Beyond Classical Nucleation Theory: A 2-D Lattice-Gas Automata Model

Abstract

Nucleation is the first step in the formation of a new phase in a thermodynamic system. The Classical Nucleation Theory (CNT) is the traditional theory used to describe this phenomenon. The object of this thesis is to investigate nucleation beyond one of the most significant limitations of the CNT: the assumption that the surface tension of a nucleating cluster of the new phase is independent of the cluster’s size and has the same value that it would have in the bulk of the new phase. In order to accomplish this, we consider a microscopic, two-dimensional Lattice Gas Automata (LGA) model of precipitate nucleation in a supersaturated system, with model input parameters Ess (solid particle-to-solid particle bonding energy), Esw (solid particle-to-water particle bonding energy), η (next-to-nearest neighbour bonding coeffiicent in solid phase), and Cin (initial solute concentration). The LGA method was chosen for its advantages of easy implementation, low memory requirements, and fast computation speed. Analytical results for the system’s concentration and the crystal radius as functions of time are derived and the former is fit to the simulation data in order to determine the system’s equilibrium concentration. A mean first-passage time (MFPT) technique is used to obtain the nucleation rate and critical nucleus size from the simulation data. The nucleation rate and supersaturation are evaluated using a modification to the CNT that incorporates a two-dimensional, radius-dependent surface tension term. The Tolman parameter, δ, which controls the radius-dependence of the surface tension, decreases (increases) as a function of the magnitude of Ess (Esw), at fixed values of η and Esw (Ess). On the other hand, δ increases as η increases while Ess and Esw are held constant. The constant surface tension term of the CNT, Σ0, increases (decreases) with increasing magnitudes of Ess (Esw) fixed values of Esw (Ess), and increases as η is increased. Together, these results indicate an increase in the radius-dependent surface tension, Σ, with respect to increasing magnitude of Ess relative to the magnitude of Esw. Σ0 increases linearly as a function of the change in energy during an attachment or detachment reaction, |ΔE|, however with a slope less than that predicted for a crystal that is uniformly packed at maximum density.