Linear and Non-Linear EIS Measurements on Li\SOCl2 Batteries
Authors: Zabara Mohammed Ahmed , Uzundal Can Berk , Ulgut Burak 
Published: February 2020

Though understudied and mostly ignored in academic research, primary batteries still dominate the commercial markets and industrial use. This dominance, in addition to legacy, is also deeply rooted in energy densities. The available volumetric and gravimetric energy densities that primary chemistries possess are still much higher compared to secondary batteries(Figure 1). Zn/air is still the main batteries for hearing aids and primary lithium cells are used in rocketry.
Even though the batteries dominate the commercial markets and the industrial use, the analysis methods for these batteries are lacking. Electrochemical Impedance Spectroscopy (EIS) is a candidate due to its versatility, ease of experimentation and low cost instruments. EIS on Li-ion secondary cells are regularly used for productive analysis[J. Electrochem. Soc. 2015 volume 162, issue 14, A2529-A2537].However, the literature of EIS measurements on primary batteries are scarce and the limited number of reports either lack experimental details, or include data that is not linear, stable or causal.
Li\SOCl2 is a chemistry that is still very actively used in the defense industry not only because it displays a high energy density, but also because it can be used as a reserve battery with the SOCl2 stored in a separate container. Li\SOCl2 batteries include SOCl2 as the cathode active material and the solvent for the electrolyte at the same time. This is one reason that enables the high energy density. On the other hand, since the electrochemical reaction in the battery involves lithium metal and SOCl2 as the reactants and elemental sulfur, sulfur dioxide and lithium chloride as the products, the activities of the components are unity and do not change throughout the discharge. Therefore the cell exhibits a stable potential throughout the discharge of the cell.
The passive film that is common to all Lithium based electrodes, acts slightly differently in the Li\SOCl2 chemistry. Contrary to secondary Lithium ion cells, the passive film cannot sustain the necessary transport of Li+ ions during moderate to high discharge rates. This causes the film to disintegrate at moderate to high discharge rate. Therefore, at various levels of discharge currents in the Li\SOCl2 cell, the existence and the integrity of the film will be different.
A fundamental assumption in the EIS measurements is that the measurement is linear and causal and that the system is stable throughout the measurement. Typically checked via compatibility with the Kramers-Kronig relations, these conditions ensure that the data is valid and that it can be fit to real life models(equivalent circuit or otherwise).
Typical EIS measurements are done using small excitation signals that oscillate between the two sides of the equilibrium point. For batteries, this is synonymous with oscillating between charge and discharge. In standard EIS measurements of Li\SOCl2 (and more generally any primary batteries), maintaining the linearity and stability conditions are problematic since the charge side results in ill-defined reactions[J. Electrochem. Soc. 1982 129(11): 2496-2499] and the discharge side results in decrease of the state-of-charge. For the Li\SOCl2 specifically, passive film formation and stability further complicates the analysis, since the integrity of the passive film depends on the level of discharge current applied.
In the current work, we will present our investigations in developing methodology to accurately measure and interpret the EIS data for Li\SOCl2 batteries. We have successfully used our methodology to measure accurate EIS for AA sized bobbin and D size cylindrical cells(Figure 2). In both cases, across all the states of charge reported, the data is compatible with the Kramers-Kronig relations and can be fit to obtain useful information about the components of the cells and how they evolve throughout the discharge process.
Our measurements are based on EIS measurements that employ the minimum amount of DC discharge current that demolishes the passive film, but is a small enough percentage of the overall capacity that the overall discharge throughout the experiment doesn’t significantly change the state-of-charge. Demolishing of the passive film is absolutely necessary for obtaining a linear spectrum. With the passive film present, the nonlinearity is clearly observed especially at the lower frequencies.
In cases where the nonlinearities persisted, harmonic analysis revealed that the second harmonic clearly dominated across all frequencies. The analyses of the second harmonic then reveals important properties of the passive film.

Figure 1