CAREER: CDS&E: Quantifying & Designing Grain Boundary Network Structure via Spectral Graph Theory

该职业奖支持理论和计算研究和教育，以表征多晶材料中晶界网络的结构、性质和演变。晶界是金属和陶瓷晶体区域之间的界面，它们形成了一个复杂的相互连接的网络，强烈影响许多材料的性能，包括抗蠕变、氢脆、光伏效率和辐射耐受性。单个晶界的性质可以有数量级的变化。如果有可能设计晶界网络的结构，这种巨大的性质变化可以用来增强能源和结构材料。受谱图理论的启发——谱图理论是为b谷歌的网络搜索算法提供动力的数学，并表征了社会、生态和生物网络——PI将开发数学工具来表征晶界网络的结构，预测它们的聚合特性，并通过应用程序定制晶界网络结构来解决材料设计问题。PI将开发一个基于社交网络的多人材料设计游戏，该游戏由该谱图理论框架提供动力，以增强科学、技术、工程和数学课程，并利用学生和公众固有的3D空间推理来解决大规模材料设计问题。研究计划提供了使能创新，以满足教育推广工作的计算需求，通过提供人类用于解决材料设计问题的启发式数据来回报这种整合，这些数据将反过来被分析，以告知算法的构建，以加速材料设计。我们今天所依赖的技术，以及有望为未来提供清洁能源、地面和太空运输以及改善医疗保健的创新，越来越依赖于先进材料的发展。通过整合材料研究、社交网络和通过游戏进行的主动学习，该项目提供了一个变革性的机会，通过扩大和增加学生在科学、技术、工程和数学教育中的参与度，同时使材料设计的新维度加速新材料的发现，从而扩大美国的技术领先地位和全球竞争力。本职业奖支持教学和研究的整合，以扩大对多晶材料晶界网络的理解和控制：1)通过谱图理论开发晶界网络结构的一般描述符；2)利用这一工具激发科学、技术、工程和数学教育，并利用基于社交网络的在线游戏解决大规模材料设计问题。这项工作将实现五个基本进展：1)描述晶界网络结构的一般框架；2)晶界敏感性质预测；3)基于应用定制晶界网络的微观结构设计；4)预测未来设计微结构合成的加工路线；5)解决大规模材料设计问题的人类云计算平台，提高学生在科学、技术、工程和数学方面的参与度。尽管晶界网络对材料性能影响很大，但其耦合拓扑晶体结构的复杂性阻碍了定量结构-性能模型的发展。如果存在晶界结构的数学描述，它将使晶界网络表征，性能预测和改进材料性能的设计/优化成为可能。谱图理论已被用于研究生态学、生物学和计算机科学中的复杂网络。例如，为b谷歌的搜索引擎提供动力的PageRank算法使用万维网网络结构的频谱分解来确定其主要特征，并将这些特征与查询相关性联系起来。这项工作利用材料网络结构的光谱分解来确定其主要的微观结构特征，并将这些特征与材料特性联系起来。晶界网络的特征值将为编码晶界网络拓扑和晶体学信息的结构度量提供一种自然语言。利用这种谱图理论框架来表征三维多晶体中的晶界网络结构，PI将使用计算机模拟来实现两个目标：(1)建立一个模型来预测多晶体中晶界网络的有效扩散率；(2)建立各向异性晶粒生长的本构模型，该模型可以反向预测加工路径，并为合成设计的显微组织提供路线。该教学计划的目标是通过整合社交网络、技术和游戏，提高学生对科学、技术、工程和数学教育的参与度。将开发一个基于社交网络的多人游戏，以增强科学、技术、工程和数学教育课程，并招募学生和公众的智力资源来设计材料。研究计划为满足教学计划的计算需求提供了有利的创新，而教学计划则通过提供人类用于解决材料设计问题的启发式数据来回报这种整合，这些数据将被分析，为材料设计数值优化算法的构建提供信息。通过开发和利用涉及谱图理论的新型计算工具，这项工作为扩展我们对晶界网络的结构、性质和演化的理解提供了一个转型的机会。这项工作还提出了一个创新的基于社会网络的计算平台来解决大规模材料设计问题。预计这一结果将对不同的材料现象和广泛的材料设计应用产生影响。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical and computational research and education to characterize the structure, properties, and evolution of grain boundary networks in polycrystalline materials. Grain boundaries are the interfaces between crystalline regions in metals and ceramics and they form a complex interconnected network that strongly influences many material properties including creep resistance, hydrogen embrittlement, photovoltaic efficiency, and radiation tolerance. The properties of individual grain boundaries can vary by orders of magnitude. If it were possible to engineer the structure of grain boundary networks, this enormous property variation could be leveraged to enhance both energy and structural materials. Inspired by spectral graph theory - which is the mathematics that powers Google's web search algorithm, and characterizes social, ecological and biological networks--the PI will develop the mathematical tools to characterize the structure of grain boundary networks, predict their aggregate properties, and address materials design with application tailored grain boundary network structures.The PI will develop a social-network-based multiplayer materials design game, powered by this spectral graph theory framework to enhance science, technology, engineering, and mathematics curricula and harness the innate 3D spatial reasoning of students and the public to solve large-scale materials design problems. The research plan provides the enabling innovation to satisfy the computational requirements of the educational outreach effort, which reciprocates this integration by providing data on the heuristics used by humans to solve materials design problems, which will in turn be analyzed to inform the construction of algorithms to accelerate materials design.The technologies that we rely on today and the innovations that promise to provide clean energy, terrestrial and space transportation, and improved healthcare for tomorrow depend increasingly on the development of advanced materials. By integrating materials research, social-networking, and active learning through game play, this project provides a transformative opportunity to expand US technological leadership and global competitiveness by broadening the reach of and increasing student engagement in science, technology, engineering, and mathematics education and simultaneously enabling new dimensions of materials design to accelerate the discovery of new materials. TECHNICAL SUMMARYThis CAREER award supports the integration of teaching and research to expand understanding and control of grain boundary networks in polycrystalline materials by: 1) developing a general descriptor for grain boundary network structure via spectral graph theory, and 2) leveraging this tool to invigorate science, technology, engineering and mathematics education and solve large-scale materials design problems using a social-network-based online game. This work will enable five fundamental advances: 1) a general framework to characterize the structure of grain boundary networks; 2) prediction of grain-boundary-sensitive properties; 3) design of microstructures with application tailored grain boundary networks; 4) prediction of processing routes for future synthesis of designed microstructures; 5) a human cloud computing platform for solving large-scale materials design problems and increasing student engagement in science, technology, engineering and mathematics. Although grain boundary networks strongly influence material properties, the complexity of their coupled topological-crystallographic structure has hindered the development of quantitative structure-property models. If a mathematical description of grain boundary structure existed it would enable grain boundary network characterization, property prediction, and design/optimization for improved material performance. Spectral graph theory has been used to study complex networks in ecology, biology, and computer science. For example, the PageRank algorithm that powers Google's search engine uses spectral decomposition of the network structure of the World Wide Web to determine its dominant features and correlate these with query relevance. This work utilizes spectral decomposition of the network structure of materials to determine their dominant microstructural features and correlate these with material properties. The eigenvalues of the grain boundary network will provide a natural language for structure metrics that encode both topological and crystallographic information for grain boundary networks.Using this spectral graph theory framework to characterize grain boundary network structure in 3D polycrystals, the PI will use computer simulation to address two objectives: (1) develop a model to predict the effective diffusivity of grain boundary networks in polycrystals; (2) create a constitutive model for anisotropic grain growth that can be inverted to predict processing paths and suggest routes to synthesize designed microstructures. The objective of the Teaching Plan is to increase engagement in science, technology, engineering, and mathematics education through the integration of social-networks, technology and games. A social-network-based multiplayer game will be developed that enhances science, technology, engineering, and mathematics education curricula and recruits the intellectual resources of students and the public to design materials. The research plan provides the enabling innovation to satisfy the computational requirements of the teaching plan, which reciprocates this integration by providing data on the heuristics used by humans to solve materials design problems, which will be analyzed to inform the construction of numerical optimization algorithms for materials design.By developing and exploiting novel computational tools involving spectral graph theory, this work presents a transformational opportunity to expand our understanding of the structure, properties, and evolution of grain boundary networks. This work also presents an innovative social-network-based computational platform to solve large-scale materials design problems. It is anticipated that the results will have implications for diverse materials phenomena and wide ranging materials design applications.