Nucleation and grains density - A theoretical model and experimental verification

The nucleation of grains during solidification is often heterogeneous. A mo del for heterogeneous nucleation on substrates (places of the nucleation) w hich size distribution is of the Weibull type is proposed. The nuclei densi ty lambda (z) is following function of the maximum undercooling DeltaT(m) : lambda (z) = lambda exp[(-b/DeltaT(m))Gamma (1 + 1/n)](n) where: n is a pos itive integer, lambda - is the substrate density in melt and b is the nucle ation coefficient (b > 0) (Gamma - denotes the gamma function). In the case when nucleation occurs on all possible substrates, the grain density N-v, after solidification is equal to lambda (z). Consequently, from N-v measure ments it is possible to conclude about the nucleation process. The experime ntal verification of the proposed model is performed for the solidification of cast iron. For different undercoolings DeltaT(m) (measured by a precise thermal analysis method) the grain structure of the metal is uniform. The grain density N-V was estimated from the density N-A of grain section by a stereological method. The experiment shows that nucleation follows the mode l for n = 1, i.e.,: lambda (z) = lambda exp [-b/DeltaT(m)]. For inoculated cast iron, the empirical lambda and b values are time dependent functions. The performed model analysis also indicates that the substrates size distri bution is of the exponential type.