Modeling the Growth of Crystals from Solution: Nonlinear Interactions of Kinetics and Transport

摘要CTS-0121467明尼苏达州双子城的德比，Ju从溶液中模拟晶体的生长：动力学和运输的非线性相互作用晶体材料的生长范围从一次性生产毫克单晶蛋白质药物到年产电子级硅。由于这些广泛的应用，所需的各种晶体，以及单晶材料通常所要求的严格质量，它们的成功生长是现代材料加工中最困难的挑战之一。本文提出的工作是利用数学模型结合数值方法和高性能计算来理解晶体生长过程以及工艺条件对晶体结构和成分的影响的长期努力的一部分。该建议中包含的研究的主要目标是开发和应用建模工具来理解溶液晶体生长过程中输运现象和晶体生长动力学之间的相互作用。本文提出的具体任务包括在连续介质水平上研究流体动力学和传质，继续发展描述邻近小面生长的阶跃生长模型，并以自洽的方式将这两个模型连接起来。拟议的研究将极大地扩展溶液晶体生长系统的建模能力和理解。本文提出的多尺度模型结合了基于台阶生长动力学思想的三维非定常流动和输运计算方法和详细的表面动力学模型。这种方法还没有成功地用于描述现实溶液晶体生长过程。此外，来自非线性动力学的强大思想，即描述体相系统的混沌混合和描述面上台阶生长的非线性动力学，将以新的方式被应用于溶液晶体生长系统的研究。本文所建立的模型所提供的预测能力将对理解溶液晶体生长实验和合理优化生长过程具有重要意义。更重要的是，从这项工作中产生的知识最终将导致将晶体性质与生长条件和影响它们的宏观因素联系起来的能力。总而言之，通过对晶体生长系统的成功建模而获得的理解将导致更好的工艺操作和设计，最终以更高的生产率和更低的成本生产出质量更好的晶体。作为这项工作的另一个成果，对这些系统进行现实建模的计算挑战是巨大的，高性能计算算法的继续发展将是值得注意的。这些发展是需要的，以推动他们使用最先进的科学计算对材料处理系统进行逼真的建模。这项拟议的活动也有更广泛的影响。这里讨论的基本问题也适用于许多其他过程，包括晶体的水热和助熔剂生长、液相外延和工业结晶(包括蛋白质晶体和其他有机晶体)。通过本研究获得的理论工具的发展和对晶体材料生长过程中输运和动力学耦合的深入了解，无疑将对这些领域产生影响。最后，这项活动的重要组成部分是对博士研究生和本科生进行有关晶体生长、数学建模和高性能计算的研究培训。

AbstractCTS-0121467Derby, JU of Minnesota - Twin CitiesModeling the Growth of Crystals from Solution: Nonlinear Interactions of Kinetics and TransportThe growth of crystalline materials ranges from the one-time creation of milligrams of single-crystal protein pharmaceuticals to the annual production of metric tons of electronic-grade silicon. Due to these broad applications, the great variety of crystals needed, and the exacting quality typically required of single-crystal materials, their successful growth ranks among the most difficult challenges of modern materials processing. The work proposed here is part of longer-term effort to employ mathematical modeling coupled with numerical methods and high performance computing to understand crystal growth processes and the influence of processing conditions on crystal structure and composition.The primary goal of the research contained in this proposal is to develop and apply modeling tools to understand the interactions of transport phenomena and crystal growth kinetics in solution crystal growth processes. The specific tasks proposed here include the study of fluid dynamics and mass transfer at the continuum level, the continued development of step-growth model to describe the growth of vicinal facet, and the linking of these two models in self-consistent manner. The proposed research will significantly extend the modeling capabilities and understanding of solution crystal growth systems. The multi-scale model proposed here couples methods for computing three-dimensional, time-dependent flow and transport in the bulk with detailed surface kinetic models based on ideas of step growth dynamics. Such an approach has yet to be successfully implemented for describing realistic solution crystal growth processes. In addition, powerful ideas from nonlinear dynamics, namely chaotic mixing to describe the bulk system and nonlinear dynamics to describe step growth on the facet, will be applied to study solution crystal growth systems in novel manner.The predictive capability provided from the models developed in this work will be of great utilityfor understanding solution crystal growth experiments and for the rational optimization of growth processes. More importantly, knowledge generated from this work will ultimately lead to the ability to link crystal properties with growth conditions and the macroscopic factors which influence them. In general terms, the understanding gained from successful modeling of crystal growth systems will lead to better process operation and design, ultimately yielding better quality crystals at higher production rates and lower costs. As another outcome of this work, the computational challenges of realistically modeling these systems are significant, and the continued development of algorithms for high performance computing will be noteworthy. Such developments are needed to advance them realistic modeling of materials processing systems using state-of-the-art scientific computation.There are also broader impacts of this proposed activity. The fundamental issues addressed hereare applicable to many other processes, including the hydrothermal and flux growth of crystals,liquid-phase epitaxy, and industrial crystallization (including protein crystals and other organiccrystals). The development of the theoretical tools and the increased understanding of the coupling of transport and kinetics during the growth of crystalline materials obtained from this research will undoubtedly impact these areas. Finally, significant component of this activity is the training of Ph.D. graduate students and undergraduate students in research involving crystal growth, mathematical modeling, and high performance computing.