Automated atomistic simulations of dissociated dislocations with ab initio accuracy

In a previous work [M. Hodapp and A. Shapeev, Mach. Learn.: Sci. Technol. 1, 045005 (2020)], we proposed an algorithm that fully automatically trains machine-learning interatomic potentials (MLIPs) during large-scale simulations, and successfully applied it to simulate screw dislocation motion in body-centered-cubic tungsten. The algorithm identifies local subregions of the large-scale simulation region where the potential extrapolates, and then constructs periodic configurations of 100–200 atoms out of these nonperiodic subregions that can be efficiently computed with plane-wave density functional theory (DFT) codes. In this work, we extend this algorithm to dissociated dislocations with arbitrary character angles and apply it to partial dislocations in face-centered-cubic aluminum. Given the excellent agreement with available DFT reference results, we argue that our algorithm has the potential to become a universal way of simulating dissociated dislocations in face-centered-cubic and possibly other materials, such as hexagonal-closed-packed magnesium, and their alloys. Moreover, it can be used to construct reliable training sets for MLIPs to be used in large-scale simulations of curved dislocations.

Figure 1

Schematic illustration of the individual steps of the active learning algorithm for fcc dislocations presented in Sec. 2b2. The coloring of the atoms is due to the centrosymmetry parameter (CSP) [52], in order to visualize their deviation from the ideal crystal.

Figure 2

Illustration of the solution (5) that is periodic over a rectangular region containing four linear elastic dislocations. Due to symmetry, the solution is even periodic up to a constant given by half of the magnitude of the Burgers vector over the smaller triclinic cell that contains only two dislocations.

Figure 3

Steps of the process of completing extrapolative neighborhoods around both partial dislocations to periodic training configurations. (a) Extraction of the extrapolative neighborhoods from the large-scale configuration $\left\{{\mathit{r}}_i\right\}$. (b) Mirroring of the displacement field along the $y$ axis in order to construct a configuration that is periodic along the dislocation glide direction. (c) Adjustment of the triclinic cell vectors to remove any artificial neighborhoods near the cell boundaries.

Figure 4

Final training configurations ${\left\{{\mathit{r}}_i\right\}}_{\mathrm{lead}}^{*}$ (left) and ${\left\{{\mathit{r}}_i\right\}}_{\mathrm{trail}}^{*}$ (right) for an edge dislocation. The dislocations have been detected using the dislocation extraction algorithm (DXA) [53], implemented in ovito [54]. The net Burgers vector is zero over each configuration, which follows from mirroring the configuration at the $yz$ plane (cf. Fig. 3). Note that for a better visualization, the configuration has been extended in the $z$ direction; the actual training configuration is confined to the triclinic cell.

Figure 5

Visualization of the edge dislocation core structure predicted by the MTP, QM/MM [7], and OF-DFT [10], using the edge and screw components of the Nye tensor, and differential displacements. Overall, the agreement between the MTP and DFT core structures is very good, and the splitting distances between the partial dislocations closely coincide, up to the usual uncertainty of about the distance between two atomic planes. The QM/MM and OF-DFT figures are reproduced from [7] and [10] with permission.

Figure 6

Visualization of the screw dislocation core structure predicted by the MTP, QM/MM [7], and OF-DFT [11], using the edge and screw components of the Nye tensor, and differential displacements. Overall, the agreement between the MTP and DFT core structures is very good, and the splitting distances between the partial dislocations remarkably coincide. The QM/MM and OF-DFT figures are reproduced from [7] and [11] with permission.

Figure 7

Dislocation energies for the edge and screw dislocations predicted by the MTP and OF-DFT. The agreement between the MTP and OF-DFT is very good and the far-field behavior corresponds to the dislocation energy predicted by linear elasticity (dashed lines) up to some constant core energy.

Figure 8

Visualization of the ${30}^{\circ }$-mixed dislocation core structure predicted by the MTP using the edge and screw components of the Nye tensor.

Figure 9

Dislocation energies for the mixed dislocation predicted by the MTP. The far-field behavior corresponds to the dislocation energy predicted by linear elasticity (dashed lines) up to some constant core energy.

Figure 10

Visualization of the dislocation cores predicted by EAM and MTP using the common neighbor analysis and the DXA.

Figure 11

Dislocation energies for the edge, mixed, and screw dislocations predicted by the MTP and the EAM potential.