## 5 Double Perovskites  
The interest on double perovskite materials (AA\({}^{\prime}\)B\({}_{2}\)O\({}_{5-6}\)) as cathodes for SOFC was motivated by the seminal studies of [PERSON] et al. [69; 136]. The secondary ion mass spectrometry work by [PERSON] et al. [73] confirmed the high oxygen self-diffusion of oxygen in GdBaCo\({}_{2}\)O\({}_{5+\delta}\) and determined a tracer diffusion coefficient of 0.6 eV. This is also in agreement with the classical molecular dynamics work of [PERSON] et al. [137] with the calculated activation energy of diffusion of 0.5 eV as the 0.1 eV difference can be traced in the methodological errors. Additionally, [PERSON] et al. [137] showed that the oxygen self-diffusion mechanism is in the a-b- plane. In particular the MD calculations revealed that oxygen migration in this double perovskite is highly anisotropic taking place in the Gd-O and the adjacent Co-O layers. The energetics and mechanisms of oxygen self-diffusion in double perovskites are also supported by the MD studies of [PERSON] et al. [138] and experimental work [139]. The classical atomistic and MD studies of [PERSON] et al. [53] showed that oxygen diffusion in PrBaCo\({}_{2}\)O\({}_{5+\delta}\) is analogous but with a lower activation energy of diffusion (0.35 eV) constituting this material very promising. An interesting feature of the double perovskites is the antisite disorder in the cation sublattice. The impact of cation ordering on oxygen diffusion was experimentally observed by [PERSON] et al. [69; 136] in the related material Gd\({}_{0.5}\)Ba\({}_{0.5}\)MnO\({}_{3\pm\delta}\). In particular, [PERSON] et al. [69; 136] determined a significant increase in the oxygen  
Figure 2: In the left part of the figure the tetragonal Pr\({}_{2}\)NiO\({}_{4+\delta}\) where O is in red, NiO\({}_{6}\) octahedra in green and Ni in blue (c-axis is the vertical axis). The right part of the figure represents the isosurface connecting the O diffusion sites in the a-b plane as derived using molecular dynamics at 1100 K and \(\delta\) = 0.09875 Reproduced by permission from the Owner Societies [125].  
diffusion coefficient in the cation ordered perovskite as compared to the cation disordered perovskite. The question that arises is: how does the antisite disorder in the cation sublattice impact the energetics and mechanism of oxygen self-diffusion in the double perovskite system? [PERSON] et al. [137] used classical MD calculations to show that the self-diffusion of oxygen in GdBaCo\({}_{2}\)O\({}_{5+S}\) is highly dependent on the cation disorder. In particular, for ordered GdBaCo\({}_{2}\)O\({}_{5.5}\), the oxygen diffusion mechanism is anisotropic along the a-b plane, whereas disorder in the cation sublattice (formation of Ba and Gd antisites) results to a reduction of the oxygen diffusivity and diffusion in the c-axis (refer to Figure 3) [137]. The higher the disorder in the cation sublattice, the more isotropic the mechanism of oxygen self-diffusion [137]. From a technological viewpoint this implies that the thermal history of the material and sample preparation are important parameters that could impact the energetics and mechanism of diffusion of these systems. For SOFC applications ordered double perovskites should be preferred.