We are applying large-scale numerical simulation and high-performance computing to better understand continuum transport and reaction in the processing of advanced materials. These exciting tools provide a means of obtaining the fundamental physical insight necessary to enable advances in many modern materials processing operations, and the sphere of accessible problems continues to enlarge with the rapid evolution of computers and numerical methods. Research areas include analyses of crystal growth processes, morphological instabilities, microstructure evolution, and colloidal crystallization (with Prof. David Norris and others). The development of efficient numerical methods are performed in support of these studies.
Our research in crystal growth is directed at understanding the complex, inherently nonlinear phenomena that control the processes used to create these materials. This understanding is motivated by needs of current and future electronic and optical systems, which require single-crystal substrates with precisely controlled properties. We are particularly interested in describing heat transfer in high-temperature melt growth systems, internal radiant heat transfer in semitransparent crystals, three-dimensional time-dependent flows in crystal growth systems, mass transfer in melt and solution growth, faceting phenomena, and morphological stability of crystal interfaces. Recent work has concentrated on the growth and properties of radiation detector crystals, such as cadmium zinc telluride, step dynamics during solution growth, and growth processes for crystalline silicon in photovoltaic devices.
In conjunction with research in the areas described above, we seek to advance state-of-the-art numerical methods and analysis. These efforts primarily involve finite element methods for solutions to continuum equations for incompressible fluid dynamics, heat and mass transfer, radiation heat transfer, and free and moving boundary problems. Methods are developed for modern parallel architectures.
- Best lecturer, 4th International Workshop on Crystal Growth Technology (IWCGT-4), Beatenberg, Switzerland, 2008
- Distinguished McKnight University Professorship, University of Minnesota, 2008-Present
- Humboldt Research Award for Senior US Scientists, Alexander von Humboldt Foundation, 2000
- Young Author Award, American Association for Crystal Growth, 1993
- McKnight-Land Grant Professorship, University of Minnesota, 1991-1993
- Presidential Young Investigator Award, National Science Foundation, 1990-1995
- Student Speaker Award, New England Association for Crystal Growth, 1983
- National Science Foundation Graduate Fellowship, 1981-1984
- A. Yeckel and J.J. Derby, "Computer modelling of bulk crystal growth" in: Bulk Crystal Growth of Electronic, Optical, and Optoelectronic Materials, Ed. P. Capper, John Wiley & Sons, West Sussex, UK, pp. 73-119 (2005).
- J.J. Derby, "Crystal Growth: Crystal growth, bulk (Theory and Models)," in: Encyclopedia of Condensed Matter Physics, Eds. F. Bassani, J. Liedl, and P. Wyder, Academic Press, pp. 274-282 (2005).
- P. Sonda, A. Yeckel, P. Daoutidis, and J.J. Derby, "Hopf bifurcation and solution multiplicity in a model for destabilized Bridgman crystal growth," Chem. Eng. Sci. 60, 1323-1336 (2005).
- A. Pandy, A. Yeckel, M. Reed, C. Szeles, M. Hainke, G. Muller, and J.J. Derby, "Analysis of the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace via a self-consistent, multi-scale numerical model," J. Crystal Growth 276, 133-147 (2005).
- B. Vartak, A. Yeckel, and J.J. Derby, "Time-dependent, three-dimensional flow and mass transport during solution growth of potassium titanyl phosphate," J. Crystal Growth 281, 391-406 (2005).
- D. Gasperino, A. Yeckel, B.K. Olmstead, M.D. Ward, and J.J. Derby, "Mass Transfer Limitations at Crystallizing Interfaces in an Atomic Force Microscopy Fluid Cell: A Finite Element Analysis," Langmuir 22(15), 6578-6586 (2006).
- J.J. Derby, Y.-I. Kwon, A. Pandy, P. Sonda, A. Yeckel, T. Jung, and G. Muller, "Developing Quantitative, Multi-Scale Models For Microgravity Crystal Growth," Ann. N.Y. Acad. Sci. 1077, 124-145 (2006).
- D. Gasperino, L. Meng, D.J. Norris, and J.J. Derby, "The role of fluid flow and convective steering during the assembly of colloidal crystals" J. Crystal Growth 310, 131-139 (2008).
- D. Gasperino, M. Bliss, K. Jones, K. Lynn, and J.J. Derby, "On crucible effects during the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace," J. Crystal Growth 311, 2327- 2335 (2009).
- Y.I. Kwon, B. Dai, and J.J. Derby, "Assessing the dynamics of liquid-phase solution growth via step growth models: From BCF to FEM," Progress in Crystal Growth and Characterization of Materials 53, 167-206 (2007).
- A. Yeckel, L. Lun, and J.J. Derby, "An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications," J. Comp. Phys. 228, 8566-8588 (2009).
- J.J. Derby, "Modeling and bulk crystal growth processes: What is to be learned?" in: Selected Topics on Crystal Growth: 14th International Summer School on Crystal Growth, Eds. M. Wang, K. Tsukamoto, and D. Wu, AIP Conference Proceedings 1270, Melville, New York, 221-246 (2010).
- L. Lun, A. Yeckel, and J.J. Derby, "A Schur complement formulation for solving free-boundary, Stefan problems in solidification," J. Comp. Phys. 229, 7942-7955 (2010).
- A. Yeckel and J.J. Derby, "Existence, stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity," J. Crystal Growth 314, 310-323 (2011).
- N. Zhang, A. Yeckel, A. Burger, Y. Cui, K.G. Lynn, and J.J. Derby, "Anomalous segregation during electrodynamic gradient freeze growth of cadmium zinc telluride," J. Crystal Growth 325, 10-19 (2011).
- G. Samanta, A. Yeckel, P. Daggolu, H. Fang, E.D. Bourret-Courchesne, and J.J. Derby, "Analysis of limits for sapphire growth in a micro-pulling-down system," J. Crystal Growth 335, 148-159 (2011).