The geometry of high-dimensional phase diagrams: I. Generalized Gibbs Phase Rule

Understand

Phase diagrams are essential tools of the materials scientist, showing which phases are at equilibrium under a set of applied thermodynamic conditions.

• Essentially all phase diagrams today are two dimensional, typically constructed with axes of temperature-pressure or temperature-composition.
• For many modern materials, it would be valuable to construct phase diagrams that include additional forms of thermodynamic work--such as elastic, surface, electromagnetic or electrochemical work, etc.--which grows the free energy of materials into higher (>3) dimensions.
• Here, we extend Gibbs' original arguments on phase coexistence to derive a generalized Phase Rule, based in the combinatorial geometry of high-dimensional convex polytopes.