Phase diagram and global structure search of bismuth using machine learning potential

Bismuth’s (Bi) unique high-pressure phase behavior has long attracted significant interest. Despite their significance in both technological applications and fundamental research, comprehensive and accurate modeling of these transitions remains challenging. To address this, we developed a neural equivariant potential machine learning potential for Bi with near first-principles accuracy. By integrating this potential with state-of-the-art computational techniques—including the MAGUS crystal structure search algorithm and GPUMD molecular dynamics simulations with enhanced sampling—we systematically explored the phase behavior of Bi under high-pressure and high-temperature conditions. The calculated solid–solid phase boundaries and solid–liquid coexistence line up to 4 GPa show good agreement with previous experimental results. Furthermore, we predict a new competitive phase of Bi with P42/mnm symmetry, which is dynamically stable around 2 GPa and competitive at free energy with the known phase C2/m near the melting line.