Fast Kinetic Monte Carlo Simulation of Crystal Growth and Evolution

Schulze0707443本项目涉及快速动力学蒙特卡罗(KMC)算法的开发及其在模拟纳米和微米晶体生长中的应用。从广义上看，KMC是模拟随机模型的数值任务。虽然该项目的重点主要是晶体生长，但KMC模拟出现在许多背景下，包括微磁学、生态学和化学过程。所开发的算法适用于所有此类模型。然而，在这项工作中，两个新的算法被用来检查凝固过程中的枝晶生长，它们的单事件执行时间与系统大小无关。枝晶生长指的是固体材料形成过程中常见的界面不稳定现象--雪花就是一个常见的例子。这些不稳定性对材料加工有许多实际意义，也具有基础科学意义。研究了在纯材料和复合材料中形成的树枝晶。这个项目涉及到计算机程序的开发，该程序模拟固体材料在长度尺度上的行为，长度尺度如此之小，以至于单个原子都被分解。因此，它对纳米技术领域有直接影响，纳米技术正迅速成为一个具有国家战略利益的领域。所开发的程序是执行这种特定类型的模拟的所有已知方法中最有效的。这些模拟通过使用数百万个随机数来模拟单个原子的随机运动来模拟固相材料的生长和演化，这些随机数本身是由单独的计算机程序产生的。从液体材料中生长出一种特殊类型的固相生长，产生雪花状的晶体结构是一个主要的研究领域，但计算机程序本身的设计方式也使它们在更广泛的问题类别中发挥了作用。学生们都参与了这个项目。

Schulze0707443This project concerns both the development of fast KineticMonte-Carlo (KMC) algorithms and their application to simulatingnano- and micron-scale crystal growth. Viewed broadly, KMC isthe numerical task of simulating stochastic models. While thefocus of the project is primarily on crystal growth, KMCsimulations arise in many contexts, including micro-magnetics,ecology, and chemical processes. The algorithms that aredeveloped are applicable to all such models. In this work,however, two new algorithms with single event execution timesindependent of the system size are used to examine dendriticgrowth during solidification. Dendritic growth refers to acommon interfacial instability that occurs during the formationof solid materials -- snow flakes being a familiar example. These instabilities have a number of practical implications formaterials processing and are also of fundamental scientificinterest. Dendrites that form in both pure and compositematerials are studied. This project concerns the development of computer programs thatsimulate the behavior of solid materials on length scales thatare so small that individual atoms are resolved. It thereforehas direct impact on the area of nanotechnology, which is rapidlyemerging as an area of national strategic interest. The programsthat arew developed are the most efficient of all known ways forperforming this particular type of simulation. These simulationssimulate the growth and evolution of solid phase materials byimitating the random motion of individual atoms using millions ofrandom numbers, which themselves are generated by a separatecomputer program. A particular type of solid phase growth from aliquid material that gives rise to a snow-flake like crystalstructure is a principal area of study, but the computer programsthemselves are designed in a way that also makes them useful in amuch broader class of problems. Students are involved in theproject.