# Kinetics of Ions in Post-Lithium Batteries
## 5 Tuning the Ionic Diffusion  
Tuning the ionic diffusion is typically carried out by doping as discussed above and by forming interfaces or using external parameters such as strain; also, interfaces are important for energy applications [6; 7; 125; 126; 127; 128; 129; 130; 131; 132; 133; 134; 135; 136; 137]. As the energetics of ionic diffusion are governed by the activation energy of diffusion that is in turn the sum of the migration energy of diffusion (i.e., the energy barrier that the ion has to overcome) and the formation energy (i.e., the number of mobile species, so for an oxygen ion migrating via a vacancy mechanism the formation energy of the oxygen vacancy is important) it is necessary for faster diffusion to lower these terms. For example, [PERSON] and [PERSON] [9] employed DFT calculations to predict the optimum strain conditions that would lower the oxygen ion migration energy barriers in strained yttria-stabilized zirconia. Considering the study by [PERSON] et al. [135] it was determined that designed ionic interfaces (heterointerface between  
Figure 5: A schematic comparison of the potential power and energy density of oxygen ion batteries with related electrochemical technologies [50]. CeO\({}_{2}\) (fluorite) and Y\({}_{2}\)O\({}_{3}\) (bixbyite)) can lead to the formation of a very high concentration of interfacial oxygen vacancies. These fluorite-bixbyite interfaces pave the way for the designed formation, transport, and control of oxygen vacancies and may have applications in memristive and iontronic devices [135]. Notably, the field benefited from the study of [PERSON] et al. [6] which determined a colossal enhancement in the ionic conductivity at ZrO\({}_{2}\):Y\({}_{2}\)O\({}_{3}\)/SrTiO\({}_{3}\) heterostructures. Although there was a lot of research on the claims by [PERSON] et al. [6; 7; 9; 127] there was significant focus and progress in the field in the direction of heterointerfaces. As it was seen in Section 3, Mg and Na ions would benefit from an enhancement in the diffusion energetics. What the energy storage community normally investigates first is the impact of the structure and composition (i.e., crystal structure and hypo-hyperstoichiometry) and doping). Future work should also explore the impact of designed heterointerfaces on the diffusion of Mg and Na ions. The key could well be designing the material interfaces rather than exploring exotic crystallographies and compositions. Designed interfaces could offer the concentration of the vehicles required for ionic transport and lower the migration energy barriers. Doping is an efficient way to tune the migration energy barrier, the number of intrinsic defects required for diffusion, and electronic properties. Considering Na\({}_{3}\)Fe\({}_{2}\)(PO\({}_{4}\))\({}_{3}\) the lowest energy intrinsic defect process is the Na Frenkel (i.e., the formation of a Na vacancy and Na interstitial pair) [95]. This, in turn, will lead to the formation of Na vacancies that are beneficial for Na ion migration as the vacancy mechanism is energetically favorable [95]. Doping the Fe of the site of Na\({}_{3}\)Fe\({}_{2}\)(PO\({}_{4}\))\({}_{3}\) with isovalent dopants (M = Sc, La, Gd, and Y) to form Na\({}_{3}\)(Fe\({}_{x}\)M\({}_{1-x}\))\({}_{2}\)(PO\({}_{4}\))\({}_{3}\) can improve electronic conductivity [95]. Importantly, for Zr doping on the Fe site increases the Na vacancy concentration [95]. Conversely, doping with Si on the P site results in the formation of Na interstitials, which can lead to the enhancement of the capacity of Na\({}_{3}\)Fe\({}_{2}\)(PO\({}_{4}\))\({}_{3}\). For NaZr\({}_{2}\)(PO\({}_{4}\))\({}_{3}\) the Na Frenkel is also the lowest energy intrinsic defect process [47]. Considering isovalent doping it was predicted that K\({}^{+}\) and Ge\({}^{4+}\) are the significant isovalent dopants on the Na and Zr sites [47]. Doping with Yb, Y, Ga, and In on the Zr site leads to the formation of oxygen vacancies and Na interstitials [47].