A dislocation equation satisfied by both horizontal displacement parallel to the glide plane and vertical displacement perpendicular to the glide plane was derived generally from the lattice dynamics. In the slow-varying approximation that could be well applied to the dislocation, the equation was changed into an integro-differential equation that possesses a universal form except the coefficients. If the higher-order derivatives of the displacement were cancelled, the classic Peierls equation was recovered. The terms proportional to the higher-order derivatives represent the lattice effects that cannot be obtained in the continuum theory, and cannot be neglected in the core of the dislocation. The results were helpful to link the plasticity with the electronic structure of material because it was rigorously shown that the dislocation structure was mainly controlled by a few factors.

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