The Interdependence model of grain nucleation: A numerical analysis of the Nucleation-Free Zone

Predictions by a 1-D analytical model and a 3-D numerical model of the formation of the Nucleation-Free Zone (NFZ) surrounding each growing grain during the initial transient of equiaxed solidification are compared. The extent of NFZ formation was studied under different solidification conditions in 1-D, 2-D and 3-D for both single-grain and multiple-grain growth scenarios with different geometric grain arrangements. The previously hypothesised NFZ concept presented by the analytic Interdependence model has been clearly demonstrated to exist for a range of solidification conditions. While there is good agreement between the 1-D numerical and analytic models, the 2-D and 3-D simulations of NFZ formation demonstrate that for some conditions the analytic model should be rederived in spherical coordinates. Further, the strong influence of the overlap of the diffusion fields between neighbouring grains was clearly demonstrated, revealing that the effect of competition between the rate of solute accumulation and cooling rate determines whether or not additional nucleation events are able to occur. It is also shown that a judicious choice of the growth rate term is essential for the analytical model to provide an accurate prediction of NFZ. Application of the computationally intensive 3-D simulations has allowed an improved solution to be derived that can be run at very low computational cost.