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We performed in-situ measurement of residual stress in an anode-supported cell using sin2 ψ method, cosα method, and Raman scattering spectroscopy. Residual stress at room temperature was evaluated by the sin2 ψ method, cosα method, and simulation. The stress values were generally consistent among the methods, with YSZ having a compressive stress of around 600 MPa. Residual stress analysis at high temperatures was attempted using Raman scattering spectroscopy which, however, was difficult to be applied above 700˚C. Instead, cosα method was successfully utilized for the measurement of residual stress during the temperature rise, reduction, and re-oxidation processes. The stress on the electrolyte observed during reduction and re-oxidation was different from that expected with a simple assumption of layered homogeneous sheets. These results showed that the cosα method is the most suitable method for in-situ measurements to validate simulated stress states.

Mechanical failures of an anode supported SOFC implies crack formation in the electrolyte, delamination of the electrode/electrolyte interfaces, and contact loss caused by cell deformation. To find the risk of those failures, it is essential to know the complicated behavior of stress state which is affected not only by thermal expansion mismatch but also by chemical change of the components. Structural analyses have been made by various groups by using mechanical property data accumulated in these decades. However, effects of chemical strain are not always taken into consideration, and even when it is properly included in the calculation, actually observed behavior does not always follow the expectation. It is thus important to make in-situ or operando measurement of the stress in cell components. Several in-situ measurement methods were tested, and cosα method of X-ray diffraction was chosen as the best suited method for the operando application [1]. With cosα method, focused X-ray beam irradiates the sample surface with a certain angle to the normal, and the Debye ring is monitored with a co-axially aligned imaging plate. The stress of the sample is estimated from the deformation of the Debye ring from the stress-free state. A specially designed one- or two-chamber cell holder was developed to be used with a portable X-ray stress analyzer (μ-X360s, Pulstec Industrial. Co. Ltd.). Anode-supported cells purchased from multiple sources were analyzed. Measurements were made focusing on the initial reduction of the nickel oxide support, re-oxidation at operation temperatures, and re-oxidation at medium temperature ranges. In the initial reduction at 700˚C, highly compressive stress of about -300 MPa appeared on the electrolyte. It, however, was gradually mitigated down to around -100 MPa in 3 hours. This behavior was explained with the reduction contraction of NiO to Ni and subsequent softening of the support layer. Similarly, as is expected, reoxidation at 700˚C caused the shift of the residual stress to the tensile direction. The transient behavior, however, was different with the cells from different manufacturers. This could be due to the difference of the microstructure of the anode support layer which causes different bending behavior. Another interesting behavior was on the reoxidation of the support at intermediate temperature range. As reported elsewhere [2,3], nickel metal shows oxidation “contraction” when it is oxidized at temperatures around 400˚C to 500˚C, which is accompanied by enhancement of creep deformation rate. The mechanism is interpreted as the formation of slightly oxidized layer which promotes mass transport at the particle surfaces and grain boundaries. It is coupled with the driving force of oxidation that makes the nickel ions move from the inside to the outside. Consequently, neck growth takes place and the separation of the particles are reduced. The same mechanism can work with Ni-YSZ cermet anode and can cause compressive stress on the electrolyte. With this expectation, the reduced cell without cathode was re-oxidized at 400˚C. Actually, increase in the compressive stress was found on the electrolyte. The magnitude of the stress, however, was unexpectedly large as -600 MPa. It is even larger than that on the initial reduction, and the stress mitigation did not work despite the enhanced creep rate. This is probably because the driving force for the contraction is the oxidation that continues to exist before all nickel is re-oxidized. In an actual cell, this large compressive stress may cause buckling delamination of the electrolyte. Reoxidation during shutdown operation must be carefully avoided. As was found in several experiments, unexpected stress state may appear in an actual SOFC operation, which emphasizes the importance of operando analyses. Acknowledgement This study was supported by the New Energy and Industrial Technology Development Organization (NEDO) . Acknowledgement [1] K. Oshima et al.,ECS Trans. 103(1), 1251-1260 (2021) [2] K. Yashiro et al., 12th European SOFC&SOE Forum, Lucerne, Switzerland, 05-08 July (2016) [3] Y. Morishita et al. , ECS Trans., 91(1) 1979 (2019).

Introduction Solid oxide fuel cells (SOFCs) are attracting attention as highly efficient energy conversion devices. However, durability and mechanical reliability are issues. To improve durability and mechanical reliability, it is essential to evaluate the residual stress generated in the constituent materials, especially the residual stress generated in the electrolyte. While residual stress is measured by various methods, the optimum measurement method has not been established yet. The purpose of this study is to evaluate the residual stress of the cell using in-situ cosα method, which has an advantage in measurement speed and easy handling. Experiment method High-temperature x-ray stress measurement was performed as a quantitative evaluation method for mechanical behaviors. A portable X-ray residual stress measuring device μ-X360s manufactured by Pulstec Industries was used. The cos α method, which is faster and easier than the sin2ψ method, was used for high-temperature X-ray stress measurement. In the cosα method, the Debye ring is acquired by a two-dimensional detector, and the stress is calculated from the difference between the stress-free Debye ring and the Debye ring of the measurement sample. High temperature chamber was designed and prepared for high temperature x-ray stress measurement. A capton film is used to separate outside and measurement atmosphere. In addition, the measurement position can be adjusted by moving stage. Commercial sofc cells (Ningbo SOFCman cell and Elcogen) were used to compare the residual stress during the various operation procedures. Results and discussion Fig. 1 shows the difference in change in residual stress of YSZ electrolyte depending on the structure of the anode. Anode of Ningbo SOFCman cell has small porosity, while anode of Elcogen cell has large porosity. We measured changes in residual stress during heating, anode reduction, and reoxidation processes. The Elcogen cell was reduced much faster than Ningbo cell, because hydrogen gas can diffuse more easily in anode due to higher porosity. Therefore, residual stress of Elcogen cell steeply changed after hydrogen introduction. Then, the residual stresses after anode reduction were completely different in these two cells at room temperature. Compressive stress of 800 MPa remained in the electrolyte of Ningbo cell. On the other hand, less compressive stress of 400 MPa remained in the electrolyte of Elcogen cell. The temperature dependence of residual stress is also different in the two cells. The deformation of the cell after reoxidation was also completely different. Ningbo cell was deformed convexly toward the anode side, although Elcogen cell was hardly deformed. The difference may come from the difference in porosity of anode. Fig. 1 Circumferential residual stress of YSZ during reoxidation heating in 20％O2-N2 and SEM images of anode structures. Figure 1

SOFCs need to be able to operate for long periods of time without significant degradation in performance, and mechanical reliability and durability are problems that need to be addressed. Since SOFC operate at high temperatures and in oxidizing and reducing atmospheres, it is difficult to measure residual stress in-situ under actual operating conditions. Therefore, evaluation methods during operation have not been fully developed. Current methods for measuring residual stress in SOFC include curvature method, X-ray stress measurement method, and Raman scattering spectroscopy. In the curvature method, the stress is obtained by combining curvature, anode substrate thickness, and elastic modulus. Therefore, it is not suitable for residual stress measurement during reduction and re-oxidation of anodes, where physical properties such as elastic modulus change with time. In the X-ray stress measurement method, the change in lattice strain is measured, and the stress is obtained by multiplying the strain by an elastic constant. Typical methods of X-ray stress measurement are sin2ψ method and cosα method. The characteristics of the sin2ψ method are as follows; (1)By using several measuring points to determine the stress value, the variation of the measured value can be suppressed, resulting in high measurement accuracy. Furthermore, the reliability limit of the measured value can be quickly evaluated from the linearity. (2)A goniometer mechanism is used to measure the diffraction profile, which requires a large device. (3)Measurement time is long because several points are measured by moving the angle of incidence. Thus, although the sin2ψ method has high measurement accuracy, it is not very suitable for in-situ measurements. The method devised to solve these problems is cosα method. The characteristics of the cosα method are as follows; (1) Since it is single-incidence, the optical system is simple and does not require goniometric scanning, making it possible to reduce the size and weight of the measurement system. It is also possible to measure in a short time. (2) From the slope of the cosα and sinα diagrams, vertical stress and shear stress can be measured simultaneously. In addition, the reliability of the stress values can be evaluated from the linearity of the diagram. (3) In the case of coarse grains or strongly aggregated structure, only continuous rings can be obtained, or the strength may be significantly non-uniform, making stress measurement difficult. It has been demonstrated that the measurement accuracy of the cosα method for vertical stress is comparable to that of the sin2ψ method, and moreover, it is suitable for in-situ residual stress measurement because of its rapidity and simplicity. In Raman scattering spectroscopy, the change in lattice volume, i.e., the change in stress conditions, can be obtained by measuring the Raman shift. The characteristics of the Raman scattering spectroscopy are as follows; (1) Since the measurement can be performed under atmospheric pressure and through glass, it is suitable for in-situ measurement in the SOFC operating environment where atmosphere control is usual. (2)High spatial resolution (up to ~1µm resolution is possible with micro-Raman spectrometers) enables measurement of small areas. (3) Since Raman peaks with sufficiently strong intensity need to appear in the Raman spectrum, there is a limit to the number of materials that can be measured. Among the SOFC constituent materials, ceria-based materials are the most suitable for observation. As mentioned in (3), Raman scattering spectroscopy is used to calculate the stress value of the interlayer (ceria-based material). Therefore, the stress in the electrolyte is calculated by assuming that the electrolyte and the interlayer are rigid bodies under the operating conditions. In this study, we performed in-situ measurement of residual stress in the anode-supported cell using sin2ψ method, cosα method and Raman scattering spectroscopy. And then we compared the results and summarized the advantages and disadvantages of each method. We used a commercially available general cell and a cell fabricated at Tsinghua University. In order to reproduce the actual operating conditions, the measurements were carried out under elevated temperature and under reduced temperature. Since the anode may be re-oxidized when the fuel runs out or during an emergency shutdown, the measurements were also conducted under re-oxidation. Furthermore, we proposed suitable conditions for each measurement method and conducted experiments under those conditions.