Interpretation of Impedance Spectra of Solid Oxide Fuel Cells: L-Curve Criterion for Determination of Regularization Parameter in Distribution Function of Relaxation Times Technique

Abstract

The distribution function of the relaxation times (DRT) technique is a powerful tool for the interpretation of impedance spectra of solid oxide fuel cells (SOFCs) because it enables direct identification of rate-limiting processes through mathematical calculations. Selection of an appropriate regularization parameter (λreg) is critical for obtaining meaningful deconvolution solutions in DRT analysis. Herein, we introduce an L-curve criterion as a reliable graphical tool for determination of the λreg value. In a parametric plot of log(solution norm) versus log(misfit norm), the λreg value at the corner of the L curve provides an optimum balance between the regularization error and perturbation error. In a case study on La0.6Sr0.4CoO3−δ-based cathodes, the DRT technique guided by the L-curve criterion enabled identification of rate-limiting processes and clarification of reaction pathways. The analytical methodology presented in this article provides guidelines for the effective use of the DRT technique for the impedance analysis of SOFCs.