Planar to cellular bifurcations during directional solidification.
Item
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Title
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Planar to cellular bifurcations during directional solidification.
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Identifier
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AAI9530897
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identifier
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9530897
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Creator
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Liu, Dongning.
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Contributor
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Adviser: Herman Z. Cummins
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Date
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1995
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Condensed Matter | Engineering, Materials Science | Engineering, Metallurgy
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Abstract
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Equilibrium phase transitions with primary and secondary control parameters may exhibit a line of first order transitions which passes through a tricritical point and becomes a line of second-order transitions. The Mullins-Sekerka planar-cellular instability in directional solidification should be subcritical when the partition coefficient k {dollar}{dollar} 0.45 if latent heat is ignored. However, Merchant and Davis (Phys. Rev. Lett. 63, 573 (1989)) predicted that as the solute concentration is reduced, the increasingly important thermal diffusion field could lead to a crossover from a subcritical to a supercritical bifurcation, producing a dynamical analogue of the tricritical point. We have designed and assembled a precision directional solidification apparatus integrated with an externally controlled laser perturbation mechanism in order to test this prediction. Directional solidification experiments were performed on a series of succinonitrile samples containing different concentrations of Coumarin 152. We have found evidence for the predicted crossover at a Coumarin concentration {dollar}C\sb{lcub}t{rcub}\sim{dollar} 0.1 wt%. In the subcritical regime, the velocity {dollar}V\sbsp{lcub}C{rcub}{lcub}+{rcub}{dollar} at which the initial planar interface first becomes unstable with increasing V and the velocity {dollar}V\sbsp{lcub}C{rcub}{lcub}-{rcub}{dollar} at which the cellular pattern reverts to planar with decreasing V determine the velocity hysteresis region {dollar}\Delta{dollar}V = ({dollar}V\sbsp{lcub}C{rcub}{lcub}+{rcub} -V\sbsp{lcub}C{rcub}{lcub}-{rcub}{dollar}). We find that {dollar}\Delta{dollar}V decreases with decreasing c, and {dollar}\Delta{dollar}V {dollar}\sim{dollar} 0 for {dollar}c\leq {dollar}0.1 wt%. A laser pulse with controlled power and duration was applied to the metastable ({dollar}V\sbsp{lcub}C{rcub}{lcub}+{rcub} < V < V\sbsp{lcub}C{rcub}{lcub}-{rcub}{dollar}) planar interface to provide a local heat perturbation. Depending on the pulling speed, i.e. V close to {dollar}V\sbsp{lcub}C{rcub}{lcub}+{rcub}{dollar} or {dollar}V\sbsp{lcub}C{rcub}{lcub}-{rcub}{dollar}, and also on the magnitude of the perturbation, the metastable planar interface either responds stably and relaxes back to a planar interface at different rates, or else the perturbation grows and the planar interface eventually evolves into a cellular pattern.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
