--------------------------------------------------------------------
   COLLOQUIUM OF THE LABORATORY FOR COMPUTER DESIGN OF MATERIALS
                   School of Computational Sciences
                           (CSI 898-Sec 001)
--------------------------------------------------------------------

 Modeling the solidification of ternary alloys in mushy layers

                      Dan Anderson
 Department of Mathematical Sciences,George Mason University

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,
which we shall review, 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 (regions of
dendritic solid and residual liquid). 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.
We compare our predictions with previous experimental results.
Finally, we discuss the potentially rich convective behavior
anticipated for other growth conditions.

		Monday , April 7, 2003
                         4:30 pm
                Room 206, Science & Tech. I

Refreshments will be served at 4:15 PM.
----------------------------------------------------------------------
Find the schedule at http://www.csi.gmu.edu/lcdm/seminar/schedule.html