First-Principles Calculations for the Energetics of the Hydration Reaction of Acceptor-Doped BaZrO₃

The fundamental factors that influence the hydration of BaZrO₃ (BZO) doped with trivalent cation M³⁺ (Al, Sc, Ga, Y, In, and Lu) for proton conductors were investigated by means of density functional theory calculations which take the configuration of complex defects into account. The creation of oxygen vacancies is favored for Al- and Ga-doped BZOs and leads to small hydration energies with stable proton sites at the nearest neighbor (1NN). Meanwhile, Y-, In-, and Lu-doped BZOs prefer protons at the second nearest neighbor (2NN). The stability of those defects can be formulated in the context of the energies of oxygen vacancy formation and hydration. BZOs with larger dopants gain more hydration energy by structural relaxation with protons located at 2NN. By isolating the associated complex defects, it is possible to increase the negative hydration energy, which in effect improves the degree of hydration of BZOs.