Distribution (Function) of Relaxation Times, Successor to Complex Non-linear Least Squares Analysis of Electrochemical Impedance Spectroscopy?

B.A. Boukamp*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

66 Citations (Scopus)
79 Downloads (Pure)


Electrochemical impedance spectroscopy (EIS) and complex nonlinear least squares (CNLS) analysis with an equivalent circuit (EqC) has been the standard research tool in Solid State Electrochemistry for many decades. With an ever increasing interest in the development of energy related materials with complex structures, the impedance spectra are becoming too complex for a simple CNLS-analysis. Inversion of the data from the frequency domain to a distribution function of relaxation times (DFRT), i.e. the τ-domain, has shown to present a better separation and visualization of the underlying electrochemical processes. These are presented by peaks with characteristic time constants that are associated with the separate processes. Hence, the interest in EIS-analysis with inversion to a DFRT has rapidly gained attention over the last decennia. In this contribution a brief review of the applications and limitations of the DFRT procedure is presented. Some examples from the field of solid oxide fuel cells (SOFC) and Li-ion based battery research are discussed. When possible a comparison is made between the exact DFRT (derived from known DFRT expressions) and three inversion methods: Fourier Transform (FT), Tikhonov Regularization and a recently developed multi-(RQ) CNLS-fit: 'm(RQ)fit'. It is shown that the three differently derived DFRT's can differ significantly, while the impedances reconstructed from the DFRT with the inverse process show a quite good match with the original data.
Original languageEnglish
Article number042001
JournalJournal of Physics: Energy
Issue number4
Publication statusPublished - 13 Aug 2020


  • Li-ion battery
  • SOFC electrodes
  • distribution (function) of relaxation times
  • electrochemical impedance spectroscopy
  • UT-Gold-D


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