Systematic Two-Dimensional DRT-Analysis of Battery and Fuel Cell Impedance Data
Authors: Mertens Andreas , Schiemann Kevin , Kayser Steffen Alexander , Yu Shicheng , Eurich Svitlana , Tempel Hermann , Kungl Hans , de Haart L.G.J. , Eichel Rüdiger-Albrecht , Granwehr Josef 
Published: February 2020

Electrochemical Impedance Spectroscopy (EIS) has become an important tool for the analysis of batteries and fuel cells. Thus, the interest in the ongoing development of this technique is high. The major drawback of EIS is the ambiguity caused by the necessity to select a particular model for fitting the experimental data. One approach to mitigate this problem is the analysis of impedance data by the distribution of relaxation times (DRT) of the underlying physico-chemical processes, which might be the reason for its recent popularity [1-3]. The DRT can be calculated by a variety of methods, such as Fourier filtering [4], maximum-entropy deconvolution [5], least-squares deconvolution [6], evolutionary programming [7] or regularization [8]. The advantage of regularization is its usability without any a priori knowledge of the system.

In this work, an evolution of the widely applied Tikhonov regularization in standard form [9] with an RC kernel is presented. The algorithm is using a uniform penalty. It has the advantage that narrow, high amplitude features are less broadened than low amplitude features in the same DRT spectrum and that it is less susceptible to unphysical oscillations [10]. This allows us to avoid a non-negativity constraint or similar penalties, therefore inductive and capacitive features can be unraveled in the spectrum by their opposite sign. In addition, by performing the regularization on two-dimensional (2D) data even if only one dimension is inverted, an improved resolution in the DRT dimension and smoother features in the non-inverted dimension are achieved. With peak-fitting algorithms each identified process is quantified and subsequently back-transformed into the frequency domain. By this, the contributions of the different processes to the overall impedance are visualized.

Regularization is, in general, vulnerable to artifacts [11]. Hence checking the validity of the inverted data to prevent false interpretations is necessary, for which a procedure is described.

2D-DRT is used for the analysis of impedance data obtained from measurements of solid oxide fuel cells (SOFC) and lithium-ion batteries (LIB). For instance, for the SOFC the impedance measurements were performed for varying temperatures between 700°C and 900°C and potentials between 1200 mV and 700 mV. With this approach five different physico-chemical processes could be quantified in the frequency range between 100 mHz and 100 kHz which is in accordance with the literature [12].

References

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[9] S. W. Provencher, “A constrained regularization method for inverting data represented by linear algebraic or integral equations”, Computer Physics Communications 27 (3) (1982) 213-227

[10] J. Granwehr, P. J. Roberts, “Inverse Laplace transform of multidimensional relaxation data without non-negativity constraint”, Journal of Chemical Theory and Computation 8 (10) (2012) 3473-3482

[11] R. L. Parker, Y.-Q. Song, “Assigning uncertainties in the inversion of NMR relaxation data”, Journal of Magnetic Resonance 174 (2) (2005) 314-324

[12] M. J. Jørgensen, M. Mogensen, „Impedance of solid oxide fuel cell LSM/YSZ composite cathodes“, Journal of Electrochemical Society 148 (2001) A433-A442

Figure Caption: Two-dimensional DRT analysis of SOFC impedance data measured at a potential of 1000 mV and temperatures between 700°C and 900°C in the frequency range between 100 mHz and 100 kHz.

Figure 1