Analysis of the self-consistency of nucleation in the diffuse interface limit of binary alloy phase field models

This paper examines the process of nucleation in phase field (PF) models, with the aim of elucidating how the use of diffuse interfaces often employed for quantitative modelling of solidification affects nucleation rates and distribution statistics in relation to the predictions of classical nucleation theory. Nucleation is simulated through the use of noise in a quantitative binary alloy PF model using different interface widths. Our results reveal that the rate of nucleation in the PF model is found to be strongly dependent on the scale of the interface width and the numerical discretization, but that careful control of these quantities offers the possibility of a consistent interpretation of nucleation rate. The paper ends by assessing some of the practical merits of seeded versus noise-induced nucleation in PF modelling in the diffuse-interface limit, while also emphasizing how nucleation in this limit is fundamentally flawed from a quantitative perspective.