Explicit Solution to Extract Self-Diffusion and Surface Exchange Coefficients from Isotope Back-Exchange Experiments

Multistep ¹⁸ O isotope exchange procedures and subsequent analytical techniques can be used to elucidate the effect of ambient gas atmospheres on the transport properties of oxide ion-conducting materials utilized in high-temperature solid oxide devices for electrochemical energy conversion. In this contribution, we provide an explicit solution to the one-dimensional transient diffusion equation to estimate oxygen self-diffusion and surface exchange coefficients of oxide ion conducting materials exposed to multistep ¹⁸ O exchange procedures. Although an analytical solution exists for representing the diffusion profiles of labeled species obtained from a single-step isotope exchange procedure, it is not applicable to the diffusion profiles resulted from consecutive procedures with dynamically altered initial and surface boundary conditions. Hence, a new analytical solution is found for the diffusion problem representing the isotope back-exchange procedure in a semi-infinite spatial domain. The explicit solution is then used to determine the self-diffusion and surface exchange coefficients as fitting parameters for tracer gas diffusion profiles obtained from multistep isotope exchange experiments conducted in different oxidizing gas atmospheres. It is demonstrated that the explicit solution provides a great flexibility in analyzing the effects of oxidizing gas atmospheres on transport properties of oxide ion conducting materials.