Thermodynamic stability of layered structures in compressed ${\text{CO}}_2$

The crystal structures of the recently discovered nonmolecular phases of ${\text{CO}}_2$ are still the subject of intense debate. Based on density-functional theory calculations, we show that a layered structure (space group $P{4}_2/nmc$) with carbon in tetrahedral coordination is thermodynamically stable between 200 and 900 GPa. The Raman spectrum for this phase agrees with that measured for ${\text{CO}}_2\text{-VI}$. Contrary to ${\text{SiO}}_2$, where octahedral coordination for silicon starts with stishovite at about 10 GPa, we find that structures with carbon in octahedral coordination are unlikely to be thermodynamically stable in ${\text{CO}}_2$ at pressures currently reachable in the laboratory. We attribute the exceptional stability of tetrahedral structures in ${\text{CO}}_2$ to the small atomic size of the carbon atom, which allows it to occupy the tetrahedral interstitial sites of the close-packed oxygen sublattices.

Figure 1

(Color online) Calculated relative enthalpies per ${\text{CO}}_2$ molecular unit for all the ${\text{CO}}_2$ structures considered in this work with respect to $\beta$-cristobalite.

Figure 2

(Color online) (a) Calculated infrared spectra of the $\beta$-cristobalite, layered, $\alpha {\text{-PbO}}_2$, ${\text{CaCl}}_2$, and stishovite structures at 410 GPa. (b) Calculated Raman spectra of the $\beta$-cristobalite, layered, $\alpha {\text{-PbO}}_2$, ${\text{CaCl}}_2$, and stishovite structures at 410 GPa and 300 K.

Figure 3

(Color online) Calculated Raman spectra at different pressures for layer $AB$ and $\beta$-cristobalite, the two thermodynamically stable structures according to our calculations. Notice that $\beta$-cristobalite is stable at 60 GPa, layer $AB$ is stable at 410 GPa, and 230 GPa is close to the pressure of transition between the two phases. The experimental spectrum of phase VI at 62.5 GPa (Ref. 14) is also shown for comparison.

Figure 4

(Color online) Atomic arrangement in layer-$AB$ and $\beta$-cristobalite structures. The big spheres represent oxygen atoms and the small spheres represent carbon atoms. Notice, in (a) and (b), the fcc close-packed structure of the oxygen sublattice. Panels (c) and (d) show the carbon sublattice in the two structures. The connections between nearest-neighbor carbon atoms in (c) and (d) do not represent chemical bonds rather they are a guide to visualize their three-dimensional (3D) arrangement. The red (dark)-colored connection in (c) and (d) is representative of the only two types of local arrangement of carbon atoms in a fcc oxygen sublattice (see text).