We use the first-principles spin-polarized energy density method (EDM) to calculate the atomic energies in isolated $a_0\left[100\right]\left(010\right)$ edge, $a_0\left[100\right]\left(011\right)$ edge, $\frac{a_0}{2}\left[\overline{1}\overline{1}1\right]\left(1\overline{1}0\right)$ edge, and $\frac{a_0}{2}\left[111\right]\left(1\overline{1}0\right){71}^{\circ }$ mixed dislocations in body-centered cubic (bcc) Fe. The distribution of atomic energies shows the energetic effects of slip, including nonlinear displacements in and near the core, and the elastic field further away. The EDM atomic energies agree well with anisotropic elasticity predictions in the elastic region, while they deviate in the core region due to the failure of linear elasticity, and the energy deviation quantifies the core widths. Dislocation-line energies are obtained by partial sums of the atomic energies within a distance $r$ of the dislocation center; the core energy is extracted from the large-$r$ behavior. We compare our results with an EAM and a GAP potential, showing that while both potentials produce core structures similar to density-functional theory (DFT) predictions, the GAP potential has a closer match with DFT and EDM in core energies.

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• Disclinations & dislocations
• Plastic deformation
• Density functional theory