### Abstract

Electrochemical Impedance Spectroscopy (EIS) is a frequently used method to characterize electrodes for Solid Oxide Fuel Cells (SOFC) or Electrolyzer Cells (SOEC). The porous microstructures, use of composite structures and sometimes extra functional layers in an electrode, result often in impedance spectra that are difficult to analyze. Transformation of the impedance into a distribution function of relaxation times (DFRT) is about to become a new standard in EIS analysis. This inversion to the τ-domain requires solving a Fredholm integral of the second kind, which is known as an ‘ill-posed inverse problem’. Hence the resulting DFRT's should not be trusted directly. In cases were impedance data can be modelled satisfactory with an Equivalent Circuit (EqC), built of known dispersion relations (e.g. (RQ), Gerischer, Finite Length Warburg) an analytic distribution function, G(τ), can be constructed. This can be compared with the inversion results obtained from Fourier Transform (FT), Tikhonov Regularization (TR) and multi-(RQ) CNLS fits (m(RQ)fit), thus allowing evaluation and validation of these methods This is illustrated in this contribution with four examples of SOFC cathodes with quite different properties. The results apply equally well to SOFC anodes (or SOEC cathodes).

Original language | English |
---|---|

Pages (from-to) | 103-111 |

Number of pages | 9 |

Journal | Solid state ionics |

Volume | 314 |

Early online date | 7 Dec 2017 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

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### Keywords

- Electrochemical Impedance Spectroscopy (EIS)
- Electrodes
- Finite Length Warburg (FLW)
- Gerischer dispersion
- Distribution function of relaxation times (DFRT)

### Cite this

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*Solid state ionics*, vol. 314, pp. 103-111. https://doi.org/10.1016/j.ssi.2017.11.021

**Use of a distribution function of relaxation times (DFRT) in impedance analysis of SOFC electrodes.** / Boukamp, Bernard A. (Corresponding Author); Rolle, Aurélie.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Use of a distribution function of relaxation times (DFRT) in impedance analysis of SOFC electrodes

AU - Boukamp, Bernard A.

AU - Rolle, Aurélie

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Electrochemical Impedance Spectroscopy (EIS) is a frequently used method to characterize electrodes for Solid Oxide Fuel Cells (SOFC) or Electrolyzer Cells (SOEC). The porous microstructures, use of composite structures and sometimes extra functional layers in an electrode, result often in impedance spectra that are difficult to analyze. Transformation of the impedance into a distribution function of relaxation times (DFRT) is about to become a new standard in EIS analysis. This inversion to the τ-domain requires solving a Fredholm integral of the second kind, which is known as an ‘ill-posed inverse problem’. Hence the resulting DFRT's should not be trusted directly. In cases were impedance data can be modelled satisfactory with an Equivalent Circuit (EqC), built of known dispersion relations (e.g. (RQ), Gerischer, Finite Length Warburg) an analytic distribution function, G(τ), can be constructed. This can be compared with the inversion results obtained from Fourier Transform (FT), Tikhonov Regularization (TR) and multi-(RQ) CNLS fits (m(RQ)fit), thus allowing evaluation and validation of these methods This is illustrated in this contribution with four examples of SOFC cathodes with quite different properties. The results apply equally well to SOFC anodes (or SOEC cathodes).

AB - Electrochemical Impedance Spectroscopy (EIS) is a frequently used method to characterize electrodes for Solid Oxide Fuel Cells (SOFC) or Electrolyzer Cells (SOEC). The porous microstructures, use of composite structures and sometimes extra functional layers in an electrode, result often in impedance spectra that are difficult to analyze. Transformation of the impedance into a distribution function of relaxation times (DFRT) is about to become a new standard in EIS analysis. This inversion to the τ-domain requires solving a Fredholm integral of the second kind, which is known as an ‘ill-posed inverse problem’. Hence the resulting DFRT's should not be trusted directly. In cases were impedance data can be modelled satisfactory with an Equivalent Circuit (EqC), built of known dispersion relations (e.g. (RQ), Gerischer, Finite Length Warburg) an analytic distribution function, G(τ), can be constructed. This can be compared with the inversion results obtained from Fourier Transform (FT), Tikhonov Regularization (TR) and multi-(RQ) CNLS fits (m(RQ)fit), thus allowing evaluation and validation of these methods This is illustrated in this contribution with four examples of SOFC cathodes with quite different properties. The results apply equally well to SOFC anodes (or SOEC cathodes).

KW - Electrochemical Impedance Spectroscopy (EIS)

KW - Electrodes

KW - Finite Length Warburg (FLW)

KW - Gerischer dispersion

KW - Distribution function of relaxation times (DFRT)

UR - http://www.scopus.com/inward/record.url?scp=85037982334&partnerID=8YFLogxK

U2 - 10.1016/j.ssi.2017.11.021

DO - 10.1016/j.ssi.2017.11.021

M3 - Article

VL - 314

SP - 103

EP - 111

JO - Solid state ionics

JF - Solid state ionics

SN - 0167-2738

ER -