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Tight Binding method for carbon nanotubes - Essay Example

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Discovery of nanotubes in the year 1991 by S. Iijima, opened a completely new field in the science of carbon related materials, especially carbon nanotubes, single-wall and multiwall structures. Nanotubes are cylindrical structures based on the hexagonal lattice of carbon atoms that forms crystalline graphite…
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Tight Binding method for carbon nanotubes
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Download file to see previous pages Carbon nanotubes are long, thin cylinders of carbon and have a very broad range of electronic, thermal, and structural properties that change depending on the different kinds of nanotube. The chiral vector of the nanotube, B'= nR1 + mR2 where R1 and R2 are unit vectors in the two-dimensional hexagonal lattice, and n and m are integers. Another important parameter is the chiral angle, which is the angle between Band R1.
Diameter D = a3 (n2 + nm + m2)/ p ,Where, ac is the distance between neighboring carbon atoms in the flat sheet. The different values of n and m lead to different types of nanotube. They are armchair, zigzag and chiral nanotubes. Armchair nanotubes are
formed when n = m and the chiral angle is 30. Zigzag nanotubes are formed when either n =0 or m==0 and the chiral angle is 0. Other nanotubes, with chiral angles between 0 and 30, are known as chiral nanotubes. The properties of nanotubes are determined by their diameter and chiral angle, both of which depend on n and m.
The electronic characteristics of the nanotubes have been done by numerical band structure, the structure of the chemical bonds. is given by the local spatial structure of the orbital. The electronic structure of the nanotube fragments are calculated by SCF-MO-LCAOVmethods. In this method, only valence electrons are taken into account and the three- and four-center integrals are omitted and the repulsion of lone electron pairs can be explained. The SCF convergence criterion was 10-8for total-energy changes and 10-5 for charge-density changes between two subsequent cycles. Band structure calculations of [n, 0] (n = 6, 7, 8, 9)tubes were performed using the tight-binding Hamiltonian, with a universal set of first and second nearest-neighbor hopping integrals that reproduce various carbon structures, including graphite.
The 2s, 2px, 2py, 2pz, and s* orbital of each carbon atom are used as the basis set for expressing the tight binding model. The Hamiltonian matrix elements and related parameters are obtained by adjusting the model to fit photoemission band-structure data. The (6, 0) carbon tube seems to have the lowest diameter and are thermodynamically unstable. The bonds at the ends of the nanotube fragments get saturated by hydrogen atoms. The structural unit of the tube is the distorted carbon hexagon. All c-c bonds were assumed to be of the same length: 1.4 .
Page 3
The distance between third-neighbor carbon atoms along the tube circumference is 2.39 . The point group symmetry of the (6, 0) nanotube fragment is determined
by the number N of carbon hexagons along the tube axis. There is a difference between
heat of formation of the nanotube fragments, caused by the boundary atoms affect,
strongly at the central part of the nanotube fragment.
In the above Figure, the dispersion curves of the (n, 0) tubes with n = 6... 11
are shown. This tube family splits into three groups. The (3n, 0) tubes have vanishing energy gaps. The gap increases in (3n + 1, 0) and in (3n + 2, 0) tubes. Consequently, (6, 0) and (9, 0) tubes will likely show metallic conductivity, similar to graph.
In graphite, orbital are represented in carbon nanotubes, the radial orbital are analogous to the lone orbital of graphite .This changes the character of the frontier orbital ...Download file to see next pagesRead More
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