Molecular static methods for the simulation of ferroelectric materials

对铁电材料在电子结构和连续介质描述之间的不同长度尺度上进行了建模和模拟。因此，原子模型和算法在近十年得到了进一步的发展，并获得了准确的结果。尽管如此，已建立的原子方法的计算成本仍然很大。因此，原子尺度模拟方法得到了进一步的发展。本项目的目标是开发和研究分子静力学方法，用于分析铁电材料的微观机电现象。因此，必须在原子尺度上对材料进行准确的描述，以研究相关区域，如畴壁和纳米膜。为了在微观尺度上模拟铁电材料，从头算方法和分子动力学方法已经应用了一段时间。然而，除了长度尺度小是限制因素外，时间步长也是限制因素。通过使用分子静态方法，将动态问题转化为准静态算法。为了模拟铁电材料，核壳模型在原子模拟中得到了广泛的应用。因此，原子核和电子壳层之间的相互作用被认为是相互作用势，例如库仑势或伦纳德-琼斯势。新开发的算法已经在原子水平上用于研究铁电现象，如畴壁。此外，还提出了一种考虑宏观连续应力的新方法。因此，该算法不仅可以计算铁电晶体的介电迟滞，还可以计算铁电晶体的蝴蝶迟滞。大多数分子静态算法不考虑温度。然而，为了模拟相变，必须考虑温度。因此，必须包括温度相关的相互作用势来扩展核壳模型，以便模拟技术上相关的结构和相变。除了目标方法学结果外，结果应直接与使用非原子方法模拟铁电材料的其他项目进行比较。

Ferroelectric materials are modelled and simulated on different length scales between the electron structure and the continuum description. Therefore, also atomistic models and algorithms have been developed further in the last decade and attain accurate results.Nevertheless the computational costs of the established atomistic methods are still significant. For that reason atomistic scale simulation methods are further developed.The goal of this project is the development and investigation of molecular static methods for the analysis of electromechanical phenomena on the micro level in ferroelectric materials. Therefore an accurate description of the material on an atomistic scale has to be made to investigate relevant regions, such as domain walls and nanofilms. In order to simulate ferroelectric materials on the micro scale, ab initio methods and molecular dynamics have been used for some time. Yet, not only the small length scale is a limiting factor but also the time step length. Through the use of molecular static methods the dynamic problem shall be transferred to a quasi-static algorithm.In order to simulate ferroelectric materials, the core-shell model is widely used in atomistic simulations. Thereby interactions between atom cores and electron shells are considered by interaction potentials, e.g. the Coulomb potential or the Lennard-Jones potential. The newly developed algorithm has been already used to investigate ferroelectric phenomena, such as domain walls, at the atomistic level. Moreover a new method has been implemented in order to consider macroscopic continuum stresses. Therefore the developed algorithm was able to compute not only the dielectric hysteresis but also the butterfly hysteresis of a ferroelectric crystal.Most molecular static algorithm do not consider temperature. However, in order to simulate phase transitions temperature has to be considered. Therefore a temperature dependent interaction potential has to be included to extend the core-shell model in order to simulate technically relevant structures and phase transitions.In addition to the targeted methodological outcome, the results shall be compared directly to the other projects which use non-atomistic methods for the simulation of ferroelectric materials.