Generalized Gibbs' Phase Rule Institutional Repository Document uri icon


  • Gibbs' Phase Rule describes the nature of phase boundaries on phase diagrams, and is a foundational principle in materials thermodynamics. In Gibbs' original derivation, he stipulates that the Phase Rule applies only to 'simple systems'--defined to be homogeneous, isotropic, uncharged, and large enough that surface effects can be neglected; and not acted upon by electric, magnetic or gravitational fields. Modern functional materials; spanning nanomaterials, multiferrorics, materials for energy storage and conversion, colloidal crystals, etc.; are decidedly non-simple, leveraging various additional forms of thermodynamic work to achieve their functionality. 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. The generalized Phase Rule offers a conceptual and mathematical framework to interpret equilibrium and phase coexistence in advanced modern materials.

author list (cited authors)

  • Sun, W., & Powell-Palm, M. J.

citation count

  • 1

complete list of authors

  • Sun, Wenhao||Powell-Palm, Matthew J

Book Title

  • arXiv

publication date

  • May 2021