The morphological evolution of dendritic microstructures during coarsening
- PDF / 21,852,967 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 54 Downloads / 206 Views
I. INTRODUCTION
A MUSHY zone, a mixture of liquid and dendrites, commonly forms during solidification. It is well known that the overall properties of a solidified metal are determined by the evolution of this dendritic solid-liquid mixture. Thus, understanding the evolution of this structure is critical in quantifying the link between the properties of the solidified ingot and its processing history. Soon after formation, the dendritic morphologies in the mush are altered through a coarsening or Ostwald ripening process. Under isothermal conditions, coarsening occurs since the composition in the liquid at the interface is a function of the mean curvature of the solid-liquid interface as expressed by the Gibbs–Thomson equation for a binary alloy: C ⫽ C ⬁ ⫹ lc H
[1]
where C is the composition in the liquid at the solid-liquid interface, C⬁ is the equilibrium composition of the liquid at a flat interface, lc is the capillary length that is a function of the solid-liquid interfacial energy, and H is the mean curvature of the interface equal to (1/R1 ⫹ 1/R2)/2, with R1 and R2 being the principal radii of curvature. Therefore, interfacial areas with different curvatures will have different liquid compositions, leading to fluxes of solute and the evolution of the morphology of the solid-liquid mixture. During this process, the total interfacial area, and with it the total interfacial energy, decreases. Figure 1(a) shows a freely grown dendrite and Figure 1(b)
R. MENDOZA, Graduate Research Assistant, J. ALKEMPER, Assistant Professor, and P.W. VOORHEES, Professor, are with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208-3108. Contact e-mail: [email protected] This article is based on a presentation given in the symposium “Fundamentals of Solidification” which occurred at the TMS Fall meeting in Indianapolis, Indiana, November 4-8, 2001, under the auspices of the TMS Solidification Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
shows the mean curvature of the interfaces. The curvature variations and the corresponding matrix concentration variations lead to fluxes of solute from high mean curvature regions to low mean curvature regions. The interface moves due to the fluxes and the dendrite coarsens. As the mean interfacial curvature is responsible for these solute fluxes, to fully understand the coarsening process, characterization of the interface curvature as a function of time during coarsening is necessary. In contrast to dendritic solid-liquid mixtures, the coarsening process in a two-phase system with a distribution of spherical particles of various radii, R, is relatively well understood. Since the mean curvature of a sphere is given by H ⫽ 1/R, the concentration at the surface of small particles will be higher than that for large particles; thus, over time, the radii of the small particles will decrease while the radii of large particles will increase. Throughout these changes, the total volume fraction of solid remains nearly constant. The averag
