The Peierls—Nabarro Model of Dislocations: A Venerable Theory and its Current Development
Dislocations are central to the understanding of mechanical properties of crystalline solids. While continuum elasticity theory describes well the long-range elastic strain of a dislocation for length scales beyond a few lattice spacings, it breaks down near the singularity in the region surrounding the dislocation center, known as the dislocation core. There has been a great deal of interest in describing accurately the dislocation core structure on an atomic scale because of its important role in many phenomena of crystal plasticity [1, 2, 3]. The core properties control, for instance, the mobility of dislocations, which accounts for the intrinsic ductility or brittleness of solids. The core is also responsible for the interaction of dislocations at close distances, which is relevant to plastic deformation.
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