Structural evolution in high-pressure amorphous ${\mathrm{CO}}_2$ from ab initio molecular dynamics

By employing ab initio molecular dynamics simulations at constant pressure we investigated the behavior of amorphous carbon dioxide between 0 and 100 GPa and 200 and 500 K. We focused on the evolution of the high-pressure polymeric amorphous form known as a-carbonia on its way down to zero pressure, where it eventually converts into a molecular state. During the simulations we observed a spectrum of amorphous forms between two limiting polymeric forms with different proportions of three- and four-coordinated carbon atoms. Besides that we also found a mixed molecular-polymeric form that shows pronounced metastability at certain conditions. The observed behavior suggests ${\mathrm{CO}}_2$ as a possible candidate for polyamorphism. We discuss the structural and physical properties of the observed amorphous forms as well as their relation to crystalline phases.

Figure 1

Simulation protocol of solid ${\mathrm{CO}}_2$. Starting from phase III (black dots and arrows) at 50 GPa and 1000 K, PIA was observed at 100 GPa, event-1 (e1), leading to formation of the polymeric a-carbonia form denoted as a-1 (blue squares and arrows). Decompression at 500 K led to the creation of another version of polymeric a-carbonia a-2 (green squares), event-2 (e2), and on further pressure drop a-3 (red squares) was formed at 5 GPa, event e3. The same a-3 form (red diamonds) was created independently at 0 GPa and 200 K, e4. In the 500 K simulation branch, a molecular state (black) appeared at 0 GPa, e5. In the inset are shown separate simulations of compression of a-2 and decompression of a-1 between 20 and 45 GPa at 500 K performed in more pressure steps and for longer times as in the original simulation. The turquoise color of the squares represents forms with intermediate character between blue a-1 and green a-2.

Figure 2

Amount of carbon coordinations (%) on compression (to 78 ps), where a-1 was formed, and on the higher-$T$ branch (500 K) decompression (from 78 to 208 ps), where all other forms appeared. The ${\mathrm{CO}}_2$ molecules are shown in red (starting and ending at 100%), $3c$ are in green, and $4c$ in blue (the $4c$ curve is systematically larger than the $3c$ curve from 52 to 144 ps and lower thereafter). Vertical dashed lines divide the graph into regions of different simulation pressures that are labeled on the top and are changed at corresponding times labeled at the bottom. The coordination limit was 1.7 Å.

Figure 3

(a) Snapshot of a-1 at 40 GPa and (b) of a-2 at 20 GPa and 500 K. $4c$ and $3c$ carbon atoms are marked as blue and green spheres, respectively. Pictures were generated by jmol [72].

Figure 4

Upper panel: RDFs of type C-C (red triangles), O-O (green squares), and C-O (blue circles) for a-1 at 40 GPa, 500 K (broad peaks) and zero-$T$ structure of phase V at 41 GPa from data provided by Datchi $et$ $al.$ [52] (sharp peaks). The tiny first C-O peak represents C=O bonds from a small number of $3c$ carbons. Lower panel: ADFs of type C-C-C (red triangles), O-O-O (green squares), O-C-O (blue circles), and intertetrahedral C-O-C (turquoise diamonds), all calculated within the first RDF minima of a-1.

Figure 5

(a) Amorphous form a-3 at 5 GPa and 500 K. One closed chain of two $3c$ atoms pinned to one $4c$ carbon is placed near the down right edge of the picture. $4c$ and $3c$ carbons are distinguished as blue and green atoms; isolated ${\mathrm{CO}}_2$ molecules are marked translucent. (b) C${}_2$O${}_4$ dimer and (c) C${}_3$O${}_6$ trimer occurring in the a-3 form.

Figure 6

Phase 3C at 10 GPa: front view (left) and chain axis direction side view (right).

Figure 7

(a) Histograms of nearest distances between $3c$ carbons and $1c$ oxygens for polymeric a-carbonia a-2 (green histogram) at 10 GPa and intermediate state a-1/a-2 (dashed green) at 30 GPa and a-3 at 10 GPa (red), and at 30 GPa (dashed red), all at 500 K. The histograms are scaled to the total number of $3c$ carbons in the system. (b) Fraction of C-O single bonds with length between 1.4 and 1.7 Å calculated for each frame during a 7 ps time interval extracted from the MD runs and scaled to total numbers of C-O single bonds. Colors and line styles represent the same systems and conditions as in (a); systems at 30 GPa are marked with dotted lines. Full lines and dashed/dotted lines are to be compared separately as different line styles represent different simulation pressures and line colors distinct between polymeric and a-3 form.

Figure 8

(a) Equations of state for V($P$): volume per ${\mathrm{CO}}_2$ unit versus pressure of phase I (line with empty circles), phase V (dashed line), phase-3C (violet dotted line with circles) and amorphous a-1 (blue squares), a-2 (green up triangles) and a-3 (red down triangles) in 1 Mbar range. (b) Enthalpies from 0 to 50 GPa relative to phase I (horizontal line) per ${\mathrm{CO}}_2$ unit of crystalline phase III (orange dashed-dotted line), phase 3C (violet dotted line with circles), phase V (black dashed line) and amorphous a-1 (blue squares), a-2 (green up triangles) and a-3 (red down triangles). All phase curves are shown only in their stability regions, where they survived optimization.

Figure 9

Static structure factors of a-1 (blue line) at 40 GPa, a-2 (green dashed-dotted line) at 10 GPa, a-3 (red dotted) at 5 GPa, and molecular amorphous form, glass (dashed black) at 0 GPa. The structural evolution from a-1 to a-2, a-3, and to molecular amorphous form is represented mainly by broadening and shifting of the first main $S\left(Q\right)$ peak to lower $Q$, from 3.3 Å${}^{-1}$  in a-1 to 2.5 Å${}^{-1}$  in the molecular phase.