Phase-field Models of Piezoelectric and Multiferroic Responses of Ferroelectric and Multiferroic Nanostructures

该奖项支持铁电和多铁纳米结构中电磁-机械耦合的理论和计算研究。铁电体和多铁材料是多功能材料，在执行器、传感器和存储器等器件中有许多应用。该项目的主要目标是从根本上了解机械和电气边界条件在其铁响应中的作用。重点研究了纳米铁电体的压电响应以及铁电晶体和铁磁晶体自组装外延纳米复合材料的磁电耦合。相场方法将与中尺度弹性、静电理论和微磁学相结合。该项目的具体目标如下：(1)PI将开发和实施基于谱方法的高效数值算法，用于求解相场，机械，静电和静磁方程，同时考虑适当的电气和机械边界条件。(2) PI将研究铁电纳米结构的压电响应对衬底约束的依赖，以及由于位错等缺陷的存在而导致的纳米结构内的不均匀应力分布。(3) PI将研究多铁性纳米复合材料微观结构与磁电耦合效应大小的相关性。该研究项目包括与应用数学家在先进数值算法的实施上的积极合作，以及与实验学家在计算预测和发现的实验验证上的积极合作。该奖项下的研究预计将(i)对纳米铁电的压电响应和多铁性纳米复合材料的磁电耦合效应的基本理解做出重大贡献，（ii）为多铁性畴结构建模提供新的相场公式，（iii）为求解涉及非周期边界条件的相场方程提供先进的数值算法。该奖项支持通过论文和暑期研究培训研究生和本科生。该项目开发的软件工具将被纳入两门研究生课程和一门本科课程。研究结果将通过档案出版物和会议、审查和概览论文、积极参加跨学科讲习班和在讲习班上讲课等方式传播给广泛的听众。该奖项支持对铁电和多铁氧化物的性质和功能的理论和计算研究。铁电体和多铁材料是多功能材料，当它们受到外场作用时可以产生两种或两种以上不同类型的响应。它们在执行器、传感器和计算机存储器等设备中有许多潜在的应用。例如，当铁电晶体受到外部机械应力时，它可以改变其形状和电极化。当晶体中原子核的正电荷分布与负电荷分布发生偏移时，就会产生电极化。在多铁性材料中，磁化和电极化的大小和方向都可以通过外部施加电场或磁场来改变。该研究计划有两个主要重点：PI将研究所谓的“压电响应”，这与机械应力下电极化变化的幅度或电场下晶体形状变形的程度有关。这些效应将在大块铁电体以及尺寸约为人类头发十亿分之一的微小结构中进行检验。其次，PI将研究所谓的“磁电”耦合，这与外加磁场下电极化的变化或外加电场下磁化强度的变化有关。PI将在这些调查中开发和应用各种计算工具。总体目标是通过计算机模拟优化这些材料的多功能。该研究计划包括与应用数学家在先进数值算法的实施上的积极合作，以及与实验学家在计算预测和发现的实验验证上的积极合作。该项目将通过论文和暑期研究培训研究生和本科生，从而促进人力资源的发展。该项目开发的软件工具将被纳入两门研究生课程和一门本科课程。研究结果将通过档案出版物和会议、审查和概览论文、积极参加跨学科讲习班和在讲习班上讲课等方式传播给广泛的听众。

TECHNICAL SUMMARYThis award supports theoretical and computational research on electro-magneto-mechanical couplings in ferroelectric and multiferroic nanostructures. Ferroelectrics and multiferroics are multi-functional materials that have many applications in devices such as actuators, sensors, and memory storage. The main objective of the project is to fundamentally understand the roles of mechanical and electrical boundary conditions in their ferroic responses. The focus is on the piezoelectric responses of nanoferroelectrics and the magnetoelectric coupling of self-assembled epitaxial nanocomposites of ferroelectric and ferromagnetic crystals. The phase-field approach will be employed in combination with mesoscale elasticity, electrostatic theory, and micromagnetics. The particular goals of the project are as follows:(1) The PI will develop and implement efficient numerical algorithms based on the spectral method for solving the phase-field, mechanical, electrostatic, and magnetostatic equations while taking into the appropriate electric and mechanical boundary conditions.(2) The PI will investigate the dependence of piezoelectric responses of ferroelectric nanostructures on substrate constraints as well as on the inhomogeneous stress distributions within a nanostructure due to presence of defects such as dislocations.(3) The PI will study the correlation between the multiferroic nanocomposite microstructure and the magnitude of magnetoelectric coupling effect. This research program involves active collaborations with applied mathematicians on the implementation of advanced numerical algorithms and with experimentalists on experimental validation of computational predictions and findings. The research under this award is expected to (i) significantly contribute to the fundamental understanding of the piezoelectric responses of nanoferroelectrics and magnetoelectric coupling effect of multiferroic nanocomposites, (ii) yield new phase-field formulations for modeling multiferroic domain structures, and (iii) produce advanced numerical algorithms for solving phase-field equations involving non-periodic boundary conditions. This award supports training graduate as well as undergraduate students through thesis and summer research. Software tools developed from the project will be incorporated into two graduate courses and an undergraduate course. The research findings will be disseminated to a wide audience through archival publications and conferences, review and overview papers, and active participation and lectures at interdisciplinary workshops. NON-TECHNICAL SUMMARYThis award supports theoretical and computational research on the properties and functionalities of ferroelectric and multiferroic oxides. Ferroelectrics and multiferroics are multi-functional materials that can produce two or more different types of responses when they are subjected to an external field. They have many potential applications in devices such as actuators, sensors, and computer memory storage. For example, a ferroelectric crystal can change both its shape and electric polarization when it is subject to an external mechanical stress. Electric polarization results when the negative electronic charge distribution is shifted from the positive charge distribution of the atomic nuclei in a crystal. In a multiferroic material, the magnitude and direction of both the magnetization and electric polarization can be altered by externally applying either an electric or a magnetic field. The research program has two main thrusts: The PI will investigate the so-called "piezoelectric response", which is related to the magnitude of the change in electric polarization under a mechanical stress or the degree of crystal shape deformation under an electric field. These effects will be examined in bulk ferroelectrics as well as in tiny structures of sizes that are approximately one billionth the size of the human hair. Secondly, the PI will investigate the so-called "magnetoelectric" coupling, which is related to the change in electric polarization under an applied magnetic field or the change in magnetization under an applied electric field. The PI will develop and apply various computational tools in these investigations. The overall goal is to optimize the multi-functionalities of such materials through computer simulations. The research program involves active collaborations with applied mathematicians on the implementation of advanced numerical algorithms and with experimentalists on experimental validation of computational predictions and findings.The project will contribute to human resource development by training graduate as well as undergraduate students through thesis and summer research. Software tools developed from the project will be incorporated into two graduate courses and an undergraduate course. The research findings will be disseminated to a wide audience through archival publications and conferences, review and overview papers, and active participation and lectures at interdisciplinary workshops.