Microstructural interaction and switching in ferroelectrics

该项目的主要目标是对铁电材料中与速率相关的微结构演化进行多尺度模拟。将在单晶水平上发展两种不同的模型，并进一步扩展到寡晶水平。作为一般的建模框架，将采用先前建立的基于层合板的方法。特别是，这一提法将扩展到包括界面的影响。在混合物理论的背景下，层板相关的体积分数代表了这种方法中的微观结构。或者，铁电微结构将借助Level-Set方法进行建模。在有限元方法的背景下，这使得能够模拟空间分辨的微结构。基于体积分数和能级集的模型都将使用单晶体上的实验数据进行校准。相关的有限元模拟可以考虑单个颗粒的位置和取向，使得能够在两个模拟框架内模拟低聚晶体。水平集方法自然比基于体积分数的模型包含更多的信息，因为水平集公式在空间上解析了微观结构。然而，这是以较高的计算成本为代价的，因此两种模型的比较有助于评估基于层合板的模型的质量、效率和适用性。这两个模型都有助于更好地理解具有技术意义的铁电材料的局域微结构演化。这使得能够改进对典型铁电致动器和传感器的寿命特性的预测。

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.