The Peierls dislocation: Line energy, line tension, dissociation and deviation

Abstract

Atomic simulations of the dislocation core show that the atomic misfit is often concentrated in the glide plane. Instead of using a step function to describe the displacement as in a classical Volterra dislocation, a better description is obtained by a Peierls dislocation for which the displacement is assumed to have an arctg like shape. The slope in the center is determined by requiring that the total energy must be a minimum. The elastic energy can be expressed in closed form, and with the availability of high speed computing the atomic misfit energy in the glide plane can be calculated by standard numerical integration without any difficulties. When the Peierls model is extended to two dimensions the resulting line energy, line tension and resistance against bow-outs of straight dislocations can be obtained realistically without any adjustable parameters and the way that these quantities are influenced by the interplanar atomic potential can be studied. In addition to undergoing the well-known “dissociation”, a mixed dislocation may lower its energy by a “deviation” in which the displacement vector deviates from the direction of the crystallographic Burgers vector even when this runs along a path of lowest misfit energy.