Bifurcation and stability analyses of horizontal Bridgman crystal growth of a low Prandtl number material
Resource
Journal of Crystal Growth 187 (2): 303-313
Journal
Journal of Crystal Growth
Journal Volume
187
Journal Issue
2
Pages
303-313
Date Issued
1998
Date
1998
Author(s)
Lan, C. W.
Chen, M. K.
Liang, M. C.
Abstract
Stability and bifurcation analyses are conducted for horizontal Bridgman crystal growth of a low Prandtl number material. The model considers two-dimensional heat transfer and fluid flow in the melt, the growth interface, and the heat conduction in the crystal. In addition to the construction of bifurcation diagrams, the stability of various solution families is further examined by their leading eigenvalues based on linear stability analysis. Transient calculation is also performed to illustrate the global behavior of the basic states after a disturbance. For the cases with a fixed interface, the results for periodically oscillatory flows are in good agreement with previous reports. With a free interface, the bifurcation diagram is slightly changed due to interface deformation, but its qualitative characteristics remain the same. Nevertheless, the dynamic evolution of the interface due to convection provides useful information for crystal growth. The oscillation amplitude of the interface velocity, which decreases with the increasing heat of fusion, is in the same order of a common growth rate used in practice. © 1998 Elsevier Science B.V. All rights reserved.
Type
journal article
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