A first-principles comparative study of lithium, sodium, and magnesium storage in pure and gallium-doped germanium: Competition between interstitial and substitutional sites.

Thermodynamics and kinetics of Li, Na, and Mg storage in Ge are studied ab initio. The most stable configurations can consist of tetrahedral, substitutional, or a combination of the two types of sites. In the dilute limit, Li and Na prefer interstitial, while Mg prefers substitutional sites. At higher concentrations of Li, Na, and Mg, there is a combination of interstitial and substitutional sites. This is an important finding, as most previous ab initio studies of alloying type electrode materials ignored substitutional sites. Insertion energies computed at dilute concentration (x = 1/64) show that Na and Mg insertion are not thermodynamically favored in Ge vs. the formation of bulk Na and Mg, as opposed to Li insertion which is favored. We investigate the effect of p-doping of Ge (with Ga) on the thermodynamics and find that it considerably lowers the defect formation energies associated with the insertion of Li/Na/Mg at tetrahedral sites. On the other hand, the energetics associated with Li/Na/Mg insertion at substitutional sites are not significantly affected. In addition, we compute the migration energy barriers for Li/Na/Mg diffusion between two tetrahedral sites (0.38/0.79/0.66 eV), between two substitutional sites (0.77/0.93/1.83 eV), and between two sites of different types (2.15/1.75/0.85 eV).