Graphite sheet

The construction of the nanotube from a conformal mapping of the graphite sheet shows that each nanotube can have up to three inequivalent (by point... 

We will now discuss the electronic structure of single-shell carbon nanotubes in a progression of more sophisticated models. We shall begin with perhaps the simplest model for the electronic structure of the nanotubes a Hiickel model for a single graphite sheet with periodic boundary conditions analogous to those im-... 

Fig. 7. Strain energy per carbon (total energy minus total energy extrapolated for the graphite sheet) as a function of nanotube radius calculated for unoptimized nanotube structures (open squares) and optimized nanotube structures (solid circles). Solid line depicts inverse square relationship drawn through point at smallest radius.

As an example of a nanotube representative of the diameters experimentally found in abundance, we have calculated the electronic structure of the [9,2] nanotube, which has a diameter of 0.8 nm. Figure 8 depicts the valance band structure for the [9,2] nanotube. This band structure was calculated using an unoptimized nanotube structure generated from a conformal mapping of the graphite sheet with a 0.144 nm bond distance. We used 72 evenly-spaced points in the one-... 

Because the cohesive energy of the fullerene Cyo is —7.29 eV/atom and that of the graphite sheet is —7.44 eV/atom, the toroidal forms (except torus C192) are energetically stable (see Fig. 5). Finite temperature molecular-dynamics simulations show that all tori (except torus Cm2) are thermodynamically stable. 

The closure of the graphite sheets can be explained by the substitution of pentagons for hexagons in the nanotube sheets. Six pentagons are necessary to close a tube (and Euler s Rule is not violated). Hexagon... 

The carbon-arc plasma of extremely high temperatures and the presence of an electric field near the electrodes play important roles in the formation of nanotubes[ 1,2] and nanoparticles[3]. A nanoparticle is made up of concentric layers of closed graphitic sheets, leaving a nanoscale cavity in its center. Nanoparticles are also called nanopolyhedra because of their polyhedral shape, and are sometimes dubbed as nanoballs because of their hollow structure. 

The elimination of the energetic dangling bonds present at the edges of a tiny graphite sheet is supposed to be the driving force to induce curvature and closure in fullerenes this phenomenon is also associated with the formation of larger systems, such as nanotubes and graphitic particles. 

It is known that the electrical properties of CNTs insulator, semiconductor or metal, are caused by the structure in graphitic sheet [2,3]. It is difficult to observe the individual graphitic structure in a sheet of CNT by TEM, because... 

Dravid et al. examined anisotropy in the electronic structures of CNTs from the viewpoint of momentum-transfer resolved EELS, in addition to the conventional TEM observation of CNTs, cross-seetional TEM and precise analysis by TED [5]. Comparison of the EEL spectra of CNTs with those of graphite shows lower jc peak than that of graphite in the low-loss region (plasmon loss), as shown in Fig. 7(a). It indicates a loss of valence electrons and a change in band gap due to the curved nature of the graphitic sheets. 

In order to examine the electronic structures of CNT it is necessary to first define the classification of structural configurations of CNT. The configuration of a CNT is constructed by enrolling a graphite sheet as illustrated in Fig. 1. That is. 

Fig. 8. Lattice distortions in a graphite sheet. For an in-plane distortion (left), the bond denoted by a thin line becomes shorter and that denoted by a thick line becomes longer, leading to a unit cell three times as large as the original. For an out-of-plane distortion (right), an atom denoted by a black dot is shifted down and that denoted by a white circle moves up.

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