Numerical simulations of the Hebb-Wagner polarization kinetics: (I) weakly acceptor-doped perovskite oxides

Abstract

The Hebb-Wagner polarization method can be used to separate the partial electronic conductivity of mixed ionic and electronic conductors (MIEC) from the partial ionic conductivity by polarizing the material between an ion-blocking and a reversible electrode using an external electric voltage. The electronic conductivity is then calculated from the steady state I-V curve where the partial current of the blocked ionic species is zero. The kinetics of the relaxation process towards the steady state and the corresponding relaxation time were, however, not investigated until now, although they are crucial to the success of the Hebb-Wagner method. In this contribution, the kinetics of the relaxation process during the Hebb-Wagner polarization of a nominally undoped perovskite-type oxide ABO3 (mixed ionic and electronic conductor) is simulated by means of numerical methods and using SrTiO3 as a model system. The simulation results show an unexpected dependence of the relaxation time of the polarization process on the applied voltage. The relaxation time first decreases until a certain voltage is reached, where it remains constant for a few voltage steps, and afterwards it increases again for higher voltage values. We show that these three different relaxation time dependencies correspond to the transition from (i) a prevailing electron hole conduction at high oxygen partial pressures to (ii) a predominant oxygen ion conduction near the p − n transition at intermediate oxygen partial pressures followed by (iii) a predominant electron conduction at low partial pressures. Additionally, the dependence on other parameters and experimental variables, such as surface exchange coefficient at the reversible electrode, acceptor concentration, temperature, and sample length, is investigated, which reveals that a slight change of one of these parameters can change the relaxation time by several orders of magnitude. The obtained insight from the numerical simulation of the electrochemical polarization process is advantageous for the experimental realization of the Hebb-Wagner polarization method, and in particular for its application to nominally undoped perovskite-type oxides, like SrTiO3.