The name 'Haeckelite' has been proposed to designate a three-fold coordinated network generated by a periodic arrangement of pentagons, hexagons and heptagons (Terrones H et al 2000 Phys. Rev. Lett 84 1716). Starting from a planar Haeckelite array, tubular structures are obtained by applying the same wrapping procedure as for the usual nanotubes, which are rolled up sheets of graphene. This paper is a short review of the structural properties of Haeckelite nanotubes, as investigated by computer molecular modelling. The Haeckelite nanotubes may adopt various shapes, among which coiled structures, double-screw molecules, corrugated cylinders, and pearl-necklace-like nanotubes are the most spectacular. It is shown that some of these structures may explain exotic forms of C nanostructures revealed by electron microscopy on samples produced experimentally. The identification of the possible Haeckelite structure of a nanotube by electron diffraction and scanning tunnelling microscopy is discussed.
We develop a model in which the ultraviolet dielectric tensor of planar graphite is transported to the spherical geometry of a nanoscale multishell fullerene with a central cavity. This is accomplished by assigning to every point of the multishell fullerene a local dielectric tensor identical to that of graphite with its c axis aligned along the local radial direction. The dynamic, multipolar polarizabilities of the model fullerene are obtained from the exact solutions of the nonretarded Maxwell equations. The ultraviolet absorption spectrum of the hollow fullerene is calculated as a function of the ratio of the inner and outer radii. Comparisons of the theoretical absorption spectra with the 2175-\AA{} interstellar extinction hump and with recent absorption measurements for synthetic multishell fullerenes indicate that the dielectric properties of graphite are qualitatively adequate for understanding the optical data. However, difficulties persist with both the astrophysical and laboratory absorption peaks which lead us to consider the possible role of multishell fullerene aggregation into small or large clusters. It is found that the effect of clustering is important and reduces but does not remove completely the quantitative difficulties of the graphitic multishell model. Finally theoretical electron-energy-loss spectra (EELS) of these structures with an empty or filled cavity are calculated from the multipolar polarizabilities of the model. The results indicate that spatially resolved EELS measurements should be ideally suited to study the dielectric properties of individual multishell fullerenes and to ascertain to what extent they differ from those of planar graphite.
Considering simple models of the scanning tunneling microscope and metallic samples, we use a finite-element method to solve Schr\"odinger's equation for the electrons tunneling from the tip to the sample. We plot current-density maps for various geometries of the electrodes: hemispherical or cylindrical tip facing a planar surface or a surface with a Gaussian boss or dip. It can be seen on the current-density maps that the electron flow passes preferentially through the thinnest region of the barrier. From the current density in the case of a planar sample, we investigate the width of the tunnel current beam when it penetrates into the sample. From the dependence of the current on the distance between a hemispherical tip and a Gaussian boss or dip, we show that the corrugation of the sample surface is attenuated by a factor of two in the constant-current image. The effective work function, determined from the logarithmic derivative of the current with respect to the distance, differs from the real work function of the sample and, as an effect of the image potential, decreases when the tip approaches the sample. A comparison between a numerical resolution of the exact Schr\"odinger equation and the transfer Hamiltonian approximation shows that the latter gives good results, even when the tip is close to the sample.
Non-adiabatic effects can considerably modify the phonon dispersion of low-dimensional metallic systems. Here, these effects are studied for the case of metallic single-walled carbon nanotubes using a perturbative approach within a density-functional-based non-orthogonal tight-binding model. The adiabatic phonon dispersion was found to have logarithmic Kohn anomalies at the Brillouin zone center and at two mirror points inside the zone. The obtained dynamic corrections to the adiabatic phonon dispersion essentially modify and shift the Kohn anomalies as exemplified in the case of nanotube (8, 5). Large corrections have the longitudinal optical phonon, which gives rise to the so-called G- band in the Raman spectra, and the carbon hexagon breathing phonon. The results obtained for the G- band for all nanotubes in the diameter range from 0.8 to 3.0 nm can be used for assignment of the high-frequency features in the Raman spectra of nanotube samples.
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