## Abstract

Microstructural changes in Ni–yttria stabilized zirconia (YSZ) near the YSZ electrolyte were examined by three-dimensional (3D) electron microscopy after electrolysis and fuel cell operation up to 10,700 h and 15,000 h, respectively. The depletion of Ni and three-phase boundaries (TPBs) close to the electrolyte was detected upon cathodic polarization. It corresponded to spatial variations of dihedral angles (θ) at TPBs and Ni surface curvature along the direction perpendicular to the electrolyte, which comport with electrowetting and Zener pinning theory on several aspects. θNi decreased by up to 6 deg next to the electrolyte after electrolysis but remained uniform after fuel cell operation. This is in line with predictions from electrowetting theory with capacitances measured by electrochemical impedance spectroscopy and distribution of relaxation times. The decrease in θNi was concurrent to transition toward concave Ni/pore interfacial shapes and lower genus of the Ni phase, which suggests the pinch-off of Ni ligaments following surface diffusion-controlled Rayleigh instability. The increase in absolute mean curvature near the electrolyte interface is a driving force for outward transport of Ni. The decrease in θYSZ further suggests that TPB lines relocate on YSZ surface features that provide higher Zener pinning force. In contrast, few localized contact losses between Ni and YSZ that can also occur under high cathodic polarization and trigger Ni depletion were detected. The results are expected to advance the understanding of the driving forces that cause Ni depletion near the electrolyte in electrolysis for the design of improved solid oxide cell electrode microstructures.

## 1 Introduction

A specific feature of the microstructural changes in the Ni–yttria stabilized zirconia (YSZ) electrode under solid oxide electrolysis (SOE) is the depletion of Ni next to the YSZ electrolyte. It contributes to a higher degradation of the electrochemical performance than in the solid oxide fuel cell (SOFC) mode, which currently remains a limitation for the commercial deployment of SOE systems.

The phenomenon is well documented in the literature under steam electrolysis [15]. It is typically enhanced by cathodic polarization at high current density during extended periods. Two-dimensional (2D) electron microscopy and representations of the heterogeneous Ni–YSZ microstructure as a packing of Ni and YSZ particles with close to spherical shapes significantly contributed to the current understanding [68]. Contact losses between Ni and YSZ are often observed near the electrolyte, along with accumulation of Ni further away. They decrease the density of connected three-phase boundaries (TPBs) and the connectivity of the Ni phase. Both degrade the electro-catalytic properties of the Ni–YSZ region next to the YSZ electrolyte until passivation.

The number of three-dimensional (3D) electron or X-ray microscopy studies is rapidly increasing but comparatively lower. The focus is mainly on the quantifying of the volume fraction and TPB density near the electrolyte and comparison with values toward the bulk of the electrode. Ni depletion by up to 6% compared to the Ni volume fraction in the reference sample was reported after 9000 h in a 25-cell stack operated in steam electrolysis [9]. The decrease in connected TPB was very high, in the range of 60–70%, and higher at the inlet, likely because of higher current density and steam partial pressure. Similarly, Ni depletion was detected up to 2.5 µm away from the YSZ electrolyte using focused ion beam-scanning electron microscopy (FIB-SEM) serial sectioning with 3D energy dispersive X-ray spectroscopy (EDS) elemental mapping and related to a decrease in Ni phase size as well as connected and accessible TPB density [10]. In contrast, 3D imaging of single cells revealed limited Ni depletion after 1000–2000 h in electrolysis [11,12]. Shimura et al. [13] further included chemical aspects in their quantitative 3D study. SiO2 was observed within Ni at grain boundaries and on Ni surface mostly near TPBs under a mild current density of 0.2 A cm−2 in SOE and to a lower extent SOFC. Quantitative analysis by 3D FIB-SEM indicated the contamination of nearly all connected TPBs after 100 h in SOE, which was opposite to the performance enhancement measured by electrochemical impedance spectroscopy (EIS). Therefore, the significant higher degradation rates in SOE than SOFC mode may not be necessarily caused only by localized microstructural changes in the Ni–YSZ electrode, at least from the standpoint of effective transport properties and connected TPB density.

The understanding of the differences in Ni–YSZ degradation upon SOFC and SOE operation remains incomplete. Surface diffusion is commonly considered the dominant Ni transport mechanism with a free surface diffusion coefficient around 1.3 µm2 s−1 at 800 °C [14]. Under the assumption that gas-phase Ni transport becomes non-negligible because of the higher steam partial pressure and its gradient, volatile Ni(OH)x species are expected to diffuse down the gradient of H2O partial pressure [1,6], suggesting Ni transport toward, rather than away from the electrolyte in SOE. Re-deposition near TPBs in the electrochemically active region may be however promoted because of more reducing conditions in electrolysis. Hauch et al. [15] also confirmed that Ni depletion occurs under dry CO2 electrolysis as well, which indicates that steam is not a necessary condition for enhanced Ni transport under cathodic polarization. Differences in electro-static potential and oxygen activities seem therefore more likely the reason for the higher degradation in SOE.

The loss of contact between Ni and YSZ is a trigger for the Ni transport mechanism proposed by Mogensen et al. [6]. It is promoted by high cathodic polarization and may be induced by different mechanisms. A first possibility is the dissolution of Zr in Ni because of partial reduction of ZrO2. A consequence under high overpotential is the formation of ZrO2 nanoparticles on the Ni surface after, e.g., steam supply failures. The estimated threshold oxygen partial pressure (p(O2)) is 3.2 × 10−29±3 bar, which corresponds to overpotentials starting from 450 mV at 850 °C [7]. A second possibility is the reduction of endogenous SiO2 impurities, which can form nano-precipitates within Ni under high overpotential [16] or even mild SOE and SOFC conditions [13]. Another is the volatilization of Ni as Ni(OH)x that may yield rounding of Ni shapes. Upon extended loss of contact and Ni percolation, the transport of Ni away from the interface occurs by competitive growth driven by differences in sizes and re-deposition under more reducing condition at remaining active TPBs further away from the YSZ electrolyte.

Contact losses between Ni and YSZ are however not systematically observed along with Ni depletion [8]. Another potential significant consequence of polarization is a change in surface tensions because of electrowetting and/or the known dependence of the work of adhesion at the metal/oxide interface on oxygen activity [6,17]. Both electrocapillary curves and the relationship between dihedral angles (θ) and p(O2) commonly follow a belly shape. Therefore, similar microstructural degradation patterns are expected at sufficiently high cathodic and anodic polarization. The practical consequences for SOE and SOFC application root from the location of the electrocapillary maximum and dependence of θ on p(O2). An increase in wettability is however not expected to cause alone transport away from the interface.

In this study, differences in the spatial distribution of microstructural properties were analyzed by 3D electron microscopy within and among samples after cathodic and anodic polarization up to 10,700 h and 15,000 h, respectively. The focus was placed on 3D local curvature and dihedral angles at TPBs to inform about the driving forces that degrade the Ni–YSZ microstructure by the transport of Ni away from the YSZ electrolyte. An estimate of the relationship between Ni dihedral angle and overpotential based on the electrowetting theory and capacitances measured by EIS and the distribution of relaxation times (DRTs) is provided to support the discussion of the detected microstructural changes.

## 2 Experimental

### 2.1 Materials and Cell Testing.

The Ni–YSZ anode-supported cell for short stack, segmented and button-cell experiments were provided by SOLIDpower.2 All the co-cast NiO-YSZ/YSZ bilayers with gadolinia-doped ceria (GDC) compatibility layers were produced using the same starting materials and processing parameters. The same Ni–YSZ material was therefore used for the functional and supporting layers. The same sealing and reduction procedures were applied to all the samples.

The samples for 3D electron microscopy include a pristine cell after Ni reduction (“0 h”), two SOE six-cell stacks operated for 2000 h and 10,700 h (“SOE 2 kh” and “SOE 10.7 kh”), and a SOFC segmented-cell operated for more than 15,000 h (“SOFC”). The aging experiments were performed at intermediate temperature (720–750 °C). The average current densities ranged from −0.8 A cm−2 to −0.5 cm−2 with H2/H2O feed in SOE and 0.3 A cm−2 with H2/N2 as fuel in SOFC. The experiments “SOE 10.7 kh” and “SOFC” were selected to facilitate the detection of differences in microstructural changes between SOFC and SOE conditions of practical relevance. They indeed correspond to the longest operation times available at École Polytechnique Fédérale de Lausanne (EPFL) under laboratory conditions. “SOE 2 kh” is provided as a confirmation of “SOE 10.7 kh.” A button-cell sample subjected to high cathodic polarization because of steam supply failure during more than 40 h is included as a limiting case for microstructural degradation (“SOE*”). Table 1 provides an overview of the experiments and volume samples imaged by 3D electron microscopy. Further information is provided in Appendices  A– C and Refs. [5,10,18,19].

### 2.2 Three-Dimensional Electron Microscopy.

The interface between the YSZ electrolyte and the Ni–YSZ electrode was imaged by 3D FIB-SEM serial sectioning [2022] (Zeiss Crossbeam 540). Samples were extracted near the middle along the flow path in the tested cells, except for the SOFC segmented-cell (segment 12). They were fractured to expose the interface between the Ni–YSZ anode and the YSZ electrolyte. EPON812 was used for impregnation with three to eight successive dilutions with acetone, before mechanical polishing with sandpaper up to 0.5 μm and gold coating. Fiducial marks embedded in Pt and C depositions were milled over a region of interest of about 30 μm by 20 μm comprising the Ni–YSZ electrode together with the interface with the electrolyte. The milled groves allow adjustments of the FIB position to ensure variations in slice thickness lower than a nanometer and post-acquisition slice alignment with a Fiji [23] script. The extraction locations and sizes of the five volume samples are listed in Table 1 and Figs. 1(a) and 1(b).

The SEM acceleration voltage was 1.5 kV with a current of 1.6 nA and dwell time of 1 μs. The FIB acceleration voltage was 30 kV with a milling current of 700 pA. The imaging conditions were set to obtain isometric voxels with a size of 10 nm and dual channel data with signals from the energy-selective backscatter (ESB) and in-lens secondary electron detectors.

The aligned ESB and in-lens secondary electrons data were first combined to remove artefacts due to slight impregnation imperfections and resin decomposition under the beam because of the dose induced by imaging at 10 nm voxel size. A 2D non-local means filter was applied twice along two orthogonal directions.

The 3D segmentation was performed using the same Matlab routines with calls to Avizo for marker generation based on the variance of the grayscale distribution, image gradient, and watershed transform computations as described in Refs. [24,25]. Such method cannot guarantee the accurate treatment of all the localized detachments between Ni and YSZ. Few manual corrections were implemented whenever needed after visual inspection. Two approaches were compared for the filling of the remaining boundary voxels, which was expected to influence the measurement of dihedral angles (Sec. 3.1): the standard labeling based on the most present phase among the 26 neighbors, and that on sequential phase dilation and assignment of two- or three-phase overlaps based on the filtered grayscale data. Tests indicated that all the trends presented in this study are unaffected. The variations in property measurements were negligible, besides for the 3D dihedral angle where the offsets were of approximately 1.8 deg, 6.9 deg, and 9.4 deg, i.e., 1.6%, 6.5%, and 6.6% for pore, YSZ, and Ni, respectively.

## 3 Methodology

### 3.1 Three-Dimensional Property Measurements.

Volume fractions, contiguity, interfacial surface area (ISA), and total, connected and isolated TPB densities were computed with methods described in Refs. [2628]. The connected TPB is the subset with connected pathways for ions, electrons, and gas species to the electrolyte, current collection, and gas channel, respectively. The applied ISA and TPB measurements consist in voxel edge and face counting, which provide overestimation. The ISA and TPB density were therefore complementarily measured using the surface mesh generated for the curvature measurement described below and the smoothed skeleton of the voxels forming the TPB lines, respectively.

Three-dimensional curvature analysis was performed as described in Ref. [25] to investigate the distribution of interfacial shapes and mean curvature (H) in the volume samples. The principal curvatures (κ1 and κ2) are measured on a smoothed triangular marching cube mesh of the phase interfaces in the volume samples using local quadratic surface fitting at each mesh patch. Probability distributions of the mean curvature H and the interfacial shape distribution are generated from κ1 and κ2 measurements at each surface patch weighted by the corresponding area.

The common classification of phase volume as connected, isolated, or regions with unknown connectivity using labeling algorithm does not inform about the topology of the regions themselves. The Euler characteristics is a topological invariant, the interpretation of which is however not intuitive when comparing sample volumes with different sizes [29]. The Euler–Poincaré formula provides its relation to the genus, which informs about the number of redundant connections and is therefore commonly illustrated as the number of handles in a structure. Therefore, the effects of cathodic and anodic polarization on a phase topology were analyzed by computing the density of handles. The Euler characteristic of a phase was computed by the counting of voxel corners, edges, and faces. It is a biased measure of topology, since the volume samples are cut from the real material and contain artificial boundaries. A correction based on the Euler number addition theorem is therefore required [29]. The number of objects and cavities in the Euler-Poincaré formula were computed using labeling algorithm as described in Ref. [27].

A procedure was developed for the 3D measurement of dihedral angles at TPBs. The TPB density measurement algorithm mentioned at the beginning of this section lists, for each detected TPB line of unit voxel length, the four voxels that share that edge (see, e.g., Refs. [26,27]). The first step is the conversion of this information into an undirected spatial graph (or network of TPB lines consisting of vertices connected by edges) to facilitate the calculation of the tangent at each TPB. A binary volume is generated from the list of quadruple voxels and skeletonized with Avizo’s implementation of the Tree-Structure Extraction Algorithm for Accurate and Robust Skeletons [30]. The generated spatial graph is analyzed to reconnect vertices closer than five voxels (50 nm) and classify its components into TPB “loops” or “open lines,” following the approach in Ref. [25]. Two of such TPB loops are shown in gray in Fig. 2(a), with computed tangent $t→$ at a TPB in white.

Skeletonization does not enforce a one-to-one correspondence between (i) edge points and (ii) list of TPBs of unit voxel length from the TPB density calculation algorithm. The use of (ii), i.e., voxel rather than skeletonization-based information, was preferred for the next dihedral angle measurement steps. The reason is to avoid slight shifts of the TPB positions that can affect the accuracy of the linear fit described below. A correspondence between (i) and (ii) within a distance of one voxel could be established for 96–97% of the TPBs. The remaining fraction was discarded for dihedral measurements, because the accuracy of the measured tangent direction is questionable.

The dihedral angle procedure illustrated in Figs. 2(b) and 2(c) is then repeated for each TPB. A sub-volume of 303 voxels centered on the TPB is first extracted to speed-up calculations. The voxels that form the Ni/Pore, Ni/YSZ, and YSZ/Pore interfaces and lie within the plane p defined by normal vector $t→$ and coordinates of the investigated TPB are identified using the algorithm for ISA measurements mentioned at the beginning of this section. The intersection of p with the interfaces within the microstructure can yield several disconnected lines in p. Those connected to the TPB are identified using labeling algorithm and the others deleted. The result is shown in Fig. 2(b). It consists in a 3D sub-volume containing a TPB point with three connected lines corresponding to the three interfaces.

The next step is a 2D measurement of the dihedral angles. A translation and rotation is first applied to the TPB and interface point coordinates to place the TPB point at the center of a 2D plane that contains all interface points (Fig. 2(c)). For each interface, a series of linear regression with increasing number of points (from the closest to the farthest to the TPB) is performed, keeping the fit that provides the highest Pearson’s correlation coefficient (inset in Fig. 2(c)). The dihedral angles are then retrieved from the computed slopes. A rotation of the 2D coordinates is applied in the singular case of an infinite slope.

The effect of voxel size (10–50 nm) on dihedral measurements was estimated numerically on a sub-volume of 103µm3 from the sample “SOE 10.7 kh.” θYSZ was the most sensitive, followed by θpore and θNi. The deviations at 20 nm compared to the reference 10 nm calculations were 3%, 5%, and 1%, respectively. The effect on standard deviations was larger (24%, 28%, and 18%, respectively). At 25 nm, the error was sufficient to affect the ranking in θi. The analysis therefore informs that a voxel size smaller than 20 nm is required for the considered Ni–YSZ material and method, with FIB-SEM imaging conditions ensuring consistent interaction volumes and spatial resolution.

The present study is focused on spatial variations of microstructural properties along the direction perpendicular to the interface between the YSZ electrolyte and Ni–YSZ electrode (x direction in Fig. 1(c)). The overpotential is indeed expected to develop within approximately the first 5–10 µm next to the electrolyte. Perfect vertical alignment of the YSZ/Ni–YSZ interface in the FIB is challenging to achieve by sample preparation. Uncorrected misalignment or 3D rotation of the volume samples can then cause inaccuracy in the measurement of spatial variations. Therefore, all the information needed for property calculations is stored as data points with corresponding 3D coordinates. Rotation for alignment on the YSZ/Ni–YSZ interface is then applied on the data points, before binning along the x direction to generate stacks of slices of averaged properties or probability density functions. Smoothing with a moving average using a window of 0–20 measurement positions (100 nm) was applied depending upon the property.

### 3.2 Electrowetting.

The electrowetting theory describes the dependence of the interfacial surface energy on applied electrical field and was established for solid–liquid electrolyte systems [31]. In the case of relevance for polarized Ni/YSZ interfaces, a change in Ni dihedral angle θNi is first anticipated. Indeed, the higher Ni mobility may result in morphological changes resembling those measurable for liquid systems. The relationship between dihedral angles θi and interfacial surface tensions γi/j is
$γNi/YSZsinθpore=γNi/poresinθYSZ=γYSZ/poresinθNi$
(1)
Integration of the differential Lippmann–Helmholtz equation d2γNi/YSZ/2 under the assumption of uniform and potential-independent double-layer capacitance CD yields Eq. (2), where ɛ is the applied potential.
$γNi/YSZ=γNi/YSZo−12CD(ε−εo)2$
(2)
Electrocapillary curves have therefore parabolic shape. The electrocapillary maximum is at ɛo, which corresponds to the potential of zero charge (pzc) and chemical component of the surface tension γNi/YSZo. Insertion of Eq. (1) in Eq. (2) provides a relationship between the Ni dihedral angle θNi and applied potential ɛ:
$sin(θNi(ε))=γYSZ/poresinθPore(γYSZ/poresinθporeosinθNio−CD2(ε−εo)2)−1$
(3)
where $θporeo$ and $θNio$ refer to the dihedral angles at the pzc.

Calculations of expected changes in θNi were performed using Eq. (3). Dihedral angles measured in the electrode bulk side of the volume samples were assumed for $θporeo$ and $θNio$. Overpotential-dependent capacitance CD measured by EIS and DRT was used in Eq. (3), using the experimental data and the DRT method described in Ref. [18]. The EIS sensitivity analyses were performed at 785 °C, with a current density range from −0.7 A cm−2 (SOE) to 0.7 A cm−2 (SOFC) and a feed of 50% H2 and 50% H2O. A similar sensitivity analysis over a range from −0.5 to 0.5 A cm−2 was performed at 700 °C on another cell.

DRT spectra obtained by the Fourier or Tikhonov methods showed good agreement with variations of the computed area under the peaks below 10%. Hence, only the latter is considered in this study. Six peaks were identified in the DRT. The distributed charge transfer process attributed to the Ni–YSZ electrode is that referred as “P5” in Refs. [18,32]. The “P5” surface specific resistance and capacitance were calculated using the area under the DRT and corresponding peak position, respectively. Both were estimated by optimization-based fitting that minimizes the difference between the sum of the estimated areas under each detected peak in the DRT and that under the total DRT [32]. The consistency of the sum of the deconvoluted resistances with the polarization resistance obtained from the Nyquist plot (Rp) was successfully verified. The analyzed spectra also passed the linear Kramers–Kronig test.

## 4 Results and Discussion

### 4.1 Visual Inspection of the Three-Dimensional Electron Microscopy Dataset.

Figure 3 shows secondary electron images in the FIB-SEM dataset, where the details of features are easier to observe than after segmentation. Their visual inspection provides first qualitative information about the microstructural changes upon operation. It suggests larger Ni size and a shift from Ni/pore surface shapes with negative curvatures in sample “0 h” to positive in “SOFC 15 kh” but not in “SOE 2 kh” and SOE 10.7 kh” near the interface (Figs. 3(a), 3(b), and 3(d)3(h)). Ni also resides mainly on apparently concave YSZ shapes, and the position of TPBs often corresponds to fine features on the YSZ surface (examples indicated by A in Fig. 3). The microstructure in “SOE*” subjected to high cathodic polarization for 43 h showcases spheroidization of isolated Ni near the YSZ interface (Fig. 3(c)). The abnormally large Ni regions indicate that competitive growth does not occur only between disconnected and connected Ni but also as expected between isolated regions (C in Fig. 3(c)). Degradation typical of high cathodic polarization is observed in “SOFC 10.7 kh” (Fig. 3(h)) but not in “SOE 2 kh.” It includes the presence of likely ZrO2 nanoparticles on the Ni surface and SiO2 within Ni grain [7,13,16] (G in Fig. 3(h)). Localized detachments between Ni and YSZ are confirmed in samples “SOFC 10.7 kh” and “SOE*” (F in Fig. 3(h)), but they remain seldom in the former, which differs from the 2D micrograph observations in Refs. [6,7] and part of Ref. [8].

### 4.2 Spatial Variations of Volume Fractions, Interfacial Surface Areas, and Three-Phase Boundary Densities.

Figure 4 provides the profiles of metric and topological properties along the x direction until x = 15 µm as defined in Fig. 1(c). Significant spatial variations in properties were not observed further away between x = 15–20 µm. The YSZ volume fraction is similar in all the samples and is close to uniform, besides mild variations most likely due to variability in manufacturing. Indeed, the mobility of YSZ listed in studies of creep in thin plasma-sprayed YSZ layers [33,34] results in an effective diffusion coefficient several orders of magnitude lower than that provided for Ni by Vaßen et al. [14]. A local minimum in YSZ volume fraction at the YSZ/Ni–YSZ interface is systematically observed at x = 1.5 µm (Figs. 4(a) and 4(b)). It may be due to differences in the starting YSZ powder sizes, interface between Ni–YSZ and YSZ slurries with different rheological properties during co-casting, and shrinkage during co-sintering. The minimum does not seem affected by SOFC or SOE operation. It can be therefore considered as an indication of the interface location for the alignment of the scans. The region x < 1.5 µm after alignment is indicated by a gray shaded area where the statistical reliability of the measured property is lower. The YSZ minimum approximately corresponds to a slight Ni rather than pore volume fraction local maximum. The apparent accumulation of Ni next to the electrolyte is present already in the pristine sample “0 h” and therefore not a consequence of SOFC operation.

The volume fractions of Ni and pore are also similar and uniform in “0 h” and “SOFC” (Fig. 4(a)). The depletion of Ni starting at approximately x = 5 µm is clearly observed in the two SOE samples and mirrored by an increase in the pore volume fraction (Fig. 4(b)). The depletion is surprisingly more severe in the sample “SOE 2 kh,” with a larger difference between the total (dashed lines) and connected (solid line) Ni volume fractions. A region characterized by Ni accumulation next to the depletion zone is not observed in “SOE 10.7 kh.” In “SOE 2 kh,” the reason for the peak in Ni volume fraction around x = 6 µm cannot be ascertained. It may also arise from the locally lower YSZ volume fraction. Besides, large overpotential for promoted re-deposition of Ni(OH)x is not expected at this location. The loss of Ni and nearby accumulation is exacerbated in the sample “SOE*” (Fig. 4(a)). The total Ni volume fraction is lower but fairly uniform in the region x = 1.5–7.5 µm, but the Ni connectivity drops to zero at x = 5 µm. Accumulation of Ni is observed at x = 10 µm and extends until approximately x = 17 µm (further away than shown in Fig. 4(a)). It compensates the depletion between x = 1.5–7.5 µm within approximately 1% (Ni volume fraction of 0.27 instead of 0.28–0.29 for all the other samples).

Table 2 lists the results of handle density calculations as described in Sec. 3.1. The density is highest in YSZ, followed by Ni and pore. The decrease in Ni handle density after aging is overall mirrored by the pore topology, with a magnitude that complies well with the trends in volume fractions discussed previously. The results in Table 2 further suggest a mild coarsening of the YSZ phase, which appears more pronounced in SOE than SOFC and scale with polarization time. This result warrants further investigations, since the YSZ microstructure is key for the pinning of the Ni phase [35]. Ongoing coarsening analyses based on surface to volume ratio, phase size distribution, and mean curvature measurements however indicate that changes are subtle at most and challenging to ascertain under the conditions considered in the present study.

The ISAs in Figs. 4(c) and 4(d) comply with the ranking of interfacial energies γNi/pore > γNi/YSZ > γYSZ/pore estimated from Eq. (1) with literature data on γNi/Pore (2 J m−2 [36]) and dihedral angles measured on the bulk side of the electrode (Secs. 3.1 and 4.4). For the latter, the ranges in averages among the different volume samples and methods for the last segmentation step (Sec. 3.1) are 113.8 ± 2.6 deg, 108.5 ± 4.7 deg, and 137.0 ± 5.1 deg for pore, YSZ, and Ni, respectively (Sec. 4.4). The ISAs computed by face counting and corrected with the factor of π/6 for close to spherical shapes were lower than those measured on smoothed triangular mesh by 22–23%, 26–28%, and 25–26% for the pore/YSZ, pore/Ni, and YSZ/Ni interfaces, respectively.

The spatial distribution of ISAs exhibits clear differences after SOFC and SOE operation. The profiles are close to uniform in the pristine “0 h” and the “SOFC” samples (Fig. 4(c)). Upon SOFC operation, energy minimization favors the decrease of ISApore/Ni, also because of highest mobility, whereas ISANi/YSZ and ISApore/YSZ remain unchanged after 15 kh. The trends are similar in both SOE sample volumes (Fig. 4(d)) with values toward the bulk of the electrode close to those in “SOFC.” ISApore/Ni remains uniform, whereas a decrease in ISANi/YSZ is mirrored by an increase of ISApore/YSZ. This observation is at a first appraisal consistent with Ni/YSZ contact losses caused by the partial reduction of ZrO2 or SiO2 but not confirmed by the visual inspection of the FIB-SEM dataset (see Sec. 4.1). Therefore, a Ni transport regime that requires detachment to trigger gas-phase transport and re-deposition of Ni volatile species on connected Ni near active TPBs did not necessarily dominate in “SOE 2 kh” and “SOE 10.7 kh.”

The ISA profiles in the sample “SOE*” differ from the other SOE samples. They are remarkably uniform in the Ni-depleted region x = 1.5–7.5 µm, with a large decrease of ISANi/YSZ up to values slightly lower than ISApore/Ni at corresponding locations. The difference with the other SOE samples may be related to the partial reduction of ZrO2 or SiO2, because the threshold cathodic overpotentials for their formation may have been reached during the extended period of 43 h. However, an approximately constant Ni surface to volume ratio is inferred from the profiles of Ni volume fraction, ISApore/Ni and ISAYSZ/Ni. This result does not follow expected history in the case of dominant competitive growth with propagation from the interface. The Ni accumulation at approximately x = 10 µm is characterized by a peak in ISANi/YSZ rather than ISAPore/Ni, which complies with the ranking of surface tensions. The location corresponds to the estimate of the region that was electrochemically active when the test was stopped, located between x = 5–10 µm, based upon the density of connected TPB in Fig. 4(e).

The TPB density profiles are close to uniform in the pristine and SOFC sample volumes (Fig. 4(e)). The isolated TPB density slightly increases near the YSZ electrolyte, despite close to uniform volume fractions and ISAs profiles. As expected, the total and connected TPB densities decrease after 15 kh, whereas the isolated subset increases, indicating a decrease in the ratio TPBconnected/TPBtot. The decrease in total TPB density after SOE operation near the YSZ electrolyte is more pronounced in the sample “SOE 10.7 kh” than “SOE 2 kh,” but this is not reflected in the decrease in connected TPB, except between approximately x = 1.5–2.5 µm. The total and connected TPB densities after 2 kh of SOE polarization are between those in the pristine “0 h” and SOFC samples. The profile of total TPB in “SOE*” is remarkably uniform, despite the decrease in ISAYSZ/Ni between x = 1.5–7.5 µm. The visual inspection of Figs. 1(c) and 3 and curvature measurements in Sec. 4.5 indicate that the reason is a re-arrangement of the Ni/YSZ interface rather than a decrease of Ni size between x = 1.5–7.5 µm because of competitive growth with the Ni accumulation region. The region x < 5 µm is passivated because of the absence of connected TPBs and the transport of oxygen ions contributes to increase ohmic losses.

The profiles in Fig. 4 clearly differ in samples exposed to anodic and cathodic polarization. They show similarities between “SOE 2 kh” and “SOE 10.7 kh.” The degradation does not seem to scale with operation time, even though the differences in current densities and temperature resulted in similar overpotentials. An estimation based upon the EIS data sensitivity in Fig. 5 suggests values in the range of 90–100 mV. It is further unclear whether or not the microstructure of “SOE*” represents the future evolution of “SOE 2 kh” and “SOE 10.7 kh.” Indeed, (i) visual inspection did not highlight extensive localized detachments between Ni and YSZ after SOE operation, (ii) the pattern in “SOE*” could not be tracked back in the subset of isolated Ni in “SOE 2 kh” and “SOE 10.7 kh,” and (iii) evidences of significant Ni spheroidization were found only in the subset of disconnected Ni in “SOE*.” Therefore, the driving forces for the degradation remain at this point unclear, which is the focus of the following sections.

### 4.3 Changes in Ni Dihedral Angle Predicted by the Electrowetting Theory.

Electrowetting and variations in the work of adhesion as a function of oxygen partial pressure [17] are two potential contributions to the differences in degradation between anodic and cathodic polarization. Figure 5(a) shows the dependence of θNi on overpotential computed by Eq. (3) ($ΔθNi=θNi−θNio$, where $θNio$ is the dihedral angle at the pzc). The estimated pzc at 800 °C is 0.009 V. It contributes, together with the capacitances dependence shown in Fig. 5(b), in significant dissymmetry in expected angle variations between cathodic and anodic polarization. The estimated uncertainty in the DRT measurements however indicates that questions remain on the exact position of the pzc, as well as predicted magnitude of change in θNi upon polarization in Fig. 5(a). The capacitances are also approximately one order of magnitude higher than those reported by the EIS study of Ni pattern electrodes with controlled variations in geometry by Doppler et al. [37]. The corresponding uncertainty is included in Fig. 5(a) for the electrocapillary curve at 800 °C.

The estimated overpotentials to which the cells were subjected during the tests are indicated by the translucent gray bars in Fig. 5(a). The ranges estimated using the closest available measurements of the Ni–YSZ charge transfer contribution measured by DRT in the button-cell tests are provided (see Sec. 3.2 and Ref. [18]). The analysis predicts a decrease in θNi by up to 4–6 deg in the electrolysis experiments, but variations after fuel cell operation should not be observed. In the case, electrowetting indeed contributes to the observed difference in between SOFC and SOE; a decrease in θNi is also expected for anodic overpotentials sufficiently larger than those included in the present sensitivity analysis.

The work of adhesion in metal/oxide systems is known dependent upon oxygen activity. The variation in contact angle between Ni and Al2O3 reported by Saiz et al. [17] within a temperature range of 1500–1650 °C, i.e., higher than the usual zero-stress temperature in solid oxide cell (SOC) [38], indicates a decrease of approximately 40 deg upon a change in p(O2) from 10−15 to 10−21 bar. The p(O2) under polarization estimated following the rapid calculations in Ref. [7] is therefore listed in the lower table in Fig. 5(a). In the case the behavior of the Ni/YSZ interface is similar to Ni/Al2O3 (the ranking of surface tensions reported in Ref. [17] is similar to the estimation for Ni–YSZ discussed in Sec. 4.2), lowest θNi are also expected under high cathodic polarization. However, significant changes due to feed composition variation only, i.e., under different local OCV conditions should be also observed, e.g., between 1.05 V (750 °C, 90% H2, and 10% H2O, p(O2) = 4.33 × 10−22 bar) and 0.90 V (750 °C, 20% H2, and 80% H2O, p(O2) = 3.92 × 10−19 bar). In the case of the experiment “SOE*,” the oxygen partial pressure is within the estimated threshold of 3.2 × 10−29±3 bar for sufficient dissolution of Zr in Ni at 850 °C leading to the formation of ZrO2 nanoparticles on the Ni surface [7]. The discussion in Sec. 4.1 indicates that such condition was also met during the steam supply failures of “SOE 10.7 kh.”

### 4.4 Three-Dimensional Dihedral Angles.

The probability density functions of dihedral angles measured on volumes segmented with the modified last filling step are close to symmetric with means and standard deviations of 112.8 ± 20.2 deg, 105.1 ± 19.7 deg, and 141.7 ± 21.4 deg for pore, YSZ, and Ni, respectively (not shown). They are in agreement with stereological measurements by spline fitting on X-ray nanotomography with a spatial resolution in the range of 50 nm in Ref. [35], which yielded 112 deg, 97 deg, and 151 deg, with variations of the means among samples of ±11 deg, ±11 deg, and ±4 deg. Three-dimensional measurements of dihedral angles using the level set method has been reported by Sun et al. [39]. The geometrical concept for the 3D measurements of dihedral angles by Sun et al. [39] is similar to the description in Sec. 3.1. The level set method is in contrast used to compute the six vectors normal to the interfaces at a TPB, before projection on the “most likely” direction of the TPB identified by formulation of a minimization problem. The results on FIB-SEM reconstructions of Ni–YSZ with isometric voxels of 34 nm are also close to the present study: 118.5–122.8 deg (pore), 92.7–98.3 deg (YSZ), and 142.7–147.4 deg (Ni) with however larger standard deviations of 38.9–40.9 deg, 44.5–46.2 deg, and 24.0–27.3 deg, respectively.

The average Ni dihedral angle listed above is overall higher than values reported from droplet measurements on polished YSZ or ZrO2 substrate [40,41], alumina substrate [17] or indirect measurements [42], which are in the range of 117–131 deg at 1250–1500 °C. For metal oxides systems exposed during extended periods to relatively high temperature compared to the oxide melting point, the response of the less mobile phase to the vertical component of the surface tension can result in the formation of ridges and a lower microscopic angle [17].

Besides aging effects, the physical information conveyed by a geometrical measurement approach on dataset with 10 nm isometric voxels is not straightforward. The relevant length scale for dihedral angles in Ni–YSZ with complex 3D heterogeneous microstructure within the temperature range of practical interest for SOC applications is difficult to assess. In solid–liquid systems or at high temperatures, dihedral angles measured by, for example, sessile drop experiments inform about interfacial energies [17]. In the present study, the length scale of interface points providing best fits ranges from 50 to 65 nm and it corresponds to 12–15% of the Ni available length measured on the same Ni–YSZ material in Ref. [25]. Therefore, the information provided by the proposed 3D dihedral angle measurement approach should be conservatively analyzed as a combination of interfacial energies and local morphology near the TPBs. Precise clarification is expected far-reaching and outside the scope of the present study.

As mentioned in Sec. 3.1, the last step of watershed segmentation causes offsets in average measured angles ranging from 1.6% to 6.6%, but all the spatial variations’ trends were found unchanged. The following analysis is therefore focused on relative variations in dihedral angles Δθi = θi/θib, where θib is the value measured in the region toward the bulk of the Ni–YSZ electrode. Figure 6 shows the average dihedral angle profiles along the x direction. The angles measured at the subset of connected TPBs are provided, except for “SOE*” because of the complete disappearance of connected TPB around x = 5 µm (see Fig. 4(e)). In the other sample volumes, the profiles for the subset measured at isolated TPBs are noisier but close to uniform and therefore not shown. Clear variations in angles are not observed in “0 h” and “SOFC” (Fig. 6(a)).

In the SOE samples, the decrease in θNi near the YSZ interface is close to 5 deg (Fig. 6(b)) with further continuation of the trend in the shaded area. It comports with the estimates from electrowetting theory in Fig. 5(a). The variations spread over approximately x = 1.5–5 µm, which is also in line with the expected overpotential profile. The change in θNi is accompanied by a decrease in θYSZ and an increase in θpore of similar magnitude. The mirroring of θNi by θpore follows intuition. In contrast, the variation in θYSZ, together with the observed decrease in ISAYSZ/Ni and Ni transport away from the interface (Fig. 4), suggests that the increase in wettability does not result in the spreading of Ni over YSZ. A potential reason is that TPBs are located on fine YSZ surface features, as observed qualitatively in Fig. 3, because of the higher Zener pinning force. Indeed, the present θYSZ measurements likely include information about the local YSZ morphology.

The standard Zener equation for spherical particles is RC,Ni = 4rYSZ/3fYSZ, where RC is the critical radius of the coarsening phase, r and f are the radius and volume fraction of the constraining particles, respectively. The dependence is qualitatively similar for cylindrical 2D shapes. It indicates that finer YSZ surface features provide higher pinning pressure, which may be further enhanced in the case of YSZ ridge formation. The variation of the pinning force FZ with the Ni dihedral angle expected from spherical simplification follows FZ = 2πcos(β)cos(πθNiβ), where β provides the angular position of the Ni/pore interface on the spherical constraining particles; the value providing maximum pinning force is assumed in the derivation of the Zener equation [43]. Upon an increase in θNi, the pinning force is reduced by a few percent. The displacement of TPBs along the interface may be further facilitated because of curvature-driven Ni transport until reaching another fine YSZ feature (see Fig. 3). Such displacement is expected to yield a decrease in ISAYSZ/Ni in the case of concave Ni/pore interface but not spheroidization, which is discussed in Sec. 4.5.

The trigger for Ni depletion can differ in “SOE*” compared with “SOE 2 kh” and “SOE 10.7 kh” (Sec. 4.2). The profiles of dihedral angles however still partially comply with electrowetting trends. A minimum in θNi mirrored by an increase in θpore is located around x = 10 µm (feature I in Fig. 6(a)), which corresponds well to the estimated region polarized last during the steam supply failure (Sec. 4.2). A decrease in θYSZ is in contrast detected only next to the YSZ electrolyte. It is currently unclear why it does not extend further until x = 10 µm. The reason for observations A, B, and C in Fig. 6 also remains unclear. There are however parallels among the profiles of θNi and θYSZ in samples “SOE*” and “SOE 10.7 kh,” which experienced both steam supply failures. As discussed later in Sec. 4.5, the history in the formation of the microstructural degradation of “SOE*” is not straightforward to establish.

### 4.5 Three-Dimensional Interfacial Shapes and Mean Curvature.

Variations in local curvature along the x direction perpendicular to the YSZ electrolyte are discussed in this section, because they are driving forces for Ni transport. Microstructural coarsening is indeed driven by the minimization of the free energy. The transport of material proceeds from regions characterized by high to low chemical potential. Assuming isotropic properties, the variation in chemical potential of an atom on a curved surface compared to another on a flat surface is proportional to the mean curvature [44,45]. Another reason is the further discussion of the relationship between θNi, θYSZ, and Ni/pore morphology.

Figure 7 provides profiles along the x direction of the areal fractions with interfacial shape classified according to the four zones in interfacial shape distribution plots [25,46,47]. The profiles are uniform in the pristine and SOFC samples (I and II). The YSZ/pore interface contains more concave (“dimple”) than convex (“bumps”) interfacial shapes without pronounced variations in areal fractions after 15 kh of SOFC operation. The Ni/YSZ interface comprises in contrast more convex than concave shapes. This indicates that Ni resides primarily on concave and saddle YSZ features, as anticipated from Sec. 4.1. As reported in Ref. [25], the Ni/pore interface comprises more concave than convex interfacial shapes after reduction. Microstructural coarsening upon 15 kh SOFC of operation causes an inversion between the areal fractions of convex and concave shapes.

The profiles in “SOE 2 kh” and “SOE 10.7 kh” show qualitative similarities that differ from “SOFC” (Figs. 7(III) and (IV)). The Ni/pore areal fraction with convex “dimple” shapes increases near the YSZ interface, which is mirrored in “SOE 2 kh” by the decrease of “bumps.” In “SOE 10.7 kh,” the increase is also compensated by the slight reduction of saddles κ1 > −κ2. Concurrently, the areal fraction of convex Ni/YSZ shapes increases. The trend suggests an increase in shapes resembling an hourglass with curved convex ends. Such a morphology with TPBs pinned on YSZ features are expected prone to pinch-off when subjected to a gradient of θNi decrease, with the consequence of lower Ni handle density (Table 2).

The changes in “SOE*” are most evident for the Ni/pore interface (Fig. 7(II)). Regions isolated after pinch-off yield a significant increase in the areal fraction of convex (“bump”) shapes to minimize their energy. The transition is compensated by the disappearance of κ1 < −κ2 saddles and to a lower extent of concave “dimples.” The trends near the YSZ electrolyte observed in “SOE 2 kh” and “10.7 kh” are not confirmed at around x = 10 µm, in contrast to the dihedral angle case. Their development may be alleviated by the accumulation of Ni (peak in Ni volume fraction around x = 10 µm in Fig. 4(a)). The areal fractions on the bulk electrode side is similar in “0 h,” “SOFC,” and “SOE*,” but differences are observed with and among “SOE 2 kh” and “10.7 kh.” The reasons for the overlap of the two Ni/YSZ areal fractions of saddles (Figs. 7(III-b) and (IV-b)) and for areal fractions of “bump” in “SOE 2 kh” and “10.7 kh” corresponding to the SOFC and pristine cases, respectively, will be the subject of future investigation.

Figure 8 shows the variations in probability density of the mean curvature H of Ni/YSZ and Ni/Pore interfaces along the x direction in selected volumes. The analysis is focused on differences in shapes rather than density of ISAs. Normalization is therefore applied slice by slice, i.e., stacks of univariate probability density functions are provided, not a bivariate probability density function. HYSZ/Pore is not depicted because it is considered a consequence of the evolution of the two other interfaces.

The H densities remain close to identical along the x direction in “SOFC” (Figs. 8(I-a) and (I-b)). The peak of HNi/YSZ is also located close to zero mean curvature, and the density is more populated at positive mean curvatures. The density of HNi/Pore is the narrowest and also shifted toward positive mean curvatures. The pristine sample exhibits similar uniformity along the x direction as “SOFC” (not shown). The HNi/Pore distribution is however narrower in the latter, because of microstructural coarsening.

Spatial variations are in contrast observed in “SOE 10.7 kh.” Toward the interface with the YSZ electrolyte, the HNi/Pore peak slightly shifts from approximately H = 0 µm−1 at x = 20 µm to negative mean curvature and the distribution spread increases (Fig. 8(II-b)). The trend is opposite but milder for HNi/YSZ (Fig. 8(II-a)) indicating that Ni rests last on more curved concave YSZ regions, which may be delimited by sharp features.

The difference between the mean curvature in the region with complete loss of Ni percolation and toward the electrode bulk in “SOE*” is clear in Fig. 8(III). The presence of close to spherical Ni regions results in a shift of the distributions HNi/YSZ and HNi/Pore toward positive mean curvature. The point of transition in H, as well as shapes (Fig. 7(II)), is around x = 10 µm, which corresponds to the peak in ISAYSZ/Ni (Fig. 4(c)). The additional Ni volume fraction between approximately x = 10–12.5 µm does not largely change the distributions.

### 4.6 Overview of Microstructural Changes Upon Cathodic Polarization.

Localized detachments or gaps between Ni and YSZ larger than the spatial resolution of the 3D electron microscopy data are not observed in “SOE 2 kh.” They are detected in “SOE 10.7 kh” but are not generalized and widespread (Sec. 4.1). Yet, Ni depletion seems more severe in the former case. The observation suggests that the transport regime that requires detachment to trigger gas-phase transport and re-deposition of Ni volatile species on connected Ni near active TPBs may not necessarily dominate in the conditions considered in this study. Loss of contact is often observed in 2D micrographs together with Ni depletion [6,7] but not reported systematically [8]. They may therefore not be a necessary condition in all cases, except if they are not observable after extended periods, because the formed Ni/pore interface is rapidly modified to minimize energy.

The measurement of 3D dihedral angles highlights a decrease in θNi in polarized region during electrolysis, which are in line with estimates from the electrowetting theory (Sec. 4.4). However, the expected effect is an increase in the work of adhesion and wettability that should promote the increase of ISANi/YSZ, hence Ni transport toward rather than away from the YSZ electrolyte. The opposite is observed in the present study (Sec. 4.2), i.e., a decrease in ISANi/YSZ compensated by ISAYSZ/pore. Uniform ISANi/Pore suggests a limited potential for further energy minimization by the modifications of the Ni/Pore interface, because of the inequality γPore/Ni > γNi/YSZ and similar values of ISANi/Pore than after 15 kh of operation. The decrease in ISANi/YSZ compensated by an increase in ISAYSZ/pore can also contribute to lower energy, depending upon the shapes (γNi/YSZ > γYSZ/Pore; Sec. 4.1).

The inspection of the three dihedral angles, interfacial shapes, and mean curvatures suggests that changes in morphology near TPBs may be a significant driving force for Ni transport away from the electrolyte, in the present Ni–YSZ microstructure and “SOE 2 kh” and “SOE 10.7 kh” conditions. A reduction in θNi under cathodic polarization at TPBs pinned by features on the YSZ scaffold and nearby concave Ni/pore shapes is expected to yield higher local curvature. The latter is a driving force for the transport of Ni away from polarized regions to minimize free energy. These trends are observed specifically near the electrolyte in Fig. 6(b) (θNi), Fig. 3 (TPB at a YSZ surface feature providing higher pinning force, qualitatively), Figs. 7(III) and (IV) (concave shapes), and Fig. 8(II-b) (increased |H|).

The above conditions do not correspond to spheroidization but to the regime of surface diffusion-controlled coarsening in two-phase high-genus structures, which proceed by ligament pinch-off induced by Rayleigh instability, such as observed in nanoporous gold [44]. The evidence for pinch-off is the decrease in the Ni handle density (Table 2). In the present three-phase case, the balance between the pinning pressure on TPBs exerted by YSZ and mean curvature minimization is likely to evolve upon necking. The relocation of TPBs is therefore possible, which can result in the observed decrease in ISANi/YSZ. The Zener force equilibrium for incoherent interfaces indicates a decrease in the pinning force for lower θNi. TPBs may therefore move until reaching another finer feature on YSZ that provides sufficient pinning force. A potential evidence of this mechanism is the observed decrease in θYSZ (Fig. 6(b)) and slight shift of HNi/YSZ toward positive values.

A salient question is whether or not SOE* is representative of the further evolution of “SOE 2 kh” and “10.7 kh.” The SOE* microstructure degradation presents at a first appraisal the pattern discussed in Ref. [6] and was subjected to high overpotential for extended periods that lead to the reduction of ZrO2 and SiO2. The history of its evolution is difficult to infer from a single sample volume, but it is almost certain that the loss of Ni percolation initiated at the interface and propagated afterwards. Yet, clear gradients in Ni volume fraction, ISA, phase size, surface to volume ratio (Fig. 4), and to a lower extent mean curvature (Fig. 8) are not detected. Furthermore, competitive growth apparently resulted in isolated Ni regions that resemble abnormal growth (Fig. 3), which may have formed either after the loss of percolation by pinch-off or somehow by the displacement of the Ni accumulation.

The electrowetting theory predicts a decrease in Ni dihedral angle at both sufficiently large cathodic and anodic overpotentials. The capacitance measurements in the present study indicate a shift of the pzc with respect to OCV, with as a consequence, negligible changes in θNi under the range of SOFC conditions considered here. The present results therefore warrant a study of limiting cases under anodic potential.

## 5 Conclusions

Microstructural changes in Ni–YSZ near the interface with the YSZ electrolyte were examined by 3D electron microscopy. The focus was on the spatial variations of properties upon anodic (SOFC) and cathodic (SOE) polarization during up to 15,000 h and 10,700 h, respectively. The migration of Ni away from the electrolyte was detected after SOE operation. The consequence is a decrease in total and connected TPB density within approximately the first 4 µm from the electrolyte, up to 10 µm following exposition to high cathodic overpotential during 43 h because of steam supply failure. Localized loss of contact between Ni and YSZ was seldom observed and only in samples subjected to steam supply failures. Therefore, they may not be necessary to trigger Ni depletion in all cases. In the conditions of the present study, Ni transport under cathodic polarization seems promoted by changes in the morphology near the TPBs. The metric and topological properties were in contrast close to uniform in the pristine sample and after 15,000 h of SOFC operation.

A method for the 3D measurement of dihedral angles was developed. A decrease in the Ni dihedral angle is detected in approximately the first 4 µm from the YSZ electrolyte in SOE. The trend comports with predictions from electrowetting theory. The dependence of interfacial capacitance upon overpotential measured by DRT on button-cell experiments indeed yields a dissymmetry in the electrocapillary curve between SOFC and SOE conditions.

Curvature analysis detected a shift of the probability density of mean curvature after cathodic polarization, from close to zero or slightly positive values after SOFC operation, to negative ones and increased dispersion near the YSZ electrolyte. This corresponds to a transition of Ni/pore interfacial shapes from mainly convex to concave, which is opposite to spheroidization.

The analysis therefore suggests that a decrease in the Ni dihedral angle at TPBs pinned by features on YSZ surface, along with nearby concave Ni/pore shapes, promotes microstructural evolution that proceeds by ligament pinch-off controlled by Rayleigh instability. The related increase in absolute mean curvature near the YSZ interface is a driving force for outwards Ni transport. Upon pinch-off, competitive growth between disconnected and contiguous Ni regions by gas-phase transport of volatile species and re-deposition near active TPB sites is also expected to contribute.

Advances in the understanding of the effects of microstructure and operation conditions on Ni depletion are required for the design of durable SOC electrodes. The present study highlights that a focus on the wettability of Ni over YSZ and dependence upon experiment history is required to provide guidance beyond the spatial control of overpotential distribution in a SOC stack, modification of electrocapillary characteristics by, e.g., Ni doping and microstructural design that maximizes the density of pinning sites in YSZ. The dissymmetry in behavior between anodic and cathodic polarization may further highlight trade-offs in microstructural design for reversible systems for energy conversion and storage.

## Acknowledgment

The research received funding from the Fuel Cells and Hydrogen 2 Joint Undertaking under grant agreement nos. 735692 (project name: CH2P), 735918 (project name: INSIGHT), 731224 (project name: BALANCE), 699892 (project name: ECo), and 825027 (project name: AD ASTRA). This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation program and from the Hydrogen Europe and Hydrogen Europe Research. Swiss partners in these H2020 projects receive funding from the Swiss Secretariat in Education, Research and Innovation (SEFRI) under Contract Nos. 16.0199 (Insight), 16.0223 (CH2P), 16.0178 (Balance), and 16.0041 (ECo). This work was also supported by the Swiss EOS Holding Ph. D. Thesis funding (G. Rinaldi) (Contract No. 2014-0365). The authors would like to thank VTT, EIFER, as well as Dr. Z. Wuillemin, Dr. D. Montinaro, J. P. Ouweltjes, and Y. Antonetti (SOLIDpower) for providing the samples from short stack and segmented-cell testing, Dr. A. P. Cocco (Army Research Laboratory, Adelphi, MD) for the discussions on the curvature and genus measurements, and S. Joris and N. Accardo (EPFL) for assistance in the sample preparation.

### Appendix A

The Ni–YSZ electrode and the support material were co-cast and sintered with the YSZ electrolyte. The GDC compatibility layer and lanthanum strontium cobalt ferrite (LSCF)-based oxygen electrode were screen-printed and sintered afterwards. The sintering temperatures were in the range of 1350–1400 °C and 1250–1300 °C for the NiO-YSZ/YSZ bilayers and for the compatibility layer, respectively. The thicknesses of the layers in the sintered cell were about 240 μm for the support, 8–10 μm for the electrolyte, 6–8 μm for the compatibility layer, and 50 μm for the oxygen electrode.

### Appendix B

A six-cell stack was tested under steam electrolysis for 2000 h at 750 °C and −0.775 A cm−2 with air and feed (90% H2O and 10% H2) flows each of 12 N mL min−1 cm−2, resulting in a steam conversion of 50% (“SOE 2 kh” in Table 1). The cell active area was 80 cm2. The average stack potential degradation rate during constant current density polarization was almost null, with the first 1500 h even characterized by a slight reduction of the measured voltage (−0.7% kh−1). The available IV characteristics data do not allow a precise analysis of the contributions to the total stack degradation. The measured improvement may be related to the electrical contact, which can further partially mask the electrode and/or cell degradation.

Another six-cell stack was tested under steam electrolysis for 10,700 h at 720 °C with air and feed (90% H2O and 10% H2) flows of 12 N mL min−1 cm−2 and 9.3 N mL min−1 cm−2, respectively (“SOE 10.7 kh” in Table 1). The cell active area was 48 cm2, with a lanthanum strontium cobaltite (LSC)-based oxygen electrode deposited on the standard Ni–YSZ/YSZ/GDC half-cell. The current density was 0.6 A cm−2 (steam conversion of 50%) for the first 3250 h and lowered to 0.5 A cm−2 for the remaining of the test. Cell potential and IV characteristics were measured. The degradation during the initial 2000 h was characterized by a potential increase of 4% kh−1, followed by stabilization below 0.5% kh−1. During the test, four steam supply interruption incidents were occurred. The test was stopped after the last one. Detailed information on the performance measurements and 2D microscopy analyses of the cell layers comprising SEM–EDS, scanning transmission electron microscopy-EDS, and selected area electron diffraction are available in Ref. [5], as well as 3D FIB-SEM/EDS in Ref. [10].

A two-cell segmented version of the 80 cm2 design was operated in SOFC mode for 15,000 h (“SOFC 15 kh” in Table 1). The second cell was divided into 20 rectangular segments (four lines of five segments along the flow path) of similar areas (3.17 cm2 and 3.97 cm2) that can be polarized individually [19]. The test was performed at 750 °C with 95 N mL min−1 cm−2 on the air side and 6 N mL min−1 cm−2 on the fuel side (60% H2 and 40% N2). The segments were first polarized for 800 h, then left at OCV until 4500 h, besides interruptions for short-term testing. Potentiostatic control was then applied for a large share of the remaining test time (cumulated time under polarization exceeding 8500 h) to ensure equipotential conditions over the cell, representative of stack operation for this design. The potential was set at 0.8 V most of the time, corresponding to an average current density of 0.3 A cm−2 (58% fuel utilization (FU)). Segment 12 was considered for the present study. It is located on one of the two central lines at the second position along the flow path. From 5000 h, EIS was performed about every 2500 h. The Ni–YSZ electrode charge transfer resistance measured by DRT increased from 0.075 to 0.1 Ω cm−2 under a current bias of 0.13 A cm−2 between 5000 h and 13,800 h, and then stabilized.

A schematic view of the experiments is provided in Fig. 9. The evolution of the segment current density is provided for the experiment “SOFC” with potentiostatic control, because it differs from the cell average.

### Appendix C

The button cell (“SOE*” in Table 1) was a disk with a diameter of 60 mm with an active area of 12 cm2. The cell is placed in a ferritic metallic setup that is partially coated with an inert spinel. A gold mesh and a Ni foam are used for current collection. Gas is fed using alumina tubes to limit contamination. The flow configuration is radial in both compartments, which are separated by a glass-ceramic sealant. EIS measurements are performed with a Zahner ZENNIUM Electrochemical Workstation with an external potentiostat (PP201) for currents higher than 2.5 A, with twisted current and voltage wire pairs to reduce the mutual inductance effect.

The “SOE*” sample sustained severe degradation because of steam supply failure after 560 h of operation in co-electrolysis at 750 °C and 0.8 A cm−2 with a feed flow of 12.5 N mL min−1 cm−2 (65% H2O, 25% CO2, and 10% H2) and same air flow. Upon the start of steam supply failure, the cell voltage increased during 33 h until reaching a plateau at 1.84 V for 10 h. During this event, the temperature variations measured by thermocouples at the center and edge of the cell were of 5 °C. The cell was then maintained at OCV interrupted for electrochemical characterizations or recovery attempts during 180 h at 750 °C, 680 h at 800 °C, and 298 h at 750 °C.

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