Metallic Icosahedron Phase of Sodium at Terapascal Pressures

Alkali metals exhibit unexpected structures and electronic behavior at high pressures. Compression of metallic sodium (Na) to 200 GPa leads to the stability of a wide-band-gap insulator with the double hexagonal $hP4$ structure. Post-$hP4$ structures remain unexplored, but they are important for addressing the question of the pressure at which Na reverts to a metal. Here, we report the reentrant metallicity of Na at the very high pressure of 15.5 terapascal (TPa), predicted using first-principles structure searching simulations. Na is therefore insulating over the large pressure range of 0.2–15.5 TPa. Unusually, Na adopts an $oP8$ structure at pressures of 117–125 GPa and the same $oP8$ structure at 1.75–15.5 TPa. The metallization of Na occurs on the formation of a stable and striking body-centered cubic $cI24$ electride structure consisting of ${\mathrm{Na}}_{12}$ icosahedra, each housing at its center about one electron that is not associated with any Na ions.

Figure 1

Crystal structures of $oP8$ (a) and $cI24$ (b) and their electron density difference maps [(c) and (d)] at ultrahigh pressures. The lattice parameters of $oP8$-Na at 2 TPa are $a=2.88\AA$, $b=2.12\AA$, and $c=4.0\AA$ with two inequivalent Na1 and Na2 atoms at $4c$ positions of (0.809, 0.75, 0.567) and (0.523, 0.25, 0.719), respectively. For $cI24$-Na at 16 TPa, $a=3.12\AA$ with Na atoms at $24g$ positions (0, 0.302, 0.183). Electron density differences are plotted within the (010) plane of $oP8$-Na (c) at 2 TPa and $cI24$-Na (d) at 16 TPa, respectively. $A1$ and $A2$ in (d) represent electron attractors located at the centers of the ${\mathrm{Na}}_{12}$ icosahedra and octahedral voids formed by the six neighboring ${\mathrm{Na}}_{12}$ icosahedra, respectively.

Figure 2

Enthalpy differences relative to $hP4$ (a) and $oP8$ (b) of Na as a function of pressure. The inset in (a) shows the pressure dependence of the volumes of the $hP4$ and $oP8$ phases. The predicted sequence of phase transitions at zero temperature in the pressure range of 0–20 TPa is provided in Fig. S1 of the Supplemental Material [47]. The volume appears to change continuously across the phase transition. [(c) and (d)] Calculated phonon dispersion relations of $oP8$-Na at 2 TPa and $cI24$-Na at 16 TPa, respectively.

Figure 3

Phonon dispersion curves of $hP4$-Na at 2 TPa (a) and the phonon frequencies of the softened TA phonon mode at $M$ (0, 0.5, 0) as a function of pressure (b). (c) Atomic vibrations of the soft TA mode at the $M$ point viewed along the $a$ axis in a $1\times 2\times 1$ supercell of the $hP4$ structure. Here, the Na1 (Na2) and Na4 (Na3) atoms vibrate parallel (antiparallel) to the $[01\overline{1}0]$ direction, while the Na5 (Na6) atoms vibrate antiparallel (parallel) to the [0001] direction. The gray and black balls indicate atoms in different planes. Arrows indicate vibrational direction of different Na atoms as labeled and are plotted from the eigenvector of the TA soft mode at the $M$ point. The blue dashed cell in (d) indicates the $oP8$ structure resulting from the distortion.

Figure 4

Electronic band structure and projected density of states of $oP8$-Na at 1.75 (PDOS, in units of ${\text{eV}}^{-1}$ per atom) (a) and $cI24$-Na at 16 TPa (b). The horizontal dotted lines indicate the Fermi level. [(c) and (d)] Variation of band gaps with pressure for $hP4$ and $oP8$-Na, respectively, using the HSE06 functional.