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

Abstract

CTS-0121467

Derby, J

U of Minnesota - Twin Cities

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

The 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 utility

for 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 here

are applicable to many other processes, including the hydrothermal and flux growth of crystals,

liquid-phase epitaxy, and industrial crystallization (including protein crystals and other organic

crystals). 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.