Collaborative Research: Computational problems in heterogeneous nanomaterials

合作研究：异质纳米材料的计算问题

• 批准号: 0915128
• 负责人: John Lowengrub
• 金额: $ 36.57万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915128&HistoricalAwards=false
• 关键词: Collaborative; Research; Computational; problems; heterogeneous

In many applications ranging from energy to biomedicine, nanocrystalline materials, such as quantum dots and nanowires, promise to yield revolutionary new technologies. The realization of this promise is hindered by the challenges inherent in reproducibly fabricating nanocrystalline materials with controlled morphologies and compositions. These nanomaterials are typically heterogeneous and consist of alloys with multiple constituents. While there has been much work on formulating conditions under which spatially ordered nanocrystals with nearly uniform shapes and sizes may be produced, a quantitative description of the mechanisms that determine the spatial distribution of the alloy components, which is crucial to device performance, is still poorly understood. The investigators and their collaborators address this issue in this proposal. They study the nonlinear dynamics of heterogeneous, strained strained nanocrystalline materials by (1) developing and applying state-of-the-art adaptive numerical methods to large-scale computation and (2) performing analytical, numerical and modelling studies of important constituent processes. The investigators focus on the dynamic, nonlinear coupling among shape, elastic stress and composition in the context of (i) the dynamics of thin film alloys and quantum dots under far-from-equilibrium processing conditions where there may be bulk and surface transport of the different constituents, as well as phase decomposition; and (ii) the coarsening dynamics and stability of capped nanocrystals. The cap material is needed in applications to provide the confinement potential for charge carriers as well as passivation against the external environment. These problems are characterized by the presence of multiple constitutive components, bulk-surface interactions, complex pattern formation and/or singularities (i.e. spatial complexity). The mathematical models involve high-order spatial derivatives (e.g. up to sixth-order), evolving free boundaries and highly nonlinear interactions that make analysis and simulation difficult, particularly in 3D. The highly nonlinear nature of these problems makes fast, accurate and robust numerical methods essential to their study.Nanocrystalline alloy materials have physical properties that make them ideally suited for a wide range of potential applications including advanced electronic and magnetic devices as well as biological and chemical sensors. The properties of nanoscale devices are determined both by the spatial composition of the heterogeneous nanocrystal components and the nanocrystal geometry. Recent advances in experimental techniques have enabled the characterization of nanoscale composition variation in nanocrystals.However, a quantitative understanding of these variations remains elusive and yet is critical to device performance. The investigators and their collaborators address this issue by developing new mathematical models, theory and computational methods that make it possible to characterize and quantify the interactions among nanocrystal shape, elastic stress and composition. The investigators also consider capped nanostructures where the cap material provides protection from the environment that is needed in many applications including the use of nanocrystals in silicon-based electronic circuits. The interaction among the nanocrystalline and capping materials introduces additional complexity. These problems are multidisciplinary and progress requires the combined expertise of the investigators in materials science and applied and computational mathematics. Through this study, the investigators provide guidance in the quantitative interpretation of experimental measurements of composition variation in nanocrystals and suggest optimized processing conditions to achieve desired device shape, composition and performance. The project establishes a new collaboration between two institutions and provides interdisciplinary training of two Ph.D students and one postdoctoral researcher. In addition, the investigators build on their recent success and continue to develop and teach a course on crystal and epitaxial growth for gifted high school students as part of the Calif. State Summer School for Mathematics and Science (COSMOS) at UC Irvine. This course also helps to recruit new math and science majors and enhance the participation of high school students in research.

在从能源到生物医学的许多应用中，量子点和纳米线等纳米晶体材料有望产生革命性的新技术。这一承诺的实现受到了可重复制造具有可控形貌和组成的纳米晶材料固有挑战的阻碍。这些纳米材料通常是非均相的，由具有多种成分的合金组成。虽然已经有很多工作来制定条件，在这种条件下可以产生形状和尺寸几乎一致的空间有序纳米晶，但对决定合金组分空间分布的机制的定量描述仍然知之甚少，这对器件性能至关重要。研究人员和他们的合作者在这项提案中解决了这个问题。他们通过(1)开发和应用最先进的自适应数值方法进行大规模计算，以及(2)对重要的组成过程进行分析、数值和建模研究，来研究非均质、应变纳米晶体材料的非线性动力学。研究人员侧重于形状、弹性应力和成分之间的动态、非线性耦合，背景是(I)薄膜合金和量子点在远离平衡的加工条件下的动力学，其中可能存在不同成分的体相和表面输运，以及相分解；以及(Ii)带帽纳米晶体的粗化动力学和稳定性。在应用中需要盖子材料来提供电荷载流子的限制电位以及对外部环境的钝化。这些问题的特点是存在多个本构成分、体表相互作用、复杂的图案形成和/或奇异性(即空间复杂性)。数学模型涉及高阶空间导数(例如，高达六阶)、不断演变的自由边界和高度非线性的相互作用，这使得分析和模拟变得困难，特别是在3D中。这些问题的高度非线性使得快速、准确和稳健的数值方法对它们的研究至关重要。纳米晶合金材料具有理想的物理性质，使其非常适合于广泛的潜在应用，包括先进的电子和磁性设备以及生物和化学传感器。纳米器件的性质既取决于非均相纳米晶体成分的空间组成，也取决于纳米晶体的几何形状。实验技术的最新进展使得表征纳米晶体中纳米级组成的变化成为可能。然而，对这些变化的定量理解仍然是难以捉摸的，但对器件性能来说是至关重要的。研究人员和他们的合作者通过开发新的数学模型、理论和计算方法来解决这个问题，这些新的数学模型、理论和计算方法使得表征和量化纳米晶体形状、弹性应力和成分之间的相互作用成为可能。研究人员还考虑了有盖子的纳米结构，在这种结构中，盖子材料提供了许多应用所需的环境保护，包括在硅基电子电路中使用纳米晶体。纳米晶体和盖子材料之间的相互作用带来了额外的复杂性。这些问题是多学科的，进步需要材料科学、应用数学和计算数学方面的研究人员的综合专业知识。通过这项研究，研究人员为定量解释纳米晶体中成分变化的实验测量提供了指导，并提出了优化的工艺条件，以实现所需的器件形状、成分和性能。该项目建立了两个机构之间的新合作，并为两名博士生和一名博士后研究员提供跨学科培训。此外，研究人员在最近成功的基础上，继续为有天赋的高中生开发和教授一门关于晶体和外延生长的课程，作为加州计划的一部分。加州大学欧文分校的国家数学与科学暑期学校(COSMOS)。这门课程还有助于招收数学和科学专业的新学生，并提高高中生对研究的参与度。