Artificial intelligence-assisted multi-scale phase field simulations for ferroelectrics: Cases for solid solution Ba<i>x</i>Sr1−<i>x</i>TiO3 and 2D ferroelectric In2Se3

Although the phase field method is a robust tool for theoretical studies of ferroelectrics, determining the parameters of the Helmholtz free energy in the phase-field model, particularly the Landau coefficients, remains a highly complex and challenging task. Here, we propose a general approach to identify all phase field parameters by developing an artificial intelligence-assisted multi-scale phase field model. This model hierarchically bridges ab initio accuracy with the mesoscale phase field model, linked by the effective Hamiltonian model and deep potential molecular dynamics (DPMD) simulations, effectively overcoming the limitations inherent in relying on a single method. Specifically, Monte Carlo simulations and DPMD calculations are used from first principles to determine temperature-dependent polarization and dielectric constants, which are then fitted to thermodynamic potentials using the particle swarm optimization algorithm. In addition to the Landau–Devonshire energy function, other material properties in the phase field simulation, such as gradient coefficients, electrostriction, and elastic coefficients, are also directly calculated from first-principles calculation, establishing a multi-scale phase field model. To effectively demonstrate the proposed multi-scale model, we have chosen BaxSr1−xTiO3 (BST) solid solutions and two-dimensional (2D) ferroelectric α-In2Se3 as representative examples, showcasing its applicability to both perovskite and 2D ferroelectrics. Based on the multi-scale phase field models developed for BST and α-In2Se3, we performed phase field simulations to explore their thermodynamic properties.