ABSTRACT Uranus and Neptune are generally assumed to have helium only in their gaseous atmospheres. Here, we report the possibility of helium being fixed in the upper mantles of these

planets in the form of NH3–He compounds. Structure predictions reveal two energetically stable NH3–He compounds with stoichiometries (NH3)2He and NH3He at high pressures. At low

temperatures, (NH3)2He is ionic with NH3 molecules partially dissociating into (NH2)− and (NH4)+ ions. Simulations show that (NH3)2He transforms into intermediate phase at 100 GPa and 1000 K

with H atoms slightly vibrate around N atoms, and then to a superionic phase at  ~2000 K with H and He exhibiting liquid behavior within the fixed N sublattice. Finally, (NH3)2He becomes a

Article 26 May 2021 DOUBLE SUPERIONICITY IN ICY COMPOUNDS AT PLANETARY INTERIOR CONDITIONS Article Open access 21 November 2023 INTRODUCTION Knowledge of the interior compositions of planets

is crucial to understanding the processes of their formation and evolution. Various methods have been used to investigate the Earth’s interior, while studies of the composition and

structure of the solar system’s ice giants, Uranus and Neptune, are limited by using only global observable properties such as gravitational and magnetic moments1. Uranus and Neptune are

generally assumed to have a three-layer structure: a rocky core, an ice mantle (contains an upper mantle and a lower mantle), and a gas atmosphere1,2,3,4,5,6. Although many studies have

focused on the interiors of Uranus and Neptune, their internal compositions remain to be fully understood7,8,9,10,11,12. A widely accepted model for each of these planets is that the upper

mantle comprises a mixture of ionized H2O, NH3, and CH45,8,11, whereas the lower mantle consists of metallic H2O, NH35,6 Much effort has been devoted to determine the ratio of the components

in the interior of the ice planets8,10,11, however, no consensus were reached. To understand realistic compositions of Uranus and Neptune, researchers have focused on high-pressure and

high-temperature phases of NH3 and H2O, and mixtures of the two13,14,15. Cavazzoni et al16. performed molecular dynamic simulations to estimate the phase diagram of water and ammonia at

pressures and temperatures in the range of 30– 300 GPa and 300–7000 K. They found that water and ammonia exhibited a superionic phase (at about 100 GPa, 1500 K) between the ionic solid phase

and ionic fluid phase. However, for the component CH4, the results of equation of state have shown that it would dissociate into hydrocarbons at the extreme conditions17. A computational

search undertaken by Pickard and Needs in 2008 found that ammonia transformed into an ionic phase consisting of (NH2)− and (NH4)+ ions at pressures above 90 GPa13; the transformation was

subsequently confirmed by experiment14,15. By combining empirical and theoretical results, Ninet et al18. found that a novel superionic conductive phase of ammonia becomes stable at about 70

 GPa and 8500 K. Using Raman spectroscopy and synchrotron X-ray diffraction, Laniel et al19. found two unusual ionic N–H stoichiometries, (N2)6(H2)7 and N2(H2)2, which are stable at about

50–GPa. While for water, it has a rich phase diagram, with at least 17 solid phases identified experimentally20,21,22, and seven other high-pressure phases predicted by theoretical

studies23,24,25,26. Ninet et al18. and Millot et al27. proposed that superionic water ice can exist in the mantles of the ice giants as a result of shock compression. Recently, Huang et

al28. found that H2O can react with H2 and form a novel superionic compound of H3O under high pressure and high temperature. For a 2:1 mixture of NH3 and H2O, Robinson et al29. predicted a

novel ionic compound, O2−(NH4+)2, to form at pressures above 65 GPa. Recent theoretical and experimental studies have shown that NH3H2O decomposes into ammonia and water at 120 GPa30,31.

Bethkenhagen et al32. used an evolutionary random structure search code to propose a superionic phase of NH3H2O at 800 GPa and high temperature (1000–6000 K). An unusual layered ionic phase

of NH3(H2O)2 was predicted for a 1:2 mixture of NH3 and H2O; it was then modeled to transform into a superionic phase at high pressure and high temperature (41 GPa and 600 K)33. These

findings contribute to our understanding of the interiors of the giant ice planets. The above results have led to the assumption that the elements (i.e., C, H, and N) in the ice giants’

gaseous atmospheres except He appear in their solid mantles. Helium is generally considered likely to remain only in the atmosphere and not form solid compounds in the mantle, because it is

the most chemically inert element due to its stable closed-shell electronic configuration. In fact, Nettelmann et al11. have proposed a three-layer structure model, in which the considering

of small amount of He/H in the outer core of the planets reproducing well the gravitational moments of the ice giants. Recent studies have indicated that high pressure can induce He to form

compounds such as HeN434,Na2He35, FeHe36, MgOHe37, H2OHe38,39, and FeO2He40. Specially, the compound of H2OHe2 exhibited a superionic property under high pressure and high temperature and

then transformed into fluid39. These results inspired us to explore whether some of the abundant elemental He from the planets’ atmospheres could be trapped inside the mantles of Uranus and

Neptune. Therefore, we carried out calculations to search for stable compounds in NH3–He systems at high pressure and high temperature. Our results show that He can react with NH3 to form

(NH3)2He under extreme conditions, to a certain extent corresponding to the upper mantles of Uranus and Neptune, thereby providing information essential to the understanding of the interior

models of these planets. RESULTS STABLE NH3–HE COMPOUNDS AT HIGH PRESSURE The formation enthalpies of the energetically most-stable structures of (NH3)_x_He_y_ (_x_ = 1 ~ 3, _y_ = 1 ~ 3) as

compared to mixtures of NH3 and He at selected pressures are summarized in Fig. 1. The phases lying on the convex hull are thermodynamically stable against decomposition into other

compositions. The figure also shows the effects of zero-point vibrational energy (ZPE). The positive formation enthalpies show that, as expected, no thermodynamically stable compositions

were found at ambient pressure. However, static-lattice enthalpy calculations revealed three stable compositions at high pressures: (NH3)2He at 10 and 300 GPa, NH3He at 50, 100, and 150 GPa,

and NH3He2 at 300 GPa (Supplementary Fig. 1). The inclusion of ZPE alters significantly the stability of (NH3)2He and NH3He2, i.e., (NH3)2He becomes energetically stable also at 150 and 300

 GPa, while NH3He2 turns to be unstable at all pressures. Figs. 2 and 3, respectively present detailed stable pressure ranges for the three obtained compositions and their corresponding

crystal structures. Optimized lattice parameters for all the structures at selected pressures are listed in Supplementary Table 1. The results indicate that (NH3)2He with space group _I_4,

labeled here as _I_4–(NH3)2He, becomes energetically stable with respect to NH3 and He at pressures as low as 9 GPa (Fig. 2). Tetragonal _I_4–(NH3)2He consists of isolated NH3 molecules and

He atoms. Figure 3a depicts the NH3 layers of this structure in the _a_–_b_ planes, with He atoms located in the pockets formed by neighboring NH3 molecules. Interestingly, the _I_4

structure displays unique channels formed by NH3 molecules that are arranged parallel to the _c_-axis, and linear He chains localize within the interstices formed by four neighboring

channels (Fig. 3b). To our knowledge, this is the first report of such a channel-bearing NH3 structure. (NH3)2He remains energetically stable up to 40 GPa, above which it decomposes into a

mixture of NH3 and He. However, (NH3)2He re-emerges as energetically stable phase at 110 GPa with the formation of an orthorhombic _F__m__m_2 structure. A similar

combination-decomposition-recombination pattern has previously been reported for CaLi244. Partial dissociation of NH3 molecules into (NH2)− and (NH4)+ ions is found to accompany the

formation of _F__m__m_2–(NH3)2He. Bader analysis demonstrates the strongly ionic nature of the species, with Bader charges of −0.57 _e_− and 0.53 _e_− for (NH2)− and (NH4)+, respectively,

similar to those observed in the ionic phase of pure NH313. The _F__m__m_2 phase is also layered, consisting of layers formed by NH3, (NH2)−, and (NH4)+ units in the _a_–_c_ planes. The

spacing between neighboring layers is 2.07 Å. Viewing the structure along the _a_-axis reveals unique channels formed by NH3, (NH2)−, and (NH4)+ units, with He atoms located in the

interstices. NH3He composition becomes energetically stable at 35 GPa, as shown in Fig. 2, adopting an orthorhombic _P__m__m__a_ structure. The _P__m__m__a_ phase is the most stable

configuration over a large pressure range up to 180 GPa for NH3He, above which it transforms into the _P_212121 structure. The _P_212121–NH3He phase will remain stable up to 300 GPa, which

is the maximum pressure considered in this study. Both the _P__m__m__a_ and the _P_212121 structures of NH3He are composed of isolated NH3 molecules and He atoms, and there is no evidence of

dissociation of NH3 in the whole pressure range studied here. The calculated phonon dispersions confirm the dynamical stability of all these structures in their energetically stable

pressure ranges (Supplementary Fig. 3). ELECTRONIC PROPERTIES To examine the interactions among N, H, and He atoms in the two compounds, we calculate electronic properties including the

electronic localization function (ELF) and Bader charges. The ELF is a quantum chemistry tool to visualize covalent bonds; values close to 1 corresponding to strong covalent bonding. The ELF

results rule out covalent bonds between N–H units (NH3, (NH2)−, (NH4)+) and He atoms, given the absence of any ELF local maxima between them (Supplementary Fig. 5). Interestingly, Bader

analysis indicates a slight charge transfer from N–H units to He atoms. Table 1 lists the Bader charge of one He atom in _I_4–(NH3)2He as  ~ -0.02 _e_− at 10 GPa, which increases to -0.03 

_e_− when the _F__m__m_2 structure is adopted at 120 GPa. Similar to that in (NH3)2He, each He atom in NH3He and NH3He2 gains nearly 0.03 _e_− from the NH3 molecules. The Bader charge of a

He atom in the three NH3–He compounds is similar to the charges predicted for H2O–He, MgF2He, MgOHe, and FeO2He (between −0.02 _e_− and -0.07 _e_−)36,37,38,40. The current results indicate

the three compounds have an ionic nature and that He atoms could serve as a Coulomb shield in stabilizing them at high pressure. Electronic band structures show that all three compounds are

insulators (Supplementary Fig. 4). At the PBE-GGA level, the band gap of (NH3)2He is calculated to be 6.0 eV at 10 GPa, which increases to 7.5 eV at 180 GPa. For NH3He, the band gaps is

calculated to be 7.2 eV at 35 GPa. SUPERIONIC PHASES OF (NH3)2HE The stable pressure and temperature regions of _F__m__m_2–(NH3)2He cover the geotherms in the upper mantle of Neptune and

Uranus. We, therefore, performed ab initio molecular dynamics simulations at the pressure of 100 GPa, 200 GPa, and 300 GPa, respectively, to examine the formation of _F__m__m_2–NH3)2He

inside Neptune and Uranus. The calculated mean squared displacement (MSD) of the atomic positions and the behaviors of three different atoms of _F__m__m_2–(NH3)2He are shown in the Fig. 4.

At _P_ = 100 GPa and _T_ = 200 K, _F__m__m_2–(NH3)2He is a solid phase with all atoms vibrating around their lattice positions and with diffusion coefficients (_D_H = _D_He = _D_N = 0). When

the temperature increasing to 1000 K, the H atoms seems diffusive with _D_H = 1.4 × 10−6 cm2 s−1. However, from the atomic trajectories shown in Fig. 4b, one can find that H atoms in NH3

become diffuse while H atoms in (NH2)− and (NH4)+ keep vibrating around their lattice positions. This means that the H atoms in NH3 units become considerable vibrate with a fixed N position

at this condition. With the temperature further increased to 2000 K, _F__m__m_2–(NH3)2He transforms into a real superionic phase with fully diffusive H atoms (_D_H = 2.0 × 10−4 cm2 s−1)

within the fixed N and He framework. With the temperature increased to 3000 K, all atoms including N, He, and H are diffusive with high diffusion coefficients (_D_N = 4.4 × 10−5 cm2 s−1,

_D_He = 2.1 × 10−5 cm2 s−1 and _D_H = 4.5 × 10−4 cm2 s−1). This result reveals that at this conditions the superionic _F__m__m_2–(NH3)2He phase transformed into a fluid phase. Here, we found

the diffusion of H atoms occurs prior to that of He atom, which is opposite to that found for He2(H2O)39, where He atoms diffuse firstly. Generally, lighter atoms are easier to diffuse. The

abnormal diffusive behavior in He2(H2O) was explained by that the H atoms has higher diffusion barrier than He atoms because of the strong covalent H-O bonds39. In fact, He atoms in

He2(H2O) share large space that allows the free diffusion, as shown in Supplementary Fig. 6. As compared to He2(H2O), although form weak interaction with N–H units, He atoms are trapped in

cages formed by NH3, (NH2)− and (NH4)+ units, this makes helium atoms are more difficult to diffuse. While for _P_ = 200 GPa and _T_ = 300 K, _F__m__m_2–(NH3)2He keeps its solid property.

With the temperature increasing to 1000 K and up to 4000 K, _F__m__m_2–(NH3)2He becomes to a superionic phase and then turns in to a fluid when the temperature is above 4200 K, as shown in

Supplementary Fig. 7. Under pressure of 300 GPa, the trend is similar to that under 200 GPa, but the critical point of the superionic phase to fluid is at the temperature of 4600 K, as shown

in Supplementary Fig. 8. Figure 5 presents the pressure–temperature (P–T) phase diagram for the mixture of NH3 and He, showing the (NH3)2He and NH3He phases. Temperature has a significant

effect on the system: _I_4–(NH3)2He and NH3He decompose at high temperature (Fig. 5 and Supplementary Fig. 2). Their maximum temperatures of stability vary, being  >700 K for

_I_4–(NH3)2He (which decomposes fully to NH3 and He),  >1000 K for NH3He (for full decomposition to NH3 and He at _P_ < 100 GPa and decomposition into _F__m__m_2–(NH3)2He and He at _P_

 > 100 GPa). In contrast, _F__m__m_2–(NH3)2He has a large stability field and thermodynamically stable in pressure range of 80–300 GPa and at any temperature in the tested range (0–5000 

K). Figure 5 also presents estimated geotherms for the interiors of Uranus and Neptune. We also pointed the phase states of _F__m__m_2–(NH3)2He in the Fig. 5. Our calculation show that the

_F__m__m_2–(NH3)2He phase presents superionic and fluid properties at the condition which is close to the geotherms in the upper mantle of Neptune and Uranus. This suggests that He could be

trapped as superionic (NH3)2He inside the upper mantles of these planets with the mixture of superionic and fluid forms during their formation. Previous studies have assumed the presence of

NH3, CH4, H2O, and H2 inside the giant ice planets. Our predicted stability of superionic (NH3)2He as well as the recent reported superionic H2OHe239 under the P–T conditions corresponding

to the ice giants’ upper mantles indicate that helium could be remained inside the planets during their formation. Coincidently, the stability of NH3–He and H2O–He compounds provide an

evidence to support the new three-layer model suggested by Nettelmann11, in which helium was considered as a small component in outer core of the planets. Therefore, the current results are

essential to the understanding of the interior models of these planets. Moreover, CH4 and H2 are another two main components in upper mantle of these planets, therefore, there is a high

possibility that helium could react with CH4 or H2 at high pressures to form new compounds, which deserves further investigation. In our submission process, we were aware of the work by Liu

et al.46 predicting plastic and superionic helium-ammonia compounds at extreme condition. They predicted three stable stoichiometries and eight new stable phases of He–NH3 compounds under

pressures up to 500 GPa and found that the predicted He–NH3 compounds exhibit superionic behavior at high pressure and high temperature. These similar results further provide knowledge for

our understanding of the composition of the planet’s interior. In summary, a combination of first-principles calculations and crystal structure predictions was carried out to search for

stable compounds in the NH3–He systems under high-_P_–_T_ conditions. Calculations at 0 K revealed two compounds ((NH3)2He and NH3He) that are energetically stable relative to the equivalent

mixture of solid NH3 and He at high pressures. Specially, (NH3)2He remains energetically stable under the extreme conditions corresponding to the upper mantles of Uranus and Neptune. The

current results provide evidence that He could be trapped inside these planets as NH3–He compounds with the mixture of superionic and fluid properties, in contrast to the current view that

He occurs only in their atmospheres. Molecule dynamic simulations results show that the _F__m__m_2-(NH3)2He phase will transform into a superionic solid and then to a fluid with the

increasing temperature. METHODS STRUCTURAL PREDICTIONS Structure predictions for NH3–He compounds were performed using a particle-swarm optimization algorithm implemented in calypso

code47,48. This method is unbiased, not using any known structural information, and has successfully been used to predict various systems under high pressure49,50,51,52,53,54,55,56,57. We

performed structural searches on (NH3)_x_He_y_ (_x_, _y_ = 1, 2, 3) at 0–300 GPa with maximum simulation cells up to four formula units. Each generation of structures was evolved by

selecting the 60% lowest-enthalpy structures in the last step and randomly producing the remaining 40%. The structure searches were considered converged when  ~1000 successive structures

were generated without finding a new lowest-enthalpy structure. AB INITIO CALCULATIONS Density functional theory calculations were performed using vasp code58 combined with the generalized

gradient approximation (GGA)59 for the exchange-correlation potential in the form of the Perdew–Burke-–Ernzerhof60 (PBE) functional. The electronic wave functions were expanded in a plane

wave basis set with a cutoff energy of 1000 eV. The electronic interaction was described by means of projector augmented wave 61 pseudopotentials with valence electrons of 1_s_1, 2_s_22_p_3

and 1_s_2 for H, N, and He atoms, respectively. Monkhorst-Pack k-point62 meshes with a grid density of 0.03 Å−1 were chosen to achieve a total energy convergence of better than 1 meV per

atom. The phonon dispersion curves were computed by direct supercell calculation63, as implemented in the phonopy program64. MOLECULAR DYNAMICS The molecular dynamics simulations were also

carried out to explore the superionic property of (NH3)2He compound at high pressures and high temperatures. The simulation supercells contain 32 NH3 molecules and 16 helium atoms and the

Brillouin zone was sampled by Γ point. Each simulation consists of 10,000 time steps with a time step of 0.5 fs. DATA AVAILABILITY The authors declare that the main data supporting the

findings of this study are contained within the paper and its associated Supplementary Information. All other relevant data are available from the corresponding author upon reasonable

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volumetric and morphology data. _J. Appl. Crystallogr._ 44, 1272–1276 (2011). Article  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS The authors acknowledge funding from the NSFC

under grant No. 11804129, No. 11722433, No. 11804128, No. 11904142 and No. 11674329. Y.L. acknowledges funding from the Six Talent Peaks Project of Jiangsu Province. X.W. acknowledges

project No. TZ2016001 of Science Challenge. All the calculations were performed at the High Performance Computing Center of the School of Physics and Electronic Engineering of Jiangsu Normal

University. Crystal structures were visualized with vesta65. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Laboratory of Quantum Materials Design and Application, School of Physics and

Electronic Engineering, Jiangsu Normal University, Xuzhou, 221116, China Jingming Shi, Wenwen Cui, Jian Hao, Meiling Xu & Yinwei Li * Jiangsu Key Laboratory of Advanced Laser Materials

and Devices, Jiangsu Normal University, Xuzhou, 221116, China Jian Hao * Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, 230031,

China Xianlong Wang Authors * Jingming Shi View author publications You can also search for this author inPubMed Google Scholar * Wenwen Cui View author publications You can also search for

this author inPubMed Google Scholar * Jian Hao View author publications You can also search for this author inPubMed Google Scholar * Meiling Xu View author publications You can also search

for this author inPubMed Google Scholar * Xianlong Wang View author publications You can also search for this author inPubMed Google Scholar * Yinwei Li View author publications You can also

search for this author inPubMed Google Scholar CONTRIBUTIONS J.S and Y.L. designed the project. J.S. and W.C performed the calculations. J.S., W.C., X.W., M.X., J.H., and Y.L. analyzed the

data. J.S., W.C., X.W., and Y.L. wrote the paper. CORRESPONDING AUTHORS Correspondence to Xianlong Wang or Yinwei Li. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing

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permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Shi, J., Cui, W., Hao, J. _et al._ Formation of ammonia–helium compounds at high pressure. _Nat Commun_ 11, 3164 (2020).

https://doi.org/10.1038/s41467-020-16835-z Download citation * Received: 17 March 2020 * Accepted: 28 May 2020 * Published: 22 June 2020 * DOI: https://doi.org/10.1038/s41467-020-16835-z

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