## 3 Results and Discussion
Therefore, considering the diffusivity showed by other perovskite oxides, the results herein suggest that the YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.5}\) is a fast oxide ion conductor. As for the electronic conductivity, the calculated DOS (Figure 3d) corroborates that the electronic charge density remains delocalized throughout the system. According to the calculated DOS, YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.5}\) is a semi-metallic compound (0 eV band gap). These results agree with the MIEC characteristics found in YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.56}\) by [PERSON] et al. [21]. Several authors have previously reported an oxygen loss of around 5% when YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.56}\) is heated above 673 K in air [15; 22]. The oxygen loss, which leads to an oxygen composition around YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.17}\), is fully reversible, and the YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.56}\) phase is recovered  
Figure 3: **(a)** MSD at 1400 K for the YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.5}\) (**b)** Arrhenius plot of diffusion coefficients obtained at each simulated temperature for YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.5}\). **(c)** Calculated trajectories for oxide ions in the FeO\({}_{1.5}\) plane of YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.5}\). Note that the diffusivity of oxygen (O3) takes place only in this plane. **(d)** Calculated atom projected DOS for the YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.5}\). on cooling. In an attempt to achieve an oxygen concentration as close as possible to that experimentally observed on heating (\(\delta\) \(\sim\) 0.17), models of YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.2}\) have also been studied by DFT. Since the \(\delta\) = 0.2 term is not compatible with a 2a\({}_{\text{p}}\)\(\times\) 2a\({}_{\text{p}}\)\(\times\) 3a\({}_{\text{p}}\) supercell, the crystallographic models are constructed taking a 2a\({}_{\text{p}}\)\(\times\) 5a\({}_{\text{p}}\)\(\times\) 3a\({}_{\text{p}}\) supercell. Among the models consisting of Fe exclusively in tetrahedra [FeO\({}_{4}\)] and octahedra [FeO\({}_{6}\)] coordination, the most stable configuration according to the Ewald summation method is selected (Figure 4a). For this configuration, AIMD calculations are performed at 800, 1000, 1200, 1600, and 1800K (up to 14 ps). The MSD (Figure 4b) indicates that oxygen ions do not diffuse in this material. Indeed, the oxygen anions appear to jump around their equilibrium position as any other ion in the structure. This proves the influence of transition metal coordination and points towards the beneficial effect of anion disorder on the oxygen ion diffusivity in the YSCFO system. More work is needed to confirm this hypothesis. The calculated DOS of the most stable configuration (Figure 4c) reveals that YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.2}\) is a metallic phase in which the electronic charge density is delocalized in the bands formed by Cu and Fe 3\(d\)-orbitals. The itinerant character of electrons in the metallic phases of the YSCFO system has been previously discussed for end-term YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{8}\)[16]. To verify that oxygen vacancies in the FeO\({}_{1+\delta}\) plane are responsible for oxygen diffusion, a YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.75}\) phase was investigated in which there is excess oxygen in the yttrium plane (Figure 5a). Note that the extra oxygen drives the coordination around some Cu ions from square pyramidal to octahedral. Although this configuration has not been experimentally observed in the YSFCO system, it is present in layered perovskite oxides GdBa(Mn, Co)\({}_{2}\)O\({}_{5-x}\)[40, 41]. AIMD simulation performed at 1400 K reveals high oxygen mobility (calculated D (1400 K) = 7.62 \(\times\) 10\({}^{-6}\) cm\({}^{2}\)/s), similar to the AIMD value found for YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.5}\) (see Figure 3a). Notably, oxygen diffusion is anisotropic, occurring only in the FeO\({}_{1+\delta}\) plane, while the oxygen added in the Y plane does not diffuse (Figure 5b).