# The Evolution of Solid Oxide Fuel Cell Materials
## 3 Materials Systems
### Perovskite-Related Materials
This is shown using MD results in Figure 2a [91]. What the MD results by [PERSON] et al. [91] showed is that cation disorder in the Gd-Ba sublattice will result in a decrease in the oxygen diffusivity with the diffusion becoming more isotropic (there is now significant diffusion in the c-axis). Figure 2c quantifies the differences in the oxygen self-diffusion in the c-axis and the a-b plane with respect to the level of cation disorder [91]. In the left y-axis of this figure is the ratio of the diffusivity in the c-axis over the diffusivity in the a-b plane, whereas the right y-axis represents the total diffusivity [91]. The x-axis corresponds to the antisite disorder, i.e., the ratio of Gd atoms occupying a Ba site over the Gd atoms occupying a Ba or Gd lattice site. Considering the zero of the x-axis, that is when there is no antisite disorder, there is in essence no diffusivity in the c-axis (anisotropic diffusion) [91], whereas the total diffusivity (predominantly in the a-b plane) is maximum [91]. At the other extreme (i.e., for the x-axis value of 0.5) where there is maximum antisite disorder, the total diffusivity is minimized, whereas the left y-axis is nearly 1 (i.e., diffusion becomes isotropic) [91]. What can be deduced is that cation disorder in the double perovskites will minimize oxygen self-diffusion [91]. Therefore, for SOFCs, these systems should be ordered and oriented in a way that they benefit from the maximum oxygen diffusion in the a-b plane. In essence, cation antisite disorder is a design parameter that can be used to tune the energetics of diffusion and direct the diffusion mechanism. The key findings and activation energies for the perovskite-related materials considered here are summarized in Table 1.  
Figure 1: The structure and oxygen self-diffusion in Pr\({}_{2}\)NiO\({}_{4+\delta}\). (**a**) The crystal structure, where NiO\({}_{6}\) octahedra are green, Ni ions are blue and O ions are red (c-axis is the vertical axis); MD calculations at 1100 K and \(\delta=0.09875\) predicting the isosurface of the O diffusion sites (in the a–b plane) and (**b**) maximum entropy method results [90]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Activation Energy/eV** & **Comments** \\ \hline La\({}_{2}\)NiO\({}_{4+\delta}\) & 0.51 & [29], Classical MD, anisotropic mechanism along the \(\mathrm{a-b}\) plane, intersticaly mechanism \\ La\({}_{2}\)NiO\({}_{4+\delta}\) & 0.54–0.56 & [29], Experiment \\ GdBaCo\({}_{2}\)O\({}_{5+\delta}\) & 0.50 & [91] Classical MD, anisotropic mechanism along the \(\mathrm{a-b}\) plane. Cation antisite disorder retards diffusion, makes it more isotropic \\ Sr\({}_{0.75}\)Y\({}_{0.25}\)CoO\({}_{2.625}\) & 1.56 & [8], Classical MD, isotropic mechanism, vacancy mechanism \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The activation energies of oxygen diffusion and comments on the mechanism of oxygen diffusion in representative oxides. Figure 2: (a) Classical MD results of the oxygen diffusion pathways in (**a**) ordered and (**b**) disordered GdBaCo\({}_{2}\)O\({}_{5.5}\) for \(\delta=0.5\) at T = 900 K. (**c**) The ratio of diffusivities in the \(\mathrm{a-}\) and \(\mathrm{c-axis}\) (D\({}_{\mathrm{c}}\)/D\({}_{\mathrm{a}}\) represented by \(+\) and the blue line) with respect to the cation disorder for \(\delta=0.5\) at T = 1200 K. The second \(\mathrm{y-axis}\) represents the diffusivity values (\(\times\), red line) with respect to the cation disorder [91].