Disclinations, dislocations, and continuous defects: A reappraisal

Disclinations were first observed in mesomorphic phases. They were later found relevant to a number of ill-ordered condensed-matter media involving continuous symmetries or frustrated order. Disclinations also appear in polycrystals at the edges of grain boundaries; but they are of limited interest in solid single crystals, where they can move only by diffusion climb and, owing to their large elastic stresses, mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, and change of shape involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, which are particularly well suited for consideration here. The notion of an extended Volterra process is introduced, which takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by a variety of applications in amorphous solids, mesomorphic phases, and frustrated media in their curved habit space. These often involve disclination networks with specific node conditions. The powerful topological theory of line defects considers only defects stable against any change of boundary conditions or relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, particularly suited for media of high plasticity or/and complex structures. It cannot analyze the dynamical properties of defects nor the elastic constants involved in their static properties; topological stability cannot guarantee energetic stability, and sometimes cannot distinguish finer details of the structure of defects.