Modelling of the nucleation-free zone formed during the initial transient of grain formation

The Interdependence Theory of nucleation highlighted the existence of a Nucleation-Free Zone (NFZ) ahead of growing grains formed by the solute diffusion field, creating a region of enhanced solute and hence reducing the free energy driving the next nucleation event. The original NFZ model was an analytical 1D diffusion limited nucleation model. In this work, we compare it to 1, 2 and 3D numerical simulations using the microscale solidification model μMatIC. The simulations solve for the full diffusion controlled dendritic grain growth, but are computationally intensive. The analytical solution is demonstrated to capture many of the pertinent features, and its benefits and limitations are discussed. Validation is achieved by comparing the predicted grain growth and solute diffusion length as a function of the constitutional supercooling profile ahead of the growing grain. The impact of coordinate system and dimensionality on the model of grain nucleation is analyzed and the sensitivity of the NFZ to the grain's interface growth rate is highlighted.