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

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