## 2 Materials and Methods  
### Synthesis of the Electrode Materials and Their Standard Characterization  
Materials of the Nd\({}_{1.6}\)Ca\({}_{0.4}\)Ni\({}_{1-y}\)Cu\({}_{y}\)O\({}_{4+\delta}\) series (y = 0.0-0.4), denoted as NCNCO00-NCNCO04, were obtained using the glycerol-nitrate combustion method. CaCO\({}_{3}\) (99.9 wt.%), Nd\({}_{2}\)O\({}_{3}\) (99.4 wt.%), and CuO (99 wt.%) (Reakhim, Moscow, Russia), Ni(CH\({}_{3}\)COO)\({}_{2}\)\(\cdot\)4H\({}_{2}\)O (99.9 wt.%) (Sigma-Aldrich, St. Louis, MO, USA) were used as starting reagents. The Nd\({}_{2}\)O\({}_{3}\), CaCO\({}_{3}\), and CuO powders were preliminarily calcinated in air to remove adsorbedwater and gases at 1100 \({}^{\circ}\)C (12 h), 500 \({}^{\circ}\)C (3 h), and 400 \({}^{\circ}\)C (3 h), respectively. The required amount of Nd\({}_{2}\)O\({}_{3}\), CaCO\({}_{3}\), and CuO, calculated as follows:  
\[0.4\text{CaCO}_{3}+0.8\text{Nd}_{2}\text{O}_{3}+(1-y)\text{Ni}(\text{CH}_{3} \text{COO})_{2}\cdot 4\text{H}_{2}\text{O}+y\text{CuO}+\text{O}_{2}\rightarrow\text{Nd}_{1,6} \text{Ca}_{0.4}\text{Ni}_{1-y}\text{Cu}_{y}\text{O}_{4}+\text{CO}_{2}+\text{H} _{2}\text{O}, \tag{1}\]  
was dissolved in a diluted nitric acid (65%) (Vekton, St. Petersburg, Russia), and then Ni(CH\({}_{3}\)COO)\({}_{2}\cdot 4\text{H}_{2}\text{O}\), dissolved in distilled water, was added and thoroughly mixed. Glycerol (Vekton, St. Petersburg, Russia), serving as a chelating agent and an organic fuel, was added in a stoichiometric amount defined by the combustion reaction:  
\[14\text{HNO}_{3}+5\text{C}_{3}\text{H}_{8}\text{O}_{3}=7\text{N}_{2}+15\text{ CO}_{2}+27\text{H}_{2}\text{O}. \tag{2}\]  
The resulting mixture, placed in a heat-resistant glass vessel, was heated under constant stirring up to 340 \({}^{\circ}\)C on the electric plate until evaporation and spontaneous combustion. The obtained NCNCO00-NCNCO04 powders were sequentially annealed in air using a PKO-1,4-100 furnace (UralElektropech', Yekaterinburg, Russia) at temperatures of 1000 \({}^{\circ}\)C (12 h, one time) and 1100 \({}^{\circ}\)C (12 h, repeatedly),with a heating/cooling rate of 200 \({}^{\circ}\)C h\({}^{-1}\) and with intermediate grindings in ethanol in an agate mortar with a pestle for 1 h. The total annealing time of the samples reached 60 h. After the final synthesis step, the powders were ground with the addition of ethanol in an agate mortar with a pestle for 2 h.  
The standard characterization of the prepared powders was performed using the Brunauer-Emmett-Teller (BET) method and an XRDanalysis. The specific surface area, \(S_{BET}\), of the NCNCO00-NCNCO04 powders was determined using a META SORBI N 4.1 analyzer (Moscow, Russia). The powder XRD data were collected in air at room temperature using a Shimadzu XRD-7000 diffractometer with a graphite monochromator in the CuK\(\alpha\)1 radiation in the 20 angle range of 20-80\({}^{\circ}\) with a step of 0.02\({}^{\circ}\) and a counting time of 5 s at each point. The parameters of the NCNCO00-NCNCO04 crystal structure were refined using FullProf Suite software [50]. The results of the standard characterization are represented in Table S1 in the supplementary materials. The electrode materials for the electrode collector layers LaNi\({}_{0.6}\)Fe\({}_{0.4}\)O\({}_{3}\) (LNF) and La\({}_{0.6}\)Sr\({}_{0.4}\)MnO\({}_{3}\) (LSM) were synthesized via a two-step ceramic technology, as described elsewhere [51,52]. The unit cell parameters and \(S_{BET}\) for the collector materials are given in Table S1. Synthesis of the Electroflite Materials and Preparation of Dense Electrolyte Substrates for the Electrochemical Studies.