Modeling oxygen diffusion in barium titanate using molecular dynamics: Comparison between Mg and Sc dopants

In this study, the diffusion coefficient of oxygen vacancies in barium titanate doped with 2.0% Sc was calculated by using molecular dynamics. The temperature was varied from 1273 K to 2500 K, and the simulation box consisted of 10 × 10 × 10 unit cells subject to periodic boundary conditions. The Sc dopants were incorporated into the B-sublattice and compensated for by using the randomly distributed oxygen vacancies on the oxygen sublattice. The diffusivity of the vacancies was determined from the slope of the mean-squared displacement of the oxygen ions over time. The Arrhenius plot of the diffusion coefficient showed a clear linear behavior, with an activation energy of 0.84 eV. The results were interpreted by computing radial pair distribution functions for various correlations (e.g., Ti–O and Sc–O) and by static lattice (nudged elastic band) calculations of energy barriers for the migration of oxygen. While Mg-doped BaTiO ₃ exhibited a strong trend of the formation of defect associates between the acceptor dopant and the oxygen vacancies that lead to a clear reduction in the observed activation energy for oxygen transport with increasing temperature (non-linear Arrhenius behavior), defect-induced interactions (associates) in case of Sc doping were nearly negligibly small, and gave rise to a linear Arrhenius plot with a single activation energy.