A microscopic approach to crystallization: Challenging the classical/non-classical dichotomy

We present a fundamental framework for the study of crystallization based on a combination of classical density functional theory and fluctuating hydrodynamics that is free of any assumptions regarding order parameters and that requires no input other than molecular interaction potentials. We use it to study the nucleation of both droplets and crystalline solids from a low-concentration solution of colloidal particles using two different interaction potentials. We find that the nucleation pathways of both droplets and crystals are remarkably similar at the early stages of nucleation until they diverge due to a rapid ordering along the solid pathways in line with the paradigm of "non-classical" crystallization. We compute the unstable modes at the critical clusters and find that despite the non-classical nature of solid nucleation, the size of the nucleating clusters remains the principle order parameter in all cases, supporting a "classical" description of the dynamics of crystallization. We show that nucleation rates can be extracted from our formalism in a systematic way. Our results suggest that in some cases, despite the non-classical nature of the nucleation pathways, classical nucleation theory can give reasonable results for solids but that there are circumstances where it may fail. This contributes a nuanced perspective to recent experimental and simulation work, suggesting that important aspects of crystal nucleation can be described within a classical framework.