Determining Multi-Component Phase Diagrams with Desired Characteristics Using Active Learning

Herein, we demonstrate how to predict and experimentally validate phase diagrams for multi-component systems from a high-dimensional virtual space of all possible phase diagrams involving several elements based on small existing experimental data. The experimental data for bulk phases for known systems represents a sampling from this space, and screening the space allows multi-component phase diagrams with given design criteria to be built. This approach uses machine learning methods to predict phase diagrams and Bayesian experimental design to minimize experiments for refinement and validation, all within an active learning loop. The approach is proven by predicting and synthesizing the ferroelectric ceramic system (1-ω)(Ba_0.61Ca_0.28Sr_0.11TiO₃)-ω(BaTi_0.888Zr_0.0616Sn_0.0028Hf_0.0476O₃) with a relatively high transition temperature and triple point, as well as the NiTi-based pseudo-binary phase diagram (1-ω)(Ti_0.309Ni_0.485Hf_0.20Zr_0.006)-ω(Ti_0.309Ni_0.485Hf_0.07Zr_0.068Nb_0.068) designed for high transition temperature (ω ⩽ 1). Each phase diagram is validated and optimized through only three new experiments. The complexity of these compounds is beyond the reach of today's computational methods.