Stabilization of ammonia-rich hydrate inside icy planets

Significance

The mantles of icy planets comprise large amounts of water, ammonia, and methane ices. To understand their interior structure, it is crucial to study these ices at the extreme pressure conditions they likely experience. Hitherto, such studies have mostly been restricted to individual ices and not considered formation of stable mixtures. We survey here mixtures of water and ammonia and show that high pressures stabilize ammonia hemihydrate, through a transformation from a molecular crystal into a fully ionic solid that involves complete deprotonation of water. We suggest that ammonia-rich hydrates can precipitate out of any ammonia–water mixture at sufficient pressures and are an important component inside icy planets.

Abstract

The interior structure of the giant ice planets Uranus and Neptune, but also of newly discovered exoplanets, is loosely constrained, because limited observational data can be satisfied with various interior models. Although it is known that their mantles comprise large amounts of water, ammonia, and methane ices, it is unclear how these organize themselves within the planets—as homogeneous mixtures, with continuous concentration gradients, or as well-separated layers of specific composition. While individual ices have been studied in great detail under pressure, the properties of their mixtures are much less explored. We show here, using first-principles calculations, that the 2:1 ammonia hydrate, (H₂O)(NH₃)₂, is stabilized at icy planet mantle conditions due to a remarkable structural evolution. Above 65 GPa, we predict it will transform from a hydrogen-bonded molecular solid into a fully ionic phase O²⁻(${\text{NH}}_4^{+}$)₂, where all water molecules are completely deprotonated, an unexpected bonding phenomenon not seen before. Ammonia hemihydrate is stable in a sequence of ionic phases up to 500 GPa, pressures found deep within Neptune-like planets, and thus at higher pressures than any other ammonia–water mixture. This suggests it precipitates out of any ammonia–water mixture at sufficiently high pressures and thus forms an important component of icy planets.

A remarkable number of recently and currently discovered exoplanets can be classified as super-Earths or mini-Neptunes, with masses up to 10 Earth masses and mean densities around 1 g/cm³ (1–3). The uncertainty in classification hints at a substantial problem: Researchers cannot distinguish from afar whether these bodies are mostly rocky (like Earth) or mostly icy (like Neptune). Inside our own solar system, we have the “ice giants” Uranus and Neptune. We know their mantle region contains large amounts of water, ammonia, and methane ices, as well as hydrogen in various forms, while their cores are presumably formed by a small amount of heavy elements (4–7). However, even for those planets, observational data are limited to global observables such as mass, radius, and gravitational and magnetic moments. These provide only a loose set of constraints on interior composition, which can be satisfied by a variety of planetary models. The low luminosity of Uranus, for instance, could be due to a thermal boundary layer, which would suggest significant composition gradients inside its mantle (7–9). To constrain plausible interior models, more astrophysical data are needed (1). At the same time, laboratory experiments and accurate calculations are necessary to establish the equations of state of the planets’ potential constituent materials. As these constituents experience extreme pressure and temperature conditions inside the planets, many of their defining properties such as viscosity and thermal or electrical conductivity are likely to change drastically from what we are used to at ambient conditions. This is a consequence of qualitative differences that can emerge in chemical bonding, and even the stabilization of entirely new compounds and stoichiometries under compression (10–14). High-pressure studies of the individual molecular ices are therefore abundant, both experimentally and theoretically. Systematic investigations of their mixtures are much more sparse, due to the increased complexity they introduce, although attempts at experimental and computational high-pressure studies on mixtures of molecular ices close to their solar abundance ratio have been performed (15, 16). However, it is not clear that this mixing ratio, roughly 4:1:7 of methane:ammonia:water (17, 18), plays a role inside any icy planets in their present state. Most pressingly, it is unknown how the different ices are distributed throughout the planetary interiors—Would they occur as homogeneous mixtures, exhibit continuous concentration gradients, or form stratified layers of specific compositions (6, 19, 20)?

All ices feature a ladder of interactions, ranging from covalent, ionic/electrostatic, and hydrogen bonding (not in methane) to weak dispersion interactions. It is the interplay of these interactions, and their relative emphasis as the molar volumes are reduced, that drive intriguing phase transitions, and the emergence of new structural features. Ammonia has been predicted to form an ionic crystal (NH₄)⁺(NH₂)⁻ above 100 GPa (21), and this has recently been confirmed in experiment (22, 23). The energetic cost of breaking the N–H bond is outweighed by ionic bonding ${\text{NH}}_4^{+}\cdots$${\text{NH}}_2^{-}$ and more compact packing. Water leaves the molecular state via another route, forming the atomic ice-X network structure with symmetric hydrogen bonds at 60 GPa (24), while, at terapascal pressures, it is predicted to take up more complex phases that can be seen as partially ionic OH⁻/H₃O⁺ (25, 26). At low temperatures, nuclear quantum effects are expected to influence the phase diagram of hydrogen-bonded systems (27), while, at high temperatures, superionicity is predicted to occur in both water and ammonia: The heavy O/N atoms form crystalline lattices, while protons are free to diffuse through the crystal (28–30).

Among planetary ice mixtures, ammonia–water compounds are arguably of the most chemical interest, because they can form fully connected HOH$\mathrm{\cdots }$NH₃ and H₂NH$\mathrm{\cdots }$OH₂ hydrogen-bonded networks. Three stoichiometric mixtures exist in nature and close to ambient conditions: ammonia monohydrate (AMH, NH₃:H₂O = 1:1), ammonia dihydrate (ADH, 1:2), and ammonia hemihydrate (AHH, 2:1) (31). Their phase diagrams are relatively complex: Six AMH phases, four ADH phases, and two AHH phases are known at various pressure–temperature (P-T) conditions, even though some of their structures have not been resolved. AHH has arguably been studied the least among the ammonia hydrates, possibly because of its high ammonia content, far removed from the solar abundance ratio 1:7, and is therefore expected to be rare in nature. However, it is a crucial phase at high pressure and temperature, where both ADH and AMH decompose into AHH + ice-VII, around 3 GPa and at 280 K and 250 K, respectively (32, 33). At slightly higher pressures (around 5 GPa to 20 GPa) and room temperature, all ammonia hydrates are found to form disordered molecular alloy (DMA) phases, which feature substitutional disorder of ammonia and water (maybe partially ionized into OH⁻/${\text{NH}}_4^{+}$) on a body-centered cubic (bcc) lattice (33–36). The AHH DMA phase has been observed in two independent experiments (35, 36) that found, at low temperatures, transitions from AHH phase II at 19 GPa to 30 GPa. AHH DMA was found to remain stable up to the highest pressure studied, 41 GPa (36).

Previous first-principles calculations have been carried out to resolve high-pressure molecular phases in the ammonia hydrates (37, 38). In AMH, calculations predicted that an ionic phase transition should stabilize ${\text{NH}}_4^{+}·$OH⁻ over NH₃·H₂O around 6 GPa (39). A more stable ionic structure was proposed recently (40), and subsequent crystal structure searches on AMH uncovered higher-pressure ionic phases, which were then used as starting points for ab initio molecular dynamics (MD) simulations to investigate the superionic regime of AMH (41). These studies attempted to explore molecular mixtures at conditions present deep within icy planetary bodies using electronic structure calculations, but there is an inherent assumption that AMH is indeed a relevant stoichiometry at elevated pressures in the water–ammonia phase diagram. This assumption needs to be clarified by studies on other mixtures, first and foremost ADH and AHH, to ultimately construct a coherent picture of the inner structure of icy planets as dependent on overall composition.

Here, we present results from crystal structure predictions in conjunction with electronic structure calculations of compressed AHH. Above 65 GPa, beyond the stability regime of the DMA phase, we find a sequence of new high-pressure phases that ensure AHH remains a stable (and indeed dominant) composition within the water–ammonia phase diagram to very high pressures. The structures uncovered here are fully ionic and combine atomic O²⁻ anions and molecular ${\text{NH}}_4^{+}$ cations. Oxides are a major thermodynamic sink and are found in virtually all fields of chemistry and materials science, but these ammonium oxide structures represent an example where water in a hydrate compound becomes completely deprotonated by application of pressure. A sequence of such structures remains stable up to 550 GPa and elevated temperatures, where decomposition into the constituents water and ammonia is predicted to occur.

Results

Two structures of AHH have been solved, phases I and II. In experiments at $T=200$ K, the transition I$\to$II is estimated to occur around 1 GPa (36). In our ground-state calculations, this transition occurs at 4 GPa, slightly above the experimental estimate, but in line with the negative Clapeyron slope seen in experiment. In Fig. 1, we show the evolution of the relative ground-state enthalpies, $\mathrm{\Delta }{H}_f=H_f(\mathrm{AHH})-[H_f({\mathrm{H}}_2\mathrm{O})+2H_f({\mathrm{NH}}_3)]$, as a function of pressure on two different scales (0 GPa to 100 GPa and 50 GPa to 800 GPa), for the known and new phases. This represents the different phases’ enthalpic stability toward decomposition into the molecular constituents of H₂O and NH₃, where, at each pressure, we have chosen the most stable H₂O and NH₃ phases.

Fig. 1.

Enthalpies of formation of AHH phases as a function of pressure, relative to decomposition into ice and ammonia (or $2/5$ NH₄ + $1/5$ N₃H₇ above 450 GPa; see arrow), shown in the range 0 GPa to 100 GPa (Left) and 50 GPa to 800 GPa (Right). The shaded region in Left denotes an approximate enthalpy range of quasi-bcc structures, with a lower bound by the most stable approximant we found (see Results). Dashed and dotted lines indicate decomposition reactions into other ammonia hydrates.

We also show, in Fig. 1, the relative enthalpies of potential decomposition products of AHH, namely $H_f(\mathrm{AMH}+{\mathrm{NH}}_3)$ and $1/2H_f(\mathrm{ADH}+3\mathrm{N}{\mathrm{H}}_3)$. A decomposition of AHH into ADH and ammonia is never favorable; in fact, just below 100 GPa, we find ADH itself becomes unstable toward decomposition into water and ammonia ice. For AMH, we find that, at low pressures, a proposed tetragonal ionic ${\mathrm{NH}}_4^{+}\cdot {\mathrm{OH}}^{-}$ phase (40) is, up to 28 GPa, more stable than AHH. This phase has not yet been seen in experiments on compressed AMH.

Among AHH phases, above 23 GPa in our calculations, AHH-II is followed by several quasi-bcc phases, which are indicated by the shaded region in Fig. 1 and which are energetically competitive up to 65 GPa. As a phase transition to a substitutionally disordered bcc structure has been observed at 19 GPa in room-temperature experiments, we would expect to find many competing quasi-bcc structures in this pressure region. All relevant structures we find in this region are half-ionized, i.e., of the composition NH₃·${\text{NH}}_4^{+}·$OH⁻, and feature hydrogen bonds. These structures are not immediately obvious to be quasi-bcc—see SI Appendix for full structural details—but occupy a pressure range where experiment has observed the bcc DMA structure. Upon closer inspection, the underlying quasi-bcc structure becomes apparent, both in real and reciprocal space: Representative structures feature locally quasi-cubic molecular arrangements, and their simulated powder X-ray diffraction peaks cluster around the peaks of an ideal bcc lattice (see SI Appendix, Fig. S1). This suggests that the structure search algorithms attempt to construct disordered phases in the pressure range around 20 GPa to 60 GPa. Similar results were also seen at low pressures, where AHH-I is stable: Searching the configuration space with too small unit cells to reproduce the actual phase I structure, which has 12 molecules in the unit cell, resulted in candidate structures that mimicked the molecular herringbone arrangements of AHH-I. In the gas phase with well-separated entities, the proton transfer process NH₃+H₂O$\to$${\text{NH}}_4^{+}$ + OH⁻ is endothermic by about 8 eV; it is enabled here by ionic bonding and a more compact packing of the constituents ($\mathrm{\Delta }V/V=-3.3\%$ for AHH-II$\to A2/m$ at 20 GPa). It is possible that these structures could be the basis of an ordered low-temperature form of the DMA phase for AHH. Experimentally, no further phase transitions have been observed in AHH up to 40 GPa.

At 63 GPa, we find in our calculations a new orthorhombic structure of $Amma$ symmetry that is energetically most stable, with the intriguing attribute of doubly deprotonated water: all H₂O have donated both protons to two NH₃ molecules, which results in a fully ionic ammonium oxide compound ${\left({\text{NH}}_4^{+}\right)}_2·$O²⁻. At 110, 180, and 505 GPa in the ground state, we find three more phase transitions, first to a trigonal $P\overline{3}m1$ structure, followed by two orthorhombic phases of $Pnna$ and $Pnma$ symmetry, and all with the same features of fully deprotonated water and molecular ammonium cations. These structures are shown in Fig. 2, and details of their crystal structures are tabulated in SI Appendix. The emergence of this sequence of ionic structures is responsible for the extended stability of AHH against decomposition into ice and ammonia to much larger pressures; see Fig. 1. We also find that ADH and AMH would decompose into AHH and appropriate amounts of ice at pressures above 60 and 85 GPa, respectively. Eventually, at 540 GPa in the ground state, we find that AHH decomposes into ice and ammonia. For this decomposition, we took into account recent computational work that found NH₃ decomposes into N₃H₇ and NH₄, which we find above 450 GPa [see arrow in Fig. 1, Right (42)]. Note that water ice is not expected to decompose until multiterapascal pressures are reached (43, 44).

Fig. 2.

Fully deprotonated AHH structures: $Amma$ phase at 80 GPa (Top Left); $P\overline{3}m1$ phase at 100 GPa (Top Right); $Pnna$ phase at 300 GPa (Bottom Left); and $Pnma$ phase at 600 GPa (Bottom Right). Red (blue, white) spheres denote O (N, H) atoms. All phases are drawn to the same scale, and hydrogen bonds from ${\text{NH}}_4^{+}$ to O are shown as dashed lines.

It has been suggested that the Perdew–Burke–Ernzerhof (PBE) functional overstabilizes charge transfer in the NH₃+H₂O$\to$${\text{NH}}_4^{+}$+OH⁻ reaction (38). We therefore reoptimized all structures using the PBE + TS functional, which includes the Tkatchenko–Scheffler (TS) dispersion correction scheme (45), and found little quantitative difference in the relevant structural evolution: The transition from half-ionic to fully ionic phases (the onset of stability of the $Amma$ phase) is found at 58 GPa, while decomposition of the $Pnma$ phase into the individual ices is calculated to occur at 458 GPa.

To estimate the effects of finite temperature, we calculated free energies for all phases using the quasi-harmonic approximation, which takes into account the vibrational entropy. The latter might well influence the phases’ stability range, as we find quite a diverse chemistry in the progression from hydrogen-bonded molecular to fully ionic phases. Fig. 3 shows the resulting P-T phase diagram. This implies an earlier onset of stability for the fully ionic phases, with the $Amma$ phase becoming stable at 40 GPa to 50 GPa at low temperatures, but also eventual decomposition at lower pressures than in the ground state, as low as 470 GPa, depending on temperature. The temperature dependence of the stability of most phases, apart from the eventual decomposition, is actually relatively weak, and changes compared with the ground-state results shown in Fig. 1 are mostly due to zero-point energy (ZPE) effects (see SI Appendix, Fig. S2 for a plot of H + ZPE as a function of pressure). This can be rationalized with the qualitative change in proton coordination at the ionization transition and its influence on the molecular vibron modes that will dominate the ZPE. We find that the stability region of the $P\overline{3}m1$ phase is much increased, at the expense of the orthorhombic $Pnna$ and $Pnma$ phases. In fact, two monoclinic phases of $P{2}_1/m$ and $P{2}_1/c$ symmetry (see SI Appendix, Fig. S3), which are the results of soft phonon modes in $P\overline{3}m1$ at very high pressures, become stable around 300 GPa to 350 GPa and 550 GPa, respectively, and dominate the high-pressure regime of the P-T phase diagram. For perspective, we show, in Fig. 3, the mantle isentropes of Uranus and Neptune, as well as the melting line of AMH obtained from MD simulations (41). Both melting and onset of superionicity (which we suspect occurs significantly below the melting line) are not considered in our quasi-harmonic approach here.

Fig. 3.

P-T phase diagram of AHH phases, computed within the quasi-harmonic approximation. The dashed region at highest pressures represents predicted decomposition into the constituent ices. The dashed black line indicates the computed melting line of AMH (41), while solid black (gray) lines indicate calculated planetary isentropes of Uranus (Neptune) (46).

The deprotonation reaction of OH⁻ in the gas phase, NH₃+OH⁻ → ${\text{NH}}_4^{+}$+O²⁻, is endothermic by about 16 eV. This is twice the energy needed to remove the first proton off water, yet comes as a natural follow-up to the partial deprotonation of H₂O. The process requires (i) more compression work being exerted on the system and (ii) a proton acceptor molecule, NH₃. Highly compressed AHH provides both and, as a consequence, forms fully ionic compounds at high pressure. These are further stabilized by more compact packing, facilitated by the presence of spherical O²⁻ anions. Some of the ionic phases resemble known structure types. The $P\overline{3}m1$ structure, for instance, is (if we assume spherical ${\text{NH}}_4^{+}$) the CdI₂ structure type, a well-known AB₂ ionic structure (47). The assignments of molecules in these high-pressure phases are supported by their structural properties: the longest nearest-neighbor N–H separations decrease from 1.10 Å in $Amma$ at 60 GPa to 0.99 Å in $Pnma$ at 600 GPa, while the shortest nearest-neighbor O$\mathrm{\cdots }$H separations decrease from 1.35 Å to 1.17 Å for the same structures and pressures. The O–H separations at 60 GPa, for instance, are well above the separations seen in molecular water in ice-VIII at the same pressure (1.03 Å). A topological Bader charge analysis (48) also supports the ionic picture suggested above. The partial charges on O/NH₄ are −1.27/+0.64$e$ at 100 GPa in $Amma$, and are almost constant across the entire pressure range: −1.28/+0.64$e$ in $P\overline{3}m1$ at 100 GPa, −1.30/+0.65$e$ in $Pnna$ at 300 GPa, and −1.26/+0.63$e$ in $Pnma$ at 600 GPa.

In Fig. 4, Inset, we show an electron localization function (ELF) isosurface and 2D cut for the $P\overline{3}m1$ phase, which confirm the presence of covalent bonds along the N–H separations, and the lack thereof around the oxygen anion—For the latter, ELF reveals its closed-shell character, but there are no local ELF maxima between the O²⁻ and ${\text{NH}}_4^{+}$ entities. Around the transition from the quasi-bcc phases, at 60 GPa, the $Amma$ phase is more compact by 1.4% than the lowest-energy quasi-bcc phase. Further transitions lead to ever more compact arrangements: $\mathrm{\Delta }V/V=-0.7/-0.5\%$ at 120/300 GPa, the respective onsets of stability of the $P\overline{3}m1$ and $P{2}_1/m$ phases at room temperature. This is, in part, facilitated by higher coordination of the O²⁻ anion: Because of its spherical character, in absence of covalent bonds or localized lone pairs, it is a much more flexible hydrogen bond acceptor than H₂O, which prefers low-density tetrahedral coordination up to very high pressures (26). In $Amma$ and $P\overline{3}m1$, the oxygen anion is sixfold coordinated to N–H bonds, which increases to eightfold coordination in $Pnna$.

Fig. 4.

Zone-centered vibrational frequencies of AHH phases in their respective room-temperature range of stability, focusing on the molecular vibron region of 2,400 cm⁻¹ to 3,800 cm⁻¹. Phases are indicated along the top, and are colored as in Fig. 1. Solid (dashed) lines represent Raman (IR) active modes. Open triangles refer to OH stretch modes (seen until 40 GPa), and filled circles refer to NH stretches. (Inset) ELF plot for the $P\overline{3}m1$ phase at 300 GPa. The isosurface value is 0.75, and 2D cut colors range from blue (ELF = 0) to red (ELF = 1).

The complete absence of O–H stretch modes in the ionic high-pressure AHH phases should aid their spectroscopic detection. In Fig. 4, we show the pressure evolution of the intramolecular N–H stretch modes up to 200 GPa, calculated within the harmonic approximation. Across phases I and II and the half-ionized quasi-bcc phases, the N–H vibron bands occupy a range that broadens from 3,300 cm⁻¹ to 3,500 cm⁻¹ at 1 atm to 3,000 cm⁻¹ to 3,500 cm⁻¹ at 40 GPa. These frequency ranges are in reasonable agreement with experimental data, but shifted by about 100 cm⁻¹, likely due to anharmonic effects (35, 49). A significant change should be noticeable at the transition from quasi-bcc to completely ionized phases: There are no vibrational modes in the previously mentioned frequency range; instead, N–H stretch modes in the $Amma$ phase occur at much higher frequencies, around 3,600 cm⁻¹ in our calculations, and increase strongly with pressure. These modes involve stretches along N–H$\mathrm{\cdots }$${\text{NH}}_4^{+}$ hydrogen bonds. Another set of modes increases very strongly from 2,700 cm⁻¹ at 40 GPa to 3,200 cm⁻¹ at 110 GPa, and involves stretches along N–H$\mathrm{\cdots }$O²⁻ hydrogen bonds. At the transition to $P\overline{3}m1$ at 110 GPa, with a much simpler mode structure, both sets of vibrational frequencies decrease, by about 20 cm⁻¹ to 80 cm⁻¹, but continue to rise significantly with further increased pressure. The continuous hardening of the molecular vibrons is an indication that the intramolecular bonds in the ${\text{NH}}_4^{+}$ units strengthen under compression; neither phase shows signs of impending transitions to a network structure, for instance with symmetric N–H–O or N–H–N bonds.

Electronically, all high-pressure phases, due to charge and/or proton transfer, are wide-gap insulators. In SI Appendix, Fig. S4, we show the evolution of the electronic band gap as a function of pressure for the most relevant phases. At low pressures, up to about 100 GPa in some structures, the band gaps increase with pressure, an effect previously noted in molecular crystals with polar units, where compression creates competing effects of widening electronic bands and shifts of intramolecular orbital states (50, 51).

Discussion

From our ground-state calculations, we deduce that compressed AHH goes through three distinct regimes as pressures are applied beyond the stability range of the known molecular phase II. First, above 10 GPa, a range of quasi-cubic, partially ionized structures are stabilized, by 100 meV per formula unit (f.u.) compared with phase II at 40 GPa; see Fig. 1. Subsequently, above 65 GPa, a sequence of fully ionic structures is stabilized, which feature the unusual motif of doubly deprotonated water (i.e., O²⁻ anions). These structures benefit from ionic bonding and high coordination of hydrogen bonds. Finally, above 500 GPa, separation into the constituents ice and ammonia (which itself is likely to decompose into other hydronitrogens) becomes favorable. This general trend is unaffected by an increase in temperature, considered here within the quasi-harmonic approximation. However, ZPE effects lead to slightly different stability ranges for each phase, and promote distortions of the CdI₂-like $P\overline{3}m1$ phase; the onset of fully ionic phases should occur around 40 GPa at room temperature. Close to ambient conditions, the formation of molecular ammonia–water compounds is aided by energetically favorable hydrogen bonds between the two species (52). With increased compression, a different factor contributes: Proton transfer, in particular in a 2:1-ammonia:water compound, results in large stabilization due to ionic interactions and higher packing densities.

Complete deprotonation of water molecules in a compound is an intriguing chemical motif, and we are not aware of its presence in other hydrous systems. Water ionization can be achieved through thermal activation, for instance in ice or AMH, in transitions to superionic phases. In those temperature-induced transitions, protons are diffusive and free to move through a quasi-static lattice of the heavy nuclei. The triple points of solid, fluid, and superionic phases in water and AMH, estimated from simulations, are at $(P,T)=(25$ GPa, 1,200 K) and $(20\text{GPa},800\text{K})$, respectively (28, 41). In AHH, the ionization of water is achieved through a different mechanism, purely through compression work, and the protons thus removed from the water molecules are not diffusive but bound in ${\text{NH}}_4^{+}$ units instead. Higher pressures ($P>\mathrm{\hspace{0.17em}65}$ GPa) are needed to induce this ionization, but the resulting molecular units are arguably more strongly bound than in the lower-pressure region.

To investigate the high-pressure AHH phases more closely at the conditions expected in large icy planets, molecular dynamics calculations at elevated temperatures are required. One interesting question is whether a superionic region exists in AHH, and, if so, how the onset temperature of superionicity is affected by (i) the presence of heavy cation and anion species both and (ii) the seemingly increased N–H bond strengths in the molecular ${\text{NH}}_4^{+}$ units as pressure increases. For ice, ammonia, and AMH, the onset temperatures of superionicity are calculated to be relatively insensitive to pressure (and therefore also insensitive to the underlying crystal structure) and to occur around 2,000, 1,000, and 1,000 K, respectively (28, 29, 41). In compressed AHH, the strongly bound ammonium cations could suggest that relatively high temperatures are needed to induce proton mobility, which, in turn, would lead to reduced thermal and electrical conductivity in any such layer present in planetary interiors.

Cosmic abundance ratios for ammonia:water are approximately 1:7, quite far removed from the 2:1 compound considered here. However, AHH is relevant at relatively low pressures, where it appears in the phase diagrams of both of the other known stoichiometric compounds: Both are more water-rich than AHH, but decompose into AHH-II and pure ice at appropriate P-T conditions. AHH is also very relevant at high pressures, and not just compared with the known AMH and ADH compositions: At 300 GPa, we find, in an extensive structure search across all (NH₃)_x(H₂O)_1−x compounds (ranging from $x=1/6$ to $x=5/6$), that, besides the pure ices, only AHH is stable against decomposition; see the convex hull plot in SI Appendix, Fig. S5. It is therefore conceivable that AHH, driven by its ability to form completely ionic phases, precipitates out of any ammonia–water mixture under high-pressure conditions. At 300 GPa in our calculations, AHH-$P\overline{3}m1$ has a density of 3.50 g/cm³, which is 16% lighter than the most stable ice phase at the same pressure ($Pbcm$ symmetry, 4.17 g/cm³). Thus, compressed water-rich ammonia–water mixtures in a planetary environment (e.g., in a 1:7 ratio or similar) could segregate into a layer of ammonia-rich ionic AHH solution above an ocean of pure water ice. The enthalpic gain achieved in this separation will need to compete with the entropy of mixing of the homogeneous mixture.

Another consequence of the prolonged stability of AHH under pressure is that ammonia reservoirs should always form compounds with water, at least until 450 GPa, where ammonia is predicted to decompose. Unless an icy planet’s ammonia:water ratio is larger than 2:1, which is unlikely due to cosmic observations, ammonia will be unlikely to exist on its own up to pressures around 500 GPa, where we see demixing become favorable.

Methods

Crystal structure prediction was performed using the particle swarm optimization algorithm as implemented in crystal structure analysis by particle swarm optimization (CALYPSO) code (53, 54) in conjunction with density functional total energy calculations. Structure predictions were performed with up to 4 f.u. of H₂O:2(NH₃), i.e., 44 atoms, and at 5, 10, 20, 30, 50, 80, and 100 to 1,000 GPa in increments of 100 GPa. CALYPSO was able to recover a phase very close to the known AHH-II phase in the low-pressure searches. Searches above 800 GPa did not find any H₂O:(NH₃)₂ structures that were energetically favorable compared with decomposition into the constituent ices. The electronic structure calculations and geometry optimizations were performed with the CASTEP code (55). Exchange-correlation effects were described within the generalized gradient approximation (GGA) using the PBE functional (56), and adaptive ultrasoft pseudopotentials. Final structure relaxations were done with “hard” pseudopotentials with radii cutoffs no greater than 1.2 Å for oxygen and nitrogen, and 0.6 Å for hydrogen. Plane wave cutoffs of $E_c=\mathrm{1,000}$ eV and k-point densities of 20 per angstrom were found to give sufficiently converged energies and forces.

Phonon calculations were performed for all structures using the finite displacement method as implemented in CASTEP (57), using supercells of at least 11 Å diameter in each direction. All structures presented here were found to be dynamically stable in their region of enthalpic stability, and dispersion curves are included in SI Appendix.