On mesoscopic description of interfaces in graphene

The article discusses a mesoscopic approach to the description of interfaces (IFs) in graphene. The approach is based on the representation of defective carbon rings with broken six-fold symmetry in hexagonal lattice of graphene as singular defects, i.e. wedge disclinations, in an elastic continuum. The angle of the sector inserted into or removed from the hexagonal lattice that results in the formation of localized quadrate, pentagon, heptagon, and octagon carbon rings, defines the strength (charge) of disclinations. The mesoscopic approach views IF in graphene as an ensemble of disclinations distributed along a line. Elementary building blocks for IFs with periodic motives of carbon atoms are structural units (SUs) containing disclination sets with zero total disclination charge. The junction of SUs of different type is considered as a virtual disclination. The approach works well in graphene when analyzing elastic fields and stored energies of IFs of two types: grain boundaries (GBs) that induce misorientation of neighboring domains of graphene lattice, and zero misorientation interfaces (ZMIs) that do not possess such a property.