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)(center dot center dot)) and protonic defects (OHO center dot). 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)(center dot center dot) is significantly higher than that of the bulk v(O)(center dot center dot), due to smaller local structural relaxations of the surface defect, leading to a finite surface segregation entropy of 53 J/mol K. OHO center dot, 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)(center dot center dot) compared to the bulk defect thermodynamically at high temperatures, but also affect the relative stability of v(O)(center dot center dot) and OHO center dot 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)(center dot center dot).