Fig. 6: Bulk ionic conductivities, activation energies, and prefactors calculated by AIMD.

Calculated room-temperature (300 K) bulk ionic conductivities (a) and activation energies (d) with error bars⁷⁷, and prefactors (g) of Na_1+2yHf_2−yMg_yP₃O₁₂ (y = 0, 0.5, 0.75, 1, 1.5, labeled blue) and Na_2+2zHf_2−zMg_zSiP₂O₁₂ (z = 0, 0.25, 0.5, 0.75, 1, labeled yellow). In these two groups, both the polyanion composition and cation radius are kept constant. Note that for compounds with y = 0, 1.5 and z = 1, the conductivities were not converged and therefore set as « 10⁻⁹ mS cm⁻¹. b, e, h Group of Na₃MM’Si₂PO₁₂ (M, M’ = Ti, Hf, Sn, Zr), with constant Na content x and polyanion composition. c, f, i Group of Na₃Hf_2−zMg_zSi_2−2zP_1+2zO₁₂ (z = 0, 0.5, 1) where \({\bar{r}}_{M}\) and the Na content x are kept constant. The error bars quantifying the statistical confidence levels of diffusion results from AIMD are calculated according to He et al. ⁷⁷.