A simple but rigorous analytical formula was derived for the Peierls stress of a dislocation within the Peierls-Nabarro model. It was a generalization and correction of a published formula which was valid only for wide dislocations. The present formula offered the possibility of estimating the Peierls stress directly from the generalized stacking fault energy surface. It was applicable to both narrow and wide dislocations. A comparison with experimental data demonstrated that the present expressions for the Peierls stress provided a rapid alternative to atomistic calculations. They also supported the Peierls-Nabarro model as being a simple treatment which was capable of providing quantitative predictions. The only inputs which were required were the maximum restoring stress, for the glide plane in question, and the corresponding elastic constant.

An Analytical Formula for the Peierls Stress of Dislocations. B.Joós, M.S.Duesbery: Physical Review Letters, 1997, 78[2], 266-9