Multistep Dissociation of Fluorine Molecules under Extreme Compression

All elements that form diatomic molecules, such as ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{Cl}}_2$, ${\mathrm{Br}}_2$, and ${\mathrm{I}}_2$, are destined to become atomic solids under sufficiently high pressure. However, as revealed by many experimental and theoretical studies, these elements show very different propensity and transition paths due to the balance of reduced volume, lone pair electrons, and interatomic bonds. The study of F under pressure can illuminate this intricate behavior since F, owing to its unique position on the periodic table, can be compared with H, with N and O, and also with other halogens. Nevertheless, F remains the only element whose solid structure evolution under pressure has not been thoroughly studied. Using a large-scale crystal structure search method based on first principles calculations, we find that, before reaching an atomic phase, F solid transforms first into a structure consisting of ${\mathrm{F}}_2$ molecules and F polymer chains and then into a structure consisting of F polymer chains and F atoms, a distinctive evolution with pressure that has not been seen in any other elements. Both intermediate structures are found to be metallic and become superconducting, a result that adds F to the elemental superconductors.

Figure 1

(a),(b) Enthalpies of various structures relative to the $Pm\overline{3}n$ structure as functions of pressure. (c),(d) Interatomic distances as a function of pressure, including the nearest F-F distances (intra F-F) and the next nearest F-F distances (inter F-F) in the $Cmca$ phase; the nearest ${\mathrm{F}}^1\text{−}{\mathrm{F}}^1$ distance (intra ${\mathrm{F}}^1\text{−}{\mathrm{F}}^1$), the next nearest ${\mathrm{F}}^1\text{−}{\mathrm{F}}^1$ distance (inter ${\mathrm{F}}^1\text{−}{\mathrm{F}}^1$), the nearest ${\mathrm{F}}^2\text{−}{\mathrm{F}}^2$ distance, and the neighboring ${\mathrm{F}}^1\text{−}{\mathrm{F}}^2$ distance in the $P6/mcc$ phase; the nearest ${\mathrm{F}}^2\text{−}{\mathrm{F}}^2$ distance, the neighboring ${\mathrm{F}}^0\text{−}{\mathrm{F}}^2$ distance, the next nearest ${\mathrm{F}}^2\text{−}{\mathrm{F}}^2$ distance in the $Pm\overline{3}n$ phase; and the nearest and next nearest F-F distance in the $Fddd$ phase.

Figure 2

(a) Crystal structure and (b) layer of $P6/mcc$. The ${\mathrm{F}}^1$, ${\mathrm{F}}^2$, and ${\mathrm{F}}^0$ are shown using blue, pink, and dark yellow spheres, respectively. The layers are stacked in an $ABXBA$ fashion. The crystal structure of $Pm\overline{3}n$ showing (c) polymeric line chains and (d) icosahedron. (e) Crystal structure of $Fddd$.

Figure 3

The calculated ELF of our predicted phases. (a) $Cmca$ in the (100) section at 3 TPa. (b),(c) $P6/mcc$ in the (001) and (100) sections at 3 TPa. (d) $Pm\overline{3}n$ in the (100) section at 5 TPa.

Figure 4

(a) Variation of band gaps with pressure for $Cmca$. Band structure and partial densities of states (PDOSs) of (b) $P6/mcc$ phase at 3 TPa, (c) $Pm\overline{3}n$ phase at 5 TPa, and (d) $Fddd$ at 30 TPa.

Figure 5

The calculated Eliashberg function ${\alpha }^2\mathrm{F}(\omega )$ (black lines) and EPC coefficient $\lambda$ (red lines) of (a) $P6/mcc$ at 3 TPa, (b) $Pm\overline{3}n$ at 5 TPa, and (c) $Fddd$ at 30 TPa.