2008:107 CIV
M A S T E R ' S T H E S I S
High Pressure Study of Double Wall Carbon Nanotubes
Magnus Grennvall
Luleå University of Technology MSc Programmes in Engineering
Engineering Physics
Department of Applied Physics and Mechanical Engineering Division of Physics
Abstract
High pressure Raman studies were performed in the High Pressure Spectroscopy Laboratory at Luleå University of Technology on Double Wall Carbon Nanotubes (DWCNTs). Laser excitation energies used were 1.96 eV and 2.33 eV. High pressure on the sample was
achieved using a Membrane Diamond Anvil Cell (MDAC). Pressure dependence of the tube’s Raman peaks were investigated in the pressure range 0 to approximately 10 GPa. Both radial (RBM) and tangential (G band) modes were investigated during pressure increase. The overall trend of the intensity of the Raman signals is that it decreases when pressure is applied. This behavior is most prominent for the metallic outer tubes. The outer tubes are more affected by pressure than the inner tubes, which are proven by their higher derivative of the Raman peak pressure dependence.
Investigating the metallic outer tubes under pressure reveals that some anomaly in the pressure dependence around 5 GPa occur for both RBM and G band. Results show that the Raman frequencies of those tubes stop shifting to higher frequencies at approximately 5 GPa and start to downshift until they reach a more or less constant value at elevated pressures.
Intensity decrease in this pressure region is also prominent.
In order to polymerize DWCNTs a heating system was designed and manufactured. The design was chosen with respect to high temperature treatment of the sample in a MDAC.
Since the cell becomes very hot, equipment and laboratory personnel have to be protected and temperatures at critical points have to be measured. Stainless steel and an insulating material called Insulfrax were chosen as the main materials since they have poor heat conductive properties.
1. INTRODUCTION ... 1
1.1. Background... 1
1.2. Motivation... 1
1.3. Thesis outline ... 1
2. THEORY... 2
2.1. Carbon based nano structural materials... 2
2.1.1. Hybridization in a carbon atom ... 2
2.1.2. Fullerenes ... 3
2.1.3. Carbon nanotubes ... 4
2.2. Characterization of carbon nanotubes using Raman spectroscopy... 7
2.2.1. RBM- and G band – first order Raman scattering ... 9
2.2.2. D- and G’ band – second order Raman scattering ... 10
2.2.3. Vibrational properties of Double Wall Carbon Nanotubes ... 11
2.2.4. Carbon nanotubes under pressure... 11
3. EXPERIMENTAL EQUIPMENT AND METHODS... 12
3.1. High pressure method... 12
3.1.1. Membrane diamond anvil cell (MDAC) ... 12
3.1.2. The gasket ... 13
3.1.3. Pressure measurement in the MDAC ... 13
3.1.4. Sample loading ... 14
3.2. High pressure, high temperature method ... 15
3.2.1. The heating system... 15
3.3. Raman spectrometer – CRM-200 ... 17
3.4. Experimental details ... 18
4. RESULTS AND DISCUSSION... 20
4.1. Pressure measurement... 20
4.2. Diameters and properties of the tubes in resonance ... 22
4.3. Raman study of high pressure response on DWCNT ... 23
4.3.1. Pressure response of radial breathing mode ... 24
4.3.2. Pressure response of the G band... 25
4.4. Pressure dependence... 26
4.4.1. RBM frequencies – 1.96 eV laser... 26
4.4.2. G band frequencies – 1.96 eV laser... 30
4.4.3. RBM-band frequencies – 2.33 eV laser... 32
4.4.4. G band frequencies – 2.33eV laser... 34
4.4.5. Groups of inner tubes ... 36
4.5. Chirality assignment – (n, m) ... 37
4.5.1. Chirality assignment of the inner tubes ... 37
4.5.2. Chirality assignment of the outer tubes ... 39
5. CONCLUSIONS ... 40
6. FUTURE WORK... 40
7. SUMMARY ... 41
APPENDIX A... 44
APPENDIX B... 50
APPENDIX C... 59
APPENDIX D... 68
APPENDIX E... 70
1. Introduction
1.1. Background
Carbon nanotubes are one of the most studied areas in science today. The tubes that consist of seamlessly wrapped cylinders of graphite became a great spin-off product from the discovery and research of fullerenes (C60). At first there were only theoretical speculations about the existence of carbon nanotubes of dimensions comparable to fullerenes but the pioneering work by Iijima in 1991 stated the existence experimentally.
The existence of carbon nanotubes has great potential due to the extraordinary properties they possess. No other element in the periodic table bonds to itself in an extended network with the strength of the carbon-carbon bond. The special nature of carbon combined with the
molecular perfection of carbon nanotubes endows them with exceptionally high material properties such as electrical and thermal conductivity, strength, stiffness and toughness. Due to their perfection of molecular structure the tubes get close to their theoretical limits in the sense of material properties.
The mechanical stability can be investigated by exposing the tubes to pressure. It has been shown that single wall carbon nanotubes in bundles collapse at ~3 GPa. The introduction of a tube inside another (double wall carbon nanotube) made it possible to protect the inner tubes by a screening effect. That made it possible to go up to even higher pressures without tube failure. Individual tubes withstand higher pressures than the bundled ones.
1.2. Motivation
Double Wall Carbon Nanotubes are produced in bundles. Bundled tubes do not have as extraordinary properties as individual ones due to their mix of various nanotubes with different properties held together by weak van der Waals forces. A polymerization process would link the tubes together by strong bonds creating a stronger carbon nanotube material.
Before polymerization good knowledge about the physical properties of the carbon nanotubes have to be collected, for instance by high pressure experiments.
High pressure studies on double wall carbon nanotubes have been carried out before in the high pressure spectroscopy lab at LTU. In order to get more data on the same kind of experiment another one had to be carried out with some method improvements. Good knowledge about the pressure response of double wall carbon nanotubes is essential when polymerization is the next aim for the research group led by Professor Alexander Soldatov at LTU. The possibility to polymerize double wall carbon nanotubes is granted by heating of the tubes at the same time as they are kept under pressure. Setting up a heating system has to be done before polymerization can be carried out. This work comprises a high pressure
experiment on double wall carbon nanotubes and the manufacturing of a heating system.
1.3. Thesis outline
This thesis starts with a short introduction, followed by a theory part where the reader is introduced to the concept of carbon nanostructures and Raman spectroscopy. Then the experimental equipment is explained as well as the methods. After that the results are presented and discussed and at the end a conclusion and summary part rounds up the thesis.
2. Theory
2.1. Carbon based nano structural materials
Carbon-based materials are unique in many ways. One distinction relates to the many forms that carbon based materials can assume. The graphite phase with strong in-plane trigonal bonding is of great interest since it contributes to the formation of carbon nanotubes. In this section some of the properties of carbon and its allotropes are discussed.
2.1.1. Hybridization in a carbon atom
The carbon atom has many possible configurations of the electronic states, which is known as the hybridization of atomic orbitals. This possibility leads to unique properties of different carbon based materials. In the ground state the electrons in a carbon atom occupy 1s2, 2s2 and 2p2 atomic orbitals. Two out of six electrons, the so called core electrons, are strongly bound in the 1s2 orbital. The other four electrons are called valence electrons and they are more weakly bound to their ground state orbitals 2s2 and 2p2. In the crystalline phase the valence electrons give rise to 2s, 2px, 2py and 2pz orbitals. Since the energy difference between the upper 2p energy levels and the lower 2s level is small compared with the binding energy of the chemical bonds, the electronic wave functions for these four electrons can readily mix with each other (see fig. 1). The carbon atom can thereby enhance the binding energy between itself and neighboring atoms by changing the occupation of the 2s and the three 2p orbitals.
The mixing of the orbitals is called hybridization. The hybridization of interest in carbon is the spn hybridization which corresponds to the mixing of a single 2s electron with one, two or three 2p electrons (n=1, 2, 3) [1].
Figure 1: Here the different orbital energies of carbon in ground state are shown. The energy gap between the core electrons and the valence electrons are large. The energy difference between the 2s and the 2p orbitals a rather small.
re
There are three different kinds of hybridized orbitals that can occur. They are sp, sp2 and sp3 hybridization. Examples of the different kinds are acetylene (sp), graphite (sp2) and diamond (sp3). In graphite one s and two p orbitals undergo hybridization and in diamond one s and
three p do. This hybridization is shown with the new energies in fig. 2. For us the sp2 is of special interest because nanotubes consist of rolled up graphene sheets.
Figure 2: This is the energies of the hybridized orbitals in carbon.
2.1.2. Fullerenes
The C60 fullerenes are named after Richard Buckminster Fuller. He was an American architect who designed the geodesic dome, an almost spherical construction based on a network of circles lying on the surface of a sphere. The fullerenes were synthesized by laser vaporization by Kroto, Smalley and co-workers in 1985 [2]. The 60 carbon atoms in C60 are located at the vertices of a truncated icosahedron where all the carbon sites are equivalent (see fig. 3).
(a) (b) (c)
Figure 3: (a) C60 fullerene (b) C70 fullerene (c) Corannulene
A closer look at the molecular structure of C60 shows that there exist both pentagons and hexagons of carbon on the spherical surface. Every pentagon is surrounded by five hexagons and this pattern builds up the molecule. The pentagon together with its five neighboring hexagons has the form of the corannulene molecule (fig. 3(c)). The double bonds in corannulene are in different positions relative to the C60 because the edge carbons in corannulene are bonded to hydrogen atoms. The C60 molecule has two bond lengths. The shorter is a double bond located at the fusion between two hexagons and the longer is a single
bond located along the pentagonal edge at the fusion of a hexagon and a pentagon. The latter is actually two single C-C bonds [3].
The C60 is not the only product of fullerene synthesis. Larger molecular weight fullerenes are also formed, for instance the rugby ball-shaped C70 (fig. 3(b)). The C70 molecule is highly stable and can be visualized adding a belt of 5 hexagons around the equatorial plane of the C60. Even higher mass fullerenes have been isolated and studied [3].
2.1.3. Carbon nanotubes
A carbon nanotube is a small tube with a diameter of nanometer size and a length of more than one mμ . There exist different types of nanotubes, for instance single wall carbon nanotubes (SWCNT), double wall carbon nanotubes (DWCNT) and multi wall carbon nanotubes (MWCNT).
The first observation of carbon nanotubes was done by Iijima in 1991 [4]. It was carried out using transmission electron microscopy and since Iijima’s work the study of nanotubes has progressed rapidly. Speculations of the existence of carbon nanotubes were discussed earlier but this discovery linked the gap between experimental and theoretical work together.
A single-wall nanotube can be described as a graphene sheet rolled into a cylindrical shape with a diameter of approximately 0.7 - 10.0 nm, though most of the observed single-walled nanotubes have diameters <2nm. There are three different classifications of the nanotube which depends on the orientation of the six-membered carbon ring (hexagon) in the
honeycomb lattice relative to the axis of the nanotube. They are called armchair, zigzag and chiral nanotubes and are shown in fig. 4. It can be seen that the hexagons are not distorted even if the directions of them vary. This provides many possible structures for carbon nanotubes, even though the basic shape of carbon nanotubes is a cylinder. Fig. 4 also shows the terminations of the tubes, or caps as they often are called, and they consist of a hemisphere of a fullerene [1].
Figure 4: Classification of carbon nanotubes:
(a) armchair, (b) zigzag and (c) chiral
The names armchair and zigzag arise from the shape of the cross-sectional ring at the edge of the nanotubes. We shall now take a closer look at the concept of chiral nanotubes.
The chirality is described by the chiral vector Ch. The vector can be expressed by the real space unit vectors â1 and â2 multiplied by real integers.
(
n mmâ nâ
Ch = 1+ 2 ≡ ,
)
(n, m are integers, 0≤ m ≤n) (1)Figure 5: The picture shows unit vectors (â1, â2), chiral vector (Ch), chiral angle (θ ) and the dotted lines symbolize the cross-sectional ring of zigzag and armchair nanotubes.
The chiral angle is defined as the angle between the vectors Ch and â1. Because of the hexagonal symmetry of the honeycomb lattice this angle will have values in the range of
°
≤
≤
° 30
0 θ . θ is the angle the hexagons tilts with respect to the direction of the nanotube axis.
Table 1: Classification of carbon nanotubes by chiral angle and chiral vector.
Type Chiral angle(θ ) Chiral vector (Ch)
Armchair 30° (n,n)
Zigzag 0° (n,0)
Chiral 0°≤θ ≤30° (n,m)
The diameter of the nanotube can be calculated using the chiral vector. The circumferential length, L, is equal to the length of the chiral vector,
h h
h C C
C
L= = ⋅ . (2)
We know from the geometry of the circle that
π
dt = , L (3)
where dt is the diameter of the nanotube.
Since aˆ1⋅aˆ1 =aˆ2⋅aˆ2 =a2 and ˆ 2 ˆ
2 2 1
a a
a ⋅ = , where a is the lattice constant in the honeycomb lattice (a=1.44Å× 3=2.49Å for carbon nanotubes), equation (1) in (2) gives
nm m
n a
L = 2 + 2 + . (4)
Equation (4) in (3) gives us the expression for the diameter,
π
nm m n
dt a + +
= 2 2 . (5)
The inner product of Ch and aˆ1 gives an expression for the chiral angle,
nm m n
m n a
C a C
h h
+ +
= +
= ⋅
2 1 2
1
2 2 ˆ
cosθ ˆ . (6)
The nanotubes can show either metallic or semiconducting behaviour. A general rule to determine if a tube is metallic or semiconducting is to look at its chiral index. If (2n+m) is a multiple of 3 then the tube is metallic, otherwise it is semiconducting [1].
Synthesis of carbon nanotubes
The most common ways of producing carbon nanotubes are:
• Arc-discharge: This method was initially used for producing C60 fullerenes but it turned out to be one of the easiest ways to produce carbon nanotubes as well. In this method two graphite rods are connected to a power supply and placed a few
millimeters apart. When the switch is turned on the discharge between the rods causes the carbon to vaporize producing “soot”. The soot contains carbon nanotubes of various sizes. The greatest problem is that the product consists of a complex mixture of components and therefore requires further purification to separate the tubes from the soot [5].
• Laser vaporization: Here laser pulses are used to vaporize a target of graphite alloy.
This is an effective technique to produce bundles of SWCNTs with a narrow diameter distribution. The target used is a graphite/Co-Ni alloy [1]. The carbon nanotube sample is then produced by vaporizing the alloy at 1200OC in flowing argon, followed by heat treatment in 1000 OC to remove fullerenes [5].
• Chemical Vapour Deposition (CVD): Here a catalyst such as Fe, Ni or Co is placed on a substrate in a furnace held at 1100 OC. A carbon-bearing gas such as methane is added. An energy source, such as plasma or a resistively heated coil, is used to “crack”
the methane molecules into reactive atomic carbon. The carbon diffuses towards the substrate where it will form carbon nanotubes.
• Peapod conversion route: This is a method to produce DWCNTs, which is
interesting because the sample used in this work is produced using this method. Close packed chains of C60 fullerenes is introduced inside a SWCNT that has a diameter range of 1.3-1.4 nm. This is accomplished by the diffusion of C60 molecules inside the tubes from the C60 vapour maintained at 400 OC in a sealed and evacuated glass ampoule. The DWCNTs were then derived from the peapods by heating them at 1200OC in vacuum. The result is a secondary tube grown inside a primary tube [6].
Properties of Carbon nanotubes
There are many unique and useful properties of CNTs. Metallic tubes can have an electrical conductivity that compared to copper is up to six times greater. The thermal conductivity is high as well, up to 6000W/mK [7] in room temperature compared to copper (401 W/mK). The mechanical properties are extraordinary. They have a Young’s modulus that is over 1 TPa which is stiff as diamond and five times greater than steel. The tensile strength has been estimated up to 150 GPa. Those estimations have been made by numerical calculations and experimental tests [8]. The strong covalent C-C bonds contribute to these mechanical properties. These properties are assigned for individual tubes.
2.2. Characterization of carbon nanotubes using Raman spectroscopy
The Raman effect was discovered by sir Chandrasekhara Raman in 1928. It is an interaction process of light with matter in which a vibrational quantum is excited or annihilated. The excitation process is called Stokes Raman scattering and the annihilation Anti-Stokes Raman scattering. The Raman technique is the study of the low energy modes of enhanced vibration and rotation which occur when the sample is illuminated by a laser.
The actual process takes place when a photon interacts with a molecule and puts it into an excited state. When the molecule relaxes it sends out light with different wavelength for each material. Most of the photons is elastically scattered but a small fraction (approximately 1 in 106) puts the molecule in a virtual excited state (fig. 6). The light backscattered has three different kinds of energy. If the final energy of the molecule is the same as the initial the spectral line is called Rayleigh which most of the scattered light give rise to. If the final state is higher than the initial it is called Stokes and these scattered photons will have less energy than the incident light or the Rayleigh peak. The third is the Anti-Stokes which occurs if the molecule already is in a higher energy state when struck by the incident photon. Scattered light of a higher energy level will then occur. If a spectrum of the scattered light is recorded the Stokes peak will be more intense since most of the molecules are in ground state.
Figure 6: Energy diagram showing the different types of Raman scattering.
Initial Final Virtual
Rayleigh
Excitation Energy
Stokes
Excitation Energy
Excitation Energy
Anti-stokes Energy
A typical Raman spectrum is symmetric to the Rayleigh line (zero on the x-axis) as shown in fig. 7. The Rayleigh line is usually filtered so we can resolve the other peaks, which is the case in this figure. Every single spectrum is unique for each specific material. If the physical conditions change the spectrum changes but the spectrum is still unique for each material.
Figure 7: A t f the peaks and t
axis the relative wavenumbers.
ypical Raman spectrum. The y-axis shows the intensity o he x-
As mentioned above the Raman signal is weak. But if the energy of the laser used to excite the material matches the energy between optically allowed electronic transitions in the
material, the scattering efficiency gets larger. This is called resonance Raman scattering and it depends on the density of electronic states (DOS) available for the optical transitions. The sharp peaks on the left in fig. 8 (a), (b) and (c) where the DOS intensity is very large is called van Hove singularities (vHS). The carbon nanotube has well defined electronic energy levels at these vHS. If the energy of the laser that we use to excite the nanotube is equal to the energy separation between vHS in the valence and conduction bands we will get an observable Raman signal [9]. This means that if we have a sample that includes nanotubes with different physical properties we see the spectrum of some specific tubes with one laser and other tubes with different laser energies. The Kataura plot in fig. 8 is a useful tool to investigate what kind of tubes that are probed by Raman spectroscopy. If we know in what diameter range the tubes in the sample have we can follow the plot vertically until it coincides with the energy of the laser (y-axis). Then it is possible to determine whether it is metallic or semiconducting tubes that are in resonance. It is also possible to assign the chirality vector of the tubes since the dots in the Kataura plot correspond to different chiralities.
Figure 8: DOS for (a) armchair (10, 10) SWNT, (b) chiral (11, 9) SWNT and (c) zigzag (22, 0). (d) shows a so called Kataura plot. This plot tells us the transition energies of the
nanotubes as a function of the tube diameter. Open circles corresponds to metallic nanotubes and cross symbols to semiconducting.
Raman spectroscopy is a quick, non-destructive and a powerful tool for material
characterization. The Raman spectrum from carbon nanotubes is rich in information about the structure and properties of the tubes. The most important features of the nanotube spectrum and what information it gives us are described below.
2.2.1. RBM- and G band – first order Raman scattering
If we illuminate a carbon nanotube sample by a laser the tubes will start to emit a Raman signal. The vibrations in a carbon nanotube sample give rise to several Raman modes (bands) that can be recorded in a spectrum.
Figure 9: A typical Raman spectrum of carbon nanotubes.
RBM is a short for Radial Breathing Mode and corresponds to the atomic vibrations of the carbon atoms in the radial direction, as if the tube were breathing (fig. 9). We will not be able to see the peaks of all the tubes, only those that are in resonance with the laser used. The
position of the peaks depends on the diameter of the tubes. We will find the tubes with a larger diameter at lower relative wavenumbers due to a lower frequency and the ones with a smaller diameter at higher relative wavenumber. The RBM appears between 100 – 500 rel.
cm-1. Since the RBM is diameter dependent, scientists have come up with a relation based upon experimental data.
d B A
t
RBM = +
ω ;dt =diameter (7)
A and B are determined experimentally. For typical SWCNT bundles in the diameter range nm, A=234cm
2 . 0 5 . 1 ±
t =
d -1 and B=10cm-1 has been found where B is an upshift of the RBM frequency assigned to the tube-tube interaction [10]. A more recent study claims that B=14cm-1 [11]. For isolated SWNTs on an oxidized Si substrate A=248 cm-1 and B=0 cm-1 has been found [12]. For diameters less than 1 nm equation (7) is not expected to hold due to nanotube lattice distortions leading to chirality dependence of the RBM frequency [13].
The most prominent peak in a Raman spectrum of carbon nanotubes is the G band. The G comes from graphite and the band appears because of tangential vibrations in the graphite sheet that the tube is rolled up from. The G band is a multi-peak feature but the most intense of them are called the G+ (around 1590 rel. cm-1) and the G- (around 1570 rel. cm-1). The G+ is for vibrations along the tube axis and the G- for the circumferential direction. The lower frequency of G- is caused by the curvature of the nanotube which softens the tangential vibration in the circumferential direction. The G band can tell us something about what kind of tubes we are dealing with in the sense of metallic or semiconducting tubes. The shape of the G- is broadened for metallic nanotubes compared with the narrow Lorenzian lineshape for semiconducting. The G- for the metallic tubes is usually fit using a Breit-Wigner-Fano (BWF) lineshape. The BWF is described by the relation
( )
[ ]
( )
[ ]
22
0 1 /
/ ) 1
( + − Γ
Γ
−
= +
BWF BWF q I
I ω ω
ω
ω ω (8)
where 1/q represents the asymmetry of the lineshape. ωBWF, I0 and Γ are fitting parameters of frequency, intensity and broadening factor.
2.2.2. D- and G’ band – second order Raman scattering
The D-band as shown in fig. 9 is a disorder induced band and appears around 1350 rel. cm-1. The D-band also have a second harmonic at approximately twice its frequency, 2700 rel. cm-1, called the G’ band. Since the D-band can tell us something about the defects on the surface of the nanotube we can study it before and after special treatment of the sample, heat treatment for instance. If more defects are induced to the tubes then the intensity of the D-band should be different. The quality of a sample can be studied by comparing the ratio of D- to G band intensity or D- to G’ band intensity [14].
2.2.3. Vibrational properties of Double Wall Carbon Nanotubes
The modes discussed above are similar in DWCNTs. The greatest difference is in the RBM region where it is split into two parts shown in fig. 10. Equation (7) tells us that the peaks at the lower frequency corresponds to the outer tubes that have a larger diameter and the higher frequency RBM peaks to the inner tubes with a smaller diameter.
Figure 10: Raman spectrum from DWCNT excited by a red laser (1.96eV). The inset window shows the RBM-band.
In the G band region the peaks from inner and outer shells mask each other so they can not be resolved for different diameters. The G- is broadened due to the metallic tubes that are in resonance with the red laser. If only semiconducting tubes were in resonance the G band would be narrower as expected.
2.2.4. Carbon nanotubes under pressure
Exposing a solid to pressure is the ideal tool to tune the bonding properties of it. The structural variations that appear affect the material properties. If carbon nanotubes are put under pressure their vibrational characteristics change. The behaviour of the Raman-active modes in carbon nanotubes under pressure provides information about their structural stability [15, 16]. This work will study the continuous behaviour of the RBM- and G band at elevated pressure.
Considering the RBM it shifts towards higher frequency and decreases in intensity at elevated pressure. This is due to pressure induced distortions that may change the DOS. Nanotubes of larger diameter are more affected than the tubes of smaller diameter [16].
The tangential G band also shifts to a higher frequency at elevated pressure. The effect is very interesting in studies of DWCNTs. As mentioned above the G band for the inner and outer tubes is masking each other, but if they are exposed to pressure the bands start to split. The G band of the outer tubes will then be visual, shifted to the right of the main G band peak.
3. Experimental equipment and methods
3.1. High pressure method
The physical properties of materials depend strongly on structure and interatomic distances.
Pressure can vary these distances which mean that we can study relationships between structure and properties of the material. More knowledge of materials under high pressure gives us more understanding of underlying phenomena and helps us improve designs of applied materials [17].
In the high pressure spectroscopy lab at LTU, where this work was carried out, pressure experiments can be carried out using a membrane diamond anvil cell. Samples under pressure can be studied using confocal spectroscopy equipment.
3.1.1. Membrane diamond anvil cell (MDAC)
The basic principle of a diamond anvil cell is very simple. A sample is placed between the flat parallel faces of two opposed diamond anvils. A force is applied to push the two anvils
together generating pressure in the sample chamber (see fig. 11). The chamber usually consists of a pressure medium (liquid) to generate hydrostatic pressure. The metal gasket confines the sample and the liquid between the anvils [18]. Since the sample chamber usually is only 200 mμ wide one obvious disadvantage is that only small samples can be studied.
Pushing the diamonds together is not a trivial thing, but the MDAC uses a membrane that push one of the diamonds attached to a piston. The membrane itself is connected to a pressure control box which can control the pressure applied on the sample by increments as small as 0.1 GPa. It is also possible to tighten four screws manually to apply pressure but that method makes it hard taking small pressure steps.
Figure 11: Opposed diamond anvil configuration, with a metal gasket for sample confinement in a pressure medium.
Using diamonds have many advantages. One obvious advantage is the hardness of the material, known as the hardest on earth, which makes it suitable for extreme conditions. It is also transparent to a wide range of electromagnetic radiation like visible light, x-ray, IR etc.
This brings possibilities to study the sample optically by microscope, spectroscope (like Raman) or different diffraction techniques (like x-ray diffraction). The cell used in this work was a MDAC (M7G) manufactured by Diacell Products Ltd, UK. The cell body is made of stainless steel and the two anvils rests on a tungsten-carbide support in the cell. The culet
diameter of the diamonds is 450 mμ . Each diamond will be referred to at which side of the cell it is mounted, as cylinder side and piston side.
Figure 12: Cross section of the M7G – 1:
Anvil support ring made of tungsten- carbide, 2: Piston, 3: Membrane pressure ring, 4: Gas membrane assembly, 5:
Membrane retaining ring, 6: Piston holding screws.
3.1.2. The gasket
The gasket used is made of hardened stainless steel. It is desirable that the sample chamber does not deform and kept in the middle of the culets while the pressure is increased as in fig.
11. Since the culets are rather small and the gasket metal will deform when a force is applied, a technique called preindentation is preferred before sample chamber drilling and sample loading. The preindentation makes a deep mark into the gasket which brings the opportunity to choose the preferred thickness of the gasket which will be the same as the distance between the two diamond culets. By applying the same load in the preindentation as in the forthcoming experiment assures that the correct gasket thickness is chosen. If a preindentation is made it is also easier centring the actual chamber when drilling the hole since you know where the culets will face the gasket. Another advantage is that a preindented gasket provides a thick belt of metal supporting the material between the culets and also supporting the flanks of the diamonds [19, 20].
The sample chamber is drilled in the middle of the preindent using an Electronic Discharge Machine, here a Betsa MH20M, which can drill holes very well centred with a precision of a few mμ . It erodes a hole in the gasket by electric discharges between the gasket and the drill’s electrode made of tungsten wire. The dimension of the chamber used in this work was 200 mμ wide and approximately 55 mμ thick. The width of the hole should be somewhere in the range of 1/3 to 2/5 of the culet diameter to ensure a safe high pressure run. If the hole starts to expand means that the diamonds starts to approach each other, in other words – gasket failure [19].
3.1.3. Pressure measurement in the MDAC
The pressure in the sample chamber can be measured using the ruby fluorescence method introduced by Forman et al. (1972) [21]. The Cr3+-doped Al2O3 (ruby) emits light of certain wavelengths when excited by a light source. If this fluorescent light is collected in a
spectrometer two prominent lines show, called R1 and R2. These lines shift to a higher wavelength linearly with hydrostatic pressure which makes it possible to determine the pressure in the chamber, just by recording the ruby spectrum. Equation (9) [22] generates the pressure in GPa.
( )
[
/ 0 −1]
= B
B
P A λ λ (9)
where λ is the measured wavelength of the ruby R1 line, λ0 =694.24 nm is the zero pressure value at 298 K, and A=1904 and B=5 are the least-squares-fit parameters. The R1 line is shown in fig. 13.
Figure 13: Ruby spectra recorded at different pressures in the MDAC. The right peak is the R1 line which is used for pressure calculation.
Wavelength
3.1.4. Sample loading
Loading a sample in the chamber which is only 200 mμ can be tricky. It is very important to keep everything as clean as possible so the sample chamber is not contaminated with dirt that can interfere with the desired spectrum of the sample. The sample studied and loaded in this work was DWCNTs synthesized by Bandow’s procedure described in section 2.1.3. The loading procedure was as follows:
• In order to get decent ruby signal small ruby grains (~2-3 mμ ) were placed on each diamond culet. The grains were dispersed uniformly over the culet surface in order to measure the pressure at different spots in the sample chamber.
• The preindented and drilled gasket is then placed on the diamond culet on the cylinder side of the MDAC. In order to work more safely without risking that the gasket would fall off the culet, it was glued at the ends to the cell using epoxy glue. When the epoxy was dry the gasket stayed in place and the loading could continue.
• At this step the sample was placed in the sample chamber. The small DWCNT sample used was less than 100 mμ in diameter.
• Now the compressing media will be added before closing the MDAC. The media transmits the pressure on the sample and the one used is a 4:1 (volume ratio)
methanol-ethanol mixture which retains its hydrostaticity up to ~10 GPa [20]. The alcohol mixture tends to evaporate fast in room temperature. Before adding it to the chamber both the media and the cell was kept in a refrigerator for a few minutes to prevent that.
• Closing the cell is a sensitive operation and was done under a microscope to assure that the sample was kept in the chamber, the pressure media did not evaporate completely and the diamond culet on the piston side approached and closed the sample chamber smoothly. An incautious closing may cause the work to be redone.
• The last step is to secure the membrane to the cell with the membrane retaining ring.
When the loading is complete the MDAC is placed under the CRM-200 Raman Spectrometer (explained further down) and connected to the pressure control box.
3.2. High pressure, high temperature method
The MDAC from Diacell is also equipped with a resistive heater which can be placed around the diamond anvils as shown in fig.14.
Diamond anvil Heater
Figure14: The MDAC with the resistive heater.
The heater is supposed to heat the sample so studies can be carried out with both high pressure and high temperature. It is designed to heat the 10 mm metal gasket used in high pressure experiments by thermal conduction. The gasket fits into a gasket holder that is a part of the heater assembly. If a power supply (DC supply) that can deliver 8 ampere at 20 volts is connected, the heater generates about 100 watts power. Under these conditions the sample achieves a temperature of 1000OC. If the sample is heated up to this temperature the exterior of the cell reaches a temperature of 400OC [23].
Adding heat to the sample could give some interesting results in the sense of Raman peaks due to polymerization of our samples.
3.2.1. The heating system
In order to run the MDAC with heating safely a heating system were manufactured. Some kind of insulating box had to be manufactured to protect users and the CRM-200 equipment from the generated heat flow. To build it in a proper way some limitations were identified as follows.
• The working distance (WD) of the objective (Olympus SLM PL 20x) is 21 mm (fig.
15). This distance resulted in a tight fit of the box’s top plate between the MDAC and the objective. The objective is recommended by the manufacturer to be operated in the temperature range 0-40OC which means that it has to be well shielded from heat
exposure. Another challenge was that it has to “see” the sample visually to be able to transmit and collect light from the sample chamber.
• The piezoelectric table can withstand a weight force of 50N, so the heating system must not have a mass over 5 kg. It must also be isolated from high temperatures.
• The diamond had to be protected from oxidization at elevated temperatures.
• The surfaces between the piston and the cylinder in the MDAC have to be protected due to oxidization at elevated temperatures. Otherwise the piston might get stuck.
• The users must be protected so they do not get in contact with any hot surfaces.
A sketch of the design is shown in fig. 15. Some details are listed below.
• We needed a poor conductor as the main material but still rigid to maintain good experimental conditions. Stainless steel was chosen since it fulfils those demands and is rather cheap and easy to find on the market. The thermal conductivity coefficient for stainless steel is 16 W/mK at 25OK compared to iron and copper which has 82 W/mK and 400 W/mK [24]. The steel was used for the bottom- and top plates as well as the walls. All the screws used to mount the system were made of stainless steel too.
• A hole was drilled in the top plate for the objective to “see” the sample. To protect it from heat two Mica windows were fastened on both sides of the hole. A pocket of air is left between them as an isolator (thermal conductivity air: 0.026 W/mK).
• The same idea of air as an insulator was used to protect the piezoelectric table.
Distance rings made of steel kept the upper and the lower bottom plates apart. Another advantage of this construction is that the screws that go through the upper bottom plate are not in contact with the table.
• The walls were made of stainless steel sheets with an insulating material in between.
This material is called Insulfrax which is a registered product of the Unifrax Corporation and has a thermal conductivity coefficient of 0.11 W/mK at 600OC.
• In order to transport heat away from the system the box is not closed. As shown in fig.
15 it has two open ends. The idea is to use forced convection by a fan at one end. The room tempered air will flush the surface of the MDAC as well as the interior of the box, transporting heat outwards at the other end.
• The diamonds will be protected from oxidizing by argon gas. The gas will be flushed through capillaries into the MDAC creating a noble gas atmosphere in the cell.
• To prevent the piston from getting stuck a dry lubricant can be used. There were three candidates for this. Graphite, molybdenumdisulfid (MoS2, or nickname Moly) and Boronnitride (BN). Graphite oxidizes in air around 380-400 OC, Moly at 450OC and BN at approximately 1000OC. The lubricants functions better in the absence of air and in an argon environment the service temperatures increase drastically (Graphite:
3000OC, Moly: 1300OC and BN: approx. 2300OC). The choice depends on which temperature range the sample will be heated to.
• Temperatures must be measured at the objective, the piezoelectric table, the MDAC surface and on the diamond (this is more or less the same temperature that the sample has). They are measured by K-type thermocouples which are good in oxidizing atmosphere and have a service range of -200-1260OC [25].
Figure 15: The heating system with some of its components.
3.3. Raman spectrometer – CRM-200
The CRM-200 made by Witek uses confocal microscopy which brings high resolution to our results. The setup is briefly described below. The numbers refer to fig. 16.
The process starts when the laser (12) is turned on. In this setup there is two different lasers to choose between: 532 nm green laser (2.33eV) or 632.8 nm red laser (1.96 eV). The laser light is collected at a coupler (13) which is connected to a single mode fibre (14) connected to the microscope at (15). The lens (16) creates a parallel light and a dichroic mirror (7) reflects the light through the objective (4) which focuses it on the sample (5). The sample is placed on a piezoelectric table (6) that makes it possible to scan an area of the sample. The emission lines of the excited sample are reflected back through the mirror (7). A Notch-filter (8) filters the laser wavelength and let other wavelengths pass through. The light is focused by a lens (9), and collected by a confocal coupler (11). The light goes through a multimode fibre (19) into a triple-grating spectrometer. A rotating grating (20) inside the spectrometer gives the
opportunity to choose resolution of measurements. In this instrument one can choose between 150, 600 and 1800 grooves/mm. An adjustable mirror (21) sends the light to either a CCD- camera (23) or a photon counting APD-camera (22) that collects the photons emitted from the sample. To be able to focus the laser beam on the sample a normal lamp (1) is used to give an optical focus. The lamp light is reflected at the mirrors (3) and (10) to give an image that is reflected into a camera (17). It is then possible to focus on the sample while actually looking at an image of the sample.
6 5
4 3 1
12
13
14
15 16
7 8 9
10
17 11
20 19 23
22
2 21
Figure 16: A schematic sketch of the Raman spectrometer CRM-200.
The CRM-200 has several options to record a spectrum. The ones used in this work are listed below.
• Single spectrum – Records a Raman spectrum at a selected spot.
• Fast image spectrum – The APD collects and counts photons of a specific wavelength.
This option is for instance a powerful tool if we search for spots of ruby. It maps the intensities tuned to a specific wavelength.
• Spectral imaging – Acquires spectra collected from each point in a scan area. The map generated can be filtered so you can find areas that emit specific wavelengths.
3.4. Experimental details
A high pressure experiment was carried out on Double Wall Carbon Nanotubes (DWCNT) at room temperature.
Excitation lasers: 532 nm (2.33 eV, green) and 632.8 nm (1.96 eV, red). The laser power used were 4.0 mW for the red and 4.5mW for the green which corresponds to a power density of approximately 2.26 kW/cm2 and 2.55 kW/cm2 respectively focused on the sample. The spot size, with the 20x objective which was used, on the sample is ~15 mμ . At the last pressure steps the power had to be increased to get a decent signal (8mW corresponding to
~4.5 kW/ cm2 for the red laser).
Sample: DWCNT grown from C60-peapod conversion.
Gasket: Stainless steel with a diameter of 10 mm and a thickness of 0.25 mm. Preindent thickness ~55 mμ , sample chamber diameter ~200 mμ .
Pressure media: 4:1 methanol-ethanol mixture.
Preparation: The loaded MDAC was mounted on the piezoelectric table under the CRM200 and a fast image spectrum told us where the best signals of the ruby grains were. Three different ruby spots were picked and named A, B and C. Three different single spectra of the spots were taken for each excitation laser. The ruby signal gave us the initial pressure.
Run of the experiment:
Pressure increase:
When running the experiment each pressure step was followed by a procedure that returned after each pressure step. The first measurement procedure was done on the initial pressure.
Our aim was to increase the pressure in steps of 0.5 GPa. Both lasers were used up to 3.4 GPa then only the red one. Each step is described below.
1. Use focus spectra on one ruby that has the most stable signal. Increase membrane pressure until desirable pressure in the sample chamber is achieved.
2. Optical image of the gasket hole. Measure the size of the chamber (gasket hole diameter).
3. Record pressure distribution of ruby A, B and C.
4. Record spectra of sample in the order of 600 grating, RBM (1800 grating) and G band (1800 grating).
5. Check ruby A for pressure change.
6. Next pressure step or change laser.
The experiment was carried out up to a pressure of about 11.4 GPa. The ruby lines at different spots turned out to differ at these higher levels so the exact pressure is uncertain. The sample chamber started to deform (gasket hole increased) at approximately 8 GPa. At this point also the ruby started to give different pressure results which indicate a beginning of gasket failure.
This trend might also indicate the beginning of nonhydrostatic pressure in the sample chamber especially if the ruby peaks are broadened.
4. Results and discussion
The results from the latest high pressure experiment on DWCNTs in the high pressure Raman lab at LTU will be presented. Those results are complementary to another experiment carried out earlier on the same kind of sample with the same equipment [26].
4.1. Pressure measurement
The pressures for each pressure step were measured using the pressure response from ruby (see section 3.1.3.). In order to receive a reliable value for the pressure in the sample chamber three different spots, A, B and C, were picked. The pressure on the ruby spot closest to the sample spot, which were probed for a Raman spectrum of DWCNTs, was chosen. The spots are shown in fig. 18.
Figure 17: Image of the DWCNT-sample in the sample chamber. The black areas are the DWCNTs.
Figure 18: Fast image scan of ruby with excitation laser 1.96 eV on the left. The ruby spots picked for pressure calculation is called A, B and C. The spots correspond to the locations in the image of the sample chamber on the right. They are marked with white circles. The green area represents the area where the spectrums of DWCNTs were recorded.
The pressures on the different spots were more or less the same up to approximately 8 GPa when they start to differ. A comparison between spot A and B is made in fig. 19 and 20. The trend is that spot B experience more pressure than A when the load is increased on the piston.
The difference at the end is up to 2 GPa.
10 8
Figure 19: The pressure on Ruby A is plotted against itself giving the straight line in the graph. The other line is ruby A plotted against ruby B to visualize the difference in pressures as we increase the load on the piston.
Figure 20: This graph shows the deviation in pressure between ruby B and A. The pressure on ruby A is plotted against the difference in pressure between ruby B and A.
A study of the gasket shape versus pressure was also made. An image of the sample chamber was taken after each pressure step and the diameter was measured in x- and y-direction of the hole. Fig. 21 shows that the hole starts to increase slightly around 7 GPa and then more rapidly after 8 GPa. The fact that the hole starts to increase means that the diamonds start to approach each other and the pressure media push the gasket material aside.
The pressure differences are explained below. As we can see in fig. 18, ruby B sits on top of the sample on the thickest sample part and ruby A is on the edge of the sample where it is supposed to the a little bit thinner. When the anvil culets approach each other ruby B is
0 2 4 6 8 10 12
0 2 4 6 12
14 RubyA
RubyB
Pr
Pressure on RubyA (GPa)
essure (GPa)
0 2 4 6 8 10 12
-0,5 0,0 0,5 1,0 1,5 2,0
Difference RubyB-RubyA (GPa)
Pressure on RubyA (GPa) RubyB-RubyA
squeezed between the culet and the sample and ruby B experience more pressure due to this.
Ruby A on the other hand is not squeezed and experience less pressure.
Comparing these two analyses of pressure and gasket indicates that something starts to
happen around 8 GPa. The pressures used to analyse the experimental data were those on ruby A since it is closest to the sample region probed and suffers less squeezing effects than B.
Ruby C located at another edge of the sample follows more or less the same pressure trend as ruby A which support this conclusion.
0 2 4 6 8 10 12
180 185 190 195 200 205 210 215 220 225 230 235 240
Gasket diameter (micrometer)
Pressure (GPa)
x-axis y-axis
Figure 21: The graph shows the diameters of the gasket in x- and y-direction at different pressures. The pressures are calculated from the ruby A spot.
4.2. Diameters and properties of the tubes in resonance
It is possible to determine the diameters of the tubes in resonance using equation (7). If the red laser (1.96 eV) is used at ambient pressure the RBM-peaks, as we shall see later on, for the outer tubes range between ~165 and ~190 rel. cm-1. The inner tubes range between ~285 and ~360 rel. cm-1. Equation (7) has been applied previously for bundled SWCNTs and as we are dealing with bundled DWCNTs here we get dt =1.33 – 1.55 nm for the outer tubes and dt
=0.68 – 0.86 for the inner tubes using this relation. The same analysis was done using the green laser (2.33 eV). The values obtained for the outer tubes were 1.30 – 1.55 nm and for the inner 0.62 – 0.91 which is more or less the same as for the red laser.
We can now use the Kataura plot to determine whether the tubes in resonance with the
different lasers are metallic or semiconducting. This is done by checking the diameter range at the energy of the laser. The tubes within that range and around the energyline are in resonance.
This is shown in fig. 22. As we can see only semiconducting tubes are in resonance with the green laser (2.33 eV) for both the inner and outer tubes. For the red laser (1.96 eV) some of the outer tubes are metallic ones but the inner in resonance are semiconducting.
1.96eV
Outer 165 – 190 rel. cm-1 dt=1.33 – 1.55 nm
Inner
285 – 360 rel. cm-1 dt=0.68 – 0.86 nm
diameter d
cm B
nm cm A
d B A
t
t RBM
=
=
=
+
=
−
− 1
1
14 234 ω
Black solid symbols are semiconducting tubes Red open symbols are metallic tubes
in out
Figure 22: The Kataura plot showing what kind of tubes that is in resonance with the red laser (1.96 eV). The diameters are calculated to the right using equation (7).
4.3. Raman study of high pressure response on DWCNT
First a Raman spectrum was recorded from the DWCNT sample at ambient pressure (1 bar) outside the MDAC using a 1.96 eV laser. Then the sample was placed into the MDAC and put under pressure. After each pressure step a new spectrum was recorded. The final pressure step exceeded 11 GPa. The spectrum at ambient pressure (1 bar) is shown in fig. 23.
0 500 1000 1500 2000 2500
0 200 400 600 800 1000
Intensity (a.u.)
Wavenumber (rel. cm-1)
Figure 23: Raman spectrum of DWCNT recorded at ambient
pressure outside the MDAC using the 600 grating and 1.96 eV laser.
4.3.1. Pressure response of radial breathing mode
In order to analyse the RBM-band the 1800 grating in the CRM 200 is used. Fig. 24 shows the response of the RBM during pressure increase. The intensity of the peaks is attenuated when the sample is exposed to pressure. Although the peaks in fig. 24 are scaled to the largest peak we clearly see that the signal from the outer tubes weakens and finally disappears. The
obvious trend is also that the peaks shift to the right and that the peaks are slightly broadened.
The weakening and broadening of the outer tubes RBMs is similar to that encountered for the RBMs in bundled SWCNTs, where the applied pressure causes the distortion of the tube cross-section through the van der Waals intertube interactions within a bundle [27]. The intensity loss can also depend on hexagonal distortion of the tubes and changes in the DOS [16]. The inner tubes are protected by the outer and are not as much affected as the outer tubes.
Step5, 4.21GPa
Step3, 3.50GPa
0 100 200 300 400 500
Wavenumber (rel. cm-1) Amb. pressure, 1bar
Step1, 1.92GPa Step6, 5.16GPa
0 100 200 300 400 500
Downstroke, 1.7GPa
In tens it y
Figure 24: Raman spectra of the RBM recorded at different pressures with 1.96 eV laser. The peaks of the outer tubes are on the left and the inner tubes on the right. The graphs are scaled to the most intense peak in the RBM for the inner tubes. The uppermost graph shows the spectrum after relaxation.
4.3.2. Pressure response of the G band
The G band as well as the RBM-band upshifts towards higher frequencies when pressure is introduced. A bulged peak can be spotted to the right of the main peak in fig. 25 at 5.16 GPa which is the G+ peak for the outer tubes. The main peak, which corresponds to the G+ of the inner tubes, masks the G+ of the outer at lower pressures. In general the higher frequencies correspond to the outer tubes and the lower frequencies to the inner. The broadened peak to the left of the main peak is due to the Breit-Wigner-Fano (BWF) shaped peak of the metallic outer tubes in resonance. This peak weakens as the pressure is increased. The splitting of the G band is due to lower pressure coefficients of the inner tubes since they are protected by the outer tubes.
In te n s ity
Step10, 7.02GPa
Step1, 1.92GPa 1400 1500 1600 1700 1800
Downstroke, 1,7GPa
Step17, 11.43GPa
Step6, 5.16GPa
1400 1500 1600 1700 1800 Wavenumber (rel. cm-1)
Ambient pressure, 1bar
Figure 25: Raman spectra of the G band recorded at different pressures with 1.96 eV laser. The G+ of the inner and outer tubes are masking each other at low pressure but splits at elevated pressure.
The BWF shaped peak to the left of the main peak
represents the metallic outer tubes G- component. The peaks that appear in some graphs at around 1400 rel.
cm-1come from ruby
fluorescence. The graphs are scaled to the most intense peak.
The G band shows a similar but a more obvious response when the sample is excited with 2.33 eV laser. In this case no metallic tubes are in resonance and a clear splitting of the G band is observed (fig.26). The main peak observed at ambient pressure is the G+ component that is split in two while increasing the pressure. The rightmost peak is the G+ of the outer tubes that is more affected by the pressure than the leftmost peak representing the G+ of the inner tubes due to pressure screening [31]. The G- components shares the region to the left of the main peaks.
Step1, 1.92GPa
1400 1500 1600 1700
Step3, 3.41GPa
1400 1500 1600 1700
Wavenumber (rel. cm-1) Ambient pressure, 1bar
In te n s it y
Figure 26: Raman spectra of the G band recorded at different pressures with 2.33 eV laser.
The G+ of the inner and outer tubes are split in two while increasing the pressure. The graphs are scaled to the most intense peak.
4.4. Pressure dependence
The high pressure experiment was carried out using two different lasers, red (1.96 eV) and green (2.33 eV). The results will be presented in the following sections. The spectrum of the bands for different pressure steps is analyzed using software called Peakfit (Jandel scientific software). Peakfit offers the possibility to use the Gaussian deconvolution method to identify peaks in the spectrum recorded. The fittings of peaks are presented in the Appendix section of this thesis. Increasing the pressure smoothly in small pressure steps ensures that we always follow the same peaks.
4.4.1. RBM frequencies – 1.96 eV laser
When analysing the RBM frequencies the inner and outer tubes were treated separately by the Gaussian deconvolution method in order to get as accurate results as possible. The line shapes of the peaks are Lorentzian. The outer tubes have a Full Width of Half Maximum (FWHM) of
about ~10-15 cm-1 and the inner tubes have a FWHM of about ~5-10cm-1 at ambient pressure, slightly increasing with increasing pressure.
Outer tubes 2
Seven peaks were followed during pressure increase and are shown at ambient pressure in fig.
27. It was possible to follow the same peaks as the pressure steps were kept small. Raman peaks could not be resolved and analyzed properly at pressures above ~7 GPa due to intensity attenuation. The fits are presented in Appendix A.
DWCNT_1.96eV_1mW_amb_1bar
Pk=Lorentz Amp 7 Peaks r^2=0.993917 SE=0.630345 F=1421.61
165.98
193.22 175.12 188.08
182.33
170.43
196.92
100 150 200 250
Wavenumber (rel. cm-1)
-5 0 5 10 15 20 25
Intensity (a.u.)
-5 0 5 10 15 20 25
Intensity (a.u.)
Figure 27: Gaussian deconvolution of DWCNT RBM peaks for the outer tubes, at ambient pressure (1 bar) outside the MDAC excited by 1.96 eV laser.
The plot in fig. 28 shows the pressure dependence of the outer tubes during pressure increase.
They show a linear behaviour up to approximately 5.2 GPa then it seems like their frequency drop and maintain more or less at a constant value. The intensity of the peaks decreases dramatically around 5 GPa as well, which brings more uncertainty to the peak positions.
Although we can conclude that some kind of transition of the pressure dependence occurs at this pressure range. A sublinear behaviour is also shown by Arvanitidis et al. [28] who also states that this trend is more pronounced for the metallic tubes. The error bars shows the uncertainties due to peakfitting and pressure calculation.
0 1 2 3 4 5 6 7 8 160
170 180 190 200 210 220 230 240
Out7 Out6Out5
Out4 Out3
Out2
Wavenumber (rel cm-1 )
Pressure (GPa) Out1
Figure 28: Pressure dependence of the RBM Raman modes for the outer tubes excited with 1.96 eV laser. The data corresponds to pressure increase. The linear fits correspond to values up to 5.16 GPa.
An evaluation of the pressure derivatives were made by fitting the data points to a linear fit up to 5.16 GPa. The values are listed in table 2.
Table 2: Pressure coefficients for the RBM components of the outer tubes using the 1.96 eV laser.
Parabolic fitting
RBM peak Frequency at Linear fitting
1 bar from linear fit
RBM ∂P
∂ω / P (cm
RBM ∂
∂ω / (cm
2 2 RBM / P∂
∂ ω
G (cm
ω (cm-1) -1 -1 2 -1/GPa)
/GPa) /GPa )
Out1 165.7 - - 7.00
Out2 170.4 - - 7.40
Out3 175.5 - - 7.62
Out 4 182.7 - - 7.43
Out5 188.4 - - 7.52
Out6 194.2 - - 7.61
Out7 198.3 - - 8.40
Inner tubes
8 of the inner tubes were followed during pressure increase. The less intense peaks and the ones at the edges of the main peaks were hard to follow due to their sensitivity to baseline subtraction. All of the fits for each pressure step is presented in Appendix B.
