Diagram and phase transition features

Yang Bai*, Jingjin He, Yanjing Su, Lijie Qiao

Beijing Advanced Innovation Center for Materials Genome Engineering, Institute for Advanced Material and Technology, University of Science and Technology Beijing, Beijing 100083, China

EXTENDED ABSTRACT: A phase diagram is a critical tool in materials science. Understanding phase transitions in systems with structural, electronic, quantum mechanical and topological degrees of freedom is an important part of modern physics and materials science. As a description of material behavior and properties, the phase diagram provides insight into physical forces underpinning a material system. Thus, capturing the physics of phase transitions via the corresponding phase diagram is a problem of considerable importance both theoretically and experimentally. Traditionally, the phase diagram is drawn based on a large number of experiments, and changes in macroscopic properties, such as specific heat, lattice parameter and polarization, are interpreted as signatures of phase transitions to demarcate phase boundaries. Drawing a complete phase diagram for a multi-component system is therefore a difficult task as the complexity increases exponentially with each additional degree of freedom 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 rapidly and accurately predict the phase diagram and the phase transition features by combining classification and regression methods. For the sample of a multi-component ferroelectric system (Ba1−x−yCaxSry)(Ti1−u−v-wZruSnvHfw)O3. 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 deep neural network regression (DNN) model is adopted to more 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 well estimated by the prediction probability after bootstrapping using a classification model. Furthermore, the dispersion degree of phase transition of materials can be obtained by combining the predictions of phase diagram and the dielectric temperature spectrum. That is, more phase transition features are obtained assisted by machine learning. Our predictions are validated by experimental synthesis and characterization in a typical sample of (Ba0.96Ca0.02Sr0.02)(Ti0.98-xZr0.02Hfx)O3. Our work provides a direct route to rapidly establish phase diagrams for multi-component systems.