Machine learning assisted predictions of multi-component phase diagrams and fine boundary information

A phase diagram is a critical tool in materials science, but establishing it often requires a large number of experiments, especially for multi-component systems. In this work, we propose a machine learning strategy to accurately predict the phase diagram for the multi-component ferroelectric system (Ba _1−x−yCa _xSr _y)(Ti _{1−u−v−w}Zr _uSn _vHf _w)O ₃ by combining classification and regression methods. Based on literature data, we construct by classification a diagram that maps composition and temperature to the phase, and identify octahedral factor, Matyonov-Batsanov electronegativity, the ratio of valence electron number to nuclear charge and core electron distance (Schubert) for the A site and B site cations as the dominant physical descriptors. A neural network (NN) regression model is adopted to accurately predict phase transition temperatures, i.e. the phase boundaries, so that a phase diagram can be established in composition space. In the region of phase boundaries, the relative proportions of coexisting phases are also estimated by their prediction probability. The predicted phase labels, location boundaries and coexisting phase proportions are experimentally validated for the ceramic (Ba _0.96Ca _0.02Sr _0.02)(Ti _0.98−xZr _0.02Hf _x)O ₃. Our work provides an effective approach to establish phase diagrams for multi-component systems and also predict fine boundary information.