Scientists Investigate EIS and Non-Linear Harmonic Analysis of Lithium Batteries

Scientists from the Department of Chemistry at Bilkent University in Ankara, Turkey, have analyzed lithium batteries using non-linear harmonic analysis and EIS. By comparing experimental measurements and mathematical simulations, the authors have identified harmonic distortions and other critical factors in these devices. Their work has appeared in the journal Electrochimica Acta.

Study: Non-linear Harmonics in EIS of Batteries with Lithium Anodes: Proper Controls and Analysis. Image Credit: Smile Fight/

Characterizing Battery Chemistries with Electrochemical Impedance Spectroscopy

Lithium-ion batteries have become a cornerstone technology in the electrification of several sectors such as transportation and industry. Accurate characterization of their chemistries is essential to ensure their optimal operation, and a number of analytical techniques are available for this purpose.

Electrochemical impedance spectroscopy (EIS) has emerged as a highly suitable analytical method for analyzing and categorizing lithium-based batteries in great detail. This method is advantageous for researchers due to its non-destructive, non-invasive, and in-situ nature. This is vitally important as batteries are extremely reactive, and it is challenging to characterize them unless they are in sealed cells.

There are limitations to EIS data, however. Concerns with linearity and measurement requirements which mean that stationary conditions must be maintained hamper the accuracy and efficacy of EIS measurements. Failure to meet these conditions can lead to inaccurate data and conclusions.

Some strategies have been developed to address these limitations in recent research. These include using Kramers-Kronig relations to check compatibility, as well as monitoring the total harmonic distortion. Both of these methods can be utilized to assess data stationarity and linearity.

Harmonic Analysis

Total harmonic distortion analyses alternating time-domain response signals in the frequency domain. This reveals the presence of high-order harmonics as well as fundamental responses. This is then assigned as distortions. By adjusting excitation parameters whilst monitoring harmonics levels below noise levels, EIS data is obtained.

Generally speaking, electrochemical responses are expected to possess a non-linear nature. The complex dynamics of electrochemical responses make stationarity difficult to achieve. If the timescale of experiments is shorter than any significant change, stationarity conditions can be satisfied. Low AC conditions satisfy linearity conditions in impedance measurements.

Several studies have attempted to correlate mechanistic and kinetic properties with non-linear harmonic events, with early work conducted in corrosion fields. Harmonic analysis has been used to reveal mass and charge transport mechanisms in Li-ion batteries.

The authors have noted that, when using harmonics to assign non-linearity, distinctions should be made between the non-linearity which occurs during electrochemical responses and the non-stationarity caused by system changes during measurements. Difficulties exist when attempting to separate the two factors, especially in complex, closed systems such as batteries.

Moreover, redox events within batteries can cause confusion during measurements due to some non-linear events being mistakenly assigned to them. Constructing an accurate picture of non-linear and non-stationarity behavior during Li-ion battery operation is a highly challenging research area.

The Study

The authors have attempted to improve electrochemical impedance spectroscopy data using total harmonic distortion analysis to overcome the current issues faced by researchers with non-linearity, non-stationarity, and the accuracy of measurements.

Measurements of four different battery chemistries were performed in the study. Commercially available Li-ion batteries were selected for analysis. A dummy cell that was close to the AC response of selected battery types was used to provide measurements under the same conditions. By using this strategy, the various features of processes could be accurately assigned.

Simulations were performed alongside experimental observations. Models were based on circuits fitted to Kramers-Kronig transformable electrochemical impedance spectroscopy data. By fitting circuits and data in this manner in the simulations, the authors were able to observe distortions under real-world equivalent non-stationary conditions.

Additionally, the authors analyzed experimental responses in the different batteries by comparing them to distortions observed in the simulated circuits. Thus, the study demonstrated an approach to the research question which improved the understanding of non-linear and non-stationary dynamics with lithium-based batteries.

Study Conclusions

Based on the experimental and simulation observations in the study, the authors have drawn a few important conclusions which will help to improve EIS measurements of lithium-ion batteries in future research.

It was observed that the processes’ capacitance nature leads to initial transient and voltage drift behaviors. In a capacitive system, these harmonic responses are expected to appear under high AC excitation conditions. Both non-stationary and non-linear behaviors in battery voltage responses in different systems were revealed by harmonic analysis.

The initial transient response signal or voltage drift plays a role in non-stationarity behaviors. Non-linear processes during measurement were demonstrated to be responsible for other harmonic responses. The study has vast benefits for the future of research in this critical area and the design of reliable and efficient devices for energy storage.

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Further Reading

Zabara, M.A., Katirici, G & Ülgüt, B. (2022) Non-linear Harmonics in EIS of Batteries with Lithium Anodes: Proper Controls and Analysis Electrochimica Acta 140969 [online, pre-proof] Available at:

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Reginald Davey

Written by

Reginald Davey

Reg Davey is a freelance copywriter and editor based in Nottingham in the United Kingdom. Writing for AZoNetwork represents the coming together of various interests and fields he has been interested and involved in over the years, including Microbiology, Biomedical Sciences, and Environmental Science.


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