Topological Defects and Morphology of Graphitic Carbon Materials: An Approach Based on Differential Geometry

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It has been known that pentagons and heptagons in hexagonal graphitic network give rise to a certain amount of curvature in the three dimensional structure of graphitic carbon materials. The amount of curvature is quantized due to the symmetry of graphite and, as a result, the structure formed by the network is also restricted. We clarify the effects of curvature quantization on the forms of graphitic carbon materials, employing the knowledge of differential geometry, especially the Gauss-Bonnet theorem.