Dislocation Core Energies and Core Fields from First Principles

Ab initio calculations in bcc iron show that a $⟨111⟩$ screw dislocation induces a short-range dilatation field in addition to the Volterra elastic field. This core field is modeled in anisotropic elastic theory using force dipoles. The elastic modeling thus better reproduces the atom displacements observed in ab initio calculations. Including this core field in the computation of the elastic energy allows deriving a core energy which converges faster with the cell size, thus leading to a result which does not depend on the geometry of the dislocation array used for the simulation.

Figure 1

Screw dislocation periodic arrangements used for ab initio calculations: (a) T and (b) AT triangular arrangements, (c) quadrupolar arrangement. $\overrightarrow{b}=\frac{1}{2}[111]$ for easy and $\frac{1}{2}[\overline{1}\overline{1}\overline{1}]$ for hard cores. $\overrightarrow{A}$ is the dipole cut vector.

Figure 2

Core energy difference between the easy and hard core configurations. Solid symbols correspond to core energies obtained when only the Volterra field is considered and open symbols to core energies when both the Volterra and the core fields are taken into account ($r_c=3\AA$).

Figure 3

Planar displacement map of a periodic unit cell containing a screw dislocation dipole obtained from ab initio calculations: (a) total displacement, (b) after subtraction of the Volterra elastic field, and (c) after subtraction of the Volterra and the core elastic fields. Vectors correspond to (111) in-plane displacements and have been magnified by a factor 50. Displacements smaller than 0.01 Å are omitted. For clarity, displacements of the six atoms belonging to the cores of the two dislocations are not shown in (c). Atomic positions are drawn as circles with a color depending of their original (111) plane.

Figure 4

Sketch of the (111) in-plane displacement created by the triangular arrangement of dislocations in their easy core configuration. For the T variant (a), the displacements due to the Volterra and the core fields have the same sign and sum up in the region between two neighboring dislocations, whereas they partially cancel for the AT variant (b).