ORALS

When synthesizing a new material, one often starts by consulting the thermodynamic phase diagram. There are four main varieties of phase diagrams today: 1) Temperature–Pressure; 2) Temperature–Composition; 3) Ellingham (T, μO2); and 4) Pourbaix diagrams (pH, Redox potential). Prof. Navrotsky performed seminal calorimetry work showing that surface energies can drive nanoscale crossovers in phase stability when metastable polymorphs have lower surface energies than the bulk equilibrium phases. In addition to surface energies, many forms of thermodynamic work may further be operative during nucleation and growth—such as  elastic, electromagnetic and electrochemical work. Here, I will describe a geometric process to ‘lift’ 2D phase diagrams into higher dimensions, exposing these additional forms of thermodynamic work on the axes. By properly accounting for these hidden thermodynamic variables, we can reconcile many surprising experimental observations of non-equilibrium intermediates during multistep crystallization. I will conclude with a broader vision for the construction and deployment of high-dimensional phase diagrams, which may serve as a powerful new conceptual framework for the design and synthesis of advanced functional materials.