Lattice theory for structure of dislocations in a two-dimensional triangular crystal

Abstract

A lattice theory for structure of dislocations in a two-dimensional triangular crystal is presented. In analogy to Peierls model, the dislocation results from nonlinear interaction of two half-infinite perfect crystals. A dislocation equation that only relates to the atoms on the borders through which two perfect crystals match together is derived explicitly by using the lattice Green's-function method. It is found that in the well-known Peierls equation a term proportional to the second-order derivative is dropped due to continuum approximation for the half-infinite crystal. This term has an important influence on the core structure of the dislocation. Based on the dislocation equation obtained here, the core configuration of a dislocation, including vertical as well as horizontal deformations has been calculated approximately. It is found that the improvement to Peierls's solution is remarkable at the neighborhood of the core center. The vertical displacements of atoms on the different borders are small in magnitude and opposite in direction.