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Morphological Instabilities in Time Periodic Crystallization

  • C. A. Chung (a1), W. Z. Chien (a1) and Y. H. Hsieh (a1)


A linear stability analysis is performed on the interface that forms during directional solidification of a dilute binary alloy in the presence of time-periodic growth rates. The basic state, in which the flat crystal-melt interface advances at a steady rate with an oscillation superimposed, is solved analytically by expanding the governing equations in terms of the assumed-small amplitude of modulation. We find that there is a frequency window of stabilization, in which the Mullins-Sekerka instability can be stabilized synchronously. Outside of the window, large input frequencies may destabilize the Mullins-Sekerka mode. The subharmonic mode, which occurs with small wave numbers, is stabilized with increasing the frequency. As for the modulation amplitude, larger amplitude tends to reduce the synchronous mode while enhance the subharmonic mode.


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*Associate Professor
**Graduate student


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1.Mullins, W. W. and Sekerka, R. F., “Stability of a Planar Interface During Solidification of a Binary Alloy,” J. Appl. Phys., 35, pp. 444451 (1964).
2.Worster, M. G., “Solidification of Fluids,” Perspectives in Fluid Dynamics: A Collective Introduction to Current Research Batchelor, H. K., Moffatt, H. K. and Worster, M. G., eds., Cambridge University Press, pp. 393446 (2000).
3.Wilson, L. O., “The Effect of Fluctuating Growth Rates on Segregation in Crystals Growth from the Melt I. No Backmelting,” J. Crystal Growth, 48, pp. 435450 (1980).
4.Wheeler, A. A., “The Czochralski Crystal Growth System with a Periodic Crystal Growth Rate and no Back-Melting,” Proc. Roy. Soc., London, A379, pp. 305325 (1982).
5.Hu, C-C., Chen, J-C. and Huang, C-H., “Effect of Pulling Rates on the Quality of YIG Single Crystal Fibers,” J. Crystal Growth, 225, pp. 257263 (2001).
6.Wheeler, A. A., “The Effect of a Periodic Growth Rate on the Morphological Stability of a Freezing Binary Alloy, J. Crystal Growth, 67 pp. 826 (1984).
7.Or, A. C. and Kelly, R. E., “The Effects of Thermal Modulation Upon the Onset of Marangini-Benard Convection,” J. FluidMech., 456, pp. 161182 (2002).
8.Chung, C. A., Ho, K. H. and Chou, P. S., “Morphological Stability during Directional Solidification into an Oscillatory Molten Zone,” J. Crystal Growth, 276, pp. 289298 (2005).
9.Coriell, S. R., McFadden, G. B., Boisvert, R. F. and Sekerka, R. F., “Effect of a Forced Couette Flow on Coupled Convective and Morphological Instabilities during Unidirectional Solidification,” J. Cryst. Growth, 69, pp. 1522(1984).
10.Gremaud, M., Carrard, M. and Kurz, W.. “The Microstructure of Rapidly Solidified Al-Fe Alloys subject to Laser Surface-Treatment,” Acta Met. Mater., 38, pp. 25872599 (1990).
11.Zimmermann, M., Carrard, M., Gremaud, M. and Kurz, W., “Characterization of the Banded Structure in Rapid Solidified Al-Cu Alloys,” Mater. Sci. Eng., 134, pp. 12781282(1991).
12.Jackson, K. A., Beatty, K. M. and Gudgel, K. A., “An Analytical Model for Nonequilibrium Segregation During Crstallization,” J. Crystal Growth, 271, pp. 481494 (2004).



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