Although discussions of structural phase transitions in prototypical ferroelectric systems with the perovskite structure, such as BaTiO$_3$ and PbTiO$_3$, started almost seventy years ago, an atomic-level description of the polar characteristics as a function of temperature, pressure and composition remains topical. Here we provide a novel quantitative description of the temperature-driven local structural correlations in PbTiO$_3$ via the development of characteristic relative cationic shifts. The results give new insights into the phase transition beyond those reliant on the long-range order. The ferroelectric-to-paraelectric transition of PbTiO$_3$ is realized by the extent of a stochastic polarization instability driven by a progressive misalignment instead of a complete disappearance of the local dipoles, which further suggests that such polarization instability is chemically induced at the morphotropic phase boundary of PbTiO$_3$-based solid solutions with giant piezoelectric effect. As such, our results not only identify the evolving atomistic disorder in a perovskite-based ferroelectric system, but also suggest that polarization-instability can serve as a generic fingerprint for phase transitions as well as for better understanding structure-property relationships in PbTiO$_3$-based ferroelectric solid solutions.

中文翻译：

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PbTiO $ _3 $的随机极化不稳定性

尽管关于钙钛矿结构的典型铁电系统中结构相变的讨论（例如BaTiO $ _3 $和PbTiO $ _3 $）始于大约70年前，但原子级描述了极性特性随温度，压力和温度的函数。组成仍然是话题。在这里，我们通过特征相对阳离子位移的发展，提供了PbTiO $ _3 $中温度驱动的局部结构相关性的新颖定量描述。结果为相变提供了新的见解，超出了依赖于长程顺序的那些。PbTiO $ _3 $的铁电到顺电转变是通过渐进的未对准而不是局部偶极子的完全消失驱动的随机极化不稳定性的程度实现的，这进一步表明，这种极化不稳定性是在PbTiO $ _3 $基固溶体的形变相界处化学诱导的，具有巨大的压电效应。因此，我们的结果不仅确定了钙钛矿基铁电体系中正在演化的原子序，而且表明极化不稳定性可以用作相变的通用指纹，并可以更好地理解PbTiO $ _3中的结构-性质关系。基于美元的铁电固溶体。