Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-16T09:18:59.325Z Has data issue: false hasContentIssue false
  • English
  • Français

Morphological Instabilities in Time Periodic Crystallization

Published online by Cambridge University Press:  05 May 2011

C. A. Chung ,
W. Z. Chien  and
Y. H. Hsieh
C. A. Chung*
Affiliation:
Department of Mechanical Engineering, National Central University, Jhongli, Taiwan 32001, R.O.C.
W. Z. Chien*
Affiliation:
Department of Mechanical Engineering, National Central University, Jhongli, Taiwan 32001, R.O.C.
Y. H. Hsieh*
Affiliation:
Department of Mechanical Engineering, National Central University, Jhongli, Taiwan 32001, R.O.C.
*
*Associate Professor
**Graduate student
**Graduate student
Get access

Abstract

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.

Keywords

Directional solidificationMorphological instabilitySynchronousSubharmonic.
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 4 , December 2007 , pp. 295 - 302
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Mullins, W. W. and Sekerka, R. F., “Stability of a Planar Interface During Solidification of a Binary Alloy,” J. Appl. Phys., 35, pp. 444–451 (1964).CrossRefGoogle Scholar
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. 393–446 (2000).Google Scholar
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. 435–450 (1980).CrossRefGoogle Scholar
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. 305–325 (1982).Google Scholar
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. 257–263 (2001).CrossRefGoogle Scholar
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. 8–26 (1984).CrossRefGoogle Scholar
7.Or, A. C. and Kelly, R. E., “The Effects of Thermal Modulation Upon the Onset of Marangini-Benard Convection,” J. FluidMech., 456, pp. 161–182 (2002).CrossRefGoogle Scholar
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. 289–298 (2005).CrossRefGoogle Scholar
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. 15–22(1984).CrossRefGoogle Scholar
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. 2587–2599 (1990).CrossRefGoogle Scholar
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. 1278–1282(1991).CrossRefGoogle Scholar
12.Jackson, K. A., Beatty, K. M. and Gudgel, K. A., “An Analytical Model for Nonequilibrium Segregation During Crstallization,” J. Crystal Growth, 271, pp. 481–494 (2004).CrossRefGoogle Scholar