## 3 Results and Discussion
[43; 44; 45] Meanwhile, the ASR value of SP-PBSCs is increased due to its structural change to the cubic Pm\(\overline{3}\)m crystal structure. A similar result was observed in the A-site doped PrBa\({}_{1-x}\)Sr\({}_{x}\)Co\({}_{2}\)O\({}_{5+\delta}\) system; a phase transition was observed for higher Sr content (orthorhombic \(\rightarrow\) tetragonal \(\rightarrow\) cubic structure) [46]. According to the Adler-Lane-Steele (ALS) model [47], the ASR is related to oxygen kinetics, such as bulk diffusion (\(D_{o}^{*}\)) and surface exchange (\(l_{o}^{0}\)); this can be expressed as,  
\[\text{R}_{\text{cathode}}=\frac{\text{RT}}{2\text{F}^{2}}\bigg{[}\frac{\tau}{(1 -\varphi)\text{Sc}_{0}^{2}\text{D}_{o}^{*}\text{K}_{o}^{0}}\bigg{]}^{\frac{1} {2}} \tag{3}\]  
where \(\varphi\), S, and \(\tau\) are the porosity, surface area, and tortuosity, respectively. Assuming that the structural parameters of both PBCO and PBSCs are similar (porosity, cathode surface area, and tortuosity), high bulk diffusion and surface exchange lead to lower ASR values. Therefore, it can be explained that Sc\({}^{3+}\) substitution results in the improvement of oxygen-related electrochemical properties (i.e., fast oxygen diffusion and high surface kinetics on the surface). Total ASR values consist of the sum of the charge-transfer resistance (R\({}_{2}\)) and the non-charge transfer resistance (R\({}_{3}\)) [48]. R\({}_{2}\) is associated with the migration and diffusion of oxygen species from the triple phase boundary to the electrolyte, while R\({}_{3}\) is generally related to the non-charge transfer process (e.g., oxygen surface exchange and gas-phase diffusion on the surface of the electrode). The non-charge transfer resistance (R\({}_{3}\)) of PBSCs is lower than that of PBCO, (Figure 5b) indicating that Sc\({}^{3+}\) substitution considerably lowers non-charge transfer resistance (R\({}_{3}\)) [25]. Arrhenius plots of the polarization resistances for PBCO, PBSCs, and SP-PBSCs are shown in Figure 5c. The activation energies determined by the slope of the Arrhenius plots are related to the oxygen kinetics of the cathode including the oxygen adsorption, dissociation, and diffusion behavior [14; 49]. The activation energies (E\({}_{\text{a}}\)) are 102 and 96 kJ mol\({}^{-1}\) for PBCO and PBSCs, respectively. This result matches well with other reports on the enhancement of oxygen surface exchange through partial substitution of Sc\({}^{3+}\)[31; 32]. Figure 6 presents the current-voltage (I-V) curves and corresponding power density curves for the cathode/GDC/Ni-GDC cell using humidified H\({}_{2}\) and air, as a fuel and oxidant, respectively. As expected from the lower ASR value of PBSCs, PBSCs exhibits excellent maximum power densities of 1.3 and 0.73 W cm\({}^{-2}\) at 550 and 500 \({}^{\circ}\)C, respectively and these are ~1.5 times higher than those of PBCO. Figure 5: **(a)** Experimental and fitted impedance spectra of symmetrical cells with PBCO, PBCSc, and SP-PBCSc at 500 \({}^{\circ}\)C. **(b)** Comparison of fitted charge-transfer resistance (R\({}_{2}\)) and non-charge-transfer resistance (R\({}_{3}\)) for samples at 500 \({}^{\circ}\)C. **(c)** Arrhenius plot of the polarization resistances for samples. Figure 6: I–V and corresponding power density curves of single cells (Cathode/GDC/Ni-GDC) in a temperature range of 450 to 550 \({}^{\circ}\)C: **(a)** PBCO, **(b)** PBCSc, and **(c)** SP-PBCSc, respectively.