Surface Segregation Entropy of Protons and Oxygen Vacancies in BaZrO₃

The perovskite BaZrO₃ has attracted considerable attention in the recent decade due to its high temperature proton conducting properties, and possible application as electrolyte in intermediate temperature fuel cells and electrolyzers. In this contribution, we performed, for the first time, first-principles calculations of the phonon contribution to the defect thermodynamics of the ZrO₂ terminated (001) surface of BaZrO₃. The approach allows us to determine both the segregation enthalpy and entropy of defects, which we apply to two fundamental defects in BaZrO₃; fully charged oxygen vacancies (v^••_O) and protonic defects (OH^•_O). The calculations show that both defects exhibit favorable segregation enthalpies of ¯65 and ¯125 kJ/mol, respectively. Further, the vibrational formation entropy of the surface v^••_O is significantly higher than that of the bulk v^••_O, due to smaller local structural relaxations of the surface defect, leading to a finite surface segregation entropy of 53 J/mol K. OH^•_O, on the other hand, displays nearly identical vibrational spectra at the surface and in the bulk, and the segregation entropy is therefore negligible. Hence, phonons not only stabilize the surface v^••_O compared to the bulk defect thermodynamically at high temperatures, but also affect the relative stability of v^••_O and OH^•_O at the surface. Finally, we apply a simplified space charge model to the (001) surface, and show that neglect of phonons results in strongly underestimated surface concentrations of v^••_O.