Revisiting the temperature-dependent dielectric permittivity of Ba(Ti_1−xZr_x)O₃

It has been a challenge to provide a unified description of the dielectric response vs temperature for ferroelectrics with diffuse phase transition (DPT) and relaxor behaviors, which can be used to fit the dielectric response both below and above the peak temperature (T_m). Most of the available functions used in fitting experimental data only provide a description of the dielectric permittivity near and above T_m. In this work, employing a macroscopic and phenomenological statistical model and using Ba(Ti_1−x Zr_x)O₃ ceramics as an example, we revisit the dielectric permittivity's temperature dependence, analyzing their DPT and relaxor behaviors and providing a complete description over the whole temperature range. We show that good agreements between theoretical and experimental results can be achieved. To better understand how Ba(Ti_1−x Zr_x)O₃ ceramics changes from DPT to relaxor with increasing x, we also discuss the relation between the fitting parameters and Ba(Ti_1−x Zr_x)O₃'s composition and structure, which suggests that the parameters from the statistical model reflect the size of the correlated Ti ions (small clusters or polar nanoregions), which largely determine the behavior of Ba(Ti_1−x Zr_x)O₃ ceramics.