Multi-scale characterization of ceramic inert-substrate-supported and co-sintered solid oxide fuel cells

The investigated cell sample (cf. Fig. 1 or [17, 29‐32]) consists of (i) a porous silicate support (layer thickness 1250 μm) composed of Zn, Mg and Si, (ii) a cathode current collector layer (CCL, layer thickness after sintering 70 μm) composed of (La_0.8Sr_0.2)_0.98MnO_3-δ (LSM), (iii) a cathode functional layer (CFL, layer thickness 16 μm) composed of LSM/8 mol.% Y₂O₃-doped ZrO₂ (LSM/8YSZ, ratio 50:50 wt.%), (iv) a dense electrolyte (8YSZ, layer thickness 15 μm) and (v) a Ni/8YSZ anode (layer thickness 15 μm). All functional layers were fabricated by screen printing and then laminated onto the substrate. The whole cell was co-fired at a temperature between 1100 °C and 1300 °C.

Due to the challenges associated with co-sintering, the composition of the screen printed inks was selected and adapted in order to tune the sintering behavior of all layers and to obtain a crack-free cell after sintering. In this context, characteristics of raw powders, paste composition and paste processing were chosen and adapted.

To avoid anode delamination, sintering and mechanical properties were adjusted by adapting raw material powders, pore forming agents as well as paste composition and paste processing.

In addition, A-site sub-stoichiometric LSM was chosen in order to avoid the formation of lanthanum zirconate during the thermal process. The implementation of alternative cathode materials was also investigated in a separate study [33, 34].

For testing, the cell was heated to 900 °C (sealing step), followed by a 4-h reduction procedure at 850 °C. The investigated sample was then operated for a few hours in a test bench at T = 750 °C with air supply at the cathode side (2 NL min⁻¹ synthetic air) and hydrogen supply at the anode side (0.7 NL min⁻¹)—with a fuel utilization of less than 5%. Cell functionality was recently tested over 1200 h operation time [29] with a constant current load of 150 mA cm⁻². The load was interrupted every 100 h for impedance measurements (1 MHz to 30 mHz with a voltage excitation signal of 50 mV and no bias). A 2000-h functionality test was also successfully performed (not published yet).

After anode reduction and operation for a few hours at T = 750 °C, the investigated cell is cooled to room temperature under reducing conditions. Then, the entire cell is broken into pieces. One of those, subsequently referred to as Sample 1A, was used without any further treatment for OM and SEM analysis for qualitatively investigating cell functional layers and support. Another piece of the same cell as Sample 1A, referred to as Sample 1B, was vacuum-infiltrated with a two-component epoxy resin (EpoFix, Struers GmbH, Willich, Germany) to provide better mechanical stability and enhance material contrast between the phases [20, 35]. For this purpose, a piece of the sample was placed in the vacuum chamber. After evacuation, the resin is injected into the chamber in a dropwise manner. This slowly encloses and covers the sample. After waiting a few minutes until remaining bubbles have escaped from the sample-resin structure, the chamber is flooded. After hardening, isolated, smaller volumes of the infiltrated sample (Sample 1B) were then prepared for further investigation with μ-CT, FIB/SEM and STEM.

A Keyence VHX-6000 digital microscope (Keyence Deutschland GmbH, Neu-Isenburg, Germany) is used for optical microscopy (light source: LED, 5700 K). The microscope is equipped with an objective lens (VH-Z500) that allows magnifications between 500× and 5000×. Virtual stitching of adjacent areas yields large fields-of-view at high resolution. A high depth of focus is achieved by a focus stacking algorithm implemented in the Keyence software.

A Bruker SkyScan 2211 system (Bruker Corporation, Billerica, USA) was used. This μ-CT system is equipped with an X-RAY WorX TCNF X-Ray source (X-RAY WorX GmbH, Garbsen, Germany) with a minimum spot size of 0.5 µm and a maximum acceleration voltage of 190 kV. The system has two X-ray detectors, the Varex CMOS 1512 detector (Varex Imaging Corporation, Salt Lake City, USA) with a high sensitivity and a resolution of up to 0.4 µm/voxel and a Ximea OnSemi KAI-11002 CCD detector (XIMEA GmbH, Muenster, Germany) for high-resolution images of up to 0.2 µm/voxel. The substrate scans were performed with the CMOS detector, which provides a better signal-to-noise ratio to achieve a clear segmentation of the material structure. The total scan time was 4.5 h, performing 3601 projections at a resolution of 0.5 µm/voxel (source voltage 60 kV, source current 500 µA). The functional layers were investigated with the CCD detector to achieve optimum structure resolution (voxel size 0.2 µm). A longer exposure time was chosen to perform 1294 projections, resulting in a total scan time of 9 h (source voltage 80 kV, source current 250 µA). Due to the high density of the functional layers, the camera is equipped with a 0.25-mm aluminum filter to achieve a better contrast ratio.

Sequential SEM imaging and FIB milling (FIB/SEM tomography) provides spatial information with a higher resolution compared to μ-CT. Small features with sizes in the order of 10 nm can be reliably detected [36]. Material contrast is improved using epoxy resin to fill the pores. Datasets for FIB/SEM tomography were obtained with a Thermo Scientific™ Helios G4 FX DualBeam™ (Thermo Fisher Scientific, Waltham, Massachusetts, USA) microscope. Material contrast for anode materials (Ni and YSZ) was obtained by secondary-electron imaging with a though-the-lens detector (TLD) using 3 keV electrons and a beam current of 0.8 nA. Backscattered-electron imaging using the in-column backscattered-electron detectors (mirror detector (MD) and in-column detector (ICD)) yielded material contrast for cathode and electrolyte materials. Imaging was performed at electron energies between 3 and 5 keV and beam currents between 0.8 and 6.4 nA. Details on FIB/SEM processing are given by Joos et al. [20, 35]. Information on image filtering, segmentation and parameter determination can be found in [20, 35, 37].

A ZEISS 1540XB CrossBeam workstation (Carl Zeiss NTS GmbH, Oberkochen, Germany) was used for standard SEM microstructure investigations of cross-sectional surfaces as well as for FIB/SEM tomography of the substrate/cathode interface using the Everhart-Thornley (ETD) and Inlens detectors. Material contrast was obtained by secondary-electron imaging with the Inlens detector, using an electron energy of 1.3 keV and a beam current of 0.15 nA.

The elemental distributions and chemical compositions of the functional layers and of the cathode/support interface were determined by EDXS in a FEI (now: Thermo Fisher Scientific) Tecnai Osiris ChemiSTEM transmission electron microscope operated at 200 kV (equipped with four Bruker silicon drift detectors). High-angle annular dark-field scanning transmission electron microscopy imaging (HAADF-STEM) yields chemically sensitive images with high spatial resolution. The acquisition time for a 1024 px by 1024 px map was 1000 s with a resolution of 14 nm/px. Image stitching was used to extend the field of view. Nine composition maps were stitched together to cover the whole SOFC structure with all relevant interfaces in one single image. Composition quantification was carried out with the Bruker Esprit software using the standardless Cliff-Lorimer thin-film method. The oxygen signal was excluded from quantification due to strong absorption of low-energy X-rays. SAED patterns for crystal structure analyses were also taken in the Tecnai Osiris ChemiSTEM.

Electron transparent cross-sectional TEM specimens were prepared by FIB-based techniques and by conventional mechanical sample preparation (including grinding, dimpling and ion-etching).

Optical microscopy allows true color images (cf. Fig. 2a). The thickness of the substrate can be determined as 1200–1250 μm, while the thicknesses of the much thinner cathode, electrolyte and anode layers cannot be determined. Macroscopic failures like cracks and fissures or other large-scale inhomogeneities which are one of the abovementioned concerns of co-firing are absent in this part of Sample 1A. Offering a very low preparation effort, OM is helpful for a first, rough quality control of the sample.

μ-CT offers nondestructive sample testing and allows one to distinguish the features of the thick, highly porous substrate and all functional layers (cf. Fig. 2b). With a voxel size of 500 nm, a total volume sector with an edge length of approximately 600 µm was scanned. The denser the materials, the more the surrounding layers within the beam path influence the scan results of the region of interest. The thick substrate is particularly well qualified to be examined by μ-CT because there is no need to differentiate between multiple material phases and since the pore sizes in the 10 μm range are sufficiently large. A raw 2D grayscale image of the scan can be seen in Fig. 3a. The grayscale value increases with density: epoxy-filled pores are black (lightest phase), the silicate support is gray, impurities appear bright. Figure 3b shows the reconstructed representative volume element of 0.18 mm³ (voxel size 500 nm). Here, the focus is set on the pore phase (rendered in brown). The material phase is transparent. Microstructural parameters such as pore fraction, ε_pore and tortuosity factor of the pore phase, τ_pore can be computed. Since different methods and definitions exist for calculating tortuosity, it should be made clear that the effective media definition (\( D_{\text{eff}} = \varepsilon \cdot \tau^{ - 1} \cdot D \), see, e.g., [35, 38]) was used here for the calculation. This approach should not be confused with other approaches such as geometric tortuosity. The tortuosity factor is here calculated with an in-house Matlab implementation of a finite element method (FEM) model which uses the reconstructed structure as computational grid; more details on this can be found in [35]. Calculations reveal a preferential pore orientation parallel to the functional layers, resulting in a higher tortuosity of the pores in gas transport direction (\( \tau_{{{\text{pore}},\parallel }} \)). This may lead to increased gas diffusion losses. The obtained CT data can be used as a basis for modeling these transport processes and performance estimation (cf. section “Cathode gas diffusion polarization”).

Inhomogeneities such as deviations in layer thickness or µm-sized, larger particles embedded in or added to the functional layers can also be visualized by CT. Figure 2b shows one example of a µm-sized out-sized particle (> 20 μm) within the CCL that was revealed by CT. In a next step, these particles were identified by SEM-EDXS as LSM. We suspect the origin in particle size inhomogeneities in the LSM powder (either remnants from the milling process, or intentional inclusions, to affect shrinkage behavior during sintering). Spatial CT analysis helps to reveal such particles that might not be noticed when inspecting the 2D cross section.

Unfortunately, the edges of features in CT images are blurred, especially when investigating particles smaller than a few micrometers. The boundaries between particles can only be approximated which leads to a degree of segmentation uncertainty. This hinders the separation of pores and material phases within CCL, CFL and anode. While large pores are visible, pores < 1 μm are not reliably detected, which impedes phase assignment. In addition, the average atomic number (LSM: 20.2, YSZ: 18.6) and the X-ray absorption rates are too similar to allow material phases differentiation in the CFL.

In general, μ-CT allows good results when investigating the macroscopic features of the inert substrate but fails to resolve the fine particle/pore structures within the functional layers. Therefore, the authors do not advise the use of μ-CT to determine the microstructural parameters of SOFC functional layers.

Figure 4a shows a secondary-electron SEM image from a FIB-milled electrolyte/anode cross section. The anode consists of rather uniform YSZ particles, but offers bimodal size distributions of nickel particles (small, dense particles and larger particles with inner porosity) and pores (large, round pores and smaller, twisted pores). Imaging with the TLD (using primary electrons with an energy of 3 keV) generates strong contrast between YSZ (gray), Ni (bright) and pores/epoxy (black), and also allows clear differentiation between the three phases. Figure 4b shows a 3D reconstruction with a large volume of 12,792 μm³, which allows reliable extraction of microstructural parameters (cf. Table 2). The necessitated voxel size of 30 nm fails to show the nanoscale MnO_x precipitates that were observed by STEM-EDXS (cf. section “STEM-EDXS”).

A cross-sectional SEM image and a corresponding color-coded element distribution map of the entire SOFC structure obtained by STEM-EDXS (nine stitched mappings, cf. section “STEM-EDXS”) are shown in Fig. 5a, b, respectively. Figure 5c shows SAED patterns confirming the crystal structure of secondary phases at the substrate/cathode interface. The following section lays special emphasis on reaction phases resulting from high-temperature co-sintering.

Cathode side: at the interface between substrate and the CCL, two layers are observable and they are characterized by high concentrations of either Zn/Mn (green) or Si (pink). SAED analysis (cf. Fig. 5c) reveals the crystal structures of these layers and allows phase identification. The Zn/Mn-rich layer was identified as cubic spinel ZnMn₂O₄ (crystal space group Fd-3 m, lattice parameter: a = 0.84 nm) and the Si-rich layer as apatite Sr₂La₈(SiO₄)₆O₂ (crystal space group P63/m, lattice parameter: a = 0.9705 nm, c = 0.7241 nm).

In addition to that, sub-µm-sized ZnMn₂O₄ precipitates spread out into the entire CCL volume, as indicated by the green arrows in Fig. 5b. In contrast, no ZnMn₂O₄ precipitates were found within the CFL volume, but a distinctive number of ZnMn₂O₄ precipitates were found at the interface between CFL and electrolyte (cf. Fig. 5d). On the other hand, the CCL and the CFL are free of Si-rich precipitates that are known to have a strong impact on cell performance.

It is assumed that both secondary phases, ZnMn₂O₄ and Sr₂La₈(SiO₄)₆O₂, are formed during high-temperature co-sintering. A solid-state diffusion of zinc and silicon cations from the support and lanthanum, strontium and manganese from the CCL is probably the mechanism that forms the spinel and apatite layers between the support and CCL. In addition, the Zn spreads out over a distance of up to 90 µm via gas diffusion through the open pore phase of both cathodic layers and precipitates as ZnMn₂O₄ within the CCL and at the CFL/electrolyte interface. The assumption that these mechanisms take place only during co-firing is supported by our finding that neither composition, location nor the amount of either secondary phases change between the “after co-firing” and “after operating” states (the full findings would exceed the scope of this paper).

The distinct reactivity between substrate and cathodic layers called for an investigation of the composition. The nominal elemental composition of LSM and YSZ was compared with the measured composition of both phases within the CCL and the electrochemically active CFL of Sample 1B. Please note that a quantification of low-energy X-rays of oxygen was omitted due to the large quantification error from strong absorption in the TEM sample. Table 1 clearly indicates deviations from the nominal LSM stoichiometry for the elements La, Sr, and Mn (for both CCL and CFL). Especially, the Mn cation concentration is more than 30% lower than expected (ratio (La + Sr)/Mn in CFL: nominal: 0.98, measured: 1.28). The elemental composition of the YSZ phase within the CFL is also different, compared to nominal stoichiometry: 4 at% of Mn and 3 at.% of La are found. Although the EDXS quantification error can be up to 10%, the findings confirm the high volatility of manganese during co-firing. The change in LSM stoichiometry alters the electrical and electrochemical characteristics of the CFL, yet no quantitative experiments have so far been performed.

Electrolyte: a STEM-EDXS elemental distribution analysis of the YSZ electrolyte validates the diffusion of Mn into the electrolyte with a linear decrease from 3 at.% Mn at the cathode side to < 1 at.% Mn at the anode side. The elements Mg, Sr and Si are below the detection limit (Mg/Sr < 0.5 at.%, Si < 1.5 at.%). The Mn content correlates directly with the YSZ grain size and the electrolyte density. It is assumed that Mn promotes YSZ sintering by accelerating grain growth and densification, which is consistent with the literature [39, 40]. This is beneficial for lower co-firing temperatures and ultimately for long-term ionic conductivity (see below). YSZ with an yttria content > 10 mol.% is permanently stabilized in the cubic phase with a high ionic conductivity, whereas 8YSZ is only partially stabilized [41, 42]. During aging, cubic 8YSZ is partially transformed into t”-ZrO₂ with a lower ionic conductivity. We examined YSZ crystal structure changes across the functional layers (from the cathode to the anode side) by SAED patterns and demonstrate the effect of the Mn concentration on the YSZ crystal structure. Figure 6a shows a SAED pattern in [111] zone-axis orientation taken in a YSZ grain in the CFL. The pattern is compatible with the cubic crystal structure (fluorite, crystal space group Fm3m, lattice parameter: a_c = 0.512 nm [42]). The same YSZ crystal structure is found in the electrolyte close to the CFL/electrolyte interface (cf. Fig. 6b) and in the center region of the electrolyte (Fig. 6c). Additional reflections are clearly recognizable in SAED patterns taken close to the electrolyte/anode interface and in anode YSZ grains. These reflections can be assigned to the t′′-YSZ phase (P4₂/nmc [43]). In contrast to the equilibrium tetragonal phase, the c/a ratio of the c and a lattice parameters in the metastable t′′-phase is 1.

A comparison of the Mn distribution across the electrolyte with the YSZ crystal structure indicates that Mn stabilizes the cubic YSZ phase (in agreement with the literature [44]). Despite a lower initial ionic conductivity, due to manganese, when compared to pure 8YSZ [40, 45, 46] one consequence could be a better long-term conductivity since the formation of the above-mentioned low-conductivity t´´-phase is delayed. However, the presence of manganese within the electrolyte must be considered carefully. Malzbender et al. observed stack failure after 19,000 h of operation due to electrolyte fracture. Manganese accumulation at the grain boundaries and subsequent crack growth along these boundaries were identified as a possible reason for failure [47].

Anode: STEM-EDXS also detected manganese at the anode side (cf. Fig. 5, small green regions). Instead of being dissolved in the YSZ grains, Mn is distributed as MnO_x precipitates (sizes from a few tens to a few hundred nanometers). SAED reveals the cubic NaCl structure (a = 0.44 nm) which is characteristic for MnO. However, additional superstructure reflections and reduced oxygen content compared to MnO indicate oxygen-deficient MnO_x (x < 1). Due to the low Mn concentration within the electrolyte at the anode side, it is assumed that manganese diffuses through the gas phase from the cathode to the anode during co-sintering. The impact on performance (e.g., blocking of triple-phase boundaries between nickel, YSZ and gas phase) may be important and has to be further investigated.

The following section shows how information obtained by STEM-EDXS (cf. Figure 5) can be used to enhance information from FIB-SEM tomography. We now focus on the substrate/CCL and CFL/electrolyte interfaces.

Substrate/CCL interface: Results from STEM-EDXS (cf. Figure 5) allow the correlation of SEM grayscale information and material composition. Figure 7 (left side) shows the SEM contrast of the substrate/CCL interface region obtained by secondary-electron SEM imaging with the TLD (Zeiss 1540XB, 1.3 keV). These imaging conditions are composition sensitive and reveal regions with different phases. Besides the black pores, two additional phases (bright next to the support and dark next to the cathode) can be recognized between the dark support and the bright CCL. Elemental information obtained with STEM-EDXS allows us to correlate the bright secondary phase with ZnMn₂O₄ and the darker one with Sr₂La₈(SiO₄)₆O₂. We note that SEM imaging with the ETD (not shown here) does not show material contrast of the secondary phases.

The presented findings allow primary- and secondary-phase segmentation for FIB-SEM tomography, as indicated by color coding in Fig. 7 (here with a large total volume of 5641 μm³). The reconstructed volume (right side of Fig. 7) shows the arrangement of ZnMn₂O₄ (green) and Sr₂La₈(SiO₄)₆O₂ (pink) and reveals gaps in the layers of the two secondary phases. The continuous network of pores across the substrate/CCL interface provides O₂ diffusion pathways. Please note, with provided sufficient gas transport across the interface, these secondary phases do not impede the cell performance of the inert-substrate-supported cells (unlike in anode or metal-supported cells). Therefore, the main interest is whether secondary phases contribute to an increase in gas diffusion losses. An exceptionally dense layer of secondary phases would block oxygen across the interface. Fortunately, the marked paths in Fig. 7 indicate that open pores are available. This suggests that the secondary phases do not impact oxygen diffusion or cell performance.

In order to unambiguously evaluate the gas diffusion losses due to the secondary phases, the reconstructed volume was imported into COMSOL Multiphysics. In contrast to 2D FEM simulations of entire stack layers (see [48]), spatially resolved 3D FEM simulations are restricted to smaller volumes as shown in Fig. 7. Subsequently, the drop of oxygen partial pressure, pO₂, across the interface was determined by FEM simulations. Depending on wall distance, a spatial differentiation between ordinary and Knudsen diffusion coefficients was implemented. The concentration overpotential resulting from the difference in partial pressure between the gas atmospheres of substrate and cathode can be derived from the Nernst equation and calculated via [49, 50]:with ideal gas constant, R, Faraday constant, F, oxygen partial pressure, pO₂, and temperature, T. The resulting area specific gas diffusion resistance is calculated as \( ASR_{\text{Gas}} = \eta_{\text{conc}} / j \) < 1 mΩ cm² (T = 750 °C) at a current density of 1 Acm⁻² neglecting strong nonlinear dependencies of the diffusion polarization. As the losses are even smaller for lower current densities, one can say that the secondary phases between support and CCL do not significantly influence cell performance. Therefore, this interface is not considered in the calculation of cathode gas diffusion polarization (cf. section “Cathode gas diffusion polarization”).

Cathode and CFL/electrolyte interface: Fig. 8 presents backscattered-electron SEM images and a large reconstructed volume of the cathode and CFL/electrolyte interface. The SEM images in Fig. 8a were taken with the ICD at 5 keV and show high contrast between the different phases (especially between LSM and 8YSZ). Exploiting the STEM-EDXS results (cf. Fig. 5), the SEM contrast of all phases can be determined with black contrast for pores/epoxy and increasing brightness for ZnMn₂O₄, 8YSZ and LSM. Unfortunately, a decrease in brightness is observed toward the edges of the low-magnification image in Fig. 8a, which is disadvantageous for segmentation in FIB-SEM tomography. This problem is avoided by backscattered-electron imaging with the MD (5 keV) which yields images without contrast change over large regions of interest. The contrast between the phases is a bit lower compared to center regions of the ICD but good enough to allow a reliable segmentation.

Figure 8b presents a 3D reconstruction of the phase distribution in a large volume of the cathode and across the CFL/electrolyte interface (42767 μm³ with 30 nm voxel size). FIB-SEM tomography confirms the results of STEM-EDXS regarding the location of ZnMn₂O₄ precipitates, which were found throughout the whole CCL volume (dark gray and green spots in Fig. 8a, b, respectively). Precipitates are located between pores and LSM, and not inside LSM particles. This indicates Zn diffusion during co-sintering via gas phase through the pores. The zinc reacts with manganese from the cathode to form ZnMn₂O₄.

The evaluated microstructural parameters can be found in Table 2. Besides material fraction, ε, and tortuosity, τ, we also calculated the triple-phase boundary length, l_TPB. The full parameter set allows future implementation of a transmission line model (TLM) to describe the cathode polarization resistance (in analogy to a TLM of the Ni/YSZ anode shown in [51]). A detailed comparison of modeled and measured impedance data would be beyond the scope of this paper and will be published soon.

The presence of accumulated ZnMn₂O₄ precipitates at the CFL/electrolyte interface revealed by STEM-EDXS (cf. Figure 5) is then confirmed in Fig. 8b and highlighted in Fig. 8c, where only the ZnMn₂O₄ precipitates at the CFL/electrolyte interface are shown. Studies on other cell systems have shown that a discontinuous layer of secondary phases can be tolerated in some cases as the performance is still good [20, 21]. ZnMn₂O₄ was also found within the electrolyte at YSZ triple points close to the cathode interface (dark gray spots in magnified SEM image in Fig. 8a). Almost no additional ZnMn₂O₄ was found within the CFL. It would become critical if triple-phase boundaries (regions where the electronic, ionic and the gaseous transport paths interact) were blocked by ZnMn₂O₄, as oxygen could not be incorporated into the YSZ. This has not yet been observed.

Activation of the LSM/YSZ cathode [29, 52, 53] enhances performance during cathodic current loading and is typically attributed to microstructural changes of the LSM near the triple-phase boundaries and improvement of LSM surface kinetics. Additionally, small ZnMn₂O₄ precipitates that cannot be resolved by SEM imaging could agglomerate with time. As a result, the surface area covered with ZnMn₂O₄ would decrease. This would facilitate the incorporation of oxygen and therefore improve cell performance at the beginning of operation. The cathode activation due to current load would be superimposed. In this case, to allow a prediction further investigations monitoring cathode performance over time would have to be performed on cells with and without secondary phases.

The determined microstructural parameters can be used to calculate the area specific gas diffusion polarization on the cathode side. Gas diffusion is regarded as a separate, non-coupled process, because the diffusion distance in the substrate and in the cathode is considerably higher than the penetration depth of the electrochemical reaction [50]. The area specific cathode gas diffusion resistance (ASR_Gas) can be calculated as follows [54]:with layer thickness l, standard pressure p₀ = 1 atm, pore tortuosity τ_p, binary gas diffusion coefficient of oxygen and nitrogen D_N2,O2 in m²/s, porosity ε, oxygen partial pressure p_O2 and oxygen Knudsen diffusion coefficient D_K,O2.

The Knudsen diffusion coefficient [55, 56] with pore diameter, d_p, and molar mass of oxygen, M_O2, can be calculated as follows:

The binary diffusion coefficients, D_N2,O2, were calculated according to the theory of Chapman and Enskog [55, 57].

Calculations on the gas diffusion resistance of the substrate/CCL interface revealed that there is no significant influence of secondary phases on total ASR_Gas. Therefore, only substrate, CCL and CFL were considered. Results shown in Table 3 demonstrate that the main contributions to gas diffusion losses are caused by the inert substrate. Due to the manufacturing process, the substrate shows an unfavorable pore orientation, as proven by μ-CT. It can be calculated that a hypothetical change in pore orientation of the inert substrate (cf. Figure 3) could reduce the ASR_{Gas,substrate} from 45.7 mΩ cm² to 21.1 mΩ cm² at T = 750 °C. The provided investigations show that only the correlation between μ-CT, FIB-SEM and STEM-EDXS can allow a comprehensive examination of the processes contributing to ASR_Gas.

FIB-SEM results (cf. Table 2) allow modeling of anode polarization resistance using a transmission line model according to [51, 58]. The model details are shown in Appendix A. At T = 750 °C with a fuel gas humidification of 5.5% H₂O, the modeled ASR_Anode at is 0.114 Ωcm². This can be compared to impedance measurements: To avoid overlapping of cathode and anode processes, the modeled ASR_Anode was compared to a symmetric anode cell fabricated under the same conditions as the full cell. With a measured ASR_Anode of 0.113 Ωcm², electrochemical impedance spectroscopy measurements at similar conditions are in perfect agreement with the simulations. In addition, the performance of the given unaged anode is competitive with state-of-the-art cells like the ASC of Forschungszentrum Jülich [5, 51].

Physicochemical meaningful modeling of the ASR_Cathode is in principal also possible using the TLM. The fact that the LSM-YSZ composite is a dynamic system [59‐61] impedes a straight forward approach as the line specific resistance changes during an initial activation phase. This current- and temperature-dependent process is often associated with microstructural changes. Combining these with expected influence of the secondary phases shown in Fig. 8 illustrates the complexity of the cathode kinetics. The authors think that this is out of the scope of this contribution. Nevertheless, this work can serve as a basis for future microstructure-based modeling of the cathode polarization resistance where several operating conditions are considered.