Modeling the solidification of ternary alloys in mushy layers
Daniel Anderson Department of Mathematical Sciences,\\
George Mason University\\
Tuesday, October 15, 2002 15:0016:00, Room 145, NIST North (820) Gaithersburg Tuesday, October 15, 2002 13:0014:00, Room 4511 Boulder
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 onedimensional 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.
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