Dynamic stability of detached solidification
A dynamic stability analysis model is developed for meniscus-defined crystal growth processes. The Young–Laplace equation is used to analyze the response of a growing crystal to perturbations to its radius and a thermal transport model is used to analyze the effect of perturbations on the evolution...
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Published in | Journal of crystal growth Vol. 444; pp. 1 - 8 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
15.06.2016
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Subjects | |
Online Access | Get full text |
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Summary: | A dynamic stability analysis model is developed for meniscus-defined crystal growth processes. The Young–Laplace equation is used to analyze the response of a growing crystal to perturbations to its radius and a thermal transport model is used to analyze the effect of perturbations on the evolution of the crystal-melt interface. A linearized differential equation is used to analyze radius perturbations but a linear integro-differential equation is required for the height perturbations. The stability model is applied to detached solidification under zero-gravity and terrestrial conditions. A numerical analysis is supplemented with an approximate analytical analysis, valid in the limit of small Bond numbers. For terrestrial conditions, a singularity is found to exist in the capillary stability coefficients where, at a critical value of the pressure differential across the meniscus, there is a transition from stability to instability. For the zero-gravity condition, exact formulas for the capillary stability coefficients are derived.
•A dynamic stability analysis model is developed for meniscus-defined crystal growth.•The dynamic stability of detached solidification is analyzed.•Stability coefficients are determined for capillarity and heat transfer.•Dynamic stability is determined for terrestrial and microgravity conditions. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0022-0248 1873-5002 |
DOI: | 10.1016/j.jcrysgro.2016.03.032 |