Structural and dielectric properties of BaTiO₃ nanoparticles

We construct and employ a machine-learning potential to perform molecular dynamics simulations on BaTiO 3 nanoparticles. The potential constructed in this study successfully reproduce rhombohedral, orthorhombic, tetragonal, and cubic phases observed in bulk BaTiO 3 at different simulation temperatures, as well as surface properties. We consider cubic-shaped and spherical nanoparticles to study how the shape and surface structures influence the structural and dielectric properties. Based on our analysis of the displacement vectors of titanium atoms relative to the surrounding oxygen atoms (corresponding to dipole moments), the surface structure strongly affects the order of the displacement vectors even near the center of the particle. A tetragonal-like order appears in cubic-shaped nanoparticles around a diameter of 11.6 nm while a similar order cannot be seen in an 18 nm spherical nanoparticle.