A dislocation equation was derived, from lattice dynamics, which was satisfied by both horizontal displacements parallel to the glide plane and vertical displacements perpendicular to the glide plane. In the slowly-varying approximation that could be applied to the dislocation, the equation changed to an integro-differential equation that had a universal form; except for the coefficients. If the higher-order derivatives of the displacement cancelled, the classic Peierls equation was recovered. Terms proportional to the higher-order derivatives represented lattice effects that could not be obtained in the continuum theory, and could not be neglected in the core of the dislocation. These results were helpful for linking the plasticity to the electronic structure of a material because it could be rigorously shown that the dislocation structure was controlled mainly by a few factors.

Dislocation Equation from the Lattice Dynamics. S.Wang: Journal of Physics A, 2008, 41[1], 015005 (15pp)