A lattice theory for structure of dislocations in a two-dimensional triangular crystal was 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 was derived explicitly by using the lattice Green’s function method. It was found that in the well-known Peierls equation a term proportional to the second-order derivative was 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 was calculated approximately. It was found that the improvement to Peierls' solution was remarkable at the neighborhood of the core center. The vertical displacements of atoms on the different borders were small in magnitude and opposite in direction.

Lattice Theory for Structure of Dislocations in a Two-Dimensional Triangular Crystal. W.Shaofeng: Physical Review B, 2002, 65[9], 094111 (10pp)