A critical reexamination of the Peierls-Nabarro model

We reexamine two essential issues within the Peierls-Nabarro model which are critical in obtaining accurate values for the Peierls stress. The first issue is related to the sampling scheme of the misfit energy across the glide plane and the second one is the effect of relaxation on the Peierls stress. It is shown that most of the current applications of the Peierls-Nabarro model do not treat properly the two issues and therefore are not able to predict reliable values for the Peierls stress. We argue that the double counting scheme for the misfit energy at both sides of the glide plane is physically more reasonable, and it can predict more accurate values for the Peierls stress, especially for dislocations with equal spacing between alternating atomic rows. We also show the importance for allowing atomic relaxation when a dislocation traverses the Peierls barrier, which in turn lowers the Peierls stress for narrow dislocations by an order of magnitude.