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MAIN TOPICS OF THE PROJECT
 NANOTUBE
STRUCTURE
The carbon nanotubes have a screw symmetry characterized
generally by two screw operations. The screw symmetry of the nanotubes allows
one to use only four structural parameters in the structural relaxation. Read
more …
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 ELECTRONIC
STRUCTURE
The electronic structure of any nanotube can be derived
from that of graphene by use of the zone-folding method. This method suffers the
severe drawback of not being able to predict the electronic wave functions.
The calculations of the electronic structure for the relaxed nanotube can
efficiently be performed for any observable nanotube only if the screw
symmetry is accounted for. An example: a symmetry-adapted
non-orthogonal tight-binding model (NTB model). Read more …
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 OPTICAL ABSORPTION
The optical absorption is characterized by the dielectric
function. It
depends on the effective mass of
the transition
and the electron-photon matrix element. For nanotubes, it has
sharp spikes at the energies of the optical transitions. Since Raman
scattering of light in nanotubes is essentially resonant, the knowledge of
the optical transitions can be used in combination with Raman spectra for
characterization of the samples. The first realistic estimation of the
optical transitions was done within the NTB model. Read more …
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 PHONON
DISPERSION
The phonon dispersion of any nanotube can be derived
from that of graphene by use of the zone-folding method. This method does not
yield the phonon eigenvectors. The direct calculation of the phonon
dispersion of the relaxed nanotube is rather time-consuming if possible at
all. However, it can be obtained for any observable nanotube in
symmetry-adapted models. Examples: force-constant
models (FC models) and a non-orthogonal
tight-binding model (NTB model). Read more …
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 Γ-PHONONS
For each nanotube there are four acoustic and numerous
optical Γ-phonons, which can be classified by their symmetry. The optical phonons can further be put
into four groups according to their atomic
displacements. For Raman spectroscopy most important are the
radial-breathing mode (RBM) and up to six tangential modes (G-modes), which
give rise to intense Raman lines. Read more …
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 LINEAR ELASTIC PROPERTIES
The small-stress elastic properties of nanotube systems
are described by the elastic moduli – Young's
modulus and shear modulus. Nanotubes are often observed in large bundles.
Their small-stress elastic properties are characterized by the elastic
constants and bulk modulus. Due to the different dominant force along and
perpendicular to the bundle axis, the elastic properties of the bundles are
highly anisotropic. Moreover, these properties depend strongly on the
nanotube radii. Read more …
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 HEAT CAPACITY
The low-temperature phonon heat
capacity of nanotubes can simply be derived from the quantum-mechanical
formula. At very-low temperatures (T < ~1 K) the specific heat is
determined by the transverse acoustic phonons. At higher temperatures (~1
< T < ~10 K) the heat capacity is due to longitudinal and twist
acoustic phonons. The bundling of nanotubes smears this behavior to a
quasi-three-dimensional one. Read more …
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 RAMAN SCATTERING OF LIGHT
In Raman scattering experiments on nanotubes, the Raman
intensity depends strongly on the laser excitation, given by the resonance
Raman profile (RRP). In particular, the Raman signal is enhanced whenever the
laser line is in the resonant window, determined by the optical transitions.
This feature is used in combination with Raman data for nanotube
characterization. Read more …
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 RBM INTENSITY
The Raman data on the RBM is most often used for
nanotube characterization because the RBM frequency is inversely proportional
to the nanotube radius. The RRP of the RBM requires the knowledge of the electron-phonon matrix element and can be done exactly or approximately
(see comparison of both approaches). The exact
NTB results for the Raman intensity amplitude can conveniently be used in a tabular, graphical, or JAVA
Applet form. Read more …
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 G-BAND INTENSITY
The Raman data on the G-modes is
not widely used for characterization purposes, the reasons for this being
different for the different G-modes. However, the Raman G-band can be useful
for distinguishing between metallic and semiconducting nanotubes, and for
determination of the doping level. The RRP of the most intense A1 G-modes can
be calculated exactly or approximately. The exact NTB results for the
Raman intensity amplitude ca be used in tabular and
graphical form. Read more …
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