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Results for “distribution of relaxation times (DRT)”

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All sourcesNASA NTRSDOE OSTI
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 OSTI2021

Towards robust autonomous impedance spectroscopy analysis: A calibrated hierarchical Bayesian approach for electrochemical impedance spectroscopy (EIS) inversion

Distribution-based analyses, such as the distribution of relaxation times (DRT) and the distribution of diffusion times (DDT), present model-free alternatives to equivalent circuit modeling for analysis of electrochemical impedance spectroscopy (EIS) data. However, reconstructing such distributions from noisy impedance data is an ill-posed problem that must be solved with specialized inversion algorithms, requiring careful control and tuning. Furthermore, most inversion algorithms developed to date can only solve problems of limited complexity. Herein, we present a new hierarchical Bayesian method for EIS inversion, leveraging efficient algorithms for optimization and Hamiltonian Monte Carlo (HMC) sampling to solve models of arbitrary complexity. We overcome the challenge of ad-hoc parameter tuning by encoding intrinsic characteristics of the DRT and DDT into flexible prior distributions and “pre-calibrating” the model to simulated data. This approach is versatile, highly robust to noise, and provides quantitative estimates of both the error structure of the data and the uncertainty in the recovered distributions. The model is validated with simulated data to demonstrate accurate recovery of the DRT and the DDT. The method also shows promise for simultaneous recovery of multiple distributions, raising the intriguing possibility of semi-autonomous EIS analysis and ad-hoc model construction. Finally, the practical utility of the method is illustrated with experimental data. Throughout, we draw comparisons to several recently published EIS inversion methodologies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The deep-DRT: A deep neural network approach to deconvolve the distribution of relaxation times from multidimensional electrochemical impedance spectroscopy data

Electrochemical impedance spectroscopy (EIS) is an experimental technique ubiquitously used to study electrochemical systems. However, conventional EIS data interpretation through physical and equivalent circuit models is challenging because physical models are problem-specific, and equivalent circuits are often just lumped-element analogs lacking physical meaning. The distribution of relaxation times (DRT) has emerged as a complementary approach to resolve these issues. One drawback of conventional DRT deconvolution is that the EIS data is understood to be (only) a function of frequency (i.e. 1D data) and deconvolved accordingly. This work proposes a novel deconvolution method based on deep neural networks (DNNs), allowing the analysis of multidimensional EIS spectra to bridge data dependency on both frequencies and experimental conditions. Two particularly appealing traits of the deep-DRT method developed in this article are that neither regularization nor specific spacing on the state variables defining the experiment are required. Finally, leveraging DNN to examine complex EIS spectra and their dependence on experimental conditions, this work opens a new research direction in the area of EIS analysis and DRT deconvolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Call attention to using DRT and EIS to quantify the contributions of solid oxide cell components to the total impedance

The contributions of anode and cathode processes to solid oxide fuel cell (SOFC) impedance were studied using electrochemical impedance spectroscopy (EIS) and distribution of relaxation time (DRT). Specifically, the role of gas composition at both anode and cathode was explored in a systematic study aimed at deconvoluting, identifying and quantifying the contributions of different anode and cathode processes. Further, five distinct relaxation time distributions were observed in the DRT spectra; although the peaks were ascribed to diffusion and charge transfer processes at the electrodes, it was found that both electrodes contributed to various peaks at the same time. Moreover, it was found that two distinctive operating conditions could return equivalent DRT spectra. While DRT analysis allows to obtain useful information regarding cell performance, extra consideration is needed when assessing and quantifying anodic and cathodic resistances within the SOFC.

08 HYDROGEN↗
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↗
DOE OSTI2024

Identifying electrochemical processes by distribution of relaxation times in proton exchange membrane electrolyzers

Distribution of relaxation time (DRT) is used to interpret electrochemical impedance spectroscopy (EIS) for proton exchange membrane (PEM) water electrolyzers, with an attempt to separate overlapped relaxation processes in Nyquist plots. By varying operating conditions and catalyst loadings, four main relaxation peaks arising from EIS can be identified and successfully separated from low to high frequencies as (P1) mass transport, (P2) oxygen evolution reaction kinetics, (P3) reaction kinetics (with faster time constant than P2), and (P4) ionic transport. Here, the shape, height, and frequency of the DRT peaks change with different membrane electrode assembly (MEA) configurations. Electron microscopy reveals distinct features from the cross-sectioned MEAs which verify critical DRT results in that increasing the iridium (Ir)-anode loading from 0.2 mgIr/cm 2 to 1.5 mgIr/cm 2 reduces kinetic losses due to higher site-access; a thick and compacted anode, however, also triggers higher ohmic resistances from membrane/catalyst layer hydration and increases transport losses due to longer ionomer pathways. DRT provides higher resolution to EIS for deconvoluting processes with different relaxation times and the quantification of DRT peaks improves the accounting of total losses from each process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2021

Surface enhanced performance of La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ cathodes by infiltration Pr-Ni-Mn-O progress

Herein the present study reports the enhancement of electrochemical oxygen reduction activity of porous La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3–δ (LSCF) cathodes by coating a thin film of Pr-Ni-Mn oxide (PNM5) using a multi-step infiltration process. XRD examination reveals that PNM5 mainly contains a multiphase mixture of Pr 6 O 11 , PrNiO 3 , MnO and NiO. SEM morphology shows a thin PNM5 film and small particles are formed on the surface of LSCF backbone particles. Impedance spectrum analysis indicates that PNM5 infiltrated LSCF exhibits dramatically reduced polarization resistance (R p ), reaching R p of 0.244 Ω cm 2 at 973 K, which is one-half of the baseline LSCF cathode. The activation energy of LSCF cathodes infiltrated with PNM5 is 1.45 eV, slightly lower than the baseline LSCF cathode (1.77 eV). Distribution of relaxation time (DRT) function analysis shows PNM5 infiltration layer significantly promotes the oxygen reduction reaction (ORR) of cathode surface. With the increase in firing temperature, the total resistance increases and R p changes from ion transport to oxygen reduction reaction. Degradation rate of the PNM5-infiltrated LSCF is also lower, 0.02168% vs 0.07093% for the baseline LSCF over a 200-h period. A single cell testing indicated that the peak power density of the PNM5-infiltrated cell was increased by 140.66%. Overall, PNM5 could be a potential catalyst for boosting the performance of a commercial LSCF cathode for solid oxide fuel cells (SOFC).

36 MATERIALS SCIENCE↗
DOE OSTI2021

Developing Accelerated Test Protocols and Tuning Microstructures of the Common Materials to Improve Robustness, Reliability, and Endurance of SOFC Cells

This work is built on our prior work where we found that phase transformation in praseodymium nickelates, e.g. Pr 2 NiO 4 (PNO) and (Pr 1-x Nd x ) 2 NiO 4 (PNNO), can be electrochemically driven, and is substantially faster when compared to thermal annealing studies. The first task aims at an attempt to further accelerate the phase transformation in the oxygen electrode by alternating the current input in the cells, which lead to the development of accelerated test protocols (ATPs). ATPs showed up to 60x faster phase transformation and up to 10x faster performance degradation in (Pr 0.50 Nd 0.50 ) 2 NiO 4 electrodes, when compared to long-term operation under constant current density. Furthermore, the phase stable Nd 2 NiO 4 and (La 0.6 Sr 0.4 )(Co 0.8 Fe 0.2 )O 3 (LSCF6482) electrodes were tested in full cells under ATPs, and showed up to 10x faster performance degradation within 1,100 hours in a comparison with long-term thermal annealing studies and electrochemical operation under constant current density. The second task aims at the quantification of the contributions of cell components to the total impedance of a solid oxide fuel cell (SOFC) using electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT). Specifically, the role of gas composition at both anode and cathode was systematically studied, aiming at deconvoluting, identifying and quantifying the contributions of different electrode processes. This was achieved by first tuning the partial pressure of H 2 at the anode and subsequently varying the partial pressure of O 2 at the cathode. The results suggest that, while DRT offers a viable way of deconvoluting different times distributions, additional attention is needed before assigning a peak to a specific electrode process due to the significant overlap of the contributions from the cathode and the anode. Density function theory studies show that both Pr-vacancies and O-defects play a key role on the activity and stability for nickelates towards oxygen reduction reaction. The resident O-interstitials and oxygen ions in the PrO layer form peroxide (O 2 2- ) nearby Pr vacancies. The O 2 2- limits oxygen-ion transport due to the required additional energy to break its O-O bond. We further calculated the formation and segregation energies for different Ln ions (La, Pr, Nd, Pm, Sm, Gd, Tb, Dy, and Ho) in PNO and CeO 2 (111) surfaces. In addition to Nd, Pm and La are suggested as potential dopants in PNO to enhance it stability without decomposition due to their more negative formation energies, lower diffusion energies, and positive separation energies.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

An Interfacial Engineering Approach toward Operation of a Porous Solid Electrolyte CO 2 Electrolyzer

Waste CO 2 can be repurposed as a carbon feedstock for synthesizing valuable chemicals via CO 2 electrolysis. Porous solid electrolyte (PSE) CO 2 electrolysis has been demonstrated as an economically viable method to produce high purity products. This work applies an interfacial engineering approach to determine key factors to improve performance in PSE CO 2 electrolyzers. We standardize the assembly by binding the ionic resin into an ionomer wafer and utilize Computational Fluid Dynamics (CFD) to design gaskets for uniform fluid flow. Here, we employ the distribution of relaxation times (DRT) method to determine that anionic-conducting interfaces are the primary contributor to energy losses. To address this, we demonstrate that enhancing the contact between the cathode and the anion exchange membrane (AEM) and the AEM-ionic resin interface allows for low overpotential in deionized water operation.

09 BIOMASS FUELS↗
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 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

Porous and Amorphous Mn x Mo 3 S 13 Chalcogel Electrode for High-Capacity Conversion-Based Lithium-Ion Batteries

While Li-ion batteries (LIBs) are a leading energy storage technology, their energy densities are limited by the low capacity of conventional intercalation cathodes, driving interest in high energy-density Li–S batteries that make use of conversion chemistry. Achieving high capacity, reversibility, and cycle stability, and controlling volume changes in conversion batteries during the charge–discharge process, however, remains challenging. Here, in this study, we present a porous, amorphous, sulfide-based Mn x Mo 3 S 13 chalcogel, which concurrently offers high capacity and cycle stability. The solution-processable room temperature synthesized Mn x Mo 3 S 13 (x = 0.25) chalcogel exhibits a local structure that resembles the Mo 3 S 13 cluster with Mn 2+ distributed across the Mo 3 S 13 matrix, as determined by synchrotron X-ray pair distribution function (PDF) and extended X-ray absorption fine structure (EXAFS). Ab initio molecular dynamics (AIMD) simulations reveal that Mn 2+ incorporation shortens the polysulfide chain in the gel matrix compared to the Mo 3 S 13 chalcogel, while forming a coordination environment with disulfide groups, analogous to the experimental findings. A Li/Mn 0.25 Mo 3 S 13 half-cell delivers 897 mAh g –1 capacity during the first discharge and retains 571 mAh g –1 capacity after 100 cycles at a C/3 rate. Distribution of relaxation time (DRT) unveils a stable solid–electrolyte interphase (SEI) formation upon cycling that enables charge–discharge reversibility. Here, the enhanced capacity retention and cycle stability compared to those of the Li/Mo 3 S 13 cell are attributed to the reduced dissolution of active mass into the electrolyte, facilitated by the formation of shorter polysulfide chains within the Mn 0.25 Mo 3 S 13 structure and the strong affinity of Lewis-acidic Mn 2+ for polysulfide anions generated during the charge–discharge process of the Li/Mn 0.25 Mo 3 S 13 cell. Thus, this work illustrates a design principle of material for high-capacity and cycle-stable Li-metal sulfide batteries.

25 ENERGY STORAGE↗
DOE OSTI2022

Quantifying the Relationship Between Microstructure and Performance in Gadolinium-Doped Ceria Infiltrated Ni/YSZ Symmetric Cells

Infiltration of mixed ionic/electronic conducting (MIEC) nanocatalysts into the anodes of solid oxide fuel cells (SOFCs) allow the hydrogen oxidation reaction (HOR) to occur at double-phase boundaries (DPBs), rather than being confined only to the triple phase boundaries (TPBs). In this research, we use a combination of cross-sectional scanning electron microscopy (SEM), three-dimensional (3-D) reconstruction, and electrochemical methods to characterize both baseline and gadolinium-doped ceria (GDC)-infiltrated symmetric cells, with the goal of establishing a comparison between the density of electrochemically active sites in uninfiltrated and GDC-infiltrated cells. Here, electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT) analysis showed GDC infiltration decreased the overall polarization of the anode by a factor of 8.78 X, and decreased the resistance associated with the reactions at the TPBs/DPBs by a factor of over 21 X. By quantifying expected GDC deposition morphology in the Ni/YSZ anode it is estimated that reactions occur in the baseline cell up to 84 nm from the active TPB lines.

36 MATERIALS SCIENCE↗
DOE OSTI2022

(La 0.8 Sr 0.2 ) 0.98 MnO 3-δ -Zr 0.92 Y 0.16 O 2-δ :PrOx for oxygen electrode supported solid oxide cells

(La 0.8 Sr 0.2 ) 0.98 MnO 3-δ (LSM)- Zr 0.92 Y 0.16 O 2-δ (YSZ) has been widely studied as the cathode for solid oxide fuel cells (SOFCs), but its low activity has been a cell performance limiting factor. Herein, LSM-YSZ:PrO x composite is developed as an active electrocatalyst for both oxygen reduction and evolution reactions. A single step PrO x infiltration into LSM-YSZ lowers the polarization resistance (Rp) 10–20 times depending on the test temperature. Distribution of relaxation times (DRT) calculation reveals that adding PrO x affects surface exchange between adsorbed/desorbed oxygen and lattice oxygen, and oxygen dissociative adsorption/desorption. A symmetrical cell with a thin YSZ electrolyte sandwiched between thick LSM-YSZ:PrO x electrode-supports is developed and its oxygen generation performance and stability are evaluated under various current densities and temperatures. Finally, reversible solid oxide cell (ReSOC) performance is also reported for LSM-YSZ:PrO x supported cells with the oxide fuel electrode Sr 0.95 (Ti 0.3 Fe 0.63 Ni 0.07 )O 3-δ (STFN).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Heavily neodymium doped ceria as an effective barrier layer in solid oxide electrochemical cells

10 mol% gadolinium doped ceria (GDC10) is widely used as a barrier layer between oxygen electrode and electrolyte to prevent interfacial reactions. A 50 mol% neodymium doped ceria (NDC50) barrier layer has been proposed and studied in this paper. Symmetrical cells with NDC50 and GDC10 barrier layers, Nd 2 NiO 4+δ (NNO)–Ce 0.5 Nd 0.5 O 2-δ (NDC50) electrode, and YSZ electrolyte have been systematically studied using impedance spectroscopy (EIS) at various temperatures and oxygen partial pressure (pO 2 ). The NDC50 barrier layer has significantly decreased polarization resistance across a wide temperature and pO 2 range compared to the GDC10 barrier layer. The rare earth C-type structure of the NDC50 barrier layer causes barrier free migration of oxygen ions resulting in improved ionic conductivity compared to GDC10. Finally, distribution of relaxation time (DRT) modeling has been used to obtain insights into the electrode processes.

08 HYDROGEN↗
DOE OSTI2021

Tracking the evolution of processes occurring in silicon anodes in lithium ion batteries by 3D visualization of relaxation times

An unconventional electroanalytical method has been used for tracking processes in silicon anodes in lithium ion batteries: a 3D visualization of relaxation times. Impedance data of the electrodes were collected at different potentials and different cycles during cyclic voltammetry, and were treated by means of the Distribution of Relaxation Times (DRT) method. A 3D visualization of the results allowed to identify the formation of a solid electrolyte interphase on the anode, composed of two layers with different relaxation times. Such findings are not possible by conventional analysis of impedance data by modeling with equivalent circuits, nor by simple DRT alone. Additionally, it was possible to observe that the characteristic relaxation time of the lithiation of the Si anode becomes smaller upon cycling, indicating that the material experiences structural transformations that allow it to lithiate faster. The result is relevant to motivate the use of micron-sized particles in the anode.

25 ENERGY STORAGE↗
DOE OSTI2023

Enhanced electrolysis performance through hierarchical nanoparticle formation in the BaCo 0.4 Fe 0.4 Zr 0.1 Y 0.1 O 3-δ cathode materials system

This study demonstrated that the activity of a triple conducting BaCo 0.4 Fe 0.4 Zr 0.1 Y 0.1 O 3-δ (BCFZY0.1) air cathode was improved by in situ formation BCFZY0.1 nanoparticles (NPs). The NPs, directly formed from the reaction of BCFZY0.1 with H 2 O and CO 2 from air under electrolysis measurements conditions, were uniformly distributed in a porous BCFZY0.1 framework. At 600 °C, the current density increased and reached a plateau of 1.12 A/cm 2 with the hierarchical BCFZY0.1 cathode under electrolysis conditions within 400 h operation. Distribution of Relaxation Time (DRT) measurements found that the polarization resistance decreased over time as NPs were formed. Furthermore, SEM and TEM results confirm the nanoparticle formation, and the chemical and structural features were assigned to a BCFZY0.1 phase.

08 HYDROGEN↗