Energy and Atomic Configurations of Complete and Dissociated Dislocations. II. Screw Dislocation in an fcc Metal

Abstract

The arrangement of atoms around a screw dislocation in copper has been calculated by a variational method. The pairwise interaction between discrete atoms was represented by a Morse potential function. The displacements parallel to the dislocation line agree well with those given by linear elastic theory except for atoms within a distance of about 5.3 \AA{} of the center of the dislocation. Because of this, there is a disparity between the atomistic and elastic energies inside a core radius of 5.3 \AA{} for a complete $〈110〉$ screw dislocation ($\mathrm{Burgers}\mathrm{vector}=(\frac{{a}_{0}}{2})〈110〉$), where ${a}_{0}$ is the lattice parameter. The corresponding core energy is 1.0 eV per nearest-neighbor distance. In the calculation of the complete dislocation, the atoms were not permitted to relax in a direction perpendicular to the dislocation line. This prevented dissociation. When this constraint is removed, dissociation into two partial dislocations occurs spontaneously. If the core is replaced by a hole of radius ${r}_{\mathrm{eh}}$ (the equivalent hole radius), the inside of which is hollow and outside of which linear-elastic theory holds at all points, this radius is 1.1 \AA{}. The energy of the screw dislocation varies as $\mathrm{ln}r$ at large radii, in agreement with elastic-continuum theory. By comparing this asymptotic behavior with the corresponding curve for the edge dislocation, atomistic values of the shear modulus and Poisson's ratio were obtained.