Atomic-scale phase-field modeling for ferroelectrics

Phase-field modeling has been used to visualize local thermodynamic states, that is, spatially inhomogeneous free energy, entropy, and stress in ferroelectrics. Here, the authors show that phase-field modeling can be extended to the atomic scale by combining variational Gaussian theory with a bond-valence interatomic potential. Using this approach, they visualize atomic-resolution thermodynamic states in PbTiO₃ and find that the ferroelectric--paraelectric transition may be driven by a local increase in the vibrational free energy of Pb atoms.