On Dislocation Patterning

A new method to consider the formation and stability of dislocation patterns is outlined. It is based on the assumption of a fluid-like dislocation state which evolves within the lattice state. This evolution is specified by the balance laws of mass and momentum together with appropriate constitutive equations for the mechanical fields associated with the dislocation state. The approach leads to nonlinear partial differential equations of the diffusion reaction type. As in the case of dissipative structures and other self-organization phenomena, the competition between diffusive and reacting terms determines the occurence and persistence of spatial instabilities, the wavelength of periodic ones, and the shape of two and three dimensional dislocation patterns such as cell walls, vein, and ladder structures.