## 2 Materials and Methods  
Nano-crystalline Ce\({}_{0.8(1-x)}\)Gd\({}_{0.2(1-x)}\)Cu\({}_{x}\)O\({}_{[1.9(1-x)+x]}\) electrolytes were prepared by modified sol-gel combustion synthesis. All precursors with high purity, Sigma Aldrich \(>\) 99.9%, (Ce(NO\({}_{3}\))\({}_{3}\cdot\)6H\({}_{2}\)O, Gd(NO\({}_{3}\))\({}_{3}\cdot\)6H\({}_{2}\)O, (Cu(NO\({}_{3}\))\({}_{2}\cdot\)2.5H\({}_{2}\)O, and C\({}_{6}\)H\({}_{8}\)O\({}_{7}\cdot\)H\({}_{2}\)O) were mixed in the desired molar ratio in deionized water according to the procedure reported in previous works [23; 24; 25]. Calcination temperature was fixed at 600 \({}^{\circ}\)C for 2 hours to obtain the final crystalline structure.  
A reference of un-doped GDC was prepared as a reference was additionally prepared. The list of all electrolytes with the general formula of Ce\({}_{0.8(1-x)}\)Gd\({}_{0.2(1-x)}\)Cu\({}_{x}\)O\({}_{[1.9(1-x)+x]}\) (0.005 \(\leq\) x \(\leq\) 0.02 and their designation are reported in Table 1.  
The effect of copper addition on lattice parameters and crystalline nature of calcined powders was examined by X-ray spectroscopy using a Miniflex II (Rigaku Co., Japan) diffractometer (CuK\(\alpha\) radiation, 2 range 5-90\({}^{\circ}\)). MAUD software was used to fit the diffractometer data and to calculate the cell parameters and crystallite size.  
Transmission electron microscopy, TEM (Tecnai G II, FEI Co., United States), was used to understand the morphology features of powders while thermo-dilatometer analysis was accomplished to investigate the sintering behavior, i.e. sintering mechanism and shrinkage, of the various samples. Dilatometer tests were carried out in air using an instrument (DIL 402 PC Netzch Instruments, Germany) in the temperature range 25-1400 \({}^{\circ}\)C. For the examination, a suitable quantity of calcined powder was uniaxially pressed at 140 MPa for 2 min to form small pellets with a diameter of 10 mm and a thickness of approx. 3.5 mm. The suitable firing temperature was fixed in the temperature range of 1000-1200 \({}^{\circ}\)C for 3 h and the microstructure of thin sintered pellets was studied by scanning electron microscopy (SEM) (Inspect F, FEI Co., USA). According to the ASTM C373-88 procedure, the relative density of the sintered electrolytes was measured by Archimedes' principle. The achieved density values were compared with the theoretical densities calculated from crystallographic parameters, allowing by the equation:  
\[\rho=\frac{Z\cdot\sum_{i}v_{i}\cdot M_{i}}{a^{3}\cdot N_{A}} \tag{1}\]  
From the Equation (1), \(v_{i}\) is the stoichiometric coefficient, \(Z\) is the number of formula units per unit cell (i.e., 4 for the fluorite structure of ceria), \(M_{i}\) is the molar mass of atom i in g\(\cdot\)mol\({}^{-1}\), \(a\) is the lattice parameter from XRD patterns, and \(N_{A}\) is Avogadro's number.  
Finally, a frequency response analyzer (FRA, Solartron 1260, Ametek, UK) coupled with a dielectric interface (Solartron 1296, Ametek, UK) was used for impedance analysis (EIS). Nyquist plots were recorded in the temperature range of 200-800 \({}^{\circ}\)C by means the frequency range of 0.1 Hz-1 MHz applying an AC voltage amplitude of 100 mV. Data fit of impedance spectra was carried out by using ZPlot and Zview software (Scribner Associates Inc, North Carolina, USA).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Samples** & **Dopant (mol\%)** & **Composition** \\ \hline GDC & - & Ce\({}_{0.8}\)Gd \({}_{0.2}\)O\({}_{1.9}\) \\ \({}^{0.5}\)Cu & 0.5 & Cu\({}_{0.005}\)Ce\({}_{0.796}\)Gd\({}_{0.199}\)O\({}_{1.8955}\) \\ \({}^{1}\)Cu & 1 & Cu\({}_{0.01}\)Ce\({}_{0.792}\)Gd\({}_{0.198}\)O\({}_{1.891}\) \\ \({}^{2}\)Cu & 2 & Cu\({}_{0.02}\)Ce\({}_{0.784}\)Gd\({}_{0.196}\)O\({}_{1.882}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Composition of electrolyte powders prepared.