Nucleation and grains density in grey cast iron -: A theoretical model and experimental verification

A model for heterogeneous nucleation on sub-strates (places of the nucleation) which size distribution is of the Weibull type is proposed. The nuclei density lambda(n) is following function of the maximum undercooling DeltaT(m): lambda(n)=lambdaexp[(b/DeltaT(m))Gamma(1+1/n)](n); where: n is a positive integer, lambda - is the substrate density in melt and b is the nucleation 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(n). Consequently, from N-V measurements it is possible to conclude about the nucleation process. The experimental verification of the proposed model is performed for the solidification of cast iron. The grain density N-V was estimated from the density N-A of grain sections by a stereological method. The experiment shows that nucleation follows the model for n = 1, ie.: lambda(n)=lambdaexp[-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 distribution is of the exponential type.