Article

# On the role of confinement on solidification in pure materials and binary alloys

07/2006;
Source: arXiv

ABSTRACT We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.

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### Keywords

$\delta$ decreases

alloy

alloy model

confinement

dendrite tip velocity

dendrite tips

dendritic growth

dilute binary alloy

finite boundaries

growth state

operating state

phase-field model

process parameters

pure material

pure material solidifying

small $\delta$

vertical domain extent