Abstract
Large-scale numerical simulation carried out via high performance computing is proving to be an increasingly useful approach to understand crystal growth systems. However, increasing realism demands new approaches for describing phenomena important at several disparate length scales. Of special importance is the ability to represent three-dimensional and transient continuum transport (flows, heat and mass transfer), phase-change phenomena (thermodynamics and kinetics), and system design (such as furnace heat transfer during melt growth). A brief overview is presented of mathematical models and numerical algorithms employed to include such multi-scale effects. Sample results are presented for Bridgman crystal growth and solution crystal growth systems
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References
Kuppurao, S., Brandon, S., and Derby, J.J. (1995) Modeling the vertical Bridgman growth of cadmium zinc telluride I. Quasi-steady analysis of heat transfer and convectionJ. of Crystal Growth155, 93–102
Kuppurao, S., Brandon, S., and Derby, J.J. (1995) Modeling the vertical Bridgman growth of cadmium zinc telluride II. Transient analysis of zinc segregationJ. of Crystal Growth155, 103–111
Hughes, T. J. R. (1987)The Finite Element MethodPrentice-Hall, Inc
Dahlquist, G., and Björck, A. (1974)Numerical MethodsPrentice-Hall
Sonda, P., Yeckel, A., Daoutidis, P., and Derby, J.J. (2001) Complex dynamics within the vertical Bridgman crystal growth process. In:Proceedings of the IFAC Symposium: DYCOPS 6
Sonda, P., Yeckel, A., Daoutidis, P., and Derby, J.J. (2001) An analysis of time-dependent flows within a vertical Bridgman crystal growth systemChem. Eng. SciSubmitted
Kurz, M., Pusztai, A., and Müller, G. (1998) Development of a new powerfull computer code CrysVUN-H- especially designed for fast simulation of bulk crystal growth processes. Presentation at: ICCG-12, the Twelfth International Conference for Crystal Growth, Jerusalem
Metzger, M., and Müller, G. (2001) Optimal Control of Crystal Growth ProcessesJ. Crystal GrowthAccepted for publication
Salinger, A.G., Xiao, Q., Zhou, Y., and Derby, J.J. (1994) Massively parallel finite element computations of three-dimensional, time-dependent, incompressible flows in materials processing systemsComput. Methods Appl. Mech. Engrg119, 139–156
Zhou, H., and Derby, J.J. (2000)Parallel Implementation of Finite Element Method with MPI: Application to Three-Dimensional Free Surface Stokes Flow. In:Proceedings of the 2000 International Conference on Parallel and Distributed Processing Techniques and ApplicationsLas Vegas, NV
Yeckel, A., Pandy, A., and Derby, J.J. (2001) Representing Realistic Complexity in Numerical Models of Crystal Growth: Coupling of Global Furnace Modeling to Three-Dimensional Flows. In:Proceedings of CHT’01 Advances in Computational Heat TransferCairns, Queensland, Australia
Yeckel, A., Pandy, A., Hainke, M., Müller, G., and Derby, J.J. (2001) A coupled, multi-scale model for continuum transport in crystal growth systemsJ. Crystal GrowthIn preparation
Bordui, P.F., and Jacco, J.G. (1987) Viscosity and density of solutions used in high-temperature solution growth of KTiOPO4 (KTP)J. Crystal Growth82, 351–355
Bordui, P.F., Jacco, J.G., Loiacono, G.M., Stolzenberger, R.A., and Zola, J.J. (1987) Growth of large single crystals of KTiOPO4 (KTP) from high-temperature solution using heat pipe based furnace systemJ. Crystal Growth84, 403–408
Wilcox, W.R. (1983) Influence of convection on the growth of crystals from solutionJ. Crystal Growth65, 133–142
Vartak, B., Kwon, Y.-I., Yeckel, A., and Derby, J.J. (2000) An analysis of flow and mass transfer during the solution growth of potassium titanyl phosphateJ. Crystal Growth210, 704–718
Vartak, B. (2001)Three-Dimensional modeling of solution crystal growth via the finite element methodPhD thesis, University of Minnesota
Hughes, T.J.R., Franca, L.P., and Hulbert, G.M. (1989) A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equationsComput. Methods Appl. Mech. Engrg73, 173–189
Vartak, B., and Derby, J.J. (2001) On stable algorithms and accurate solutions for convection-dominated mass transfer in crystal growth modelingJ. Crystal Growth230, 202–209
Saad, Y., and Schultz, M. (1986) GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systemsSIAM J. Sci. Stat. Comput7, 856–869
Yeckel, A., and Derby, J.J. (1997) Parallel computation of incompressible flows in materials processing: Numerical experiments in diagonal preconditioningParallel Computing23, 1379–1400
Burton, W.K., Cabrera, N., and Frank, F.C. (1951) The growth of crystals and the equilibrium structure of their surfacesPhil. Trans. Roy. Soc. London243, 299–358
Kwon, Y.-I., and Derby, J.J. (2001) Modeling the coupled effects of interfacial and bulk phenomena during solution crystal growthJ. Crystal Growth230, 328–335
Kim, K.M., Witt, A.F., and Gatos, H.C. (1972) Crystal growth from the melt under destabilizing thermal gradientsJ. Electrochem. Soc119, 1218–1226
Turner, J.S. (1973)Buoyancy effects in fluidsCambridge University Press
Kwon, Y.-I., and Derby, J.J. (2001) Step growth dynamics during solution crystal growthJ. Crystal GrowthIn preparation
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Derby, J.J. et al. (2002). High-Performance Computing, Multi-Scale Models for Crystal Growth Systems. In: Breuer, M., Durst, F., Zenger, C. (eds) High Performance Scientific And Engineering Computing. Lecture Notes in Computational Science and Engineering, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55919-8_21
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DOI: https://doi.org/10.1007/978-3-642-55919-8_21
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