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 Al-Cu4wt% 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 micro segregation 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 micro segregation 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. (C) 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.