Multiscale modeling for ferroelectric materials: a transition from the atomic level to phase-field modeling

To link the atomic level and the mesoscale within a knowledge-based multiscale modeling approach for ferroelectric materials, a method is suggested to transfer results from first-principles calculations into a phase-field model. DFT calculations and atomistic simulations are applied and provide a set of intrinsic and extrinsic material properties for PbTiO₃ and tetragonal Pb(Zr_0.5Ti_0.5)O₃. The Helmholtz free energy of the phase-field model that contains all crystallographic and domain wall information is discussed in detail, and a sensitivity analysis is performed to identify the coefficients of the energy function. Then, a method is developed to adjust the coefficients of the Helmholtz free energy solely based on results from first-principles calculations. Full sets of adjusted energy coefficients for PbTiO₃ and Pb(Zr_0.5Ti_0.5)O₃ are presented and discussed, as well the limits of the suggested adjustment method.