## 3 Results and Discussion
### In-Situ XRD Studies of the Electrode Materials  
Initial RT (room temperature) lattice parameters and the unit cell volume of the as-synthesized samples are presented in Figure 2a,b, respectively. With increasing the copper content, there was a gradual decrease in the \(a\) and \(b\) parameters. The exception was the value of the \(b\) parameter for the NCNCO01 sample, which was higher than that for the NCNCO00 sample. This fact might be explained by an unequilibrated state of the sample after the synthesis. Such adecrease in the \(a\) and \(b\) parameters is assumed to be caused by a smaller ionic radius of Cu cations compared to the Ni cations in the structure. Considering the oxygen content of these samples, probed by neutron diffraction, being close to stoichiometric, there should be a prevalence of Ni(II) cations in the samples (e.g., 60% for the NCNCO1 sample and more for the compositions with increased copper content), the ionic radius of which, in octahedral coordination, is 0.69 A [71]. Ionic radius in the octahedral coordination of Cu(I) is 0.77 A, and Cu(II) is 0.73 A [71], which is larger than that of Ni(II). Hence, we can suggest that Cu cations have a smaller coordination number in the structure (most likely close to IV: Cu(I) is 0.6 A, Cu(II) is 0.57 A [71]). \begin{table}
\begin{tabular}{c c c} \hline
**NCNCO04** & **As Synthesized** & **After the Treatment in Air** \\ \hline \(a\), Å & 5.2987 (1) & 5.2992 (1) \\ \(b\), Å & 5.3742 (1) & 5.3779 (1) \\ \(c\), Å & 12.4573 (2) & 12.4516 (3) \\ \(V\), Å\({}^{3}\) & 354.739 (9) & 354.85 (1) \\ y (Nd/Ca) & \(-\)0.0119 (8) & \(-\)0.0121 (9) \\ z (Nd/Ca) & 0.3595 (2) & 0.3603 (2) \\ \({}^{1}\)U (Nd/Ca). Å\({}^{2}\) & 0.0113 (7) & 0.0126 (8) \\ U (Ni/Cu). Å\({}^{2}\) & 0.0079 (8) & 0.0098 (9) \\ z (O1) & \(-\)0.0123 (3) & \(-\)0.0102 (4) \\ U (O1). Å\({}^{2}\) & 0.010 (1) & 0.013 (1) \\ \({}^{2}\)F (O1) & 0.97 (2) & 0.94 (2) \\ y (O2) & 0.0369 (7) & 0.0433 (7) \\ z (O2) & 0.1736 (4) & 0.1731 (5) \\ U (O2). Å\({}^{2}\) & 0.017 (1) & 0.017 (1) \\ F (O2) & 0.92 (1) & 0.92 (2) \\ wR/GoF & 4.72/2.13 & 4.84/2.39 \\
4+\(\delta\) & 3.77 (4) & 3.72 (5) \\ \hline \end{tabular} \({}^{1}\)U—atomic displacement factor; \({}^{2}\)F—occupancy of a site.  
\end{table} 
Table 3: Results of the Rietveld refinement of the NCNCO04 structure obtained at 50 \({}^{\circ}\)C by TOF NPD. The \(c\) lattice parameter, on the contrary, increased with increasing the copper content. This shows elongation of the oxygen octahedrons in the \(c\) direction, in agreement with the tendency of Cu ions to form a square-plane coordination, and further confirms our suggestion. Moreover, the neutron diffraction experiments showed the presence of oxygen vacancies mostly in the apical sites for the compositions with high copper content. This can explain the non-linear behavior of the \(c\) parameter for the NCNCO03 and NCNCO04 samples in relation to the \(c\) parameter of the NCNCO00-NCNCO02 samples. The unit cell volume initially increased (being higher for NCNCO01 than for NCNCO02) and then remained almost the same for the NCNCO03 and NCNCO04 samples. This might suggest reaching the solubility limit in this series. These results agree well with those obtained in [49], where the solubility limit in the Nd\({}_{1.6}\)Ca\({}_{0.4}\)Ni\({}_{1-y}\)Cu\({}_{y}\)O\({}_{4+\delta}\) series was established to be equal to y = 0.35. Figure 3a,b and Figure 4a,b show the change in the lattice parameters and the unit cell volume of the NCNCO02 sample when heating first in the synthetic air flow and then in the He flow. The dependencies for other samples are presented in the supplementary materials (Figures S12-S19). Upon heating in both atmospheres, there was a decrease of orthorhombic strain that manifested itself in a gradual increase in the \(a\) parameter value and a simultaneous decrease in the \(b\) parameter value.