Quantitative Valence-Loss Spectroscopy of Carbon Nanostructures

Carbon tubes or spheres synthesized by arc-discharge are usually mixed with other byproducts, prohibiting direct measurements of their physical properties by the well established optical techniques because a large quantity of pure specimen is required. Electron energy-loss spectroscopy (EELS) is a unique technique that can be applied to probe the electronic structure of a single carbon tube or sphere. In this paper, the classical dielectric response theory is applied to calculate the EELS spectra acquired from a graphitic carbon sphere at various impact parameters. Graphite is an anisotropic dielectric medium whose dielectric function is described by a tensor. A graphitic carbon sphere is composed of concentric graphitic shells whose dielectric tensor in the spherical geometry, under the local response approximation, is given by (Figure 1)where are the dielectric function of graphite for an electric field perpendicular and parallel, respectively, to the c axis. In the non-relativistic approximation, the surface excitation is calculated by [1]