## 3 Results
### Electrochemical Properties  
Electrochemical properties were evaluated on the samples sintered at 1000 \({}^{\circ}\)C due to the best morphology achieved. Data were recorded in the air between 200 and 800 \({}^{\circ}\)C to evaluate the influence of copper precursors on conductivity as well as to separate the bulk and the grain interior influences. The impedance data can be fitted with three equivalent circuits connected in series. Each circuit is founded by a resistance and a constant phase element in parallel corresponding to the different responses (semi-circles or arcs) of the grain interior, grain-boundary, and electrode to the electrochemical properties. Generally, due to the microstructure and the relaxation properties of the different electrolytes, the separation of the three semi-circles cannot be always identified during the tests. At the same time, the occurrence of these contribution depends also by the operating temperatures, However, as described in the brick-layer theory [33], the Nyquist plots of the copper-doped GDC samples show in the experimental frequency range all three arcs only at 200 \({}^{\circ}\)C as reported in Figure 7a. In the temperature range of 300-450 \({}^{\circ}\)C, both the grain boundary contribution and electrode polarisation influence the electrochemical properties, and the bulk response is not visible or is more difficult to record (Figure 7a'). Increasing the operative temperature (T \(>\) 450 \({}^{\circ}\)C), the electrochemical semi-circles related to the bulk and grain boundaries cannot be examined, and only the electrode contribution lies inside the studied frequency range [34], as reported in Figure 7a'. The electrochemical data are arranged in the form of Arrhenius plots in Figure 7b,c. Compared to un-doped GDC the electrochemical data of total conductivity are not fitted with a single straight line because of a change in the slope at 450 \({}^{\circ}\)C relieves the presence of the grain boundary contribution. As a consequence, the Arrhenius plots of total conductivity can be separated into two different areas correlated to different temperatures and related to two activation energies as reported in Table 4. For GDC, in the temperature range of 200-700 \({}^{\circ}\)C, the conductivity is an order of magnitude lower in comparison to Cu co-doped samples. Additionally, there is no significant difference in \(\mathrm{E_{a}}\) below and above 450 \({}^{\circ}\)C because according to SEM images un-doped GDC has a rough microstructure and very low densification. This behavior reflects the ohmic resistance recorded at all temperatures investigated and the insignificant incidence of grain boundary resistance. Copper doped samples instead have a similar behavior above 450 \({}^{\circ}\)C indicating that electrochemical properties are comparable while at temperatures lower than 450 \({}^{\circ}\)C the differences are ascribed to the grain boundary conductivities. Figure 7d summarizes an extensive examination of literature to compare the results obtained in this study at 700 \({}^{\circ}\)C, using the impedance values, the sintering temperatures, and the different types of co-dopants [9; 14; 16; 17; 35; 36; 37; 38; 39; 40]. In this work, the value of conductivity increases with dopant composition reaching a maximum for \({}^{2}\)Cu of 2.23\(\cdot\)10\({}^{-3}\)-9.19\(\cdot\)10\({}^{-2}\) S cm\({}^{-1}\) in the operative temperature of 200-800 \({}^{\circ}\)C. The achieved result is an improvement considering samples with similar compositions and sintered at high temperatures. These improvements can be directly associated with the sol-gel synthesis procedure. Compared to the traditional synthesis process where aids are mixed and milled to the electrolyte powders by mechanical methods, during the sol-gel process nanometer and submicron powders can be produced.