Designing Pb-Free High-Entropy Relaxor Ferroelectrics with Machine Learning Assistance for High Energy Storage

High-entropy tactics present exceptional promise in advancing the dielectric energy storage of relaxor ferroelectrics, thereby benefiting various pulsed-power electronic systems. However, their vast composition space poses challenges in the rational design of a high-performance system. Herein, we present a machine learning-supplemented strategy to design high-entropy relaxors, demonstrating an ultrahigh energy-storage density of 17.2 J cm^-3 and high efficiency of 87% at a high breakdown strength of 79 kV mm^-1. By integrating six A-site and one B-site critical intrinsic features of constituent ions, deduced from a constructed random forest regression model, the (Bi_2/5Na_1/5K_1/5Ba_1/5)(Ti,Hf)O₃ high-entropy system is identified. Atomic-level local structural analysis reveals that incorporating these certified cations, with diverse local polar and lattice construction characteristics, results in a highly fluctuating local polarization structure. This favorable structure is characterized by pronounced orientation disorder and a broadly distributed length of unit-cell polarization vectors within the expanded lattice framework. Macroscopically, the optimized relaxor displays high dielectric susceptibility and large resistance. Moreover, a large discharge energy density of 5.8 J cm^-3 and power energy density of 447 MW cm^-3, along with outstanding operational stability, are achieved. This study presents a data-driven model to explore complex intrinsic features and facilitate the design of high-performance relaxors.