Parameterization of a phase field model for ferroelectrics from molecular dynamics data

In this work, molecular dynamics (MD) simulations of ferroelectric BaTiO${}_3$ are used to generate parameters for a phase-field (PF) model. The MD simulations provide important input parameters, such as elastic and piezoelectric properties, as well as domain wall (DW) widths and velocities. A parameterization technique is proposed to incorporate the MD results into the PF simulations, allowing for the generation of relevant parameters. Anisotropic interface energy coefficients are used to match the widths of both the 180° and 90° DWs in the PF simulations to the MD data. The velocities of the DWs are calculated and compared to the results obtained from MD simulations, demonstrating excellent agreement. Furthermore, we investigate the disparity between coercive fields obtained from PF simulations and MD simulations. Initially, our PF simulations yield coercive fields approximately twice as high as those observed in MD simulations. To address this discrepancy, we introduce a nucleus into the PF simulation system. The parameters of this nucleus are derived from a statistical analysis of coercive field data from MD simulations. By incorporating the nucleus model, we achieve a coercive field in PF simulations that closely aligns with the MD results. Validation of the parameterized PF model using MD data obtained with different initial conditions and thermodynamic constraints shows good agreement, further confirming the model’s accuracy.