Promising performances for a La_0.6Sr_0.4Co_0.8Fe_0.2O_3-δ cathode with a dense interfacial layer at the electrode-electrolyte interface

Abstract

As for the commonly studied La_0.6Sr_0.4Co_0.2Fe_0.8O_3-δ (6428), here, a very low area-specific resistance (ASR) was measured for La_0.6Sr_0.4Co_0.8Fe_0.2O_3-δ (6482) cathode deposited on a Ce_0.9Gd_0.1O_2-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.

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:

$$ {Z}^{\ast}\left(\mathrm{CPE}\right)=\frac{1}{Q\kern0.5em {\left( j\omega \right)}^{\alpha}}\kern0.5em \mathrm{with}\kern0.5em -1\le \alpha \le +1\kern0.5em \mathrm{and}\kern0.5em Q>0, $$

(1)

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:

$$ {Z}^{\ast }=\frac{R}{1+ RQ{\left( j\omega \right)}^{\alpha}}=\frac{R}{1+ RQ{\omega}^{\alpha}\left( \cos \frac{\alpha \pi}{2}+ j \sin \frac{\alpha \pi}{2}\right)}={Z}^{\prime }+ j{Z}^{{\prime\prime} } $$

(2)

so,

$$ {Z}^{\prime }=\frac{R\left(1+ RQ{\omega}^{\alpha} \cos \frac{\alpha \pi}{2}\right)\ }{1+{\left( RQ{\omega}^{\alpha}\right)}^2+2 RQ{\omega}^{\alpha} \cos \frac{\alpha \pi}{2}} $$

(3)

and

$$ {Z}^{{\prime\prime} }=\frac{-{R}^2 Q{\omega}^{\alpha} \sin \frac{\alpha \pi}{2}}{1+{\left( RQ{\omega}^{\alpha}\right)}^2+2 RQ{\omega}^{\alpha} \cos \frac{\alpha \pi}{2}}. $$

(4)

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:

$$ {F}_{\mathrm{C}}=\frac{1}{2\pi {(RQ)}^{\frac{1}{\alpha}}}. $$

(5)

Then, it is possible to determine the expressions of Z’_C and Z”_C at this characteristic frequency F _C :

$$ {Z}_{\mathrm{C}}^{\prime }=\frac{R}{2} $$

(6)

$$ {Z}_{\mathrm{C}}^{{\prime\prime} }=-\frac{R}{2} \tan \frac{\alpha \pi}{4}. $$

(7)

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:

• 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.

• 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 .

• 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:

$$ Q=\frac{1}{R{\left(2\pi {F}_{\mathrm{C}}\right)}^{\alpha}}. $$

(8)

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.:

$$ C=\frac{1}{2\pi {RF}_{\mathrm{C}}}, $$

(9)

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.