Phase field and analytical study of mushy zone solidification in a static thermal gradient: From dendrites to planar front

We present phase field simulation results of the directional solidification of an AlCu4wt% alloy followed by a holding stage during which the mushy zone solidifies in a static thermal gradient. During the holding stage, the initially dendritic morphology solidifies through the TGZM (Temperature Gradient Zone Melting) process, in accordance with recent in-situ X-ray measurements. This yields a planar solid/liquid interface that evolves towards a partial equilibrium where the liquid is homogeneous and the solid still shows a microsegregation pattern. A slow solid state diffusion then drives the subsequent evolution towards the final stationary state where chemical fluxes vanish. We study analytically the microsegregation in the solid, showing that TGZM has a major influence on its development during directional dendritic growth and on its evolution during the holding stage. Especially, we develop an expression for the concentration profile within a secondary dendrite arm during growth. We also develop theoretical arguments to determine the position in the thermal gradient of a transition region that separates the solid at partial equilibrium into two spatial domains. Close to the solid/liquid interface, the microsegregation exhibits a simple pattern resulting from a full remelting of the dendritic solid, while at lower temperatures the pattern is more complex and results from an only partial remelting.

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