Parametrization of Ferroelectric Phase-Field Model based on Static and Dynamic Atomistic Simulation Data
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Ab-initio derived MD core-shell potentials now give a reliable representation of ferroelectric BaTiO3 (BTO) and various other pristine and defective perovskite systems [1]. Phase-field models (PFMs) of the Landau-Ginzburg-Devonshire type extend time and length scales to enable studies of polarization switching [2], fatigue-related defect migration and impact of grain boundaries. The energy landscape formed by the Landau polynomial defines the microscopic pathways for polarization switching. The interpretation and adaption of its parameters remains a crucial step for a correct up-scaling of MD results. We combine both simulation techniques to elucidate the micro-scale mechanisms of domain switching, domain wall (DW) motion and defect interaction. Material properties such as elastic, dielecric and piezoelectric tensor components, kinetic coefficients, as well as domain wall characteristics are extracted from the MD simulations to adjust the elastic and electrostatic energies. To define the other parameters, including the Landau polynomial coeffcients, we have implemented a procedure that relies on both statistical analysis of MD data, and the application of a physics-informed neural network (PINN). MD simulation results prove the role of thermal activation for domain nucleation, resulting in a notable scatter in coercive fields within small systems. From statistical analysis of this data we calculate the activation parameters for BTO that govern polarization switching at coercive fields, and the domain wall energies. Static polarization distributions of 180° and 90° DWs from MD simulations are used as training data for a neural network, which reconstructs polarization, strain and stress fields. A second physics-based learning mechanism involves the residuals of the phase-field, mechanical and electrostic equations to adapt the remaining polynomial coefficients and phase-field parameters. The method presented is time-saving and useful for PF simulations of domain nucleation and domain wall motion in presence of point defects carrying mono- or dipolar electric fields as well as elastic strain fields. Interestingly, the proposed Landau energy explains that polarization switching in two subsequent 90° steps can be favorable over 180° switching, which was observed experimentally and in recent MD simulations [1]. [1] H. Azuma et al., Acta Materialia Vol. 296, pp. 121216, 2025. [2] D. Durdiev et al., Acta Materialia, Vol. 283, pp. 120513, 2025.
