Modeling the paraelectric aging effect in the acceptor doped perovskite ferroelectrics: Role of oxygen vacancy

The time dependence of physical properties in the paraelectric phase was probed recently in a Mn³⁺ doped (Ba_0.8Sr _0.2)TiO₃ ceramic, providing a simple situation (without spontaneous polarization or domain walls) to quantify the role of the oxygen vacancy during aging. In the present study, we propose a quantitative model for paraelectric aging to understand how the distribution of the oxygen vacancy evolves with time and consequently influences the dielectric response of the paraelectric phase. First, by comparing dielectric behavior of paraelectric aging in a Mn³⁺ doped (Ba_0.75Sr_0.25)TiO ₃ ceramic and the dielectric tunable effect, an internal bias field E_in related to the oxygen vacancy is shown to exist in the paraelectric phase. Second, by introducing such a time dependent E_in in a Landau-type model, we reproduce the dielectric response of Mn³⁺ doped (Ba_0.8Sr_0.2)TiO₃ ceramic during paraelectric aging. It is suggested that the increase of dielectric permittivity can be ascribed to the decrease of E_in with time. The investigation of paraelectric aging is helpful for understanding the role of the oxygen vacancy in influencing the physical properties of ferroelectric materials.