Proton Conduction in Acceptor-Doped BaSnO₃: The Impact of the Interaction between Ionic Defects and Acceptor Impurities

Barium stannate is known as a promising proton-conducting material for clean energy applications. In this work, we elucidate the effect of the interaction of protons and oxygen vacancies with acceptor impurities on proton conduction in acceptor-doped BaSnO₃. The analysis relies on our theoretical developments in hydration and proton hopping in proton-conducting perovskites. The transport theory, based on the master equation and effective medium approximation, provides the analytical description of hopping conduction considering the effects of disorder and changes in the potential energy landscape for protons caused by acceptor impurities. Using the proposed approach, we establish the dependence of the proton mobility and conductivity on the energies of the acceptor-bound states of ionic defects and external conditions. It is shown that the considered interactions can substantially affect the effective activation energies and prefactors of these transport coefficients. We also demonstrate that the correlation between the ionic radius r_A of an acceptor impurity and the energies of its interaction with ionic defects leads to a non-monotonic dependence of the proton conductivity on r_A. The obtained results are in reasonable agreement with the experimental data on the bulk conductivity of BaSnO₃ doped with different acceptors.