Defect clusters in hexagonal networks: characterization and strain field

Abstract

A detailed analysis of defect clusters (topological and geometrical) in hexagonal networks is presented. The conditions that have to be met by a cluster for it to be embedded in an hexagonal network are enunciated, which are related to the sequence of saturated (3-connected) and unsaturated (2-connected) vertices at the periphery of the cluster (vertex sequence). The type of hexagonal network (perfect, dislocated or disclinated) in which a defect is embedded depends on simple parameters (the strength P of the cluster and a Burgers vector B for dislocation clusters) which can be obtained from the vertex sequence. Equivalent clusters can be embedded in hexagonal networks of the same topology and equivalence classes are identified for all types of clusters. Disclination defects of given strength, P , may fill into one or more classes, depending on P. For dislocation defects (P = 0) there are infinitely many classes, each defined by a vector B. The strain field and strain energy density in the hexagonal network around a single defect cluster is evaluated for geometrical and topological defects of any type, using a continuum approach.