Melting phase relations in Fe–Si–H at high pressure and implications for Earth’s inner core crystallization

Hydrogen could be an important light element in planetary cores, but its effect on phase diagrams of iron alloys is not well known because the solubility of H in Fe is minimal at ambient pressure and high-pressure experiments on H-bearing systems have been challenging. Considering that silicon can be another major light element in planetary cores, here we performed melting experiments on the Fe–Si–H system at ~ 50 GPa and obtained the ternary liquidus phase relations and the solid/liquid partition coefficient, D of Si and H based on in-situ high-pressure X-ray diffraction measurements and ex-situ chemical and textural characterizations on recovered samples. Liquid crystallized hexagonal close-packed (hcp) (Fe0.93Si0.07)H0.25, which explains the observed density and velocities of the Earth’s solid inner core. The relatively high DSi = 0.94(4) and DH = 0.70(12) suggest that in addition to Si and H, the liquid outer core includes other light elements such as O, which is least partitioned into solid Fe and can thus explain the density difference between the outer and inner core. H and O, as well as Si, are likely to be major core light elements, supporting the sequestration of a large amount of water in the Earth’s core.


Methods
High P-T experiments. Laser-heated DAC techniques were used to generate high P-T conditions. The starting materials were ~ 10 µm thick Fe-Si foils containing 4.0 and 6.5 wt% Si. The culet size of the diamond anvils used was either 200 µm or 300 µm depending on the hydrogen source, and the sample chamber was prepared by drilling a hole with a diameter of ~ 80 µm or ~ 100 µm, respectively, in a rhenium gasket pre-indented to ~ 25 µm thickness. Hydrogen was introduced to the system by sandwiching the Fe-Si sample between C n H 2n+2 paraffin layers (run #4) or cryogenically loading liquid hydrogen into the sample chamber 30 (runs #1-#3, #5). In the latter case, an NaCl ring prepared with a focused ion beam (FIB) was employed inside the rhenium gasket as an H 2 insulator and a pressure medium. In addition, the culet of the diamond anvils was coated with a thin layer of Ti by sputtering to avoid anvil failure 31 . After cooling the DAC to 20 K with the sample chamber open, the chamber was flooded with liquid H 2 30 . The sample was then sealed by weak compression and brought back to room temperature. The presence of hydrogen in the sample chamber was confirmed by Raman spectroscopy. Subsequently, it was further compressed to ~ 20 GPa and weakly annealed at < 1000 K to prompt hydrogenation of the alloy. The hydrogen content was different in each run because of differences in temperature and duration of the thermal annealing and in the quantity of H 2 directly in contact with Fe-Si alloys. In order to remove excess hydrogen, the DAC was then again cooled to ~ 90 K using liquid N 2 and decompressed back to 1 atm, so that any hydrogen in excess was released from the sample chamber while preventing the decomposition of hydrogenated iron 32 . Heating was conducted at the beamline BL10XU, SPring-8 synchrotron radiation facility using a couple of 100 W single-mode Yb fiber lasers (YLR-100, IPG Photonics) with flat-top beam shaping optics 9 . The samples were heated to melting temperatures for a limited duration of ~ 3 s in an attempt to avoid temperature fluctuation. This time scale has been shown to be long enough to reach chemical equilibrium due to the short length scale of DAC samples; in previous DAC melting experiments, liquid and coexisting solid compositions did not change after 1 s in the Fe-S system 33 . We obtained sample temperature profiles using spectroradiometry and estimated the temperature at the liquid-solid boundary (liquidus temperature) in combination with a sample cross section 12,22 (Table 1).

Sample analyses.
In-situ angle-dispersive X-ray diffraction (XRD) measurements were conducted before, during and after heating (melting) using an X-ray beam with an energy of ~ 30 keV 9 (Figs. 1, S1 and S2). The beam was focused on a sample using compound refractive lenses and collimated so that the full-width at half maximum was 6 μm. The 2D diffraction patterns were collected on a flat panel detector (Perkin Elmer), and integrated to 1D patterns using the IPAnalyzer software and analyzed with the PDIndexer software 34 . Pressure was estimated on the basis of the unit-cell volume of CsCl-type NaCl 35 considering its temperature following Ref. 36 , except for run #4 where it was obtained from the Raman shift of diamond 37 and corrected for a contribution of thermal pressure 12,38 . The overall uncertainty should be ± 5% (Table 1).
Textural and chemical characterizations were carried out on all the samples after decompression and recovery (Figs. 2 and S3). A Ga-ion FIB (VersaTM 3D DualBeamTM, FEI) was used to mill the sample parallel to the compression axis and prepare a cross section of the laser-heated portion. The sample was then examined by a field-emission (FE)-type scanning electron microscope (SEM) and energy dispersive X-ray spectrometry (EDS). Furthermore, a field-emission-type electron probe micro-analyzer (FE-EPMA, JEOL JXA-8530F) was used for quantitative chemical analyses with an accelerating voltage of 12 kV and a current of 15 nA. We used , LDE2H (C) and LDE1 (O) as analyzing crystals. Carbon (C) concentration was quantified from a calibration curve obtained by a C-free copper mesh, Fe-0.84 wt%C (JSS066-6, the Japan Iron and Steel Federation) and Fe 3 C. Since hydrogen escapes from iron lattice at low pressure (less than ~ 3 GPa) and room temperature 6,9,39 , we determined the H content x of (Fe,Si)H x based on the volume expansion of the Fe-Si crystal lattice at room temperature 23 (Fig. S4); where V is lattice volume and ΔV H is the volume increase caused per H atom 40 . The reference lattice volume of Fe-Si at identical high pressure was estimated from those of pure Fe 41,42 and Fe-6.5 wt%Si 20 . The H abundance in liquid was estimated from the volume of face-centered cubic (fcc) or hcp crystals formed upon quenching temperature. The use of other equation of state for an Fe-Si alloy 43 increases the x values only by 0.01-0.04. The 10

Results
Liquidus phase relations in Fe-Si-H. We performed five separate experiments in the Fe-Si-H ternary system at ~ 50 GPa, in which C and O concentrations in liquids were less than 0.6 and 0.7 wt%, respectively ( Table 1). The coexisting liquid and solid (liquidus phase) compositions are plotted in Fig. 3a, which constrains the liquidus fields of hcp Fe, fcc FeH and B2 Fe-Si.
In the first two runs, liquids coexisted with (Si, H)-bearing hcp Fe. In run #1, the XRD pattern showed hydrogenated hcp Fe + 4 wt%Si together with the NaCl pressure medium before heating at 56 GPa (Figs. 1a, S2 and S3a). During heating to 2100 K, we observed diffuse scattering signal from liquid around two-theta angle of 12°, coexisting with weak reflections from the hcp phase (liquidus phase). Upon quenching to 300 K, the fcc phase appeared. Combined with microprobe analyses of the cross section of the recovered sample, these observations indicated that liquid Fe-4.0 wt%Si-0.67 wt%H coexisted with hcp Fe-3.7 wt%Si-0.47 wt%H during heating. Similarly in run #2 performed at 57 GPa, the XRD pattern collected at 2150 K included the peaks from the hcp phase and the NaCl pressure medium (Figs. 1b and S3b). The diffuse signal was not clear, which is consistent with the microprobe observation of a small melt pocket at one side of the recovered sample surface. Liquid Fe-5.9 wt%Si-0.56 wt%H coexisted with hcp Fe-4.3 wt%Si-0.30 wt%H at high P-T in this experiment. It is, however, uncertain that this solid composition represents that of the liquidus phase, because the small liquid pool suggests that the coexisting liquidus phase was volumetrically even smaller and the determination of its chemical composition was difficult.
On the other hand, liquids coexisted with fcc (nearly) stoichiometric FeH in other runs. In run #3, hcp (Fe,Si) H 0.81 was found before heating at 61 GPa (Figs. 1c and S3c). Upon heating to 2350 K, the peaks from the hcp phase were lost, and alternatively those of fcc appeared together with the diffuse scattering signal from liquid.    (Fig. S4). It is difficult to estimate its H content from the smaller unit-cell volume of B2; alternatively, we approximated it from the relative proportions of bubbles and cracks between the B2 and neighboring stoichiometric FeH in the cross section of this sample (Fig. 2a). It gives an approximate amount of H in the B2 phase to be (Fe,Si)H 0.4 . The recent experiments by Ref. 46 also reported a reduction in the volume of B2 stoichiometric FeSi upon hydrogenation and argued that it can be caused by the substitutional incorporation of H into the B2 structure. In run #5, we observed that H-rich liquid (Fe,Si)H, which was similar in composition to that in run #4, coexisted with fcc stoichiometric FeH (Figs. 1e and S3d). Figure 3a illustrates the compositions of these liquids and coexisting solids (liquidus phase) plotted in the Fe-Si-H ternary diagram. The recent experiments 22 reported the Fe-FeSi binary eutectic liquid composition to be Fe + 11.5 wt% Si at 50 GPa, which is helpful to obtain the ternary liquidus phase relations. While the liquids formed in runs #2 and #3 were similar to each other, they coexisted with hcp Fe and fcc FeH, respectively. It indicates that these two liquid compositions are close to the Fe + FeH cotectic line (showing liquids coexisting two solid phases). The liquid in run #1 coexisted with the hcp phase, which also constrains the location of this Fe + FeH cotectic line. The H-rich liquid found in run #4 crystallized both fcc FeH and B2 Fe-Si (Fig. 2) and is therefore on the FeH + Fe-Si cotectic line. It is consistent with the result of run #5.
These observations show each liquidus field (showing a compositional range of liquids that first crystallize a given solid phase) of Fe, FeH and Fe-Si at ~ 50 GPa (Fig. 3a). Considering that we often obtained liquids with compositions close to binary eutectic point or ternary cotectic lines in similar melting experiments on Fe alloy systems such as Fe-Fe 3 S 33 and Fe-S-O 12 , the results of runs #1-#3 suggest the Fe-FeH binary eutectic composition to be around FeH 0.45 at 50 GPa.
The liquidus temperatures (temperatures at solid/liquid boundary) found in runs #1-#3 were 2100-2350 K, which are much lower than the Fe-FeSi binary eutectic temperature of 2900 K at 50 GPa 19 , indicating a large effect of hydrogen to reduce melting temperature 24,44 . The ternary invariant point at which liquid coexists with three solid phases (Fe, FeH and Fe-Si) may be a peritectic (not eutectic) point at ~ 2400 K.

Solid-liquid partitioning of Si & H. The solid/liquid partition coefficients of Si and H between (Si,
H)-bearing hcp Fe and coexisting liquid were obtained in run #1, where strong diffuse signal from liquid was observed in the high-temperature XRD pattern (Fig. 1a); D Si = 0.94 (4) and D H = 0.70(12) (weight basis) ( Table 1). The D Si = 0.94(4) is consistent with those previously observed in the H-free Fe-FeSi binary system at ambient and high pressures 18,21 .
Fcc stoichiometric FeH included the least amounts of Si when coexisting with Fe-Si-H liquids (Fig. 3a), suggesting that Si atoms do not substitute Fe when octahedral interstitial sites are fully occupied by H atoms 28

Discussion
Crystallization of hcp Fe-Si-H at Earth's inner core. The solid inner core of our planet consists of hcp Fe containing some light elements; the inner core density deficit with respect to pure Fe has been estimated to be about 4% 41,47 . While the least amounts of O and C are incorporated into solid Fe in the inner core 10,12,22 , Si, H and S are known to form solid solution with Fe to some extent 18,19,23,33 and likely present in the solid core. Nevertheless, interactions among Si, H and S atoms in hcp Fe could be strong and affect their simultaneous solubilities as well as solid-liquid partitioning 48,49 . Indeed, the liquid immiscibility, a typical consequence of the strong interaction, has been observed between Fe-H and Fe-S liquids to > 100 GPa 50 .
Recent ab initio simulations performed by Refs. 17 and 51 emphasized the presence of C and/or H in the solid inner core, in order to account for not only the density but the low P-and S-wave velocities observed. As mentioned above, C is unlikely to be an important impurity element in the inner core because of its low D C (solid-hcp/ liquid) ~ 0.1 22 ; otherwise the liquid core should be enriched in C, which is not compatible with its density and velocity observations 52,53 . Alternatively the inner core alloy may be H-bearing hcp Fe 60 Si 4 H 1-15 when T ICB ranges from 5500 to 6500 K (more H is necessary for lower T ICB ) 17 .
The present high-pressure experiments demonstrated that liquid crystallized hcp (Fe 0.93 Si 0.07 )H 0.25 (Fe 60 Si 4.5 H 16 ), which is almost equivalent to the inner core solid proposed by Ref. 17 when T ICB is 5500 K. Although Ref. 29 examined the compression behaviors of hcp (Fe 0.88 Si 0.12 )H 0.61-0.79 at 300 K, this study first confirmed that the hcp Fe-Si-H alloy proposed for the inner core is stable to melting temperatures. While D H (solid-Fe/liquid) has never been reported in the literature, D Si = 0.94(4) obtained in this study is similar to those previously found in the Fe-Si system, indicating no remarkable dependence on H concentration in liquid 18,21 . It contrasts the large effects of sulfur (S) 48,49 and C 22 , which remarkably enhance the solid/liquid D Si . D H = 0.70 (12) observed in this study will be independent from Si concentration in liquid Fe; the little interaction between Si and H in Fe is suggested from the fact that Si atoms substitute Fe, while H atoms occupy the interstitial sites 53 . Possible range of the outer core composition. The liquidus phase relations, in particular the liquidus field of Fe in the Fe-Si-H ternary system at the ICB pressure constrain the liquid core composition. Those determined at ~ 50 GPa (Fig. 3a) (Fig. 3b). Si concentration in the Fe-FeSi eutectic liquid has been shown to decrease from 11.5 wt% at 50 GPa to 8 wt% at 330 GPa 22 . On the other hand, the Fe-FeH eutectic composition (Fe + 0.8 wt% H) at ~ 50 GPa would remain similar at higher pressures because the temperature/pressure slope of the melting curve of stoichiometric FeH is comparable to that of Fe at > 40 GPa 54 . The outer core composition should be within the liquidus field of Fe-the (Si, H)-depleted hcp phase-at 330 GPa (blue area in Fig. 3b) to form the dense inner core when both Si and H are important impurity elements. It is noted that the presence of other light elements such as O and S diminishes the Si and H variations in the liquidus field of Fe. The possible range of the inner core composition proposed by Ref. 17 for T ICB = 6000-6500 K is Fe 60 Si 4 H 1 -Fe 60 Si 4 H 8 . If T ICB = 5500 K, it can be Fe 60 Si 4 H 15 . With D Si and D H , the compositions of liquids in equilibrium with these possible inner core solids are calculated to be Fe + 3.5(2) wt% Si + 0.04(1)-0.61(11) wt% H. Such liquid compositions are almost fully within the liquidus field of Fe at 330 GPa (Fig. 3b), which ensures that they crystallize hcp Fe-Si-H under inner core conditions. However, both D Si = 0.94 (4) and D H = 0.70 (12) are close to 1.0 and do not make large differences in Si and H concentrations between the outer and inner core. Indeed, such Fe-Si-H liquid compositions require additional light elements to explain the observed outer core density and velocity according to the ab initio calculations by Ref. 53 . Recent experiments on the metal-silicate partitioning of C during core formation suggested that the core contains at most 0.2 wt% C 55,56 . If O is an additional impurity element in the outer core (note that O is not soluble into the inner core and thus does not alter the possible range of the inner core composition considered here) and T ICB = 6000 K, the outer core liquid may include 1. While the inner core temperature is still uncertain 2 , these results suggest that H and O, in addition to Si, are likely to be important light elements in the core (note that the liquid core constitutes 95% of the bulk core by mass). It supports recent arguments 3-5 on the delivery of a large amount of water to the accreting Earth and its sequestration in metals during core formation for the most part [6][7][8][9] .

Conclusions
Recent theoretical calculations 17 found that hcp Fe 60 Si 4 H 1-15 alloys, depending on core temperatures, account for the density and velocities observed in the Earth's solid inner core. Our experiments demonstrated that liquid metal crystallized hcp Fe 60 Si 4.5 H 16 which is close in composition to the predicted inner core alloys, indicating that hcp Fe can simultaneously include both Si and H unlike fcc FeH that does not incorporate Si. We determined the liquidus phase relations in the Fe-Si-H ternary system, suggesting the Fe-FeH eutectic composition to be around FeH 0.45 . We also obtained the solid hcp-Fe/liquid partition coefficients for Si and H, D Si = 0.94(4) and D H = 0.70 (12). While these experiments were carried out at ~ 50 GPa, the D H value is likely not sensitive to pressure because the size of H atom is substantially smaller than those of Fe and Si atoms even at 330 GPa 53 . Similar temperature/pressure slopes between the melting curves of Fe and stoichiometric FeH 54 suggest that the Fe-FeH liquidus phase relations change little with increasing pressure. Therefore, the Fe-Si-H ternary liquidus diagram may be extrapolated to ICB conditions by primarily considering the change in the Fe-FeSi liquidus phase relations reported in previous studies 19,22 .
Such liquidus phase relations, in particular the liquidus field of Fe along with D Si and D H between the solid and liquid cores help constrain the Earth's core composition. We explored the possible compositional range of the outer core liquid that is in equilibrium with the predicted solid inner core alloy 17 . The relatively high D Si and D H close to 1.0 do not make much differences in Si and H concentrations between the outer and inner core, requiring other light elements such as O that is least partitioned into solid Fe [10][11][12] . Depending on the ICB temperature that is still uncertain, we found H and O, as well as Si, are important core light elements, which support recent arguments on the sequestration of a large amount of water in the Earth's core [6][7][8][9] .

Data availability
All data supporting the findings of this study are available in the paper or from the corresponding author upon request.