Modeling Non-Equilibrium Microstructure Formation

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。技术概述该奖项支持理论和计算研究及教育，以进一步发展相场模拟到原子长度尺度和扩散时间尺度的方法，并使多组分合金的模拟成为可能。通过使用“相场”模拟方法，加深了对许多非平衡过程的理解。事实证明，这些方法在模拟凝固现象的许多方面都非常成功，现在已被纳入商业可用的软件包中。最近，PI及其合作者引入了第二代相场模型，该模型描述了原子长度和扩散时间尺度上的现象。这种“相场晶体”方法自然地结合了弹性、塑性、各向异性和多晶体取向，以及传统的凝固和相分离模型的所有物理性质。虽然为单原子和二元合金建立的相场晶体模型可以描述许多物理现象，包括晶体生长、外延生长、共晶凝固、多晶材料的屈服强度、爬升和滑移以及晶界熔化，但有许多重要的现象是现有模型无法描述的。例如，二元模型不能描述多元合金中的亚晶格有序性。这是一个关键问题，因为亚晶格有序是非常常见的，并影响结构性质。目前相场晶体模型的另一个局限性是它们描述的是球对称的粒子，因此不能描述与额外自由度相关的物理，如旋转。利用这些自由度的一个重要技术例子是弹性体；拉长的交联型聚合物的旋转允许剪切应变，而能源成本几乎为零。该项目的目标是极大地扩展相场晶体建模的适用性，以包括亚晶格有序和各向异性粒子。PI还计划将Goldenfeld和合作者开发的单原子相场晶体的振幅展开扩展到二元系统。振幅法结合了许多基本的弹性和塑性行为，更易于进行解析和数值计算。所得到的模型将用于研究晶格的离散性质和组成均匀对应变外延薄膜中形态不稳定性的影响。PI与Wiley出版公司签订了一本关于材料科学中相场建模的书。正文的大部分内容将致力于本提案和到期的NSF拨款中开发的相场晶体配方。该文本将作为一个教学指南谁希望学习相场建模的基本原理和技术细节的工程和物理学生。PI将招聘和培训尖端计算材料物理方面的本科生。这项工作还将对许多研究领域产生影响，因为开发的方法适用于广泛的现象，如多组分合金的结构属性、弹性体的奇异弹性属性以及应变外延生长中量子点的形成。非技术总结该奖项支持理论和计算研究以及教育，以进一步开发一种潜在的强大方法，用于材料的计算机模拟，该方法由PI及其合作者开发。这项研究涉及到一种名为相场建模的建模技术的扩展，这种建模技术在计算上很快，但在许多原子的长度尺度上很有用。这一扩展使计算机模拟能够访问短得多的长度尺度、原子长度尺度和更长时间的信息。从单个原子到微米的许多长度尺度上的材料加工和相关材料现象的模拟是新方法的很有前途的应用。PI还将撰写一本关于相场建模及其在模拟材料和材料相关现象中的应用的书。本科生将参与与该项目直接相关的研究活动。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Technical SummaryThis award supports theoretical and computational research and education to further develop methods of phase field modeling to the atomic length scale and diffusive time scales and enable the simulation of multi-component alloys.The understanding of many non-equilibrium processes has been enhanced by the use of "phase-field" modeling methods. These methods have proven very successful in modeling many aspects of solidification phenomena and are now incorporated in commercially available software packages. More recently the PI and collaborators have introduced a second generation of phase field models that describe phenomena on atomic length and diffusive time scales. This "phase field crystal" method naturally incorporates elasticity, plasticity, anisotropy and multiple crystal orientations in addition to all the physics of traditional models of solidification and phase segregation.While the phase field crystal models developed for monatomic and binary alloys can describe many physical phenomena, including grain growth, epitaxial growth, eutectic solidification, the yield strength of polycrystalline materials, climb and glide, and grain boundary melting, there are many important phenomena that are beyond description by the current models. For example, the binary model cannot describe sublattice ordering in multi-component alloys. This is a key issue since sublattice ordering is extremely common and influences structural properties. Another limitation of current phase field crystal models is that they describe spherically symmetric particles and thus cannot describe the physics associated with extra degrees of freedom, such as rotation. A technologically important example which exploits these freedoms is elastomers; the rotation of elongated cross-linked polymers allows shear strains at almost zero energy cost. The goal of this project is to greatly extend the applicability of phase field crystal modeling to incorporate sublattice ordering and anisotropic particles. The PI also plans to extend the amplitude expansion of the monatomic phase field crystal developed by Goldenfeld and collaborators to binary systems. The amplitude approach incorporates much of the essential elastic and plastic behavior and is more amenable to analytic and numerical calculations. The resulting model will be used to examine the influence of the discrete nature of the crystalline lattice and compositional in homogeneities on morphological instabilities in strained epitaxial films.The PI has a contract with Wiley publishing to write a book on phase field modeling in materials science. Much of the text will be devoted to the phase field crystal formulations developed in this proposal and in the expired NSF grant. The text will be written as an instructional guide for engineering and physics students who wish to learn the fundamentals and technical details of phase field modeling. The PI will hire and train undergraduate students in cutting edge computational materials physics. The work will also have an impact on many areas of research since the methods developed are applicable to a wide range of phenomena such as the structural properties of multi-component alloys, the exotic elastic properties of elastomers and the formation of quantum dots in strained epitaxial growth.Non-Technical SummaryThis award supports theoretical and computational research and education to further develop a potentially powerful method for computer simulation of materials that was developed by the PI and collaborators. The research involves the extension of a modeling technique, called phase field modeling, that is computationally fast but useful on length scales of many atoms. The extension enables computer simulations to access information on much shorter length scales, atomic length scales, and longer times. Simulations of materials processing and related materials phenomena that span many length scales from single atoms to microns are promising applications of the new method.The PI will also write a book on phase field modeling and its application to modeling materials and materials related phenomena. Undergraduate students will be involved in research activities directly related to this project.