Kinetic Monte Carlo Modeling and Simulation of Phase Boundaries and Polycrystals

该项目涉及具有相界和晶界的晶体演化的动力学蒙特卡罗（KMC）模型。KMC对于探索原子尺度晶体生长问题的动力学特别有用，其中许多问题与纳米技术有重大关系。该思想的实质是对分子动力学（MD）进行粗粒度模拟。虽然MD在概念上简单、健壮且忠实于底层物理，但在许多情况下，它的速度慢得令人绝望。在模拟结晶固体的演化时，这个问题尤其明显，因为在晶体固体中，单个原子在相互吸引的盆地中停留很长时间，然后偶尔过渡到邻近的结构。当晶体被很好地定义时，一种用马尔可夫链取代牛顿动力学的替代模型很容易出现：一种用晶格的占位数组取代原始构型空间，这种占位数组理想化了吸引力盆地的排列，并引入了基于过渡态理论的转移概率。显然，当晶体是均匀的——没有位错、晶界、杂质和表面结构时，这种方案效果最好。与MD不同的是，KMC模型必须仔细调整以处理这些不规则现象。虽然这很复杂，每种情况下都需要专门的模拟软件，但其回报是能够在纳米器件的规模上进行模拟，这是MD基本上不可能做到的。在这个项目中，首席研究员解决了KMC晶体生长建模的两个具体挑战。首先是晶体-熔体界面、熔体-蒸气界面和三结的建模，目的是将该模型应用于纳米线的生长。第二种是多晶内部晶界的运动。技术，特别是微电子工业中的技术，越来越集中在越来越小的设备上。因此，现在能够在原子长度尺度上模拟设备制造和性能是很重要的。相对而言，很少有计算工具可以解决包含几千个原子的复杂系统的原子尺度行为。一种更有前途的方法是动力学蒙特卡罗——一种近似原子尺度运动的模型，这些原子具有完美的堆叠排列，即形成完美的晶体。然而，晶体是理想化的，它们具有许多需要特别考虑的缺陷。任何附着在晶体上的原子级装置也同样需要特殊处理。这个项目旨在扩展动力学蒙特卡罗模型，使它们能够处理这种不规则现象。该项目由数学科学部和材料研究部资助。

SchulzeDMS-1108643 This project concerns kinetic Monte Carlo (KMC) models for the evolution of crystals with phase and grain boundaries. KMC is especially useful for exploring the dynamics of atomistic scale crystal growth problems, many of which have a significant bearing on nanotechnology. The essence of the idea is to coarse-grain a molecular dynamics (MD) simulation. While MD is conceptually simple, robust, and faithful to the underlying physics, it is hopelessly slow in many instances. This problem is particularly apparent when simulating the evolution of crystalline solids, where individual atoms hover for long periods of time in basins of attraction before making occasional transitions to neighboring configurations. When the crystal is well defined, an alternative model that replaces the Newtonian dynamics with a Markov chain readily suggests itself: One replaces the original configuration space with an occupation array for a crystal lattice that idealizes the arrangement of the basins of attraction, and introduces transition probabilities based on transition state theory. Clearly, such a scheme works best when the crystal is uniform -- free of dislocations, grain boundaries, impurities and surface structures. Unlike MD, KMC models have to be carefully adapted to handle these sorts of irregularities. While this is complicated and requires specialized simulation software in each case, the payoff is the ability to perform simulations on the scale of nano-devices -- something that is essentially impossible with MD. In this project, the principal investigator addresses two specific challenges to KMC modeling of crystal growth. The first is modeling of crystal-melt interfaces, melt-vapor interfaces and tri-junctions, with the aim of applying the model to the growth of nanowires. The second is the motion of grain boundaries within a polycrystal. Technology, particularly within the micro-electronic industries, is increasingly focused on smaller and smaller devices. As a result, it is now important to be able to simulate device manufacturing and performance on atomic length scales. There are relatively few computational tools that can resolve the atomic scale behavior of a complicated system containing, say, a few thousand atoms. One of the more promising approaches is kinetic Monte Carlo -- a model that approximates the atomic scale motion of atoms that have perfect stacking arrangements, i.e., that form perfect crystals. Crystals are, however, idealizations, and they feature many defects that require special consideration. Any atomic scale devices attached to crystals would similarly require special treatment. This project is aimed at extending kinetic Monte Carlo models so that they can handle such irregularities. The project is funded by the Division of Mathematical Sciences and the Division of Materials Research.