ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Modeling the solidification of ternary alloys in mushy layers

Daniel Anderson
Department of Mathematical Sciences,\\ George Mason University\\

Tuesday, October 15, 2002 15:00-16:00,
Room 145, NIST North (820)
Tuesday, October 15, 2002 13:00-14:00,
Room 4511

Abstract: We describe a model for the solidification of a ternary (three component) alloy cooled from below at a planar boundary. The modeling extends previous theory for binary alloy solidification by including a conservation equation for the additional solute component and coupling the conservation equations for heat and species to equilibrium relations from the ternary phase diagram. We focus on growth conditions under which the solidification path (liquid line of descent) through the ternary phase diagram gives rise to two distinct mushy layers. A primary mushy layer, which corresponds to solidification along a liquidus surface in the ternary phase diagram, forms above a secondary (or cotectic) mushy layer, which corresponds to solidification along a cotectic line in the ternary phase diagram. These two mushy layers are bounded above by a liquid layer and below by a eutectic solid layer. The mathematical model is comprised of a system of partial differential equations in each layer, coupled through interfacial boundary conditions between each layer. We obtain a one-dimensional similarity solution and investigate numerically the role of the control parameters on the growth characteristics. In the special case of zero solute diffusion and zero latent heat an analytical solution can be obtained. We compare our predictions with previous experimental results. Finally, we discuss the potentially rich convective behavior anticipated for other growth conditions.
Contact: A. J. Kearsley

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