Size-Dependent Nucleation in Crystal Phase Transition from Machine Learning Metadynamics

In this Letter, we present a framework that combines machine learning potential (MLP) and metadynamics to investigate solid-solid phase transition. Based on the spectral descriptors and neural networks regression, we develop a scalable MLP model to warrant an accurate interpolation of the energy surface where two phases coexist. Applying it to the simulation of B4–B1 phase transition of GaN under 50 GPa with different model sizes, we observe sequential change of the phase transition mechanism from collective modes to nucleation and growths. When the size is at or below 128 000 atoms, the nucleation and growth appear to follow a preferred direction. At larger sizes, the nuclei occur at multiple sites simultaneously and grow to microstructures by passing the critical size. The observed change of the atomistic mechanism manifests the importance of statistical sampling with large system size in phase transition modeling.

Figure 1

Comparison of the B4–B1 PES of GaN at 50 GPa computed using (a) DFT and (b) MLP methods.

Figure 2

The metadynamics simulation of 128 atoms GaN’s B4–B1 transition. (a) Evolution of enthalpy ($H$) in MLP-based metadynamics (yellow) simulation. The enthalpies along the trajectory were recomputed with DFT (red) for a comparison. (b) Evolution of CVs along the trajectory. ($a$, $b$, $c$) and ($ab$, $bc$, $ac$) denote uniaxial and shear modes, respectively. (c) Stress tensors from DFT and MLP calculations. (d) Atomistic motions at critical steps, in which atoms in orange and white denote the four-coordinated B4 and six-coordinated B1 environments.

Figure 3

The size-dependent metadynamics simulations of GaN’s B4–B1 transition. (a) Evolution of phase transition barrier ($\mathrm{\Delta }{E}_3$) as a function of system size. (b) and (c) Time evolution of enthalpy ($H$) during the phase transition for several selected systems. Two representative inset snapshots show directional [in (b)] and homogeneous [in (c)] nucleation mechanisms.

Figure 4

The size-dependent nucleation process in GaN’s B4–B1 transition. (a) Variation of enthalpy and temperature as a function of time for $N=16000$, 128 000, and 524 288. (b),(c) Selected MD snapshots for $N=128000$ and 524 288, respectively. Several representative nucleus sites ($\mathbf{A}$, ${\mathbf{B}}_1$, ${\mathbf{B}}_2$, $\mathbf{C}$) are marked in gold color to guide the eye. To compute $H_{\mathrm{GaN}}$, the atomic volumes are estimated by Voronoi tessellation from ovito [36].