# The Evolution of Solid Oxide Fuel Cell Materials
## 3 Materials Systems
### Interfaces and Strain  
Understanding the impact of strain and interfaces is key for the development of more efficient and sustainable materials for SOFC applications [101; 102; 103; 104]. The intriguing study of [PERSON] et al. [4] determined that in nanostructured SrTiO\({}_{3}\)/YSZ/SrTiO\({}_{3}\) heterostructures, there is colossal conductivity. In particular, in this heterostructure, yttria stabilized zirconia (ZrO\({}_{2}\) with 8 mol% Y\({}_{2}\)O\({}_{3}\)) layers under 7% tensile strain have conductivities eight orders of magnitude higher than bulk YSZ [4]. This extreme enhancement in ionic conductivity was treated with skepticism from the community but it nevertheless led to numerous studies in SrTiO\({}_{3}\)/YSZ/SrTiO\({}_{3}\) and related heterostructures [5; 9; 103; 104]. [PERSON] et al. [103] determined that in the SrTiO\({}_{3}\)/YSZ/SrTiO\({}_{3}\) heterostructure, the total conductivity dependence is inconsistent with ionic diffusion in YSZ, whereas the DFT work by [PERSON] and [PERSON] [9] in biaxially strained bulk YSZ predicted ionic enhancement by up to four orders of magnitude. Notably, in that study, the migration energy barriers were calculated using the nudged elastic band (NEB) method in relatively small supercells [9]. What is profound in the studies following the work by [PERSON] et al. [4] is that tensile strain does significantly increase ionic conductivity but this does not translate to an eight-order of magnitude increase in ionic diffusion. Nevertheless, there is increased interest in the oxygen diffusion properties at oxide interfaces [105; 106; 107; 108; 109]. [PERSON] et al. [24] employed ionic interfaces to produce a nonstoichiometric oxygen vacancy concentration. This in turn is very important as oxygen vacancy concentrations at equilibrium are limited, and, therefore, there is a requirement to increase their content as oxygen vacancies are the vehicles of oxygen diffusion in these systems. [PERSON] et al. [24] used the oxide nanobrush architecture to form a substantial nonequilibrium oxygen vacancy concentration at the interface between CeO\({}_{2}\) and Y\({}_{2}\)O\({}_{3}\). This is an important example of how the material architecture (here, the designed interfacial oxide) can be used to increase the formation and tune the diffusion properties of defects. With a similar objective but with a more fundamentally scientific viewpoint, the investigation by [PERSON] et al. [22] showed that the modification of nonstoichiometry in grain boundaries can be employed to tune the diffusion properties. [PERSON] et al. [22] effectively determined that point defects induced by strain in the grain boundaries of La\({}_{1-x}\)Sr\({}_{x}\)MnO\({}_{3\pm 8}\) increase the oxygen diffusivity and diminish the electronic and magnetic order. [PERSON] et al. [109] employed static atomistic simulations to examine the minimum energy oxygen diffusion pathways and activation migration energies at the STO-LCO interface (refer to Figure 3). It was predicted by these calculations that curved pathways have lower migration energies [109]. [PERSON] et al. [109] showed that at the Sr-Cr-La interface layer, the fastest oxygen transport occurs along the a-axis (i.e., in the Cr layer) with an activation energy of migration of 0.36 eV. This migration energy is significantly smaller than the 0.53 eV calculated for oxygen diffusion in bulk LCO using the same methodology [109]. Considering the c-axis of the Cr layer, the activation energy of migration for oxygen is 0.48 eV, i.e., lower by only 0.05 eV as compared to the activation energy of migration in LCO bulk [109]. Therefore, oxygen will preferentially diffuse along the a-axis in the interface layer. In the La-Cr-Sr layer, the b-axis oxygen activation energy of migration is 0.60 eV, which is not significantly lower than the activation energy of migration (0.64 eV) calculated in bulk STO [109].