Rules of formation of H-C-N-O compounds at high pressure and the fates of planetary ices

Abstract

The solar system's outer planets, and many of their moons, are dominated by matter from the H-C-N-O chemical space, based on solar system abundances of hydrogen and the planetary ices [Formula: see text]O, [Formula: see text], and [Formula: see text] In the planetary interiors, these ices will experience extreme pressure conditions, around 5 Mbar at the Neptune mantle-core boundary, and it is expected that they undergo phase transitions, decompose, and form entirely new compounds. While temperature will dictate the formation of compounds, ground-state density functional theory allows us to probe the chemical effects resulting from pressure alone. These structural developments in turn determine the planets' interior structures, thermal evolution, and magnetic field generation, among others. Despite its importance, the H-C-N-O system has not been surveyed systematically to explore which compounds emerge at high-pressure conditions, and what governs their stability. Here, we report on and analyze an unbiased crystal structure search among H-C-N-O compounds between 1 and 5 Mbar. We demonstrate that simple chemical rules drive stability in this composition space, which explains why the simplest possible quaternary mixture HCNO-isoelectronic to diamond-emerges as a stable compound and discuss dominant decomposition products of planetary ice mixtures.

Keywords: H–C–N–O chemistry; high pressure; planetary ices; structure search.

Fig. 1.

H–C–N–O phase diagram at 500 GPa from structure searches. (A) Full quaternary phase diagram, with the “balanced redox” subspace (see text) shaded in gray and the “planetary ice” triangle ${\mathrm{H}}_2$O–${\mathrm{C}\mathrm{H}}_4$–${\mathrm{N}\mathrm{H}}_3$ in green. Red/blue symbols are stable/metastable phases as labeled; for the latter, size represents closeness to stability, i.e., larger symbols are closer to the convex hull. For reference, the “synthetic Uranus” composition is marked. (B) The balanced redox ${\mathrm{C}\mathrm{O}}_2$–${\mathrm{C}}_3{\mathrm{N}}_4$–${\mathrm{H}}_2$O–${\mathrm{N}\mathrm{H}}_3$ subspace of H–C–N–O, with select internal one-dimensional cross-sections highlighted. Full/open symbols are stable/metastable phases. Circles/upward triangles/sideways triangles are from searches of the full H–C–N–O space/the ${\mathrm{C}\mathrm{O}}_2$–${\mathrm{C}}_3{\mathrm{N}}_4$–${\mathrm{H}}_2$O–${\mathrm{N}\mathrm{H}}_3$ plane/the ${\mathrm{H}}_2$O–${\mathrm{C}\mathrm{H}}_4$–${\mathrm{N}\mathrm{H}}_3$ plane; square symbols are manually added known structures. Larger open symbols are closer to the convex hull. (C–E) Binary convex hulls from select one-dimensional paths traversing the ${\mathrm{C}\mathrm{O}}_2$–${\mathrm{C}}_3{\mathrm{N}}_4$–${\mathrm{H}}_2$O–${\mathrm{N}\mathrm{H}}_3$ plane as shown in B; enthalpies are relative to the binary end members which may not be stable in the full quaternary. (C) ${\mathrm{H}\mathrm{C}}_2{\mathrm{N}}_3$–${\mathrm{H}}_2{\mathrm{C}\mathrm{O}}_3$ phases; (D) ${\mathrm{C}\mathrm{H}}_2{\mathrm{N}}_2$–${\mathrm{H}}_2$O phases; (E) ${\mathrm{C}\mathrm{O}}_2$–${\mathrm{N}\mathrm{H}}_3$ phases.

Fig. 2.

HCNO at 500 GPa. (A) Relative formation enthalpy plot, including all relevant decomposition paths. (B) $Pca{2}_1$-II crystal structure. Pink/brown/gray/red spheres denote H/C/N/O atoms. Unit cell is shown, and ${\mathrm{C}\mathrm{O}\mathrm{N}}_3$ tetrahedra are highlighted. (C) Electronic band structure of HCNO-$Pca{2}_1$-II.

Fig. 3.

Crystal structures of stable ternary H–C–N–O phases, with C/N coordination highlighted as appropriate. (A) ${\mathrm{C}\mathrm{H}}_2{\mathrm{N}}_2$ (with ${\mathrm{C}\mathrm{N}}_4$ tetrahedra). (B) ${\mathrm{H}}_3{\mathrm{N}\mathrm{O}}_4$ (with ${\mathrm{N}\mathrm{O}}_4$ tetrahedra). (C) ${\mathrm{H}\mathrm{C}}_2{\mathrm{N}}_3$ (with ${\mathrm{C}\mathrm{N}}_4$ tetrahedra). (D) ${\mathrm{C}\mathrm{N}}_2{\mathrm{O}}_6$ (with ${\mathrm{C}\mathrm{O}}_6$ octahedra).

Fig. 4.

Chemical bonding analyses. (A) Electron localization function isosurfaces (ELF = 0.80) for stable H–C–N–O phases at 500 GPa, all drawn to the same scale. (B) COHP analysis for the same structures, projected onto different bond types as indicated.

Fig. 5.

Ground state phase diagram of the ${\mathrm{H}}_2$O–${\mathrm{C}\mathrm{H}}_4$–${\mathrm{N}\mathrm{H}}_3$ ice plane at 500 GPa. Black (gray) circles denote stable (metastable) phases as labeled, and open circle points to the 7:4:1 solar composition ratio. Regions with different decomposition pathways are colored and labeled.

Fig. 6.

Calculated H–C–N–O phase diagram at 100 GPa. (A) Chemical subspace of “balanced redox”–compliant compounds, drawn to the same specifications as in Fig. 1B. (B) Crystal structure of HCNO-$Pca{2}_1$-I at 100 GPa, with unit cell and carbon coordination indicated.