Thermodynamics of nucleation and growth

Abstract

Nucleation and growth are often discussed in terms of kinetics, i.e. the adsorption of atoms from the gas phase or a solution onto a surface, the diffusion of these atoms on that surface, and their attachment to a growing nucleus, island or layer. In recent years, scanning tunneling and atomic force microscopy studies have tremendously improved our understanding of such kinetic processes for a wide range of materials. At relatively low temperatures where diffusion is slow, and where typical deposition rates result in adatom concentrations that far exceed the equilibrium concentration of adatoms on the surface, growth is indeed controlled by irreversible atomic scale kinetics. But at higher temperatures this is not necessarily the case. Indeed, the equilibrium concentration of adatoms can be so high that it is only slightly increased by an external flux. Diffusion can be so fast that spatially separated regions on the surface interact on a time scale that is not slow relative to the growth process. In such cases reversible, collective phenomena are more important than individual atomic events, and thermodynamics is more important than kinetics. In this paper we examine a number of cases related to nucleation and growth on surfaces, where a deep and quantitative insight into the growth process can be obtained by detailed consideration of the thermodynamics involved. It is our hope that this paper will help to bring about a balanced understanding of these phenomena, where kinetics and thermodynamics are two poles on a continuum with an importance that depends on the particulars of each experiment.