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| Home > Publications database > Unravelling the Interplay between Degradation and Impedance through Physical Modeling – a White Box Approach |
| Home > Publications database > Unravelling the Interplay between Degradation and Impedance through Physical Modeling – a White Box Approach |
| Abstract | FZJ-2026-01076 |
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2025
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Please use a persistent id in citations: doi:10.1149/MA2025-031280mtgabs
Abstract: The accurate interpretation of measured electrochemical impedance spectroscopy (EIS) data is crucial for understanding degradation mechanisms in solid oxide cells (SOCs) [1]. EIS is a powerful tool for measuring SOCs in operando, but the analyses of EIS data requires physical models to decipher and interpret the underlying cell processes [2].In this contribution, two connected physical models are presented. The first part focuses on a model of degradation processes in SOC. The key feature of the model that will be presented is the hierarchical approach linking local degradation at the particle level with performance effects on the electrode level. In the second part, a model for the electrochemical impedance spectrum of the anode active layer and the anode support layer will be presented. The underlying white box approach allows the interpretation of cause and effects involved in EIS experiments. In combination, the two models connect materials, component and cell properties, with the operating conditions of a SOC to the outcome of EIS experiments. The whole modeling framework allows fast computation on a normal laptop.In the first part, the degradation model will be described in more detail. The degradation model focusses on the fuel electrode, since the most severe degradation contribution originates in it [3]. The degradation framework, illustrated in Figure 1, comprises three interdependent structural levels. On the particle level, degradation takes place by Ostwald ripening, coagulation or poisoning of particles [4, 5, 6, 7, 8]. The rate of these particle degradation processes is influenced by the local reaction environment. First and foremost, the local electrode potential drives Ostwald ripening.On the electrode level, the ensemble of solid particles within the electrode is modeled. A statistical electrode is assumed and the local potential and current are calculated. The statistical electrode is built up in three steps with essential parameters passed from one to the next. We start with spherical particles describing the electrode. Two particle radius distributions (PRDs) – for metal and ceramic particles – capture the structural evolution. While ceramic particles remain static, the metal particles change with time under the influence of local conditions during cell operation and dependent on electrode properties [4, 5, 6, 7, 8]. In the “percolation theory” step (see Fig. 1), the electrode’s statistical microstructure is calculated from the PRDs. Assuming that the electrode is described by a porous medium, we can use percolation theory to extract the essential microstructural properties, such as the triple phase boundary length, and electronic and ionic conductivity [9, 10, 11, 12, 13]. These parameters provide a bridge between the structural evolution and the macroscopic performance of the electrode. In the performance model, we assume that the electrode consists of two interpenetrating homogeneous phases. Hence the electrode can be described by the phase’s conductivity and the reaction area between them. With porous electrode theory, spatially dependent variables, such as phase potentials and current distribution, are derived [14]. These local variables is fed back to the degradation processes, focusing on potential-driven Ostwald ripening as the dominant mechanism. This feedback loop allows for the iterative, self-consistent calculation of degradation in the fuel electrode.At the device level, the model computes the performance and health indicators like remaining useful life as functions of operational conditions over the lifetime of the cell. Additionally, diagnostic information like polarization curves and EIS spectra can be analyzed [15].The description of the numerical model for electrochemical impedance spectra follows [15]. It is assumed that the SOC is isothermal and the pressure gradient across the cell is negligible. For the anode active layer, reaction processes are captured by the Butler-Volmer-equation and charge conservation is assumed. The transport of hydrogen through the anode support layer is described using Fick’s law of diffusion. The set of ordinary differential equations (ODEs) in the frequency domain, obtained for this system, can be solved numerically as a boundary value problem. Solving the ODE system for a range of perturbation frequencies leads to the electrochemical impedance spectrum. Our research has shown that the Warburg element alone is insufficient to describe the transport-related impedance contribution [15]. This contribution depends not only on the support layer's parameters but also on the electrochemical activity and capacitance of the adjacent active layer. The transport impedance of the support layer always depends on the adjacent electrode, especially on the electrode’s capacitance [16]. In case of a planar electrode, which was the adjacent electrode in case of Warburg’s experiment, the capacitance is three orders of magnitude smaller than the capacitance of a porous electrode [16]. In an SOC, the support layer is next to a porous electrode, and thus its transport impedance is not sufficiently described by the Warburg impedance [16]. This knowledge provides new access to understand impedance data as well as may help unravel degradation mechanisms in the electrode. From fitting, the impedance model can reveal effective parameters of the electrode like the effective ion conductivity and hydrogen diffusivity.When connecting this impedance model on the right loop in Figure 1 with the degradation model in the left loop, we found that the growth rate of metal particles increases with local potential, leading to faster growth near the dense electrolyte layer. This reduces the active surface area and the reaction rate in the active layer. Hence the anode active layer impedance increases. The model for the electrochemical cell impedance [15] shows that this local electrode degradation is connected to an increase of the transport impedance in the adjacent anode support layer. Furthermore, over time particle growth results in a loss of structural connectivity. When the metal particle network collapses, affected regions of the electrode become inactive and contribute only as ion-conducting domains. Over time, this leads to a shift the most active zones from the region near the electrolyte to region near the porous layer, increasing the ohmic resistance obtained from the impedance spectra.The feedback loop between the particle level and electrode-level properties allows the model to calculate lifetime, performance loss, and impedance spectra.We introduced a white-box modeling approach that captures the impact of local structural changes in the metal phase on the performance and impedance of a SOC fuel electrode, including its support. Two main observations become clear when performing a simulated degradation experiment: local degradation, originating at the dense electrolyte, affects hydrogen transport impedance in the anode support layer and the anode active layer shifts due to connection losses, increasing the ohmic resistance of the SOC.
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