Measurability of the diffusion and surface exchange coefficients using isotope exchange with thin film and traditional samples

The coefficients of diffusion and surface exchange (D and k, respectively) are critically important parameters to determine the ability of a material to perform well within solid state electrochemical systems. For oxide materials operating as components within solid oxide fuel cells or other oxygen ion-based devices, the oxygen self diffusion and surface exchange are often measured using an isotopic tracer. Recently, there has been concern regarding the ability of this technique to measure k with high precision when thick ceramic samples are measured. Here, we show that isotope exchange with thin film samples can lead to an increased range of experimental conditions where k can be precisely determined. Thin samples require a more generalized solution to the diffusion equation than typically used in order to understand the ionic motion within the material. Through numerical analysis of the more complex analytical model that results, we describe conditions when k and/or D can be measured using both thin film and traditional samples. Further, we derive characteristic parameters related to the exchange time (t), material thickness (l), D, and k that can be used to quantify these conditions. Of particular interest is that traditional isotope exchange experimentation can be used to robustly determine k   even in situations where l≫Dk so long as 5·10−6≤k2·tD≤20.

► We model practical isotope exchange experiments using thin film and bulk samples.
► Limits on the practical measurability of D and/or k are quantified.
► As predicted, thin films can ease measurement of k but reduce measurability of D.
► Useful isotope exchange times are given for a range of k, D, and thickness values.
► We report k   is measurable when thickness ≫≫D/k   so long as 5·10−6≤k2·tD≤20