Thermodynamic analysis of heterogeneous nucleation on refractory nanoparticles

The present study investigates the influence of size effects and wettability on the process of heterogeneous nucleation of crystalline phase on refractory nanoparticles of different shapes. This work is based on the classical theory of nucleation. Formulas for the nucleation energy, incorporating linear tension as well as the influence of the nucleation surface curvature on surface tension, were employed for two distinct scenarios: the nucleation being formed on a convex (spherical) nanosubstrate or on a flat nanosubstrate. From the equilibrium condition of a spherical-cap nucleus on a convex surface, an equation defining the wetting contact angle by the standard angle of a large nucleus on a flat surface was obtained, and from the condition of the extremum of the nucleus energy, an equation for its critical radius was obtained. The method of successive approximations by the small parameter was utilized to solve these equations. A similar approach was adopted for the case of spherical-cap nucleation on a flat surface. This approach enabled the derivation of explicit expressions for the wetting function on both convex and flat substrates. The analysis of the obtained dependencies demonstrated that incorporating the linear tension and the Tolman effect resulted in a reduction of the energy required for heterogeneous nucleation. This effect is most significant on well-wetted convex nanosubstrates.