Structural Details of the Dislocation Core

Thus far, our discussion of dislocation core effects has been built around those tools admitting of direct analytic progress such as is offered by the Peierls-Nabarro dislocation core model. This model has many virtues. However, it is also strictly limited, with one of its primary limitations being that without huge machinations, it may only be applied to dislocations with planar cores. To explore the full atomic-level complexity that arises in dislocation cores, we must resort to numerical techniques, and direct atomistic simulation in particular. The remainder of our discussion on dislocation cores will take up the question of how one goes about carrying out such simulations and what may be learned from them. 

One of the central conclusions derived from the Peierls-Nabarro analysis is the role of nonlinear effects in the dislocation core. From an atomistic perspective, the far field atomic displacements could be derived just as well from linear elasticity as the full nonlinear function that results from direct atomistic calculation. By way of contrast, in the core region it is the nonlinear terms that give rise to some of the complex core rearrangements that we take up now. Our discussion will be built around two key examples cores in fee metals and the core reconstructions found in covalent semiconductors such as in Si. 

Before embarking on the specifics of these cores, we begin with an assessment of the basic ideas needed to effect an atomistic simulation of the dislocation core. We begin with a picture of lattice statics in which the core geometry is determined by energy minimization. To proceed, what is needed is an energy function of the type discussed in chap. 4 which may be written generically as 

For the moment, we describe the most naive approach to this problem and will reserve for later chapters (e.g. chap. 12) more sophisticated matching schemes which allow for the nonlinear calculations demanded in the core to be matched to linear calculations in the far fields. As we have repeatedly belabored, the objective is to allow the core geometry to emerge as a result of the full nonlinearity that accompanies that use of an atomistic approach to the total energy. However, in order to accomplish this aim, some form of boundary condition must be instituted. One of the most common such schemes is to assume that the far field atomic positions are dictated entirely by the linear elastic fields. In particular, that is 

A more substantial rearrangement in the dislocation core can be found in the case of a covalent material. Probably the single greatest influence on the structures adopted by defects in covalent materials is the severe energy penalty that attends dangling bonds. Free surfaces, grain boundaries and dislocation cores all have geometries that reconstruct in a manner that preserves (albeit in a distorted way) 

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