Issue 11, 2002

Topo-combinatoric categorization of quasi-local graphitic defects

Abstract

A quasi-local graphitic defect is defined as finite network surrounded by a trivalent planar hexagonal-faced network extending to infinity. A general classification of such quasi-local defects is developed, so as to attend to infinite-range structural consequences. A first classification stage identifies a discrete “combinatorial curvature” characteristic κ, associating closely to geometric Gaussian curvature of embeddings of the network surface in Euclidean space. If κ = 2π, a singly capped bucky-tube results, whereas if 0 < κ < 2π, it is a positive-curvature graphitic cone. If κ < 0, a “fluted” or “crenelated” cone results, and if κ = 0, it is a globally “flat” (in a Euclidean sense) structure. A second stage of classification identifies a topo-combinatoric “circum-matching” characteristic. For the graphitic-cone case there may be more than one “circum-matching” class for each κ, so that 8 such classes arise for the 5 allowed values of κ, with 0 < κ < 2π. A similar result applies for the negatively curved cones with −2π < κ < 0. On the other hand, there is an infinity of classes for the “flat” κ = 0 case, where each circum-matching class corresponds to a standard Burgers dislocation vector. There are also an infinity of classes for κ = 2π or for κ any positive integer multiple of −2π. A further “quasi-spin” characteristic refines the classes of quasi-local defects into “irrotational” subclasses, as are relevant for multi-wall cones. Combining rules for pairs of defects are considered.

Article information

Article type
Paper
Submitted
19 Nov 2001
Accepted
24 Jan 2002
First published
02 May 2002

Phys. Chem. Chem. Phys., 2002,4, 2099-2110

Topo-combinatoric categorization of quasi-local graphitic defects

D. J. Klein, Phys. Chem. Chem. Phys., 2002, 4, 2099 DOI: 10.1039/B110618J

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