Experimental constraints on light elements in the Earth’s outer core

Earth’s outer core is liquid and dominantly composed of iron and nickel (~5–10 wt%). Its density, however, is ~8% lower than that of liquid iron, and requires the presence of a significant amount of light element(s). A good way to specify the light element(s) is a direct comparison of density and sound velocity measurements between seismological data and those of possible candidate compositions at the core conditions. We report the sound velocity measurements of a model core composition in the Fe-Ni-Si system at the outer core conditions by shock-wave experiments. Combining with the previous studies, we found that the best estimate for the outer core’s light elements is ~6 wt% Si, ~2 wt% S, and possible ~1–2.5 wt% O. This composition satisfies the requirements imposed by seismology, geochemistry, and some models of the early core formation. This finding may help us to further constrain the thermal structure of the Earth and the models of Earth’s core formation.

have been investigated experimentally. Likewise compressional velocity measurements for liquid Fe alloys by static experiments are very few, only a few solid samples are measured up to ~100 GPa [20][21][22][23] .
Recently, density and sound velocity measurements on liquid Fe-O-S at the core conditions were reported by use of shock-wave experiments 24 , which suggested a possible O-depleted outer core so that Si or S might be required. However, the available experimental data for model systems at the core conditions are still insufficient to make direct comparisons with the observed seismological data.
Shock wave compression is a proven technique to study properties of materials throughout the entire Earth's core conditions in the laboratory 24 . In this paper, we report a direct measurement of sound velocity at the core conditions for an Fe-Ni-Si system in both solid and liquid regimes by shock-wave experiments and the previously reported pressure-density relation 25 . Combining the present result with the previous work on liquid Fe and Fe-O-S (refs 24, 26, 27), we show the effects of Si, O, and S present in the Fe at the core conditions. The results constrain the light elements in the liquid outer core together with the current geochemical models by selecting a most probable composition.

Experimental Results
Hypervelocity impact experiments were conducted to a pressure of ~280 GPa so as to obtain the sound velocity and melting behavior of Fe-9Ni-10Si system (81Fe9Ni10Si in weight per cent), which was proposed as a model composition of the outer core. Hugoniot equation of state was previously determined for this material having a density of 6.853 (± 0.036) g/cm 3 (ref. 25), using the impedance matching method (ref. 28). Shock velocity (U s ) and particle velocity (u p ) relation has been described by a linear relation: U s (km/s) = 3.95 (± 0.15) + 1.53 (± 0.05) u p (km/s) (ref. 25). In the present study, measurements were extended to sound velocities of the same Fe-9Ni-10Si material using the optical analyzer technique 24,27,29 (see Methods). The experimental conditions and results are listed in Supplementary Table 1.
Sound velocity versus shock pressure measurements are shown in Fig. 1, and compared with previous shock data on pure Fe and other Fe-O-S systems. Abrupt changes of the sound velocity for Fe-9Ni-10Si along the Hugoniot were found at shock pressures of 147 ± 5 GPa and 183 ± 5 GPa, that were interpreted as the onset and complete melting (Fig. 1), respectively. It is noteworthy that these pressures are significantly lower than those of pure Fe (225 ± 3 GPa and 260 ± 3 GPa, respectively 26 ). The sound velocity decreased by 7-8% for Fe-9Ni-10Si at the solid-melt transition. This behavior is similar to that of pure Fe (~6%) 26 . When compared to those of Fe-O-S systems 24,30 , the onset pressures of melting are close (144 GPa for Fe-2.2O-5.3S and 149 GPa for Fe-8O-2S, respectively), indicating that Si, O, and S have similar effects on the shock-induced melting. Figure 2A,B show longitudinal sound velocity (C L ) in solid phase and bulk sound velocity (C B ) after melting, as a function of density (ρ) for various compositions. Previous studies show that the effect of Ni can be ignored on the elastic properties of Fe at the core conditions (up to ~22.9 wt%, in Fig. 2) 31 , though it can expand the stability field of body-centered cubic (bcc) 32 and/or face-centered cubic (fcc) phases 33 to higher pressures. As shown in Fig. 2A, Fe-9Ni-10Si has significantly faster C L than both Fe 23,26,27,34,35 in shock and static isothermal compression at 300 K and Fe-4.3Ni-3.7Si 22 at 300 K, but slightly slower C L than Fe-8Si at 300 K 23 . Temperature effect on C L may be seen in the comparison of Fe data with shock 26,27 and static data at 300 K 23,34,35 , indicating that C L is  26 triangles for pure Fe. Solid-liquid phase transition of Fe-9Ni-10Si starts at 147 ± 5 GPa (3700 ± 500 K) and completes at 183 ± 5 GPa (4150 ± 500 K). Solid red line is the bulk sound velocity of liquid Fe-9Ni-10Si calculated using a hydrodynamic and thermodynamic model 28,29 . Dotted red curves indicate the spread due to a 50% uncertainty in electronic contributions, which results in a ~1.6% uncertainty of sound velocity calculations at 330 GPa. Black, wine, and blue solid lines represent the calculated bulk sound velocities for three liquids: Fe, Fe-8O-2S, and Fe-2.2O-5.3S, respectively. Note that they are in good agreement with the experimental data. Dash lines are the longitudinal sound velocities at the state of solid or partial melting.
Scientific RepoRts | 6:22473 | DOI: 10.1038/srep22473 significantly reduced at high temperatures induced in shock. Therefore, C L for solid Fe-9Ni-10Si must decrease at high shock temperatures relative to the results on Fe-8Si at 300 K 23 , indicating that both the results are consistent with each other.
C B of liquid Fe-9Ni-10Si along Hugoniot can be calculated as a function of pressure by a hydro-thermodynamic model 28,29 (see Methods). The result reproduces well the experimental data (solid red line, Fig. 1), indicating that liquid Fe-9Ni-10Si has a slightly faster C B than liquid Fe on its Hugoniot. The corresponding C B -ρ relation for liquid Fe-9Ni-10Si is shown in Fig. 2B, and compared with the previous data for liquid Fe 26,27 and Fe-O-S systems 24 measured in shock compression. Figure 2B also shows the C B of solid Fe 34,35 , Fe-8Si 21 and Fe-22.9Ni 31 in static compression at 300 K, that are derived from measured longitudinal and shear sound velocities. All the liquids of Fe-9Ni-10Si, Fe-2.2O-5.3S, and Fe-8O-2S show significantly faster C B than liquid Fe as a function of density, but Fe-9Ni-10Si has a shallower slope than the Fe-O-S systems. Liquid Fe-9Ni-10Si is located between Fe-8Si at 300 K and liquid S-rich Fe-2.2O-5.3S. The differences in C B and slope of C B /ρ between Fe at 300 K and liquid state of Fe in shock measurements show that C B in Fe above the melting temperature increases significantly, suggesting that the C B of liquid Fe-9Ni-10Si should increase in a similar fashion. Consequently, the addition of limited amounts of light elements Si, O, and/or S into liquid Fe should increase C B . On the other hand a comparison of C B between Fe-O-S and Fe-Ni-Si liquids indicates that the presence of 8 wt% O in Fe-8O-2S increases C B too much, while 10 wt% Si in Fe-9Ni-10Si and 5.3 wt% S in Fe-2.2O-5.3S may have similar effects on C B at the outer core pressures.

Discussion
In order to determine the melting curve at the core conditions based on the present shock data, we need to use the total melting condition at 183 GPa (Fig. 1). Shock temperature along the Hugoniot was not measured in our The melting curve of Fe-9Ni-10Si, T m (ρ), was modeled by the Lindeman law 36 , d(lnT m )/d(lnρ) = 2γ − 2/3, using the calculated melting temperature at 183 GPa as a reference point. γ is the Grüneisen parameter of Fe-9Ni-10Si that includes both the lattice and electronic contributions. When extrapolated to the core-mantle boundary (CMB) and the inner core boundary (ICB), the corresponding melting temperatures are 3700 ± 500 K at 136 GPa and 5200 ± 500 K at 330 GPa, respectively. Additionally, it is known that the alloying of 5-10 wt% Ni with Fe has no significant effect on the melting temperature based on the known melting curve of Ni 37 . Thus, in combination with previously determined melting curves of Fe-9Si 18 , Fe-5Ni-10Si and Fe-5Ni-15Si 38 (Fig. 3), the melting temperatures at pressures of CMB and ICB are estimated to be depressed by about 300-500 ± 500 K and 600-1000 ± 500 K in the presence of 10 wt% Si, respectively, compared to those of pure Fe 26,27,[39][40][41] . These results are consistent with the previous study that the melting temperature of Fe is depressed by ~30 K per wt% Si at CMB and estimated by a linear interpolation 42 . The present estimation of temperature at CMB is significantly lower than those of the solidi of primitive peridotite and chondritic model mantles (above ~4150 K) 43,44 , but close to the recent reports on the solidi at CMB for a hydrous pyrolite (3570 ± 200 K) 45 and a subducted basalt with volatiles (3800 ± 150 K) 46 .
Sulfur (S) has a greater effect on the depression of melting temperature of Fe than Si and O. According to the previous studies, melting temperatures for S-rich (~8-12 wt%) 38,47 and O-rich (~12 wt%) 42 core models were estimated to be ~3000 K and ~3650 K at CMB, respectively. To be consistent with the temperature at CMB, no more than 8 wt% S can exist in the outer core because such an S-rich core will make itself too cool to drive sufficient heat flow through the CMB. This interpretation supports a minor role of S and agrees with the current geochemical model (ref. 5).
In order to compare our results with seismological data directly, thermal corrections to the measured C B were calculated using the Mie-Grüneisen theory 27,28 (see Methods). Adiabatic geotherm, T g = T ICB (ρ/ρ ICB ) γ′ , is assumed for the correction where Grüneisen coefficient γ′ = 1.5 for the outer core 6 , density ρ ICB = 12.17 g/cm 3 , and temperature T ICB = 5200 K. Figure 4 shows the corrected ρ and C B relationships for the model outer core compositions of liquid Fe 27,48 , liquid Fe-9Ni-10Si, liquid Fe-O-S 24 , and solid Fe-9Si 18 in comparison with the PREM 16 at the outer core conditions. The density profile of liquid Fe-9Ni-10Si is consistent with the PREM at the Earth's outer core within 1% discrepancies 25 (Fig. 4A). Its C B at CMB is slower by ~3% than that of the PREM, but come closer to the PREM values at ICB (Fig. 4B). Also the C B profile agrees with the corrected C B of solid hexagonal closed-packed (hcp) Fe-9Si along the geotherm 18 (Fig. 4B), but the densities of liquid Fe-9Ni-10Si and hcp Fe-9Si are different because of differences in Si content (by 1 wt%) and their phase (liquid or solid).
Regarding the densities of the model core compositions (Fig. 4A), it is clear that Fe-9Ni-10Si and Fe-2.2O-5.3S are close to the PREM at the core pressures, but Fe-8O-2S with high oxygen content is not. Also on C B (Fig. 4B), PREM is found to be close to Fe-9Ni-10Si and Fe-2.2O-5.3S. Thus, it may be concluded that both a silicon-rich and a sulfur-rich core composition can match well both density and sound velocity at the outer core conditions and meet the geophysics requirements.
Additionally, if we consider the geo-and cosmochemistry 5,7 constraint that S in the core is ~2 wt%, silicon will be the most dominant candidate among Si, O, and S in the outer core. Then, considering the constraints 5,6,13 from the geochemical and Si isotope data that the core may include ~6 wt% Si and ~2 wt% S, we select 85.6Fe-5.4Ni-6Si-2.1S-0.9O (by wt%) as the most probable candidate for the outer core. This composition corresponds to a mixture of 40 wt% Fe-2.2O-5.3S 24 and 60 wt% Fe-9Ni-10Si. As illustrated in Fig. 4, both the density and C B for this composition match the seismological data over the whole range of the outer core conditions. However, the slope, dC B /dρ, is slightly higher than the seismic observations. This may indicate a need for further research on the uncertainties in the material parameters used, possible presence of additional light elements and outer-core compositional stratification 49 .
The presence of Si in the Earth's core suggests highly reducing conditions of the core and mantle and that Si was dissolved in liquid Fe at the time of the early core formation. However, given the current estimation of FeO content in the mantle (~8 wt% 8,50 ), the present-day mantle is in a relatively oxidized state. Then, the reducing conditions should have gradually evolved to oxidizing conditions during the Earth's growth. This interpretation is consistent with the proposed heterogeneous continuous accretion models that the Earth accreted initially from highly-reduced materials, but that the finally-accreted mass was more oxidized 3,51,52 . Recent metal-silicate partitioning experiments of niobium (Nb) and tantalum (Ta) also suggest a need of reducing conditions to explain the Nb/Ta ratio in the bulk silicate Earth, because lithophile elements such as Nb and Ta can become siderophile at high pressures under reducing conditions 53 . Such heterogeneous continuous accretion models predict significant amounts of Si in the core. Examples are ~6 wt% Si 51 , 4-5 wt% Si with 1.9 wt% S and possible > 1 wt% O 3 , or ~8 wt% Si with ~2 wt% S and ~0.5 wt% O 52 . However, the metal-silicate partitioning data of vanadium and chromium suggest that the core could have formed under oxidizing conditions and oxygen may be an abundant light element in the core 54 . Sound velocity calculations using ab initio molecular dynamics 55 suggest that oxygen (3-6 wt%) may be the dominant element to account for the density deficit in the outer core, though there is no direct experimental work to support the suggestion yet.  16 . CMB and ICB are the boundaries for the core-mantle and the outer-inner core, respectively. "L" in parentheses represents liquid state. Crosses at both ends of the lines represent the error bars of ~1-2% in density and ~4-5% error in bulk sound velocity for the Fe-Ni-Si and Fe-O-S systems.
According to the seismological data, a marked change in density across the ICB cannot be reconciled based only on the density difference between liquid and solid. Thus, when taking into account the density jump across ICB (ref. 12) and combining the oxidizing process during the later stage of accretion (ref. 51), a proper amount of O must be considered together with Si to account for the seismic observations of the outer core. However, the previous shock wave data for liquid Fe-O-S models indicate that more than 2.5 wt% O cannot provide sufficient matches to both density and bulk sound velocity profiles of the liquid outer core (ref. 24).
In summary, we select a model for the outer core composition consisting of liquid Fe-Ni with light elements of ~6 wt% Si, ~2 wt% S, and possible ~1-2.5 wt% O. This will satisfy the requirements imposed by the density and sound velocity experiments, seismology, geochemistry, and some evolutionary models of the early core formation. Although further considerations are needed to define the chemical composition of the core, a combination of silicon and oxygen as the light elements in the outer core may be essential and plausible. In the case of a Si-rich outer core, its relatively cool geotherm at the CMB implies that water may be present at the base of lower mantle. Such a cool geotherm is in fact critical to explain the nature of the ultra-low velocity zones near the CMB, supported by recent studies 56,57 on dense hydrous minerals that are stable at high pressure and high temperature (δ -phase and aluminum-rich phase D and H) and can transport water into the lowermost mantle.

Material.
We prepared the starting material of Fe-9Ni-10Si (wt%), by sintering a mixed powder of Fe, Ni, and Si at ~1000 °C under vacuum 25 . This composition, as in the previous study 25 , was selected based on the Si-rich Fe-Ni outer core model that satisfies the geochemical and geophysical data, as well as the Si isotope data (ref. 6). Samples had a diameter of ~15.0 mm, and their average initial density is 6.853 (± 0.036) g/cm 3 . Sample was analyzed using micro-X-ray diffraction techniques and electron probe microanalyzer to identify the phases and to determine their compositions, as described in the previous study 25 . Results show that the starting material contains a major phase of (Fe, Ni) 3 Si (~70 wt%), minor phases of bcc (Fe, Ni, Si) (~15 wt%), and fcc taenite (Fe, Ni) (~15 wt%). Grain sizes of these phases were less than ~200 μm, and the total oxygen was less than 0.3-0.5 wt% detected as SiO 2 . Although the starting material was heterogeneous, sample thickness (~1.0-3.5 mm) and the optical probe area (~0.6 mm in diameter) were large enough to measure averaged shock velocity and sound velocity. In addition, shock melting at high shock pressures makes the sample homogenized.
Sound velocity measurement. The sound velocity behind the shock front for metals was obtained by an optical analyzer technique 24,27,29 . Experimental setup for sound velocity measurements of Fe-9Ni-10Si was illustrated schematically in Supplementary Fig. 1. The target had three to four steps with known thicknesses as optical analyzer positions. These optical analyzers monitor particle velocity profiles simultaneously at the analyzer points. Sample thickness at which rarefaction wave overtakes the shock wave was determined through the observed profiles. On impact, a shock wave propagates toward both backward (with speed of U f ) and forward (with speed of U s ) sides of the impact surface as shown in Supplementary Fig. 2. The backward-moving shock wave in the flyer is reflected as a rarefaction wave on arrival at the rear surface of the flyer and then propagates forward through the flyer (with speed of C f L ) and to the sample (with speed of C s L ). Because the rarefaction wave in the shocked sample moves faster than that of the forward-moving shock wave in the sample (C s L > U s ), it overtakes the shock wave in the Lagrangian coordinate system and causes a drop in the particle velocity and the shock pressure. The observed rarefaction wave velocity is either C L for solid or C B for liquid on Hugoniot state (ref. 29). Therefore, the decrease in sound velocity along Hugoniot indicates possible shock-induced melting, that is otherwise difficult to observe through Hugoniot measurements (U s -u p and P-ρ relations) 29 .
Hypervelocity planar impact experiments were conducted using two-stage light-gas guns at the Institute of Fluid Physics of China Academy of Engineering Physics and Southwest Jiaotong University, China. Flyer impact velocities were measured by an electromagnetic method with an accuracy of ~0.5%. A single-crystal lithium fluoride LiF (100) coated with ~2 μm Al coating is used as the window, which is held tightly to the rear face of sample. Particle velocity histories were recorded in real time at all steps of sample-Al coating interfaces using a displacement interferometer system for any reflector simultaneously (DISAR) 58 . DISAR has a multimode fiber with a core diameter of 600 μm to transmit reflected light from a moving interface. Recorded signals with DISARs are integrated to obtain average responses from sample surfaces (600 μm in diameter). The sample diameter is large enough compared with the maximum grain size of less than 200 μm.
Four particle velocity histories were presented for shot B3 at a pressure of ~160 GPa in Supplementary Fig. 3). Supplementary Fig. 4 shows how a target thickness at which rarefaction waves overtake the shock wave was estimated by linear fitting. Time intervals for the overtake at the different steps are measured on the observed particle velocity histories.
Lagrangian sound velocities of the rarefaction wave were obtained using a velocity-distance relation, Eulerian sound velocity of sample is related to the Lagrangian velocity as follows, where ρ 0 and ρ are initial and shocked density of sample, respectively. Uncertainty of measured sound velocities is within ~4-5%, that results from measurement and propagation errors. There is a general relationship among the acoustic speeds: C L , C B , and transverse sound velocity (C T ).
C T equals to zero in liquid and gas phases, so C L and C B become same. A Bulk sound velocity and shock temperature calculations. Bulk sound speed C B in molten sample can be computed using the following equations 28,29 along the Hugoniot pressure P H , where V 0 and V are volumes at the initial and shocked states, respectively. Grüneisen parameter (γ) in equation (5) includes lattice (γ l ) and electronic (γ e ) 59 contributions, where D(T) is Debye function given by D(T) = 3R, R = the gas constant, T temperature, and C V specific heat capacity at constant volume consisting of lattice (C Vl ) and electronic (C Ve ) contributions. The lattice contribution of Grüneisen parameter is described by γ l = γ 0 (ρ 0 /ρ) n , where γ 0 = 2.22 at ambient conditions and n = 1 from the measurement on Fe-9Si 18 . The electronic contribution of Grüneisen parameter is assumed same as that of hcp Fe 59 , i.e., γ e = 2. For the electronic contribution parameter β e is set to be 40 ± 20 J Mg −1 K −2 , and κ = 1.34, through empirical fitting to the Hugoniot data. If samples are in thermodynamic equilibrium at shocked states, temperatures along the Hugoniot (T H ) may be calculated from the following thermodynamic relation 27,28 , V 0 0 When integrated, this equation gives the temperature of 3700 ± 500 K at the measured, onset-melting pressure of 147 ± 5 GPa for Fe-9Ni-10Si. Upon completion of melting, sample T H will be reduced, resulting from the latent heat of melting, by ΔT = T om ΔS/C V , where ΔS (melting entropy) = (0.79 ± 0.01) R (ref. 60), and T om is the onset melting temperature at pressure of 147 ± 5 GPa.
Errors in the calculations of the bulk sound velocity and shock temperature computations come from uncertainty sources such as material parameters, especially for electronic contributions to γ and C V . Effects of the electronic contributions are shown in Supplementary Fig. 5. It shows that the calculation and the experimental results on sound velocity match. Below ~200 GPa the electronic contributions may be omitted, and the error of temperature calculations is estimated to be ~500 K based on the possible variations in ΔS, γ, C V , and the Hugoniot.
A non-reactive, ideal mixing model may be used to estimate the sound velocity of a composite if the sound velocity of each component was known. That is, reciprocal average sound velocity (C) is the sum of reciprocals of each component velocity (C i ) weighted by volume fraction (N i ) of each component 28 , i i i Thermal corrections to C B along the core geotherm. In order to compare the measured sound velocities with seismological data, thermal corrections to bulk sound velocities along the adiabatic core geotherm were estimated using the Mie-Grüneisen theory 27,28 . Thermal pressure offset (P t ) at volume V is calculated by, where M the molar mass of Fe-9Ni-10Si and adiabatic core geotherm T g = T ICB (ρ/ρ ICB ) γ . Then, the thermal correction to the C B is calculated by,