Analytical and Phase-Field Study of Anomalous Electromechanical Behaviors in NBT--xST

  • Zhou, Yucheng (Technische Universität Darmstadt)
  • Wang, Kai (Technische Universität Darmstadt)
  • Xu, Bai-Xiang (Technical University of Darmstadt)

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Electromechanical coupling and nonlinear hysteresis in functional ceramics near morphotropic phase boundaries (MPBs) are strongly influenced by quenched disorder. Despite extensive experimental evidence, a unified mechanical framework that explicitly links 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. This formulation provides a transparent mechanical interpretation of relaxor-like behavior in terms of free-energy flattening, suppression of long-range ferroelectric order, and a disorder-induced shift of MPB composition. Guided by analytical analysis, a fully coupled phase-field model is constructed by integrating Landau–Ginzburg–Devonshire energetics with elastic, electrostatic, polarization-gradient, and random-field contributions. The model captures mesoscale polarization evolution, domain miniaturization, diffuse phase boundaries, and nonlinear electromechanical hysteresis. Using NBT--xST 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 under finite random fields. These results demonstrate that quenched disorder serves as a key mechanical control parameter governing phase stability and nonlinear electromechanical response.