Microstructural interaction and switching in ferroelectrics

该项目的主要目标是铁电体中速率相关微结构演化的多尺度模拟。两种不同的模型将在单晶水平上发展，并进一步扩展到寡晶水平。 作为一个通用的建模框架，以前建立的层压材料为基础的方法将被采用。特别是，这一提法将扩展到包括接口的效果。在混合物理论的背景下，层压体相关的体积分数表示在这种方法中的微观结构。 或者，铁电微结构将建模与水平设置方法的帮助下。在有限元法的背景下，这使得能够模拟空间分辨的微观结构。 体积分数和水平集为基础的模型将使用单晶的实验数据进行校准。 相关的有限元模拟，它可以考虑单个晶粒的位置和方向，使两个建模框架内的寡晶体的模拟。 水平集方法自然包括比基于体积分数的模型更多的信息，因为水平集公式在空间上解析了微观结构。 这是在一个较高的计算成本，但是，使两个模型的比较有助于评估的质量，效率和适用性的层压板为基础的模型。 这两种模型有助于更好地理解局部微结构的演变，在技术上有意义的铁电体。 这使得能够改进预测，典型铁电致动器和传感器的寿命特性。

The main goal of this project is the multi-scale modelling of rate-dependent microstructure evolution in ferroelectrics. Two different models will be developed on the level of single-crystals and further extended to the level of oligo-crystals. As a general modelling framework, the previously established laminate-based approach will be employed. In particular, this formulation will be extended to include the effect of interfaces. Within the context of mixture theory, the laminate-related volume fractions represent the microstructure in this approach. Alternatively, the ferroelectric microstructure will be modelled with the help of level-set methods. In the context of the finite-element method, this enables the simulation of spatially resolved microstructures. Both the volume-fraction- and level-set-based models will be calibrated using experimental data on single-crystals. Related finite element simulations, which can consider the positions and orientations of individual grains, enable the simulation of oligo-crystals within both modelling frameworks. The level-set approach naturally includes more information than the volume-fraction-based model, since the level-set formulation spatially resolves the microstructure. This is at a higher computational cost, however, so that a comparison of both models contributes to the evaluation of the quality, efficiency and applicability of the laminate-based model. Both models contribute to a better understanding of the local microstructure evolution in technologically meaningful ferroelectrics. This enables an improved prediction of, e.g., lifetime properties of typical ferroelectric actuators and sensors.