Bai-Xiang Xu

Optimizing antiferroelectric (AFE) energy-storage microstructures via phase-field modeling is computationally prohibitive due to immense spatial and temporal constraints. First, accurately capturing the highly frustrated commensurate and incommensurate AFE phases requires exceptionally fine spatial resolutions to resolve sharp, high-frequency antiparallel dipole gradients. Second, simulating path-dependent double hysteresis loops requires quasi-static loading, where time-dependent evolution equations must be rigorously integrated at every electric-field increment until the macroscopic polarization reaches thermodynamic equilibrium. Together, these requirements render high-throughput simulations of polycrystalline structures practically unfeasible. To overcome this, we introduce a physics-informed multigrid neural operator (PI-MgNO) as a highly scalable, autoregressive surrogate model. Constrained by the physical Landau free energy, PI-MgNO accurately tracks AFE-to-FE domain evolution without catastrophic integration drift. This physical regularization imparts a distinct thermodynamic error-healing mechanism, bounding spatial phase-shift errors during coercive switching and rapidly forcing the system into stable energy minima. Rigorous evaluations demonstrate exceptional scale-invariance, effectively bypassing the quasi–static relaxation bottleneck and reducing simulation times from hours to seconds while maintaining R ² > 0.96.

Space charge layers (SCLs) at grain boundaries play a crucial role in modulating electric fields and thereby influence functional properties of materials. However, experimental analysis of these localized electric fields and the corresponding charge distribution remains challenging. Conventional center‐of‐mass (CoM) analysis in scanning transmission electron microscopy differential phase contrast (STEM‐DPC) is strongly affected by orientation‐dependent contrast and dynamical scattering. Here, we demonstrate that combining electron beam precession with advanced post‐processing, employing iterative edge detection and singular value decomposition (SVD), enables reliable, unbiased diffraction shift measurements with minimal crystallographic artefacts. The new method accurately refines the central disk position in nanobeam electron diffraction (NBED) patterns and thus significantly improves the extraction of the local electric field and corresponding charge distribution. Comparison with conventional CoM methods shows superior accuracy and robustness for random grain boundaries in BaTiO ₃ and SrTiO ₃ as exemplary case studies. The experimental work is complemented by atomistic simulations to separate the electric field of the SCL from the mean inner potential difference of the grain boundary and the elemental segregation around the grain boundary. The in‐depth analysis shows that our approach enables high‐fidelity mapping of electromagnetic fields and their charge distribution in complex polycrystalline specimens for improved quantitative analysis.

Metallic structures operating under elevated-temperature cyclic service are susceptible to fatigue crack growth driven by the simultaneous action of thermal loading, cyclic plasticity, and progressive damage accumulation. Although the phase-field approach to fracture has been extended to fatigue and, separately, to thermo-mechanical problems, no existing model simultaneously incorporates Chaboche-type cyclic plasticity, bidirectional fracture–thermal coupling, and the partition of plastic dissipation between heat generation and crack driving. To address this gap, we propose a phase-field fatigue model for thermo-elastoplastic solids with Chaboche cyclic hardening that treats the displacement, temperature, and crack phase-field as three fully coupled primary variables. J2 plasticity with Chaboche combined hardening—Voce isotropic plus Armstrong–Frederick kinematic hardening—faithfully reproduces the Bauschinger effect, ratcheting, and cyclic stress relaxation under load reversal. The crack-driving force combines tensile elastic strain energy with the Taylor–Quinney-weighted isotropic plastic stored energy; the effective Taylor–Quinney coefficient χ_eff acts as a single energy-partition parameter that simultaneously controls the plastic heat source and the fraction of plastic work available for fracture, thereby removing one otherwise free fitting parameter. Svolos rational conductivity degradation models the directional loss of heat conduction across crack faces, while additive thermal expansion strains close the bidirectional thermo-mechanical coupling loop. A threshold-based fatigue degradation function encodes a physically motivated endurance limit. The model is verified at the constitutive, single-element, and structural levels through single-edge-notched-tension (SENT), compact-tension (CT), and V-notched thermal fatigue benchmarks; the V-notched case is further validated against experimental crack-length measurements. The full source code is publicly released to support reproducibility.

Point defects govern 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 perturb phase stability and domain configurations. They can give rise to relaxor-like behavior and, under certain conditions, core--shell microstructures. The mechanisms governing their coupled effects on domain evolution and ferroelectric response, however, remain incompletely understood. A defect-mediated phase-field framework is developed based on the second law of thermodynamics, incorporating Vegard eigenstrains, defect-dependent elasticity, Curie-temperature shifts, and Landau-type phase-transition energetics, together with quenched random electric fields. Random electric fields locally break symmetry and fragment polarization, whereas Vegard-induced eigenstrains generate long-range elastic interactions that promote domain coherence. Their competition produces distinct electromechanical responses and defines regimes dominated by disorder or elasticity. The model is implemented in the finite element method and used to simulate Bi-modified NBT-based systems near MPBs. Simulation results capture the experimentally observed transition from homogeneous ferroelectric states to heterogeneous structures, including core--shell morphologies in certain systems, and relaxor-like behavior. The framework provides a general connection between defect statistics, mesoscale structure, and macroscopic response, offering a mechanistic foundation for interpreting and designing defect-controlled functional oxides.