The origin of the Peierls model, and its relationship to the Frenkel-Kontorova model, was described. It was noted that, within the former model, there were 3 essentially different formulae (Peierls, Nabarro, Huntington) for the stress that was required to move a dislocation rigidly through a perfect lattice. There were also 3 distinct measurement approaches (Bordoni internal friction, low-temperature flow stress, Harper-Dorn creep) to experimental estimation of the Peierls stress. It was concluded that the analytical elegance of the Peierls solution depended upon the assumption of a sinusoidal force law across the glide plane; which was physically unrealistic. Others had obtained interesting results by using different force laws, while still operating within the framework of the Peierls model. The locking-unlocking model also extended the idea to the case where the dislocation core possessed 2 mechanically stable configurations.

Fifty-Year Study of the Peierls-Nabarro Stress. F.R.N.Nabarro: Materials Science and Engineering A, 1997, 234-236, 67-76