Machine learning models for predictive materials science from fundamental physics: An application to titanium and zirconium

Here we present new neural network potentials capable of accurately modeling the transformations between the α, β, and ω phases of titanium(Ti) and zirconium (Zr), including accurate prediction of the equilibrium phase diagram. The potentials are constructed based on the rapid artificial neural network (RANN) formalism which bases its structural fingerprint on the modified embedded atom method. This implementation allows the potential to reproduce density functional theory results including elastic and plastic properties, phonon spectra, and relative energies of each of the three phases at classical molecular dynamics (MD) speeds. Transitions between each of the phase pairs are observed in dynamic simulation and, using calculations of the Gibbs free energy, both potentials are shown to accurately predict the experimentally observed phase transformation temperatures and pressures over the entire phase diagram. The calculated triple points are 8.67 GPa and 1058 K for Ti and 5.04 GPa and 988.35 K for Zr, close to their experimentally observed values. The mechanism of transformation is also observed for each phase pair. The neural network potentials can be used to further investigate the behavior of each phase and their interaction.