(High-Temperature Energy, Materials, & Processes Division Subhash Singhal Award) From Electrochemical to Mechanical Modeling of SOFCs and Their Experimental Validation
Authors: Kawada Tatsuya , Watanabe Satoshi , Budiman Riyan Achmad , Yashiro Keiji , Sato Kazuhisa , Hashida Toshiyuki , Kimura Yuta , Nakamura Takashi , Amezawa Koji , Sato Masami , Nomura Reika , Muramatsu Mayu , Terada Kenjiro 
Published: September 2023

Due to the asymmetric structure with multiple materials, SOFCs are subjected to various modes of mechanical stress, resulting in a risk of failure. Of particular importance are thermal and chemical strains, which depend on the micro- and macroscopic distribution of electrochemical reaction sites. Therefore, SOFC modeling must include electrochemistry, mass and charge transport, thermo-fluid dynamics, and structural analysis. In addition, appropriate experiments must be performed to validate the modeling results. This research group is working to develop a comprehensive environment for modeling and validation in order to evaluate the mechanical reliability of SOFCs.
Electrochemical modeling of cathode was made based on the defect chemistry and mass transport of (La,Sr)CoO3 (LSC) and (La,Sr)(Co,Fe)O3 (LSCF). An empirical equation for the surface reaction of the porous electrode was determined by electrochemical analysis of a dense film electrode taking into account the difference between the dense film and porous electrodes [1]. Anode reaction rate on a unit length of triple phase boundary of Ni-YSZ-gas was determined using circular Ni model electrodes of various size [2]. Evaluation of 3D oxygen potential distribution inside the constituent oxides was made using an in-house code called SIMUDEL where mixed ionic/electronic conduction and oxygen nonstoichiometry were taken into consideration [3,4]. It was combined with commercial software to make structural analysis. Mechanical properties used for calculation were obtained from measurements by the resonance method and the small punch method or collected from the literature. Non-linear stress-strain behaviors were observed with Ni-YSZ cermet [5] and inelastic behaviors were found in most nonstoichiometric oxide materials. Large ferro-elasticity emerged in the LSC and LSCF [6] and in Sc stabilized ZrO2 electrolyte at elevated temperatures. Chemical strain in vacancy formation was formulated with a linear function of the defect concentration as an independent factor from the thermal expansion. In the structural analysis, it was treated as the additional temperature change of the local material. Volume change of Ni-YSZ cermet on red-ox operation was a difficult factor to formulate because of its complex dependence on composition, temperature, and atmosphere. As expected, Ni-YSZ showed expansion when oxidized, but under certain conditions at an intermediate temperature range, it rather contracted on oxidation [7].
In reality, the calculated stress distribution does not always match the actual behavior of the cell since there often are unconsidered factors. Thus, experimental validation is essential. For this purpose, we have developed methods for in-situ or operando measurements of cell shape and the residual stress. Long-focus laser profilometer was used to measure the warping of a planar cell during heating, operating, and cooling operations. For the change in the diameter of a tubular cell, the laser projection type dimension meter was employed. Residual stress measurements were made with a handy X-ray analyzer (μ-X360s, Pulstec Industrial. Co. Ltd.) combined with a newly developed one- or two-chamber cell holder [8,9]. Anode-supported cells from multiple sources were analyzed, showing different stress histories in red-ox operations depending on the microstructure of the anode support layer.
Currently, we are developing a protocol for testing robustness of planar SOFCs. Here, temperature distribution is intentionally applied on a cell with segmented heater allays on the top and the bottom of the cell. Severe condition tests will be performed, and the results will be analyzed with the above-mentioned simulation.
Acknowledgement
This study was supported by the New Energy and Industrial Technology Development Organization (NEDO) .
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