The terrestrial abundance anomalies of helium and xenon suggest the presence of deep-Earth reservoirs of these elements, which has led to great interest in searching for materials that can host these usually unreactive elements. Here, using an advanced crystal structure search approach in conjunction with first-principles calculations, we show that several Xe/He-bearing iron halides are thermodynamically stable in a broad region of P–T phase space below 60 GPa. Our results present a compelling case for sequestration of He and Xe in the early Earth and may suggest their much wider distribution in the present Earth than previously believed. These findings offer insights into key material-based and physical mechanisms for elucidating major geological phenomena.

The composition of the Earth has long been of wide interest and has been a topic of significant scientific research. The relative absence of Xe from the Earth’s atmosphere compared with its chondritic abundances and the anomalous ratios of 3He/4He in the Earth’s mantle1,2 suggest the presence of He and Xe reservoirs in the Earth’s interior. Early studies hypothesized that Xe might have escaped from the atmosphere3,4 or be stored in the interior of the Earth;5,6 meanwhile, He was predicted to be trapped in compounds stabilized in the lowermost mantle regions. Solving these prominent geoscience puzzles requires finding stable structures and understanding the physics and chemistry of Xe/He-bearing compounds under high pressure–temperature (P–T) conditions, which is challenging because both He and Xe have full-shell electronic structures and tend to be unreactive. Only a small number of Xe compounds have been synthesized under ambient conditions.7–9 Pressure is a clean and effective tool to tune electronic properties10 and can often increase chemical reactivity.11 A slew of He and Xe compounds have been synthesized or predicted at high pressures.6,12–23

On the geoscience research front, attempts to incorporate Xe into ices, clathrates, and sediments of the Earth’s crust were not successful.24–26 Later experiments found trapped Xe in quartz27 and predicted stable xenon oxides,13,28 but these oxides are unstable in equilibrium with metallic iron in the lower mantle, and xenon silicates may decompose spontaneously in the lower mantle.28 Theoretical studies show the possible presence of Xe trapped in the Earth’s core in the form of stable Fe–Xe compounds,6 and Fe and Xe may form solid solutions.17,29 Recently, He and Xe have been predicted to react with FeO2 with the formation of compounds that are thermodynamically stable under deep-Earth conditions.30,31

There is a lack of Xe/He crystalline compounds (not He inclusions in crystals) reported to date as being thermodynamically stable under the P–T conditions corresponding to the great depths near to or inside the core of the present Earth, where pressures rise above 130 GPa and temperatures are higher than 3000 K. Study of the relevant compounds may provide insight into the geological trapping of He and Xe. It should be noted that several studies have suggested that halogen concentrations may actually not be as low as previously thought in chondrites,32–36 which motivates us to search for stable Xe/He iron halides crystal compounds at high pressures.

In this work, we show by extensive computational study that Xe/He-bearing iron halides can be stabilized at moderate pressures below 60 GPa over wide ranges of temperature relevant to diverse geological environments. Our crystal structure searches in conjunction with first-principles energetic calculations and molecular dynamics simulations establish pertinent P–T phase diagrams and demonstrate the thermodynamic stability of several Fe–F–He, Fe–F–Xe, and Fe–Cl–Xe compounds that could have existed in the interior of the early Earth. These findings introduce a new paradigm for sequestration of He and Xe inside the Earth by establishing a critically needed connection to the primordial origin of the geological trapping of these elements, making possible the scenarios of previously proposed Xe/He-bearing compounds that are only viable at much greater depths in the lowermost mantle or core regions of the present Earth.

Our crystal structure search employs a global free-energy optimization algorithm as implemented in the CALYPSO methodology37,38 in conjunction with first-principles calculations to determine energetic and dynamic structural evolution under wide-ranging P–T conditions. The different components of the compounds in this study are shown in Table S1 (supplementary material). The search has identified viable FeF2He, FeF3He, FeF2Xe, FeF3Xe, and FeCl3Xe compounds, as indicated in the ternary phase diagrams at selected pressures shown in Figs. 1(a)1(c). The formation energies of FeF2He, FeF3He, FeF2Xe, and FeF3Xe at 60 GPa and of FeCl3Xe at 65 GPa are −0.53, −0.56, −0.10, −0.54, and −0.01 ev/f.u., respectively, as shown in Table S2 (supplementary material). Calculated phonon dispersions show no imaginary modes in the full Brillouin zone over the pertinent pressure range for any of these ternary compounds (Fig. S1, supplementary material), establishing their dynamical stability. The corresponding crystal structures are shown in Fig. 2. The reference systems for evaluating relative structural stability include FeF2 in Fmmm, Pnma, and Pa-3 symmetries, FeF3 in R-3c symmetry, FeCl3 in R-3c symmetry, solid Xe, Fe, and He in P63/mmc symmetry, solid Cl in Cmca symmetry, and solid F in Cmca symmetry in the 20–100 GPa pressure range.39–41 The binary Xe–F (F2Xe, F4Xe, F6Xe), Xe–Cl (XeCl XeCl2), and FeCl2 compounds are also considered in the ternary phase diagram. XeF2 is I4/mmm phase, XeF4 is I4/m phase, and XeF6 is Cmcm phase at 60 GPa.42 XeCl is Cmcm phase, XeCl2 is P43212 phase,43 and FeCl2 is Pa-3 phase at 65 GPa.40 The composition–pressure phase diagrams based on energetic (enthalpy) calculations [Fig. 1(d)] shows that at pressures ranging from 27 to 63 GPa, the predicted ternary compounds become stable against decomposition that would release Xe or He, and their stability persists to higher pressures.

FIG. 1.

(a)–(c) Ternary phase diagrams of the Fe–F–He, Fe–F–Xe, and Fe–Cl–Xe systems at selected pressures and 0 K. Five thermodynamically stable ternary compounds have been identified. (d) Composition–pressure phase diagram of the five ternary compounds over a wide range of pressure and at 0 K.

FIG. 1.

(a)–(c) Ternary phase diagrams of the Fe–F–He, Fe–F–Xe, and Fe–Cl–Xe systems at selected pressures and 0 K. Five thermodynamically stable ternary compounds have been identified. (d) Composition–pressure phase diagram of the five ternary compounds over a wide range of pressure and at 0 K.

Close modal
FIG. 2.

Crystal structures of stable ternary compounds: (a) Fm-3m-FeF2He; (b) P63/m-FeF3He; (c) P21/m-FeF2Xe; (d) Pmmn-FeF3Xe; (e) P63/mmc-FeCl3Xe. The lattice parameters of these compounds are given in Table S3 (supplementary material).

FIG. 2.

Crystal structures of stable ternary compounds: (a) Fm-3m-FeF2He; (b) P63/m-FeF3He; (c) P21/m-FeF2Xe; (d) Pmmn-FeF3Xe; (e) P63/mmc-FeCl3Xe. The lattice parameters of these compounds are given in Table S3 (supplementary material).

Close modal

Of the two He-bearing compounds, FeF2He crystallizes in the AlCu2Mn (Heusler) structure type in Fm-3m symmetry, adopts a face-centered-cubic lattice, and comprises FeF8 units that host He atoms. In this structure, the FeF8 hexahedrons are connected to each other via common edges, and He atoms sit between the hexahedrons. At 60 GPa, the Fe–F, Fe–He, and F–He nearest distances take uniform values of 2.07, 2.39, and 2.07 Å, respectively. Meanwhile, FeF3He in P63/m symmetry comprises FeF9 units and He atoms in otherwise similar structural arrangements, where the Fe–F, Fe–He, and F–He nearest distances are 2.02, 3.03, and 1.98 Å, respectively. There are three Xe-bearing compounds, namely, FeF2Xe in P21/m symmetry, FeF3Xe in Pmmn symmetry, and FeCl3Xe in P63/mmc symmetry. The P21/m-FeF2Xe comprises FeF6 units arranged in planar structures with the Xe atoms positioned between the planes, and the nearest Fe–F distances in this phase are 1.94–2.11 Å, while the Fe–He and F–Xe nearest distances are 2.69 and 2.67 Å, respectively. In Pmmn-FeF3Xe, each Fe atom is surrounded by eight F atoms, and the FeF8 decahedron units form a planar structure by sharing the same edges, where Fe–F nearest distances are in the range of 1.96–2.05 Å, while the Fe–Xe and F–Xe nearest distances are 2.69 and 2.59 Å, respectively. The P63/mmc-FeCl3Xe contains FeCl6 units, which are arranged in chains that share the same plane, and the Fe–Cl, Fe–Xe and F–Xe nearest distances are 2.21, 3.62, and 2.93 Å, respectively.

We also performed Bader charge analysis on the predicted ternary compounds, as shown in Table S4 (supplementary material). In the He-bearing compounds, electrons transfer from Fe to F and He atoms. Specifically, in FeF2He, each Fe loses 1.56e, while each F gains 0.76e and each He gains 0.04e; in FeF3He, each Fe loses 2.07e, while each F gains 0.69e and each He gains 0.01e. Meanwhile, in the Xe-bearing compounds, electrons transfer from Fe and Xe to F or Cl. In FeF2Xe, each Fe loses 1.35e and each Xe loses 0.11e, while each F gains 0.71e/0.75e; in FeF3Xe, each Fe loses 1.92e and each Xe loses 0.27e, while each F gains 0.73e; in FeCl3Xe, each Fe loses 1.28e and each Xe loses 0.28e, while each Cl gains 0.52e. These findings indicate that He atoms show little direct bonding interaction with the other atoms in the compounds and mainly serve as a Coulomb shield in stabilizing the compound, as is seen in similar materials,44 but Xe atoms exhibit notable participation in the bonding process. The Bader analysis of FeF3He and FeF2He shows that there is almost no charge transfer between He and Fe or F atoms, indicating that He is unlikely to react with Fe or F. However, previous simulations44 found that He has a general tendency to react with ionic compounds containing unequal amounts of cations, where the Madelung energy plays a critical role in stabilizing the structure by the insertion of He that could lower the Coulomb repulsion between the ions. Our predicted structure may have a similar stability mechanism, as reported in the previous work.44 

To assess the geological viability of the predicted Xe/He-bearing compounds, it is essential to establish their PT phase diagrams under the conditions corresponding to the interiors of both the early and present Earth. To this end, we have performed two sets of calculations. We first computed the phonon dispersions and the corresponding phonon densities of states of all the predicted structures and associated binary and elemental systems, and then used the results as input to evaluate the vibrational contribution to the entropy. Combining this with the total internal energy, pressure, and volume determined by first-principles calculations, we obtained the Gibbs free energies for FeF2He, FeF3He, FeF2Xe, FeF3Xe, and FeCl3Xe, along with the results for the related binary and elemental crystals, which allow a systematic determination of phase boundaries separating the ternary compounds from the decomposed constituent binary iron halides and Xe/He. Additionally, we performed ab initio molecular dynamics (AIMD) simulations over wide PT ranges to evaluate the temperature-driven diffusive and melting behaviors, which further characterize the distinct states of matter of the Xe/He-bearing ternary compounds under the PT conditions encountered in widely changing geological environments.

On the basis of Gibbs free energy calculations and AIMD simulations, we have constructed the PT phase diagrams for the five Fe–F–He and Fe–X–Xe (X = F, Cl) compounds (Fig. 3), which show that these compounds become thermodynamically stable against binary and elemental decompositions over large swaths of PT space, starting at moderate pressures. Rising temperature helps to stabilize most of the examined ternary compounds at reduced pressures, indicating favorable entropic contributions to the structural stabilization, with the exception of FeF3He, which requires higher pressures for stabilization at rising temperatures, indicating a pressure-dominated stabilizing mechanism as previously seen in FeO2He. Overall, all the ternary compounds possess stability fields that are compatible with the PT conditions inside the early Earth, and this finding offers a plausible scenario for the sequestration of He and Xe in the initial stages of Earth’s differentiation when the volatile elements were separated and redistributed from the primordial chondritic contents. The stability fields of these ternary compounds extend to higher PT regions coinciding with the geotherm of the present Earth, enlarging considerably the regions in the Earth’s interior where Xe/He-bearing compounds can exist in stable nongaseous forms, which has major implications for interpreting the origin and cycling derived from the geochemical analysis of mineral assemblages entrained from distinct mantle regions. For example, primordial He observed in plumes at volcanic hot spots has been taken as a key evidence of its entrainment from the deep lower mantle,45 yet the present results indicate that the minerals containing primordial He could have come from much shallower depths near the top of the lower mantle, allowing fresh interpretation of the dynamic evolution of the Earth’s interior.

FIG. 3.

Pressure–temperature (PT) phase diagrams of the Fe–F–He and Fe–X–Xe (X = F, Cl) compounds FeF2He (a), FeF3He (b), FeF2Xe (c), FeF3Xe (d), and FeCl3Xe (e). The lines connecting black squares indicate phase boundaries. Green circles, blue triangles, and red diamonds represent the solid, sublattice melting and liquid phases, respectively, dividing PT space into the same-color shaded regions for these distinct states of matter. The geotherm of the present Earth is indicated by the thick orange line.

FIG. 3.

Pressure–temperature (PT) phase diagrams of the Fe–F–He and Fe–X–Xe (X = F, Cl) compounds FeF2He (a), FeF3He (b), FeF2Xe (c), FeF3Xe (d), and FeCl3Xe (e). The lines connecting black squares indicate phase boundaries. Green circles, blue triangles, and red diamonds represent the solid, sublattice melting and liquid phases, respectively, dividing PT space into the same-color shaded regions for these distinct states of matter. The geotherm of the present Earth is indicated by the thick orange line.

Close modal

The results of our AIMD simulations further reveal an interesting phenomenon of partial melting of the ternary compounds as the temperature rises above certain threshold values, characterized by the onset of an intriguing partial melting state where the lighter-element sublattice melts, with the corresponding constituent atoms turning diffusive while the remaining crystal frame remains intact in the solid phase. As the temperature increases further, the entire crystal transitions into a liquid phase where all the constituent atoms of the entire crystal becomes diffusive. This scenario is illustrated for the representative cases of FeF3He, FeF3Xe, and FeCl3Xe in Fig. 4 and Fig. S6 (supplementary material), where the mean-square displacements (MSDs) of the constituent atoms in the crystal lattice measured relative to their equilibrium positions are plotted vs simulation time, together with plots of the snapshots of trajectories of the atomic positions. In the superionic states of the FeF2He, FeF3He, and FeF3Xe compounds, the freely moving atoms are He and F, respectively. Our simulation results suggest there are no superionic state in the FeCl3Xe system. These results reveal three distinct states of matter: (i) a solid state, where all atoms remain near their equilibrium crystal lattice sites, (ii) a partial melting state, where the light-element (He) atoms become diffusive, as indicated by the MSDs showing significant deviations from their equilibrium sites, while the other atoms remain near their equilibrium sites, and (iii) a liquid state, where all atoms exhibit MSDs showing large deviations from their equilibrium sites.

FIG. 4.

(a)–(c) Mean-square displacements (MSDs) of atoms in P63/m-FeF3He from AIMD simulations: (a) there is no atomic diffusion at 1500 K and 52 GPa in the solid phase; (b) He atoms are diffusive at 2000 K and 57 GPa in the sublattice melting phase; (c) all atoms become diffusive at 3000 K and 65 GPa in the liquid phase. (d)–(f) Trajectories showing the corresponding real-space atomic displacements over the simulation time span.

FIG. 4.

(a)–(c) Mean-square displacements (MSDs) of atoms in P63/m-FeF3He from AIMD simulations: (a) there is no atomic diffusion at 1500 K and 52 GPa in the solid phase; (b) He atoms are diffusive at 2000 K and 57 GPa in the sublattice melting phase; (c) all atoms become diffusive at 3000 K and 65 GPa in the liquid phase. (d)–(f) Trajectories showing the corresponding real-space atomic displacements over the simulation time span.

Close modal

During the initial phase of its differentiation process, the early Earth is considered to have harbored P–T conditions up to 60 GPa–3000 K,46 and the phase diagrams in Fig. 3 thus indicate that the sublattice melting and liquid phases of the iron–halide–Xe/He compounds are viable constituents deep inside the planet during the crucial initial phase of its differentiation process, along with the corresponding solid phases in the outer layers with lower P–T conditions during core–mantle separation. Moreover, since the stability fields of these ternary compounds extend from the top to the bottom of the lower mantle of the present Earth, primordial He and Xe can exist in solid, partial melting solid, or liquid phases in the entire vast volume of Earth’s lower mantle either as stable deposits or as part of the dynamic mineral cycling process.

The present study also sheds light on the anomalously low terrestrial abundance of halogens relative to chondritic meteorites.47 Previous studies40 proposed that halogens may be sequestered in the Earth’s mantle and core via the formation of iron halides. Our results suggest a new mechanism for halogen sequestration via halogen-bearing Fe–X–Xe/He (X = F, Cl) compounds that can be stabilized under moderate P–T conditions corresponding to those inside the early Earth and also in the present Earth’s vast lower mantle. These results provide an additional material platform to account for the terrestrial halogen distribution that holds the key to understanding geological evolution during the Earth’s formation and subsequent differentiation and accretion.

In conclusion, through an extensive crystal structure search in conjunction with first-principles energetic calculations, we have identified a series of Xe/He-bearing iron halides FeF2He, FeF3He, FeF2Xe, FeF3Xe, and FeCl3Xe that are thermodynamically stable at moderate pressures below 60 GPa over wide ranges of temperatures and are thus viable inside the early Earth during its initial stages of differentiation. This discovery offers insights into the long-standing puzzle of terrestrial abundance anomalies of He and Xe that have their roots in the earliest geophysical and geochemical evolutions of the Earth, and expands considerably the range of existence of Xe/He-bearing compounds in the present Earth. Moreover, AIMD simulations reveal partial melting of these iron–halide–Xe/He compounds at rising temperatures, resulting in intriguing sublattice melting states with the lighter elements in diffusive modes inside the remaining solid crystal framework, before transitions into the liquid states occur at further increased temperatures. These findings make a compelling case for sequestration of He and Xe in the early Earth, thereby establishing a crucial but hitherto missing link to the presence of these elements inside the present Earth as suggested by extensive existing studies. The present results also have broad implications for interpretation and elucidation of geophysical and geochemical processes that are sensitive to the origins of such minerals entrained from distinct deep-Earth localities, which offer insights into the evolutionary dynamics and mineral cycling inside the Earth.

See the supplementary material for calculation details, figures and tables. Fig. S1: Calculated phonon dispersion curve. Fig. S2: Electronic structures and the nature of Fe-Xe, F-Xe, Fe-He, F-He and Cl-Xe bonds. Fig. S3: ELF of FeF2He. Fig. S4: The band structures. Fig. S5: The enthalpy-pressure relation of FeF2He at different U-J values. Fig. S6: Mean-square displacements (MSDs) of atoms in FeF3Xe and FeCl3Xe from AIMD simulations. Table S1: The different components of the compounds in this study. Table S2: The formation energy of new structures of FeF2He, FeF3He, FeF2Xe, FeF3Xe at 60 GPa and FeCl3Xe at 65 GPa. Table S3: Calculated structural data of Fe-Fe-He, Fe-F-Xe, Fe-Cl-Xe phases at selected pressures at 0 K. Table S4: The gain and loss electrons for the elements in different newly predicted compounds in Bader calculation. Table S5: lists the solar system abundances published over time on a scale relative to 106 silicon atoms.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12204280 and 12147135), the Postdoctoral Science Foundation of China (Grant No. 2021M691980), Natural Science Foundation of Shandong Province (Grant No. ZR202103010004), the Jilin Province Science and Technology Development Program (Grant No. YDZJ202102CXJD016), the Program for Jilin University Science and Technology Innovative Research Team (2021TD-05), and the Program for Jilin University Computational Interdisciplinary Innovative Platform. We used the computing facility at the High-Performance Computing Center of Jilin University.

The authors have no conflicts to disclose.

Jurong Zhang: Formal analysis (equal); Investigation (equal); Writing – original draft (equal). Hanyu Liu: Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Changfeng Chen: Formal analysis (equal); Supervision (equal); Writing – review & editing (equal). Yanming Ma: Formal analysis (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material. Other relevant data are openly available in https://doi.org/10.1063/5.0164149.

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