Quanti ﬁ cation of the degradation of Ni-YSZ anodes upon redox cycling

(cid:129) Quanti ﬁ cation of redox damage by coupling 3D tomography, EIS and nanoindentation. (cid:129) YSZ fracture, Ni detachment and agglomeration led to irreversible mechanical damage. (cid:129) Ni nanoparticles obtained upon redox cycling improve electrochemical performance. (cid:129) Loss in TPB density estimated by model matches 3D FIB-SEM data. Ni-YSZ anodes for Solid Oxide Fuel Cells are vulnerable to microstructural damage during redox cycling leading to a decrease in the electrochemical performance. This study quanti ﬁ es the microstructural changes as a function of redox cycles at 800 °C and associates it to the deterioration of the mechanical properties and polarisation resistance. A physically-based model is used to estimate the triple-phase boundary (TPB) length from impedance spectra, and satisfactorily matches the TPB length quanti ﬁ ed by FIB-SEM tomography: within 20 redox cycles, the TPB density decreases from 4.63 μ m − 2 to 1.06 μ m − 2 . Although the polarisation resistance increases by an order of magnitude after 20 cycles, after each re-reduction the electrode polarisation improves consistently due to the transient generation of Ni nanoparticles around the TPBs. Nonetheless, the long-term degradation over-shadows this transient improvement due to the nickel agglomeration. In addition, FIB-SEM tomography reveals fractures along YSZ grain boundaries, Ni-YSZ detachment and increased porosity in the composite that lead to irreversible mechanical damage: the elastic modulus diminishes from 36.4 GPa to 20.2 GPa and the hardness from 0.40 GPa to 0.15 GPa. These results suggest that microstructural, mechanical and electrochemical properties are strongly interdependent in determining the degradation caused by redox cycling.


Introduction
The solid oxide fuel cell (SOFC) is currently one of the most promising energy conversion devices, offering a high operating efficiency with minimal air pollution. Ni-YSZ cermets are the most commonly used SOFC anode materials, offering a combination of relatively low cost and good performance. However, the material can degrade when subject to certain operating conditions, such as redox cycling during operation [1][2][3][4][5].
Past work has often concentrated on Ni-YSZ microstructural evolution by annealing for long periods of time. It is commonly agreed that under these conditions the accompanying performance loss is caused by an increase in average Ni particle size and a decrease in active triple phase boundary (TPB) length per unit volume. The active TPB is the theoretical contact perimeter between percolating Ni, YSZ and pore phase, where fuel oxidation and charge transfer occur [6][7][8]. Ni-YSZ anodes are typically fabricated by mixing YSZ and NiO particles, which are subsequently reduced by H 2 during the fuel cell start-up. Reduction of the NiO-YSZ involves a quasi-reversible dimensional shrinkage of 41.6% by converting NiO to Ni. However, Ni is strongly sensitive to oxidising atmospheres, such as those present during operation at high fuel conversion or during emergency shut-down, which can rapidly convert Ni into its oxidised state, involving a 71.2% volume expansion. These Ni volume changes result in irreversible microstructural damage, which include bulk deformation of the microstructure, commonly leading to electrolyte cracking [1,2,9]. The size changes of Ni particles were suggested to be due to the agglomeration of metallic nickel [10] and the formation of porosity upon reduction [11]. These parameters also show a direct relationship with the change of the effective TPB length [7]. The increase in Ni particle size could lead to a corresponding drop of TPB density and growth of polarisation resistance [12], moreover, due to the potential loss of Ni-Ni contact, the electrical conductivity can decrease as well.
Focused ion beam (FIB)-SEM tomography [13,14] allows the microstructural change seen in Ni-YSZ electrodes after redox cycling to be quantified through ex-situ analysis, due to the good phase contrast between Ni and YSZ, and the relatively high resolution of the technique. From the 3D tomography reconstructed microstructure, parameters such as volume fractions, interfacial areas, TPB length and tortuosity factors can be quantified [9,[15][16][17][18][19]. In terms of electrochemical performance, electrochemical impedance spectroscopy (EIS) is commonly used, as it is an effective technique to follow electrochemical changes in real time [20][21][22]. It has been found that after redox cycling, polarisation resistance increased due to TPB length reduction and Ni surface area decrease [5,9,19]. The relationship between electrode microstructure properties and electrochemical impedance response has been recently quantified by Bertei et al. [24], using a physically-based model [25,26].
Knowledge of the behaviour of Ni-YSZ is also important for the mechanical design of the SOFC. The mechanical properties of Ni-YSZ have been widely studied with a wide range of techniques. The Impulse Excitation Technique (IET) was used to determine parameters in thick Ni-YSZ electrodes, 300 μm or above, comparing elastic modulus with porosity, Ni content and sintering temperature [1,[27][28][29]. The empirical relationship of porosity and elastic modulus of Ni-YSZ has been reported and validated in several studies [29,30]. A comparison of different mechanical properties determined by these experimental techniques has been undertaken [31]. The nanoindentation technique has been developed and used to study the response of the material at smaller length scales [32,33]. However, there is currently no study available on the nanoindentation characterisation of the micromechanical properties of porous Ni-YSZ films upon redox cycling.
This paper presents an integrated study of the impact of redox cycling on the microstructure, electrochemical performance and mechanical properties of porous Ni-YSZ cermets, using a variety of methods such as 3D tomography, nanoindentation, EIS and modelling to develop an improved understanding of the coupled nature of anode behaviour under such redox cycling conditions.

Fabrication of NiO-YSZ cell
Ni-YSZ symmetrical cells were prepared with a NiO-YSZ slurry made from NiO and YSZ powder (Nexceris, USA, 60 wt% NiO, 2.45 m 2 g −1 surface area) mixed with terpineol, binder (Hercules ECN-7) and dispersant (Hypermer KD15). A ceramic triple-roll mill was used to homogenise the slurry and eliminate agglomerates above 5 μm. The slurry was deposited by tape casting on an 8YSZ electrolyte (Nexceris, USA, Ø = 2 cm, 250-300 μm) and fired at 1200°C for 2 h in air. The final electrodes had a thickness of 25-30 μm and 2 cm 2 geometric surface area.

Redox cycling
Redox cycling was carried out by sequentially exposing the cell to two different gas streams, air and diluted hydrogen (a mixture of 5 vol % H 2 and 95 vol % N 2 ), both humidified with 3% vol H 2 O, with a flush of N 2 in between. The process was carried out at 800°C within a quartz tube furnace. For each redox cycle, the samples were kept in air for 1 h, flushed for 10 min in N 2 and then reduced in H 2 for approximately 5 h, as schematically reproduced in Fig. 1. This procedure, already adopted by Shimura et al. [9], rather than mimicking any specific accidental or emergency situation, represents a benchmark scenario for reproducible redox cycling measurements around the typical working condition of an SOFC.

Characterisation procedure
EIS measurements were performed within a frequency range of 10 6 Hz-10 −1 Hz with 20 mV AC amplitude using a potentiostat (Autolab PGSTAT302N), every 30 min during the reduction process in diluted hydrogen atmosphere. The measurement data were fitted to an equivalent electrical circuit, shown in Fig. 2, by using ZView3.5 (Scribner Associates Incorporated). The active TPB density was estimated from the intermediate-frequency polarisation resistance R 2 using a validated physically-based model [24], as follows: where the factor 2 represents the two electrodes for the symmetric cell, t an is the anode thickness, F the Faraday constant, R the gas constant, T the operating temperature in K, k eff is the effective conductivity factor Fig. 1. Representation of redox cycling procedure. Impedance spectra were taken during each reduction process as a function of time. Fig. 2. Impedance spectra recorded after 0, 5, 10, 15, 20 redox cycles at 800°C, 2 h after the introduction of wet 5 vol % H 2 , AR represents as-reduced, R5 represents 5 redox cycles, R10 10 redox cycles and so on. The inset shows equivalent circuit fitting result. R 1 , R 2 , R 3 represent the high-frequency intercept resistance, intermediate frequency resistance and low-frequency resistance respectively; CPE 2 , CPE 3 represent constant phase element for the corresponding frequency 28 .
of the YSZ phase, σ io is the ionic conductivity of YSZ, i 0 is the exchange current density per unit of TPB length calculated according to Bieberle et al. correlation [34], L TPB is the active TPB density per unit of electrode volume. Electronic ohmic losses were omitted because proved to be negligible as long as Ni phase percolates [24,35], the parameters k eff , i σ , io 0 and YSZ volume fraction used in this simulation were assumed to be constant with time during reduction and equal to the as-reduced conditions. It is assumed that polarisation degradation is caused solely by a decrease in TPB density [24]. L TPB can be evaluated by using Eqs.
A scanning electron microscope (LEO, Gemini 1525 FEGSEM) was used to study the surface and cross-sectional microstructure of samples before and after redox cycling. Tomography was used to gain insight into the resultant microstructural changes, using a FIB-SEM dual-beam instrument (Auriga Cross Beam, Zeiss) for 3D reconstruction. The crosssection of the anode was repeatedly milled by FIB and observed by SEM with approx. 25 nm between each slice. The series of FIB-SEM images were processed and segmented in Avizo 9.0.0 image processing software (Visualization Science Group, Mérignac, France) and the 3D microstructure of Ni-YSZ samples was reconstructed.
The porosity, surface areas and active TPB density were evaluated from the segmented 3D datasets. The tortuosity and effective conductivity factor of the YSZ and Ni phases were calculated using the open source Matlab application TauFactor [36]. All the calculations were made on a voxel-basis. This advanced characterisation allowed for the quantification of microstructure parameter changes between samples after redox cycling.
The mechanical properties of five samples after 0(AR), 5(R5), 10(R10), 15(R15) and 20(R20) redox cycles were measured by nanoindentation (NanoTest Platform, Micromaterial, UK) at room temperature. A sharp tip was indented into the material surface and the material response during the loading and unloading was recorded. Over 200 indentations per sample were carried out with a Vickers diamond tip with a 200 μm interval to obtain a statistically representative dataset and avoid outliers due to inhomogeneities.
The elastic modulus, E, and hardness, H, were calculated from the load-depth curves using Oliver-Pharr analysis: where v is the Poisson's ratio of the specimen, which is 0.387 approximately [37]; E i and v i are the elastic modulus = 1220 GPa and Poisson's ratio = 0.07 of the diamond indenter, respectively; M is the indentation modulus, β is a geometrical correction factor, which is 1.055 for a Vickers diamond tip [38]; P max is the maximum load applied and A is the contact area between indenter and material, which is, 2 for a Vickers indenter, where h c is the indentation loading depth.

Electrochemical degradation on redox cycling
The electrochemical degradation of the cell was quantified by measuring the impedance upon introduction of hydrogen during the redox cycles. Five selected redox cycles are presented in Fig. 2: a minor change of ohmic resistance (R 1 ), a significant increase in polarisation resistance (R 2 ) and a relatively steady diffusion resistance (R 3 ) are observed. This is consistent with work performed by Laurencin et al. [28]. The inset shows an example of fitting with the equivalent circuit, performed within the frequency range 10 6 -10 −1 Hz. Fig. 3 presents the resistances extracted from the fitting. The ohmic resistance (R 1 ) shows a relatively steady performance during 20 redox cycles, apart from a sharp improvement after 14 cycles and a uniform performance afterwards. This corroborates that there has not been a significant degradation of R 1 , which mainly reflects the resistance of the YSZ electrolyte, which is 0.393 Ωcm 2 based on a calculation for a 250 μm thick YSZ pellet, with 2 cm [2] area at 800°C [39]. Not surprisingly the measured ohmic resistance is higher than the calculated electrolyte ionic resistance (compare black squares with the pink line in the lower section of Fig. 3) as the measured ohmic resistance takes into account additional interfacial and electrode ohmic losses. An improvement in contact resistance between anode surface and Pt mesh may be responsible for the sharp change in R 1 observed at cycle 15. The diffusion resistance (R 3 ) is attributed to losses by gas conversion and gas diffusion [5] occurring outside the porous electrode microstructure [24], the minor change after cycle 8 may be caused by accidental rig movements during the testing. Notably, R 1 and R 3 show sudden changes only, which are uncorrelated from the change in R 2 . Finally, the polarisation resistance (R 2 ) shows in general a continuous increase after redox cycling. Changes in R 2 are mostly considered to be related to charge transfer and the activation overpotential of the fuel oxidation process at the TPB as observed also in Ni-infiltrated scaffolds [26]. As pointed out by Laurencin et al. [28], the characteristic frequency associated to R 2 remained relatively constant upon redox cycling, suggesting that the increase in R 2 could be due to a mechanical damage along the electrochemical interfaces, that is, to a loss in effective TPB length. Another interesting feature is that, within each reduction process, R 2 shows a good initial value followed by a rapid degradation before approaching a more stable value, similar to observations by Shimura et al. [9] in cermet anodes as well as by Bertei et al. in nanostructured anodes [26]. By comparing between two adjacent cycles, it appears that R 2 shows significant performance improvement at the start of a new reduction process. This phenomenon suggests that the reduction of the NiO leads to a significant increase in TPB density at the initial stage, but as the annealing proceeds, the TPB length reaches a more stable level. Bertei et al. suggested this might be due to the rapid evolution of the nanometric roughness of Ni surface generated in-situ during the reduction process [26].
A physically-based model was used to estimate the active TPB density from the evolution of R 2 , under the assumption that the electrochemical performance changes are directly linked to the TPB density only [24]. Fig. 4 shows the TPB density estimated by the electrochemical model for the as-reduced sample and after 5, 10, 15 and 20 redox cycles. These data points are compared with the active TPB density evaluated from tomographic reconstruction at selected points. Within any redox cycle, the model predicts a fast decrease in TPB density within 2 h, followed by stabilisation. The Ni surface roughness and nanoparticles observed using SEM (see next section) may contribute significantly to the TPB evolution. Although not exhaustively proved yet, it could be proposed that, at an early stage, NiO-Ni deformation or asymmetrical reduction processes lead to a rough surface [26] and generate a large number of Ni nanoparticles [40]. This surface roughness and the nanoparticles attached to the percolating Ni and YSZ frameworks can lead to a significant increase in TPB density. However, these features start to agglomerate with other Ni particles or form volatile Ni species [41], resulting in a subsequent rapid drop in TPB density. This rapid evolution of TPB density has also been reported in nano-infiltrated anodes [25,26]. For the samples with more redox cycles, the initial degradation tends to be slower, as Ni particles are comparatively bigger (see next section). Overall, after stabilisation, the TPB density of samples shows a decreasing trend versus redox cycle number. This may be caused by Ni agglomeration during the overall redox cycling process.
The comparison of the active TPB density between FIB-SEM tomography and the model prediction shows a good consistency for the AR, R5 and R10 samples, see Fig. 4. For the samples after 15 and 20 redox cycles, as the number of redox cycles increases, the difference between the 3D tomography data and the electrochemical model values increases. This is because the complex microstructural changes caused by redox cycling may not all be detected by 3D tomography since Ni nanoparticles, nano surface roughness and cracks may be beyond the resolution level, as shown in Fig. 5 and extensively discussed by Bertei et al. [26]. Moreover, the electrochemical model attributes all the degradation to the decrease in TPB density, while cracks in the YSZ framework would reduce the effective ionic conductivity, which is considered constant in the model. Thus, the discrepancy of values for R15 and R20 suggests that the YSZ cracks, generated during redox cycling, led to a decrease in the effective ionic conductivity, not considered by the electrochemical model.

Microstructural characterisation on redox cycling
The microstructural characterisation was carried out with both SEM image analysis and 3D tomography reconstruction. Five different samples, with various numbers of redox cycles, were tested. The approximate time scale of sample observation points is indicated in Fig. 3 using black crosses. Fig. 5 shows the SEM image of the Ni-YSZ electrode. In the as-reduced sample (a), detachment between Ni and YSZ particles is observed as a consequence of Ni volume shrinkage after reduction. The bottom two images show the SEM top surfaces of redox cycled samples. Ni particle agglomeration is observed, that could result in porosity increase. More interestingly, a growing number of Ni nanoparticles appeared on the Ni surface and at the boundary between Ni and YSZ. In addition, no impurities were noticed beyond the detection limits of energy dispersive X-ray spectroscopy (EDX). This is consistent with the Ni microstructure change reported by Hanasaki et al. [3]. The Ni nanoparticles located at the boundary between Ni and YSZ can significantly extend the TPB length, which is consistent with the increase in TPB density seen in the early stage of each reduction process as estimated by the model from the analysis of EIS data (Figs. 3 and 4). In addition to this, cracks are found between YSZ grain boundaries, especially after a large number of redox cycles (> 10). This could be due to the mechanical damage caused by Ni volume expansion during reoxidation, since this type of crack does not appear in the as-reduced samples. By constantly breaking the YSZ grain boundaries around Ni particles, the YSZ framework within the electrode results in smaller isolated regions, thus losing its ionic transport path and supporting function. This contributes to the steady increase in polarisation resistance as well as to the decrease in the material hardness and elastic modulus as discussed in the next section.
The microstructural characterization is complemented by 3D tomographic reconstruction. The middle column of Fig. 6 shows the crosssectional images from FIB-SEM. The Ni particle (light grey) agglomeration is confirmed here, as well as the trend of the YSZ structure to be broken into smaller pieces, as discussed above. However, due to the limitation of FIB-SEM image resolution, the Ni nanoparticles cannot be detected. This is because the average voxel size of these FIB-SEM images is around 20-25 nm, which is about 2-5 times the diameter of the Ni nanoparticles observed with SEM [26]. The presence of small nanoparticles around the TPB may also cause errors in the microstructural tomographic quantification because the colour of each pixel around the TPB is highly affected by the surrounding Ni nanoparticles, which makes image segmentation harder in redox-cycled samples.
A tomographic microstructural reconstruction was carried out for each sample [42,43]. The original images were segmented into three different colours (Blue: Ni, green: YSZ, grey: pore phase), as shown at the right-hand side of Fig. 6. The calculated microstructural parameters are shown in Table 1. The anode porosity, initially similar to that of anode-supporting layers [44,45], increases with redox cycling, consistent with the previously-reported result from Holzer et al. [46]. In addition, the TPB density decreased as redox cycles are repeated. The Ni surface area per volume decreased after the redox cycles, which corroborates the increase in Ni particle size observed from SEM and FIB-SEM images. The interfacial area between Ni and YSZ also decreased, suggesting that the detachment caused by Ni volume shrinkage during reduction can be one reason for the decrease in effective TPB density. Therefore, the quantitative 3D tomographic analysis confirms the trends detected with SEM analysis regarding Ni agglomeration, loss in TPB density and cracking of the YSZ network upon redox cycling.

Mechanical properties after redox cycling
The elastic modulus and hardness of each sample were measured by using the nanoindentation technique. The load-depth curve of redoxcycled samples are plotted in Fig. 7-a. In this experiment, the maximum indent load is 115 mN, producing a maximum indentation depth between 3.5 and 5.0 μm. This indentation depth is kept to less than 20% of the electrode thickness (25-30 μm), so that the substrate effect on the measurement is negligible [47]. Having used a symmetric setup rather than an anode-supported configuration makes the electrode constrained on one side by the stiffer YSZ substrate. Thus, the propagation of the mechanical stresses, internally generated within the anode by redox cycling, affects mainly the anode itself, without causing cracking of the YSZ electrolyte and subsequent stress relaxation. Therefore, the symmetric setup allows for the focusing on the intrinsic mechanical behaviour of the porous anode alone, although the stiffness of the thick YSZ electrolyte may slightly amplify the internal anode cracking if Fig. 5. a) Top-surface SEM images of an as-reduced Ni-YSZ electrode showing the detachment between Ni and YSZ caused by Ni volume shrinkage after reduction, leading to a relatively large space in between; b) Top-surface SEM images of Ni-YSZ electrodes after 5 redox cycles showing the crack along the YSZ grain boundaries, with approximately gap of 10 nm and the Ni nanoparticles c) Top-surface SEM images of Ni-YSZ electrodes after 10 redox cycles showing YSZ grain fall off from its framework and Ni surface roughness, agglomeration along with Ni nanoparticles. The clear shift in the load curves indicates that the samples with more redox cycles display lower hardness since the same loading force results in greater penetration depth. Since the nanoindentation has a strong sensitivity to individual dislocation interactions, oscillations in each loading curve were observed. This is caused by a complex combination of factors, such as mechanical instabilities, development of dislocation networks, and incipient plasticity [19]. The variance of these oscillations shows that the sample with more redox cycles has a steadier loading curve. Probably, the redox cycling promoted the fragmentation of YSZ framework, which simplified the disorder interactions between the Ni-YSZ composite and indenter, as observed from both SEM and FIB-SEM. Fig. 7-b and c show the nanoindentation results for elastic modulus and hardness of the electrodes as a function of the number of redox cycles. The results show a clear decreasing trend in both the elastic modulus and hardness, accompanied by a different standard deviation which reflects the combined effects of surface roughness, densification and internal structure changes. With different indentation depths, the generally larger scatter in the data might be related to the greater roughness of the films when compared with the bulk samples. Nevertheless, for both the elastic modulus and the hardness, the standard deviation first increases until 10 cycles and then decreases, indicating that more reproducible data were collected after 20 redox cycles. The maximum in data scattering around 10 cycles can be explained by considering the progressive fragmentation of the microstructure in comparison with the indentation depth, which is 3-5 μm. In the asreduced sample, the microstructure is macroscopically homogeneous, although Ni-dense and YSZ-dense regions are present at the μm scale as evident in Fig. 6, causing a relatively narrow standard deviation. As the number of redox cycles increases to 5 and 10 cycles, cracks separate relatively big and stiff YSZ fragments from softer Ni regions (Fig. 5), thus the microstructure becomes more locally heterogeneous, as revealed by a larger standard deviation in the mechanical properties. As the redox cycling proceeds (i.e., 15 and 20 cycles), the microstructure is fragmented into pieces smaller than the indentation depth (5 μm), so that the mechanical properties appear to be more spatially homogeneous, resulting overall in a lower standard deviation of mechanical properties (Fig. 7). Fig. 8 shows the measured Ni-YSZ elastic modulus versus porosity compared with two empirical fitting formulas. The black dashed line represents a linear fitting of porous Ni-YSZ samples prepared by varying the porosity by changing the reduction temperature between 600 and 1000°C as reported in the literature [29]. The blue dashed line shows an exponential fitting of a porous tape cast Ni-YSZ electrode, sintered at 1400°C in air for 2 h, as reported by Radovic et al. [27]. The dense elastic modulus values E 0 and porosity constants b are listed in Table 2. While the data points obtained in this study (red symbols) cannot be fitted by a linear correlation, the exponential equation allows for a good fitting once the porosity constant is increased to b* = 3.813 (see the red dashed line in Fig. 8). This increase in porosity constant could be related to differences in the measuring techniques and input parameters as well as to the microstructural changes occurred during the redox cycling. In fact, redox cycling does not increase the porosity only, but it also leads to the internal YSZ framework break down, Ni agglomeration and change in pore shape, resulting in an elastic modulus smaller than that expected for non-redox cycled electrodes.

Conclusions
The electrochemical and mechanical deterioration of Ni-YSZ anodes after up to 20 redox cycles was quantified by a combination of FIB-SEM tomography, impedance spectroscopy, nanoindentation and modelling.
Upon redox cycling the hardness changes from 0.4 GPa to 0.15 GPa and the elastic modulus from 36.4 GPa to 20.2 GPa. This can be qualitatively associated to observations in the SEM: fractures at the YSZ grain boundaries, Ni-YSZ detachment, continuous nickel agglomeration and increasing porosity after each redox cycle, all of which seem to be irreversible. The effect of porosity in the mechanical properties can be suitably understood with the empirical elastic modulus-porosity exponential relation where only the porosity constant was re-fitted.
The electrochemical degradation was followed by impedance spectroscopy and a physically-based model was used to infer the active TPB length from the temporal evolution of the polarisation resistance, revealing a good matching with TPB density obtained through FIB-SEM tomography. In particular, the model fits very well the initial, 5 redox and 10 redox samples, with a less satisfactory fit for higher redox cycles due to the changes in the effective conductivity of the composite caused by YSZ fractures and nickel agglomeration. It is also observed that the polarisation resistance decreased temporarily by a factor ca. 2 upon each re-reduction, probably due to the transient generation of Ni nanoparticles around the TPB coming from the volume shrinkage from NiO to Ni. Although this causes a temporary decrease in polarisation resistance, after each redox cycle the degradation rate is even faster due to the promoted Ni agglomeration. This results in an overall increase in polarisation resistance by about an order of magnitude as a consequence of a reduction in active TPB density (from 4.63 μm −2 to 1.06 μm −2 ) and fragmentation of the YSZ network along its grain boundaries due to Ni expansion upon oxidation.
This study shows that the microstructural changes during redox cycling are the primary cause of Ni-YSZ material degradation in both electrochemical performance and mechanical properties. The repeating Ni volume changes are the main cause of this degradation process, damaging the YSZ framework and reducing the TPB density as a consequence of accelerated Ni coarsening. The study further demonstrates that a comprehensive quantification of redox cycling can be achieved by coupling 3D tomography, real-time impedance spectroscopy and mechanical analysis.  Table 2 Linear and exponential correlations of elastic modulus vs porosity. E 0 is the elastic modulus of the fully dense material, b is a porosity constant and p is fractional porosity. b* is the porosity constant fitted in this study, considering the microstructure damage caused by redox cycling.