Linking Electronic Structure with Continuum Fields: Coarse-Graining Density Functional Theory

该奖项的研究目标是通过量子力学密度泛函理论计算来研究晶体缺陷对材料行为的根本影响。特别是，提出了一种无缝的多尺度方法，使在实际浓度下能够准确地研究缺陷。这种方法将在密度泛函理论的一种新的线性标度技术的框架下发展，该技术传统上具有关于原子数量的立方标度。此外，还将利用针对缺陷性质量身定做的数值粗粒化近似。通过严格的数学分析，将确保整体配方的最佳性。作为应用，提出的多尺度方法将用于研究合金化对镁合金强度和塑性的影响，以期发现新的合金。此外，还将生成用于位错动力学模拟的本构定律，并将利用这些本构定律来研究在纳米柱压缩过程中观察到的尺寸依赖强度。如果成功，该项目将在连接晶体缺陷的电子结构和连续描述方面取得突破。这将极大地促进目前对固体变形和破坏机制的理解。因此，它将加速发现具有针对技术应用而量身定做的性能的新材料。例如，具有更高比强度的新型镁合金将对需要在不影响结构完整性的情况下减轻重量的运输行业产生显著影响。这种合金将有助于降低燃料消耗，从而对环境也有积极的影响。该项目的教育努力包括通过社交媒体和学术课程广泛传播研究成果，创建一个记录晶体缺陷计算最新水平的新网站，组织会议研讨会，以及培训研究生、本科生和高中生。

The research objective of this award is to investigate the fundamental impact of crystal defects on material behavior through quantum-mechanical Density Functional Theory calculations. In particular, a seamless multiscale method that will enable the accurate study of defects at realistic concentrations is proposed. This method will be developed in the framework of a novel linear-scaling technique for Density Functional Theory, which traditionally has a cubic-scaling with respect to the number of atoms. Additionally, numerical coarse-graining approximations tailored to the nature of the defect will be utilized. The optimality of the overall formulation will be ensured through rigorous mathematical analysis. As an application, the proposed multiscale method will be used to study the effect of alloying on the strength and ductility of Magnesium with the goal of discovering novel alloys. Also, constitutive laws will be generated for dislocation dynamics simulations and, using these, the size-dependent strength observed during compression of nanopillars will be investigated. If successful, the project will provide a breakthrough in bridging the electronic structure and continuum descriptions of crystal defects. This will significantly advance the current understanding of deformation and failure mechanisms in solids. Consequently, it will accelerate the discovery of novel materials with properties tailored to technological applications. As an example, new magnesium alloys with improved specific strength will have a noticeable impact on the transportation industry where there is a need for weight reduction without compromising structural integrity. Such alloys will help reduce fuel consumption, thereby also having a positive influence on the environment. The educational efforts of the project include broad dissemination of research results through social media and academic curriculum, creating a new website that documents the state of the art in crystal defect calculations, organizing conference symposia, and training graduate, undergraduate and high school students.