The Morphological Evolution of Particles in Elastically Stressed Solids

小行星9322687 许多具有工程意义的合金的性能与共格第二相粒子的形态和空间分布有关。 在许多情况下，弹性应力存在于这些两相系统中，这是由于少数相颗粒和基体之间的晶格参数的差异或施加的应力造成的。 由于对受应力结晶固体中控制颗粒形态的因素的理解还没有掌握，因此很难预测这些多相材料的性质。 这种理解的缺乏可以追溯到有限数量的研究已经调查了控制相干失配粒子的平衡形状的因素，即使系统的总能量最小化的形状受到粒子形态的所有可能变化的影响。 然而，这些少数研究表明，弹性应力的存在可以导致与不存在应力时性质不同的现象，例如对于给定的一组材料参数的多个平衡形状，颗粒分裂和非凸的沙漏状平衡形状。 %%%% 这个项目的一个主要目标是提供一个图片的一般作用弹性应力发挥在发展中的平衡形态的一个不匹配的三维粒子。 由于确定失配粒子的平衡形状的方程是高度非线性的，因此在三维中存在比在先前关于二维中粒子的平衡形状的工作中观察到的复杂得多的粒子形状分叉结构。 尽管研究的数值性质和工作的每一部分中采用的具体假设，理解和预测的颗粒在应力固体形态演变的一般框架将提供。 最后，这个理论将与实验一起使用，以研究在弹性各向异性系统中的非膨胀铝错配对错配粒子形态的影响。 ***

9322687 Voorhees The properties of many alloys of engineering significance are related to the morphology and spatial distribution of coherent second-phase particles. In many cases elastic stress is present in these two-phase systems resulting from either a difference in lattice parameters between the minority phase particles and the matrix, or an applied stress. As an understanding of the factors controlling the morphology of a particle in a stressed crystalline solid is not at hand, it is difficult to predict the properties of these multiphase materials. This lack of understanding can be traced to the limited number of studies that have investigated the factors controlling the equilibrium shape of a coherent misfitting particle, i.e. the shape that minimizes the total energy of the system subject to all possible variations in particle morphology. Nevertheless, these few studies have shown that the presence of elastic stress can lead to qualitatively different phenomena than in the absence of stress, such as multiple equilibrium shapes for a given set of materials parameters, particle splitting and non convex, hourglass-like, equilibrium shapes. %%%% A major goal of this project is to provide a picture of the generic role elastic stress plays in the development of the equilibrium morphology of a misfitting three-dimensional particle. As the equations which determine the equilibrium shape of a misfitting particle are highly nonlinear, a far more complex particle shape bifurcation structure is present in three-dimensions than observed in previous work on the equilibrium shape of a particle in two- dimensions. Despite the numerical nature of the study and the specific assumptions employed in each section of the work, a general framework for understanding and predicting the morphological evolution of particles in stressed solids will be provided. Finally, this theory will be used in concert with experiments to investigate the effects of a nondilation al misfit on the morphology of misfitting particles in an elastically anisotropic system. ***