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.

中文翻译：

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回顾Ba（Ti1-xZrx）O3随温度变化的介电常数

提供具有扩散相变（DPT）和弛豫特性的铁电介质的介电响应与温度的统一描述是一个挑战，可用于在峰值温度（T _m）之下和之上拟合介电响应。用于拟合实验数据的大多数可用功能仅提供对T _m附近和之上的介电常数的描述。在这项工作中，采用宏观和现象学统计模型，并使用Ba（Ti _{1- x} Zr _x）O ₃以陶瓷为例，我们回顾了介电常数与温度的关系，分析了它们的DPT和弛豫特性，并在整个温度范围内提供了完整的描述。我们表明，理论和实验结果之间可以达成良好的协议。为了更好地了解Ba（Ti _{1− x} Zr _x）O ₃陶瓷随x的增加而从DPT变为弛豫器的原因，我们还讨论了拟合参数与Ba（Ti _{1− x} Zr _x）O _{3的关系。}的组成和结构表明，统计模型中的参数反映了相关Ti离子（小簇或极性纳米区域）的大小，这在很大程度上决定了Ba（Ti _{1- x} Zr _x）O ₃陶瓷的性能。