On the solute diffusion length in the interdependence model: Dendritic versus non-dendritic interface

The Interdependence model currently uses an analytical expression for a moving planar interface to calculate the solute diffusion length designated as x'dl in the model. Upon nucleation within an alloy melt (i.e. when the solid embryo starts to grow), the interface grows with a spherical front which then breaks down into a dendritic interface. The time required for this breakdown is a subject for separate research. In this paper, we explore the validity of using a planar interface in the early stages of nucleation and growth of metal alloys as used in the Interdependence model. The diffusion field ahead of a planar interface, in theory, has an exponentially changing composition of infinite length. In the Interdependence model, x'dl is assumed to be where this exponentially decreasing composition profile in the liquid ahead of the interface (for k < 1) reduces to within 1% of a quantity proportional to the nominal alloy composition, C0, far from the interface. A numerical solidification model, µMatIC, is used to simulate the growth of a single grain with a dendritic interface in 2D and 3D. The numerical model is capable of generating the solute profile ahead of the growing grain which is used to evaluate the solute diffusion length that can be compared with the results obtained from the planar interface model. The comparisons were made with both 1% and 0.1% cut-off criteria. The results indicate that the 1% assumption being used in the planar front diffusion length calculation is a good approximation for the Interdependence model