# Toward Defect Engineering Strategies to Optimize Energy and Electronic Materials
## 3 Defect Engineering Oxygen Diffusion in Ceria
### Doping and Strain Strategies  
Oxygen self-diffusion in ceria is mediated by oxygen vacancies. Under equilibrium conditions the oxygen vacancy formation energy is high. A way to introduce oxygen vacancies to form an oxygen  
Figure 1: (**a**) Cu-Nb bilayer; (**b**) quasiperiodic pattern formed by the interface between Cu and Nb planes; (**c**) unrelaxed interface vacancy; (**d**) relaxed interface vacancy; (**e**) ground state Cu-Nb interface with 5 at % vacancies; (**f**) ground state Cu-V interface with about 0.8 at % vacancies. Dark red atoms that have less than six nearest neighbours in the interface Cu plane. Reproduced with permission from [20]. American Institute of Physics, 2010.  
deficient structure is via doping with trivalent cations. Trivalent cations can substitute at cerium lattice sites with the defect equation in Kroger Vink notation being expressed as:  
\[\mathrm{X_{2}O_{3}\overset{CeO_{2}}{\rightarrow}2X_{Ce}^{\prime}+V_{O}+3O_{O}^{X}} \tag{1}\]  
Every oxygen vacancy is charge compensated by two trivalent ions that are introduced into the cation sublattice. Trivalent doping in ceria is an efficient strategy leading to a SOFC electrolyte material with high oxygen ion diffusivity (for example, 2-3 orders of magnitude higher diffusivity as compared to yttria stabilized zirconia) in conjunction with relatively lower reduction temperatures [23]. In a previous molecular dynamics (MD) study [26], the activation energies of the oxygen migration of rare-earth doped ceria (Ce\({}_{0.9}\)R\({}_{0.1}\)O\({}_{1.95}\) where R = Yb, Er, Ho, Dy, Gd, Sm, Nd, and La) as a function of the dopant ionic radius were considered (black line of Figure 2). The molecular dynamics calculations revealed that Nd-doped ceria had the lowest activation energy of oxygen migration (refer to Figure 2) [26]. This is reflected also in the oxygen diffusivities and therefore Nd-doped ceria is appropriate for intermediate temperature (500-700 \({}^{\circ}\)C) SOFCs. It should be stressed, however, that at very high temperatures the energy barrier for oxygen diffusion is not significantly impacted by the association energy (Coulombic interactions and relaxation of the ceria lattice) of the dopant-oxygen vacancy clusters [26; 27]. The community also imposes strain to increase oxygen diffusion and other physical properties in metal oxides [26; 28]. From an experimental viewpoint, strain can be introduced by the formation of interfaces between dissimilar oxides and due to the complexity, atomistic simulation is commonly used to gain insights [29]. The advantage of computational modeling techniques is that they can be employed to deconvolute different contributions so that it becomes clear how strain impacts defect processes such as oxygen diffusion. This is essential in order to gain an understanding of the effect of strain and to be able to tune and optimize strain fields to achieve enhanced oxygen diffusion (Figure 3). Strain fields can be introduced (a) locally via doping with isovalent atoms or (b) by the formation of heterostructures resulting in epitaxial strain fields mainly near the interface between the layers of the dissimilar materials [30; 31; 32]. Interestingly, the work of [PERSON] et al. [33] determined up to an eight order-of-magnitude increase in conductivity for epitaxially-grown zirconia/strontium titanate heterostructures and this motivated the community [26; 34]. To clarify this unprecedented result, numerous atomistic simulation studies were employed given that in these it is easier to employ and control strain as compared to the experiment [26; 34]. Figure 2: Molecular dynamics derived activation energies of oxygen migration with respect to the dopant ionic radius and uniaxial strain in Ce\({}_{0.9}\)R\({}_{0.1}\)O\({}_{1.95}\)[26]. At any rate, the accuracy of molecular dynamics simulations to describe oxygen diffusion in doped ceria will depend upon the potential model that should appropriately describe the thermal expansion of doped CeO\({}_{2}\).