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Comparison of alpha- and beta- tin for lithium, sodium, and magnesium storage: an ab initio study including phonon contributions

We present a comparative ab initio study of Li, Na, and Mg storage in tin, including phononic effects and phase competition between alpha and beta Sn. Mg doping at low concentration is found to stabilize the beta phase. On the contrary, Li and Na doping is shown to reverse the stability of the phases at room temperature: Li/Na-doped alpha-Sn is more stable than Li/Na-doped beta-Sn up to a temperature of around 380/400 K. This may rationalize the formation of alpha-Sn upon lithiation and delithiation of beta-Sn anodes reported in experimental studies. The changes in phase stability with Li/Na/Mg doping are directly related to the intercalation energies of Li/Na/Mg in one phase versus the other: at 300 K, Li/Na is easier intercalated in alpha-Sn (-0.37/-0.08 eV) than in beta-Sn (0.06/0.49 eV), while Mg intercalation energy is, although positive (i.e. unfavored intercalation), lower in beta-Sn (0.53 eV) than in alpha-Sn (0.66 eV). The temperature effect is found to affect significantly the intercalation energy, by up to 0.13 eV at 300 K. Analysis of diffusion barriers shows that Li, Na, and Mg diffusion in beta-Sn is anisotropic with migration barriers along the (001) direction (respectively 0.01, 0.22, and 0.07 eV) significantly lower than those in alpha-Sn (respectively 0.20, 0.52, and 0.40 eV).