Representative Volumes in Highly Heterogeneous Fuel Cell Materials
Authors: Epting William K , Hsu Tim , Gerdes Kirk , Ohodnicki Paul R , Abernathy Harry , Litster Shawn , Salvador Paul A 
Published: February 2020

Solid oxide fuel cells (SOFCs) are a promising technology for clean, efficient electrochemical energy conversion, particularly for stationary applications. Performance degradation over their lifetime, however, still presents a hindrance to widespread SOFC commercialization. Understanding this degradation, which is tied in part to reaction rates and overpotentials associated with the electrodes, is therefore a crucial research direction. Many studies have used various tomographic techniques on research-grade SOFC electrodes to examine the porous, composite electrodes’ microstructures, which bear a strong relationship to their performance. This approach has yielded much insight. However, because commercially available, mass-produced SOFC electrodes must meet cost targets, they tend to exhibit more heterogeneous microstructures than research-grade cells (1). The required magnitude of measured volume in these more heterogeneous cells must be quantified.
One particular work by Harris & Chiu (2) provided a good theoretical framework for estimating the representative volume element (RVE) for such materials using the characteristic particle size as an input for the estimation. The results of that work appear to hold true for a wide range of tomographic SOFC studies in the literature, including those authors’ own application to their experimental data (3). However, we have found that for mass-produced cells that exhibit significant heterogeneity over 5-10 µm, larger RVEs are required, in contrast to the more homogeneous academically fabricated cells found in most of the literature. Specifically, the mass-produced cells’ characteristic particle sizes are in the range of 0.5-1 µm (similar to academically fabricated cells), yet we find that the RVEs for characterizing mass-produced cells are significantly larger than expected, reaching into the 203 - 303 µm3 range – see, for example, an excerpt of our results in Figure 1, which illustrates the change in triple phase boundary density variability as the size of the studied region increases.
In this presentation, we will discuss our experimental results and analysis of the heterogeneity of commercial, mass-produced SOFC electrodes using microscale and nanoscale X-ray computed tomography. We will then discuss an updated theoretical framework for determining the RVE using limited knowledge of the electrode, similar to that of Harris & Chiu (2), but modified to account for the poorer mixing and greater heterogeneity that we observe in mass-produced cells.
Figure 1: Variability (in terms of 90% confidence interval according to Student’s t-test, expressed as a fraction of the overall mean) in triple phase boundary density shown as a function of the side-length of cubic regions of interest, for the cathode and anode active layers of a commercial SOFC, as determined using analysis of 3D nanoscale X-ray CT imagery (inset).

References

1. S. J. Dillon, L. Helmick, H. M. Miller, L. Wilson, R. Gemman, R. V. Petrova, K. Barmak, G. S. Rohrer, and P. a. Salvador, J. Am. Ceram. Soc., 94(11), 4045 (2011).
2. W. M. Harris and W. K. S. Chiu, J. Power Sources, 282, 552 (2015).
3. W. M. Harris and W. K. S. Chiu, J. Power Sources, 282 , 622 (2015).

Figure 1