## 3 Results and Discussions  
Figure 1 shows the XRD patterns of PBCCux powders before and after the application of thermal stress. All the peaks were indexed as a single phase of the tetragonal lattice structure with a space group of P4/mmm for the pristine specimen [21, 22]. In the XRD pattern after thermal stress application, as shown in Figure 1b, additional peaks corresponding to the secondary phase, BaO, were observed. Thermal degradation formed the BaO secondary phase, which is an insulating phase that could lead to a reduction in the conductivity of PBCCux [13, 14]. This result corresponds to study of [PERSON] et al., which is that A\(-\) metal ions are easily precipitated on the surface in an oxidizing atmosphere, air atmosphere, and this is due to the nature of the perovskite oxide to terminate the surface with the AO layer [23]. Figures 2 and 3 exhibit XPS core level spectra for pristine PBCCux and PBCCux after applying thermal stress for 100 h on 1050 \({}^{\circ}\)C. The core level spectra of the Co 2p\({}_{3/2}\) and Ba 3d\({}_{5/2}\) states were observed at 775 eV to 785 eV and a weak satellite shake-up peak induced by Co\({}^{2+}\) and Co\({}^{3+}\) appeared at 785 eV to 790 eV in Figure 2 [24, 25, 26, 27]. Cu 2p\({}_{3/2}\) and Pr 3d\({}_{5/2}\) core-level spectra were detected in the range of 922 eV to 938 eV in Figure 2 [28, 29]. Table 1 shows the oxidation values of the B-site metal ions in the specimen before and after the application of thermal stress which is calculated by area ratio shown in Figures 2 and 3. For both specimens, the average oxidation value exhibited a decreasing trend as the Cu content increased, and it was calculated that the average oxidation value increased in all specimens after thermal stress was applied. As BaO forms on the surface, the A-site metals have fixed oxidation states, whereas the B-site transition metals Co and Cu can change their  
Figure 1: XRD patterns of PBCCux: (**a**) Pristine and (**b**) After applying thermal stress for 100 h on 1050 \({}^{\circ}\)C.  
oxidation states more easily [30, 31]. The charge imbalance induced by BaO formation can be compensated by increasing the oxidation value of the B-site metal ion in Equation (1):  
\[\Pr^{3+}\text{Ba}^{2+}\text{Me}_{2}^{n+}\text{O}_{5+\delta}\rightarrow\Pr^{3+} \text{Ba}_{1-x}^{2+}\text{Me}_{2}^{(n+x)+}\text{O}_{5+\delta}+x\text{BaO (surface)} \tag{1}\]  
Figure 2: Core-level spectra (black solid line) together with the fit results (colored area) for pristine PBCCu0., Ba 3d\({}_{5/2}\) and Co 2p\({}_{3/2}\): (**a**) PBCO; (**b**) PBCCu0.2; (**c**) PBCCu0.5, Pr 3d\({}_{5/2}\) and Cu 2p\({}_{3/2}\). (**d**) PBCO; (**e**) PBCCu0.2; (**f**) PBCCu0.5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & \multicolumn{3}{c}{**Pristine**} & \multicolumn{3}{c}{**After Applying Thermal Stress for 100 h on 1050 \({}^{\circ}\)C**} \\ \cline{2-7}  & & **PBCCu0** & **PBCCu0.2** & **PBCCu0.5** & **PBCCu0** & **PBCCu0.2** & **PBCCu0.5** \\ \hline \multirow{3}{*}{Co} & Co\({}^{2+}\) (\%) & 5.39 & 4.18 & 3.69 & 5.97 & 4.66 & 4.05 \\  & Co\({}^{3+}\) (\%) & 63.13 & 62.05 & 70.81 & 35.96 & 46.95 & 50.27 \\  & Co\({}^{4+}\) (\%) & 31.48 & 33.77 & 25.5 & 58.07 & 48.39 & 45.68 \\ \hline \multirow{2}{*}{Cu} & Cu\({}^{1+}\) (\%) & – & 12.41 & 6.59 & – & 28.42 & 25.31 \\  & Cu\({}^{2+}\) (\%) & – & 87.59 & 93.41 & – & 71.58 & 74.69 \\ \hline \multicolumn{7}{l}{Average oxidation number} & 3.26 & 3.15 & 2.89 & 3.52 & 3.26 & 2.99 \\ \hline \end{tabular}
\end{table} 
Table 1: Ionic ratio of B-site metal ions and average oxidation state for pristine and thermally degraded specimens. Figure 3: Core-level spectra (black solid line) together with the fit results (colored area) for PBCCu0 after applying thermal stress for 100 h on 1050\({}^{\circ}\)C, Ba 3d\({}_{5/2}\) and Co 2p\({}_{3/2}\): (**a**) PBCO; (**b**) PBCCu0.2; (**c**) PBCCu0.5, Pr 3d\({}_{5/2}\) and Cu 2p\({}_{3/2}\); (**d**) PBCO; (**e**) PBCCu0.2; (**f**) PBCCu0.5. Figure 4 shows the O 1 s core-level spectra before and after the application of thermal stress.