Abstract
As for the commonly studied La0.6Sr0.4Co0.2Fe0.8O3-δ (6428), here, a very low area-specific resistance (ASR) was measured for La0.6Sr0.4Co0.8Fe0.2O3-δ (6482) cathode deposited on a Ce0.9Gd0.1O2-δ (GDC) electrolyte with addition of a thin (1 μm) dense LSCF film deposited by spin coating at the interface between the GDC electrolyte and a 40-μm-thick screen-printed electrode. The ASR ranged from 1 Ω.cm2 at 500 °C, 0.11 Ω.cm2 at 625 °C and value as low as 0.03 Ω.cm2 at 700 °C. Impedance spectra collected in between 500 and 700 °C were carefully studied. They could all be modelled with two R//CPE in series which are likely associated to the oxygen reduction reaction itself (dissociation/adsorption/ionization) at low frequency and to the oxide ion transfer at the electrode/electrolyte interface at high frequency.
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The authors are grateful to the Région Nord-Pas de Calais for the attribution of an “Emergent Project” called OPERAH which funded a part of this work.
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Appendix
Appendix
The complex impedance of a resistance R in parallel with a constant phase element CPE circuit can easily be calculated and the determination of the characteristic parameters such as F C, R, α, Q and C can be made.
For the definition of the CPE, we took the one proposed by P. Zoltowski [32] as follows:
α and Q are constants independent of frequency but which could depend on temperature. Moreover, Q is directly proportional to the active area.
The complex impedance of the R//CPE circuit can be written as follows:
so,
and
From Nyquist diagram, it can be seen that Z” presents a maximum Z”C at a characteristic frequency F C . The expression of F C is obtained from the derivative dZ”/dF = 0. After some calculations, we obtain the following:
Then, it is possible to determine the expressions of Z’C and Z”C at this characteristic frequency F C :
It can be noted that Eqs. 2, 3 and 4can be written as a function of R, α, F and F C by replacing RQω α by (F/F C)α and (RQω α)2 by (F/F C)2α.
Now, it is possible to determine the values of R, α and F C with graphical means as follows:
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R is obtained from Z’(logF) curve such as R = R 0 − R ∝ where R 0 corresponds to the Z’ value measured at the lowest frequency and R ∝ to the highest frequency. In the same way, R can be obtained from the Nyquist diagram with the intercepts of the curve with the Z’ axis.
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F C is obtained from the maximum Z” C of the peak of Z”(logF) curve. It can also be obtained from the Nyquist diagram as F C corresponds to the frequency of the maximum Z” C .
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α is obtained from the amplitude Z” C such as α \( =-\frac{4}{\pi}\ {tan}^{-1}\left(\frac{2{Z^{"}}_{\mathrm{C}}}{R}\right) \). It can also be obtained from the Nyquist diagram such as \( \alpha =\frac{\beta \left(\mathrm{rad}\right)}{\pi} \) or \( \alpha =\frac{\beta \left(\mathrm{degrees}\right)}{180} \), where β is the angle determined by the center of the semicircle and the two radius joining respectively R 0 and R ∝ on the Z’ axis. In this case the use of a compass and a protractor permits to determine α.
So, for each of the three parameters R, α and F C two values can be determined graphically by two manners. Then, for each parameter, a mean value can be calculated which also permits to deduce a mean value for the parameter Q as follows:
It is possible to introduce a capacitance C of a parallel R//C circuit which would have the same characteristic frequency F C as the R//CPE circuit, i.e.:
C is not the physical capacitance of the sample but an equivalent capacitance as the R//C circuit simulates only one time constant τ c = RC whereas in the sample at high temperature, there are a distribution of time constants.
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Dumaisnil, K., Carru, JC., Fasquelle, D. et al. Promising performances for a La0.6Sr0.4Co0.8Fe0.2O3-δ cathode with a dense interfacial layer at the electrode-electrolyte interface. Ionics 23, 2125–2132 (2017). https://doi.org/10.1007/s11581-017-2061-6
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DOI: https://doi.org/10.1007/s11581-017-2061-6