The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

Gavrilyuk, A.L.; Осинкин, Д.А.; Бронин, Д. И.

doi:10.1134/s1023193517060040

Cited by 106 publications

(39 citation statements)

References 32 publications

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“…Distribution of relaxation times (DRT) was used to identify the bulk and grain boundary contributions to the total conductivity. For DRT analysis, a program code developed in [18], based on Tikhonov’s regularization [19] was applied.…”

Section: Methodsmentioning

confidence: 99%

Effect of A-Site Nonstoichiometry on Defect Chemistry and Electrical Conductivity of Undoped and Y-Doped SrZrO3

et al. 2019

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The effect of Sr-nonstoichiometry on phase composition, microstructure, defect chemistry and electrical conductivity of SrxZrO3−δ and SrxZr0.95Y0.05O3−δ ceramics (SZx and SZYx, respectively; x = 0.94–1.02) was investigated via X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray spectroscopy and impedance spectroscopy followed by distribution of relaxation times analysis of impedance data. It was shown that at low Sr deficiency (x > 0.96 and 0.98 for SZx and SZYx, respectively) a solid solution of strontium vacancies in strontium zirconate crystal structure forms, whereas at higher Sr deficiency the secondary phase, zirconium oxide or yttrium zirconium oxide, is precipitated. Yttrium solubility limit in strontium zirconate was found to be close to 2 mol%. Y-doped strontium zirconates possess up to two orders of magnitude higher total conductivity than SZx samples. A-site nonstoichiometry was shown to have a significant effect on the electrical conductivity of SZx and SZYx. The highest total and bulk conductivity were observed at x = 0.98 for both systems. Increasing the conductivity with a rise in humidity indicates that proton conduction appears in the oxides in wet conditions. A defect model based on consideration of different types of point defects, such as strontium vacancies, substitutional defects and oxygen vacancies, and assumption of Y ions partitioning over Zr and Sr sites was elaborated. The proposed model consistently describes the obtained data on conductivity.

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Section: Methodsmentioning

confidence: 99%

Effect of A-Site Nonstoichiometry on Defect Chemistry and Electrical Conductivity of Undoped and Y-Doped SrZrO3

et al. 2019

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“…An overview about the multitude of present approaches regarding the calculation of the DRT is shown in. [9,17,20,22] One of the most frequent mathematical procedures used for this purpose is the Tikhonov regularization: [23,24] min x F l ¼ kAx À yk 2 |ffl ffl ffl ffl ffl ffl {zffl ffl ffl ffl ffl ffl } least squares þl kLxk 2 |fflffl {zfflffl } penalty :…”

Section: Theorymentioning

confidence: 99%

Direct Access to the Optimal Regularization Parameter in Distribution of Relaxation Times Analysis

2020

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The distribution of times (DRT) method has become an important extension for electrochemical impedance investigations. Calculating the DRT is particularly advantageous for complex systems, as it yields an increased resolution in frequency domain. However, the determination of the DRT from experimental impedance data requires special mathematical effort. An often‐used method for the calculation of the DRT is the Tikhonov regularization. The quality of the result of this method depends on the choice of a suitable regularization parameter. This parameter has to be selected by the user. In a former work (N. Schlüter, S. Ernst, U. Schröder, ChemElectroChem 2019, 6, 6027–6037), we showed a method that helps to find the best regularization parameter for given impedance data. However, this test was based on repetitive impedance measurements, which have to be performed at least twice. In this paper, we optimize our previous method to assure the determination of an optimal regularization parameter from just one single impedance spectrum. Eventually, this revision saves measurement time and makes our test also applicable for less time stable measurements.

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“…Details of the experimental setup are presented elsewhere [36]. For the distribution of relaxation time (DRT) analysis, a program code, developed by the authors of [37] on the basis of Tikhonov's regularization [38], was applied. For fuel cell studies, the sample was sealed in the measuring cell by high-temperature glass having a transition temperature of 950 • C. Anode reduction was performed at 900 • C in wet hydrogen.…”

Section: Methodsmentioning

confidence: 99%

Application of Promising Electrode Materials in Contact with a Thin-Layer ZrO2-Based Supporting Electrolyte for Solid Oxide Fuel Cells

et al. 2020

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The paper presents the results of an investigation into thin single- and triple-layer ZrO2-Sc2O3-based electrolytes prepared using the tape-casting technique in combination with promising electrodes based on La2NiO4+δ and Ni-Ce0.8Sm0.2O2-δ materials. It is shown that pressing and joint sintering of single electrolyte layers allows multilayer structures to be obtained that are free of defects at the layer interface. Electrical conductivity measurements of a triple-layer electrolyte carried out in longitudinal and transverse directions with both direct and alternating current showed resistance of the interface between the layers on the total resistance of the electrolyte to be minimal. Long-term tests have shown that the greatest degradation in resistance over time occurs in the case of an electrolyte with a tetragonal structure. Symmetrical electrochemical cells with electrodes fabricated using a screen-printing method were examined by means of electrochemical impedance spectroscopy. The polarization resistance of the electrodes was 0.45 and 0.16 Ohm∙cm2 at 800 °C for the fuel and oxygen electrodes, respectively. The distribution of relaxation times method was applied for impedance data analysis. During tests of a single solid oxide fuel cell comprising a supporting triple-layer electrolyte having a thickness of 300 microns, a power density of about 160 mW/cm2 at 850 °C was obtained using wet hydrogen as fuel and air as an oxidizing gas.

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The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

Cited by 106 publications

References 32 publications

Effect of A-Site Nonstoichiometry on Defect Chemistry and Electrical Conductivity of Undoped and Y-Doped SrZrO3

Effect of A-Site Nonstoichiometry on Defect Chemistry and Electrical Conductivity of Undoped and Y-Doped SrZrO3

Direct Access to the Optimal Regularization Parameter in Distribution of Relaxation Times Analysis

Application of Promising Electrode Materials in Contact with a Thin-Layer ZrO2-Based Supporting Electrolyte for Solid Oxide Fuel Cells

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