Engineering Relative Stability in Four Dimensions with The Generalized Clausius-Clapeyron Relation

Sequential learning algorithms based on Bayesian optimization are routinely being deployed for materials stability optimization in high-parameter spaces. We anticipate these optimization methods would perform better if they were built upon stronger priors, for example, as derived from the fundamental thermodynamics underlying the equilibrium behavior of materials. Here, we present a thermodynamics-based technique to optimize the relative stability of a materials in high-dimensional thermodynamic space, based on a new derivation of a generalized high-dimensional Clausius Clapeyron relation. Using this thermodynamic infrastructure, we design several pathways to enhance the relative acid stability of Mn-oxides versus its dissolved states for potential electrochemical catalyst application. We construct a 4-D Pourbaix diagram with <i>p</i>H, redox potential <i>E</i>, particle radius 1/<i>R</i> and a chemical potential <i>μ</i>_K as axis. By exploring the gradients of the high-dimensional phase boundaries, we derive first-principles insights that nano-sizing (1/R) and certain doping ions (<i>μ</i>_K) can stabilize some metastable Mn-oxides polymorphs,where 1/R decreases acid stability and <i>μ</i>_K increases it. Our high-dimensional thermodynamic framework is a general method to engineer relative stability in parameter spaces that leverage multiple forms of thermodynamic work.