Nucleation Work on Curved Substrates

Abstract

Nucleation is the initial phase transition process when nuclei of a new phase form within an undercooled or supersaturated parent phase under appropriate conditions. Nucleation most often occurs through a heterogeneous process on active centers on which the probability of nucleus formation is high. In general, the origin of active centers may be difficult to distinguish. In this work, we consider the formation of crystalline nuclei in a melt on various curved substrates. Knowledge of excess free energy plays a key role in understanding the process of formation of clusters and it is not easy to express this quantity in a considered system. Excess free energy is often approximated within the framework of capillarity approximation based on interfacial energy, which depends on interatomic interactions near the interface, as well as the misfit between melts, surface roughness, temperature, composition, etc., near the phase interface. The formation of nuclei requires overcoming a certain energy (nucleation) barrier that is a consequence of balancing the volume and the interfacial free energy. Knowing the nucleation barrier (W) is crucial for understanding this process, as nuclei predetermine the physical properties of a newly formed phase. W is typically expressed as a function of the nucleus radius; however, in nucleation kinetics, one needs to determine (W) as a function of the number of molecules forming the nucleus. We analyze nucleation work on various substrates (flat, convex, and concave) for crystallization from an aluminum melt to show that the formation of nuclei is the most probable on concave substrates. An analytical expression for W can be easily applied to other systems under consideration. We show that under the same conditions, the critical radius of nuclei is identical for various substrate, in contrast with the critical number of molecules forming a nucleus.