# Kinetics of Ions in Post-Lithium Batteries
## 1 Introduction  
The growing need for electricity generation and storage has led to a plethora of techniques seeking better energy materials to meet growing needs in technological applications that include, but are not limited to, electric vehicles, grid electricity storage, electronic products, energy harvesting, and nanoelectronics [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Lithium compounds such as lithium carbonate (Li\({}_{2}\)CO\({}_{3}\)), lithium oxide (Li\({}_{2}\)O), and lithium hydroxide (LiOH) offer favorable electrochemical fundamentals and cost-effective manufacturing options for the fabrication of rechargeable batteries, which utilizes approximately three-quarters of the global production of lithium at present. In recent years, the explosive demand for lithium is raising questions of sustainability mostly due to rather limited known global reserves and regional concentration. Nearly half of the world's known economically recoverable reserves of 105 million tonnues are concentrated in Bolivia, Chile, and Argentina (the so-called _lithium triangle_) while nearly half of the annual production of lithium is currently taking place in Australia. On the demand, side there are doubts as to whether there is enough lithium to move into electricity for the nearly 1.5 billion cars on the planet, let alone provide for grid storage and non-transportation applications. Although there seems to be sufficient lithium to enable, at least the early stages of, the green transition and Net Zero by 2050, numerous environmental, supply chain, and sustainability challenges, motivate, with a sense of urgency, scientific research and development in post-lithium energy storage technologies. The novel materials considered for post-lithium energy storage have typically exotic crystallography and are composed of substances that are not abundant or sustainable considering the massive scale required for technological solutions to make a real difference [26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50]. Here, we consider three paradigms in energy storage applications, such as sodium (Na), divalent conductors (magnesium (Mg)), and finally oxygen (O), which have been proposed as alternatives to Li-ion conductors. The drive to substitute Li ions is due to its high price and the limited lithium resources [43]. Sodium in comparison is more than four orders of magnitude more abundant in the Earth's crust and also in seawater, whereas the working principle of Na-ion batteries is similar to Li-ion batteries [43]. The technological issues in Na-ion battery materials include slow insertion/extraction kinetics and low theoretical capacity and these can be traced to the larger size of the sodium ion as compared to the lithium ion. The crystal structure is the matrix where the ions migrate and the community is trying to assess which crystal structures will provide the necessary kinetics for Na ion that will compensate for its larger size as compared to Li ion. Magnesium-based rechargeable batteries are currently being considered by the community as potential candidates for the next generation energy storage because of their high gravimetric and volumetric capacity, non-toxicity, abundance, and higher melting temperature [44; 45]. Importantly, the ionic size of the Mg\({}^{2+}\) ion is comparable to the Li\({}^{+}\) ion, however, the stronger ionic interaction of Mg\({}^{2+}\) ions in the lattice will make intercalation harder [44; 45]. These issues can be rectified by reducing the size of the cathode ions in the crystal and by increasing the shielding of Mg\({}^{2+}\)[33; 34]. The first part of this review briefly discusses the computational methods to model oxides. In this part, molecular dynamics (MD) and density functional theory (DFT) are discussed. The second part of the review is focused on recent efforts to substitute lithium ions for energy storage applications.