Thermodynamical phase-stability of a Cu-Al binary system using machine-learning interatomic potentials

The mechanical properties of structural materials are critically affected by the solid phases that are present in their microstructure, including both their crystallographic structure and chemical order. Predicting the stability of these phases as a function of thermodynamic state variables such as temperature and composition is therefore essential for the study of mechanical properties. In equilibrium, these stabilities are determined by the free energies of the various phases, which we compute from first principles as a function of composition and temperature for the Cu-Al binary alloy. Using two types of machine-learning interatomic potentials fitted to density functional theory calculations, we perform thermodynamic integration across various paths to determine the relative free energies of liquid, face-centered cubic, body-centered cubic, and hexagonal close-packed structures, both with and without chemical ordering. We compare the resulting stable phases and phase boundaries to experimental observations in the high-temperature copper-rich region of the phase diagram. Our results demonstrate that MLIPs fitted without prior knowledge of the material's crystal structure can reproduce the first principles reference potential energy surface with sufficient accuracy and speed to bridge the length and time scales necessary for calculation of free energies, enabling phase stability calculations.