A Unified Theoretical Framework for Describing Diffusion

We propose a unified theoretical framework for describing diffusion that naturally incorporates free energy (e.g., Gibbs free energy) and phase diagram information to generate a self-consistent free energy functional. We establish the general conditions for the Cahn-Hilliard free energy/approximation to hold, and recover the Cahn-Hilliard equations rigorously in the regular solution limit. By studying binary interdiffusion processes, we demonstrate novel predictions near a tricritical point and discuss how the Cahn-Hilliard model and the new theory predictions diverge in their predictions of spinodal decomposition and nucleation. Based on this theory, we discuss a new physical interpretation of the Cahn-Hilliard gradient energy term and how the standard interpretation can break down. We further consider the applications of this theory with respect to semiconductor interdiffusion, demonstrating how an interplay between self-diffusivity and chemical potential can amplify the driving force due to gradient contributions, which is relevant in the thermal annealing of nanoscopic semiconductor devices exhibiting sharp compositional interfaces.