Authors: Yucheng Zhou, Kai Wang, Wanxin Chen, Chunli Zhang, Kefu Huang, Shuai Wang

Electromechanical coupling and nonlinear hysteresis in functional ferroelectric ceramics near morphotropic phase boundaries (MPBs) are strongly influenced by phase competition and quenched disorder. Despite extensive experimental evidence, a unified mechanical framework that explicitly connects chemical heterogeneity, phase competition, and macroscopic constitutive behavior remains elusive. In this work, a multiphysics theoretical framework is developed to clarify the role of quenched disorder in reshaping the free-energy landscape and governing electromechanical responses in MPB systems. Gaussian-distributed random electric fields are incorporated analytically into the Landau free energy, yielding disorder-renormalized thermodynamic coefficients and closed-form expressions for spontaneous polarization, coercive field, and Curie temperature. Relaxor-like behavior can therefore be interpreted mechanically through free-energy flattening, suppression of long-range ferroelectric order, and a disorder-induced shift of the MPB composition. Guided by analytical analysis, a fully coupled phase-field model is constructed by integrating Landau–Ginzburg–Devonshire energetics with elastic, electrostatic, electromechanical, polarization-gradient, and random-field contributions. The model captures mesoscale polarization evolution, domain miniaturization, diffuse phase boundaries, and nonlinear electromechanical hysteresis. Applying Na0.5Bi0.5TiO3– xSrTiO3 as a representative system, simulations reproduce the experimentally observed transition from conventional ferroelectric behavior to MPB-enhanced and relaxor-like responses with increasing disorder strength. In particular, the emergence of double-peak polarization–electric field hysteresis loops near the MPB is shown to arise intrinsically from rhombohedral–tetragonal phase coexistence with finite random fields. The findings demonstrate that quenched disorder serves as a key parameter governing phase stability and nonlinear electromechanical response.