## 1 Introduction  
The solid oxide fuel cell (SOFC) is an attractive eco-friendly energy conversion system because of its high energy conversion efficiency, fuel flexibility, and low emission of pollutants [1; 2; 3; 4; 5; 6; 7; 8]. Recently, many studies have focused on developing low-temperature (400-600 \({}^{\circ}\)C) SOFCs (LT-SOFCs) because the intermediate-to-high-operating temperature (600-1000 \({}^{\circ}\)C) causes critical issues, such as material degradation and expensive maintenance costs [9; 10]. However, the low-operating temperature leads to high cathodic polarization due to the slow kinetics of oxygen ion transfer. In this respect, mixed ionic and electronic conductors (MIECs) have received great attention because of their high electrocatalytic activity for the oxygen reduction reaction (ORR), high electrical conductivities, fast surface exchange coefficient, and high oxygen diffusivity characteristics. Also, the ORR occurs not only at the triple phase boundary (TPB) but at the entire surface of the cathode (i.e., the two-phase boundary, 2 PB), because oxygen anions can transport through the MIEC bulk [11]. Among MIECs, layered perovskites have been widely used for SOFC cathode material because of its exceptional electrochemical catalytic activity [12; 13; 14; 15; 16]. These layered perovskites have a general formula of AA'B\({}_{2}\)O\({}_{5+\delta}\), where A, A', and B are trivalent lanthanide ion, alkaline earth metal, and a first-row transition metal, respectively. The layered perovskite consists of a stacking sequential layer of... \(\mid\)A'O \(\mid\) BO\({}_{2}\)\(\mid\) AO\({}_{\delta}\)\(\mid\) BO\({}_{2}\)\(\mid\)... along the \(c\)-axis [4; 10; 17]. This layered structure possesses a disorder-free channel for ion motion in the \(\mid\) AO\({}_{\delta}\)\(\mid\) and \(\mid\) BO\({}_{2}\)\(\mid\) planes that can provide fast oxygen-ion transport [18; 19]. Recently, many researchers have devoted efforts to further improving the electrochemical performance of the layered perovskite by substituting various metal ions [20; 21; 22; 23; 24; 25; 26]. For example, substituting constant-valence state metal ions (e.g., Nb\({}^{5+}\), Ta\({}^{5+}\), and Ti\({}^{4+}\)) into the perovskite could increase the ionic conductivity by reducing the lattice strain that occurs during the oxygen ion transport [27; 28; 29; 30]. Especially, in the oxygen transport membrane system, it was reported that doping scandium into the perovskite-type oxide improves the electrochemical property by lowering the activation energy for oxygen ion transfer [31; 32]. In this regard, the Sc\({}^{3+}\) doped layered perovskite oxide is expected to exhibit a lower cathode polarization of the LT-SOFC. The crystal structure along with the A and/or B site cations play a significant role in determining the electrical and ionic properties of PrBaCo\({}_{2}\)O\({}_{5+\delta}\) (PBCO) perovskite oxides. Based on the literature data and experimental observations, several interesting relationships between the crystal structure, composition, and electrochemical properties have been established. In this regard, the critical radius for the oxide-ion transfer, unit cell free volume, and Goldschmidt tolerance factor (t\({}_{\text{f}}\)) are the key factors that govern the oxide ion conductivity in PBCO perovskite oxides [33; 34; 35]. Among those properties, the Goldschmidt tolerance factor is a useful indicator for evaluating distortion of the crystal structure [36; 37]. A Sc\({}^{3+}\) ion substitution into the layered perovskite material PBCO could provide a beneficial effect on the of lattice crystal structure. The Goldschmidt tolerance factor (t\({}_{\text{f}}\)) approaches 1 by substitution of Sc\({}^{3+}\) in PBCO. Since the t\({}_{\text{f}}\) value of PBCO is 1.012, it is possible to reduce the t\({}_{\text{f}}\) by doping the B site with an ion larger than the Co ion.