Fifty-year study of the Peierls-Nabarro stress

The origin of the Peierls model and its relation to that of Frenkel and Kontorova are described. Within this model there are three essentially different formulae for the stress required to move a dislocation rigidly through a perfect lattice, associated with the names of Peierls, Nabarro and Huntington. There are also three distinct approaches to experimental estimates of the Peierls stress, depending on the Bordoni internal friction peak, the flow stress at low temperatures and Harper-Dorn creep. The results in the case of close-packed metals can be reconciled with the aid of ideas due to Benoit et al. and to Schoeck. The analytical elegance of Peierls's solution depends on the assumption of a sinusoidal law of force across the glide plane. This is physically unrealistic. Foreman et al. and others have obtained interesting results using other laws of force, while still operating in the framework of the Peierls model. The locking-unlocking model extends the ideas to the case in which the dislocation core has two mechanically stable configurations.