## 3 Results
### Electrochemical Study of Composites  
YSZ-based solid electrolyte possesses ionic conductivity with a hopping mechanism. According to [PERSON]'s circuit, an impedance spectrum of YSZ ceramics consists of two arcs, one is located at high frequencies and refers to grain resistivity while the other is located at low frequencies and refers to the resistivity of grain boundaries [33; 34]. When the percolation threshold in graphene-zirconia composites is reached (at -2 wt.%. rGO addition), the conductivity mechanism changes and the electronic component appears in the impedance spectra. In particular, two arcs disappear and total resistivity decreases for at least four orders of magnitude with the drop of activation energy from 1.1 eV to 0.1-0.2 eV [8].  
Figure 6: SEM images of the surface of sintered (**a**) Z0; (**b**) Z0.25; (**c**) Z1; (**d**) Z2 ceramics.  
The obtained impedance spectra of the Z0-Z2 samples are close to typical for YSZ without substantial change of conductivity, even after 2 wt.% rGO is introduced in the ceramic matrix (Figure 8). Nevertheless, the shapes of the obtained arcs are flattened, and they slightly merge with each other. The resistivities of grains (Figure 8a) for Z0, Z0.25 and Z2 ceramics are close to each other. At the same time, the resistivity of Z1 is 4.3 times higher than that for Z2 and Z0 ceramics. When the temperature increases, arcs corresponding to grain boundaries become visible (Figure 8b). A minimum value is observed for Z0, and then it monotonically increases with the rGO content increase. This results in a \(R_{Z0.25}/R_{Z0}\) ratio equal to \(\sim\)2.5 and \(R_{Z1}/R_{Z0}\) ratio equal to \(\sim\)4. The ratio for the Z2 sample is out of the existing trend with \(R_{Z2}/R_{Z0}\) -1.73.  
Based on the obtained spectra, temperature dependencies of conductivity (Figure 9) were plotted using Equation (2). All the samples obey linear log Arrhenius dependence with the determination coefficient R\({}^{2}\) > 0.99. The maximum conductivity level of \(\sigma\) \(\sim\)0.01 S/cm at 650 \({}^{\circ}\)C was reached for the Z0.25 sample, which is close to the typical value for YSZ ceramics [35]. The conductivities of grains for all samples are almost equal in the whole temperature range with activation energies of 1.06 and 1.10 eV, respectively. Ceramics Z0 shows relatively lower conductivity values with the same activation energy of 1.06 eV. At the same time, the Z1 sample possesses much lower conductivity and higher activation energy of 1.23 eV, which leads to the \(\sigma_{Z0.25}/\sigma_{Z1}\) ratio change from \(\sim\)8 at 200 \({}^{\circ}\)C to \(\sim\)2.6 at 450 \({}^{\circ}\)C.  
Figure 7: SEM images of the cross section of sintered (**a**,**b**) Z0; (**c**,**d**) Z0.25; (**e**,**f**) Z1; (**g**,**h**) Z2 ceramics.  
Figure 8: Impedance arcs of ceramics Z0–Z2 obtained at (a) 300 \({}^{\circ}\)C, (b) 500 \({}^{\circ}\)C.  
Figure 9: Temperature dependencies of conductivity of (a) \(Z1\) sample, (b) grain conductivity for Z0–Z2 samples, (c) grain boundary conductivity for Z0–Z2 samples.  
Data obtained for grain boundary conductivities differ from the ones for grain components (Figure 9c; Table 3). Activation energies of grain boundaries in the series gradually decrease from 1.31 eV for the Z0 sample to 1.16 eV for the Z2 sample. It results in the following specific conductivity changes: the Z2 sample possesses the highest conductivity values of the grain boundaries at relatively low temperatures (250-350 \({}^{\circ}\)C); at temperatures higher than 450 \({}^{\circ}\)C, Z0 ceramics turns to be more conductive; the lowest conductivity among all the compositions and the highest activation energy of 1.35 eV are observed for the Z1 sample. The ratios \(\sigma_{Z0.25}/\sigma_{Z1}\) are the same as seen previously, i.e., \(\sim\)4.5 at 350 \({}^{\circ}\)C and only \(\sim\)1.6 at 650 \({}^{\circ}\)C.