## 3 Materials
### Cathode  
The reduction of the oxygen in SOFC takes place at cathode. The reaction that takes place at cathode is given by [10; 12]. \[\frac{1}{2}\mathrm{O}^{2}\left(\mathrm{gas}\right)+2e^{-}\left(\mathrm{ cathode}\right)\rightarrow\mathrm{O}^{2-}\left(\mathrm{electrolyte}\right) \tag{1}\]  
The cathode must have high electronic and oxygen ion conductivity, matching thermal expansion coefficient with electrolyte, chemical stability at operating temperatures, sufficient porosity and better catalyst for reduction reaction [10; 12]. It is generally considered that electrochemical reaction takes place at triple phase boundary, _i.e._, at the point of contact of electronic conductor, oxygen ion conductor and gas as shown in Figure 2[10; 12; 37; 38]. It is liable for the significant loss of voltages in SOFC mostly due to a great deal of polarization losses connected to reduction reaction [10; 37; 38]. The excessively used cathode material is strontium doped lanthanum manganite (La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3}\) (LSM)) in high temperature SOFC [10; 12; 39; 40; 41; 42; 43; 44; 45; 46]. It is associated to a manganite family of perovkites in which lanthanum is partially replaced with strontium. Perovskite structures give a great deal of variation in compositional and oxygen stoichiometry that helps in optimizing catalytic and electrical properties. This cathode material exhibits better performance at high temperatures because this efficiency is significantly good at a temperature above 800 \({}^{\circ}\)C. If stoichiometrically there is excess lanthanum or strontium oxide, it will result into the formation of insulating phase like La\({}_{2}\)Zr\({}_{2}\)O  
Figure 1: Schematic of solid oxide fuel cell. Figure 2: Schematic of triple phase boundary. and SrZrO\({}_{3}\) due to its interaction with yttria stabilizer zirconia leading towards poor performance. This problem can be resolved by increasing the Mn concentration and keeping fabrication temperature \(<\)1300 \({}^{\circ}\)C [10; 12; 42; 45; 46; 47; 48; 49; 50]. LSM has negligible oxygen ion conductivity at 900 \({}^{\circ}\)C with high electronic conductivity. Hence, the region of reaction is limited only to interface of electrode and electrolyte. This leads toward the necessity that cathode must be porous enough to diffuse oxygen at interface of electrode/electrolyte so that reduction of oxygen can take place. A composite layer or graded structure of LSM/YSZ is in practice to increase triple phase boundaries (TPB) [12; 39; 41; 46]. The cathode reaction in electron conducting perovskite type materials can take place in many steps and across different paths depending upon the type of electrode material. In pristine electronic conductor materials, the most accepted mechanism is surface pathway. The bulk pathway is an accepted mechanism in mixed ionic electronic conductor (MIEC) and while electrolyte surface pathway is considered in composite materials like LSM/YSZ [10; 38]. Figure 3 represents three pathways of oxygen reduction. A lot of efforts/concentrations are being given to increase the performance of electrode for low and intermediate temperature SOFCs [10; 37; 39; 40; 42; 43; 44; 45; 46; 47]. A number of cathode materials having better electronic/ionic conductivity and increased oxygen exchange rate are investigated. It would permit the oxygen reduction action to prolong inside the cathode structure or at the fuel/cathode interconnection, which will consequently increase the reaction rate [10; 12; 37; 39; 40]. For this purpose, other perovskite materials like a La\({}_{1-x}\)Sr\({}_{x}\)Fe\({}_{1-y}\)Co\({}_{y}\)O\({}_{3}\) (LSCF) are being explored. The electronic and ionic conductivity of some cathode materials (MIEC, mixed ionic and electronic conductivity) are shown in Table 2[12; 43; 47; 48]. Although these materials have good performance but they exhibit poor chemical stability due to their reaction (solid state) with YSZ electrolyte.