Mechanistic Phase-Field Modelling of Woven-Domain Formation in Ferroelectric Material

Abstract: A recent experimental study reports the spontaneous formation of a three-dimensional woven ferroelectric domain fabric in bulk KTN:Li during sufficiently slow cooling through the ferroelectric transition. The present work develops a nondimensional phase-field framework to examine a physically plausible route by which such a state can emerge. A large-area two-dimensional model first resolves the cooling-rate-dependent formation of a frustrated crossing precursor by combining first-order ferroelectric thermodynamics, electrostatic and elastic interactions, compositional modulation, and effective charge screening. Slow cooling produces a persistent population of charge-associated crossings, whereas the corresponding fast-cooling pathway does not. A three-dimensional extension then incorporates cubic gradient anisotropy, flexoelectric coupling, and strain-gradient regularization to examine whether the planar precursor can develop a genuine woven topology. Within the explored nondimensional parameter regime, slow cooling produces a directly resolved geometrical separation and exchange of depth ordering between the intersecting wall families, whereas the corresponding fast-cooling pathway does not. This distinction is reproduced across independent realisations and remains robust to timestep refinement and changes in computational domain size. The simulations suggest that slow cooling provides a kinetic window for topological selection and that global charge relaxation can coexist with strong local charge concentration at surviving crossings. The model is not calibrated to material-specific KTN:Li coefficients and does not reproduce the experimentally observed low-temperature disappearance of the woven state.