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A deterministic nucleation model for equiaxed solidification
Several approaches to model nucleation in dendritic-equiaxed solidification have been made [1-4]. The most recent model by Rappaz and Gandin  relates the grain diameter to dendritic growth velocity and thereby to cooling rate and undercooling. The individual grain grows until it reaches the next nucleation site. Within this work a deterministic delta-like nucleation density is examined. The model describes the propagation of a front of equiaxed grains into the liquid. Due to recalescence the temperature of the front oscillates with the frequency of the nucleation rate, which determines the final grain density. The model is applied to AL-Si-casting. The calculated grain densities are compared with experimental data given in literature. The columnar to equiaxed transition is discussed with reference to its dependencies on growth velocity and temperature gradient in the liquid.