Role of an acceptor impurity in the proton transfer in proton-conducting oxides

The influence of interaction of protons with defects (acceptor impurities, oxygen vacancies) and with each other on the proton transfer in acceptor-doped proton-conducting oxides $A^{\mathrm{II}}B^{\mathrm{IV}}_{1-x}R_x^{\mathrm{III}}$O$_{3-\delta}$ with the perovskite structure and in oxides $A^{\mathrm{III}}_{2-x}R^{\mathrm{II}}_x$O$_{3-\delta}$ with the structure of a distorted fluorite (bixbyite) has been investigated theoretically. The tracer diffusion coefficient $D^*$ and proton mobility have been calculated by the Monte Carlo method and analytically. It has been shown that the interaction of protons with defects substantially affects the magnitude and behavior of the transfer coefficients. The interaction with acceptor impurities plays the most important role. The proton mobility significantly decreases even at a low dopant concentration ($x\sim$ 1–3 at%). The dependence of the proton conductivity $\sigma$ on the impurity concentration can exhibit maxima. For oxides with the bixbyite structure including nonequivalent cation sites, the distribution of the dopant over these sites has a strong influence on the dependence $\sigma(x)$. The obtained results have been used to interpret the experimental data on the proton conductivity for a number of oxides.