Dissertations in Forestry and Natural Sciences ANDREY OREKHOV ELECTRON MICROSCOPY STUDY OF STRUCTURAL PECULIARITIES OF CARBON MATERIALS PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND
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Dissertations in Forestry and Natural Sciences
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ANDREY OREKHOV
ELECTRON MICROSCOPY STUDY OF STRUCTURALPECULIARITIES OF CARBON MATERIALS
PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND
This work presents results of high resolution transmission electron microscopy analysis
of structural peculiarities of some of nanocarbons materials forms. It was
performed the optimization of optical system of aberration corrected transmission electron
microscope to increase of the signal-to-noise ratio. The optimized TEM instruments
were used in this work for structural characterization of the nanodiamonds, two-
dimensional (2D) structures and needle-like diamonds, onion-like nanocarbons and other graphene-based structures, including
composites consisting of linear (1D) CuCl and Hg2Cl2 crystals encapsulated in single-walled carbon nanotubes. Obtained results allowed
appropriate development of production processes for these carbon nanostructures and
understanding of their physical properties.
ANDREY OREKHOV
ANDREY OREKHOV
Electron Microscopy Study
of Structural Peculiarities of
Carbon Materials
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
Number 258
Academic Dissertation
To be presented by permission of the Faculty of Science and Forestry for public
examination in the Auditorium AU100 in Aurora Building at the University of
Eastern Finland, Joensuu, on December, 22, 2016, at 12 o’clock noon.
Department of Physics and Mathematics
Grano Oy
Joensuu, 2016
Editors: Prof. Pertti Pasanen,
Prof. Pekka Toivanen, Prof. Jukka Tuomela, and Prof. Matti Vornanen
Distribution:
University of Eastern Finland Library / Sales of publications
P.O.Box 107, FI‐80101 Joensuu, Finland
tel. +358‐50‐3058396
www.uef.fi/kirjasto
ISBN: 978‐952‐61‐2381‐3 (Print)
ISBN: 978‐952‐61‐2382‐0 (PDF)
ISSNL: 1798‐5668
ISSN: 1798‐5668
ISSN: 1798‐5676 (PDF)
Author’s address: University of Eastern Finland
Department of Physics and Mathematics
P.O.Box 111
80101 JOENSUU
FINLAND
email: [email protected]
Supervisors: Professor Alexander Obraztsov, Ph.D.
University of Eastern Finland
Department of Physics and Mathematics
P.O.Box 111
80101 JOENSUU
FINLAND
email: [email protected]
Professor Yuri Svirko, Ph.D.
University of Eastern Finland
Department of Physics and Mathematics
P.O.Box 111
80101 JOENSUU
FINLAND
email: [email protected]
Reviewers: Professor Angela Vella, Ph.D
Normandie Université, Université‐INSA de Rouen
Groupe de Physique des Matériaux
Avenue de lʹUniversité BP 12
76801 SAINT ETIENNE DU ROUVRAY
FRANCE
email: angela.vella@univ‐rouen.fr
Professor Rupert Schreiner, Ph.D
OTH Regensburg Fakultät AM
Seybothstr. 2
93053 REGENSBURG
GERMANY
email: rupert.schreiner@oth‐regensburg.de
Opponent: Professor Albert Nasibulin, Ph.D.
Skolkovo Institute of Science and Technology
Skolkovo Innovation Center, Building 3
143026 MOSCOW
RUSSIA
email: [email protected]
ABSTRACT
Carbon materials attract growing interest of researchers due to
their numerous unique properties and potential applications.
These properties are originated of atomic structure of carbon
which exhibits great variety of its nanostructured forms
including graphene, carbon nanotubes, fullerenes,
nanodiamonds and other. Revealing structural peculiarities of
these nanostructured forms of carbon materials is very
important for understanding of origin of their electronic, optical,
thermo‐physical, mechanical and other properties. In this
Thesis, the high resolution transmission electron microscopy is
applied to study structural peculiarities of some of nanocarbon
materials. The Thesis includes brief overview of some forms of
nanostructural carbon materials, description of methodological
problems of the transmission electron microscopy and
possibilities for their resolving. These descriptions are
illustrated by examples of the researches performed by the
author and include his original publications.
Universal Decimal Classification: 538.911, 548.1
CAB Thesaurus: high resolution transmission electron microscopy, analytical
methods, atomic structure; nanostructured materials, nanocarbon materials,
carbon nanotubes, nanodiamonds;
Preface
I would like to express my thanks to all those who have
helped me in this work:
Above all, I am profoundly indebted to my supervisors
Professor Alexander Obraztsov for his guidance, fundamental
insight, his time and great efforts supporting this work. I am
also very grateful to my supervisor Professor Yuri Svirko and to
the Head of the Department of Physics and Mathematics
Professor Timo Jääskeläinen for their support and for providing
me this opportunity to realize my research project in the
University of Eastern Finland.
Author of this Thesis greatly appreciates support from the
collaborators and colleagues from research groups headed by
Professor Alexander Obraztsov, Professor Elena Obraztsova and
Professor Alexander Okotrub which made great and valuable
inputs providing ideas, materials and discussion.
Special thanks are to Professor Andrey Chuvilin for giving
the opportunity to carry out the TEM measurements and
support in image processing and for discussions of results.
I am grateful to the Examiners of this work, Professor Angela
Vella and Professor Rupert Schreiner, and to the Opponent,
Professor Albert Nasibulin, for their review and encouraging
comments.
And finally, I would like express my gratitude to my family,
parents and brothers for their patience, love and comprehensive
support.
This work made with partial support from Russian Science
Foundation (grant #14‐12‐00511).
Joensuu December 22, 2016 Andrey Orekhov
LIST OF ORIGINAL PUBLICATIONS This thesis consists of the review of author’s work in field of
electron microscopy study of structural peculiarities of carbon
materials and the following selection of the author’s
publications, referred to by the Roman numerals I‐VIII:
I D’yakova Yu. A., Suvorova E. I., Orekhov Andrei S.,
Orekhov Anton S., Alekseev A. S., Gainutdinov R. V.,
Klechkovskaya V. V., Tereschenko E. Yu., Tkachenko N. V.,
Lemmetyinen H., Feigin L. A., Kovalchuk M. V. Study of
Structural Order in Porphyrin–Fullerene Dyad ZnDHD6ee
Monolayers by Electron Diffraction and Atomic Force
Microscopy, Crystallography Reports 58(6): 927–933, 2013 DOI:
10.1134/S1063774513060096
II Rybkovskiy D. V., Arutyunyan N. R., Orekhov A. S.,
Gromchenko I. A., Vorobiev I. V., Osadchy A. V., Salaev E.
Yu., Baykara T. K., Allakhverdiev K. R., Obraztsova E. D.
Size‐induced effects in gallium selenide electronic structure:
The influence of interlayer interactions, Physical Review B 84:
085314, 2011 DOI: 10.1103/PhysRevB.84.085314
III Orekhov A.S., Savilov S.V., Zakharov V.N., Yatsenko A.V.,
Aslanov L.A. The isolated flat silicon nanocrystals (2D
structures) stabilized with perfluorophenyl ligands, Journal
of Nanoparticle Research 16(1): 2190, 2014 DOI: 10.1007/s11051‐
013‐2190‐4
IV Tonkikh A. A., Rybkovskiy D. V., Orekhov A. S., Chernov A.
I., Khomich A. A., Ewels C.P., Kauppinen E. I., Rochal S. B.,
Chuvilin A.L., Obraztsova E. D. Optical properties and
charge transfer effects in single‐walled carbon nanotubes
filled with functionalized adamantane molecules, Carbon 109:
87‐97, 2016 DOI: 10.1016/j.carbon.2016.07.053
V Kleshch Victor I., Tonkikh Alexander A., Malykhin Sergey
A., Redekop Eugene V., Orekhov Andrey. S., Chuvilin
Andrey L., Obraztsova Elena D., Obraztsov Alexander N.
Field emission from single‐walled carbon nanotubes filled
with CuCl, Applied Physics Letters 109: 143112, 2016 DOI:
10.1063/1.4964273
VI Bokova‐Sirosh S. N., Pershina A. V., Kuznetsov V. L.,
Ishchenko A. V., Moseenkov S. I., Orekhov A. S.,
Obraztsova E. D. Raman Spectra for Characterization of
Onion‐Like Carbon, Journal of Nanoelectronics and
Optoelectronics 8: 106–109, 2013 DOI: 10.1166/jno.2013.1444
VII Alexeev Andrey M., Ismagilov Rinat R., Ashkinazi Evgeniy
E., Orekhov Andrey S., Malykhin Sergei A., Obraztsov
Alexander N. Diamond platelets produced by chemical
vapor deposition, Diamond & Related Materials 65: 13–16,
2016 DOI: 10.1016/j.diamond.2015.12.019
VIII Orekhov Andrey S., Tuyakova Feruza T., Obraztsova
Ekaterina A., Loginov Artem B., Chuvilin Andrey L.,
Obraztsov Alexander N. Structural defects in single crystal
diamond needles, Nanotechnology 27(45): 455707, 2016 DOI:
10.1088/0957‐4484/27/45/455707
The above publications have been included at the end of this
thesis with their copyright holders’ permission.
AUTHOR’S CONTRIBUTION Author has planned and performed the experimental parts of
transmission electron microscopy study, analyzed and
interpreted data received, contributed in discussions and in
writing the experimental part of the papers I, II, IV, V, VI, VII,
VIII. The main ideas were generated in fruitful discussions of all
co‐authors team. The papers III and VIII were written by the
author. The experimental setup discussed in these papers,
samples preparation was performed by the author.
Interpretation of results which most important in electron
microscopy experiments were done by author on basic of
proposed atomic models materials studied. For these model
series of HRTEM images and electron diffraction patterns were
calculated.
Contents
INTRODUCTION ............................................................................. 1
1 Review of the structural features of carbon materials ............. 3
1.1 Types of hybridization of atomic orbitals in carbon ................ 3
1.2 Graphene and its derivatives ...................................................... 7
1.3 Methods of synthesis .................................................................. 20
1.4 Techniques for carbon materials structural characterization27
Objectives of this work ..................................................................... 34
2 GENERAL PRINCIPLES AND PRACTICAL ASPECTS OF
TEM ANALYSIS .............................................................................. 35
2.1 Theoretical aspects of electron microscopy ......................... 35
2.2 Optimization of spherical aberration correction for nano‐
carbon materials (Experimental part) ............................................ 55
Summary of the Chapter 2 .............................................................. 66
3 ATOMIC ARRANGEMENT OF GUEST CRYSTAL IN THE
INNER CHANNEL OF FUNCTIONALIZED SINGLE‐
WALLED CARBON NANOTUBES ............................................. 67
3.1 Singe walled carbon nanotube functionalized by adamantane
molecules ........................................................................................... 68
3.2 Structure characterization of Hg2Cl2 crystals located in the
inner channel of SWCNT ................................................................. 70
3.3 Crystal structure of 1D CuCl@SWCNTs .................................. 73
Summary of the Chapter 3 .............................................................. 77
4 THE STRUCTURAL PECULIARITIES OF NANO‐ AND
MICRO‐METER SIZE SCALE DIAMOND CRYSTALS ......... 79
4.1 The transformation of Sp3 to Sp2 C‐C bond in nanodiamond
under heat treatment ........................................................................ 80
4.2 Diamond platelets produced by chemical vapor deposition 82
4.3 Structural peculiarities of single crystal diamond needles of
nanometer thickness ......................................................................... 84
Summary of the Chapter 4 .............................................................. 88
5 CONCLUSIONS ........................................................................... 89
REFERENCES ................................................................................... 91
ORIGINAL PUBLICATIONS ..................................................... 105
Dissertations in Forestry and Natural Sciences Number 258 1
Introduction
Carbon materials always attracted great attention of
research community because of their importance for practical
applications and for fundamental science. During last decades,
especial interest has been dedicated to production and
comprehensive characterization of nano‐structured forms of
carbon materials such as nanodiamonds, fullerenes, carbon
nanotubes, graphene, numerous graphene‐like species and their
composites. These relatively “new” types of carbon materials
exhibit numerous unique properties promising important and
breakthrough achievements in fundamental science and
technology. Study of nanocarbon materials structural
peculiarities is necessary for deeper understanding of the
mechanisms determining their physical properties and for
optimization these properties for practical application purposes.
In spite of intensive study in this area many problems remain to
be open especially for specific forms of the nanostructured
carbon materials. This work presents results of high resolution
transmission electron microscopy analysis of structural
peculiarities of some of nanocarbons materials forms.
We performed optimization of optical system of
aberration corrected transmission electron microscope (TEM).
This adjustment allowed to increase of the signal‐to‐noise ratio
up to 30 % for the graphene TEM images with sub‐angstrom
spatial resolution at 80 kV accelerated voltage.
The optimized TEM instruments were used in this work
for structural characterization of the nanodiamonds, two‐
dimensional (2D) structures and needle‐like diamonds, onion‐
like nanocarbons and other graphene‐based structures,
including composites consisting of linear (1D) CuCl and Hg2Cl2
crystals encapsulated in single‐walled carbon nanotubes.
Obtained results allowed appropriate development of
Andrey Orekhov: Electron Microscopy Study of Structural Peculiarities of
Carbon Materials
2 Dissertations in Forestry and Natural Sciences Number 258
production processes for these carbon nanostructures and
understanding of their physical properties.
In this Thesis after brief Introduction we are reviewing in
Chapter 1 most common structural features and methods used
for synthesis of carbon nanomaterials. Thereafter in Chapter 2
we are considering methodology of TEM experiments with
special emphasis to TEM instrument adjustments which are
necessary to achieve suitable reproducibility and interpretation
of obtained results. Chapters 3 and 4 present description of
obtained original experimental results and conclusions made on
their basis which are presented together with copies of the
articles where they were published.
Dissertations in Forestry and Natural Sciences Number 258 3
1 Review of the structural
features of carbon
materials
Carbon materials have a wide range of properties which
make them suitable for various applications. Depending on type
of interatomic bonding and on crystal structure, carbon
materials could possess very different mechanical, thermo‐
physical, optical and electronic properties. Thus, diamond is the
hardest material which is used for indenters, anvils and similar
applications. On the other hand, graphite softness allows to use
it in gaskets and in lubricants. Diamond is transparent dielectric
material with the highest thermal conductivity. Conversely,
graphite is opaque, has good electrical conductivity and may be
used (in some cases) as thermal insulator [1], [2]. The
information about crystal structure composition and presence of
lattice defects is especially essential for carbon materials for
development of their production methods and for their
applications.
The following paragraphs present brief overview of the
structural features of carbon materials, the methods of their
synthesis and the most common techniques used for structural
characterization.
1.1 TYPES OF HYBRIDIZATION OF ATOMIC ORBITALS IN CARBON
The most common model describing interatomic bonding
assumes, so called, hybridization of atomic orbitals which
allows explanation of electronic structure formation of
Andrey Orekhov: Electron Microscopy Study of Structural Peculiarities of
Carbon Materials
4 Dissertations in Forestry and Natural Sciences Number 258
molecules. In particular, it explains modification of atomic
orbitals during formation of a covalent chemical bond,
alignment of the lengths of chemical bonds and bond angles in
the molecule. Linus Pauling has proposed the scheme of valent
atomic orbitals hybridization. Spatial orientation of the hybrid
orbitals is defined the type Each type of hybridization. These
hybridized orbitals model is used for carbon material
characterization. Four valence electrons of carbon atom in its
ground state are arranged in one ‘2s’ orbital and two ‘2p’ orbitals.
With excitation of the atom one of two ‘2s’ electrons moves to
the free ‘2p’ orbital. The process of hybridization can be
represented as different combinations of one ‘s’ and one, two or
three ‘p’ orbitals. Thus there is potential possibility to form two,
three or four new orbitals. Each of these formed orbitals retains
some part of properties of the ‘s’ orbital and some part of
properties of the ‘p’‐orbitals. These new orbitals are called ‘sp1’,
‘sp2’, ‘sp3’ hybridized orbitals, correspondingly [3], [4], [5].
Orientation of the hybrid orbitals is determined by Coulomb
interaction between electrons and condition of minimization of
free energy of the system:
sp1‐hybridization occurs when one s and one p orbitals are
mixed; these two equivalent sp‐atomic orbitals have axial
symmetry and are arranged linearly with an angle between the
axis of 180 degrees and with opposite directions from the core of
the central atom; the remaining two non‐hybrid p‐orbitals are
perpendicular to the hybrid one and to each other; these non‐
hybrid orbitals provide formation of π‐bonds (Fig. 1‐1a);
sp2‐hybridization occurs when one of s‐ and two of p‐orbitals
are mixed; the obtained hybrid orbitals are arranged in one
plane with their axes directed from the atom to the vertices of
the triangle at an angle of 120 degrees; the non‐hybrid p‐orbital
is situated perpendicular to the plane and is may be involved in
the formation of π‐bonds (Fig. 1‐1b);
sp3‐hybridization occurs when one of s and all three p
orbitals are mixed to form four equivalent in form and energy
hybrid orbitals; the axes of the sp3‐hybrid orbitals are directed
from the atom toward the corners of a tetrahedron; the angle
Chapter 1: Review of the structural features of carbon materials
Dissertations in Forestry and Natural Sciences Number 258 5
between any two axes is approximately 109°28ʹ, which
corresponds to the lowest electron repulsion energy (Fig. 1‐1c).
Figure 1‐1. The scheme of hybridization of atomic orbitals corresponds to sp1‐ (a) sp2‐
(b) and sp3‐ hybridization (c). Hybridized orbitals are shown by red and non‐hybrid
orbitals are shown by blue.
Type of hybridization determines atomic arrangements in
condensed carbon materials which may be represented by
different variants and combinations of amorphous carbon, one‐
dimensional linear atomic structures (carbyne), planar two‐
dimensional structures (graphene) or bulky three‐dimensional
structures (diamond):
amorphous carbon consists of a mixture of individual atoms
and/or atomic clusters with different hybridizations; typical
examples of amorphous carbon are wood charcoal, coke, soot
and similar objects which frequently contain small fragments of
stacked planar structures with interplanar distance of 0,350‐
0,365 nm; at high temperatures amorphous carbon may be
transformed into crystalline phase of graphite with different
levels of ordering; consideration of the structural organization of
amorphous carbon and its ordering is out of the scope of this
work;
carbyne is carbon materials with sp1‐hybridization of atomic
orbitals [6],[7]; this type of hybridization leads to formation of
the polymer‐like chains; there are two possibilities for carbyne
formation ‐ in β‐carbyne carbon atoms are arranged with double
Andrey Orekhov: Electron Microscopy Study of Structural Peculiarities of
Carbon Materials
6 Dissertations in Forestry and Natural Sciences Number 258
atomic bonds (=С=С=С=) and in α‐carbyne with alternating of
single and triple bonds (‐C≡C‐C≡C‐); the polymer chains have
chemically active ends with localized negative charge; the
chains may be arranged by different manners to provide further
structurization; however this type of carbon materials is not
considered in this work also;
graphene is a monolayer of carbon atoms bonded together by
sp2 hybrid orbitals; orientation of the atomic orbitals leads to
formation hexagonal (or honey‐comb) atomic structure of
graphene; the non‐hybridized p orbital of each atom is oriented
perpendicular to the atomic plane and participate in formation
additional interatomic π‐bonding; similar to carbyne all atomic
bonds in graphene are saturated except dangling bonds on its
periphery; little variation of the angles between axes of the
hybridized orbitals make possible formation other numerous
types of carbon materials with spherical, cylindrical, conical,
wavy shape of the atomic layer; chemical interaction, which is
possible for atoms located in planar part of the atomic layer,
results in formation 2D corrugated structure of graphene; weak
Wan der Waals interaction between the layers is responsible for
coupling of graphenes into multilayer graphite or into
multishell spherical and cylindrical structures; some of these
graphenic structures will be analyzed in this work;
diamond structure is formed by carbon atoms with sp3
hybridized atomic orbitals; tetrahedral orientation of these
orbitals is responsible for 3D atomic arrangement in diamond
structure; at the same time each atomic layer in diamond
structure is similar to graphene sheet, which is corrugated due
to bonding with other carbon atoms, and, thus, ʹdiamondʹ
structure may be considered as stacked corrugated graphenes;
in this work we will consider some examples of diamond
structures.
Chapter 1: Review of the structural features of carbon materials
Dissertations in Forestry and Natural Sciences Number 258 7
1.2 GRAPHENE AND ITS DERIVATIVES
Graphene and its numerous derivatives attract especially
great attention after pioneering works of Andrey Geim and
Konstantin Novoselov from Manchester University. In 2004 they
extracted a single sheet of graphene using a micromechanical
cleavage technique [8]. Later in 2005, the same group measured
the quantum Hall effect and experimentally proved linearity of
energy spectrum of electrons in graphene and applicability of
Dirac equation for the charge carriers in graphene [9]. However,
graphene has been known long before these works. In form of
graphene oxide it was first discovered in 1859 by chemist
Benjamin Brodie. Late G. Ruess and F. Vogt have detected
evidence of presence of carbon crystals of atomically small
thickness by Transmission Electron Microscopy. Although, these
crystals have been not pure graphene and their thickness have
been of several nanometers. The first graphene layers on metal
(Ru, Rb, Ni) substrates have been obtained in 1970s by Blakely et.
al.[10], [11]. The history of graphene is started much before 2004
also because it has been considered for a long time as a model
for structural analysis of carbon allotropes including fullerenes,
carbon nanotubes and graphite. In these studies many
properties of graphene such, as a thinnest, strongest and perfect
2D crystalline structure with very high electron mobility and
thus it excellent conductivity of both heat and electricity, have
been analyzed. And at present days graphene become an ideal
object for both fundamental studies and for variety of exciting
applications.
Let’s consider crystal structure of graphene which essentially
determines all its properties. Crystal lattice of graphene,
schematically shown in Fig. 1‐2a, consists of regular hexagons.
The unit cell of graphene could be represented as two sublattices
of red (A) and blue (B) carbon atoms. Each equivalent atoms
participates in formation of a triangular sublattice which may be
described by translating vector , = m + n , where m and
n – integers, and and are Bravais crystal vectors for a unit
cell (marked as yellow rhombus). The vectors , and
Andrey Orekhov: Electron Microscopy Study of Structural Peculiarities of
Carbon Materials
8 Dissertations in Forestry and Natural Sciences Number 258
specify position of atom B around site of atom A. Distance
between the nearest carbon atoms in the hexagons, marked a, is
0.142 nm. The unit cell parameter can be derived by ao=√3 , it is
equal to 0.246 nm.
Red tetravalent carbon atom A is covalently linked to three
neighboring blue carbon atoms B arranged in a plane, so the
angle between the bonds is 120°. The fourth electron occupies
2pz orbital, which is oriented perpendicular to the plane of the
graphene. These electrons are responsible for the unique
electronic properties of graphene and form a π‐zone in the
electron energy spectrum. Due to weak interaction of the π‐
electrons with a particular atom they may be easily moved
along graphene plane providing its high electrical and thermal
conductivity.
Figure 1‐2. Schematic representation of the hexagonal structure of graphene with unit
cell marked by yellow rhombus (a). Atomic model of perfectly flat sheet of graphene (b)
and the wavy roughness (c) at the molecular level found experimentally (adopted from
[12] with permission num. 3997280548454).
The atomic structure of an isolated single‐layer graphene has
been studied by transmission electron microscopy (TEM) [12].
Obtained electron diffraction patterns evidenced about expected
honeycomb crystal lattice. Detailed analysis of the diffraction
spots intensities reveals that the graphene sheet has a wavy
roughness with amplitude of about one nanometer (Fig. 1‐2c).
Chapter 1: Review of the structural features of carbon materials
Dissertations in Forestry and Natural Sciences Number 258 9
This roughness may be due to instability of the two‐dimensional
crystals [13–15]. It is believed that only through this wavy
roughness the graphene sheet could exists in a free‐standing
form and do not curl up spontaneously.
Despite of detailed analysis in previous studies many
problems related to identification and explanation of structural
peculiarities of graphenic materials require further research. The
interest to this research is stimulated by recent technology
developments which make possible reproducible production of
nanostructured materials with unique properties and their
practical usage. This includes purely carbon materials (such as
graphene and graphite, carbon nanotubes and fullerenes,
diamonds) as well as their different composites (like
heterostructures, filled single‐ and multi‐walled carbon
nanotubes).
1.2.1 Graphite
The most typical example of graphene‐based materials is
graphite. The structure of graphite consists of stacked parallel
graphene layers. Because of saturation of all valence bonds of
carbon atoms in graphene, the parallel atomic layers in graphite
are joined together only by weak Wan der Waals interaction. It
provides one of the most distinguishable properties of graphite
which consists in easily detaching material from a piece of
graphite when it is moving in contact with a surface. The
stacked atomic layers have some planar displacement from each
other and probability to form certain type 3D structure is
determined by free energy of the system. The most common (i.e.
the most probable) forms of graphite have hexagonal and
rhombohedral crystal lattice. The hexagonal lattice is formed by
alternation of A and B graphene layers in ‐A‐B‐A‐B‐ stacking
(Fig. 1‐3). A and B atoms on consecutive layers are on top of one
another (marked by yellow color) and A’ atoms in one plane are
over the hexagon centers of the adjacent layers and similarly for
the B’ atoms [16]. This graphene layer arrangement is called
Bernal stacking. In‐plane the nearest neighbor distance ac‐c of
0.142 nm, in‐plane lattice constant ao of 0.246 nm, and c‐axis
Andrey Orekhov: Electron Microscopy Study of Structural Peculiarities of
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10 Dissertations in Forestry and Natural Sciences Number 258
lattice constant co of 0.670 nm. This structure belongs to P 63/mmc
space group and has four atoms per unit cell (see Fig. 1‐3b).
In the rhombohedral (β‐phase) graphite the alternation
follows to the ‐A‐B‐C‐A‐B‐C‐ stacking order. It has ao of 0.246
nm, co of 1.005 nm and belongs to R‐3m space group with six
atoms per unit cell. This structure of β‐graphite is metastable
unlike to more stable α‐phase of graphite. In graphite of natural
origination about 30% of content may have rhombohedral
structure. Artificially synthesized graphite contains practically
only hexagonal form.
Figure 1‐3. Scheme of two consecutive graphene layers arrangement in hexagonal
graphite structure. A and B atoms are on top of one another (depicts by yellow color)
and A’ atoms in one plane are over the hexagon centers of the adjacent layers (a). The
hexagonal unit cell selection is represented in (b).
The crystal structure of hexagonal graphite belongs to
P63/mmc space group [17]. The symmetry elements of this space
group are schematically represented in Fig. 1‐4 [18]. This space
group includes following axes: vertical sixfold screw axis 62
which is a composition of a rotation by an angle 60° followed by
a translation along this axis of 1/3 of the lattice vector c,
inversion threefold axis, vertical twofold screw axis 21 which is a
composition of a rotation by an angle 180° followed by a
translation along this axis of ½ of lattice vector c, horizontal
twofold axis 2 and horizontal twofold screw axis 21 with the
translation along the horizontal coordinate and diagonal
directions. The group P63/mmc also contains symmetry planes:
horizontal mirror plane, vertical mirror planes which alternate
Chapter 1: Review of the structural features of carbon materials
Dissertations in Forestry and Natural Sciences Number 258 11
with glide planes b (composition of the reflection and translation
along half the lattice vector b) and vertical glide planes c which
alternate with n glide planes (composition of the reflection and
translation along half a face diagonal). The interaction of the
twofold axes and planes perpendicular to them leads to the
appearance of the centers of symmetry. Carbon atoms occupy
two types of symmetrical non‐equivalent positions which are
characterized by Wyckoff positions 2b and 2c. These initial
atoms are multiplied by all symmetry elements of the space
group in a way that carbon atoms are arranged in hexagonal
layers alternating along lattice vector c in a checkerboard
pattern.
Figure 1‐4. Graphical representation of symmetry elements of crystal structure with P
63/mmc space group (adopted from [18]. Reproduced with permission of the
International Union of Crystallography).
Table 1‐1. Crystal unit cell parameters for known graphite phases.
Modification a, b, c, (nm)
α, β, γ Space Group
Cryst. Sys. ICSD ref.
α-phase (2H) 0.246 0.246 0.670
90.00 90.00 120.00
P63/mmc hexagonal 52230
β-phase (3R) 0.370 0.370 0.370
39.75 39.75 39.75
R3mR rhombohedral 53780
The crystal lattice symmetry determines physical properties
of graphite. Particularly the properties of graphite have strong
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anisotropy which is determined by its layered structure [19],
[20]. Also presence of symmetry center leads to absence in
graphite polar directions and, consequently, physical properties
which may be assigned to the polar symmetry characteristics.
The unit cell parameters, space group and references on
Inorganic Crystal Structure Database (ICSD) for hexagonal α‐
phase (2H) and rhombohedral β‐phase (3R) graphite phases are
presented in Table 1‐1.
1.2.2 Single and Multi‐Walled Carbon Nanotubes
The nanotubes are graphene layers rolled into a cylinder‐type
structure with diameter of several nanometers. Rolling of a
single graphene sheet leads to formation of single‐walled carbon
nanotubes (SWCNT), whereas multi‐walled carbon nanotubes
(MWCNT) consist of several coaxial single‐walled nanotubes.
Nanotube diameter corresponds to geometry of the graphene
honey‐comb lattice and twisting angle of the rolled graphene
sheet. Twisting type is specified by the chiral vector [21], [22],
[23].
The diameter and chirality of the nanotube can be expressed
using by vector Ch = n + m ≡ (n, m). This vector connects
two crystallographically equivalent sites in the 2D graphene.
The and are the graphene lattice vectors, n and m
determine the diameter and the twisting angle of the nanotube.
If m = 0, carbon nanotubes belong to the zigzag type if n = m, the
nanotubes belong to armchair type. Otherwise, when n ≠ m they
are called as chiral tubes (Fig 1‐5). Armchair and zig‐zag type
tubes structure have a high symmetry. These terms refer to
location of the hexagons along the circumference. While chiral
type of tube means, that tube can exist in two mirror‐related
forms.
Diameter of carbon nanotubes can be calculated from n, m as
follows:
Where a is length of unit cell vector a1 or a2. Length of a is related to carbon‐carbon bond length: a = |a1|=|a2|=acc√3. For graphite carbon‐carbon bond length is acc = 0.142 nm. But for
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Dissertations in Forestry and Natural Sciences Number 258 13
nanotubes due to curvature of atomic sheet this value slightly
large as acc = 0.144 nm [24]. Nanotube sizes may vary in a wide range. The minimal
diameter of SWCNTs is 0.4 nm and maximal diameter does not
exceed 2‐3 nm. Length of nanotubes may reach up to several
mm. Outer diameter of multiwalled nanotubes may be from 4 to
30 nm and its length may be reach several μm. Inter‐walled
distance in MWCNT is similar to inter‐planar spacing in
graphite and equals to 0.335 nm.
Figure 1‐5. Schematic illustration of carbon nanotube (SWCNT and MWCNT)
formation by rolling up graphene sheet with different chiral vector: n=m – armchair
tubes, m=0 zigzag tubes and n≠m chiral tubes.
The values of n and m determine the chirality of nanotube
and affects to the electronic, optical and mechanical properties.
The differences of interatomic bonds angles in the planar atomic
structure of graphene and in the nanotubes lead to modification
of electronic properties. These differences are negligible for
direction along the nanotube axis. So, quasi‐one‐dimensional
character of structural and electronic properties of the
nanotubes is observed. Also variation of twisting angle and
diameter of the nanotubes produce their different electronic
properties. In particular, the twisting determines conductivity
type and band gap of the nanotubes. Nanotubes with |n—m| =
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3i (i is an integer) possess a metallic properties while for |n—m|
= 3i ± 1 the nanotubes are semiconductors. Recent advances in
nanotube study are discussed, for example, in papers [25], [26].
1.2.3 Fullerenes
Defects of atom packing in planar graphene structure may
lead to distortion of an ideal honeycomb atomic arrangement
and formation of pentagon and heptagon‐like configuration of
carbon bonds [27], [28]. The specific sequence of pentagon and
heptagon arrangement results in keeping of sheet planar
structure, but may initiate grain boundaries formation. The
individual grains may be stitched together in graphene sheet
through the pentagon‐heptagon pairs. In other case
geometrically noncompensated defects may cause formation of
roughness on graphene sheet as well as formation of spherical
structures. Typical example of such kind of structural
modification is formation of closed structure of fullerene.
Similar to carbon nanotubes, possible sizes and geometries of
the fullerenes are completely determined by geometry of carbon
net in graphene. Stability of the fullerene molecules is
determined by a number of distorted interatomic bonds and
thus decreases with increase of their atomic weight (i.e. increase
of number of carbon atoms or diameter of the molecule). This
tendency determines existence of optimal diameter of the
fullerene which corresponds to the most stable and the most
probable configuration. This diameter equals about 0.7 nm.
Number of carbon atoms which is necessary to form such
fullerene is 60 and they should be arranged into 12 pentagons
and 20 hexagons [29]. This is the most common type of fullerene
– C60 (see Fig. 1‐6). Other fullerenes may be produced and
obtained as pure fraction also but their stability and yield in
synthesis process will be less in comparison with C60. The
smallest available fullerene consists of 20 carbon atoms and its
diameter is about 0.3 nm. Larger fullerenes are also possible (the
most common fullerenes contain up to 100 carbon atoms).
Similar to multi‐walled carbon nanotubes and to multilayer
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Dissertations in Forestry and Natural Sciences Number 258 15
graphite structure there are fullerenes consisting of few co‐
centric shells called also as onion‐like molecules.
The deviations of interatomic bonding which happens in
fullerenes in comparison with that in planar graphene, induce
formation of unique electronic and chemical properties in these
spherical structures, which are attractive for numerous
applications. Similar modifications are possible also with
introduction into hexagonal network of undisturbed graphene
not only pentagons but other polygons (e.g. heptagons) also [30].
Figure 1‐6. Schematic presentation of defects in the ideal graphene package – pentagon
(a) and heptagon (b) atomic arrangements. C60 molecular structure consisting of 12
pentagons surrounded by 20 hexagons (с).
An example of packing defects in graphene sheet is shown in
Fig. 1‐7. The series of high resolution TEM images represent the
transformation of C‐C bonding appeared under electron beam
irradiation. The pentagons and heptagons formations are
occurred in the honey comb structure. The defects formation
mechanism in graphene sheets is reviewed in detail in [12,31,32].
Figure 1‐7. A series of high resolution transmission electron images of graphene sheet
with packing defect.
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1.2.4 Functionalized Graphene
Alternatively, the distortions in interatomic bonds (and
corresponding properties modifications) of flat graphene may
be achieved via interactions of carbon atoms with other atoms or
molecules. This modification of graphene is called as its
functionalization [33], [34], [35]. There are two main categories
of functionalization: chemical and nonchemical. Chemical
functionalization is realized through the formation of new
covalent bonds between carbon atoms and the guest functional
groups; nonchemical functionalization is mainly based on π
interaction between unhybridized orbitals of carbon atoms and
guest molecules i.e., mainly a physical interaction. For example,
a regularly corrugated structure of the graphene sheet may be
formed, as a result of chemical reaction with suitable precursors
when three hybridized bonds of carbon atom are shifted from
graphene plane. This type of structural modification opens
attractive possibility for creation the heterostructures consisting
of the stacked functionalized graphene sheets. An example of
graphene structure modification due to its functionalization is
shown in Fig. 1‐8. The image shows schematic model of
hydrogenated graphene (also called as graphane). Advances in
the graphene functionalization are well described in the review
[36].
Figure 1‐8. Graphane atomic structure as an example of graphene structure
modification due to its functionalization.
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1.2.5 Diamond
Atomic arrangement in individual atomic layers of diamond
is similar to graphane (i.e. hydrogenated graphene). This is
because of sp3 hybridization which is necessary to provide
covalent bonding with participation of forth valence electron.
Thus 3D atomic structure of diamond may be represented as
stacked corrugated graphane layers where hydrogen atoms are
replaced by carbons from adjacent layer (Fig. 1‐9). This
approach naturally explains, for example, difference in
electronic properties of diamond and graphite by
transformations which happened due to deviation of the
interatomic bonds from planar graphene configuration. Crystal
structure of diamond, resulted of this, is described by a face‐
centered cubic (or FCC) lattice.
Figure 1‐9. Schematic representation of cubic diamond crystal structure by ‐A‐B‐C‐
stacked corrugated graphene layers. Alternatively diamond structure may be
represented by combination of tetrahedrons.
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There are four types of the diamond phases: cubic phase 3C
[37], [38] and tree hexagonal modifications 4H, 6H, 8H
(lonsdaleite) [39], [40]. Crystallographic parameters of these
phases are represented in Table 1‐2. Cubic diamond structure
can be considered as corrugated graphene layers arranged in –
A‐B‐C‐ sequence normal to [111] direction. Otherwise, structure
of diamond can be represented as a combination of two
interpenetrating FCC sub lattices which are displaced along the
body diagonal of the cubic cell on 1/4th length of the diagonal.
Each carbon atom is joined with four other carbon atoms
forming a regular tetrahedron with the distance of 0.154 nm,
angle between the carbon‐carbon bonds is 109.28o.
Cubic diamond belongs to 3 space group. The symmetry
elements of this space group are schematically represented in
Fig. 1‐10 [18]. This space group include following axis: fourfold
screw axis with 1/4 shifting along c, inversion fourfold axis
perpendicular to a mirror plane, treefold rotation axis, threefold
screw axis with 1/3 shifting along c, twofold rotation axis,
twofold screw axis with 1/2 shifting along c. 3 consists also
of planes of symmetry: glide planes along and perpendicular to
c axis, mirror planes along to c axis and diagonal glide planes.
Figure 1‐10. Graphical representation of symmetry elements of crystal structure with
F d 3 m space group (adopted from [18]. Reproduced with permission of the
International Union of Crystallography).
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Dissertations in Forestry and Natural Sciences Number 258 19
The crystal lattice symmetry and strong covalent interatomic
bonding determine physical properties of diamond. For
example, diamond is the hardest known naturally occurring
material. Diamond crystals predominantly are good electrical
insulators. But diamonds with substitutional boron impurities
reveal semiconductor properties. Diamond also is a good
conductor of heat because of strong covalent bonding and low
phonon scattering.
At the same time, interatomic bonding deviations from flat
graphene configuration leads to increase of specific free energy.
Thus, diamond structure possesses metastable characteristics.
However, under normal conditions diamond will not decay into
graphite due to large potential barrier for this transition.
Table 1‐2. Crystal unit cell parameters for known diamond phases.
Modification a, b, c (nm) α, β, γ Space
Group Cryst Sys ICSD ref.
Diamond 3C 0.356 0.356 0.356
90.00 90.00 90.00
F d 3 m cubic 44100
Diamond 4H 0.252 0.252 0.823
90.00 90.00 120.00
P63/mmc hexagonal 66466
Diamond 6H 0.252 0.252 1.235
90.00 90.00 120.00
P63/mmc hexagonal 66467
Diamond 8H 0.252 0.252 1.647
90.00 90.00 120.00
P63/mmc hexagonal 66468
1.2.6 Filled Carbon Nanotube
Closed structure of fullerenes and carbon nanotubes allows
alternative possibilities for variation of their properties (first of
all electronic) via filling by different components [41], [42]. In
contrast to that considered above, it may be that there are no
new covalent bonding between carbon atoms and filling
precursors [43]. However, modification of electronic properties
and structural parameters might be quite large. It is possible to
achieve the structural ordering of the filled compound inside the
fullerenes or nanotubes. During metallic nanotubes filling by
electron‐donor with Fermi level higher than SWCNT level the
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electron density of the nanocomposite will increase. On other
hand, the nanocomposite will possess the semiconductor
properties when nanotube is filled by electron acceptor [44], [45].
The nanotube filling provides realization of attractive
possibility for chemical synthesis. In this case inner volume of
one‐dimensional carbon tubes is considered as a nanoreactor
[46], [47]. With filling this reactor by chemical reagents one can
obtain conditions for production, for example, new compounds
with untypical crystal structure and stoichiometry due to
encapsulated crystal‐nanotube interaction. It was shown that
structures of encapsulated crystal may differ from bulk crystal
structure with changing the crystal symmetry, bond lengths,
and bond angles. Geometrical distortions are caused by limit
inner nanotube space and adjustment of encapsulated crystal
structure to the internal diameter of SWNT channel.
1.3 METHODS OF SYNTHESIS
Structural and physical properties of nanocarbon materials
depend essentially on conditions of their synthesis. The most
general approach to carbon materials production assumes
condensation of carbon atoms (or clusters) from a vapor phase.
Thus, from this ’general’ point of view, the most important
synthesis process steps include:
(1) Formation of atomized (vaporized) carbon environment.
(2) Procuring sufficient activation energy to carbon atoms.
(3) Formation of appropriate type of carbon materials by
applying controlled condensation conditions.
Phase diagram of carbon (see Fig. 1‐11) predicts possibility
for obtaining diamond (sp3) type of carbons by transformation
of other condensed carbon containing materials (usually
graphitic – sp2) at certain conditions. Below we will consider
some typical growth methods which seem to be the most
representative in view of results discussed in this work.
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Figure 1‐11. Phase diagram of carbon. The transformations between different phases
are possible with appropriate conditions.
1.3.1 High pressure, high temperature method
Method using high pressure and high temperature (HPHT) is
still widely used because of its relatively low cost. HPHT is a
relevant process for the synthesis of sp3 carbon structures as
well as other ultra‐hard materials as cubic BN with sp3
hybridization. In the HPHT method for obtaining the pressure
and temperature, which are necessary to produce synthetic
diamond, may use three press designs: the belt press, the cubic
press and the split‐sphere press [48], [49], [50]. The graphite
particles are generally used as the precursor which placed at the
bottom of the press. The internal part of press is heated above
1400 °C and melts the solvent metal. The molten metal dissolves
high purity carbon source. The dissolved carbon is then
transported towards to small diamond precursors and forms a
large synthetic diamond. Adding metallic solvents leads to an
important lowering of pressure and temperature required for
diamond synthesis. Without addition of those catalytic metals,
crystal structure of graphite remains unchanged after
compression up to 15 GPa at room temperature and loses some
of graphite features at higher pressure. Possible transformation
into metastable hexagonal diamond form (lonsdaleite) appears
to depend on many factors as temperature or degree of
disorganization of the initial sp2 carbon form.
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1.3.2 Detonation of explosives
Methods of explosive synthesis of diamonds are similar to
HPHT with the high pressures and temperatures achieved
during short‐term detonation and subsequent rapid cooling of
carbon‐containing explosive material. Immediately with
diamond other carbon phases are formed in this process usually
because of wide spread of achievable pressure and temperature
parameters [51].
Pure graphite may be transformed into diamond by a shock
compression [52], [53], [54]. By this method transformation of
rhombohedral graphite into diamond by shock wave pressure at
30 GPa has been obtained. Exposure time has been a few
microseconds and temperature of 1300‐1800 K. Small diamonds
(2‐5 nm) have been produced. In another method diamond
crystals have been produced from graphite powder enclosed in
a metallic matrix undergoing by high pressures (9‐20 GPa) and
temperatures (2300‐3300 K) during microseconds. Cubic
diamond phase and up to 30‐50% hexagonal diamond phase
(lonsdaleite) have been formed by this techniques.
The short duration pressure and temperature increase up to
values corresponding to graphite‐diamond transformation may
be achieved also in synthesis processes based on usage of high
intensity pulse laser irradiation initiating explosion of graphite
dispersion in liquid xenon.
1.3.3 Arc‐discharge
There are numerous version of methods providing synthesis
of condensed carbons from a vapor phase. One of the most
simple (and thus popular) is the arch‐discharge methods [55],
[56]. In accord with this method synthesis occurs in a chamber
with two electrodes, one of which contain a powdered carbon
precursor. The pre‐evacuated chamber is filled with inert gas
(like helium or argon) at low pressure (between 50 and 700
mbar) (Fig. 1‐12). One of the electrode ‐ anode may be arranged
axially and moveable relative to other ‐ cathode in longitudinal
direction. To initiate arc discharge the electrodes are moved
closer (typical distance is about 1 mm ). A constant current is
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Dissertations in Forestry and Natural Sciences Number 258 23
maintained through the electrodes
to obtain a non‐fluctuating arc. The
fluctuating arc results in unstable
plasma and affects on quality of
the synthesized product. The arc
discharge current generates
plasma of very high temperature
~4000–6000 K, which sublimes the
carbon precursor, which are filling
the anode. The vaporized carbon
atoms (clusters) aggregate in the
gas phase and drift towards the
cathode where they are cooled down due to the temperature
gradient. During the condensation different types of carbon
clusters, including fullerenes and/or carbon nanotubes, may be
obtained depending on process conditions. However nanotube
production requires usage of catalysts particles which may be
produced immediately in the gas discharge plasma [57][58]. A
comprehensive review of arc synthesis technique is done in [59].
1.3.4 Laser Ablation
There are many other variants
of techniques providing
vaporization and excitation of
carbon atoms via different types
of gas discharge or by thermal
evaporation. For example, in the
laser ablation method intense
laser pulses are used to heat and
ablate a carbon target, which is placed in a tube‐furnace heated
to 1200°C (Fig. 1‐13). During the process inert gas like helium or
argon is flowed through the chamber to carry the grown
nanotubes to the copper collector. After cooling of the chamber
nanotubes and by‐products, like fullerenes and amorphous
carbon, can be collected [60], [61], [62].
With pure carbon laser ablation methods leads to synthesis of
multi‐walled nanotubes while addition of a catalyst like iron,
Figure 1‐12. A schematic
illustration of arc‐discharge
technique.
Figure 1‐13. A scheme of laser
ablation synthesis technique.
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yttrium, sulphur, nickel and molybdenum leads to formation of
single‐walled carbon nanotubes [63], [64].
1.3.5 Chemical vapor deposition (CVD)
Essential peculiarity of chemical vapor deposition (CVD)
methods (from point of view of this particular work) consists in
its ability to produce thin film materials on suitable substrates.
In this method the film growth occurs under low pressure
(below atmospheric pressure). The method involves feeding a
mixture of gases (typically methane and hydrogen) into a
chamber and their decomposition onto chemically active
radicals. Potentially, for activation of the gas mixture different
methods can be used including microwave or direct current gas
discharges, optical discharge in focused laser beam, acetylene
torch or gas decomposition on ʹhot filamentʹ, etc. These methods
are mostly used for production of polycrystalline diamond films.
These diamond (i.e. mainly sp3 carbon) films usually contain
some amount of graphitic (i.e. sp2 carbon) and amorphous
carbon material. Depending on the process conditions the
percentage of different phases (sp3, sp2 and amorphous) in the
films may be changed in a wide range [65].
Figure 1‐14. Scheme of the CVD system with gas mixture activation by direct current
discharge.
There is great variety of technical solutions allowing
realization of the CVD process. Let us consider, as an example,
with more details, CVD system which has been used for
production materials studied in this work. Schematically this
system is presented in Fig. 1‐14.
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Dissertations in Forestry and Natural Sciences Number 258 25
The reactor chamber of the system is made of stainless steel
with double walls with water cooling system. Inner diameter
and height of the chamber is 90 cm. Two quartz windows in the
reactor chamber are used for controlling of the deposition
process including substrate temperature measurement by
optical pyrometer. The substrate is located on the sample holder
which is electrically connected with ground. Other electrode,
which is electrically connected to negative source of the power
supply, is located above the substrate on distance of about of 40
to 50 mm. The substrate holder (which plays role of anode, i.e.
positive electrode in electric circuit) and cathode (i.e. negative
electrode in the circuit) are made of molybdenum and have
shape of disks with diameter of 50 mm and thickness of 10 mm.
The disks are tightly attached to the holders cooled by flow
water.
After substrate is loaded the chamber is pumped out by
rotary pump up to vacuum level of about 10‐3 Torr. After that
the chamber is filled by a mixture of hydrogen and methane
with predetermined proportion depending on type of produced
material. Typical pressure of the gas mixture during deposition
is about 100 Torr. The direct current (DC) discharge is ignited
between the electrodes by applying voltage. The discharge
plasma contains chemically active radicals produced from
hydrogen and methane molecules. The system contains control
elements allowing support of necessary discharge voltage and
current, total gas mixture pressure and composition during long
time (up to hundreds hours) which is necessary for production
carbon films of different thickness [66].
The CVD method is widely used for the diamond fabrication
[67], [68], graphene synthesis [69] and production of nanotubes
[70], [71].
1.3.6 Methods of carbon nanotubes filling
There are two approaches to production of filled carbon
nanotubes. In the first approach the encapsulation of the
inorganic elements takes place during nanotube synthesis (in‐
situ methods). This method can be used to encapsulate metal
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carbides or pure elements (Se, Ge, Sb, Cr, Mn, Co, Cu, Re, Au,
Sm, Gd, Dy, Yb) into nanotube under special synthesis
conditions in presence of catalyst. The disadvantage of this
approach is problem of control the filling process due to large
temperature gradient in the cathode area. Another disadvantage
of this method of synthesis is that it does not allow filling of
nanotubes with transition metals, as well as low efficiency of the
synthesis: the yield of filled nanotubes is only several percent
[43], [72], [73], [74].
Second approach is ex‐situ methods, when already
synthesized carbon nanotubes are undergo the filling. Special
treatment of the nanotubes is necessary to open their ends
(which are usually capped in as‐grown material). Depending on
type of desired compound to be filled into the nanotubes there
are few techniques are used for the filling.
Gas phase filling of CNT
Filling of carbon nanotubes from gas phase is carried out in
vacuum at high temperatures [75,76]. During nanotube heating
the low‐pressure vapor consisting of the compounds, which
should be encapsulated, undergoes capillary condensation and
thus penetrates into the nanotube. During subsequent cooling
the compounds are crystalized.
Liquid phase filling of CNT
Filling of SWNTs from liquid phase is performed using so‐
called capillary method, which involves impregnation of opened
nanotubes with solutions or suspensions of selected compounds
[47,77]. Higher concentration provides higher yield of this
method in comparison with usage gaseous environment.
Encapsulation from melts
This method uses liquid environment consisting of melted
components. The technique provides a 2‐3 times larger yield of
encapsulated nanotubes as compared to filling from
suspensions and solutions. The encapsulation procedure is
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Dissertations in Forestry and Natural Sciences Number 258 27
usually performed under vacuum conditions at temperatures
10‐100°C higher than the melting point of the guest material.
During subsequent slow cooling encapsulated material is
crystallized [43,78].
1.4 TECHNIQUES FOR CARBON MATERIALS STRUCTURAL CHARACTERIZATION
Structural and physical properties of carbon materials may be
characterized by common analytical methods used in material
science. Specificity some of these methods are considered below
briefly in view of their usage in this particular work. These
methods allow obtaining additional information for
identification of morphological features, crystal structure,
chemical composition, lattice defects, grain boundaries, phase
transitions, defects, and other parameters of studied materials.
This information can be obtained by applying a complex of
modern diagnostic methods including Raman spectroscopy (RS),
X‐ray diffraction (XRD), scanning electron microscopy (SEM),
energy‐dispersive X‐ray spectroscopy (EDS), electron diffraction
(ED), transmission electron microscopy (TEM), scanning
transmission electron microscopy (STEM) which are the most
widely applied techniques for characterization of carbon
materials.
1.4.1 Raman spectroscopy
Raman scattering is one of the most informative and widely
used non‐destructive methods for structural and chemical
diagnosis of various forms of carbon allotropes. Spatial
localization of phonons in nanostructured carbon materials
provides additional ability of RS to detect size dependent
structural changes and deformations in atomic bonding. Each
band in RS spectra is directly related to a specific frequency of
intramolecular vibrations. The vibration frequencies and, thus,
the positions of the Raman bands are very sensitive to
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interatomic bonds orientation and to number of atoms at the
bond ends.
In Raman spectroscopy the sample is irradiated with
monochromatic light, produced by a laser source, and scattered
light is registered using high resolution spectrometers and
sensitive detectors [79], [80], [81], [82]. Practically, most of the
scattered light has the same frequency as the incident laser
radiation. Only very small amount of scattered light contains
information about studied matter, which is measured by a
frequency shift from the laser frequency. Fig. 1‐15 represents a
typical Raman spectrum of single‐walled carbon nanotube
which contain, so called, G (~1500 cm‐1), D (~1355 cm‐1) and
RBM‐bands. The G‐band is associated with optical vibrations of
two adjacent carbon atoms in lattice having ʺgraphiticʺ atomic
structure. D‐band indicates presence of structural defects. In
low‐frequency region Raman spectra could contain, so‐called
Radial Breathing Mode ‐ RBM‐band, which is a typical
characteristic of nanotubes. The RBM‐band is associated with
symmetric vibrations of carbon atoms in the radial direction.
The RBM‐band frequency is proportional to the nanotubes
diameter (~ 1/dNT). The G to D bands intensity ratio allow
estimation of density of structural defects. If intensity of D‐band
is significantly lower than intensity of G‐band this indicates
presence of sufficiently small amount of structural defects [76].
Figure 1‐15. An example of typical Raman spectrum of single‐walled carbon nanotube.
The structural models represent schematically atomic vibrations corresponding to
different RS modes.
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Dissertations in Forestry and Natural Sciences Number 258 29
Popularity of Raman spectroscopy in studies of carbon
materials is determined by important advantages of this method.
It requires little or no sample preparation and does not depend
of water absorption band. This allows carrying out
measurements of solids, liquids and gases through the
transparent containers such as glass, quartz and polymers.
1.4.2 X‐ray diffraction
X‐ray diffraction is a classical method for determining crystal
structure of different types of material. Structural studies of
carbon materials with usage of this method have been carried
out for a long time. This method allows distinguishing the
carbon allotropes, graphitic and amorphous carbon. When
carbon materials produce it, structure can vary over a wide
range depending on temperature and other conditions applied.
In particular, carbon atoms in plane of graphite layers can be
rotated or shifted laterally in respect of their ideal orientation in
the graphite structure. These detailed features are mirrored in
the X‐ray spectra. Estimation of diffraction peak width provide
information about coherent scattering region size and area with
large crystal distortions [83], [84].
The shape of diffraction peak can relay to phase composition.
So, the asymmetry of the diffraction peak profiles which
observed in some samples for both small and large scattering
angles is typical characteristic of multiphase materials. It may be
caused by presence of ordered and amorphous carbon in the
samples. X‐ray diffraction allows controlling functionalization
process of carbon materials. Due to functionalization some
characteristic peaks of spectra are shifted and changed their
parameters [85], [86].
The analysis based on observations of X‐ray diffraction has
some disadvantages. One of the most significant relates to size
of sample. While the method allows determination of sample
cell parameters with high accuracy volume of the sample should
be quite large that often difficult for nanomaterial studies.
Additionally, the method provides integral information, i.e. it
cannot be used for identification local structural distortions.
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1.4.3 Scanning Electron Microscopy
Morphology, shape and size distribution of carbon‐contained
micro and nanoparticles, local and average microstructure
information, presence of pores, cracks and other defects – these
data are very important in structure characterization and
growth processes optimization of carbon materials [87], [88].
Scanning electron microscopy allows obtaining
microstructure information with high accuracy, as well as
integrated information from different areas of the sample. The
resolution of a SEM image depends on electron beam probe size
and on volume of interaction between the incident beam and the
sample. Microstructure information could be obtained from a
depth in range of tens of nanometers up to few microns
depending on e‐beam accelerating voltage (from 1 kV to 30 kV)
and on atomic number of sample material. The smallest electron
beam probe size and the highest signal to noise ratio is required
to achieve the SEM image with the best spatial resolution. The
smallest diameter of the probe size for the LaB6 cathode is ~ 5
nm while for field emission gun is ~ 5‐25 nm. The resolution of
the modern SEM instruments is about several Angstroms, which
is achieved with field emission electron source and special
design of optical system of electron column. SEM images could
be formed by registration of secondary and backscattered
electrons. Secondary electron imaging, being more surface
sensitive, has greater resolution. On the other hand,
backscattered electrons are sensitive to atomic mass of nuclei
they scatter from. Therefore, heavier elements which back
scatter electrons with high energy more efficiently appear
brighter than lighter elements. Thus SEM image in backscattered
electrons mode will possess a composite or Z‐contrast.
1.4.4 Energy‐Dispersive X‐ray Spectroscopy
The scanning electron microscopes (and transmission
electron microscopes (TEM) also) could be equipped with
facilities for chemical analysis of the samples by registration the
X‐ray signals generated in interaction of e‐beam with the matter.
Chapter 1: Review of the structural features of carbon materials
Dissertations in Forestry and Natural Sciences Number 258 31
EDS technique allows to carry out local qualitative and
quantitative chemical analysis [89], [90], [91].
The main advantage of X‐ray microanalysis of thin specimen
is improved spatial resolution over that obtainable in a bulk
sample. In the bulk samples normally analyzed in SEM, the
electron beam diffuses in the sample to a depth of 1‐5 μm. This
limits spatial resolution of EDS by about 1 μm for bulk samples.
In TEM thin foil the electron beam passes through the sample
and X‐rays are generated in a volume corresponded to the
focused probe size and the electron scattering area, which is a
function of both the thickness of the sample and the accelerating
voltage. The accelerating voltage for microanalysis in SEM is
choose to provide minimum volume of beam and sample
interaction which may be estimated by using Monte‐Carlo
simulation. On the other hand the energy should be sufficient to
excite the characteristic lines of the analyzed element.
The X‐ray qualitative analysis is based on the ability of a
spectrometer system to measure characteristic line energies of
specific elements. This analysis can now be performed with
accuracy about 1%, so measurement of the characteristic X‐ray
intensity should be not less than 1% in accuracy. The analysis includes Fourier filtering technique which is necessary to
remove background signal and to obtain intensities of the lines
corresponding to analyzed elements [92].
1.4.5 Transmission electron microscopy
Transmission electron microscopy is one of the most effective
methods of structural analysis. One of the greatest TEM
advantage is opportunity to analyze information both in real
and reciprocal space. TEM is widely used nowadays for analysis
different types of carbon nanocomposites and, in particular, for
filled nanotubes; for identification grain boundaries, twin
boundaries; for determination particle morphology, size
distribution, inclusions and other important structural
characteristics [93–95].
Typical range of accelerating voltages in a transmission
microscope is 80 ‐ 300 kV. It depends on sensitivity of the
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analyzed sample to e‐beam irradiation. Typical resolution of
transmission microscope is about 0.2 nm for 300kV. The
resolution is reduced due to chromatic and spherical aberration
of the e‐beam optical system. Chromatic aberration contribution
can be decreased or minimized by applying electron source with
high coherency (typically field emission gun) or with use e‐
beam monochromator. More details related to this problem will
be discussed in Chapter 2. For minimization of spherical
aberration Cs‐corrector is used.
The procedures of the transmission electron microscopy
observation include wide range of techniques. In the bright field
TEM the image is formed by transmitted e‐beam. In this case
obtained contrast in TEM image is proportional to the thickness
and density variations in a sample. Dark field TEM allows
visualization of the particles or sample areas having different
compositions. Formation of the dark field image requires usage
of only single diffracted e‐beam. This techniques allows
detection of distribution of size and orientation of the particles
in the sample [96], [97]. Electron diffraction (ED) analysis can
provide important information about crystallinity of the
samples, i.e. about amorphous, polycrystalline and single crystal
structure. Phase identification of the samples can be revealed
through ED data, including interplanar distance, angles between
reciprocal vectors.
1.4.6 High resolution imaging
The high resolution transmission electron microscopy
(HRTEM) technique is currently one of the most informative
methods for structural analysis with atomic precision. Among
wide range of structural information, the linear defects of the
crystal lattice could be identified by this technique. The HRTEM
allows revealing of the grains and interphase boundaries
structure and measurement of the lattice distortions [98], [99],
[100].
The HRTEM image is formed by transmitted and diffracted
beams interference. Thus, the correct interpretation of the
HRTEM image contrast is not possible without usage of modern
Chapter 1: Review of the structural features of carbon materials
Dissertations in Forestry and Natural Sciences Number 258 33
methods of image simulation. More detail information on
formation of the TEM images could be found e.g. in [101].
1.4.7 Scanning transmission electron microscopy (STEM)
Modern transmission electron
microscopes are equipped frequently
by STEM mode attachements. In this
mode specimen is illuminated by
convergent beam and scanned similar
to the SEM technique. A schematic of
the STEM technique is presented in
Fig. 1‐16. STEM images are formed by
collecting incoherently scattered
electrons which are highly sensitive
to variations in the atomic number of
atoms in the sample (Z‐contrast
images) [102]. The scattered electrons
are recorded with a high angle
annular dark‐field detector (HAADF). So far thickness of the
samples analyzed with TEM is quite small the volume of
electron beam interacting with the sample is quite small too and
0.2 nm resolution could be achieved. The resolution could be
improved up to 0.08 nm by applying spherical aberration (Cs)
correctors. It should be noted that interpretation of STEM
images contrast is not complicated because of image contrast
proportional to the atomic number of the element. Using this
mode a significantly improvement of carbon material phase
analysis accuracy could be obtained [103], [104], [105].
1.4.8 Atomic structure simulation
Proper phase refinement and crystal orientation relative to
incident beam couldn’t be done without experimental and
simulated HRTEM images compassion. For this purpose, the
atomic models of studied nanocarbon material should be
elaborated. The atomic model may be calculated according to
known data for bulk carbon material and measured interplanar
distances and crystal orientation. On the base of the calculated
Figure 1‐16. Scheme of
scanning transmission
electron microscopy
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model and according to the TEM optical parameters the series of
simulated HRTEM images with different defocus and sample
thickness are formed. The criterion of fidelity of the phase
composition and crystal orientation determination according to
the STEM data will be a function of images correlation.
OBJECTIVES OF THIS WORK
This brief review of the carbon materials and their structural
features presents basis for motivation of the Thesis where the
following topics of scientific interest are highlighted:
to perform the theoretical analysis of the carbon atoms
contrast optimization in spherical aberration corrected
transmission electron microscope;
to analyze the atomic arrangement of guest crystal in the
inner channel of functionalized single‐walled carbon
nanotubes filled with 1‐bromoadamantane, mercury
chlorine and cupper chlorine molecules;
• to reveal the structural features of nanocrystalline and
single crystal diamond; in particular, to study of carbon
bonds transformation under high‐temperature annealing;
and to identify of structural defects in crystalline
diamond produced by CVD method;
Dissertations in Forestry and Natural Sciences Number 258 35
2 General principles and
practical aspects of TEM
analysis
This Chapter will be focused of some aspects of transmission
electron microscopy techniques which are important in carbon
materials studying. In first part the theoretical principles of
electron diffraction and TEM images formation will be
discussed. The second part of the Chapter the practical methods
of electron‐optical system adjustment at spherical aberration
corrected TEM will be considered. Fine tuning of Cs‐corrected
TEM allows to achieve enhanced signal‐to‐noise ratio.
2.1 THEORETICAL ASPECTS OF ELECTRON MICROSCOPY
2.1.1 Electron diffraction
Structure analysis in transmission electron microscopy (TEM)
is based on effects occurring during interaction of electron beam
(e‐beam) with material of the sample. The periodic structure of
the sample acts as a diffraction grating, scattering the electrons.
Thus, analysis of the diffraction patterns formed by the scattered
electrons may be used for determination of the sample
structural characteristics.
In accord with L. de Broil hypothesis [106] electron has
quantum wave properties which may be described by wave
with wavelength λ, which are determined by accelerating
voltage V (i.e. by energy of electrons) by equation: ħ ħ ħ
(2.1)
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where – mass of electron, e – charge of electron, ħ – Plank
constant. For example, at accelerating voltage 100 kV the
wavelength of electron equals to 0.0037 nm, which is about
hundred times less in comparison with interatomic distances of
about 1Å (i.e. 0.1 nm) in order.
Let us consider the case of electron scattering in the sample of
material where long‐range order exists (i.e. atoms are located in
space with periodical regularity). In this case incident wave of
electron will be diffracted on atomic planes in according with
equation of Wolf‐Bragg [107]:
2 sin ɵ (2.2)
where d – interatomic distance in material of the sample, ɵ ‐ diffraction angle, n – integer. The correspondence between
structural characteristics of the material and parameters of the
diffraction pattern may be expressed by formula:
= Camera constant (2.3)
where L – distance from the sample to the plane of the
diffraction image which is registered by the camera, λ –
wavelength of electron, r – distance from the central spot
(corresponding to non‐scattered electrons) of the diffraction
pattern, and d – interatomic distance. The combination of (2.2)
and (2.3) formulas allows establishment of interatomic distance
from the diffraction pattern analysis. Further analysis may be
used for revealing of the crystal symmetry characteristics and
calculation of unite cell of the crystal. Additionally, to this
information revealing from location of the diffraction spots
analysis of their intensities allows determination of shape and
dimensions of the crystal contained in the analyzed sample.
Application of this method could be considered in example
of analysis of the electron diffraction pattern obtained from a
monolayer of close packed porphyrin−fullerene dyads
molecules (see details in Article I in the Appendix). Fig. 2‐1
shows the diffraction pattern consisting of diffraction rings that
correspond to polycrystalline structure of the sample with
randomly oriented crystalline domains. Small width of the
diffraction rings corresponds to domains size up to 10 nm.
Interpretation of experimental diffraction data is carried out, as
Chapter 2: General principles and practical aspects of TEM analysis
Dissertations in Forestry and Natural Sciences Number 258 37
a rule, by applying the atomic modeling and simulation of
diffraction patterns techniques. In the Article I the analysis of
possible types of the molecules ordering in close packed
structure was made for porphyrin−fullerene dyads molecules.
Primitive cell and atoms coordinates were determined for each
possible type of the packing. Obtained data were used for
simulation of diffraction patterns using JEMS software [108].
The simulated patterns were compared with experimental data.
The best correspondence was for molecules packing into triclinic
structure with parameters of unite cell: а = 1.37 nm, b = 1.40 nm,
c = 2.47 nm, α = 89.6°, β = 90°, γ = 91°. Further details about
motivation of this work, methods for material fabrication and
other experimental conditions are disclosed on Article I (see
Appendix).
Figure 2‐1. Atomic model of the porphyrin−fullerene dyads molecule on the water sub‐phase (a). Model of the triclinic unit cell of close packed molecules (b).
Experimental (c) and simulated (d) diffraction patterns for a monolayer of close
packed molecules. Diffraction intensities distribution is shown for the simulated
pattern (d). (The images reproduced in accord with Article I – see in Appendix).
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2.1.2 Principles of image formation
The combination of electron diffraction and imaging provides
the unique capability in TEM for understanding the properties
of the crystals and possible defects. TEM image is formed from
the interaction of the electrons transmitted through the
specimen. These images represent distribution of intensity of the
electron beam passed through the sample occurred due to
absorption or/and scattering in material of the sample. Similar to
diffraction patterns, the TEM images are captured using
luminescent screen, photo plate/film or CCD camera. The
example of TEM image is shown in Fig.2‐2 representing the
GaSe particles (see details in Article II from Appendix). The
TEM images demonstrate intensity distribution for e‐beam
passed through the GaSe particles located on perforated
amorphous carbon film used as a support. Intensity difference
of e‐beam may be characterized by contrast which is a ratio of
brightness of the neighboring local areas of the image. Analysis
of TEM image contrast variation allows obtaining of information
about dimensions and location of the structural peculiarities in
the sample. Relatively weak contrast for GaSe particles in Fig. 2‐
2 witnesses about small thickness of these particles which have
platelet (quasi two dimensional) shape. Other details about this
study are presented in Article II (see Appendix).
Figure 2‐2. TEM image of GaSe particles on holey carbon support film. The
images are reproduced from Article II (see Appendix).
Chapter 2: General principles and practical aspects of TEM analysis
Dissertations in Forestry and Natural Sciences Number 258 39
2.1.3 TEM optical system
Formation of the diffraction patterns and TEM images in
transmission electron microscopes forms by electro‐optical
(called also as ‘optical’) system. Fig. 2‐3 schematically presents
main modes of this system. The electron gun produces a
diverging beam of electrons, which passes through aperture and
then is focused by condenser lens. Upper objective lens forms
parallel electron beam which illuminates the sample. Part of
electrons of the primary beam, which are not deflected in
sample, and electrons diffracted due to scattering on atomic
planes in material of the sample are focused then by lower
objective lens. Intermediate and projective lenses focus the
primary and diffracted beams on luminescent screen (or CCD
camera). Objective aperture allows formation of diffraction
pattern only for selected area on the sample. This scheme was
used for obtaining of the diffraction patter shown previously in
Fig. 2‐1.
The scheme of two types of TEM images formation ‐ bright‐
field and dark‐field is shown in Fig. 2‐3 (b and c,
correspondingly). In both cases sample is illuminated by parallel
e‐beam formed by the condenser lens. Bright‐field imaging (Fig.
2‐3 (b)) is obtained by focusing on detector screen (covered by
luminescent material, photo‐film/plate or CCCD camera) only
non‐scattered part of the e‐beam. Diffracted beams are rejected
in this case by objective aperture. In the opposite case of dark‐
field imaging (Fig. 2‐3 (c)) the non‐scattered part are eliminated
by objective aperture while diffracted beams are passed through
and focused on the screen.
Contrast on the bright‐field images is determined mostly by
electron‐beam absorption in the material of the sample. The
dark‐field images are formed by diffracted beams and thus
possess so called ‘diffraction contrast’. In many cases, dark‐field
imaging is very informative and use, for example, to visualize
small particles and determine their morphology.
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Figure 2‐3. Scheme of transmission electron microscope with electron trajectories in
diffraction mode (a), bright‐field (b) and dark‐field (c) image mode.
To demonstrate the difference between the bright‐ and dark‐
TEM images Fig. 2‐4 shows the images of both types captured
for the area of sample containing GaSe nanoparticles on
amorphous carbon film. The dark‐field image (Fig. 2‐4 (b)) was
obtained using e‐beam corresponding to the spot, which is
denoted by circle on the diffraction pattern (see inset in Fig. 2‐4
(b)). Other details of this research are disclosed in Article II (see
Appendix).
Chapter 2: General principles and practical aspects of TEM analysis
Dissertations in Forestry and Natural Sciences Number 258 41
Figure 2‐4. Examples of bright‐field (a) and dark‐field (b) TEM images of the same
GaSe nanoparticle on holey carbon support film. The dark‐field image was
obtained using diffracted e‐beam corresponding 010 spot marked on the diffraction
pattern (shown in inset to the panel) (b). See details in Article II (Appendix).
2.1.4 TEM resolution limit
The most important characteristic of TEM is, probably, its
resolution ability. The resolution itself is defined as device
ability in displaying closely located objects. A quantitative
measure of this parameter is the resolution limit of the
microscope, that is the shortest distance between two point
objects, at which they are distinguishable as separate (i.e.,
appear in the microscope as two points) (see Fig. 2‐5). The
diffraction limit ( ) is the most important value which
determines the resolution ability of the microscopes. In
accordance with Rayleigh criterion there are several
equations that have been derived to express the relationship
between wavelength and resolution [101]:
1.22 (2.4)
=.
=. (2.5)
where α is aperture angle of the lens or Numerical Aperture
(NA) of objective and condenser lens. Equation (2.5) is used
when the microscope is in perfect alignment (parallel
illumination), in this case NAcond=0. The resolution limit is
achieved at 90° opening of the objective aperture (sinα= 1).
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For example, the diffraction limit would be 2.3 pm for
electron energy of 100 kV and would decrease with the
energy. Practically, the NA for electromagnetic lenses cannot
be set to 1 due to generic limitations [109]. Thus, the real
resolution of the microscopes is limited by different factors
including various imperfections of the optical system, energy
spread of electrons, instability of accelerating voltage, thermal
drift of the sample etc.
The optical systems imperfections are called lens
aberrations. The most important types of the aberrations are:
spherical and chromatic aberration, axial astigmatism, and
coma. Fig. 2‐6 presents scheme of rays in an optical system
which illustrates definitions of spherical and chromatic
aberrations.
Spherical aberration is the reason that the rays pass
through the lens are focused at different distances from the
geometrical focus of the lens. This occurs due to the
inhomogeneity of the electromagnetic field in the objective
lens. The rays passing through the lens at a distance different
from the optical axis will be undergo the various effect of the
spherical aberration which lead to deviation of rays focus
Figure 2‐5. Ray diagram representing
the lens diffraction limit. Two spots
are believed to be resolved (bottom
right) when distance between them is
more than spot radius. Focus position
may be changed from image plane
position (defocus) when lens strength
becomes weaker (underfocus) or
stronger.
Chapter 2: General principles and practical aspects of TEM analysis
Dissertations in Forestry and Natural Sciences Number 258 43
position. Therefore, the focus of the lens is smeared along the
optical axis. The dimension of the focus spot determines
resolution limit of the microscope and may be estimated as
, where CS is, so called, coefficient of spherical
aberration [110]. In contrasts to the diffraction limit ( ),
which is reversaly proportional to the aperture angle of the
lens, the aberration limit is proportional to the angle aperture
in third power (Fig. 2‐5c). It follows that for any given lens of
fixed spherical aberration coefficient there should be an
optimum angular aperture which could be derived at
condition = С . Hence, we obtain:
0.61 (2.6)
Figure 2‐6. Schematic representations of spherical (a) and chromatic aberration (b)
that prevent the beam focusing at single point. The diffraction (εd) and the
spherical aberrations (εсs) limit resolution in dependence on angular aperture (α)
of the lens (c). The αopt is optimal value.
Chromatic aberration reflects the situation when the rays
of radiation with shorter wavelengths are refracted
differently than rays with longer wavelengths. It leads to
appearance of blur of focus point along the optical axis.
Chromatic aberration is a generic aberration for
electromagnetic lenses [109] and its coefficient is always
positive, i.e. electrons with higher energy are focused further
of the lens. Resolution limit due to chromatic aberration can
be expressed as [111]:
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Сс Сс∆
(2.7)
where СС – coefficient of chromatic aberration, ΔE/E – relative
energy spread of electrons determined by both instabilities of
accelerating voltage and energy distribution of electrons
leaving the tip. Thus, the negative influence of chromatic
aberration can be partially overcome by using
monochromatic electron beams and highly stable accelerators.
The energy spread of electron beam is determined by type
of used electron source (or cathode). Currently two types of
cathodes are applied in TEM: thermionic electron sources,
which produce electrons as a result of thermionic emission
from tungsten filaments or crystals of lanthanum hexaboride
LaB6, heated up to high temperature; and field emission gun
(FEG), which produce electrons as a result of field emission
effect, when strong electric field is applied to the tip‐shaped
conductive material (usually made of very sharp W needle).
Typical brightness of electron beam produced by thermionic
W and LaB6 cathodes are 109 and 1010 A/m2sr,
correspondingly, while energy spread of electrons in the
beams is about 3 eV for W and 1.5 eV for LaB6 [101]. Schottky
type field emission sources provide e‐beam brightness up to
1012 A/m2sr and electron energy spread of about 0.7 eV. The
energy spread of electrons in the beam may be reduced well
below 0.1 eV by using gun monochromator. The drawback of
monochromation is a significant reduction in total beam
current, thus high brightness sources are very beneficial on
mochromated systems.
Another type of TEM optical system imperfections is
distortion of an axial symmetry of the lens which causes an
appearance of another type of aberration in focusing systems
for optical, electron and other beams. This type of aberration
is called as astigmatism. Schematic presentation of such kind
of system with astigmatism is shown in Fig. 2‐7 where it
leads to difference between the focal length for rays passing
in the plane of the figure, and for rays, which are located in
the perpendicular plane.
Chapter 2: General principles and practical aspects of TEM analysis
Dissertations in Forestry and Natural Sciences Number 258 45
Figure 2‐8. Scheme of rays in the
optical system illustrating formation of
coma aberration.
Figure 2‐7. Astigmatism is the result of axial asymmetry and leads to variations
in the focal length for different angles around the optic axis. This is resulting in
co‐existence of two principle focus lines located at right angles along the axis.
Axial asymmetry of the system results in azimuthal focal
length dependence (Fig. 2‐7). In contrast to the spherical and
chromatic aberrations, astigmatism may be compensated by
special non‐round optical elements ‐ stigmators, which are
incorporated into the microscope lens to create additional
magnetic field.
Another important type
of aberrations is coma. This
aberration may appear
when incident beam is
tilted in respect of optical
system axis (see Fig. 2‐8).
Focusing of the incident
rays in different points
creates specific blurring of
the focal point with shape
of coma. Adjustment of the
optical system to avoid formation of the coma is critical for
high resolution TEM image formation.
2.1.5. Phase contrast formation and imaging with atomic
resolution
The imaging contrast which was discussed before in
Section 2.2 is formed by in‐plane variation of the amplitude
of the electron wave which is happens because of difference
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in absorption and scattering of separate areas of the object.
This contrast is called ‘amplitude contrast’. Alternatively,
‘phase contrast’ in the TEM images appears as a result of
phase shift of electrons passing through the sample. The
phase shift itself cannot be detected as far the detection
system records intensity (a square of amplitude) of electron
wave. In order to convert the phase variations into the
variations of intensity an optical system should possess
particular types of geometrical aberrations, the deficiency of
focus (“defocus”) being the main used for this purpose.
The geometrical aberrations of the optical system of the
microscope may be defined via phase shift of the plane wave
after it passed throughout. Typically, these aberrations are
defined in reciprocal space as a phase shift χ dependence on
space frequency u. The space frequency u is parameter
equivalent to the reciprocal space vector which is used for
description of radiation scattering in crystals. If only defocus
and 3rd order spherical aberration are considered the
aberration function may be represented by equation [101]:
χ πΔf (2.8)
where Cs ‐ spherical aberration coefficient, Δf – defocus. The
aberration function produces main input into contrast
transfer function (CTF) of the microscope which determines
how the amplitude and phase of electron wave are
transferred from the object to the image plane.
For a weak‐phase object (thin sample) CTF is given by
[101]:
2 (2.9)
where A( ) is aperture function: A( )=1 at u≤ and A( )=0 at
u> , where is spatial frequency corresponding to the
aperture radius. The optimal shape of this function is
shown in Fig. 2‐9a. The contrast transfer function oscillates
depending on space frequency. The phase contrast can be
maximized by maximizing the integral below CTF. As far as
Cs is fixed (for non‐corrected microscopes, see consideration
for corrected case below) this optimization is done by
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Dissertations in Forestry and Natural Sciences Number 258 47
varying the value of Δf. The optimal value for Δf is given by
the formula [109]:
(2.10)
and is commonly called Scherzer focus. Due to the fact that
Cs is generically positive for electromagnetic lenses, Δfopt is
negative and as a consequence CFTfopt has broad band path at
negative values. Practically this means that optimal phase
contrast will be negative, i.e. atoms in TEM image will
appear dark on light background.
The equation (2.8) describes an ideal case with constant
aperture function A(u) while in a real microscope the transfer
function is attenuated according to equation [101]:
(2.11)
where с and are, respectively, the damping envelopes
due to chromatic aberration (Cc) and beam convergence (α):
exp (2.12)
exp (2.13)
where δ is defocus spread caused by fluctuation of
accelerating voltage (ΔEv), the energy spread of the electrons
(ΔEe), emitted by the filament, and the energy loss of
electrons (ΔEs) due to inelastic scattering in a specimen
generated by variations of wavelength, resulting in chromatic
aberration (Cc). Additionally, to that variations of current (ΔI)
of the objective electron lens lead to the focal length change.
Defocus spread (δ) can be expressed as [101]:
δ= Сс 2 (2.14)
The resulting CTF function of the microscope Ttotal(u) may
be presented graphically as it shown in Fig. 2‐9b. To exclude
effect of phase variation the images should be obtained in the
range of space frequencies (u) spans from zero coordinate
point to first intersection point of the function Ttotal(u) and
horizontal axis. This point defines point‐to‐point resolution
(pp) and corresponds to a minimum distance between two
point‐like features in the object, which can be distinguished
from each other:
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0.65 (2.15)
Figure 2‐9. The ideal CTF function of microscope without taking into account
chromatic aberration and beam convergence dumping envelops (a). Dependence of
with respect to u modified by the damping envelope (blue dashed
curve) – (b). The calculations are made for Δf=‐100nm, Cs=2.2 mm.
Spatial frequency at which Ttotal(u) becomes zero defines so
called information limit (marked at Fig. 2‐9 (b) as ). This
point determines the highest frequency which can be
transferred through the optical system:
(2.16)
The information limit is far beyond limits of point
resolution for the microscopes with FEG sources because of
their high space and time coherency. The high resolution
atomic scale imaging may be achieved but the complex
dependence of the contrast on space frequency requires
usage of image simulations for correct determination
positions of atoms.
Fig. 2‐10 shows an example of the high resolution imaging
with TEM. This image presents atomic structure of thin
Chapter 2: General principles and practical aspects of TEM analysis
Dissertations in Forestry and Natural Sciences Number 258 49
quasi‐two‐dimensional Si crystal. The distances and angles
between atomic columns were determined using Fourier
transformation and diffraction patterns simulations.
Estimation of the distances between spots in the diffraction
patterns and angles between vectors directed from the center
to the analyzed diffraction spots allows establishing of cubic
primitive cell and determining the orientation of the crystal in
respect to the incident beam of electrons. To confirm
correspondence of the experimentally obtained image to
silicon, the methods of computer simulations were used to
obtain images with atomic structure and the simulated
images were compared with the experimental data. Inset in
Fig. 2‐10а’ shows calculated images for silicon crystal with
thickness of 6.9 nm at defocus 65.5 nm. Inset in Fig. 2‐10b’
shows the calculated image for the crystal with thickness of
9.3 nm at defocus 64.5 nm. More details about this study may
be found in Article III (see Appendix).
Figure 2‐10. HRTEM image of the flat Si crystals. The diffractograms of the
selected areas (a) and (b) correspond to [101] (c) and [112] (d) zone axis,
respectively. Image simulation (insets) are shown on filtered image correspond to
crystal thickness of 6.9 nm and defocus of 65.5 nm (a’); and for crystal thickness
9.3 nm and defocus is 64.5 nm (b’). See further details in Article III (Appendix).
2.1.6 Improvement of resolution by aberration correction
Resolution of the microscope can be significantly
improved by correction of one of the most important
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parameter – the spherical aberration of the objective lens. For
the first time the method of the aberration corrections has been
proposed by Sherzer in 1947 [112], who has developed strategies
to correct the chromatic and the spherical aberration of a round
magnetic lens. In one of proposed variants the corrections
include introduction of non‐round optical elements into
magnetic lens system. In this case the magnetic field of reduced
azimuthal symmetry is produced due to rotational asymmetry
of the lenses. Efficient correction of the lens aberrations may be
achieved, potentially, with such multi‐pole lenses. In 1990 the
first aberration corrector with a new hexapole correction system
has been proposed by Rose [113]. These correctors have proved
possibility for increasing of resolution of electron microscopes.
Figure 2‐11. Schematic presentation of the spherical aberration corrector with
hexapoles.
The compensation of the spherical aberration for STEM mode
has also been started in the 1990s. The proof of principle has
been demonstrated in 1997 by Krivanek [114]. At now days two
designs of spherical aberration corrector are in use: the
octupole/quadrupole type and the hexapole type. A schematic
representation of the hexapole corrector is shown in Fig. 2‐11.
Corrected system is thus composed of the objective lens, the
telescopic transfer doublet, and the hexapole corrector itself. The
corrector consists of two sextupoles (hexapoles) and another
telescopic round lens doublet formed by two identical round
lenses separated from each other by a distance of double focal
length. The doublet reverses the course of the paraxial
trajectories images the sextupole located at the front‐focal plane
Chapter 2: General principles and practical aspects of TEM analysis
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of the first lens with magnification onto the second sextupole
placed at the back focal plane of the second lens.
For aberrations correction, it is necessary in the first stage
to measure aberrations and then to compensate them. There
are different approaches for the aberration estimation,
including: applying correlation functions for simulated and
experimental images; estimation of the reconstructed wave
functions; and diffractograms analysis. The most widely used
approach is the diffractograms analysis of the amorphous
carbon film including Fourier transformation of high
resolution TEM image. This method was proposed at the first
time by Thon [115]. An example of diffractogram of
amorphous film with 23 nm defocus is represented in Fig. 2‐
12. It consists of series of light and dark rings and their
intensity may be expressed by equation (compare to 2.8):
| | ~sin (2.17)
From this dependence one can see that dark and light rings
of the diffractogram correspond to bands and gaps of CTF.
The values of defocus, two‐fold astigmatism, spherical
aberrations, and even high‐order aberrations may be
calculated on the basis of analysis of the diffractograms using
contrast transfer function which is determined by the optical
system aberrations.
Small two‐fold astigmatism may be calculated using
measured values for diameters of light and dark rings which
will have elliptical form (see Fig. 2‐12d). The light rings
correspond to sin(χ(u))= 1, and the dark rings correspond to
sin(χ(u))=0. Thus, we obtain two values:
for dark rings χ u , where n is odd, (2.18)
for light rings χ u , with even n. (2.19)
Substituting these values into equation for aberration
function (2.7) we obtain:
2 (2.20)
For defocus estimation, it is better to use first dark rings than
first light ring. For the first dark ring n=2. The second term in
(2.20) can be neglected for the microscopes with spherical
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aberration correction because of small value of the spherical
aberration coefficient (tens of μm). Thus, we obtain:
(2.21)
By estimation of diameter of first ring in two perpendicular
directions (u1 and u2 in Fig. 2‐7d) we can calculate defocus and
astigmatism values:
, (2.22)
The resulting defocus and two‐fold astigmatism may be
calculated as average and difference of these two parameters:
(2.23) | |
(2.24)
Figure 2‐12. (а) – Profile of relative intensity distribution created from the center of
the diffraction pattern along arrow shown in panel c. (b) ‐ CTF function of the
microscope (300 kV, Cs=1.2 mm, С1=23 nm). (c) and (d) – calculated diffraction
patterns for double‐axis astigmatism A=0 nm and A=81 nm, correspondingly.
The estimation of spherical aberration coefficient is more
complicated. For uncorrected microscopes one should take it
into account dependence of Cs versus positions of rings in
equation (2.19). By plotting nu‐2 versus u2 one obtains the
straight line with slope Csλ3 [116].
For Cs corrected microscopes usually aberration estimations
carried out by analysis of diffractograms obtained at tilted
illumination. This method was proposed in 1978 by Zemlin and
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Dissertations in Forestry and Natural Sciences Number 258 53
is realized using, so called, Zemlin tableau. It provides more
accurate aberrations measurement [117]. Moreover, it allows
calculation of higher‐order and non‐centrosymmetric
aberrations. The Zemlin tableau example is shown in Fig. 2‐13.
The diffractograms were obtained under beam tilting (with
azimuthal rotation from 0 to 2π) and along optic axis (central
image). Fig. 2‐13(b), (c) shows diffractograms before and after
aberration compensation. Aberration compensation leads to
ellipse‐to‐rings shape transformation (Fig. 2‐13c).
Figure 2‐13. Zemlin tableau: series of diffractograms obtained at tilted electron beam
(a). Examples of diffractograms before (b) and after (c) aberration correction.
Cs‐correction allows reduction or even conreverce the
value of spherical aberration. Comparison of the CTF
functions at Sherzer defocus for uncorrected (Cs=1.2 mm)
and corrected (Cs=0.02 mm) TEM with accelerating voltage of
300 kV are presented in Fig. 2‐14. The point resolution is
drastically improved from 0.22 nm to 0.08 nm. The
simulations are made using CTF Explorer software [118].
Thus, Cs‐correction allows control over the value of Cs in
addition to ∆f, thus extending the parametric space available
for optimizing the imaging. At these conditions the
aberration function should be reviewed. The (2.7) equation
was derived with assumption that Cs is `dominantʹ and fixed
geometrical aberration. The role of higher order aberration
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was assumed to be negligible. To describe the information
transfer for ultra‐high resolution imaging besides the correctable
twofold axial astigmatism, additional anisotropic axial
aberrations, such as threefold astigmatism and axial coma,
would need to be considered[119,120].
Figure 2‐14. Comparison of the contrast transfer functions at Sherzer defocus for
uncorrected and corrected TEM with accelerating voltage of 300 kV: (a) ‐ Cs=1.2
mm, (b) ‐ Cs=0.02 mm.
The aberration function will have a more complex view
taking into account higher order and asymmetric geometrical
aberrations. Using a common notation [121,122], it could be
represented as:
12
12
13
14
14
… (2.25)
where complex scattering angle , and its complex
conjugate is . The notations of geometrical axial aberrations
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used from now on are represented in Table. 2.1. The detail
review of theory of aberration is presented in [122].
Table 2.1. Geometrical axial aberrations
Aberration Symbol Defocus (∆f) C1 Two-fold astigmatism (A) A1 Second-order axial coma B2 Three-fold astigmatism A2 Third-order spherical aberration (Cs) C3 Third-order star aberration S3 Four-fold astigmatism A3 Fourth-order axial coma B4 Fourth-order three-lobe aberration D4 Five-fold astigmatism A4 Fifth-order spherical aberration C5 Six-fold astigmatism A5
So, for Cs‐corrected microscopes the estimation of
aberration for it proper adjustment is necessary.
2.2 OPTIMIZATION OF SPHERICAL ABERRATION CORRECTION FOR NANO-CARBON MATERIALS (EXPERIMENTAL PART)
Significant improvement of spatial resolution and ability for
study of the samples at low accelerating voltages become
possible with application of the spherical aberration correctors.
Low accelerating voltage allows increase image contrast, to
reduce the radiation damage (which is important for radiation
sensitive materials), increase of sample stability and other
important enhancements. All these advantages of structural
characterization at low accelerating voltage are especially
important for low atomic number materials such as nano‐
carbons [123].
As it was mentioned before, the possibility to vary C3 in
addition to ∆f gives the opportunity for further optimization of
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CTF in order to compensate untunable fifth‐order spherical
aberration C5. The C5 parameter is the next after С3 in its
contribution into aberration function (2.25). Currently C5
correctors are still in the development stage and are not in
common use, so we will assume that the value of this aberration
is fixed by the construction of the optical system. The criteria for
phase contrast CTF optimization is essentially the same as was
mentioned before for uncorrected systems: the integral under
sin should be maximized. This is achieved by a proper
choice of the combination of defocus C1 and third‐order
spherical aberration C3 in order to compensate the action of
fifth‐order spherical aberration C5.
There is substantial number of works [124–126] discussing
optimal settings for Cs‐corrector. Typical factors, which are
accounted for are the values of C5 [121,127,128], chromatic
aberration [113,119,125], contribution of non‐linear terms in CTF
[117,129], contribution of amplitude contrast [122]. It is a
common perception that negative spherical aberration imaging
(NCSI) [130,131] in preferential for the corrected systems.
However, this was so far demonstrated for strongly scattering
crystals, and up to our knowledge was not confirmed
theoretically for light materials like carbon. There are a number
of other issues related to carbon materials, which should be
considered as additional parameters contributing to
optimization, namely: necessity to maximize the contrast in
order to reduce the dose, necessity to use sub‐threshold
accelerating voltage (≤80kV), stringent constrains for accuracy of
aberration correction at low accelerating voltages to mention a
few. These considerations lead us to perform an extensive
theoretical study on optimization of the contrast of carbon
atoms in corrected system and in particular the performance of
the corrector itself.
2.2.1 Equipment
The measurements in this work were performed on a high‐
resolution transmission electron microscope Titan 60‐300
TEM/STEM (FEI, The Netherlands) with high‐brightness field
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Dissertations in Forestry and Natural Sciences Number 258 57
emission gun X‐FEG at an accelerating voltage of 80 kV (Fig.2‐
15). To minimize the contribution of the chromatic aberration,
the microscope was equipped with a monochromator, which
allows reducing energy beam spread less than 0.1 eV. The
spherical aberration of the objective lens was compensated by
CEOS (CEOS, Germany) corrector. HRTEM images were
acquired by Gatan (Gatan, USA) UltraScan1000 2k x 2k CCD
camera.
2.2.2 Test samples
The graphene was chosen as a test sample because it has one
atom thickness, which eliminates unambiguity in thickness
determination and allows for direct interpretation of the images
in terms of atomic structure. Graphene samples were grown by
chemical vapor deposition method using 25 μm copper foil as
the substrate. The graphene monolayer is transferred onto TEM
Au Quantifoil grids with holey carbon film using
polymethylmethacrylate (PMMA) as the sacrificial polymer
layer and ferric chloride as the copper etching agent [132].
Figure 2‐15. Transmission electron microscope FEI Titan 60‐300 with X‐FEG gun,
monochromator and CEOS Cs‐spherical aberration corrector.
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2.2.3 Procedure of aberrations measurement and correction
The screenshot of CEOS Cs‐corrector interface is presented in
Fig. 2‐16. Correction procedure consists of two main parts: first
aberration evaluation and second correction of them. Aberration
estimation is carried out by acquiring Zemlin tableau [117]. The
process takes place in an interactive mode, where the role of the
operator is to select the optimum measurement conditions
(magnification, beam tilt angle, exposure time, defocus),
measuring and evaluating the correctness of the decision to the
subsequent step. The aberration measurements and correction
are made by corrector software.
2.2.4 Roadmap for corrector optimization
Following steps were performed to achieve the purpose of
this Chapter:
Evaluation the aberration measurements algorithm,
revealing systematic errors and accuracy;
Determination of the optimal measurement
conditions (beam tilt angle, magnification) for better
accuracy;
Determination the optimal combination of C1, C3 and
C5 parameters for maximum contrast of carbon atoms
(maximal signal‐to‐noise ratio);
Experimental evaluation of the findings on graphene
sample.
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Dissertations in Forestry and Natural Sciences Number 258 59
Figure 2‐16. Layout of Zemlin tableau measurement.
2.2.5 Evaluation of corrector software algorithm
For evaluation of CEOS software aberration measurements
algorithm the series of calculated images with specified
aberrations are simulated. These calculated images are then
analyzed by the corrector program, which measures these
aberrations value. Comparison of simulated and measured
values gives the estimation of corrector performance.
Emulating of Zemlin tableau requires simulation of the
images at tilted illumination with account for off‐axial
incoherent aberrations, in particular for off‐axial chromatic
aberration. In contrast to on‐axis case, where chromatic
aberration can be accounted for as the blur of defocus and thus
as in‐plane symmetric smearing of the image, at tilted
illumination this blur of defocus is directional (see fig.2‐17 left).
In practice this aberration is seen on the FFTs of high resolution
images as so called “bananas”. An example of (simulated) image
of amorphous film at tilted conditions and corresponding FFT is
represented at fig.2‐17 middle and right respectively. Simulation
of this phenomena so far was not demonstrated, though there
are a few papers discussing CTF for tilted illumination for a
very simplified cases (not accounting for the sample, dose,
camera, aberrations higher than defocus, etc.) [125,133]. Here we
propose and realize the method of simulating tilted illumination
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with account for the sample properties (thickness, density,
composition, structure, inclination), all axial aberrations, as well
as imaging parameters (magnification, dose, CCD MTF). The
method uses a direct integration of images through
(2.26)
assuming Gussian distribution of energy spread. An example of
thus calculated Zemlin tableau is represented at fig 2‐18.
Figure 2‐17. (a) – Scheme of considered tilted illumination geometry for simulating
the HRTEM image of amorphous carbon film (b) and it FFT (c).
The data set of 17 calculated diffractorgams calculated from
simulated images with illumination inclination of 18 mrad is
shown in Fig. 2‐18.). Calculations are done for every tilt angle (τ)
from 10 to 35 mrad with 1 mrad step (Fig2‐18, left). For each tilt
angle, the set of diffractogram is calculated. Thus, around 600
diffractograms are calculated and analyzed. All sets of
simulated data are loaded into corrector software and aberration
value are estimated.
Simulated data are compared with experimental
measurements on graphene sample. As well as to the calculated
data, aberration measurements are carried out in the
illumination tilt range from 10 to 35 mrad.
Measured C3 value versus electron beam inclination angle for
the calculated and experimental data are shown in Fig. 2‐19. The
experimental points are shown on the plot by blue squares, the
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Dissertations in Forestry and Natural Sciences Number 258 61
theoretical values shown by crosses. Analysis of obtained data
by fitting curve allows evaluation C5 parameter.
Figure 2‐18. An example of tableau calculated from simulated images which include
aberrations up to C5 (beam tilt angle τ=18 mrad). Nominal defocus C1 is ‐250 nm,
C3= ‐30 μm, C5=12 mm, 500 nm of coma is introduced in addition.
We have calculated such tableau for the tilt ranges (τ) from 10
to 35 mrad assuming the following settings: amorphous carbon
sample thickness 1nm, sample temperature 300K, accelerating
voltage 80kV, C3=‐30um, C5=12mm, defocus 250 nm, defocus
spread 10nm, magnification x250K. All sets of simulated data
are loaded into corrector software and Cs‐values and its
“confidence” levels are measured. The results of these
measurements are represented on Fig. 2‐19.
Defocus value measured by corrector is right (250.1 nm),
however the values of C3 significantly deviate from the
simulated value (horizontal dashed line, Fig. 2‐19). Error bars of
the measured points represent confidence levels reported by the
corrector software and are order of magnitude smaller than the
deviations of C3 from the true value. Observed dependence of C3
from the tilt range could be potentially explained by neglecting
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the contribution of C5 in fitting algorithm (which is most
probably the case). In this case the measured value of C3 would
deviate from true value (for the type of tableau used) as:
С 1.576 (2.27)
This curve calculated for simulation parameters is shown in
green on Fig2‐19. It is seen that even after accounting for C5
there are substantial deviation of the measurements from the
real data. The closest (and precise) measurement is achieved at
18 mrad with a systematic shift from the true value of about
+7 um. In the further practical work, we will be using this value
for measurements as well as will be accounting for this
systematic shift in C3.
Independent calculations (not shown here) revealed
optimum magnification, optimal defocus, signal‐to‐noise ratio
necessary for reliable measurement as well as potential errors
induced by sample tilt, sample thickness and calibrations
imperfection.
2.2.6 Contrast transfer function adjustment
As has been discussed above CTF optimization consists of
estimation of optimal combination of defocus C1 and third‐order
spherical aberration C3 providing the maximum integral under
the CTF. This achieved by shifting the high frequency cutoff of
CTF to maximum possible value. Two limiting factors can be
considered in this respect: cut‐off due to incoherent envelope
and cut‐off due to phase contrast oscillations caused by
uncorrectable C5 contribution. These two cases can be
discriminated by comparing contributions of one and another
shown in Fig. 2‐20. Presented here are the dumping envelope
and phase shift induced by C5 calculated for the parameters of
our microscope (80kV, Cc=1.7 mm, C5=12.4 mm, ∆E=90meV). It
is seen that dumping envelope still allows a substantial contrast
transfer at 0.1 nm, while the phase shift induced by C5 crosses
π/2 value at about 0.2 nm, meaning from this frequency CTF will
start oscillating. Thus, we can conclude, that our imaging is C5
limited and we will aim to optimize C1 and C3 for compensating
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C5 (see also [127]). Such optimization results in the values
C1=10 nm, C3=‐24 μm assuming C5=12.4 mm.
Figure 2‐19. Dependencies of coefficient С3 on deviation angle of the beam in respect
to the optical axis. The crosses – data obtained by analysis of the calculated
diffractograms. Dashed line shows the value implemented in simulations. Green curve
represents the correction curve accounting for C5 (see text and eq. 2.25).
Figure 2‐20. Two limiting factors of Cs‐corrected microscope: incoherent envelope
and phase contrast oscillations caused by uncorrectable C5 (calculated for the
microscope parameters: 80kV, Cc=1.7 mm, C5=12.4 mm, ∆E=90 meV).
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We will demonstrate the importance of perfect alignment of
correcting system on the base of the following examples:
In the first case CTF is treated in a “classical” way, i.e. the
contribution of C5 is neglected and optimum C1 and C3 are
found in a classical Scherzer sense. Such approach is still
common in scientific literature (see for example [134]). At the
same time the value of C3 reported by corrector is trusted in
addition. The consequence of such approach is illustrated on Fig.
2‐21 (a‐c), where (a) is the CTF the operator expects to have, (b)
is the true CTF and (c) shows how this reflects on the image of
graphene dislocation core.
In the second case the operator is smart enough to account
for C5, though is not sufficiently smart to be concerned about
corrector measurements. In this case the value of C3 set up for
imaging will differ but systematic offset discussed above, which
will result in deviation of CTF from expected shape (Fig. 2‐21 d‐
e) and corresponding disturbance of the image (Fig. 2‐20f).
Only complete accounting for system aberrations and
corrector systematic errors allows forming a perfect CTF shape
(Fig. 2‐20 g‐h) ensuring clear structural image (Fig. 2‐20 i) and
maximum contrast which represented on relative intensity
profile (Fig2‐20 j). Proper setup of conditions thus allows to
increase the contrast (and thus to decrease necessary dose) by
almost 30%.
An example of experimental images of a single wall carbon
nanotube and graphene were obtained using optimized
corrector adjustments are shown in Fig. 2‐22.
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Dissertations in Forestry and Natural Sciences Number 258 65
Figure 2‐21. Comparison of different CTF optimization and simulation of HRTEM
images of graphene in accordance with optical system parameters. (a‐c) In the first case
CTF is treated in assumption of neglected C5 and optimum C1 and C3 are found. (a) is
the CTF the operator expects to have, (b) is the true CTF and (c) simulated HRTEM
image. In the second case C5 is considering in accordance with measured by corrector
software value. (d) and (e) expected and real CTF and (f) simulated HRTEM. Last case
the complete accounting for system aberrations and corrector systematic errors.
Coincide of expected (g) and real (h) CTF shapes and corresponding HRTEM image (i).
Profile of relative intensity distribution (j) obtained along lines selected in HRTEM
images (c, f, i).
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Figure 2‐22. Examples of experimental HRTEM images for single wall carbon
nanotube (a) and for single layer graphene (b) obtained after optimization of the
microscope adjustments.
SUMMARY OF THE CHAPTER 2
Analysis of aberration measurement algorithm of CEOS
software revealed the presence of a systematic error due to the
absence of fifth‐order spherical aberration coefficient in fitting
algorithm. Dependence of the aberration evaluation accuracy
with respect to standard beam tilt angle was determined. The
beam tilt angle about 18 mrad corresponds to the most correct
optical system aberration evaluation. Analysis of contrast
transfer function of microscope with С5 optimization in different
assumptions reveals optimized defocus and C3 parameters for
highest signal‐to‐noise ratio.
Dissertations in Forestry and Natural Sciences Number 258 67
3 Atomic arrangement of
guest crystal in the inner
channel of functionalized
single‐walled carbon
nanotubes
The functionalization of the carbon nanotubes leads to
significant change of nanotube electronic properties [26,76].
Doping of SWCNT films with inorganic materials can increase
the film conductivity and change the optical absorption [76,135–
137]. Besides SWCNT could be used to create novel one‐
dimensional structures inside the nanotube channels, which are
unstable as freestanding systems [138–140]. Among the various
functionalization nanotubes methods, the filling by guest crystal
molecules is the most effective one [43,73]. Properties of the
nanocomposite based on filled nanotubes can be correctly
interpreted only if structural organization of internal channel of
the nanotube is revealed [47,77]. Among different structural
methods high‐resolution transmission electron microscopy is a
leader due ability provide local analysis and high spatial
resolution [78,141]. These parameters are very essential for
studying crystals with size of few nanometers and rarely
possessing of high order of atomic arrangement. Application of
chemical analysis techniques in TEM allows revealing
composition and the real crystal structure of the encapsulated
crystal [47,78,101].
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In this Chapter, we will consider different structural
organization of the guest crystal molecules in inner channel of
filled SWNTs:
SWCNT filled by 1‐bromoadamantane molecules
(1‐bromoadamantane@SWCNT)
SWCNT filled by mercury chloride molecules
(Hg2Cl2@SWCNT)
SWCNT filled by copper chloride molecules
(СuCl@SWCNT)
3.1 SINGE WALLED CARBON NANOTUBE FUNCTIONALIZED BY ADAMANTANE MOLECULES
CNTs may be used as a nanoreactor for producing of new
one‐dimensional crystals. One of the most interesting tasks is to
grow one‐dimensional diamond crystal. One of the approaches
to reach this goal is to analyze the 1‐bromoadamantane
molecules packing into single walled carbon nanotube channel.
It is supposed that after CNTs filling procedure and heat
treatment these molecules will crystallize into diamond
structure. Control of filling results by spectroscopic techniques
is difficult due impossibility to detect the presence of carbon‐
containing molecules inside carbon nanotubes. Due to presence
of bromine atom in the guest molecule filling results could be
analyzed by EDS technique.
The SEM image of the filled SWCNTs film and STEM image
of the nanotubes bundle are presented in Fig. 3‐1. EDX spectrum
obtained from the selected area (white rectangle) is clearly
revealed the presence of bromine Fig. 3‐1c. Bromine K‐ and L‐
lines were detected for 1‐bromoadamantane@SWCNT. Low
signal from Fe, which can be attributed to the presence of
catalytic particles in the samples, is also observed.
Structure of filled nanotubes was studied by high resolution
electron microscopy technique. The carbon structures, which
looks like deformed nanotube in the inner SWCNT channel,
were revealed. A series of HRTEM images with 0.1 sec exposure
Chapter 3: Atomic arrangement of guest crystal in the inner channel of
functionalized single‐walled carbon nanotubes
Dissertations in Forestry and Natural Sciences Number 258 69
were recorded (Fig. 3‐2 (a)‐(e)). This technique was applied for
visualization of free bromines atoms, which were detected as
bright spots (marked by arrows).
Figure 3‐1. SEM (a) and STEM (b) images of 1‐bromoadamantane@SWCNT. An
EDS spectra from nanotubes bundle (selected by white box in (b)) – (c).
Figure 3‐2. Series of HRTEM images of 1‐Bromoadamantane@SWCNT for
visualization of free bromines atoms and carbon structures moving inside the carbon
nanotube (a‐e). Experimental (white box in (b)), simulated HRTEM images and
atomic model of SWCNT with Br atom (f), (g), (l). The relative intensity profiles
through the marked line for experimental and simulated images (h) and (k). (The
images reproduced in accord with Article IV – see in Appendix)
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Analysis of series of HRTEM images revealed that bromine
atoms migrate inside the tube during recording. Some of them
vizualized as free‐standing atoms or embedded in the carbon
structures. For proper contrast interpretation of the HRTEM
images, the simulations were performed for filled SWCNT and
for free bromine atom into accordance the TEM optical
parameters (Fig. 3‐2g). The relative intensity profiles through
the marked line (red line) from simulated and experimental
images are shown in Fig. 3‐2 (h)‐(k). Free bromine atom inside
SWCNT can be easily identified by high contrast difference due
to their low atomic number. Good agreement is observed for
experimental and calculated profiles.
Thus, it was shown that functionalization of SWCNT by 1‐
bromoadamantane leads to formation in inner nanotube carbon
structure and free standing bromine atoms. Other details are
presented in Article IV (see Appendix).
3.2 STRUCTURE CHARACTERIZATION OF HG2CL2 CRYSTALS LOCATED IN THE INNER CHANNEL OF SWCNT
Another example of functionalized carbon nanotubes studied
in this work is SWCNT filled by mercury chlorine molecules.
The molecules were loaded inside channels of single‐walled
CNTs using melting‐phase filling procedure, which provide
larger encapsulation yield. Powders of SWCNTs and HgCl2
were heated at temperature 290° C which higher than HgCl2
melting temperature by 17° C. The heat treatment was carried
out during 16 hours.
On the first step the control of the filling results was
reformed by scanning transmission electron microscopy and
EDS techniques. Due to large difference of carbon, mercury and
chlorine atomic numbers HAADF STEM image with Z‐contrast
clearly discriminate filled (bright contrast inside nanotube) and
empty tubes. Typical STEM images of the filled SWCNTs are
presented in Fig. 3‐3. About 80% of tubes were filled that
Chapter 3: Atomic arrangement of guest crystal in the inner channel of
functionalized single‐walled carbon nanotubes
Dissertations in Forestry and Natural Sciences Number 258 71
indicates good outcome of filling process. Encapsulated crystals
with length varying from 1 to 150 nm were uniformly
distributed in the channels of SWCNTs. Chemical composition
was determined by EDS analysis. The obtained spectra shown
peaks of mercury, chlorine, carbon, copper and oxygen (Fig. 3‐
3c). Copper signal is a common artifact because used TEM
support grid is made of copper; oxygen is, most probably,
related to oxygenation of carbon nanotubes during sample
exposure in air.
Figure 3‐3. STEM images with various magnification of Hg2Cl2 filled SWCNT (a), (b).
EDS spectra from filled SWCNT rope (c).
The structure of mercury chloride nanocrystals was
evaluated on the base of a set of series of HRTEM images. Two
distinct crystal orientations were observed and analyzed.
Diameter of SWCNTs evaluated by unfilled region of
corresponding nanotubes is about Dm= 1.7 nm. The {110}
graphene reflections were used as internal calibration standard.
Applying the Fast Fourier Transform (FFT) the 2D lattice
parameters of encapsulated crystal and angles between
reciprocal vectors were measured. In Fig. 3‐4 and Fig. 3‐5 are
presented HRTEM images with various encapsulated crystal
orientations. A periodicity of encapsulated crystal d1 was
determined to equal to 0.271 nm and d2 = 0.248 nm (the ratio
d1/d2 = 1.09), an angle α = 88°. A periodicity is S1 = 0.269 nm, S2 =
0.324 nm, the ratio S1/S2 = 0.83, an angle α = 85°.
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Experimental data were compared with crystallographic
parameters for HgCl2 (ICSD 23277) and Hg2Cl2 (ICSD 65441)
phases of bulk crystal. Comparison of calculated diffraction
patterns with experimental FFTs shows the best match for
Hg2Cl2 phase.
Figure 3‐4. HRTEM image of Hg2Cl2 filled SWCNT (a). Interplanar distances and
angles between reciprocal vectors were evaluated by FFT form selected region of
nanotube (b). Simulated diffraction patterns for Hg2Cl2 crystal with [100] zone axis (c).
Comparison of filtered HRTEM image (d) of encapsulated crystal with simulated one
(e) which calculated in according to proposed atomic model (f).
Crystal orientation was evaluated as [100] Hg2Cl2 zone axis
(Fig. 3‐4c) and as [110] Hg2Cl2 zone axis (Fig. 3‐5c).
The atomic model of filled nanotube was proposed in
accordance with the identified structure and orientations of
encapsulated crystal. A fragment of (13, 13) SWCNT with
diameter 1.7 nm corresponded to measured one from the
HRTEM images was taken for simulation. Encapsulated crystal
is oriented [001] Hg2Cl2 direction along to the long tube axis.
Calculated HRTEM images simulated according to atomic
models of filled SWCNT was in good agreement with
experimental images. Thus, it could be concluded that
Chapter 3: Atomic arrangement of guest crystal in the inner channel of
functionalized single‐walled carbon nanotubes
Dissertations in Forestry and Natural Sciences Number 258 73
encapsulated crystal structure identified on base of HRTEM
data is correct.
To summarize, we observed that stochiometry of mercury
chloride crystals changes from HgCl2 to Hg2Cl2 during the guest
molecule loading into the inner channel of S2WCNTs.
Encapsulated crystals were oriented [001] Hg2Cl2 direction
parallel to nanotube long axis. This study provides new
information about chemistry inside the carbon nanotubes and
synthesis of new functionalized nanocarbon material.
Figure 3‐5. HRTEM image of Hg2Cl2l@SWCNT (a). FFT form selected region of
nanotube (b). Simulated diffraction patterns for Hg2Cl2 crystal with [110] zone axis (c).
Comparison of filtered HRTEM image (d) of encapsulated crystal with simulated one
(e) which calculated in according to proposed atomic model (f).
3.3 CRYSTAL STRUCTURE OF 1D CUCL@SWCNTS
Functionalization of nanotubes by gas phase filling is one of
widely applied technique. During the filling procedure
treatment of nanotube almost does not damage the structure of
the media. Gas‐phase approach leads to much cleaner SWCNT
surface comparing with a liquid method of filling. This filling
method was used for loading the CuCl molecules into SWCNT
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channel. It was shown that this functionalization leads to a
significant increase in transmittance of the initial nanotube films.
We shown that this type of filling allows improvement of optical
properties of the macroscopic samples of SWCNTs (for instance,
films) without damaging their crystalline structure.
Transmission electron microscopy was applied for structure
characterization of the film of filled SWCNTs. TEM analysis of
the SWCNT sample filled by copper chloride shown that
nanotubes were predominantly bundled together into ropes.
Estimation of the yield of the nanotubes filling was performed
by STEM and EDS methods. The CuCl nanocrystals were clearly
distinguished by HAADF STEM imaging with Z‐contrast (Fig.
3‐6a). The EDS spectra acquired from the filled tubes shown
peaks corresponding to gold, copper, chlorine, oxygen, and
carbon (Fig. 3‐6b). Gold signal in this case is explained by usage of golden TEM support grid. Oxygen was most probably related
to oxygenation of carbon nanotubes during procedures used for
opening of nanotube ends. Besides a very low signal to noise
ratio the presence of both of Cu and Cl in the tubes can be
concluded without doubt.
Figure 3‐6. STEM image of CuCl@SWCNT (a) and EDS spectra (b) from selected on
(a) area.
Formation quasi one‐dimensional CuCl crystals inside the
SWCNT inner channel was revealed by HRTEM. The {110}
graphene reflections from SWNTs was used for precise
magnification calibration as internal standard. The diameter of
Chapter 3: Atomic arrangement of guest crystal in the inner channel of
functionalized single‐walled carbon nanotubes
Dissertations in Forestry and Natural Sciences Number 258 75
SWCNTs was evaluated on unfilled region of nanotubes as
Dm=1.7 nm. Several crystal orientations were observed and
analyzed. The projection of CuCl crystals observed most often in
the CNT sample is shown at Fig. 3‐7a. The interplanar distances
and angles between the reciprocal vectors were analyzed using
fast FFT method (Fig. 3‐7b). The obtained values are: d1=0.33 nm,
d2=0.33 nm, α≈60o. The interplanar distances and angles for
second orientation were determined as follows: d1=d2=0.19 nm,
α≈90o (Fig. 3‐7d).
Experimental data were compared with crystallographic
parameters for known polymorphs of copper chloride. The best
agreement was achieved for CuCl described by zinc blende type
structure with cell parameter a = 0.541 nm [142]. Comparison of
CuCl interplanar distances with experimental data shown a
good agreement for [110] CuCl projection. The main motif in
this projection is similar to observed “open hexagon”. But to
precise fitting to observed data some lattice distortions should
be supposed. CuCl lattice could be represented by two subcells
superposition. Due to integration of nanotube wall with CuCl
subcells, the ~8% subcell displacement could be assumed. As a
result, the unit cell symmetry is decreased: cubic type is
transformed to rhombohedral type. According to this
assumption the atomic model of CuCl filled nanotube was
proposed (Fig. 3‐8). Simulation of HRTEM images was
performed for this model. As could be seen from Fig. Fig. 3‐8 the
rotation of encapsulated crystal around long tube axis at 90°
allows the cubic motif which also was observed experimentally.
The coincidence of the experimental and calculated HRTEM
images for two crystal orientation confirm correctness of the
proposed atomic model.
To summarize, the functionalization of single walled carbon
nanotube by filling with CuCl molecules leads to quasi 1D
crystal formation. Applying of HRTEM techniques allows to
identify the crystal structure of encapsulated crystal. Loading of
copper chloride molecules into the nanotubes during gas‐phase
synthesis leads to crystal lattice transformation from cubic to
rhombohedral symmetry types.
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Other details about CuCl functionalized single walled
carbon nanotubes are presented in Article V (see Appendix).
Figure 3‐7. HRTEM images of encapsulated 1D CuCl@SWCNT with two typical
orientations are presented in (a), (c) and corresponded Fast Furrier Transformation (b),
(d). The main motif of atomic arrangement is represent by the models in the middle.
Figure 3‐8. Atomic model of CuCl filled SWCNT viewed in two orientations and
simulated HRTEM images.
Chapter 3: Atomic arrangement of guest crystal in the inner channel of
functionalized single‐walled carbon nanotubes
Dissertations in Forestry and Natural Sciences Number 258 77
SUMMARY OF THE CHAPTER 3
The results presented in Chapter shown that high‐resolution
transmission electron microscopy is a powerful method for
carbon materials study on atomic level. It allows control of
nanotube filling process, structural peculiarities of guest
molecules inside the tubes and provides an information about
structural transformation during synthesis.
In particular, we found that functionalization of SWCNT by
1‐bromoadamantane leads to formation in inner volume of
nanotube carbon structures with free standing bromine atoms. It
was observed also that during functionalization of the
nanotubes in gas phase by mercury chloride molecules crystal
with parameters of bulk one may be obtained. Loading the
molecules of copper chloride into the nanotubes during gas‐
phase synthesis may lead to crystal lattice transformation from
cubic to rhombohedral symmetry types.
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Dissertations in Forestry and Natural Sciences Number 258 79
4 The structural
peculiarities of nano‐ and
micro‐meter size scale
diamond crystals
Diamond is one of the most well‐known allotropic
modifications of carbon. It is widely applied in industry due to
its exclusive physical properties which include: superior
hardness, biocompatibility, high thermal conductivity and
electrical resistivity, chemical stability, unique properties for
optical elements and coatings [1,39,66,143,144]. There are
various methods for production of diamond, amongst which the
best known is detonation diamonds, and crystals obtained by
CVD [66,67]. Depending on the synthesis methods it is possible
to control size of the producing crystals from nano‐ to micro‐
meter scale. Nanodiamonds, for example, are widely used in
biomedical and mechanical applications [145–147]. Variation of
synthesis conditions allows growth a quasi two‐dimensional
diamonds and single crystal needles with perfect pyramid shape
[148]. Fabrication of well‐shaped and defect‐free diamond single
crystals and especially low‐dimensional diamonds (such as
nanowires and nanoplatelets) is very important for
nanotechnology applications [149,150].
Revealing structural characterization is necessary for
determination of optimal conditions providing fabrication of
materials with desired properties and for correct revealing of
their physical properties. This chapter is focused on description
of study of nanodiamonds structure and its transformations
under heat treatment, as well as on revealing of structural
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peculiarities of quasi two‐dimensional and micro‐meter sized
diamonds crystals.
4.1 THE TRANSFORMATION OF SP3 TO SP2 C-C BOND IN NANODIAMOND UNDER HEAT TREATMENT
An example of the structure transformation of the
nanodiamonds (ND) is formation of so‐called “onion‐like”
structures. The onion‐like carbon (OLC) obtained their name
because of structure resembling concentric layers similar to that
in onion. OLC structures may be produced by graphitization of
nanodiamond and revealed potential for different applications,
including, for example, in energy storage devices, for composite
production and in catalysis [2,151,152]. The sp2/sp3 composites
consisting of one or few nanodiamond cores enveloped with a
few graphene layers and OLC were produced by a controllable
graphitization of explosive NDs in vacuum within the
temperature range of 1200–2140 K [153]. A transformation of the
defective curved graphene sheets into OLC structure occurs
after a complete transformation of diamond cores.
Structure of samples was monitored by Raman spectroscopy
and by high resolution electron microscopy techniques [154–
156]. Nanodiamonds with crystallite size varied from 4 to 12 nm
were analyzed. For all samples, the pristine nanodiamonds were
characterized by two peaks in the Raman spectra. The first one
is a relatively narrow and low intensity Raman band around
1325 cm−1 (D‐mode of sp2‐bonded phase). The second one is a
broad and intense band around 1600 cm−1 (G‐mode of sp2‐
bonded carbon). While the annealing temperature increases D‐
mode shifts towards high frequencies, and G‐mode shifts
towards low frequencies. In addition, after annealing at
temperatures higher than 1800 K a two‐phonon 2D‐mode
appears. The obtained results were interpreted as modifications
occurred at different stages of onion‐like structures formation.
An example of TEM analysis of ND transformation under
heat treatment is presented in Fig. 4‐1. High resolution TEM
Chapter 4: The structural peculiarities of nano‐ and micro‐meter size scale
diamond crystals
Dissertations in Forestry and Natural Sciences Number 258 81
image of nanodiamonds before heat treatment procedure is
presented in Fig. 4‐1a. Crystals with average size of 4‐5 nm have
high atomic order which is revealed by lattice fringes of
enlarged HRTEM image and by sharp rings on FFT pattern
corresponding to 111 and 220 interplanar distances in diamond
(Fig. 4‐1a insert). After heat treatment particles possess structure
of graphitic layers rolled into the onion structure (Fig. 4‐1b).
Distance between layers is about 0.33 nm. Small empty hole in
central part of the particles (see enlarged HRTEM) testifies
complete transformation of diamond into graphite‐like structure.
This fact was also confirmed by disappearance of diffraction
peaks in FFT. The schematical representation of ND crystal
structure transformation is illustrated in Fig. 4‐1c. Other details
about nanodiamonds characterizations are presented in
Article VI (see Appendix).
Figure 4‐1. HRTEM images and FFT of nanodiamond before (a) and after (b) heat
treatment. Schematically representation of sp3 to sp2 transformation (c).
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4.2 DIAMOND PLATELETS PRODUCED BY CHEMICAL VAPOR DEPOSITION
Diamond crystal characteristics might be controlled by
varying the CVD parameters such as substrate temperature,
carbon‐containing gas composition and others [66–68]. The most
usual is fabrication of columnar polycrystalline diamond films
consisting of needle‐like crystallites [157,158]. At the same time
production of diamond crystallites with other shapes remains
challenging. This work was dedicated to fabrication of
hexagonal diamond with nanometer thickness and with lateral
size of few micrometers. The material synthesis was performed
using a direct current discharge plasma enhanced chemical
vapor deposition from hydrogen and methane gas mixture. SEM
analysis revealed that obtained diamond films were composed
of several densely packed thin platelets (quasi two‐dimensional
crystal) with lateral size of few micrometers and thickness of
about few tens nanometers (Fig. 4‐2a). TEM analysis of different
diamond platelets revealed absence of significant structural
defects within the crystallites, which indicates their high
structural quality. Characteristics of the registered diffraction
pattern indicate obvious six‐fold rotational symmetry of the
crystallite structure. The interplanar distances in this structure
were evaluated to be 0.1260 nm proving that the platelets are
composed of stacked (111) diamond plane. TEM observations
reveal presence of structural traces caused by planar stacking
faults and twin boundaries in {111} planes (see Fig. 4‐2b, c).
Usage of the HRTEM technique allows analysis the atomic
structure of twinned grain boundary (see Fig. 402d). The
assumption that diamond platelets are composed by stacked
(111) planes is in excellent agreement with previously observed
nanostructures with quasi‐2D shapes for materials with face
centered cubic (FCC) unit cell. On our opinion, the low methane
concentration and relatively high temperature are the key
parameters which provide lateral growth and, as a result,
predominant platelet‐like morphology of the crystallites in CVD
film. Such conditions highly reduce probability of formation of
Chapter 4: The structural peculiarities of nano‐ and micro‐meter size scale
diamond crystals
Dissertations in Forestry and Natural Sciences Number 258 83
three‐atom nucleus on atomically smooth {111} planes. In
combination with absence of twinning on {111} planes (i.e. re‐
entrant corners in {111} area) it causes extremely low growth
rate in <111>directions and strong 111‐faceting of resulting
crystallites.
Figure 4‐2. Typical SEM image (a) and TEM image of cross‐section (b) of the diamond
platelet. (c) Electron diffraction pattern revealed (111) twin’s boundary at cross‐
section of platelet. (d) High resolution bright field TEM image showing the twin
boundary atomic structure. The images reproduced in accord with Article VII (see
in Appendix)
The 2D shapes for FCC nanostructures might be described in
a framework of kinetic and thermodynamic approach of
modified Wulff constructions for twinned nanoparticles.
Accordingly, such type of shapes can be constructed by
considering a particle with several lamellar twins and with fast
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{100} surface growth velocities (i.e. slow {111} growth) and
applying kinetic growth enhancements (at twin plane or/and re‐
entrant surfaces). The resulting structure is also expected to be
hexagonal platelet with (111) main plane.
Thus, in our case formation of the hexagonal diamond
platelets is, apparently, a result of lateral growth between
parallel planar stacking faults in {111} planes in combination
with extremely low growth velocity in <111> directions. The
stacking faults appeared probably at initial stage of the
deposition process. The low growth rate is because of rather
high temperature. More details are presented in Article VII
(see Appendix).
4.3 STRUCTURAL PECULIARITIES OF SINGLE CRYSTAL DIAMOND NEEDLES OF NANOMETER THICKNESS
Fabrication of textured diamond films with controlled
crystallographic orientation of individual crystallites is very
important nowadays because it provides mass production of the
diamond needles with high structural perfection [159]. Such
kind of diamond needles are attractive for different application
including atomic force microscopy, cutting tools etc. [160,161].
The SEM images of diamond needles with shape of perfect
rectangular pyramids are presented in Fig. 4‐3a, b. These
diamond needles were produced by chemical vapor deposition
with appropriate adjustment of the process parameters.
However, some defects may occur during diamond films
fabrication. The structural defects analysis was performed to
understand the relationship between fabrication condition and
diamond structural perfection. Combination of Raman
spectroscopy and transmission electron microscopy techniques
allows revealing and analysis of the crystal defects [82,162].
In this work, we applied some CVD techniques modification
to find new parameters of film growth. During CVD process
nitrogen for a short time was added into gas mixture because it
is known the nitrogen addition changes the ratio of the growth
Chapter 4: The structural peculiarities of nano‐ and micro‐meter size scale
diamond crystals
Dissertations in Forestry and Natural Sciences Number 258 85
rates of {100} and {111} surfaces almost by a factor of about 4.
One may expect that the nitrogen addition could significantly
increase amount of sp2 carbon. It was revealed in our study that
Rama spectra change may be attributed to sp3 type defects
appeared during synthesis without nitrogen addition. The
existence of graphitic carbon (detected by Raman spectroscopy)
may indicate growth conditions which are not enough optimal
for diamond formation. Similar coexistence of diamond (sp3)
and graphitic (sp2) carbon is often observed in CVD diamond
films. Addition of 1% of nitrogen into the gas mixture during
the growth not only leads to an abrupt and substantial decrease
in the diameter of the diamond needle, but also causes changes
in the defect concentration in the growing crystal.
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Figure 4‐3. SEM images of a diamond with perfect pyramidal crystallite shape (a, b).
HRTEM image reveals a multiple twin’s boundaries/stacking faults propagating in the
crystallites (c). Bright field TEM image of needle apex with variations of the diffraction
contrast, which indicate the presence of numerous extended defects in this area (d).
The images reproduced in accord with Article VIII (see in Appendix)
Transmission electron microscopy provides an information
about atomic structure of the needles. SEM and TEM images
revealed that lateral surface of the diamond needles is generally
rougher in comparison with their basal facets (Fig. 4‐3b, d). This
roughness is mostly determined by the oxidation step of the
fabrication process. Thorough oxidation results in almost flat
surface; while insufficient oxidation cycle leaves residuals of the
Chapter 4: The structural peculiarities of nano‐ and micro‐meter size scale
diamond crystals
Dissertations in Forestry and Natural Sciences Number 258 87
dendrite‐like shape crystallites. The needle itself is represented
by a perfect undisturbed diamond crystal, what is evidenced by
the large area convergent beam electron diffraction (LACBED)
pattern with straight and sharp high‐order Laue‐zone
diffraction. According to LACBED the pyramid base is formed
by {100} plane, and the lateral surfaces are close to {110} planes.
The observed (001) texture of obtained films indicates that
applied conditions of CVD process provide the slowest crystal
growth along ⟨100⟩ crystallographic direction. The fastest growing direction at these conditions is ⟨110⟩ leading to degeneration of {110} facets into edges between {100} and {111}
facets.
The dendrites structure is dramatically differ from the rest of
the needle in crystal quality—they acquire a high density of
stacking faults and {111} twins, thus creating a high
concentration of planar defects in the near surface region of the
needles (Fig. 4‐3c). The distance between stacking faults/twin
boundaries is averaged at about 5 nm. Figure 4‐3d shows the
region of the needle near the apex. The crystal here contains
much more defects, which are visible as the irregularity of
thickness fringes.
Raman scattering analysis reveals a few peculiar features
related to the defects found in the needle. Incorporation of
possible point defects into the volume of growing crystal may be
explained on the basis of detailed molecular modeling of the
diamond growth on {100} surface. By kinetic analysis it may be
shown, that migration of CH2 fragments leads to their
alignment in dimers chain direction on the reconstructed
C{100}:H 2 × 1 surface. Aligned CH2 bridges inevitably contain
one atom gaps. Thus, even at moderate growth rates, there is a
high probability that these monoatomic voids are trapped inside
the crystal, forming vacancy type point defects. High growth
rate upon nitrogen addition may be also the reason for sp2
fragments inclusion into bulk of the diamond crystal showing
broad Raman lines in 1500–1600 cm−1 spectral range. Further
details about this structural study is presented in Article VIII
(see Appendix).
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SUMMARY OF THE CHAPTER 4
In this Chapter, it was briefly shown that applying various
synthesis methods diamonds crystals from nano‐ to micro‐mete
crystal sizes could be grown.
It was shown that the heat treatment of nanodiamonds leads
to gradually transformation of carbon‐to‐carbon bonds sp3 to sp2,
and thus, to carbon onion‐like structure formation.
Adjustment of CVD process parameters allows formation of
quasi two‐dimensional hexagonal diamond platelets with
several micrometers in size. TEM structure analysis revealed
that platelets are consists of stacked (111) atomic planes.
It was demonstrated that needle grown by optimized CVD
possess a perfect undisturbed diamond crystal structure. The
needles have rough surface which consist of high density of
stacking faults and {111} twins.
Dissertations in Forestry and Natural Sciences Number 258 89
5 Conclusions
In this Thesis, experimental analysis of structural
peculiarities of various carbon materials were presented. The
comprehensive analysis of electron microscopy methodology
was performed. Corresponding adjustment of spherical
aberration corrector allowed improvement of TEM instrument
parameters with increase of signal‐to‐noise ratio up to 30%. This
TEM tuning allowed revealing of important peculiarities in
structures of carbon materials, including:
‐ formation of carbon structures with free‐standing isolated
Br atoms in 1‐bromoadamantane functionalized single
walled carbon nanotubes;
‐ formation of ordered compounds of guest molecules of
different types inside single wall carbon nanotubes and
detection their structural transformation during synthesis;
‐ gradual transformation during heat treatment sp3
carbon‐to‐carbon bonds of nanodiamond particles into
sp2 and formation onion‐like carbon structures formation;
‐ obtaining quasi two‐dimensional hexagonal diamond
platelets of micrometer scale by chemical vapor
deposition and revealing their structure consisting of
stacked (111) atomic planes;
‐ determination of structural characteristics of single‐
crystal diamond needles and elicitation of high density
stacking faults and {111} twins in these diamond
crystallites.
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258
ANDREY OREKHOV
ELECTRON MICROSCOPY STUDY OF STRUCTURALPECULIARITIES OF CARBON MATERIALS
PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND
This work presents results of high resolution transmission electron microscopy analysis
of structural peculiarities of some of nanocarbons materials forms. It was
performed the optimization of optical system of aberration corrected transmission electron
microscope to increase of the signal-to-noise ratio. The optimized TEM instruments
were used in this work for structural characterization of the nanodiamonds, two-
dimensional (2D) structures and needle-like diamonds, onion-like nanocarbons and other graphene-based structures, including
composites consisting of linear (1D) CuCl and Hg2Cl2 crystals encapsulated in single-walled carbon nanotubes. Obtained results allowed
appropriate development of production processes for these carbon nanostructures and
understanding of their physical properties.
ANDREY OREKHOV