Fig. 1. (a) Convex hull of Na–B compounds at 100–300 GPa. The reference elementary structures are fcc, tI19, and hP4 for Na,⁷ and the α-Ga phase for B,⁶⁰ adopted at the corresponding stable pressures. (b) Pressure–composition phase diagram of the Na–B system. The black stars represent the new stable phases identified in this work.

Fig. 2. Crystal structures of (a) Imma Na₉B at 200 GPa, (b) P-1 Na₅B at 300 GPa, (c) Cmcm Na₂B at 200 GPa, (d) P2₁/m Na₃B₂ at 300 GPa, (e) Imma Na₂B₃ at 300 GPa, (f) Cmmm NaB₂ at 200 GPa, and (g) Pmm2 NaB₇ at 300 GPa. (h) Variations of Na/B atomic building blocks of stable compounds with Na content. Blue and green spheres represent Na and B atoms, respectively.

Fig. 3. (a) Amount of charge donated/accepted from the Na/B atom in stable Na–B compounds. (b) Electron localization function (ELF) in the (100) plane and (c) crystal orbital Hamilton population (COHP) of the Na–B pair with a distance of 2.30 Å (−0.32 eV/pair) in Imma Na₉B at 200 GPa. (d) Donated (Na)/accepted [B and interstitial anion electrons (IAEs)] charge amount in Imma Na₉B under different pressures. (e) Mean-squared displacement (MSD) of Na₉B at different temperatures with NVT conditions. (f) ELF in the (100) plane and (g) COHP of the Na–B pair with a distance of 2.25 Å (−0.36 eV/pair) in P-1 Na₅B at 300 GPa. (h) Projected density of states (PDOS) in the valence band region of P-1 Na₅B at different pressures. (i) Atomic orbital energy levels (AOELs) for Na and B atoms as functions of external pressure.

Fig. 4. (a) Schematics of the mechanism of the superionic behavior (left side), and ELF (right side) of Na₉B. (b) Early trajectories of selected Na atoms in a representative polyhedron (left side) and the late trajectories of all atoms (right side) of Na₉B at 200 GPa and 2000 K after the onset of superionicity. The blue and green spheres represent Na and B atoms, respectively, and the red spheres are the initially diffusing Na atoms.

Fig. 5. (a) ELF in the (001) plane, (b) projected electronic band structure, (c) Eliashberg spectral function α²F(ω), electron–phonon coupling (EPC) parameter λ, projected phonon density of states (PHDOS), and (d) phonon dispersion curves (with the magnitude of λ indicated by the thickness of the red curves) of Pmm2 NaB₇ at 300 GPa. (e) Pressure-dependent T_c, λ, and ω_log, and (f) total and projected DOS at the E_F of Pmm2 NaB₇.