0 0.5 0 0 0.5 0 0 0.5 0 0.5 0.5 0.5 0.5

0.068 0.168 0.305 0.398 0.5 0.305 0.398 0.5 0 0.237 0.068 0.157 0.237 0.352 0.449

1 1 0.8 0.8 0.8 0.2 0.2 0.2 1 1 1 1 1 1 1

ized as a layer structure formed by stacking of fivefold (Y,Ce) fluorite layers between (PbO–Cu–PbO) blocks. The observed image of Figure 6.12 (a) was examined in detail with the aid of computer simulations. Multislice calculations were carried out with the z coordinates obtained from high-resolution image. Two types of oxygen positions (left: tetrahedral sites, right: octahedral sites) between (Eu,Ce) layers were assumed, as shown in Figure 6.12 (d). The calculated image of Figure 6.12 (d) with oxygen positions at tetrahedral sites, under the condition of a defocus of −35 nm and a crystal thickness of 1.93 nm, is in good agreement with the observed image of Figure 6.12 (a), compared with Figure 6.12 (d). This result shows that the positions of oxygen atoms can be determined by comparing calculated images with observed images. The observed image of PbBa0.7 Sr1.3 YCe2 Cu3 O11 in Figure 6.12 (c) was also investigated by comparing with computer simulations. The z coordinates obtained from the high-resolution image of Figure 6.12 (b) were used, as listed in Table 6.3, and two types of oxygen positions at tetrahedral sites and octahedral sites between (Y,Ce) layers were assumed. The calculated image of oxygen positions at tetrahedral sites in Figure 6.12 (e) agrees well with the observed image of Figure 6.12 (b).

6.8 Structures of Sm-based copper oxides Oxygen positions can be estimated by comparing experimental HREM images and simulated images. As described above, metal atoms with a larger atomic numbers are ob-

130 | 6 HREM analysis of nanostructured materials served as dark dots. On the other hand, oxygen atoms with a smaller atomic number indicate only weak contrast in the structure images, compared with metal atoms. Therefore, the direct determination of oxygen atom positions is difficult, except under special conditions. However, comparison of the HREM images with simulated images enables us to determine the oxygen atomic positions with a smaller atomic number. First of all, metal atom positions are determined from the HREM images, and oxygen positions can be assumed from appropriate distance between oxygen and cations based on the crystal chemistry. Based on the assumed positions of oxygens, image simulation is carried out, and oxygen atom positions are determined by comparing the HREM images with calculated images.

O Cu

* * * * * *

O Cu

Cu

Sm O

La Sr

Sm

Sm c a Cu Sm O

A *

* * *

Cu O La Sr Sm

t = 1.18

1.57

1.96

2.35

2.74 nm

t = 1.18

1.54

1.92

2.32

2.70 nm

* *

Cu O La Sr Sm

c a

Fig. 6.14: HREM images of (a) Sm2 CuO4 and (b) SmLa0.75 Sr0.25 CuO4 taken along the a-axis. (c) Structure models and calculated images of the (d) Sm2 CuO4 and (e) SmLa0.75 Sr0.25 CuO4 , respectively.

6.9 Y-based copper oxides with high Jc

| 131

A high-resolution image of Sm2 CuO4 taken with the [100] incidence is shown in Figure 6.14 (a) [21]. The specimen thickness increases from the top to the bottom in this HREM image. The observed image shows the projected arrangement of metal atoms. There are two kinds of dark spots in the image. The larger ones in the zigzag arrays correspond to the Sm atoms. Cu atoms, with a smaller atomic number, are represented as less dark spots between the double Sm layers. Figure 6.14 (b) is an HREM image of SmLa0.75 Sr0.25 CuO4 taken along the a-axis. Fairly large separation between two lines of La ions is clearly observed in the HREM image, which is in accord with X-ray diffraction analysis [22]. Based on the crystal structure models of Figure 6.14 (c), image calculations on the Sm2 CuO4 and SmLa0.75 Sr0.25 CuO4 were carried out to confirm the structures, as shown in Figure 6.14 (d) and (e), respectively. The images of Figure 6.14 (d) and (e) calculated at a Scherzer defocus of −45 nm and a crystal thickness of 1.2–2.7 nm, agree well with the observed image contrast for both thin and thick regions. For the SmLa0.75 Sr0.25 CuO4 structure, the difference of oxygen atom positions in the Sm and La-Sr layers are clearly observed both in the observed and calculated image, which indicates the HREM image includes information both on metal and oxygen atoms in the crystal.

6.9 Y-based copper oxides with high Jc Superconducting thin films can be used for electronic devices and other applications. Chemically vapor deposited (CVD) YBa2 Cu3 O7 thin films with high critical current density (Jc ) of 6.5 × 104 A/cm2 at 77.3 K and 27 T were investigated [23, 24]. The films were deposited on the SrTiO3 (100) substrate. 𝛽-diketonate complexes (2,2,6,6-tetramethyl 1-3, 5-heptanedionate chelated Y3+ , Ba2+ , and Cu2+ ) were used as the three vapor sources [25]. The films were deposited in a mixed gas atmosphere or Ar/O2 = 3/1 at 10 Torr on the substrate which was heated at 900°C close to the melting point of YBa2 Cu3 O7 − y . The post-annealing was carried out in the O2 atmosphere at 1 atm. To view the cross-section of the CVD film, two pieces of cut substrate and film were pasted together, film to film, then cut again perpendicular to the film and polished in an Ar ion sputtering mill. Figure 6.15 (a) is a low magnification image obtained with the incident beam perpendicular to the substrate. Relatively large grains of 20–100 nm in size are observed in the image. Many observed precipitates showed Moiré fringes, which indicates that the precipitates are semicoherent with the matrix and have very similar crystal lattice. A cross sectional high-resolution image is shown in Figure 6.15 (b). Relatively large precipitates ∼ 30 nm in size are embedded parallel to the c-planes. These precipitates could act as the flux-pinning-centers, which would result in the high Jc . Many defect regions are formed parallel to c-planes, as shown in Figure 6.15 (c). The defect regions consist of extra layers and ∼ 20 nm in diameter with deformed regions adjacent to them. Those faulted regions may also act as the flux-pinning centers. Figure 6.15 (d)

132 | 6 HREM analysis of nanostructured materials

c c

1 c 2 Cu

c

Ba

O CuO

Y

c

CuO

c a Cu O

Ba Y Ba

OV OV OV

c a

Fig. 6.15: (a) Low magnification image of CVD-YBa2Cu3 O7 film taken with the electron beam perpendicular to the substrate. Round precipitates with Moiré fringes on them are observed. (b) Crosssectional HREM image of CVD-YBa2Cu3 O7 film taken with the electron beam parallel to the a-axis. (c) Stacking faults in the film. HREM image of (d) a grain and (e) grain boundary of the film. (f) Structure model and (g) structure image of YBa2 Cu3 O7 together with a projected structure model.

is a cross-sectional HREM image of a grain in the CVD film, and most of the grains have a preferred c-axis orientation perpendicular to the SrTiO3 (100) substrate, as indicated by region 1. On the other hand, the c-axis is oriented parallel to the SrTiO3 (100) substrate in a region 2. An enlarged HREM image at the grain boundary interface is shown in Figure 6.15 (e), and the c-axis of the YBa2 Cu3 O7 structure is perpendicular to one another. A structure model and a structure image of YBa2 Cu3 O7 are shown in Figure 6.15 (f) and (g), respectively. Undeformed YBa2 Cu3 O7 − x domains, interleaved by the faulted regions, are ∼ 50 nm in size. The electron diffraction pattern taken with the incident beam parallel to [010] did not change when the specimen was tilted by 5°, which is appreciably wider than the usual crystals. Such morphology indicates

6.9 Y-based copper oxides with high Jc

|

133

that the sample was grown quickly at a temperature just below the melting point or YBa2 Cu3 O7 − x where the homogeneous nucleation process followed by the preferential crystal growth in the c-planes occurs. Bulk types of YBa2 Cu3 O7 − x superconductors with high Jc were also investigated. Oxide powders or Y, Ba, and Cu were mixed with the composition of YBa2 Cu3 O7 − x phase. The mixture was calcined at 900°C for 24 h and then reground. After this process was repeated twice, a small amount of additive oxide powder with a perovskite structure BaZrO3 was added, 3 mol%, to the YBa2 Cu3 O7 − x powder [26]. Again, grinding and calcining was repeated, and the pellets were sintered at 950°C for 24 h and then cooled slowly. The bulk sample showed high critical current density of 2.0 × 105 A/cm2 at 77.3 K and 0.1 T. Figure 6.16 (a) is a TEM image of an YBa2 Cu3 O7 − x bulk specimen with BaZrO3 additive, where two types of fine particles with spherical and irregular shapes are lying in the YBa2 Cu3 O7 − x matrix. Their minimum size was ∼ 20 nm and the average size was roughly estimated to be ∼ 100 nm, and they were confirmed to be BaZrO3 phase from electron diffraction. Figure 6.16 (b) is an HREM lattice image near the grain boundary between the BaZrO3 phase and the YBa2 Cu3 O7 − x matrix, where both lattice planes generating a lattice fringe are assigned as indicated in the Figure 6.16 (b). The lattice plane continues across the interface, but the extra half-plane is inserted in every 20 fringes within the BaZrO3 phase, while the interval for the extra half plane is theoretically suggested to be every 14 fringes. Therefore, the interface in this region was suggested to be semicoherent. The mechanism of fine dispersion of ABO3 oxides in the matrix is not yet fully understood. It is suggested that the grain growth takes place during sintering and ABO3 phase is dragged into the growing grain as the same species as the matrix, because both phases have a similar crystal structure and have a semicoherent interface as mentioned above. Several types of pinning centers such as Y2 BaCuO5 [27], CuO [28], and SnO2 [29] have been reported to be effective for the YBa2 Cu3 O7 − x superconductor. A perovskite type oxide, ABO3 seems to be a promising candidate as pin-

YBa2Cu3 O6+x (012) 0.319 nm

YBa2Cu3 O6+x

(110) 0.296 nm BaZrO3

Fig. 6.16: (a) TEM image of 3 mol%-BaZrO3 dispersed YBa2 Cu3 O6+x . (b) HREM image at the BaZrO3 nanoparticles and YBa2 Cu3 O6+x matrix interface.

134 | 6 HREM analysis of nanostructured materials ning center for the superconducting copper oxides, because the crystal structure is similar to the host superconducting phase. A remarkable flux-pinning effect could be expected by introducing the oxide. Homogeneous distribution of nonsuperconducting fine particles is very effective, when they distribute in the same dimension with the fluxoid lattice. In addition, the matrix is distorted around the particles with different unit volume by the coherent interface with the matrix, and a significant change of the superconducting property is expected around the coherent particles.

6.10 BN nanotubes Since the development of BN nanotubes [30], various types of BN nanostructured materials have been reported because of the great potential for using materials with low dimensions in an isolated environment [31, 32]. Many studies have been reported on BN nanomaterials such as nanotubes, bundled tubes, nanocorns, nanohorns, nanocapsules, nanoparticles, BN clusters, and BN metallofullerenes, which are expected to be useful as electronic devices, field-effect transistors, high heat-resistant semiconductors, insulator lubricants, nanowires, magnetic nanoparticles, gas storage materials, and optoelectronic applications including ultraviolet light emitters. BN nanotubes and nanoparticles were reviewed in this chapter, which were synthesized by arc melting, thermal annealing, and chemical vapor deposition methods. They were characterized by TEM, and their properties were investigated and discussed. To confirm the atomic structures and investigate the stabilities, electronic states, and hydrogen storage, total energy calculations were carried out by molecular mechanics and molecular orbital calculations. BN nanotubes have a hexagonal ring structure with various chiralities, which is similar to carbon nanotubes. To investigate the chiralities of BN nanotubes, electron diffraction patterns have been used commonly. HREM is also used for structure analysis of BN nanotubes, and lattice images on the side of the tubes had been taken because of the Bragg’s diffraction condition. However, it is difficult to take an image of the hexagonal network that should appear at the center of BN nanotubes because of the resolution limit, overlapping of atoms, electron beam damage, and so on. Although the network structure of the carbon nanotubes have already been observed by scanning tunneling microscopy (STM), the hexagonal plane of BN nanotubes has never been observed through STM because of the insulating behavior. The atomic structures and stabilities of BN nanotubes were presented here, which were investigated by HREM and theoretical calculations. To determine the nanotube structures, hexagonal networks of BN nanotubes were directly observed at the atomic level by HREM. BN nanotubes were synthesized through the arc melting method in an Ar/N2 gas mixture from YB6 with Ni powder [33]. The YB6 powder (4.0 g, 99.6%) and Ni powder (0.8 g, 99.9%), with an atomic ratio of 1 : 1, were set on a copper mold in an electric arc furnace, which was evacuated down to 1 × 10−3 Pa. After introducing a mixed gas of Ar (0.025 MPa) and N2 (0.025 MPa), arc melting was applied to the samples at

6.10 BN nanotubes |

135

an accelerating voltage of 200 V and an arc current of 125 A for 10 s. Arc melting was performed with a vacuum arc melting furnace (NEV-AD03; Nisshin Engineering), and a gray to white powder was obtained around the copper mold. A low magnification image of BN nanotubes produced from YB6 /Ni powder is shown in Figure 6.17 (a). The lengths and diameters of BN nanotubes are ∼ 5 and 3–50 nm, respectively [34]. An HREM image of a B36 N36 cluster inside a BN nanotube is shown in Figure 6.17 (b) (JEM-3000F, 300 kV). Hollow BN clusters were often observed on and inside BN nanotubes, and BN fullerene clusters had a single BN sheet, as shown in Figure 6.16 (c). The sizes of BN clusters were in the range of 0.7–1.0 nm,

(BN)36

Fig. 6.17: (a) Low-magnification image of BN nanotubes. (b) HREM image of B36 N36 cluster in BN nanotube. (c) Structure model of the center of (b). (d) HREM image of bundled BN nanotubes. BN clusters are indicated by arrows. (e) Atomic structure model from three different directions for bundled BN nanotubes.

136 | 6 HREM analysis of nanostructured materials which corresponds to the size of the B36 N36 clusters. The B36 N36 cluster consists of six four-membered rings and 32 six-membered rings, as shown in Figure 6.17 (c). The simulated images of B36 N36 also agreed well with the observed HREM image. BN nanotube has a multiwalled structure, and the diameter of the innermost tube is 1.75 nm. An atomic structure model of the center of Figure 6.16 (b) is shown in Figure 6.17 (c). The diameter and chirality of BN nanotube are 1.747 nm and (22, 0), respectively. This kind of peapod-type self-organized structure would be useful for the nanoscale devices. Another HREM image of BN nanotubes with a bundled structure is shown in Figure 6.17 (d), and an atomic structure model observed from three different directions is shown in Figure 6.17 (e). There are some spaces among BN nanotubes, and the space would be useful for gas storage such as hydrogen. Figure 6.18 (a) is an HREM image of a quadruple-walled BN nanotube (JEM-3000F, 300 kV). In this work, all HREM images were taken close to the Scherzer defocus (𝛥fs = −41.2 nm), which is an optimum defocus value of electron microscope, to investigate the atomic structures in detail. HREM observations and electron diffraction analysis on BN nanotubes have been reported, and direct observations of nanotube chirality were tried in this work. An enlarged HREM image is shown in Figure 6.18 (b), which indicates lattice fringes in BN nanotubes. A filtered Fourier transform of Figure 6.18 (b) showed that this nanotube had a zigzag-type structure, as shown in Figure 6.18 (c). An HREM image with clear contrast processed after Fourier noise filtering is shown in Figure 6.18 (d). The intervals of the bright and dark dots are 0.14 nm, which corresponds to the structure of hexagonal BN (h-BN) rings, as shown in Figure 6.18 (e). Layer intervals of each tube are 0.35 nm, as shown in Figure 6.18 (f). Diameters of each nanotube are 2.8, 3.5, 4.2, and 4.9 nm from the inside to the outside. Another HREM image of a BN nanotube produced from YB6 powder is shown in Figure 6.19 (a) (JEM-3000F, 300 kV). The width of the multiwalled BN nanotube is 8.5 nm. BN nanotube consists of nine layers and has an asymmetric layer arrangement. The layer distances are in the range of 0.34–0.51 nm, which is larger than that of {002} of ordinary h-BN (0.34 nm). The diameters of the first and second internal nano tubes are 1.7 and 2.6 nm, respectively. Hexagonal net planes of BN nanotube are observed in an enlarged image of Figure 6.19 (b). Figure 6.19 (c) is a filtered Fourier transform of Figure 6.19 (b), which indicates 002 and 100 reflections of BN structure. The inverse Fourier transform of Figure 6.19 (c) is shown in Figure 6.19 (d), which clearly shows the lattice fringes of the hexagonal networks. An h-BN ring is shown in Figure 6.19 (d), and BN has an armchair-type structure. The atomic structure models were proposed from the observed diameters of BN nanotubes, which were based on layer intervals of 0.34–0.35 nm. The chirality of (n, m) is derived from the equation dt =

√3 aB-N √n2 + nm + m2 𝜋

(6.1)

6.10 BN nanotubes

| 137

Fig. 6.18: (a) HREM image of zigzag-type BN nanotube. (b) Enlarged HREM image of (a). (c) Filtered Fourier transform of (b). (d) Inverse Fourier transform of (c). Enlarged images of center (e) and edge (f) of BN nanotube in (d).

where dt means the diameter of BN nanotube with nanometer scale and a B–N corresponds to the nearest distance of boron and nitrogen atoms. For BN nanotubes, the value of a B–N is 0.144 nm When a BN nanotube has a zigzag structure, the value of m is zero. Figure 6.20 (a) shows a proposed structure model of the quadruple-walled BN nanotube. Chiralities of each zigzag BN nanotube are (35, 0), (44, 0), (53, 0), and (62, 0) from the inside to outside. These chiralities were derived from Equation (6.1).

138 | 6 HREM analysis of nanostructured materials

010 002

110

000 100 002 010

B N 0.14 nm

Fig. 6.19: (a) HREM image of armchair-type BN nanotube. (b) Enlarged HREM image of (a). (c) Filtered Fourier transform of (b). (d) Inverse Fourier transform of (c).

The arrangement of boron and nitrogen atoms was reversed at each layer, as boron atoms exist just above the nitrogen atoms while maintaining the layer intervals of 0.35 nm. The calculated images of the proposed model as a function of defocus values are shown in Figure 6.20 (b) (JEM-3000F, 300 kV). The contrast of the hexagonal rings was clearly imaged at the defocus values in the range of −40 to −50 nm, and these simulated images agree well with the observed HREM image of Figure 6.18 (d). A proposed structure model of the double-walled BN nanotube corresponding to Figure 6.19 is shown in Figure 6.20 (c). The chiralities of BN nanotube are (13, 13) and (19, 19) for the first and second layers, respectively. The layer intervals of the lattice fringes of the {002} planes are in accordance with those observed in Figure 6.19 (a). Based on the projected structure model, the image calculations were carried out for various defocus values, as shown in Figure 6.20 (d), and an HREM image calculated at −40 nm agrees well with the experimental data of Figure 6.19 (d). When the zigzag-type BN nanotubes are characterized using HREM, BN atom pairs at sides of the nanotubes are sometimes imaged as dots, as observed in Figure 6.18 (f). Taking such dot contrast would be difficult for armchair-type BN nanotubes because of high density distribution of atoms along the nanotube axis, and the HREM image contrast would show straight lines at the sides of the nanotubes. Multihelix BN nanotubes

6.10 BN nanotubes | 139

2.61 nm

0.48 nm

Df = –10 nm

–20 nm

–30 nm

0.34 nm

2.78 nm (35,0) 3.49 nm (44,0) 4.21 nm (53,0) 4.92 nm (62,0)

(c)

Df = –10 nm –40 nm

–50 nm

–40 nm

B (a)

–20 nm

–30 nm

–60 nm

–50 nm

–60 nm

N (b) –70 nm

–80 nm

–90 nm (d)

–70 nm

–80 nm

–90 nm

Fig. 6.20: (a) Proposed structure model of quadruple-walled BN nanotube. Chiralities of zigzag BN nanotubes are (35, 0), (44, 0), (53, 0), and (62, 0) from inside to outside. (b) Calculated images of the proposed model (a) as a function of defocus values. (c) Proposed structure model of doublewalled BN nanotube. Chiral vectors of nanotube are (13, 13) and (19, 19) for the first and second layers, respectively. (d) Calculated images of the proposed model (c).

would also show unclear dot contrast at the side of the nanotube, which indicates that the contrast of the side edges of BN nanotubes would also give us useful information on the chirality. If a clear dot contrast is observed at the sides of BN nanotubes, the possibility of a zigzag-type BN nanotube is high. The image contrast also could be changed by the rotation of the nanotubes, and further study on the rotation of BN nanotubes has been presented. The structural stabilities of BN nanotubes were investigated and summarized. As an effect of the nanotube edges should be considered, short and long nanotubes were investigated. The total energies of the zigzag-type structures showed lower values than those of the armchair-type structures, which indicates that the zigzag type is more stable compared with the armchair-type structures. This agrees with the experimental data [34] on distorted nanotube structures, and the present calculations also confirm the stability of the zigzag-type BN nanotubes. The encapsulation of a BN cluster in a BN nanotube showed a reduction of the total energy, which indicates that the encapsulation of BN cluster in a BN nanotube would stabilize BN cluster [32].

140 | 6 HREM analysis of nanostructured materials

6.11 BN nanotubes with cup-stacked structures Although the arc melting method is a good technique for producing BN nanocage materials; the amount produced is not very high, and a mass production method should be developed. There are several methods, and one which is described here [35]. Fe4 N (99%) and boron (B) powders (99%) were used as raw materials. Their particle sizes were about 50 and 45 mm, respectively. After the Fe4 N and B [weight ratio (WR) 1 : 1] were mixed by a triturator, the samples were set on an alumina boat and annealed in the furnace. The furnace was programmed to heat at 6°C/min from ambient to 1000°C and hold for 1 h and then cooled at 3°C/min to ambient temperature. Nitrogen pressure was 0.10 MPa, and its gas flow was 100 sccm. The as-produced soot synthesized from Fe4 N/B via the above method was purified by the following steps. The as-produced soot were poured in 4 m HCl solution and stirred for 4 h at room temperature. The green color of the solution provides an indication of the dissolution of Fe ions. After HCl treatment, the samples were poured in 1 M HNO3 solution and stirred for 30 h at 50°C. The yellow color of the solution provides an indication of the dissolution of boron. After both acid treatment, the solution was filtered and rinsed with deionized water until the pH of the filtrate became neutral and dried. Then, the samples were poured in pyridine to eliminate bulk BN, and high-purity BN nanotubes with a cup-stacked structure were obtained by collecting supernatant. The XRD patterns in the purification process are shown in Figure 6.21 (a). The diffraction peaks of hexagonal BN, boron, and 𝛼-Fe are observed for the sample annealed at 1000°C for 1 h. Fe was removed after HCl treatment, and boron was removed after HNO3 treatment. After pyridine treatment, a strong peak of BN was obtained, as shown Figure 6.21 (a). Figure 6.21 (b) and (c) shows the TEM images of BN nanotubes with a cup-stacked structure after purification process. The diameters and lengths of BN nanotubes are in the range of 40–100 nm and 5–10 mm, respectively. Fe nanoparticles and bulk BN were eliminated during the process. An enlarged image of one of BN nanotubes is shown in Figure 6.21 (d), which shows a cup-stacked structure as indicated by the lines of BN {002}. Figure 6.21 (e) shows the electron diffraction pattern of Figure 6.21 (c). The 002 reflections of BN are splitting in Figure 6.21 (e), which indicates that BN nanotube has a cup-stacked structure and the cone angle between BN layers at both nanotube walls is ∼ 20°. Most of BN nanotubes (∼ 90%) have this cup-stacked structure with a cone angle of ∼ 20°, and normal structures with a cone angle of 0° were sometimes observed (∼ 10%). An optical absorption spectrum of BN nanotubes is shown in Figure 6.21 (f). In Figure 6.21 (f), a strong peak is observed at 4.8 eV, which would correspond to the energy gap of BN nanotubes. A broad, weak peak is also observed around 3.4 eV, which is considered to be the impurity level (oxygen or hydrogen) of BN layers. Comparable data (4.5–5.8 eV) were reported for other optical measurements [36]. An HREM image of the edge of the nanotube side wall in Figure 6.21 (d) is shown in Figure 6.22 (a) (JEM-3000F, 300 kV), and a cup-stacked structure was observed.

6.11 BN nanotubes with cup-stacked structures

Intensity [A.U.]

As-synthesized BN B

B

10

a-Fe

a-Fe a-Fe

BN

HCl treatment

BN

HNO3 treatment

BN

Pyridine treatment

20 30

40

| 141

50 60 70

80

90

2q [°] BN {002}

000

4.8 eV 100

Absorbance [A.U.]

002

010

200

3.4 eV

300

400

500

600

700

800

Wavelength [nm]

Fig. 6.21: (a) XRD patterns of samples after synthesis, HCl treatment, HNO3 treatment, and pyridine treatment. (b) TEM and (c) enlarged image of the sample after pyridine treatment. (d) Enlarged image of BN nanotube with cup-stacked structure. (e) Electron diffraction pattern of (d). (f) Optical absorption spectrum of BN nanotubes.

142 | 6 HREM analysis of nanostructured materials

y

y

z

z BN{002} B, N

0.14 nm

y z

y x

y B, N y

z

z

BN{002}

0.14 nm

y z Fig. 6.22: (a) HREM image of edge of BN nanotube wall in Figure 6.21 (d). (b) Processed HREM image after Fourier filtering of the nanotube center of Figure 6.21 (d). Proposed model of BN cup structure projected along (c) the z-axis (nanotube axis) and (d) the x-axis. (e) Simulated HREM image of fourlayered, cup-stacked BN nanotube at defocus values of −40 nm. Enlarged image of (f) edge and (g) center of BN nanotube in (e).

6.11 BN nanotubes with cup-stacked structures

|

143

The edge structures are observed as indicated by the arrows, and BN {002} planes are inclined compared with the nanotube axis (z-axis). Figure 6.22 (b) shows the processed HREM image after Fourier filtering of the nanotube center of Figure 6.21 (d), and hexagonal arrangements of white dots are observed, which would correspond to BN six-membered rings. From these observations, a structure model for BN cup structure was proposed, which consists only of h-BN rings, as shown in Figure 6.22 (c) and (d). Based on the structure model of a four-layered cup-stacked B2240 N2240 nanotube, an image simulation was carried out, as shown in Figure 6.22 (e). The enlarged calculated HREM images of the edge and the center of BN nanotube in Figure 6.22 (e) are shown in Figure 6.22 (f) and (g), respectively. These calculated images agree with the experimental data of Figure 6.22 (a) and (b), respectively. BN nanotubes with cup-stacked structures in this work would be one of the candidates for atomic and gas storage, as well as carbon nanotubes. The cone angles of BN cup stacks were measured to be ∼ 20°, which agreed well with that of the model in Figure 6.22 (d). Although the atomic structure models for BN nanotubes with a cupstacked structure have been proposed from HREM observation and molecular mechanics calculations [37], the cone angles were ∼ 36°, and they had bamboo-type structures. In this work, there is no bamboo-type structure, which was removed during the purification process, and the more stable cup-stacked structure with a cone angle of 20° was formed. Cone angles of carbon nanotubes with a cup-stacked structure were reported to be in the range of 45–80° [38]. The cause of the different cone angles of the present cup-stacked BN nanotubes could be due to the different stacking of BN layers along the c-axis (B–N–B–N . . . ) from the carbon layers. Although the network structure of carbon nanotubes has already been observed by STM, only few works on the STM observation of the hexagonal plane of BN nanotubes have been reported because of the insulating behavior. The STM image of BN nanotubes on highly oriented, pyrolytic graphite (HOPG) is shown in Figure 6.23 (a) [39]. Three BN nanotubes are observed in the image, and the smallest one is selected for enlarged observation and electronic measurements. The nanotube axis is indicated as the z-axis. An enlarged image of the surface of BN nanotube is shown in Figure 6.23 (b). The surface of BN nanotubes is indicated by arrows. A lattice image of BN nanotubes is observed, and an enlarged STM image of BN nanotubes is shown in Figure 6.23 (c). Hexagonal arrangements of dark dots are observed, which correspond to the size of the six-membered rings of BN. Current–voltage (I–V) measurements were also carried out for BN nanotubes, as shown in Figure 6.23 (d). The I–V curve indicates an onset voltage at 5.0 V, which agreed with the optical measurement of Figure 6.21 (f) and is almost comparable to the energy gap of BN nanomaterials [40, 41]. To investigate the stability of the cup-stacked structure, four types of nanotubes are considered [42]. The atomic structure models of double-walled BN nanotubes with zigzag- and armchair-type structures and atomic structure models of four layered, cup-stacked BN nanotubes with different cone angles were summarized

144 | 6 HREM analysis of nanostructured materials

z z y y

HOPG

160 140

z

y

0.14 nm

Tunnel current [nA]

120 100 80 60 40 20 0 0 (d)

1

2

3 4 5 6 Sample bias [V]

7

8

Fig. 6.23: (a) STM image of BN nanotubes on HOPG. (b) Enlarged image of the surface of BN nanotube indicated by a square in (a). (c) Enlarged STM image of BN nanotube. (d) I–V characteristic of the single BN nanotube.

as in Tables 6.4 and 6.5, respectively. The total energies of these four type structures indicate that BN multilayered nanotubes with and without a cup-stacked structure would be stabilized by stacking h-BN networks. The distance between the BN layers of nanotubes with a cup-stacked structure in an HREM image was found to be ∼ 0.35 nm, and the basic structure model was constructed based on this observation. The geometry optimizations at the molecular mechanics level result in interlayer distances of ∼ 0.38 nm. Comparing the empirical total energies of all the considered structures, a cup-stacked structure (B2240 N2240 ) with a cone angle of 20° was found to be the lowest in energy, which indicates the high stability of this structure.

6.12 BN nanotubes encaging Fe nanowires

|

145

Table 6.4: Calculated values for various BN nanotubes. B273 N273 B390 N390 B273 N273 @B390 N390

B264 N264 B384 N384 B264 N264 @B384 N384

Zigzag type

Armchair type

Structure type Outer diameter (nm)

–

2.3

2.3

–

2.2

2.2

Inner diameter (nm)

1.6

–

1.6

1.5

–

1.5

Number of layers

1

1

2

1

1

2

1921

2935

2326

1952

2900

3261

Total energy (kJ/mol) Total energy (kJ/mol atom)

3.52

3.76

1.75

3.69

3.77

2.51

Table 6.5: Calculated values for various BN nanotubes with a cup-stacked structure. B560 N560 Corn angle [°]

B1120 N1120

B2240 N2240

B494 N494

20

B988 N988 36

Outer diameter (nm)

3.4

4.2

Inner diameter (nm)

2.4

2.4

Number of layers Total energy (kJ/mol) Total energy (kJ/mol atom)

1 131.6 0.117

B1976 N1976

2

4

1

2

4

−1205

−3918

3745

5309

8627

−0.540

−0.874

3.43

2.69

2.18

6.12 BN nanotubes encaging Fe nanowires Several studies have been reported on metal-filled BN nanomaterials. Nanowires constructed from magnetic materials, especially Fe, Co, and some Fe-based alloys are of interest because they are likely to be used in nanoelectronics devices, magnetic recording media, and biological sensors. BN nanocables have a potential use for nanoscale electronic devices and nanostructured ceramic materials because of their good stability at high temperatures with high electronic insulation in air. Therefore, metalfilled BN nanomaterials would have significant advantages for technological application. However, their surface oxidation and corrosion resistance are the weak points of metallic nanowires. Although it is reported that Fe- [43] and Y-filled [44, 45] BN nanotubes could be achieved, they still have some problems such as low production and low yield. These are due to the poor wetting property of BN to metal, making direct fabrication of BN nanocable with metal cores difficult. In this work, BN nanotubes

146 | 6 HREM analysis of nanostructured materials with cup-stacked and metal-filled structures were synthesized. The formation mechanism and atomic structures were investigated by HREM, high-angle annular darkfield scanning transmission electron microscopy (HAADF-STEM), electron diffraction, energy dispersive X-ray spectroscopy (EDX), and molecular mechanics calculations. It is also possible to use HAADF-STEM to detect single heavy atoms on a light support. Scattering is caused by the nucleus and follows roughly a Z 2 dependence. The formation mechanisms of Fe-filled BN nanotube and cup-stacked structures were proposed based on these results. Figure 6.24 (a) and (b) are the TEM and HAADF-STEM images of Fe-filled BN nanotubes [46], which were the remaining sediment after centrifugation. The contrast in the TEM image is weak and direct observation of Fe-filled BN nanotubes is difficult. The same area imaged by HAADF-STEM shows excellent contrast, and the morphology of Fe-filled BN nanotubes can be observed in detail. A great number of Fe-filled BN nanotubes were observed by HAADF-STEM. A high weight ratio of Fe4 N would be necessary for synthesis of Fe nanowires [35]. The TEM image of one of the Fe-filled BN nanotubes is shown in Figure 6.24 (c). Figure 6.23 (d) is an EDX spectrum of the Fefilled BN nanotube. In Figure 6.24 (d), two peaks of boron and nitrogen are observed. This shows the atomic ratio of B/N = 46.5:53.5, which indicates the formation of BN. A strong peak of Fe (0.70 keV) is also observed, whereas a Cu peak arises from the HREM grid. Figure 6.24 (e) is an enlarged image of Figure 6.24 (c). Figure 6.24 (f) shows an electron diffraction pattern of the Fe-filled BN nanotube. The strong peaks of BN nanotubes correspond to the planes of (002) of BN. The diffusion of the 002 reflections of BN in Figure 6.24 (f) is due to the structural disordering of BN layers and bending of BN nanotube, as observed in Figure 6.24 (c). Strong peaks are also indexed as metallic Fe with a bcc structure, and the incident beam is parallel to the [111] zone axis of 𝛼-Fe. Figure 6.25 (a) is an enlarged HREM image of Figure 6.24 (e) (JEM-3000F, 300 kV), and Figure 6.25 (b) is a filtered Fourier transform of Figure 6.25 (a). Figure 6.25 (c) shows the inverse Fourier transform of Figure 6.25 (b), and Figure 6.25 (d) shows the enlarged image of Figure 6.25 (c). Figure 6.25 (d) shows a lattice image of the bcc Fefilled BN nanotube. The nanotube axis is parallel to the [110] direction of Fe, which indicates that bcc Fe is epitaxially grown to the [110] zone axis. The tubular layers around the nanowire have an average interlayer spacing of 0.34 nm, which corresponds to the (002) spacing of BN. Figure 6.25 (e) shows the inverse Fourier transform ̄ reflections, and Figure 6.25 (f) shows of Figure 6.25 (b) using 000, Fe (011̄ and 011) the enlarged image of Figure 6.25 (e). Several edge-on dislocations are observed as indicated by arrows, which could be due to the lattice distortion produced during Fe-filled nanotube growth. The lattice distortion of Fe is also observed as diffusion ̄ reflections in the electron diffraction pattern (indicated by arrows) of Fe (011̄ and 011) of Figure 6.24 (f). A small amount of nanocrystalline Fe2 B compounds was observed at the tip of BN nanotubes. Chemical formulas of Fe4 N reaction with B that generate Fe and BN in the

6.12 BN nanotubes encaging Fe nanowires

| 147

Fe nanowire

Fe nanowire

BN

Intensity [A.U.]

Fe

B N

Cu

0

0.5

1 1.5 Energy [keV]

2

2.5

Fe 211

BN Fe 110

Fe 101

BN 002

Fe 011

Fe nanowire 000

BN

Fig. 6.24: (a) TEM and (b) HAADF images of Fe-filled BN nanotubes. (c) TEM image of Fe-filled BN nanotube. (d) EDX spectrum of Fe-filled BN nanotube. (e) Enlarged image of (c). (f) Electron diffraction pattern obtained from (e).

experiments can be proposed as follows: Fe4 N + 3B → BN + 2Fe2 B

(6.2)

Fe2 B and dissolution of boron were obtained, and BN was produced in the reaction expressed as (6.2) because Fe2 B is thermodynamically more stable than Fe4 N. Although the Fe2 B is stable up to 1389°C, the Gibbs–Thompson effect shows that melting occurs at a significantly lower temperature compared with values in the standard phase dia-

148 | 6 HREM analysis of nanostructured materials

BN {002}

Fe 101

Fe 110 BN 002

Fe 011 000

Fe {112} Fe {110}

BN {002}

BN {002} 0.34 nm

Fe {112} Fe {110}

Fe

Fe {110} Fe {110}

Fig. 6.25: (a) HREM image of Fe-filled BN nanotube. (b) Filtered Fourier transform of (a). (c) Inverse Fourier transform of (b). (d) Enlarged image of square in (c). (e) Inverse Fourier transform of (b) using 000, Fe 011,̄ and Fe 011̄ reflections. (f) Enlarged image of square in (e).

gram. Therefore, fluidlike Fe2 B can be attained more easily. In the next process, the following reaction would take place: 2Fe2 B + N2 (g) → 2BN + 4Fe

(6.3)

Boron in liquid-like Fe2 B started to segregate on the surface of the particle, and the boron would react with N2 gas, producing BN. 𝛼-Fe in liquid-like Fe2 B is epitaxially grown to the [110] direction, and Fe nanowires were produced in reaction (6.3). In ad-

6.13 Nanoparticles with 5-fold symmetry

| 149

dition, high WR would be mandatory for the formation of Fe-filled BN nanotubes. As a result of these reactions, the [110] direction of Fe is parallel to the BN nanotube axis. Gibbs’ energy on each formula is calculated as −374 and −97.1 kJ for formulas (6.2) and (6.3) at 1000°C, respectively. These negative values would stand for the correctness of the proposed formulas. It is considered that the formation of Fe-B compounds might play an important role for the growth of BN nanotubes and that amorphous boron might change to BN and Fe2 B on the surface of the Fe4 N nanoparticles. When magnetic materials are used as catalyst metals for BN nanotube formation, the magnetic nanoparticles would move around by the magnetic field of a coil heater during the reaction. Then, segments of BN {002} layers would be produced in the tubes, which results in the formation of bamboo structures. The interval of BN layer segments might be related to the amount of iron nanoparticles, and further studies are needed on the control of the bamboo structure.

6.13 Nanoparticles with 5-fold symmetry Five-fold symmetry is allowed only in small particles and quasicrystals [47]. Various types of multiply twinned particles with 5-fold symmetry have been reported for fcc structures in the early stages of particle growth [48, 49]. However, the 5-fold symmetry that consists of an fcc structure should have distortion due to the geometric arrangements along the 5-fold axis. The maximum size of these particles without distortion has been reported to be 40 nm because the inner stress of the crystal increases as they grow [48]. The atomic structures and stability of h-BN, diamond, and Au nanoparticles with a 5-fold symmetry were investigated by HREM and molecular orbital calculations, which would predict the structural stability of the clusters. CVD-BN nanoparticles were synthesized from B3 N3 H6 and BCl3 –NH3 –H2 gas systems at temperatures of 1400–2000°C and total gas pressures of 0.2–30 Torr on graphite substrates [50]. An SEM image of the CVD-BN nanoparticles, synthesized from a BCl3 –NH3 –H2 gas system at deposition temperatures 2000°C, is shown in Figure 6.26 (a), which shows a surface structure of pyramidal pentagonal facets. The twin boundaries are indicated by solid lines, and the c-axis of the h-BN is indicated by arrows. The TEM images of CVD-BN nanoparticles, synthesized from a BCl3 -NH3 -H2 gas system at deposition temperatures of 2000°C and 1800°C and synthesized from B3 N3 H6 gas at 2000°C, are shown in Figure 6.26 (b)–(d), respectively. In Figure 6.26 (b)–(d), a number of particles are visible with the structures of pentagons, stars, and maple leaf shapes, respectively. It should be noted that only those particles that satisfy certain diffraction conditions are visible in the images. A considerable number of particles are contained in the samples, as confirmed by tilting. An electron diffraction pattern of Figure 6.26 (b) is shown in Figure 6.26 (e). The electron diffraction pattern was taken from a wide area (1 μm) and shows many diffraction spots

150 | 6 HREM analysis of nanostructured materials

112 110 102 100 002 000

Fig. 6.26: (a) SEM image of BN nanoparticles. TEM images of CVD-BN nanoparticles, synthesized from a BCl3 –NH3 –H2 gas system at deposition temperatures of (b) 2000°C and (c) 1800°C and synthesized from (d) B3 N3 H6 gas at 2000°C. (e) Electron diffraction pattern of (b).

attributed to the nanocrystalline particles and also the Debye–Scherrer rings from the t-BN matrix. The rings are indexed as 002, 100, 102, 110, and 112 of h-BN. An enlarged image of BN nanoparticles in Figure 6.26 (c) is shown in Figure 6.27 (a). Five twin boundaries are observed in the particle, and the strain contrast results from some defects in the particles. Figure 6.27 (b) is a filtered HREM image

6.13 Nanoparticles with 5-fold symmetry

N

| 151

B

Fig. 6.27: (a) TEM image of BN nanoparticle. (b) Filtered HREM image of the center of BN nanoparticle. (c) Electron diffraction pattern of BN nanoparticle. (d) Atomic structure model. (e) Atomic structure models of B164 N156 , B328 N312 , and B656 N624 .

of the center of BN nanoparticle. The twin boundaries are indicated by arrows. In the image, two-dimensional lattice fringes are visible with separations of 0.18 and 0.22 nm, which correspond to the lattice spacings of {102} and {100}, respectively. The image clearly shows that the five parts have twin relations at their boundaries. The center of the 5-fold axis indicates some distortion. Figure 6.27 (c) is an electron diffraction pattern of the 5-fold multiply twinned h-BN in Figure 6.26 (b). All the diffraction spots in the pattern in Figure 6.27 (c) can be interpreted by the superposition of five twin-related electron diffraction patterns. A selected area of electron diffraction pattern of one of the five parts can be indexed

152 | 6 HREM analysis of nanostructured materials by the h-BN structure with lattice constants a = 0.25044 nm and c = 0.66562 nm. The twin boundaries are {112}, and the 5-fold axis (equal to incident beam direction) ̄ A projection of the atomic arrangement of the 5-fold multiply twinned h-BN is [201]. nanoparticle is illustrated schematically in Figure 6.27 (d), where the open circles correspond to the rows of an alternate sequence of boron and nitrogen atoms lying par̄ The twin planes {112} are indicated by dotted allel to the 5-fold symmetry axis [201]. lines, and the h-BN cell is shown by solid lines. The 5-fold axis, normal to the Figure at the star mark, is tilted 37° from the c-axis of the hexagonal cells. Taking account of the lattice parameters of h-BN, the misfit of the multiply twinned h-BN particle is 1.6°, which is much smaller than the 7° 20’ of the multiply twinned fcc nanoparticles. This small amount of misfit allows the growth of relatively large particles with little inner distortion. The atomic cluster at the center of the particle consists of B24 N21 , and the structure was optimized by molecular orbital calculation, giving a calculative total energy of −49.3 kJ/mol [51]. BN clusters such as B24 N24 and B36 N36 have been reported to have cage structures [52]. However, BN nanoparticles have a layered structure with 5-fold symmetry. The heat of formation of B24 N24 cluster was calculated to be −72.4 kJ/mol atom, which is a little lower than that of the present B24 N21 cluster with 5-fold symmetry. This result may indicate that the growth kinetics cause a change in the structure of BN clusters into decagonal shapes from octahedral shapes during cluster growth. The atomic structure models of B164 N156 , B328 N312 , and B656 N624 clusters with stacking structures are shown in Figure 6.27 (e). The total energies per mole atom of BN clusters were reduced by the stacking of the BN layers, and it is believed that the electrons below and above h-BN networks would have a role in the van der Waals bonding between stacking layers, and the structure of BN nanoparticles with 5-fold symmetry would be stabilized by multiplying the h-BN ring networks. The particle size dependences on the deposition temperature for CVD-BN were investigated for both systems. The sizes increase as the deposition temperature increases and decrease as the total gas pressure increases. It is believed that high temperature and low gas pressure are effective for the formation of 5-fold BN nanoparticles, which could be due to the growth rate of h-BN on the graphite substrates. Thermodynamic calculations of the Gibbs free energies for BN synthesis at 2000°C are as follows: B3 N3 H6 (g) = 3BN + 3H2 (g) − 636(kJ)

(6.4)

BCl3 (g) + NH3 (g) = BN + 3HCl(g) − 301(kJ)

(6.5)

The activation energy of particle growth with the 5-fold symmetry was also measured to be 2.3 eV [53]. Au nanoparticles (ULVAC Inc., Kanagawa, Japan) with a size of ca. 5 nm were selected, and the samples for HREM observation were prepared by dispersing materials on perforated carbon grids using toluene [54, 55]. The HREM images of Au nanoparticles with 5-fold symmetry are shown in Figure 6.28 (a) and (b) (ARM-1250, 1250 kV), and

6.13 Nanoparticles with 5-fold symmetry

|

153

five twin boundaries are indicated by arrows. In these images, Au atoms are imaged as dark dots and the atomic arrangements of Au are observed directly. For both Au nanoparticles, Au atoms exist at the center of nanoparticles, which indicates the 5-fold axis of [111]. In Figure 6.28 (b), a disordered twin boundary is observed, as indicated by a star. In Figure 6.28 (a), there is no atomic disordering in the Au nanoparticles, with a smaller size of 3.8 nm compared with that in Figure 6.28 (b) (5 nm). Diamond films were prepared by a hot-filament thermal CVD with a CH4 -H2 gas system. Silicon substrates were kept at 750°C and a total gas pressure of 7 Torr [56]. An SEM image of a diamond particle with 5-fold symmetry is shown in Figure 6.28 (c). The particle with a size of 5 μm has a decahedral shape. A selected area electron diffraction pattern of diamond particles is shown in Figure 6.28 (d). The diffraction pattern shows many diffraction spots, and all diffraction spots in the pattern can be interpreted by the superposition of five twin-related electron diffraction patterns [57]. One of the five parts can be indexed by a diamond structure with a lattice constant a = 0.35670 nm. The twin boundaries are {111}, and the 5-fold axis (equal to the incident direction) is [110]. The 5-fold symmetry is not perfect, and there is distortion, as indicated by split diffraction spots (arrows). In addition, a number of streaks along the five directions are observed, which is due to many defects, such as dislocations and stacking faults.

Au7

Fig. 6.28: HREM images of gold nanoparticles (a) without and (b) with distortion. Twin planes are indicated by arrows. (c) SEM and (d) electron diffraction pattern of diamond particle.

154 | 6 HREM analysis of nanostructured materials A structural model of the Au7 cluster projected along the 5-fold axis with a perspective view is shown in Figure 6.28 (a). The atomic arrangements of the cluster agree well with observed atomic arrangements in Figure 6.28 (a). The Au7 and Au18 structures were optimized by molecular mechanics calculations, and the total energy was calculated to be 3761 and 15050 kJ/mol, respectively. This indicates that the total energy increases with the increasing size of the Au clusters, which results in the instability of the clusters, as shown in Figure 6.28 (b). Multiplied twinned particles with a 5-fold symmetry are sometimes observed in metal nanoparticles, such as Ag, Ni, and Co [48, 49]. The maximum size of these nanoparticles is ca. 40 nm because the inner stress of a crystal increases as it grows. This stress could be induced by the elastic deformation to accommodate the misfit angle of 7° 20’ between the twin units [48]. The stress is released at one specific twin boundary and a small gap is produced, as observed in Figure 6.28 (b). A structural model of a C25 diamond cluster was also constructed [57], and the atomic arrangements of the cluster agree with the observed electron diffraction pattern of Figure 6.28 (d). The C25 structure was optimized by semiempirical molecular orbital calculations, and the total energy was calculated to be 212 kJ/mol, which is smaller compared with that of the Au clusters. This small total energy would facilitate the growth of diamond particles. The stress is released at the five regions between the twin boundaries by inducing many stacking faults and dislocations, which results in an increase in the diamond particle size of more than 1 μm. The total energy of the Au18 , diamond (C25 ), and h-BN (B12 N13 ) clusters were calculated to be 15050, 212, and 28 kJ/mol, respectively, and these stabilities agreed well with the results of HREM observation and electron diffraction.

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A Appendix A.1 7 crystal systems and 14 Bravais lattices in three dimensions Primitive (P): lattice points on the cell corners only. Body (I): one additional lattice point at the center of the cell. Face (F): one additional lattice point at the center of each of the faces of the cell. Base (C): one additional lattice point at the center of each of one pair of the cell faces. 7 cristal systems

Axes and angles

Triclinic

a ≠ b ≠ c 𝛼 ≠ 𝛽 ≠ 𝛾 ≠ 90∘

Monoclinic

a ≠ b ≠ c 𝛼 = 𝛽 = 90∘ ≠ 𝛾

Orthorhombic

a ≠ b ≠ c 𝛼=𝛽=𝛾= 90∘

Tetragonal

a1 = a2 ≠ a3 𝛼=𝛽=𝛾= 90∘

Cubic

a1 = a2 = a3 𝛼=𝛽=𝛾= 90∘

Rhombo- a1 = a2 = a3 hedral 𝛼=𝛽=𝛾< 120∘ , ≠ 90∘

Hexagonal

a1 = a2 ≠ a3 𝛼 = 𝛽 = 90∘ , 𝛾 = 120∘

Bravais lattices

c b a

P

a b

b

P

C

c

a

a

b

P

c

a

I

a

a

I

a

a

R

I

c

a

P

a

b

a

P

a

c

a

c

C

a

a

a

b

F

c

b c

c

a

a

F

a

a

a

a

c a

P

Rhombohedral structure can be indexed as hexagonal lattice by increase the unit cell size to three times.

A.2 Miller indices and direction in the crystals

| 159

A.2 Miller indices and direction in the crystals The Miller indices that represent the lattice planes are indicated like (100). Note that the Miller indices are indicated by the inverse of five vectors as shown in the figure below. Sometimes the crystals have the equivalent lattice planes, which are summarized like {100}. For example in the cubic system, nine lattice planes of (110), (101), ̄ ̄ ̄ (110), ̄ (101), ̄ and (011)̄ are equivalent to each other, and can (011), (110), (101), (011), be summarized as {110}. The directions are indicated like [100], and the equivalent directions in the crystal can be summarized as ⟨100⟩. The directions are indicated as integer ratios of the direction vectors (which is not the inverse of the vector). For the hexagonal and tetragonal systems, representations of a-plane, c-plane, aaxis, and c-axis are commonly used for the {100}, {001}, ⟨100⟩, and ⟨001⟩, respectively. If the crystal structure is confirmed, the lattice–plane distance and distance of atoms can be determined from the lattice constant. [111]

[001]

c

c

(110)

[111] (200)

[021]

(111)

b

b [010]

a [100]

[410] [210]

a (001)

[110]

[001]

(001) (110)

c

(112)

[010]

b [100]

a

[110]

Miller indices in the cubic (top) and the hexagonal (bottom) structure.

160 | A Appendix

A.3 Distances dhkl and angles 𝜙 of lattice planes a, b, c, 𝛼, 𝛽, and 𝛾 are indicated in the figure below. c

a

b g

b

a

(1) Cubic: a = b = c,

𝛼 = 𝛽 = 𝛾 = 90°

1 d2hkl

=

h + k 2 + l2 , a2

h1 h2 + k1 k2 + l1 l2

2

cos 𝜙 =

√(h21 + k12 + l21 ) + (h22 + k22 + l22 )

(2) Tetragonal: a = b ≠ c, 1 d2hkl

=

𝛼 = 𝛽 = 𝛾 = 90°

h2 + k 2 l2 + 2, a2 c

h1 h2 +k1 k2 a2

cos 𝜙 =

1 √( h1a+k + 2 2

2

l21 ) c2

+

+(

l1 l2 c2 h22 + k22 a2

+

l22 ) c2

(3) Hexagonal: a = b ≠ c, 1 d2hkl

𝛼 = 𝛽 = 90°, 𝛾 = 120° 2

=

3 h + hk + k 2 l2 ) + , ( 4 a2 c2

cos 𝜙 =

h1 h2 + k1 k2 + √(h21 + k12 + h1 k1 +

1 2

(h1 k2 + h2 k1 ) +

3a2 2 l) 4c2 1

3a2 ll 4c2 1 2

+ (h22 + k22 + h2 k2 +

3a2 2 l) 4c2 2

(4) Rhombohedral: a = b = c,

𝛼 = 𝛽 = 𝛾 < 120°, ≠ 90°

(h + k 2 + l2 ) sin2 𝛼 + 2 (hk + kl + hl) (cos2 𝛼 − cos 𝛼) 1 , = a2 (1 − 3 cos2 𝛼 + 2 cos3 𝛼) d2hkl 2

a4 dh1 k1 l1 dh2 k2 l2

[sin2 𝛼 (h1 h2 + k1 k2 + l1 l2 ) V2 + (cos2 𝛼 − cos 𝛼) (k1 l2 + k2 l1 + l1 h2 + l2 h1 + h1 k2 + h2 k1 )]

cos 𝜙 =

A.3 Distances dhkl and angles 𝜙 of lattice planes | 161

(5) Orthorhombic: a ≠ b ≠ c,

𝛼 = 𝛽 = 𝛾 = 90°

2

1 d2hkl

=

h k 2 l2 + 2 + 2 , 2 a b c

cos 𝜙 =

h1 h2 a2 2

√( ah21 +

k12 b2

+

+

k1 k2 b2

l21 ) c2

+ h2

l1 l2 c2

+ ( a22 +

k22 b2

+

l22 ) c2

(6) Monoclinic: a ≠ b ≠ c, 1 d2hkl

=

𝛼 = 𝛾 = 90° ≠ 𝛽

1

(

2 h2 k 2 sin 𝛽 l2 2hl cos 𝛽 + + 2 − ) , ac a2 b2 c

sin2 𝛽 dh k l dh k l h h k k sin2 𝛽 l1 l2 (l1 h2 + l2 h1 ) cos 𝛽 + 2 − ] cos 𝜙 = 1 1 1 2 2 2 2 [ 1 2 2 + 1 2 2 ac a b c sin 𝛽

(7) Triclinic: a ≠ b ≠ c, 𝛼 ≠ 𝛽 ≠ 𝛾 1 1 = 2 (S11 h2 + S22 k 2 + S33 l2 + 2S12 hk + 2S23 kl + 2S13 hl ) , V d2hkl cos 𝜙 =

dh1 k1 l1 dh2 k2 l2 V2

[S11 h1 h2 + S22 k1 k2 + S33 l1 l2 + S23 (k1 l2 + k2 l1 )

+ S13 (l1 h2 + l2 h1 ) + S12 (h1 k2 + h2 k1 ) ] S11 = b2 c2 sin2 𝛼,

S12 = abc2 (cos 𝛼 cos 𝛽 − cos 𝛾) ,

S22 = a2 c2 sin2 𝛽,

S23 = a2 bc (cos 𝛽 cos 𝛾 − cos 𝛼) ,

S33 = a2 b2 sin2 𝛾,

S13 = ab2 c (cos 𝛾 cos 𝛼 − cos 𝛽) ,

V = abc√1 − cos2 𝛼 − cos2 𝛽 − cos2 𝛾 + 2 cos 𝛼 cos 𝛽 cos 𝛾

Index 5-fold axis 74 7 crystal systems 158 A 𝛼 42 absolute atomic position 15 absorption contrast 12 accelerating voltage 15, 38, 42, 43, 78 activation energy 152 AFM 19 Ag2 SnO3 56 Al2.6 Cu1.8 B105 120 Al70 Ni20 Ru10 24 amorphous 41, 100 amorphous carbon 73 amplitude 11, 13, 51 aperture 8 arc melting 135 armchair-type 138 astigmatism 36 astigmatism correction 40 atom 1 atomic composition 5 atomic coordinate 54, 122 atomic disordering 64, 153 atomic displacement modulation 57 atomic force microscope 19 atomic nucleus 4, 10 atomic number 51, 67 atomic observation 46 atomic position 16, 48 atomic scattering factor 10, 11 atomic species 13, 15 Au 149, 153 B B12 121 (B12 )13 65 B36 N36 135 B84 121 B2240 N2240 143 bamboo structure 149 bamboo-type 143 barrier height 118 BaZrO3 133

bcc 34, 146 Bi-2223 99 (BiPb)2 Sr2 Ca2 Cu3 O10 41, 52 (Bi,Pb)2 Sr2 Ca2 Cu3 Ox 98 BN 21, 22 BN nanomaterial 145 BN nanotube 20, 134 body-centered cubic 34 boron nitride 18, 100 Bragg diffraction 9 Bravais lattice 158 bright field image 23 bundled BN nanotube 135 Burgers vector 112 C Cc 42 C60 solid cluster 77 Cs 6, 40 Cs corrected TEM 6, 42 Cs corrector 6 cage structure 119 carbon onion 72 carrier transport 123 CBED 7 c-BN 101 CCD camera 9 characteristic X-ray 19, 22 charge-up 28 chemical vapor deposition 18 chirality 136 chromatic aberration 42 cleavage 30 cluster growth 152 coherency 6 coherent 95, 117, 134 commensurate unit cell 57 composition 2 compositional modulation 57 condenser 8 cone angle 143 contact resistance 116 contamination 43 convergent beam electron diffraction 7 coordinate 48

164 | Index coordination 125 core-loss electron 19 critical current density 131 cross-sectional HREM 132 crushing 29 crystal edge 122 crystal growth 133 crystal structure 2 crystal structure factor 13 crystal system 32 crystal thickness 38, 80, 81 crystallographic image processing 46, 47, 51, 55 crystallographic symmetrization 55 cubic 100 cumulative distribution function 66 Cu–O 97 cup-stacked structure 140, 146 current density 43 current–voltage 143 CVD 18 CVD-BN 101, 149 D dark field image 23 data storage 44 database 32 Debye–Scherrer ring 104, 107, 150 defect 131 defect structure 110 defocus value 38, 80, 82 density of states 19 diamond 101, 149, 153 diamond structure 14, 31, 35 difference image 61, 64, 79, 80, 83 differential image 67 diffracted wave 13 diffraction amplitude 70 diffraction contrast 12 diffuse streak 97 dimple grinder 30 dislocation 112, 146, 153 disordering 2 disordering of light element 70 divergence angle 42 domain structure 61 domain wall 25 doping atom 77, 80, 83 dynamical diffraction effect 13, 15, 83

E 𝜀s 40 EBSD 18 ED 5 edge-on 146 EDS 5 EDX 5, 9, 22 EELS 6, 9, 19 elastic-scattered electron 10 electric field 4, 10, 24 electric field potential 10 electron 1 electron backscatter diffraction 18 electron beam 8, 10 electron beam damage 43 electron beam incidence 40 electron biprism 9 electron cloud 4, 10 electron diffraction 5, 56 electron diffraction pattern 11 electron energy-loss spectroscopy 6, 19 electron gun 8 electron holography 6, 24 electron intensity 44 electron lens 11 electron microscope 1 electron microscopy 2 electron transport 118 electron wave 11, 24 electron-beam irradiation 73 electronic bonding state 19 electronic state 2 electropolishing 30 ELNES 21 energy barrier 118 energy dispersive X-ray spectroscopy 5, 22 energy filtering 21 energy level 73 energy loss near edge structure 21 Euler rule 74 EXELFS 21 extended energy loss fine structure 21 extra half plane 133 extra reflection 60 F face-centered cubic 33 fcc 33, 149, 152 𝛼-Fe 148

Index | 165

Fe nanowires 146 Fe4 N 146 Fe-filled BN nanotube 146 field emission 17 field-emission electron microscope 24 five-fold symmetry 149 fluorescent screen 9 fluxoid lattice 134 flux-pinning 134 flux-pinning-center 131 focus 12 focused ion beam 31 Fourier filtering 41 Fourier transform 4, 12, 41 fundamental reflection 87 G GaAs 116 geometry optimization 144 Gibbs’ energy 149 Gibbs’ free energy 152 Gibbs–Thompson effect 147 grain boundary 132, 133 H HAADF 23 HAADF-STEM 7, 146 hardness 101 hcp 37 heavy doping 117 hexagonal close-packed 37 hexagonal networks 134 hexagonal structure 102 Hg0.5 Tl0.5 Ba2 CuO5 122 HgTlBa2 CuO5 61 high-angle annular dark-field 23 high-angle annular dark-field scanning transmission electron microscopy 7 high-resolution electron microscope 5 high-resolution electron microscopy 3, 15 high-voltage alignment 36 hologram 24 HREM 3, 5, 15, 38, 46 HREM simulation 53 I icosahedral symmetry 74 image analysis 45 image calculation 53

image intensity 15 image processing 41 image simulation 26 imaging condition 45 imaging plate 44 impurity level 140 incidence depth 17 incommensurate 88 inelastic-scattered electron 10, 19 inner stress 154 in-situ observation 6 intensity profile 49 interaction constant 15 interface 113 interfacial energy 107 interference 38 interference fringe 24 intergrowth 48, 49, 110, 111 inverse Fourier transform 41, 51, 95 Inx Ga1 − x As 118 ion milling 30, 103 ionic radius 125 IPR 74 isolated pentagon rule 74 I–V 143 J Jc 131 Josephson junction 114 K K𝛼 22 K𝛽 22 K-edge 20 L 𝜆 40 L𝛼 22 lattice constant 14, 26, 32, 159 lattice defect 112 lattice distortion 146 lattice image 38 lattice spacing 151 L𝛽 22 L-edge 20 life material 31 line profile 71 Ln2 CuO4 91 Lorentz microscopy 6, 24 low barrier height 117

166 | Index M magnetic domain 6, 25 magnetic field 24 magnetic flux 2, 25 magnetic force 25 magnetization 6 magnification 34 matrix 131, 150 M-edge 20 mental attitude 45 MESFET 116 metallofullerene 77 microgrid 29 microtwin 102, 105 Miller index 8, 159 modulated structure 58, 59 modulated superstructure 87, 92, 99, 125 modulated wave vector 88 modulation wave vector 89, 97 Moiré fringe 131 molecular mechanics 144 molecular mechanics calculation 154 molecular orbital calculation 72, 149, 152 morphology 132 multiply twinned particle 149 multislice calculation 129 multislice method 38 N [Na48 ][Al48 Si144 O384 ] 119 nanoparticle 149 nanotube wall 142 native oxide layer 116 N@C60 77 Nd2 CuO4 92, 93 negative film 44 neutron 1 neutron diffraction 1 NiGe 118 Nix GaAs 116 nucleation process 133 number of atoms 16 O objective aperture 23, 38 objective lens 8, 40 occupancy 69 octahedral site 129 ohmic contact 116

onset voltage 143 optical absorption 140 organic material 43 ortho-II 98 ortho-III 98 orthorhombic structure 87 oxygen atom 50 oxygen atom position 130 oxygen deficiency 91 oxygen ordering 94 oxygen vacancy 17, 38, 50, 61 oxygen vacancy ordering 91 oxygen vacant position 47

P Pb(Ba,Sr)2 (Ln,Ce)n Cu3 O5 + 2n 128 Pb2 Sr2 (Ln,Ce)n Cu3 O6+2n 128 Pb2 Sr2 (Y,Ce)5 Cu3 O16 126 Pb2 Sr2 Y0.5 Cu3 O8 115 Pb2 Sr2 YCe4 Cu3 O16 129 PbBa0.7 Sr1.3 EuCeCu3 O9 115, 125 PbBa0.7 Sr1.3 YCe2 Cu3 O11 127 PbBa0.7 Sr1.3 YCe3 Cu3 O13 111 PbBaSrYCu3 O7 111, 124 pentagonal structure 18 perovskite 110, 112, 113, 133 personal feeling of art 45 phase 70 phase contrast 12, 15, 40 phase displacement 113 phase image 25 phase information 4, 25, 51 phases of the wave 11 𝜋-bonding 21 pinning center 133 plane group 52 plasmon-loss electron 21 point resolution 42 potential 13, 38, 40 potential distribution 10, 75 powder 29 Pr1.85 Ce0.15 CuO4 93 Pr2 CuO4 93 precipitate 131 projected potential 15 proton 1 purification 140

Index | 167

Q quantitative analysis 61 quark 1 quasicrystal 24, 149 R RHREM 63, 66, 78 RbC60 77 real space 4, 11, 12 reciprocal lattice 4, 12 reciprocal space 4, 11, 12 regrown GaAs 119 relative atomic position 13 residual index 61, 63, 78 resolution limit 71 rhombohedral 100 rhombohedral structure 102 S sample preparation 28 satellite peak 97 satellite reflection 57, 94, 96, 125 scanning electron microscope 7, 17 scanning transmission electron microscopy 23 scanning tunneling microscope 19 Scherzer defocus 38, 80 Scherzer focus 16, 40 secondary electron 17 SEM 7, 17, 150, 153 semicoherent 131 short range ordering 97 Si 26 side-entry-type holder 33 𝜎-bonding 20 silicon 14, 32 slow-scan CCD camera 44 Sm2 CuO4 93, 130 Sm–Co 25 SmLa0.75 Sr0.25 CuO4 130 space group 7, 26, 51, 52 specimen holder 9 specimen preparation 29 spherical aberration 38, 42 spherical aberration coefficient 6, 40 stacking fault 104, 125, 153 statistical value 67 STEM 23 STM 19, 143 streak 105, 125, 153

structural isomer 74 structural optimization 72, 74 structural stability 139 structure factor 4, 13 structure image 38, 46 superconducting copper oxide 110, 134 superconducting transistor 114 supericosahedral (B12 )13 68 superlattice 94 supersonic wave cutter 30 superstructure 57 superstructure reflection 88 surface structure 113, 123 T Tc 16 t-BN 150 TEM 4, 5, 33 temperature factor 122 tetrahedral carbon onion 74 tetrahedral site 129 tetrahedral structure 72 thermal conductivity 101 thermal parameter 69 thermodynamic calculation 152 three-dimensional HREM 74 three-dimensional image 75 three-dimensional potential 76 through-focus imaging 64 tilting 36 Tl0.5 Pb0.5 Sr2 CuO5 115 Tl2 Ba2 Ca2 Cu3 O10 89 Tl2 Ba2 Ca3 Cu4 O12 48 Tl2 Ba2 CaCu2 O8 16, 89 Tl2 Ba2 CuO6 3, 54, 87, 113 Tl2 BaSrCuO6 89 TlBa2 Ca2 Cu3 O9 90 TlBa2 Ca3 Cu4 O11 39, 46, 110, 115 TlBa2 CaCu2 O7 90, 113 Tl-vaporized region 111 top-entry type holder 33 total energy 72, 144 transition temperature 16, 38 transmission electron microscope 5 transmission electron microscopy 4 transmitted electron 10 tunneling mechanism 119 turbostratic 100 twin 87

168 | Index twin boundary 95, 97, 103, 149, 151 twin plane 96, 152, 153 twin structure 100, 105, 106 U ultra microtome 31 unit cell 62 unoccupied antibonding orbital 20 V van der Waals force 74 vibration 37 VLSI 116 W wavelength 1 wavelength of electron 40, 42 weak phase contrast 12 weak-phase-objective approximation 15, 51 wurzite 100

X X-ray diffraction 1, 31, 48 X-ray scattering 11 XRD 31, 48, 141 XRD database 14 Y Y-B24 65 YB56 64, 74 YBa2 Cu3 O7 94, 131 YBa2 Cu3 O7−x 97 Y-hole 64, 67 Z Z contrast 7, 23 z coordinate 55, 129 zeolite 119 zigzag-type 136 ZnS-type structure 36