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基本影响。特别是，提出了一种无缝的多尺度方法，可以在实际浓度下精确研究缺陷。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内发展，密度泛函理论传统上是关于原子数量的立方标度。此外，将利用适合缺陷性质的数值粗粒化近似。通过严格的数学分析，保证整体配方的最优性。作为一种应用，所提出的多尺度方法将用于研究合金对镁的强度和延展性的影响，以发现新的合金。此外，将生成位错动力学模拟的本构定律，并使用这些，将研究纳米柱压缩过程中观察到的尺寸相关强度。如果成功，该项目将在连接电子结构和晶体缺陷的连续描述方面提供突破。这将极大地促进目前对固体变形和破坏机制的理解。因此，它将加速发现具有适合技术应用的特性的新材料。例如，具有更高比强度的新型镁合金将对运输行业产生显著影响，因为运输行业需要在不影响结构完整性的情况下减轻重量。这种合金将有助于减少燃料消耗，从而对环境也有积极的影响。该项目的教育工作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技术的新网站，组织会议专题讨论会，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.