In the late 19th century, J. Willard Gibbs and his contemporaries forever transformed classical materials thermodynamics with a purely geometric description of free energy space, which provides us with many of the foundational tenets of modern materials thermo in use today, such as Gibbs’ Phase Rule, the Clausius-Clapeyron relation, etc. However, when Gibbs was writing his seminal “On the Equilibrium of Heterogeneous Substances”, life as a material thermodynamicist was much easier— natural variables other than temperature, pressure, and concentration were uncommon, and the study of “simple” systems describable by 3D free energy spaces held more than enough mystery to get them through the next hundred years.

Material reality today, however, is much more complex. New modes of thermodynamic work - surface work, epitaxial strain, electromagnetic work, electrochemical work, and many more — dominate phase selection and stability in many exciting modern materials, and as such, the simple, elegant 3D free energy spaces that’ve dominated the last century and half of materials thermodynamics are becoming increasingly insufficient in describing advanced modern materials.

In our lab, we are partnering with collaborators at the University of Michigan, University of Washington, and NASA to bring classical material thermodynamics into the nth dimension, transforming the mathematical and phenomenological foundation of geometric thermo in order to grapple with complex modern material reality.

This includes building new mathematical approaches to analyze n-dimensional free energy spaces using the tenets of modern convex geometry; re-deriving the integral analytical tools of material thermo for n-dimensional use; developing the phenomenology of phase boundaries and transitions in n-dimensions; and ultimately constructing n-dimensional phase diagrams that can drive classical materials thermo into the future.