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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Bibliographic Details
Published inJournal of crystal growth Vol. 444; pp. 1 - 8
Main Authors Mazuruk, K., Volz, M.P.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.06.2016
Subjects
A1. Solidification
A1. Stability analysis
A2. Bridgman technique
A2. Detached growth
A2. Growth from melt
A2. Microgravity conditions
Capillarity
Crystal growth
Detaching
Dynamic stability
Mathematical analysis
Mathematical models
Perturbation methods
Stability
A1. Stability analysis
A2. Bridgman technique
A2. Microgravity conditions
A1. Solidification
A2. Detached growth
A2. Growth from melt
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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.
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