Atoms, Defects and the Kinetics of Phase Transformations

在活性材料的研究中，对相界动力学的基本理解，以及更广泛的滞后，仍然是一个开放的挑战。动力学信息的缺乏一直是包括位错机制和薄膜生长在内的各种问题中的一个难题。目前奖项的研究虽然集中在活性材料上，但将对这些领域产生影响。现在已经有一个公认的框架来基于动力学关系的概念对此进行建模，但它是现象学的，因为它没有解决为什么某些相边界比其他相边界更具流动性，以及如何改变迁移率。这个项目通过计算和严格的数学来检验人们是否可以从更基本或更小尺度的材料描述出发，在位移相变的背景下推导出动力学关系。原子和缺陷是两个特别值得关注的尺度。首先，该项目试图通过从能够相变的原子(离散)模型开始并以捕捉相变过程的基本动力学的方式传递到连续统来理解原子-连续统之间的联系。其次，该项目试图了解缺陷，如空位、杂质和第二相沉淀物在决定相界的整体传播中的作用。形状记忆材料和铁电材料等活性材料具有特殊但有用的性质，这使得它们对于牙科支架、心脏支架、空间天线、超声波设备、压力传感器和微执行器等各种应用至关重要。这些不同寻常的性质源于这些材料可以在微观尺度上形成的非常独特和复杂的图案。在过去的十年里，在理解微观结构的性质、它与基础结晶学的关系以及它对材料性能的影响方面取得了很大的进展。特别是，已经出现了一种关于静态微结构的复杂的数学理论，该理论通过预测和解释新的现象和应用，产生了重要的实际影响。然而，当我们对这些材料施加压力时，微观结构如何变化仍是个未知数。这一点很重要，因为它决定了这些材料的一个重要属性，即滞后或形状记忆。该奖项支持的工作将建立微观结构演化的数学理论。它还将培训研究生和本科生在新兴和重要的多尺度建模领域进行研究。

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.