Continuous growth model for interface motion during alloy solidification

Abstract

A model is developed that predicts the steady state velocity of a planar interface and the chemical composition of the growing phase in terms of the interface temperature and the composition of the parent phase at the interface. The model is applied to solidification of a two-component melt. Solute partitioning is treated by a previously developed continuous growth model for solute trapping. The interface velocity is found by generalizing the driving force in a velocity-vs-driving force function used for solidification of one-component melts. Two different ways of generalizing the driving force are used, with and without the inclusion of a “solute drag” term. Predictions are made both with and without solute drag for an ideal solution and for Ag-Cu, a simple eutectic system in which the terminal phases have the same crystal structure. In both cases, a transition from diffusion-controlled to diffusionless solidification and a falling interface temperature occur as the interface velocity increases. In the model without solute drag, significantly less interfacial undercooling is predicted than in the model with solute drag. The relationship to previous theoretical work, especially to the continuum treatments of Baker and Cahn, and to pertinent experiments is discussed.