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A phase-field model is developed for simulating quantitatively microstructural pattern formation in solidification of dilute binary alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i). the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii). kinetic effects are negligible. A recently derived antitrapping current [Phys. Rev. Lett. 87, 115701 (2001)]] is used in the solute conservation equation to recover precisely local equilibrium at the interface and to eliminate interface stretching and surface diffusion effects that arise when the solutal diffusivities are unequal in the solid and liquid. Model results are first compared to analytical solutions for one-dimensional steady-state solidification. Two-dimensional thermosolutal dendritic growth simulations with vanishing solutal diffusivity in the solid show that both the microstructural evolution and the solute profile in the solid are accurately modeled by the present approach. Results are then presented that illustrate the utility of the model for simulating dendritic solidification for the large ratios of the liquid thermal to solutal diffusivities (Lewis numbers) typical of alloys.

AbstractÐTwo-dimensional Ostwald ripening of an Al±4% Cu alloy solid/liquid mush in the presence of melt convection, and the in¯uence of ripening on the¯ow, is studied numerically using a recent extension of the phase-®eld method that accounts for¯ow in the liquid phase. Through a parametric study, the ripening kinetics are investigated and compared for cases with and without melt convection. The cases without convection show good agreement with available coarsening theories for a ®nite fraction of solid. In the cases with¯ow the mean radius of the solid particles increases at a faster rate than without convection. The ripening exponent changes from 1/3 to 1/2, while the rate constant depends on the fraction of solid. Comparisons are made with the convective ripening theory of Ratke and Thieringer. Although the present analysis of coarsening is hampered by the limited number of particles in the domain, some qualitative results are presented for the eect of convection on the particle radius distribution. Finally, the present simulations allow for a determination of the permeability of the mush as a function of the fraction of solid, and the dependence of the permeability on the ripening kinetics is shown to be scalable using the speci®c surface area or the mean radius. #

An improved version of a previously developed mesoscopic model is used to simulate transients and thermal interactions during growth of equiaxed dendrites of a pure substance. The model is validated through comparisons with exact, analytical solutions and direct, fully resolved phase-field simulations. The issue of constancy in the selection parameter, s n ; during transients is addressed in some detail. The model is first applied to realistically simulate previously performed microgravity experiments involving the growth of succinonitrile dendrites from a stinger inside a growth chamber. It is shown how the thermal interactions between the seed and the dendrite and between the growth chamber wall and the dendrite cause temporal variations in the dendrite tip velocities. Excellent agreement with microgravity measurements is obtained. A scaling relation is derived that provides the duration of the seed size effect during the initial transient. The model is also used to investigate the transients arising during the growth of two equiaxed dendrites towards each other. A scaling relation for the duration of the transient decay of the tip velocities is derived. Additional study is needed to fully understand cases where equiaxed grains interact early before a fully dendritic structure is established. r

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The MICAST research program focuses on a systematic analysis of the effect of convection on the microstructure evolution in cast Al-alloys. The experiments of the MICAST team are carried out under well defined thermally and magnetically controlled, convective boundary conditions and analyzed using advanced diagnostics and theoretical modeling, involving phase field simulation, micro-modeling and global simulation of heat and mass transport. The MICAST team uses binary, ternary and technical alloys of the Al-Si family. This paper gives an overview on recent experimental results and theoretical modelling of the MICAST team.