Fig. 3: 2D displacement maps, mapped onto the three principal Cartesian planes (X-Y, X-Z, and Y-Z) in a series of NpT 4 × 4 × 4 simulations with restricted cubic geometry.
From: Thermodynamics and dielectric response of BaTiO3 by data-driven modeling
The 20 K trajectory shows fast fast-freezing of the Ti degrees of freedom to the nearest cubic sites (depending on the initial configuration) in the first few ps of trajectory. In this specific case, only states corresponding to positive displacements along the y-axis are sampled across the 4 × 4 × 4 supercell. At 80 K the presence of one single maximum in the 3D density marks the onset of a clear “rhombohedral-like” ferroelectric state (with a polarization parallel to the [−1, +1, +1] axis), showing how the GAP favors aligned displacements even in the presence of geometric constraints on the supercell. Simulations at higher temperatures (250 K and beyond) restore instead the eight-site structure of the displacement density.
