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 Mn(3+) doped (Ba0.8Sr0.2)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 Mn(3+) doped (Ba0.75Sr0.25)TiO3 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 Mn(3+) doped (Ba0.8Sr0.2)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.