## 3 Results and Discussion
The oxygen contents (\(5+\delta\)) of samples at room temperature were determined by iodometric titration. Average \(\delta\) values of PBCO and PBCSc at room temperature were 0.6833, 0.6367 with standard deviation values of 8.916 \(\times\) 10\({}^{-3}\) and 9.251 \(\times\) 10\({}^{-3}\), respectively. In the temperature range of 100-900 \({}^{\circ}\)C, the Sc\({}^{3+}\) substitution into PBCO leads to relatively decrease the oxygen content. Figure 3b presents the electrical conductivities of the samples at various temperatures. The electrical conductivities of all samples increase with decreasing temperature, implying a typical metallic behavior. All the samples show sufficient electrical conductivity values of 589, 503, and 344 S cm\({}^{-1}\) for PBCO, PBCSc, and SP-PBCSc, respectively at 500 \({}^{\circ}\)C, which are higher than the requirement for efficient SOFC operation (>10 S cm\({}^{-1}\)). PBCSc shows smaller electrical conductivity than PBCO due to disturbance of the electron conduction, which originated from the substitution of constant valance state Sc\({}^{3+}\) ion for multivalent Co ion [24; 40; 41]. Substitution of the Sc\({}^{3+}\) reduces the overlapping between multivalent Co ion with the oxygen 2p orbitals and decreases the electron transport between the multivalent cobalt cations, which is known as Zener double exchange. The Goldschmidt tolerance factor is a useful indicator to determine the distortion of a unit cell structure, defined by the following equation;  
\[\mathrm{t}_{\mathrm{f}}=\frac{(\mathrm{r}_{\mathrm{A}}+\mathrm{r}_{\mathrm{O}} )}{\sqrt{(\mathrm{r}_{\mathrm{B}}+\mathrm{r}_{\mathrm{O}})}}, \tag{1}\]  
where \(\mathrm{r}_{\mathrm{A}}\), \(\mathrm{r}_{\mathrm{B}}\), and \(\mathrm{r}_{\mathrm{O}}\) are the ionic radii of cation A, cation B, and oxygen, respectively. Figure 4 shows that the substitution of Sc\({}^{3+}\) into PBCO can converge the Goldschmidt tolerance factor of PBCO near to 1 (e.g., from 1.012 to 1.006), implying that Sc\({}^{3+}\) doping could reduce distortion of the perovskite structure and alleviate the local strain of the lattice. Figure 4: Goldschmidt tolerance factor and specific free volume of PBCO, PBCSc, and SP-PBCSc. Figure 3: (**a**) thermogravimetric analysis (TGA) and (**b**) electrical conductivity for the samples as a function of temperature in air. The evaluation of free volume could be also a significant structural parameter to estimate electrochemical performance. Free volume is defined as the difference between the perovskite unit cell volume and the total volume occupied by the ions [36]. The large free volume could provide sufficient space for oxygen transport in the unit cell, resulting in the reduction of activation energy for oxygen diffusion [42]. Therefore, we calculated the specific free volume of PBCO and PBSCs, defined as follows;  
\[\text{(specific free volume)}=\text{(free volume)}/\text{(unit cell volume)}, \tag{2}\]  
As seen in Figure 4, PBSCs exhibits higher specific free volume, 0.213, than that of PBCO, 0.206, indicating that PBSCs can be considered as a more favorable structure for oxygen transfer due to larger free volume for oxygen migration than that of PBCO. Figure 5a shows impedance spectroscopy to evaluate the electrocatalytic activities of samples. The area specific resistances (ASRs) were evaluated by alternating current (AC) impedance spectroscopy with GDC symmetrical cells in air. As can be expected from the favorable structural properties of PBSCs for oxygen anion transfer and ORR, (i.e., Goldschmidt tolerance factor and specific free volume) the PBSCs shows a lower ASR value of 0.44 \(\Omega\) cm\({}^{2}\) than that of PBCO (0.58 \(\Omega\) cm\({}^{2}\)). Substitution of the Sc\({}^{3+}\) ion into PBCO is a more effective method to reduce the impedance of the cathode material than several approaches recently reported to enhance the electrocatalytic activity of cathode materials.