## 3 Results
### Sintering Behavior  
The shrinkage, \(\delta\)L/L\({}_{0}\), and the shrinkage rate, \(\delta\)(\(\delta\)L/L\({}_{0}\))/\(\delta\)T, are showed in Figure 3. As reported in the dilatometer analysis, Cu accelerates the sintering process with marked enhancement in the relative densities compared to the undoped GDC (inset of Figure 3). In fact, GDC shrinkage behavior shows a weak sinterability in the temperature range investigated while Cu-doped samples show a prominent peak in the shrinkage rate profile for all compositions investigated. The maximum rate is detected at the highest concentration of copper. The sintering mechanism follows three distinctive stages (denoted by roman numerals, from I to III). The phases are intensely affected by the aid amount. For example, during the first stage, \({}^{2}\)Cu densification begins at approximately 690 \({}^{\circ}\)C with an adequate increase in the shrinkage degree. After this stage, the second phase occurs with the maximum shrinkage rate at  
Figure 2: TEM micrographs of (**a**) pure GDC, (**b**) \({}^{0.5}\)Cu, (**c**) \({}^{1}\)Cu, and (**d**) \({}^{2}\)Cu calcined powders. 915 \({}^{\circ}\)C and the densification process slows down until the end of the last stage (III). Similar sintering behavior can be observed in the other electrolytes with a shrinkage rate delayed, i.e. by \(\sim\)100 \({}^{\circ}\)C in the sample with the lowest copper content. The effect of the copper composition can be furthermore evaluated by the density behavior, as a function of the temperature, in the insets of Figure 3. In this case, \({}^{2}\)Cu and \({}^{1}\)Cu show a similar value of a final density of 93-94%. According to [PERSON] et al. [14], the rapid densification for Cu-doped GDC samples in the temperature range 910-1050 \({}^{\circ}\)C, suggests a liquid phase sintering mechanism due to the formation of a Gd\({}_{2}\)O\({}_{3}\)-CeO\({}_{2}\)-CuO ternary system. The liquid phase sintering is encouraged by the incorporation of copper oxide, which has a lower melting point (1326 \({}^{\circ}\)C) then ceria (2400 \({}^{\circ}\)C) and gadolinium (2420 \({}^{\circ}\)C), decreasing the total melting point of the ternary composition. However, from dilatometer analysis, the significant result is that the temperatures of maximum shrinkage rate: 915 \({}^{\circ}\)C for \({}^{2}\)Cu, 1000 \({}^{\circ}\)C for \({}^{1}\)Cu, and 1090 \({}^{\circ}\)C for \({}^{0.5}\)Cu are greatly lower than pure GDC (above 1500 \({}^{\circ}\)C). According to shrinkage outcomes, to achieve dense electrolytes bodies sintering temperature was fixed in the range 1000-1200 \({}^{\circ}\)C. The values of relative densities after sintering are reported in the following Table 3.  
Compared to densities illustrated in the inset of Figure 3, a slight but acceptable variance is visible. The difference can be ascribed to the different types of analysis. The densities achieved by dilatometer were continuously measured isotropically without fix a dwell time. Table 3 instead shows the relative density after sintering at fixed temperature with a dwell of three hours and final geometrical measurements were found on compacted sintered pellets. The effect on morphology and density cannot be predicted by preliminary analyses because at a comparable density, the microstructure is completely different as visible in Figures 4-6. At sintering  
Figure 3: Shrinkage rate (solid) and linear shrinkage (dotted) as a function of temperature for GDC and Cu co-doped samples and densification curves as a function of temperature (inset). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Sintering Temperature**} \\
**Samples** & **1000 \({}^{\circ}\)C** & **1100 \({}^{\circ}\)C** & **1200 \({}^{\circ}\)C** \\ \hline GDC & 48.7 & 56.8 & 82.4 \\ \({}^{0.5}\)Cu & 90.2 & 98.7 & 99.5 \\ \({}^{1}\)Cu & 98.3 & 98.2 & 98.3 \\ \({}^{2}\)Cu & 99.4 & 99.7 & 99.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Density values of sintered bodies.