We present a comparative computational study of Li, Na, and Mg insertion into α and β tin. While β-Sn is most stable at normal conditions, reports suggested that α-Sn should be stabilized by Li ion insertion (e.g. ), which is also intuitive as the β phase is much denser. Energetics of doping and diffusion properties of the two phases being very different, the question of phase competition in Sn is critical for the performance of Sn anodes for Li - as well as post-Li - batteries, such as Na and Mg ion batteries.
Using a DFT / LCAO setup tuned to reproduce well absolute and relative cohesive energies of α and β tin, we compute insertion energetics for interstitial Li, Na, and Mg well-dispersed defects at a range of concentrations. While dopants prefer tetragonal sites in the cubic diamond lattice, several unique insertion sites exist in β-Sn. The most energetically favored sites in β-Sn are different for different dopant types.Phase competition is dopant-type dependent. Specifically, at low concentrations ( MSn where M=Li, Na, and x<1/8), interstitial insertion sites of Li and Na in α-Sn are more favored to those in β-Sn (by of the order of 0.1 eV), but β-Sn becomes more favored for higher x values. However, Mg insertion sites in β-Sn are preferred to those in α-Sn for all concentrations studied here (by about half an eV). Insertion energetics of Li and Na in both α-Sn and β-Sn is competitive with the metal's cohesive energies, and therefore both phases might play a role in storage depending on the cycling rate. On the contrary, the insertion energy of Mg, while lower vs. the vacuum reference state, is much higher than Mg cohesive energy for the α phase. The energy in the β phase is higher than the cohesive energy by 0.1-0.2 eV which is near the expected DFT accuracy. β-Sn could therefore work as the anode for Mg batteries.We will also discuss the often ignored effect of vibrations on relative phase stability of the Sn anode.