Neural network potential for Al-Mg-Si alloys

The 6000 series Al alloys, which include a few percent of Mg and Si, are important in automotive and aviation industries because of their low weight, as compared to steels, and the fact their strength can be greatly improved through engineered precipitation. To enable atomistic-level simulations of both the processing and performance of this important alloy system, a neural network (NN) potential for the ternary Al-Mg-Si has been created. Training of the NN uses an extensive database of properties computed using first-principles density functional theory, including complex precipitate phases in this alloy. The NN potential accurately reproduces most of the pure Al properties relevant to the mechanical behavior as well as heat of solution, solute-solute, and solute-vacancy interaction energies, and formation energies of small solute clusters and precipitates that are required for modeling the early stage of precipitation and mechanical strengthening. This success not only enables future detailed studies of Al-Mg-Si but also highlights the ability of NN methods to generate useful potentials in complex alloy systems.

Figure 1

Energies per atom of sample structures obtained by the NN potential and the DFT calculation. The $y=x$ line indicates ideal matching between NN and DFT values.

Figure 2

Generalized stacking fault curve for bulk Al along the [112] direction, as computed using DFT, two MEAM potentials, and the present NN potential. These structures are included in the training data.

Figure 3

Nye tensor distribution of the screw component of the Burgers vector for the dissociated edge dislocation core in pure Al; the result agrees well with direct DFT [29, 30], $x$ and $y$ axes are in units of the Burgers vector $b=2.86\AA$. This structure is not in the training data.

Figure 4

Energy vs separation for rigid block separation across the (111), (110), and (100) surfaces of bulk Al, as computed via DFT, two MEAM potentials, and the present NN potential. These structures are included in the training data.

Figure 5

(a) Solute-solute binding energies as a function of distance between solutes, and (b) solute-vacancy binding energies, obtained by the NN potential (filled markers and solid lines) and DFT (open markers and broken lines). These values are obtained using $4\times 4\times 4$ cubic FCC cells which are not in the training data, but the relevant structures with $2\times 2\times 2$ cells are in the training data.

Figure 6

Formation energies per atom of the system described in Sec. 2 obtained by the NN potential (red squares) and the DFT-PBEsol (blue circles), as differences from the DFT-PBE results. Since these structures are not in the training data set, this can be treated as the prediction error of solution/precipitation energies by the NN potential.

Figure 7

(a) Typical simulation cell of ${\mathrm{Mg}}_5{\mathrm{Si}}_6$ precipitate of $N_{\mathrm{FU}}=4$ in Al matrix, which corresponds to $7\times 7\times 1$ FCC Al cell. The system is periodic in $z$ direction, ${\left[001\right]}_{\mathrm{Al}}$. The green rectangle indicates a monoclinic cell of ${\mathrm{Mg}}_5{\mathrm{Si}}_6$. (b) Formation unit of ${\mathrm{Mg}}_5{\mathrm{Si}}_6$ indicated in the red rectangle in (a). In case of ${\mathrm{Mg}}_5{\mathrm{Al}}_2{\mathrm{Si}}_4,{\mathrm{Si}}_3$ sites in ${\mathrm{Mg}}_5{\mathrm{Si}}_6$ are replaced by Al, while ${\mathrm{Mg}}_1$ site is also replaced by Al in ${\mathrm{Mg}}_4{\mathrm{Al}}_4{\mathrm{Si}}_4$. (c) Size dependency of the precipitation energy of ${\mathrm{Mg}}_5{\mathrm{Si}}_6,{\mathrm{Al}}_2{\mathrm{Mg}}_5{\mathrm{Si}}_4$, and ${\mathrm{Al}}_3{\mathrm{Mg}}_4{\mathrm{Si}}_4$ obtained by the NN potential and the DFT (from D. Giofré et al. [19]). These structures are not in the training data set.

Figure 8

Interactions between a dissociated dislocation core in Al and a solute in (a) Mg and (b) Si. These structures are not in the training data set.