The Peierls model: Progress and limitations

The basic features of the Peierls model are reviewed. The original model is based on the concept of balance of stresses in 1D and has serious limitations. These limitations can be overcome by a treatment as a variational problem on the energy level in 2D. The fundamental equations are given and applications to determine displacement profiles for dislocations and their dissociations are discussed. When the core misfit has a planar extension and the misfit energy in the glide plane - the γ-surface - is determined from ab initio methods, very reliable core configurations can be determined. For dislocations along close-packed lattice directions the misfit energy can be obtained by a summing procedure using Euler coordinates. When these dislocations are dissociated multiple equilibrium configurations with different splitting widths can exist, but the values of energy difference in between - the Peierls energy - are too small to be determined reliably, considering the simplifying assumptions of the model.