Ab initio Determination of the Phase Diagram of ${\mathrm{CO}}_2$ at High Pressures and Temperatures

The experimental study of the ${\mathrm{CO}}_2$ phase diagram is hampered by strong kinetic effects leading to wide regions of metastability and to large uncertainties in the location of some phase boundaries. Here, we determine ${\mathrm{CO}}_2$’s thermodynamic phase boundaries by means of ab initio calculations of the Gibbs free energy of several solid phases of ${\mathrm{CO}}_2$ up to 50 Gigapascals. Temperature effects are included in the quasiharmonic approximation. Contrary to previous suggestions, we find that the boundary between molecular forms and the nonmolecular phase V has, indeed, a positive slope and starts at 21.5 GPa at $T=0\mathrm{K}$. A triple point between phase IV, V, and the liquid phase is found at 35 GPa and 1600 K, indicating a broader region of stability for the nonmolecular form than previously thought. The experimentally determined boundary line between ${\mathrm{CO}}_2\text{−}\mathrm{II}$ and ${\mathrm{CO}}_2\text{−}\mathrm{IV}$ phases is reproduced by our calculations, indicating that kinetic effects do not play a major role in that particular transition. Our results also show that ${\mathrm{CO}}_2\text{−}\mathrm{III}$ is stabilized at high temperature and its stability region coincides with the $P\text{−}T$ conditions where phase VII has been reported experimentally; instead, phase II is the most stable molecular phase at low temperatures, extending its region of stability to every $P\text{−}T$ condition where phase III is reported experimentally.

Figure 1

${\mathrm{CO}}_2$ phase diagram adapted from Ref. [15]. Yellow, green, blue, and purple areas correspond to the molecular, nonmolecular, fluid, and amorphous forms of ${\mathrm{CO}}_2$, respectively. Solid lines correspond to thermodynamic phase boundaries, while dashed lines are kinetic boundaries. Names in bold and italic indicate thermodynamic and metastable phases, respectively.

Figure 2

Pressure-volume relation of phases (a) II, (b) III, (c) IV, and (d) V of ${\mathrm{CO}}_2$ at room temperature are shown in black solid lines. For each case, reported values from experimental (red circles) and theoretical (blue squares, purple diamonds, and yellow crosses) studies for the different phases are displayed as well.

Figure 3

(a) Phase boundaries between ${\mathrm{CO}}_2\text{−}\mathrm{II}$ and ${\mathrm{CO}}_2\text{−}\mathrm{III}$ (green, stars), ${\mathrm{CO}}_2\text{−}\mathrm{II}$ and ${\mathrm{CO}}_2\text{−}\mathrm{IV}$ (brown, down triangles), and ${\mathrm{CO}}_2\text{−}\mathrm{III}$ and ${\mathrm{CO}}_2\text{−}\mathrm{IV}$ (magenta, diamonds). Suggested boundaries reported by Iota et al. [5] (experimental) and Bonev et al. [48] (theoretical), are shown in orange dotted-dashed line and violet dotted line, respectively. (b) Phase boundaries between molecular phases ${\mathrm{CO}}_2\text{−}\mathrm{II}$ (red, circles), ${\mathrm{CO}}_2\text{−}\mathrm{III}$ (blue, up triangles), and ${\mathrm{CO}}_2\text{−}\mathrm{IV}$ (gray, crosses), and the nonmolecular phase ${\mathrm{CO}}_2\text{−}\mathrm{V}$. Proposed limits of the kinetic region from experimental data from Ref. [32] (orange squares) are also included.

Figure 4

Theoretical phase diagram for carbon dioxide at high pressure and temperature. Our calculated phase boundaries are shown with solid black lines, while previously reported thermodynamic boundaries are shown in gray. Yellow, green, and blue regions correspond to molecular, nonmolecular, and fluid forms of ${\mathrm{CO}}_2$.