The line-tension effect in heterogeneous nucleation

The theory of heterogeneous vapor-solid nucleation is reformulated to include the line-tension contribution to the free energy of formation of a nucleus. The nucleation theory used is based on the Pound description which employs a cap-shaped model of the critical nucleus. The line-tension effect has been shown to increase the contact angle for small crystals above that of the macroscopic contact angle that would obtain between the phases considered. The role of the contact angle in achieving solutions to the nucleation rate equation is considered in detail. It is shown that in the absence of line-tension there exists one and only one physically real contact angle that satisfies the nucleation equation. However, the nucleation rate equation becomes multivalued in respect to its dependence on contact angle if the line-tension effect is considered. The resultant contact angle derived from the nucleation data need not be the macroscopic contact angle. A general method is derived for plotting nucleation data in which three nucleation effects may be readily distinguished: (1) a mechanism involving direct addition of atoms from the vapor to the critical nucleus, (2) a mechanism involving addition of atoms to the critical nucleus via surface diffusion on the substrate, and (3) the occurrence of the line-tension effect in heterogeneous nucleation. These predictions are compared with data available in the literature. The Zeldovich factor which depends very strongly on contact angle for values less than 60° is found to not affect the conclusions.