Electrochemical Impedance Spectroscopy (EIS) is a well-known technique in battery technology due to being non-destructive and providing crucial insights about what’s happening in the battery. One of the biggest challenges that electrochemists encounter during impedance measurements is the ambiguity of the analysis of EIS data. Equivalent circuit modelling is the state of art analysis method for EIS data. However, as shown by Dahn et.al. as well as others before, showed that same impedance data can be fitted via different equivalent circuits. To reduce or get rid of this ambiguity, we will present a new method where we employ non-linear harmonics and temperature dependent EIS results as extra information. We will demonstrate that using non-linear harmonics and temperature dependent measurements, we can overcome the degeneracy in the EIS data analysis.

We will illustrate that, through engineering the proper objective function and selecting proper frequency and temperature ranges, it is possible to obtain specific results for EIS data and follow important physical constants such as electrode thickness, cation transfer number, and diffusion coefficients. For simulations, we are employing PyBaMM, and for fitting, we are using a downhill simplex algorithm. By generating a sinusoidal current within a frequency range, simulating the voltage response, and applying the Fourier transform, we can calculate the EIS spectra with initially presented physical constants. Then, doing this step over a temperature array provides us the temperature-dependent EIS response. Along with the temperature-dependent response, the higher harmonics are followed by analyzing multiples of the period number in the Fourier transform data. Finally, temperature-dependent EIS data and higher harmonics are gathered in an objective function where downhill simplex varies the physical constant values which eventually changes the EIS response and harmonics. Minimizing the objective function by comparing with the experimentally provided data results the calculation of desired physical constants. Also, in order to reduce the computation time and increase the accuracy of the resulting physical constants, it is possible to do further engineering by adding weights to the objective function. The effect of weights can be followed by the second derivative of objective function results for each physical constant and decide the best weighting values. Ultimately, this new EIS data fitting method makes it possible to understand which physical event can be analyzed best at which temperature and frequency window and improves the accuracy of making conclusions regarding EIS data.