An Epitaxial Model for Heterogeneous Nucleation on Potent Substrates

In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (Delta T (c)). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h (c)), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h (c) and Delta T (c); h (c) decreases; and Delta T (c) increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.