Electron Distribution about an Edge Dislocation in a Metal

The self-consistent electrostatic potential and charge density associated with a straight edge dislocation in a free-electron metal are calculated to the first order in perturbation theory, the positive-ion background being replaced by a continuum of positive charge which is assumed to deform according to the equations of isotropic elasticity. The potential obtained is identical with the deformation potential outside the core of the dislocation, but approaches zero on the dislocation line. In contrast to the deformation-potential approach, the screening by the conduction electrons of the positive charge shift is incomplete, with the result that the total charge density behaves as $r^{-\frac{5}{2}}sin(2\mathrm{}{k}_{f}r+\frac{1}{4}\pi )$ outside the core of the dislocation. The effects of the core region, which is not well described by the model, are briefly considered, and the effects of the periodic lattice are obtained in the nearly-free-electron approximation.