A lattice theory for the structure of dislocations in a 2-dimensional triangular crystal was presented. In analogy to the Peierls model, the dislocation resulted from the non-linear interaction of 2 half-infinite perfect crystals. A dislocation equation that related only to atoms on the borders through which 2 perfect crystals matched together was derived explicitly by using the lattice Green’s function method. It was found that, in the Peierls equation, a term which was proportional to the second-order derivative was dropped due to the continuum approximation for the half-infinite crystal. This term had an important effect upon the core structure of the dislocation. Based on the present dislocation equation, the core configuration of a dislocation (including vertical and horizontal deformations) was calculated approximately. It was found that the improvement to the Peierls solution was remarkable in 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. S.Wang: Physical Review B, 2002, 65[9], 094111 (10pp)