# The Evolution of Solid Oxide Fuel Cell Materials
## 3 Materials Systems  
### Perovskite-Related Materials  
Perovskite and perovskite-related materials are particularly important for a range of applications from SOFC to high-temperature superconductivity [78; 79; 80; 81; 82; 83; 84; 85; 86; 87]. For example, the community has investigated the ReBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\delta}\) (where Re = rare earth element or Y) system following the discovery of high-temperature superconductivity [78]. Through doping and external conditions, these systems showed improvements in the critical temperature of superconductivity (T\({}_{\rm c}\)) [80; 81]. In fact, these systems are still also being investigated for fusion applications [85; 86; 87]. Regarding materials for SOFC lanthanum nickelate (La\({}_{2}\)NiO\({}_{4+\delta}\)), gadolinium barium cobaltate (GdBaCo\({}_{2}\)O\({}_{5+\delta}\)) and other perovskite-related systems have been considered in the past two decades [29; 35; 88; 89; 90]. Considering first oxygen self-diffusion in La\({}_{2}\)NiO\({}_{4+\delta}\), it should be considered that the experimental determination of its energetics and mechanism is difficult due to its crystal structure and oxygen hypo- or hyperstoichiometry. For example, it was difficult to determine the energetics and mechanism of oxygen self-diffusion in La\({}_{2}\)NiO\({}_{4+\delta}\)[10; 29]. Experimental time-of-flight secondary ion mass spectrometry investigations on La\({}_{2}\)NiO\({}_{4+\delta}\) by [PERSON] et al. [29] determined an activation energy of oxygen migration of 0.54-0.56 eV in excellent agreement with the classical [PERSON] work (0.51 eV [89]). [PERSON] also revealed that the dominant oxygen self-diffusion mechanism in La\({}_{2}\)NiO\({}_{4+\delta}\) is the interstitialcy mechanism (in the a-b plane) in which oxygen interstitials displace apical oxygens from the NiO\({}_{6}\) octahedron, which are thereafter promoted to adjacent oxygen interstitial sites [89]. Although praseodymium (Pr) has a very negative effect in perovskite-related high-T\({}_{\rm c}\) superconductivity, Pr-based perovskite materials such as PrBaCo\({}_{2}\)O\({}_{5+\delta}\) or Pr\({}_{2}\)NiO\({}_{4+\delta}\) were considered by the SOFC community due to their high oxygen self-diffusion [90; 93]. In the intermediate temperature range, Pr\({}_{2}\)NiO\({}_{4+\delta}\), similarly to the isostructural La\({}_{2}\)NiO\({}_{4+\delta}\), has a tetragonal crystal structure (I4/mmm space group, refer to Figure 1a). This structure can be described as perovskite layers (PrNiO\({}_{3}\)) intergrown with rock salt layers (PrO) [90]. There is a mismatch between the layers which leads to the introduction of oxygen interstitials in the Pr\({}_{2}\)O\({}_{2}\) bilayers [90]. This, in turn, leads to the local distortion of the NiO\({}_{6}\) octahedra (refer to Figure 1a) due to the Coulombic repulsion between the oxygen interstitial and the apical ions in the NiO\({}_{6}\) octahedra [89]. This effect is key if the aim is to understand the mechanism of oxygen self-diffusion of Pr\({}_{2}\)NiO\({}_{4+\delta}\) at the atomic level. The interstitial oxygen self-diffusion mechanism in the a-b plane in Pr\({}_{2}\)NiO\({}_{4+\delta}\) is common with related systems such as La\({}_{2}\)NiO\({}_{4+\delta}\), as mentioned above, and La\({}_{2}\)CoO\({}_{4+\delta}\)[92]. Figure 1a is based on classical MD calculations and shows the isosurface connecting the oxygen diffusion sites in the a-b plane [90]. This isosurface is in agreement with the maximum entropy method results reported in a related system (Figure 1b, reference [90] and references therein). The community has also investigated the impact of intrinsic point defects such as antisites on the diffusion properties in perovskite materials for SOFCs. An interesting example is GdBaCo\({}_{2}\)O\({}_{5+\delta}\) (double perovskite structure), which has high oxygen diffusivity with an activation energy of 0.5 eV [91]. In ordered GdBaCo\({}_{2}\)O\({}_{5+\delta}\), oxygen self-diffusion is highly anisotropic and takes place primarily in the Gd-O and adjacent Co-O layers [91].