A detailed analysis was made of defect clusters in hexagonal networks. The conditions that were necessary for a cluster to be embedded in an hexagonal network were identified. These were related to the sequence of saturated (3-connected) and unsaturated (2-connected) vertices at the periphery of the cluster. The type of hexagonal network (perfect, dislocated, disclinated) in which a defect was embedded depended upon simple parameters, such as the strength of the cluster or the Burgers vector for dislocations. Equivalent clusters could be embedded in hexagonal networks of the same topology, and equivalence classes were identified for all types of cluster. Disclination defects of a given strength could fit into one or more classes; depending upon the strength. In the case of dislocation defects, for which the disclination strength was zero, there were infinitely many classes; each of which was defined by a Burgers vector. The strain field and strain energy density in the hexagonal network around a single defect cluster was evaluated, using a continuum approach, for geometrical and topological defects of any type.

Defect Clusters in Hexagonal Networks: Characterization and Strain Field M.A.Fortes, M.F.Vaz: Journal of Physics - Condensed Matter, 1998, 10[34], 7519-34