The duality between chemical potential diagrams and convex hulls

Equilibrium phase diagrams are not well-poised to evaluate material stability under dissolution and growth—for example, corrosion and etching; synthesis and deposition; or solid-solid interfacial reactions. These non-equilibrium situations would be better analyzed by phase diagrams that visualize the tendency for a material to gain or lose chemical species, e.g., with a chemical potential axis. Here, we present a generalized phase diagram framework to mix composition and chemical potential axes, providing a new stability representation that applies to these non-equilibrium situations. Our theoretical framework relies on the geometric duality between convex hulls and half-space intersections. It leads to a computational platform that scales efficiently to describe high-dimensional phase boundaries and multi-phase coexistence regions. We discuss how to evaluate and interpret the axes, widths, stability windows, and driving forces on chemical potential diagrams and, importantly, how to connect these to real-world laboratory conditions. Altogether, these mixed composition- and chemical potential diagrams enable materials scientists to evaluate stability in more diverse chemical environments.