Dislocations and crowdions in two-dimensional crystals. I. Atomic-lattice models and a continuum description of these defects in elastic anisotropic 2D media

Abstract

A rigorous continuum description of dislocations and crowdions as intrinsic structural defects in two-dimensional (2D) crystals is proposed. The two types of defects are studied in a unified approach: a crystal is treated as a strictly 2D anisotropic elastic medium and the defects as point carriers of plastic deformation and singular sources of elastic deformation fields, with each having distinct crystal-geometric and topological properties. The continuum description is preceded by a discussion of simple atomic-lattice schemes illustrating the microscopic structure of these defects. The two types of defects are each assigned a plastic distortion tensor that matches their crystal-geometric characteristics. Based on a linear theory of the plasticity of 2D media, equations are derived for the distribution of the elastic fields around isolated defect centers, as well as for a continuous distribution of defects in a crystal. General solutions of these equations are found for fixed dislocations and crowdions in an infinitely extended elastic anisotropic 2D continuum.