In our treatment of dislocations thus far, we have avoided the dislocation core. For example, in Volterra's dislocation model, the stress–strain fields diverge on the dislocation line, so that a cylindrical region of material is usually removed around the dislocation line to avoid the singularity. In the line tension model, the dislocation is modeled as a string that carries a line energy per unit length, but is otherwise featureless. In Chapter 11, we have seen that perfect dislocations in close-packed metals tend to dissociate into partial dislocations, but the partial dislocations were still treated as Volterra's dislocation lines. In reality, every (perfect or partial) crystal dislocation has a core region, which possesses a specific atomistic structure, called the core structure. The core structure is determined by non-linear interatomic interactions and the crystal structure, and, in turn, strongly influences the energetics and mobility of the dislocations. In this chapter, we discuss typical dislocation core structures and their effects on dislocation properties in several crystal structures.
In Section 12.1, we start our discussion with the classical Peierls–Nabarro (PN) model, which was the first physical model for the dislocation core and naturally predicts that the dislocation core should have a finite width. In Section 12.2, we generalize the original PN model to account for the presence of stacking faults in FCC metals. Consistent with the hard sphere model in Chapter 11, the generalized PN model also predicts dissociation of perfect dislocations into partials, except that each partial now has a finite width.
For crystals whose structures are sufficiently different from close-packed, hard spheres are no longer a good model for the atoms. Nonetheless, the geometry of the stacking of atomic layers is still useful for understanding the dislocation core structures in these crystals, as discussed in Section 12.3 (diamond cubic crystals) and Section 12.4 (BCC crystals). Finally, in Section 12.5 we discuss the interaction between dislocations and point defects, which usually leads to segregation of point defects around the dislocation core.
The classical model by Peierls and Nabarro [111, 112] considers the spreading of the dislocation over the glide plane.