Hexagonal networks

The question whieh then arises is What do we call a defect in a nanotube To answer this question, we need to define what would be a perfeet nanotube. Nanotubes are mieroerystals whose properties are mainly defined by the hexagonal network that forms the eentral cylindrical part of the tube. After all, with an aspect ratio (length over diameter) of 100 to 1000, the tip structure will be a small perturbation except near the ends. This is clear from Raman studies[4] and is also the basis for calculations on nanotube proper-ties[5-7]. So, a perfect nanotube would be a cylindrical graphene sheet composed only of hexagons having a minimum of defects at the tips to form a closed seamless structure. 

From Euler s theorem, one can derive the following simple relation between the number and type of cycles n, (where the subscript / stands for the number of sides to the ring) necessary to close the hexagonal network of a graphene sheet ... 

Fig. 4. Hexagonal network of graphite and the 4 different pairs of carbon atoms across which the 5p -like defect tine may form(18].

It is known that a metallic ID system is unstable against lattice distortion and turns into an insulator. In CNTs instabilities associated two kinds of distortions are possible, in-plane and out-of-plane distortions as shown in Fig. 8. The inplane or Kekuld distortion has the form that the hexagon network has alternating short and long bonds (-u and 2u, respectively) like in the classical benzene molecule [8,9,10]. Due to the distortion the first Brillouin zone reduees to one-third of the original one and both K and K points are folded onto the F point in a new Brillouin zone. For an out-of-plane distortion the sites A and B are displaced up and down ( 2) with respect to the cylindrical surface [11]. Because of a finite curvature of a CNT the mirror symmetry about its surface are broken and thus the energy of sites A and B shift in the opposite direction. 

We can understand the differences in properties between the carbon allotropes by comparing their structures. Graphite consists of planar sheets of sp2 hybridized carbon atoms in a hexagonal network (Fig. 14.29). Electrons are free to move from one carbon atom to another through a delocalized Tr-network formed by the overlap of unhybridized p-orbitals on each carbon atom. This network spreads across the entire plane. Because of the electron delocalization, graphite is a black, lustrous, electrically conducting solid indeed, graphite is used as an electrical conductor in industry and as electrodes in electrochemical cells and batteries. Its... 

Under deposition of cobalt nanocrystals, self-assemblies of particles are observed and the nanocrystals are organized in a hexagonal network (Fig. 2). However, it can be seen that the grid is not totally covered. We do not have a simple explanation for such behavior. In fact, the size distribution, which is one of the major parameters in controlling monolayer formation, is similar to that observed with the other nanocrystals, such as silver and silver sulfide. One of the reasons could be that the nanocrystals have magnetic properties, but there is at present no evidence for such an assumption. 

The formation of a 3D lattice does not need any external forces. It is due to van der Waals attraction forces and to repulsive hard-sphere interactions. These forces are isotropic, and the particle arrangement is achieved by increasing the density of the pseudo-crystal, which tends to have a close-packed structure. This imposes the arrangement in a hexagonal network of the monolayer. The growth in 3D could follow either an HC or FCC struc-... 

FIG. 7 Absorption spectra under polarization 5 (A) andp (B) of 5-nm nanocrystals self-organized in a hexagonal network on HOPG. 

From comparison of the optical properties of particles deposited on the same substrate and differing by their organization (Figs. 7 and 8) it can be concluded that the appearance of the resonance peak at 3.8 eV is due to the self-organization of the particles in a hexagonal network. This can be interpreted in terms of mutual dipolar interactions between particles. The local electric field results from dipolar interactions induced by particles at a given distance from each other. Near the nanocrystals, the field consists of the ap-... 

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

Figure 26. Constant current mode STM image of isolated (A), self-organized in close-packed hexagonal network (C) and in fee structure (E) of silver nanoclusters deposited on Au(l 11) substrate (scan size (A) 17.1 x 17.1 nm, f/t=—IV, /t=ltiA, (C) 136 X 136 nm, f/t = — 2.5 V, /t = 0.8 tiA, (E) 143 x 143 nm, = —2.2 V, /, = 0.72 nA). I U) curves and their derivatives in the inserts of isolated (B), self-organized in close-packed hexagonal network (D) and in fee structure (F) of silver nanoclusters deposited on Au(l 11) substrate. (Reprinted with permission from Ref. [58], 2000, Wiley-VCH.)...

Fig. 44.22. Three commonly used Kohonen network structures, (a) One-dimensional array (b) two-dimensional rectangular network (each unit, apart from the borderline units has 8 neighbours) and (c) two-dimensional hexagonal network (each unit, apart from the borderline units, has 6 neighbours). (Reprinted with permission from Ref. [70]).

In a real-time spectroellipsometric measurement in which the kinetics of a-Si H deposition is studied, trajectories are recorded in the A-4 plane at various photon energies between 2 and 4 eV. These trajectories can be simulated and fitted to models that represent the growing a-Si H layer. Canillas et al. [347] have made a detailed study of the deposition of the first few layers of a-Si H on a NiCr/glass substrate. Similar results are obtained for a c-Si substrate. They have proposed several models to explain the data. One possible model is the hemispherical nu-cleation model, which describes a hexagonal network of spherical a-Si H nuclei located at an average distance d between them. The growth is represented by an... 

Structural and textural characterisation of pure SBA-15 and hybrid GFP/SBA-15 Pure SBA-15 and GFP/SBA-15 hybrid were characterised by X-ray powder diffraction, HRTEM and volumetric analysis. Calcined SBA-15 (Fig. 1, curve A) show the typical XRD pattern of an ordered hexagonal network of mesopores with (10), (11) and (20) reflections. The presence of well resolved (11) and (20) peaks indicate that the calcined material used for the preparation of the hybrid materials have a long-range order. The hexagonal XRD pattern was still clearly observed in the hybrid material (GFP/SBA-15), as all the three main reflections were found (Fig. 1, curve B), indicating that the sonication and the GFP physical adsorption does not affect the framework integrity of the material. 

All BaCvN nanotubes are made of a hexagonal network of sp2 bonded atoms, with three nearest neighbors to each atom (15, 55, 69, 78, 79). In the case of BC2N nanotubes, two different arrangements of the sheet are possible, leading to two isomers with different structures and with distinct electrical properties (78b). 

A < 0, i.e. attractive walls. A hexagonal network of domain walls (HI) will be formed at the commensurate (C-I) transition, because the number of wall crossings tends to be as large as possible. This C-HI transition should be first order. 

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