Fig. 1: The four phases of BaTiO3.
From: Thermodynamics and dielectric response of BaTiO3 by data-driven modeling
a Time evolution of the lattice vector lengths (a, b, and c) and angles (α, β, γ) over fully flexible MD simulations at (from left to right) 250, 100, 50 and 15 K; b 3D histograms of the unit-cell polarization predicted by the SA-GPR polarization model, computed across the same simulations; c projections of those 3D histograms onto the three principal Cartesian planes (X-Y, X-Z, and Y-Z). The light gray boxes mark the range ±2e for easier comparison between the phases. The structure of the high-frequency (dark blue) regions characterizes the different phases of BaTiO3, while the phase transitions are marked by a clear symmetry-breaking pattern that restricts the cell dipole to visit only a subset of the available off-centered sites.
