Fig. 3: Na+ migration mechanism of NLZCx-HM.

a Normalized electrostatic energy of 500 Na-free configurations in NLZC supercell model with representative high-energy (upper) and low-energy (lower), and corresponding results of the relaxation of two of the structures (Na ions were removed for clearer exhibition). b 221 supercell of NLZC for better displaying the c axis channel. c bond length for La-Cl, Zr-Cl, and NaCl in NLC or NLZC. d Arrhenius plot of Na+ migration pathways. Diffusivity in the NLZC lattice from AIMD simulations. e Na+ probability density, represented by green isosurfaces from AIMD simulations at 300 K in the NLZC lattice.