Duality Between Compositional Phase Diagrams and Chemcial Potential Diagrams

Equilibrium phase diagrams are not well-poised to evaluate materials 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; and leads to a computational platform that scales easily 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 the chemical potential diagram, 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.