Modelling of surface exchange reaction, oxygen diffusion, and conductivity relaxation of solid oxides: Application to the van der Pauw method on disk-shaped samples

Abstract

The surface exchange reaction and diffusion of oxygen through oxide ceramic samples as well as the relaxation of the dc conductivity upon an instantaneous change of the oxygen activity in the surrounding atmosphere have been modelled simultaneously by means of the finite element method. The simulations of conductivity relaxation curves are valid for mixed ionic–electronic conducting disk-shaped (cylindrical) samples with predominant electronic conduction, employing a four-point dc method in van der Pauw geometry. Numerical results, based on a three-dimensional finite element model, are compared with the pertinent analytical solutions to the diffusion equations. Interestingly, in the case of diffusion-controlled kinetics the relaxation curves for the total amount of exchanged oxygen (mass transport) deviate remarkably from those for the normalized conductivity (conductivity relaxation). Constraints for the accuracy of the determination of chemical diffusion coefficients and surface exchange coefficients in terms of sample geometry (diameter and thickness) have been elaborated. Basically, identical relaxation curves for mass transport and dc conduction are anticipated, when the transport processes can be assumed to be one-dimensional, which is fulfilled for disk-shaped samples with a ratio of diameter/thickness being higher than 4.