Interacting Defect Equilibria—O Vacancy Formation in Oxides for Thermochemical Hydrogen

First principles calculations of defect formation energies provide the basis for prediction of defect concentrations and equilibria. Previous extensions of the dilute defect model have focused on exchange of electronic charge between defects and the Fermi level, including the resulting attractive forces between oppositely charged defects that lead to the formation of pairs and complexes. In oxides for thermochemical hydrogen production, we encounter high concentrations of oxygen vacancies which are subject to a repulsive interaction. Unlike in case of attractive forces between different defects, this situation does not lend itself to description with a simple law-of-mass-action model. Instead, we formulate an approach that utilizes a statistical enumeration of pair and triplet configurations in supercells of varying size. The distribution of defect energies is then condensed into a temperature-dependent free energy of defect formation capturing both the enthalpies and configurational entropies of the statistical ensemble. In conjunction with ideal-gas chemical potentials for O₂, H₂, and H₂O, this model allows the simulation of the reduction and oxidation processes for solar thermochemical hydrogen production with Sr_1–xCe_xMnO₃.