Solid-liquid phase boundary of oxide solid solutions using neural network potentials

We propose a cost-effective computational approach for predicting the phase boundary of oxide solid solutions, i.e., melting point, by identifying the point where the free energies of the solid and liquid phases are equivalent. To evaluate the melting point, we computed the temperature-dependent free energies of both phases using the thermodynamic integration (TI) method. This was combined with the reverse-scaling technique, employing the Einstein model for the solid and the scaled Uhlenbeck–Ford model for the liquid as the reference systems. The change in free energy between the real and reference states in the present TI method was calculated as the ensemble average of the configurations sampled from molecular dynamics (MD) simulations using neural network potentials (NNPs) trained on first-principles density functional theory (DFT) data. Initially, we benchmarked copper (Cu) as a typical metal. Tungsten (W) and magnesium oxide (MgO) were then tested as typical high melting-point metals and oxides, respectively, achieving good agreement with both ab initio MD (AIMD) results and experimental data. We then applied our established approach to a BaO–CaO oxide solid solution, observing that the computed phase boundary aligns well with Calphad predictions from previous studies. The integration of NNPs into phase boundary prediction is essential for reducing computational costs while ensuring accuracy, compared with AIMD-based approaches. • Neural network-based potentials are proposed for cost-effective and high-accuracy prediction tools of phase diagrams. • The above concepts are validated for solid–liquid phase boundaries of metal-oxides with high melting points. • Accuracies of phase boundaries calculated by molecular dynamics using neural network potentials are comparable to those of the Calphad method.