The design of compositionally modulated lead-free ferroelectrics with large electromechanical response via high-throughput phase-field simulations and machine learning

Compositionally graded ferroelectrics (CGFEs) have attracted great interest due to their exceptional and tunable electromechanical properties , which are anticipated to be superior to traditional ferroelectrics. However, an effective design of CGFEs with desired properties from a huge compositional space remains an enormous challenge. In this study, we present an efficient design strategy for CGFEs through a combination of high-throughput phase-field simulation and machine learning (ML) algorithm. Systematic phase-field simulations are first performed to establish a dataset of electromechanical properties for various CGFEs, which are characterized by three degrees of freedom, including compositions of two end materials and gradient index. A ML-assisted optimization process is then conducted on this dataset to yield optimal electromechanical properties, which are further analyzed by phase-field simulations. The ML-guided simulations lead us to discover that the large optimal electromechanical responses can be achieved in CGFEs with average composition near the morphotropic phase boundary yet large compositional gradient. These CGFEs accommodate a coexistence of tetragonal, orthorhombic, and cubic phases in their domain structures, which flatten the energy barrier landscape and facilitate the rotation of polarization under mechanical field. Our proposed highly efficient design strategy can be readily adapted to identify CGFEs possessing other principal elements and properties, which will accelerate the discovery of new high-performance CGFE materials .