Fig. 2: Features of the vacancy-mediated superionic diffusion.

a, Arrhenius plots of vacancy-rich β-Li3N (that is, β-Li3N-400rpm-16h) and other nitrides (α-Li3N single crystals39, α-Li3N sinter26, β-Li3N27 and LiPON film42) for comparison. The room-temperature (25 °C) ionic conductivity is calculated based on Arrhenius plots. For α-Li3N single crystals, the anisotropic lithium-ion conductivities parallel and perpendicular to the hexagonal c axis are presented, denoted as α-Li3N single crystal || c, and α-Li3N single crystal ⊥ c, respectively. b, Lithium-ion conductivity at 25 °C and activation energy of vacancy-rich β-Li3N as a function of lithium vacancy concentration (4f sites). c, Arrhenius plots of lithium-ion diffusivity in vacancy-rich β-Li3N with different lithium vacancy concentrations in AIMD simulations. The vacancy concentration is 2.7% for Li2.92N0.97 and 5.6% for Li2.83N0.94. Statistical deviations in lithium-ion diffusivity were evaluated due to the stochastic nature of ion hopping, with error bars representing standard deviations calculated from the total diffusional displacements and effective ion hops observed in AIMD simulations. d,e, Lattice structures and superimposed lithium-ion probability density (marked by green iso-surfaces) in vacancy-rich β-Li3N with different lithium vacancy concentrations, 2.7% in Li2.92N0.97 (d) and 5.6% in Li2.83N0.94 (e), based on AIMD simulations at 600 K.