## 2 Materials and Methods
For the \(\upmu\)-CT measurements, the following parameters were set up: Source Voltage (kV) = 50, Source Current (\(\upmu\)A) = 180, Z-spacing = 1, Pixel size (\(\upmu\)m) = 1.500. The distance from the object to the source was 4.95 mm and 150.040 mm from the camera to the source. The exposure time for each frame was 2000 ms. The resulting image pixel size was 0.35 \(\upmu\)m. From the \(\upmu\)-CT runs, we obtained a series of 2D images of slices, which then need to be reconstructed by post-alignment, smoothing, beam-hardening correction, and ring-artifacts removal to a 3D distribution of the local linear attenuation coefficient and stored as a 3D image or a stack of virtual 2D slices. The reconstructed 3D volume can be used to obtain quantitative results (so called morphometric parameters) after using the software package CT-Analyser (Bruker(r)), version 1.15.4.0, delivered with the instrument. Among many parameters that can be extracted from the tomographs [31], time-dependent changes in the porosity and tortuosity of the microstructure are of interest to this study. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Treatment** & **Time** & **Temperature** & **Gas in** & **Fuel** \\  & & **[h]** & [\({}^{\circ}\)C] & **(Anode/Cathode)** & **Utilization** \\ \hline Cell 6 & No (only reduction) & 4 & 850 & H\({}_{2}\)/O\({}_{2}\) & - \\ Cell 7 & Thermal & 100 & 850 & H\({}_{2}\)/O\({}_{2}\) & - \\ Cell 8 & Thermal & 1000 & 850 & H\({}_{2}\)/O\({}_{2}\) & - \\ Cell 9 & Thermal & 100 & 850 & H\({}_{2}\) (humid)/O\({}_{2}\) & - \\ Cell 10 & Thermal & 1000 & 850 & H\({}_{2}\) (humid)/O\({}_{2}\) & - \\ Cell 1 & Electrochemical & 100 & 850 & H\({}_{2}\)/O\({}_{2}\) & 60 \\ Cell 2 & Electrochemical & 1000 & 850 & H\({}_{2}\)/O\({}_{2}\) & 60 \\ Cell 3 & Electrochemical & 100 & 850 & H\({}_{2}\) (humid)/O\({}_{2}\) & 60 \\ Cell 5 & Electrochemical & 1000 & 850 & H\({}_{2}\) (humid)/O\({}_{2}\) & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental parameters of the chemical (thermal) and electrochemical treatment of the cells. Morphometric parameters are calculated by CT-analyzer either in direct 3D, based on a surface-rendered volume model, or in 2D from individual binarized cross section images as we distinguish between different types of analysis for 3D and 2D measurement. Using a histogram and manually set threshold values, we obtained binary sets of the 2D pictures and, from them, the morphometric parameters. It is of utmost importance to choose carefully the threshold values as the porosity depends strongly on them. We used porosity values calculated from single 2D pictures using the Fiji(tm) software Release 1.52d package in order to adjust the starting threshold values. Information on important morphometric parameters can be found in the manuscript of the Bruker ScycScan 2011 nano-tomograph (Bruker, Billerica, MA, USA) [31]. The tortuosity factor \(\tau\) (or simple tortuosity) is defined as the change in transport properties through a porous medium due to non-linearity in the path. It can describe the electrical current, heat transfer, or mass transport interchangeably. As an example, the effective diffusion coefficient is defined as  
\[\mathrm{D}^{\mathrm{eff}}=\mathrm{D}\frac{\varepsilon}{\tau} \tag{1}\]  
with \(\varepsilon\) being the volume fraction of the conductive phase and \(\tau\) the tortuosity factor in this direction. For \(\tau=1\), the diffusion path is direct. As \(\tau\), by definition, must be \(\geq\)1, the diffusion is slower because the path is no more direct [36; 37]. TauFactor(r) is a MatLab(r) application for simply and efficiently calculating the reduction in diffusive transport caused by convolution in the geometry of heterogeneous media based on microstructural image data [38]. Tortuosity factors have been calculated using the same \(\mu\)-CT pictures by using TauFactor(r).