The dissociation of a dislocation, in the {111}-plane of a face-centered cubic lattice, into 2 Shockley partials was studied by using a variational procedure within the framework of the Peierls model; as generalized to 2 dimensions. Each partial was made up of a distribution of infinitesimal dislocations having a density which was obtained by superposing 3 closely-spaced Lorentz peaks of adjustable height, width and separation. The atomic misfit energy in the glide plane was obtained from the γ surface as represented by a 2-dimensional Fourier series which exhibited the symmetry of the {111} plane. The procedure was applied to Al, for which a set of γ-values on the {111} plane had been obtained by using ab initio electron density functional theory. The dissociation width of the edge dislocation was found to be 0.74nm. This almost agreed with the experimental value of about 0.8nm. The screw dislocation was not split in the usual way, but instead involved a widely extended core plus some edge components. The energy which was required to compress the core to a pure screw dislocation was equal to 0.042eV/b. The Peierls energy could be evaluated via numerical summation of the energy at the atom positions. Contrary to previous treatments, the core configuration was relaxed, and changes in elastic energy therefore contributed to the Peierls energy.

The Core Structure, Recombination Energy and Peierls Energy for Dislocations in Al. G.Schoeck: Philosophical Magazine A, 2001, 81[5], 1161-76