$\alpha$-$\beta$ phase transition of zirconium predicted by on-the-fly machine-learned force field

TL;DR

This study employs on-the-fly machine-learned force fields to accurately simulate the $ ext{α}$-$ ext{β}$ phase transition in zirconium at finite temperature, capturing its first-order nature and matching experimental transition temperatures.

Contribution

The paper introduces an automated on-the-fly machine learning approach for generating force fields during first-principles MD, enabling accurate simulation of phase transitions without human intervention.

Findings

Successfully reproduces the first-order displacive phase transition in Zr.

Predicted phase transition temperature aligns well with experimental data.

Improved force field accuracy using singular value decomposition in the training process.

Abstract

The accurate prediction of solid-solid structural phase transitions at finite temperature is a challenging task, since the dynamics is so slow that direct simulations of the phase transitions by first-principles (FP) methods are typically not possible. Here, we study the $\alpha$-$\beta$ phase transition of Zr at ambient pressure by means of on-the-fly machine-learned force fields. These are automatically generated during FP molecular dynamics (MD) simulations without the need of human intervention, while retaining almost FP accuracy. Our MD simulations successfully reproduce the first-order displacive nature of the phase transition, which is manifested by an abrupt jump of the volume and a cooperative displacement of atoms at the phase transition temperature. The phase transition is further identified by the simulated x-ray powder diffraction, and the predicted phase transition temperature is in reasonable agreement with experiment. Furthermore, we show that using a singular value decomposition and pseudo inversion of the design matrix generally improves the machine-learned force field compared to the usual inversion of the squared matrix in the regularized Bayesian regression.