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DOE OSTI2023

How reliable is distribution of relaxation times (DRT) analysis? A dual regression-classification perspective on DRT estimation, interpretation, and accuracy

The distribution of relaxation times (DRT) has gained increasing attention and adoption in recent years as a versatile method for analyzing electrochemical impedance spectroscopy (EIS) data obtained from complex devices like fuel cells, electrolyzers, and batteries. The DRT deconvolutes the impedance without a priori specification of a generative model, which is especially useful for interpretation and model selection when the governing principles of the system under study are not fully understood. However, DRT estimation is an ill-posed inversion problem that must be addressed with a subjective choice of regularization and tuning, which leaves substantial risk of misleading interpretations of EIS data. In this work, we suggest a new classification view of the DRT inversion to clarify DRT estimation and interpretation. We introduce a dual regression-classification framework that unifies the classification and regression views of the DRT inversion with wide-reaching implications for DRT analysis. The dual framework is employed to demonstrate a new kind of DRT inversion algorithm and develop novel evaluation metrics that capture previously ignored aspects of DRT accuracy. These approaches are applied to both synthetic data and experimental spectra collected from a protonic ceramic fuel cell and a lithium-ion battery to illustrate their broad utility. The dual inversion algorithm shows promising performance for accurate DRT estimation and autonomous model identification, while the dual evaluation approach produces metrics that meaningfully assess the strengths and risks of DRT algorithms. Here this work provides valuable insight for both practical application of the DRT to experimental data and further development of EIS analysis methods.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Voltage and temperature effects on low cobalt lithium-ion battery cathode degradation

Degradation of low cobalt lithium-ion cathodes was tested using a full factorial combination of upper cut-off voltage (4.0 V and 4.3 V vs. Li/Li + ) and operating temperature (25 °C and 60 °C). Half-cell batteries were analyzed with electrochemical and microstructural characterization methods. Electrochemical performance was assessed with galvanostatic cycling, cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS) supported by distribution of relaxation times (DRT) analysis. Electrode microstructure was characterized with scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray absorption near edge structure (XANES) imaging. Higher cut-off voltage cycling shows presence of NiO x formation, a low diffusivity rock-salt phase, in both CV and XRD data. XRD patterns confirmed that the rock-salt phase was beginning to form at the low cut-off voltage at high temperature, but in much lower intensity than at the high cut-off voltage. Higher temperature accelerates degradation processes at both voltages. Degradation factors at high temperature include NiO x formation, cathode material dissolution, and electrolyte decomposition. SEM analysis suggests that supporting phases may isolate and disconnect active material particles reducing capacity retention and battery life cycle. DRT analysis and XANES imaging show that both high temperature samples revealed a NiO x phase based on an increased diffusive impedance and a visible shift in the XANES spectra. The low cut-off voltage, high temperature sample showed a split peak and shift to lower energies indicating early formation of the NiO x phase. The diffusive impedance, which hinders intercalation and deintercalation, is driven by the formation of the NiO x phase. While primarily driven by cut-off voltage, elevated temperature also contributes to this degradation mechanism.

electrochemical impedance spectroscopy↗

DOE OSTI2023

Reversible solid oxide cells: Early performance and microstructural evolution during electrolysis and switched mode operation

Incorporating more renewables into our energy mix will require a diversity of technological solutions. Reversible solid oxide cell systems (RSOCs) operating reversibly between fuel cell and electrolysis modes with high round-trip efficiencies offer one such solution. However, questions remain about the stability of the oxygen and fuel electrodes under reversible operation. Here, in this study, single cells with the configuration Ni-YSZ|YSZ|GDC10|NNO-NDC50|NNO are operated by reversible cycling under potentiostatic conditions. Test conditions are chosen to be representative of average stack conditions that are likely to be encountered during operation of a stack constructed of such cells. The results of reversible cycling over 500 h (21 cycles) are compared with operating the cells under potentiostatic conditions in the electrolysis-only mode (i.e., without cycling). Voltage-current density (DC), AC complex impedance spectroscopy, distribution of relaxation times (DRT) analysis, and scanning electron microscopy (SEM) indicate excellent reversibility and stability of the neodymium nickelate-based oxygen electrodes in both electrolysis and reversible cycling modes. Degradation behavior is attributed to the loss and coarsening of connected Ni particles in the fuel electrode, particularly in the active layer. However, reversible operation mitigates this degradation compared to operation in the electrolysis-only (SOEC-only) mode.

25 ENERGY STORAGE↗

DOE OSTI2024

Advancing electrochemical impedance analysis through innovations in the distribution of relaxation times method

Electrochemical impedance spectroscopy (EIS) is a key tool across various scientific disciplines, including energy sciences, chemistry, and biology, enabling the analysis of electrochemical systems. However, conventional methods for interpreting EIS data are often complex and model dependent. The distribution of relaxation times (DRT) offers a non-parametric approach that simplifies the interpretation process by providing a timescale interpretation of EIS data. This article provides a comprehensive review of current methods for DRT inversion. Additionally, a survey of practitioners highlights key challenges in the field. Here, the findings underscore the need for standardized DRT analysis and benchmarks, as well as the development of automated analysis tools. These advancements would improve the usability and interpretability of EIS data. Ultimately, implementing these improvements could not only propel the field forward but also expand the application of DRT in scientific research by making it accessible to a broader range of researchers, including those without specialized expertise in programming or statistics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Coupled Interfacial Kinetics and Transport Resistances Govern High-Current Behavior in Bipolar Membranes

Bipolar membranes (BPMs) enable electrochemical systems that operate across large pH gradients; however, high-current operation is often limited by voltage losses whose origins remain difficult to resolve in membrane−electrode assemblies. Here, we combine electrochemical impedance spectroscopy with distribution of relaxation times (EIS–DRT) analysis and operando synchrotron X-ray diffraction to examine interfacial polarization, membrane hydration, and transport in commercial and synthesized BPMs. EIS–DRT isolates the BPM-associated interfacial contribution and shows that the commercial BPM exhibits larger water-dissociation-associated overpotentials than the synthesized BPM. Operando hydration mapping shows that both membranes retain water at the bipolar junction during high-current operation, while anode-adjacent hydration gradients are more pronounced in the commercial membrane. These results indicate that high-current voltage losses are not governed by junction water starvation alone but by coupled interfacial polarization and transport resistances.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Monitoring the long-term performance of organic redox flow battery by a distribution of relaxation time analysis

Organic redox flow batteries hold great promise as an energy storage technology, but their intricate chemistry makes them vulnerable to various degradation mechanisms. Monitoring this degradation is essential for identifying the limiting processes within the cells. Electrochemical impedance spectroscopy (EIS) offers a straightforward, in-situ method for measuring the total resistance of an operating cell. However, to pinpoint the limiting processes during long-term cycling, EIS data must be complemented by other techniques. Distribution of relaxation time (DRT) analysis is particularly effective for differentiating resistance components. Here, in this study, we perform a comprehensive analysis of resistance evolution and the separation of anode and cathode contributions during long-term cycling of a full cell employing 7,8-dihydroxyphenazine-2-sulfonic acid (DHPS) as the anolyte. Separate analyses of the DHPS anolyte and ferri-/ferrocyanide catholyte were conducted using a symmetric cell setup. The relaxation times derived from symmetric cells facilitate the identification of peaks in the DRT profiles from the full cell. Importantly, the DRT profiles indicate a correlation between the evolution of charge transfer resistance and the chemical degradation of DHPS. The methodologies and results outlined in this study offer significant insights for developing diagnostic tools applicable to other types of redox flow batteries.

Distribution of relaxation time↗

DOE OSTI2025

Analysis of Niobium Electropolishing Using a Generalized Distribution of Relaxation Times Method

Using electrochemical impedance spectroscopy, we have devised a method of sensing the microscopic surface conditions on the surface of niobium as it is undergoing an electrochemical polishing (EP) treatment. The method uses electrochemical impedance spectroscopy (EIS) to gather information on the surface state of the electrode without disrupting the polishing reaction. The EIS data is analyzed using a so-called distribution of relaxation times (DRT) method. Using DRT, the EIS data can be deconvolved into discrete relaxation time peaks without any a priori knowledge of the electrode dynamics. By analyzing the relaxation time peaks, we are able to distinguish two distinct modes of the EP reaction. As the polishing voltage is increased, the electrode transitions from the low voltage EP mode, characterized by a single relaxation time peaks, to the high voltage EP mode, characterized by two relaxation time peaks. We theorize that this second peak is caused by the formation of an oxide layer on the electrode. We also find that this oxide induced peak transitions from to a negative relaxation time, which is indicative of a blocking electrode process. By analyzing EPed samples, we show that samples polished in the low voltage mode have significantly higher surface roughness due to grain etching and faceting. We find that the surface roughness of the samples only improves when the oxide film peak is present and in the negative relaxation time region. This shows that EIS combined with DRT analysis can be used to predict etching on EPed Nb. This method can also be performed before or during the EP, which could allow for adjustment of polishing parameters to guarantee a smooth cavity surface finish.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Electrochemical Response of Alkaline Batteries Subject to Quasi-Static and Dynamic Loading

We report electrochemical changes were successfully monitored through the coupling of external loading, electrochemical impedance spectroscopy (EIS), and distribution of relaxation times (DRT) analysis. The development of the testing methods allows for detailed observation of changes due to mechanical loading and distinguishes responses between different cell geometries. Comparison of the force vs displacement, voltage vs displacement, and distribution of relaxation times plots to the different cell geometries display failure modes specific to geometry as well as the impact of different loading profiles. Numerical modeling confirmed the movement within individual cells and predicted locations with the most deformation based on the external loading condition applied. The results gathered from combining mechanical loading, electrochemical response, and numerical modeling, yield a viable approach to establishing an improved understanding of the effects of mechanical loading on the electrochemical response of multiple battery geometries and the methods herein may be extensible to additional battery chemistries.

25 ENERGY STORAGE↗

DOE OSTI2023

Computationally Guided Design of Multiple Impurities Tolerant Electrode (Final Report)

The current project was based on a combined experimental and computational approach, which can help recommend better cathode materials under multiple impurities conditions. The PI will mainly take in charge of experimental and computational thermodynamics of the selected cathode materials for the SOFC applications under multiple impurities. While the co-PI will run the electrochemical tests of the cathodes recommended and eventually the long-term degradation tests. At the end of the project, a multiple tolerant cathode material based on the combined experimental and computational approach will be recommended and the reliability of the commonly used accelerated testing will be evaluated. It will address multiple impurities poisoning effect of SO2, CO2, Cr and H2O on the LSM, LSCF and LNO cathodes by identifying the formation of the detrimental secondary phases by XRD, SEM and TEM techniques. And further recommended cathode material will be subjected to electrochemical testing and the most promising ones will be applied to long-term tests. The hybrid approach the PI proposed will not only be applied to the design of multiple impurities tolerant cathodes but will also be considered in the future oxygen electrode applications in SOECs or reversible SOCs. This hybrid computational and experimental approach includes four sections: 1) Investigation of single impurity poisoning on LSM, LSCF and LNO cathodes in the presence of SO2, CO2, Cr. In this section, LSM, LSCF cathodes from FuelCellMaterials and LNO cathodes from Sol-Gel synthesis will be heat-treated in the above single impurity. And the formation of the secondary phases as well as the corresponding simulations will be cross compared, which shows good agreement between each other. Meanwhile, the accelerated testing approach will be evaluated in these systems compared with the previous published work to understand the reliability of the approach. 2) Investigation of multiple impurities poisoning on LSM, LSCF and LNO cathodes in the presence of Cr+H2O, SO2+Cr and SO2+Cr+H2O conditions. We have also applied these 3 candidate cathodes under these multiple impurities’ conditions and the long-term degradation mechanism of the multiple impurities will be understood with the help of the combined experimental and computational approach. Meanwhile, the synergistic effect of those impurities will be compared with the individual ones in the same cathode system to further reveal the actual operating conditions. 3) Electrochemical testing and polarization of the recommended cathode. We have demonstrated very low polarization resistance in LSCF (core)-LSM (shell) electrodes using MSD process and analyzed impedance spectra using DRT analysis and confirming that the low polarization resistance in LSM infiltrated MSD cells is due to reduction in polarization resistance associated with O2-adsorption process. 4). Long-term degradation testing. We have developed a versatile MSD-based process to deposit various continuous coatings onto porous scaffolds and established baseline for longer term Cr-impurity testing in future projects.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Rapid mapping of electrochemical processes in energy-conversion devices

Electrochemical impedance spectroscopy (EIS) is ubiquitously applied to identify physicochemical processes governing the performance of energy-conversion devices. However, deconvolution and interpretation of impedance phenomena are limited by measurement throughput and a dearth of scalable analysis methods. Here, we demonstrate an approach to quickly collect and coherently analyze large volumes of electrochemical data. In this study, we accelerate impedance characterization by combining rapid measurements in time and frequency domains, which are interpretably transformed using the distribution of relaxation times (DRT) and a new distribution of phasances (DOP) model. This method provides excellent agreement with EIS and decreases measurement time by an order of magnitude. High-throughput spectra are then distilled into detailed electrochemical maps. This approach is applied to a Li-ion battery and a protonic ceramic electrochemical cell as practical case studies, demonstrating how mapping can richly characterize physicochemical relationships that are difficult to decipher with conventional measurement and analysis methods.

25 ENERGY STORAGE↗