On the Correlation of Kramers-Kronig (KK) Analysis and Non-Linear Harmonic Analysis (NHA)

Abstract

Primary lithium batteries are known for their elevated volumetric and gravimetric energy densities and production cost efficiency. Within this category, lithium thionyl chloride (Li/SOCl2) batteries exhibit a constant discharge voltage (~3.6 V) and a broad operational temperature range (-50ᵒC to 80ᵒC). Moreover, forming a LiCl passivation layer on the metallic Li anode can extend its shelf-life up to 20 years at optimal storage temperature. These characteristics render lithium thionyl chloride batteries applicable in military and security applications, microcomputers, measurement devices, and medical instruments. Therefore, the characterization of lithium thionyl chloride batteries accurately has the utmost importance. Understanding the critical electrochemical processes that occur inside the battery without damaging or disassembling the cell requires delicate techniques.EIS has emerged as a non-destructive and in-situ measurement technique with increasing popularity. Essential battery properties can be derived from EIS data. The credibility of EIS data, considering linearity, causality, and stability, can be verified through Kramers-Kronig relations. The obtained spectrum is fitted with an optimal number of Voigt elements (RC components in parallel)[1]. Given the linearity and stability of these individual Voigt elements, the entire spectrum should exhibit linearity if it is Kramers-Kronig compatible[2].Non-linear harmonic analysis (NHA) is a complementary technique to EIS, wherein the response signal undergoes conversion from the time domain to the frequency domain through Fast Fourier Transformation (FFT). While EIS employs a single-phased pure sinusoidal signal as the input, the response includes a fundamental frequency and harmonics at integer frequencies of this fundamental response signal. NHA can be utilized in the diagnosis of non-linear, non-stationary situations alongside the identification of drift and initial transients.This study first explains a new EIS measurement method for Li/SOCl2 batteries and Li/SOCl2/SO2Cl2 mixture batteries. The new method describes the solid electrolyte interface (SEI) stability of the batteries and the modifications needed to get KK-compatible results. After that, the equivalent circuit fits applied to the acquired spectra. Essential battery parameters such as solution resistance, charge transfer resistance, and double-layer capacitance were calculated. Kramers-Kronig analysis of the batteries was conducted, and the residuals of the fits were investigated. Subsequently, the NHA of the batteries was examined and compared to the Kramers-Kronig residuals. A correlation between the residuals and NHA of the batteries was extended based on the terms "KK-compatible" and "non-KK-compatible" in comparing KK-residuals and NHA results.[1] Boukamp, B. A. , Journal of the Electrochemical Society 142.6 (1995): 1885.[2] Agarwal, et al., Journal of the Electrochemical Society 142.12 (1995): 4159. Figure 1