Solute trapping in non-equilibrium solidification: a comparative model study
K. Reuther, S. Hubig, I. Steinbach, M. Rettenmayr.
A sharp interface model and a diffuse interface model describing rapid solidification are compared. Both models are based on the assumption of two independent processes at the solid/liquid interface that together consume the available driving force. These two processes are (1) the interface motion and (2) the redistribution of atoms between the two phases. The sharp interface model is based on an interface thermodynamics model (Hillert and Rettenmayr, [3,4]) and derives its driving force for the phase transformation directly from Gibbs free energy formulations of the liquid and solid phases. In contrast, the Finite Interface Disspiation model (Steinbach et al., ), a diffuse interface model, is based on a grand potential formulation. The models are benchmarked against experimental data on solute trapping in the Al–Sn system (Smith and Aziz, ). The sharp interface model reproduces the experimental data with a single set of kinetic parameters, the diffuse interface model requires a velocity dependent interface permeability. It is concluded that due to the investigated high Péclet number regime the permeability in the diffuse interface model does not only describe the transport processes through the interface, but also the diffusion processes in the layer directly in front of it.
Left: Comparison between the thermodynamic driving forces of the investigated sharp and diffuse interface models. In a solidification setting, like it is shown here, the phase field driving forces (green) will be higher than the sharp interface driving forces (red). Right: k-v-curves predicted by phase field and sharp interface model in a rapid solidification setting of an Al-0.2at.%Sn alloy.