Electromechanical Impact of Non-stoichiometry in Ferroelectrics: A Defect-Informed Phase-Field Study of Competing Random Electric Fields, Strain Fields, and Phase Stability

Point defects play a central role in governing the electromechanical response of non-stoichiometric ferroelectrics, particularly near morphotropic phase boundaries (MPBs), where competing phases coexist within a flattened free-energy landscape. Defect-induced elastic interactions and electrostatic disorder can perturb phase stability and domain configurations, but their coupled effects on domain evolution and ferroelectric response remain incompletely understood. A thermodynamically consistent phase-field framework is developed in which a prescribed defect concentration field acts as a source of coupled elastic and electrostatic disorder through Vegard eigenstrains, defect-dependent elasticity, Curie-temperature shifts, Landau-energy modulation, and quenched random electric fields. Random electric fields locally break symmetry and fragment polarization, whereas Vegard eigenstrains generate long-range elastic interactions that promote cooperative domain organization. Their competition produces a correlation-length-dependent crossover between disorder-dominated and elasticity-dominated electromechanical behavior. The framework is implemented using the finite element method and applied to Bi-modified NBT-based systems near MPBs. Simulations capture key experimentally observed electromechanical signatures of heterogeneous states, including the effects of core–shell architectures, two-step switching features in hysteresis loops, and relaxor-like responses. The framework establishes a mechanistic connection between defect statistics, mesoscale phase competition, and macroscopic electromechanical response, providing a general basis for understanding and designing defect-controlled functional oxides.