Machine learning metadynamics simulation of reconstructive phase transition

Simulating reconstructive phase transition requires an accurate description of potential energy surface (PES). Density-functional-theory (DFT) based molecular dynamics can achieve the desired accuracy but it is computationally unfeasible for large systems and/or long simulation times. Here we introduce an approach that combines the metadynamics simulation and machine learning representation of PES at the accuracy close to the DFT calculations, but with the computational cost several orders of magnitude less, and scaling with system size approximately linear. The high accuracy of the method is demonstrated in the simulation of pressure-induced $B4\text{−}B1$ phase transition in gallium nitride (GaN). The large-scale simulation using a 4096-atom simulation box reveals the phase transition with excellent detail, revealing different simulated transition paths under particular stress conditions. With well-trained machine learning potentials, this method can be easily applied to all types of systems for accurate scalable simulations of solid-solid reconstructive phase transition.

Figure 1

Summary of the training data set and test calculations for the MLP. (a) Left: Distribution of energies and volumes for all structures in the training sets calculated using vasp. Structures in five data sets are distinguished by different colors and shapes. Right: energy distribution of randomized (data set 1) and coarse-MLP-relaxed structures (data set 3). (b) Calculated enthalpies for the $B4$ and $B1$ phases in the pressure range 0–80 GPa using MLP (points) and vasp (lines). The enthalpies of the $B4$ phase calculated by vasp (red line) are taken as the zero-energy reference. (c) The RDFs of N-N, Ga-N, and Ga-Ga obtained from the NVT simulation of $B4$ phase at 50 GPa and 300 K using vasp and MLP respectively.

Figure 2

The “tetragonal” and “hexagonal” transition paths. Both paths consist of two steps, closure of angle γ and increase of the relative spacing $u$, but have opposite sequences. The Ga and N atoms are represented by green (larger) and blue (smaller) balls, respectively.

Figure 3

Evolution of the enthalpy in 64-atom MetaD simulation using MLP under isotropic and uniaxial pressures starting from the $B4$ structure at 300 K and 50 GPa.

Figure 4

Snapshots of the 4096-atom simulation box of the $B4$ phase in MetaD simulation using MLP at 50 GPa under hydrostatic conditions. In (a)–(f), Ga and N atoms are not distinguished but colored by coordination numbers (CN) determined by a cutoff radius 2.3 Å. Blue, grey, and red represents atoms with $\mathrm{CN}=4$, 5, and 6, respectively. For clarity, a nucleation center is enlarged from the snapshot at metastep 33. In (g), only Ga atoms are shown and colored by their atomic energy obtained from MLP and the lowest atomic energy is taken as the reference. The shearing caused by soft $s_3$ mode and the direction of atomic realignment along the face diagonal are highlighted. Figures are generated using ovito [64].

Figure 5

Snapshots of the 4096-atom simulation box of the $B4$ phase in MetaD simulation using MLP at 50 GPa under uniaxial stress conditions. Additional uniaxial stress of 5 GPa is loaded in $h_{33}$ [001] direction. Ga and N atoms are not distinguished but colored by coordination numbers (CN) determined by a cutoff radius 2.3 Å. Blue, grey, and red represents atoms with $\mathrm{CN}=4$, 5, and 6, respectively.