Efficient ab initio prediction of liquidus curves

The liquidus curve captures the high-temperature eutectics, peritectics, congruent melting and incongruent melting regions of a phase diagram. Being able to predict liquidus curves would enable ab initio design of materials synthesis conditions, as well as the design of materials stable in high-temperature environments. Liquidus curves are available in databases like Thermocalc or SGTE, but the available chemical spaces in these databases lag far behind computational materials discovery efforts. Direct simulation of liquid free energies across chemical space is probably infeasible (even using machine-learned interatomic potentials) given the wide range of temperatures and compositions that must be sampled. Here, we present a CALPHAD-inspired approach to reference liquidus curves from published ASM phase diagrams to DFT convex hulls from the Materials Project. Using this technique, we fit non-ideal liquid mixing free-energies on a 70x70 matrix of binary alloy phase diagrams. Using very simple machine-learning models, we can then predict liquid free energies in novel chemical spaces, including ternary or quaternary+ spaces, at a computational cost low-enough to be integrated with high-throughput DFT databases like the Materials Project. Our technique predicts liquidus curves, intermetallic melting temperatures, and three-phase invariant points (eutectics and peritectics) with surprisingly good accuracy, despite the known magnitude of formation energy errors in DFT convex hulls.