Atoms, Defects and the Kinetics of Phase Transformations

原子、缺陷和相变动力学

• 批准号: 0311788
• 负责人: Kaushik Bhattacharya
• 金额: $ 19.28万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-15 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0311788&HistoricalAwards=false
• 关键词: Atoms; Defects; Kinetics; Phase; Transformations

A fundamental understanding of the kinetics of phase boundaries, and more broadly hysteresis, remains an open challenge in the study of active materials. The lack of kinetic information is a consistent difficulty in various problems including dislocation mechanics and growth of thin films. The research in the current award, though focussed on active materials, will impact these areas. There is now an accepted framework to model this based on the notion of kinetic relations, but it is phenomenological in that it does not address why some phase boundaries are more mobile than others and how one can change the mobility. This project examines through computation and rigorous mathematics whether one can derive a kinetic relation starting from a more fundamental or smaller scale description of materials in the context of displacive phase transformations. Two scales are of particular interest, atoms and defects. First, the project seeks to understand the atomic-continuum linkage by starting from an atomistic (discrete) model capable of phase transformations and passing to the continuum in such a manner that captures the essential dynamics of the phase transformation process. Second, the project seeks to understand the role of defects such as vacancies, impurities and second phase precipitates in determining the overall propagation of a phase boundary. This leads to the mathematical problem of homogenization of a non-local free boundary problem.Active materials like shape-memory materials and ferroelectric materials possess unusual but useful properties that make them vital for a variety of applications like dental braces, cardiac stents, space antennas, ultrasonic devices, pressure sensors and microactuators. The unusual properties arise from very characteristic and intricate patterns that these materials can form at a microscopic scale. Over the last decade, much advance has been made in understanding the nature of the microstructure, its relation to basic crystallography and its consequences for material properties. In particular, a sophisticated mathematical theory for static microstructures has emerged, and this theory has had important practical impact by predicting and explaining new phenomena and applications. However, much remains unknown regarding how the microstructure changes as we apply stress to these materials. This is important since it determines an important property of these materials known as hysteresis or shape memory. Work supported by this award will build a mathematical theory of the evolution of microstructure. It will also train graduate and undergraduate students in research in the emerging and important area of multiscale modeling.

对相位边界的动力学以及更广泛的磁滞的基本理解仍然是活跃材料研究的开放挑战。 在包括错位力学和薄膜的生长在内的各种问题中，缺乏动力学信息是一个一致的困难。当前奖项中的研究虽然着重于活性材料，但会影响这些领域。 现在有一个公认的框架来基于动力学关系的概念进行建模，但是它是现象学的，因为它不能解决为什么某些相位边界比其他相位更容易移动以及如何改变移动性。该项目通过计算和严格的数学来检查是否可以从更基本或较小的规模描述材料的材料中得出动力学关系。两个量表特别感兴趣，原子和缺陷。 首先，该项目试图通过从能够相变和传递到连续体的原子（离散）模型开始，以捕获相变过程的基本动力学的方式来理解原子界链接。 其次，该项目试图了解缺陷的作用，例如空缺，杂质和第二相中造成在确定相边界总体传播中的作用。 这导致了非本地游离边界问题均质化的数学问题。活跃的材料（如形状记忆材料和铁电材料）具有不寻常但有用的特性，使它们对于牙齿括号，心脏支架，太空天线，超声波设备，压力传感器和小动物等多种应用至关重要。 异常的特性是由这些材料可以在微观尺度上形成的非常有特征和复杂的模式引起的。 在过去的十年中，在理解微观结构的性质，与基本晶体学的关系及其对材料特性的后果方面取得了很多进步。 特别是，已经出现了静态微观结构的复杂数学理论，该理论通过预测和解释新现象和应用，产生了重要的实际影响。但是，关于微观结构如何在我们对这些材料施加压力时如何变化仍然未知。 这很重要，因为它决定了这些材料的重要特性，称为滞后或形状记忆。 该奖项支持的工作将建立一个微观结构演变的数学理论。 它还将在多尺度建模的新兴和重要领域的研究中培训研究生和本科生。