Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate
We use a real-space formulation of orbital-free DFT to study the core energetics and core structure of an isolated screw dislocation in Aluminum. Using a direct energetics based approach, we estimate the core size of a perfect screw dislocation to be $\approx$ 7 $|{\bf b}|$, which is considerably larger than previous estimates of $1-3~|{\bf b}|$ based on displacement fields. The perfect screw upon structural relaxation dissociates into two Shockley partials with partial separation distances of 8.2 \AA~and 6.6 \AA~ measured from the screw and edge component differential displacement plots, respectively. Similar to a previous electronic structure study on edge dislocation, we find that the core energy of the relaxed screw dislocation is strongly dependent on macroscopic deformations. Next, we use the edge and screw dislocation core energetics data with physically reasonable assumptions to develop a continuum energetics model for an aggregate of dislocations. Further, we use this model in a discrete dislocation network, and from the variations of the core energy with respect to the nodal positions of the network, we obtain the nodal core force which can directly be incorporated into discrete dislocation dynamics frameworks. We analyze and classify the nodal core force into three different contributions based on their decay behavior. Two of these contributions to the core force, both arising from the core energy dependence on macroscopic deformations, are not accounted for in currently used discrete dislocation dynamics models which assume the core energy to be a constant. Using case studies involving simple dislocation structures, we demonstrate that the contribution to the core force from the core energy dependence on macroscopic deformations can be significant in comparison to the elastic Peach-Koehler force even up to distances of $10-15$ nm between dislocation structures.