On the Hebb–Wagner polarisation of SrTiO3 doped with redox-active ions

Hebb–Wagner polarisation is analysed for the case that internal redox-reactions complicate the situation. In the general case current–voltage characteristics deviate significantly from the Hebb–Wagner equation. Analytical results are derived and relevant approximations given. Theoretical and experimental current–voltage relations obtained for a 2.15×1018 cm−3 Fe-doped SrTiO3 single crystal at PO2=105 Pa, agree reasonably well, and the results of the partial conductivities match findings obtained from other experiments. In addition, the fact is emphasised that a Hebb–Wagner-type current–voltage relation only requires the fulfilment of a power law for the non-blocked carrier concentrations with respect to the component partial pressure and not a field-free situation. In this case the Faraday constant appearing in the Hebb–Wagner equation has to be replaced by αF, where α is the product of the number of electrons necessary to ionise the gaseous component (n) times the absolute characteristic exponent (|N|). The condition of zero field, i.e. negligible chemical potential gradient with respect to the non-blocked species is identical to |N|=1/n. If |N|=const≠1/n, the internal field is non-zero but is still proportional to the gradient of the component potential.