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Finite graphite systems having a zigzag edge exhibit a special edge state. The corresponding energy bands are almost flat at the Fermi level and thereby give a sharp peak in the density of states. The charge density in the edge state is strongly localized on the zigzag edge sites. No such localized state appears in graphite systems having an armchair edge. By utilizing the graphene ribbon model, we discuss the effect of the system size and edge shape on the special edge state. By varying the width of the graphene ribbons, we find that the nanometer size effect is crucial for determining the relative importance of the edge state. We also have extended the graphene ribbon to have edges of a general shape, which is defined as a mixture of zigzag and armchair sites. Examining the relative importance of the edge state for graphene ribbons with general edges, we find that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges. We demonstrate that such an edge shape with three or four zigzag sites per sequence is sufficient to show an edge state, when the system size is on a nanometer scale. The special characteristics of the edge state play a large role in determining the density of states near the Fermi level for graphite networks on a nanometer scale. ͓S0163-1829͑96͒11048-1͔

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Raman spectroscopy has historically played an important role in the structural characterization of graphitic materials, in particular providing valuable information about defects, stacking of the graphene layers and the finite sizes of the crystallites parallel and perpendicular to the hexagonal axis. Here we review the defect-induced Raman spectra of graphitic materials from both experimental and theoretical standpoints and we present recent Raman results on nanographites and graphenes. The disorder-induced D and D' Raman features, as well as the G'-band (the overtone of the D-band which is always observed in defect-free samples), are discussed in terms of the double-resonance (DR) Raman process, involving phonons within the interior of the 1st Brillouin zone of graphite and defects. In this review, experimental results for the D, D' and G' bands obtained with different laser lines, and in samples with different crystallite sizes and different types of defects are presented and discussed. We also present recent advances that made possible the development of Raman scattering as a tool for very accurate structural analysis of nano-graphite, with the establishment of an empirical formula for the in- and out-of-plane crystalline size and even fancier Raman-based information, such as for the atomic structure at graphite edges, and the identification of single versus multi-graphene layers. Once established, this knowledge provides a powerful machinery to understand newer forms of sp(2) carbon materials, such as the recently developed pitch-based graphitic foams. Results for the calculated Raman intensity of the disorder-induced D-band in graphitic materials as a function of both the excitation laser energy (E(laser)) and the in-plane size (L(a)) of nano-graphites are presented and compared with experimental results. The status of this research area is assessed, and opportunities for future work are identified.

Character tables for the "group of the wave vector" at certain points of symmetry in the Brillouin zone are given. The additional degeneracies due to time reversal symmetry are indicated. The form of energy vz wave vector at these points of symmetry is derived. A possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure will be presented. HE e6'ect of symmetry on the energy band structures of crystals of the zinc blende type can be readily derived using the machinery developed by