2,468 research outputs found
Plane polarized-longitudinal Phonons in realistic low dimensional systems
A realistic one-dimensional system has not only longitudinal phonons, but
also possible transverse modes, which derive their restoring force from
longitudinal interaction. We show that transverse motion results in a quartic
displacement term in transverse direction as the first non-vanishing term in
the potential energy. This results in solution of a composite longitudinal
motion superimposed by a transverse motion propagating along the length
direction identified as a plane polarized phonons. Interestingly, solutions of
the quartic nonlinear equation have been expressed accurately, though
approximately in terms of sinusoidal solutions by modifying the periodicity of
sin function. The phonons along the transverse direction, now with a weakened
frequency compared to the longitudinal has interesting impact- it gives rise to
negative Gruneisen parameter with a value of -1 and is responsible for negative
thermal expansion in the low temperature regime. Similar results of graphene
sheet based on consideration of transverse (surface ripple like) modes to the
planar direction, provides explanation to the observed negative thermal
expansion in low temperature regime. The concept of plane polarized phonons
seems new and interesting. All dynamics of atomic motion, despite involving
quartc nonlinear equation is expressible in terms of simple harmonic motion.
The most important feature of the transverse modes of an open surface or chain
is their dependence on lateral or longitudinal modes, and as soon as more
chains or more surfaces are added, bulk interactions are initiated and
longitudinal dependence of transverse motion is lost and so also very
distinguishing thermodynamic properties.Comment: 4 pages, 3 figures and 8 reference
Thermal expansion in 2D honeycomb structures: Role of transverse phonon modes
Graphene and its derivatives including hexagonal BN are notorious for their
large negative thermal expansion over a wide range of temperature which is
quite unusual. We attempt to analyze this unusual behavior on the basis of
character of the phonon modes. The linear thermal expansion coefficients (LTEC)
of two-dimensional honeycomb structured pure graphene, h-BN and B/N doped
graphene are studied using density functional perturbation theory (DFPT) under
quasi harmonic approximation. The dynamical matrix and the phonon frequencies
were calculated using VASP code in interface with phonopy code. The approach is
first applied to pure graphene to calculate thermal expansion. The results
agree with earlier calculations using similar approach. Thereafter we have
studied the effect of B/N doping on LTEC and also compared it with LTEC of h-BN
sheet. The LTEC of graphene is negative in the whole temperature range under
study (0-1000K) with a room temperature (RT) value of -3.51X10-6K-1. The value
of LTEC at room temperature becomes more negative with B/N doping in graphene
as well as for h-BN sheet. In order to get an insight into the cause of
negative thermal expansion, we have computed the contribution of individual
phonon modes of vibration. We notice that it is principally the ZA (transverse
acoustic) mode which is responsible for negative thermal expansion. It has been
concluded that transverse mode in 2D hexagonal lattices have an important role
to play in many of the thermo dynamical properties of 2D structures.Comment: 18 pages, 37 references and 11 figures. arXiv admin note: text
overlap with arXiv:1107.2469, arXiv:cond-mat/0412643 by other authors. Some
change in the language an 3 new references adde
Implicit Phonon Shifts and Thermodynamical Properties of Rigid Carbon Nanotube Ropes
We calculate phonon shifts of external modes of a bunch of carbon nanotubes.
A simple model based on atom-atom potential has been used to calculate the
implicit anharmonicity in the phonons of carbon nanotube bundles having rigid
tubes, with the assumption that under hydrostatic pressure only the intertube
distance in the bunch varies. Such a model is important as long carbon nanotube
ropes will be an extension of a fixed length ropes as is done here. Various
bulk and thermodynamic properties like thermal expansion, bulk modulus and the
Gruneisen constants and external phonon shifts which naturally enter into the
calculation are also described and compared with the available data. The
specific heat capacity has also been calculated.Comment: 31 pages, 6 figures, 4 tables and 26 reference
Model for High Temperature Phase of C70 Solid
Depending on the temperature, the C70 solid crystallizes in several
structures. At high temperature (T > 340K), the ellipsoidal C70 molecule
rotates freely in all directions and may be treated as a uniform thick
spherical shell with inner and outer radii as the minimum and the maximum
distance of C-atom from the center of the molecule. At lower temperatures the
free rotations of molecules freeze out. We have calculated the lattice
parameters, energies and bulk modulus at the minimum energy configuration of
fcc and hcp phase of pure C70 solid at high temperature using a simple model
based on atom-atom potential.Comment: 13 pages, 6 figures and 12 references, reported in part in DAE
Symposiu
Modification of Thermal Conductivity of PMMA and PC by making their Nanocomposites with Carbon Nanotubes
PMMA and Poly carbonate (PC) are wonderful low cost materials which can be
easily tailored and shaped. However they have poor mechanical, thermal and
electrical properties which are required to be enhanced in several applications
where along with high strength, a quick heat transfer becomes a necessity.
Carbon nanotubes (CNT) are excellent new materials having extraordinary
mechanical and transport properties. In this paper we report results of
fabricating composites of varying concentrations of CNTs with PMMA and PC and
measurements of thermal conductivity data by a simple transient heat flow. The
samples in disk shapes of around 2 cm diameters and 0.2 cm thickness with CNT
concentrations varying up to 10 wt percent were fabricated. By keeping one end
of the discs at steam temperature, the temperature of the other end was noted
for each sample after 10 s. The rise in temperature was correlated with thermal
conductivity which was appropriately calibrated. We found that both PMMA and PC
measured high thermal conductivity with increase in the concentration of CNTs.
The thermal conductivity of PMMA rose from about 0.2 W/mK to 0.4 W/mK at 10
wtpercent of CNT whereas for PC, it rose from about 0.2 W/mK to 0.9 W/mK at 10
wt percent of CNT. It is thus observed that modification in thermal properties
is easily achieved by making CNT based composites using only up to 10 wt
percent of CNTs in PMMA and PC and enabling quicker heat dissipation in these
materials.Comment: 8 pages, 4 figures, 9 references,FiNSTA '14-International Conference
on Frontiers in Nano Science, Technology and Application
Modeling and characterizing single-walled carbon nanotubes by pressure probe
We compare the behavior of bond lengths, cross sectional shape and bulk
modulus in equilibrium structure at ambient conditions and under hydrostatic
pressure of all the three kinds of uncapped single walled carbon nanotubes.
Results of our numerical calculations show that two bond lengths completely
describe the structure of achiral SWNT whereas only one bond length is required
to determine structure of chiral SWNT. In armchair tubes, one bond length is
found to be larger than that of graphitic value while in zigzag tubes one bond
length has a constant value. These bond lengths are very sensitive to tube
radius. In chiral tubes, the value of bond length is found to depend on the
chirality and slightly on the tube radius. Different responses of these bond
lengths are found on application of pressure. At some critical pressure, both
bond lengths become equal to each other in achiral tubes. An analysis regarding
the cross sectional shape of the nanotubes and its pressure dependence has also
been done. The shape transition, from circular to oval shape takes place. At
this transition, the behavior of bond lengths is found different and dependent
on the chirality of the tubes. Chiral tubes with chiral angle which is mid way
between zigzag and armchair tubes are found to have most prominent effects of
chirality. Thus we demonstrate that pressure is a useful probe to characterize
various kinds of carbon nanotubes.Comment: pages 8, references 19, Figures
Orientational Ordering and Binding in Alkali doped C60 solids
The binding energy of A3C60, a conductor, is described well by an ionic solid
type calculation. This succeeds because there is little overlap between
molecular wave functions on neighbouring sites, so that electrons are
practically localized on-shell. This leads one to believe that even in A4C60
and A6C60 systems such calculation may suffice. However, for large charge on
the anion, there is a possibility for some electrons to delocalize and go into
the s-band. We calculate binding energy, keeping these delocalised electrons x,
as a parameter and minimize the energy w.r.t. it. We take the intermolecular
interaction to be arising out of a C-C potential of 6-exp form and a screened
Coulomb interaction between the anions and cations and among themselves. Model
calculations are presented for K1C60, K3C60, K4C60 and K6C60 for which the
minimum energy state shows no delocalisation. Cohesive Energy dependence on
Lattice constant is used to calculate Bulk Modulus for all systems. We have got
a reasonably good resemblance with experimental values. Further, we observe
that the cohesive energy shows poor resemblance with experimental values.
Further, delocalisation of a fraction of electron at the centre of double bond
show considerable increase in cohesive energy.Comment: Presented in National Seminar MSTF-2000, Frb. 24-25,2000 SLIET, Indi
Modeling Pressure Induced Structural Modification of Armchair Single-Wall Nanotubes
Based on the helical and rotational symmetries and Tersoff-Brenner potential
with couple of modified parameters, we investigate the variation of bond
length/lengths in equilibrium structure due to tube length as well as due to
applied hydrostatic pressure for a series of high symmetry armchair (n,n)
single-wall nanotubes having different radii. Assuming that two different bond
lengths dictate the tube geometry, these are monitored as a function of radius.
It turns out that one of these bond lengths is greater than bond length of
graphite whereas other one was less than it. These deviations from graphite
value appear to be related to the curvature-induced rehybridization of the
carbon orbitals. Lengths are found to have very important effect on the values
of both bond lengths. The results under hydrostatic pressure indicate many
linear behaviors having different slopes in the values of bond lengths with
increasing pressure leading to a pressure induced-phase transition. This
behaviour is strongly dependent on the tube radius. We also calculate the bulk
moduls for this structure which reflects clearly this behavior of armchair
nanotubes and thus predicts mechanical resilience of nanotubes.Comment: 15 pages, 22 references, 6 figures. Submitted to Phys. Rev.
Structure of chiral single-walled carbon nanotubes under hydrostatic pressure
We investigate the structural parameters, i.e. bond lengths and bond angles
of chiral tubes of various chiralities. The procedure used is based on helical
and rotational symmetries and Tersoff potential. The results indicate that at
ambient condition, there are equal bond lengths and three unequal bond angles
in the structure of chiral tubes. The bond length depends much more on the
chirality and very slightly on the tube radius. Length of the tubes does not
play very significant role on bond length and bond angles. These C-C bonds were
recalculated under hydrostatic pressure. The bond length compresses with
pressure while the bond angles remain practically unchanged. We also carry out
analysis regarding the cross sectional shape of chiral tubes and its pressure
dependence. It is found that at some pressures, transition from circular to
oval cross section takes place. The transition pressure is found to strongly
depend on the radius and chirality of tube. At this transition, corresponding
to given elliptical cross section, the bond length for all chiral tubes is
identical. This behavior of bond length is different from achiral tubes.Comment: 16 pages, 9 figures, 32 reference
Cohesive energy of zinc blende (AIIIBV and AIIBVI) structured solids
In this letter we present an expression relating the cohesive energy for the
A3B5 and A2B6 semiconductors with the product of their ionic charges and
nearest neighbor distance. The cohesive energy values of these solids exhibits
a linear relationship when plotted on a log-log scale against the nearest
neighbor distance, but fall on different straight lines according to the ionic
charge product of the solids. A good agreement has been found between the
experimental and calculated values of the cohesive energy for A3B5 and A2B6
semiconductors.Comment: 7 pages, 21 reference
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