## 3 Results and Discussion
### Oxygen Mobility in the NCNCO Materials  
Oxygen mobility was studied by a temperature-programmed isotope exchange of oxygen (TPIE) with C\({}^{18}\)O\({}_{2}\) in a flow reactor. According to the TPIE data for the NCNCO00-NCNCO04 samples (Figure 7), the isotope exchange started at the temperature of 250-300 \({}^{\circ}\)C The TPIE peak in the range of 400-450 \({}^{\circ}\)C corresponds to the oxygen fraction with the fastest substitution rate, and its intensity decreases with increasing copper content as evidence of a decrease in the fraction of the most mobile oxygen fraction (interstitial oxygen [67]). The tracer diffusion coefficients for this form of oxygen, \(D_{over}^{*}\), and its fraction with respect to the total oxygen amount, \(\theta_{fast}\), were determined based on the numeric modeling described in the details elsewhere [78; 79] (Table 6). It was impossible to unambiguously distinguish other peaks on the TPIE curves; hence, the average weighted tracer diffusion coefficient, \(D_{over}^{*}\), values were used for the comparison of oxygen mobility in the samples with different copper content, calculated as follows:  
\[D_{over}^{*}=\sum_{i}\frac{\theta_{i}\times D_{i}^{*}}{100\%}, \tag{3}\]  
where \(\theta_{i}\) is the fraction of oxide anions characterized by a tracer diffusion coefficient, \(D_{i}^{*}\). Temperature dependencies and concentration dependencies of the oxygen tracer diffusion coefficients for the NCNCO00-NCNCO04 samples are presented in Figure 8a,b, respectively. It is seen that kinetics of oxygen transport decreases with the copper content increasing, which manifests itself in the decrea \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \(D_{fast}^{*}\) **(cm\({}^{2}\) s\({}^{-1}\))** & \(\theta_{fast}\) **(\%)** & \(D_{over}^{*}\) **(s\({}^{-1}\))** & \(E_{a,D_{t}}\) **(k) mol\({}^{-1}\))** \\ \hline NCNO & & 60 & \(1.3\times 10^{-9}\) \\ NCNCO1 & & 25 & \(4.9\times 10^{-10}\) \\ NCNCO2 & \(3.3(\pm 1.6)\times 10^{-9}\) & 20 & \(3.3\times 10^{-10}\) & \(120\) \\ NCNCO3 & & 5 & \(2.6\times 10^{-10}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Oxygen tracer diffusion coefficients (\(D^{*}\)) at 700 \({}^{\circ}\)C and their effective activation energies (\(E_{a,D}\)) for Nd\({}_{1.6}\)Ca\({}_{0.4}\)Ni\({}_{1-y}\)Cu\({}_{y}\)O\({}_{4+\delta}\) samples according to TPIE with C\({}^{18}\)O\({}_{2}\) data. Figure 7: Temperature-programmed isotope exchange of oxygen with C\({}^{18}\)O\({}_{2}\) in the flow reactor for the NCNCO samples with different copper content. Points—experiments, lines—modeling. share of fast oxygen, \(\theta_{\text{\emph{fast}}}\). There is a lack of information in the literature on the copper doping effect on oxygen transport properties. In [35], decreasing the \(D^{\ast}\) values for the La\({}_{2}\)Ni\({}_{1-x}\)Cu\({}_{x}\)O\({}_{4+\delta}\) by increasing the copper content was demonstrated. Along with this, a non-monotonous dependence of oxygen permeability of the Pr\({}_{2}\)Ni\({}_{1-x}\)Cu\({}_{x}\)O\({}_{4+\delta}\) (x = 0.1-0.5) membranes on the copper content was demonstrated, with the maximum corresponding to x = 0.2. Nevertheless, for x > 0.2, a decrease in oxygen permeability was demonstrated and probably related to a decrease in oxygen excess [80]. Infiltration of porous lanthanum strontium ferrite (LSF) electrodes with aqueous nitrates solutions containing Pr, Ni, and Cu related to the Pr\({}_{2}\)Ni\({}_{0.7}\)Cu\({}_{0.3}\)O\({}_{4}\) and Pr\({}_{2}\)Ni\({}_{0.6}\)Cu\({}_{0.4}\)O\({}_{4}\) compositions significantly reduced the polarization resistance at 650 \({}^{\circ}\)C from 0.98 \(\Omega\) cm\({}^{2}\) to 0.16 and 0.13 \(\Omega\) cm\({}^{2}\), respectively, due to an increased surface exchange rate [81]. For the B-site excessive Pr\({}_{2}\)Ni\({}_{0.8}\)Cu\({}_{0.2+x}\)O\({}_{4+\delta}\) (x = 0-0.10) and Pr\({}_{2}\)Ni\({}_{0.5-x}\)Cu\({}_{x}\)O\({}_{4+\delta}\) (x = 0-0.25), increasing oxygen permeability with increasing copper content was attributed to the anomalous grain growth caused by a Cu-rich liquid phase.