THE TRANSITION FROM SHORT-RANGE DIFFUSION-LIMITED TO COLLISION-LIMITED GROWTH IN ALLOY SOLIDIFICATION

Short-range diffusion-limited growth, collision-limited growth, and the transition between the two regimes are explained as natural consequences of a single model for the kinetics of alloy solidification; Analytical expressions are developed for the velocity-undercooling function of a planar interface during dilute alloy solidification, using Turnbull's collision-limited growth model and the Continuous Growth Solute Trapping Model of Aziz and Kaplan both with and without a solute drag effect. The interface mobility, -dv/dT, is shown to be very high (proportional to the speed of sound) if the alloy is sufficiently dilute or if the growth rate is sufficiently rapid for nearly complete solute trapping. The interface mobility is reduced by about three orders of magnitude (becoming proportional to the diffusive speed) at intermediate growth rates where partial solute trapping occurs. Differences in low velocity predictions of the models with and without solute drag are also discussed. Comparison of the results of the analytical expressions to numerical solutions of the non-dilute kinetic model for Al-Be alloys shows that the dilute approximation breaks down at melt compositions on the order of 10 at.%. Similar variations in the interface mobility are shown for the disorder-trapping model of Boettinger and Aziz.