Theoretical model for heterogeneous nucleation of grains during solidification

Abstract

Grain nucleation during solidification is generally a heterogeneous process. In this work, a model for heterogeneous grain nucleation on substrates is proposed where the size distribution is given by a Weibull type expression. In this model, the nuclei density λ_z is described by a function of the maximum undercooling ΔT _m through an expression of the type λ _z =λ exp[(-b/Δ T _m) Γ (1 + 1/n), where n is a positive integer, λ is the substrate density in the melt, b is the nucleation coefficient (b > 0), and Γ is the second order Euler function. When nucleation occurs on all possible substrates, the grain density N _V after solidification equals λ _z. Hence, measurements of N _V can be employed to disclose the active nucleation process. The proposed model was experimentally corroborated for cast iron solidification after inoculation. In this case, precise determinations of grain densities versus cast iron undercooling were made experimentally. A comparison of the experimental results with the proposed model indicates that the nucleation process is in good agreement with this model for n = 1, with the λ and b terms being time dependent functions. In particular, the outcome suggests that the substrate size distribution is of an exponential nature.