Earth and Planetary Science Letters 272 (2008) 620–626

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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l

In situ determination of Fe–Fe3S phase diagram and liquid structural properties up to 65 GPa G. Morard a,b,c,⁎, D. Andrault d, N. Guignot a,e, C. Sanloup b,f, M. Mezouar a, S. Petitgirard a,g, G. Fiquet b,c a

European Synchrotron Radiation Facility, Grenoble F-38043, France Institut de Physique du Globe de Paris, Paris F-75252, France Institut de Minéralogie et de Physique des Milieux Condensés, Paris F-75252, France d Laboratoire Magma et Volcans, Clermont-Ferrand F-63006, France e Synchrotron SOLEIL, Gif-sur-Yvette F-91192, France f Université Pierre et Marie Curie-Paris 6, case 110, 4 Place Jussieu, Paris F-75252, France g Laboratoire de Sciences de la Terre, Ecole Normale Supérieure de Lyon, Lyon F-69007, France b c

A R T I C L E

I N F O

Article history: Received 4 March 2008 Received in revised form 20 May 2008 Accepted 22 May 2008 Available online 5 June 2008 Editor: L. Stixrude Keywords: Laser heated diamond anvil cell Fe–Fe3S Partial melting Liquid structure In situ X-ray diffraction

A B S T R A C T Lighter elements than iron such as sulphur are required in the Earth's core to account of the core density deficit. Accurate determination of the evolution of the Fe–FeS phase diagram at high pressure is essential to determine sulphur amount in the Earth's core. Ab initio calculations predict extensive solubility of S in solid Fe at core pressures of 330 GPa, whereas multi anvil quench analysis exhibits deep eutectic system at moderate pressure of 21 GPa. In this study, we investigated the Fe-rich part of Fe–FeS phase diagram up to 65 GPa and 2200 K using in situ angle dispersive X-ray diffraction. We report a uniform increase with pressure of the eutectic temperatures (TEut), of about 15 K/GPa. Above 50 GPa, we evidence a decrease of S content in eutectic liquid with increasing pressure. Extrapolating this trend to inner core boundary pressures suggests that S cannot account for the 10 wt.% outer core density deficit and that other light elements, such as Si and O, are needed. Diffraction pattern recorded at 42 GPa and 2150 K was selected for structural investigations of the Fe–S liquid. By applying liquid structure simulation based on Gaussian distribution of atoms around crystalline positions, a good agreement has been found with hcp Fe model-structure, rather than with Fe3S structure. It suggests that S acts as an interstitial impurity in the liquid state. Therefore, S could have a relatively minor effect on sound velocities in liquid outer core. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Iron is generally accepted as the main constituent of the terrestrial planetary cores, but alloyed with Ni and other lighter elements. For the Earth, the outer and inner cores are estimated to be 6–10% and 2–3% less dense than pure iron, respectively (Birch, 1964; Badro et al., 2007). Influence of light elements on the Earth's core dynamics is largely dependent on their solubility in the inner core, because their rejection to the outer core promotes solutal convection (Kutzner and Christensen, 2000). Formation of a Fe-alloy solid solution with a small melting loop like in Fe–FeSi system at 21 GPa (Kuwayama and Hirose, 2004) or a large eutectic depression with extended melting loop like in Fe–FeS system at 21 GPa (Fei et al., 2000) lead to drastically different core properties, such as fractional crystallisation with small or large difference of density between liquid and solid.

⁎ Corresponding author. Institute for Study of the Earth's Interior, Misasa, Tottori, Japan. E-mail address: [email protected] (G. Morard). 0012-821X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2008.05.028

Melting temperature in Fe–FeS system is an essential information concerning planetary cores (Boehler, 1996; Campbell et al., 2007; Chudinovskikh and Boehler, 2007; Stewart et al., 2007). Sulphur is believed to be present in small amount in Earth's core due to its high volatility (around 2 wt.% (Allègre et al., 1995)). Its content may be even higher if sulphur was trapped in the metallic phase at relatively low temperatures during an homogeneous accretion process during the Earth's formation (Righter et al., 1997). In this sense, sulphur is even more relevant for the Martian core. Indeed, it could contain a significant larger amount of volatile light elements, potentially up to more than 14 wt.% S (Sohl and Spohn, 1997) because lower temperature is expected for planetary orbital further from the Sun. Liquid properties are intimately linked with their local structure. For example, Si does not modify largely the local structure of Fe-alloys up to 40 at.% Si (Kita et al., 1982), leading to high bulk modulus close to values of liquid pure Fe (Sanloup et al., 2004), whereas Fe–S alloys poorly ordered structures under low pressure (Urakawa et al., 1998; Sanloup et al., 2002) is linked with a low bulk modulus (Sanloup et al., 2000). Recently, we showed that the evolution toward compact atomic packing of the local structure in Fe–S eutectic liquid could lead

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to change in bulk modulus (Morard et al., 2007). It must be noted that a small percentage of S added to a Fe–Si, Fe–O or Fe–C liquid provoke the formation of two immiscible phases for P b 15 GPa (Raghavan, 1988), which may have peculiar implication for planetary core's formation. In this study, we will first discuss evolution of the eutectic temperature in the Fe–S system up to 65 GPa determined by in situ detection of melting, using X-ray diffraction in laser-heated diamond anvil cell (LH-DAC). Then, information about evolution of S contents in eutectic liquid and solid will be estimated from phase identification at high pressure and temperature. Finally, liquid structure properties will be discussed through partial distribution function g(r) derived from analysis of the X-ray diffusion scattering recorded at high pressure and temperature for liquid Fe–S alloys.

reported elsewhere (Mezouar et al., 2005). Sample pressure has been evaluated using the equation of state of (a) NaCl pressure medium at 300 K and (b) hcp Fe at high temperature during the YAG laser heating (Dewaele et al., 2006). The quenched hcp Fe indicates pressure 10% lower than the NaCl pressure medium, possibly due to S incorporation. Similar effect was also observed in previous study (Seagle et al., 2006). Thus, we use positive error bars of 10% of the nominal pressure at all temperatures. Negative error bars are evaluated at 2 GPa, from the maximal uncertainty in determining the unit-cell volume of hcp Fe with this experimental set set-up (Guignot et al., 2007). When melting of Fe-alloys is completed, we assume that pressure is similar to the lower temperature spectra, when crystalline Fe was still visible. Therefore, pressure uncertainty is estimated to ±5 GPa at the highest temperatures.

2. Experimental techniques

3. High temperatures

The starting material was composed of a mixture between Fe (GoodFellow, 99.99% purity) and FeS (Sigma Aldrich, 99.9% purity) powders finely grinded ground in an agate mortar in order to obtain a homogeneous material with micron grain size. We used starting materials with two different compositions: 12.5 wt.% S (20 at.% S) and 6 wt.% S (10 at.% S). High pressures were generated with a Le Toullec type diamond anvil cell using diamonds with 250 and 300 µm diameter culets. Samples were pre-pressed between two diamonds to a thickness of ~ 10 µm, from which a 50 µm diameter flake was taken. Sample flakes were loaded between two dry NaCl layers in 70 to 100 µm diameter holes drilled in a preindented rhenium gasket. NaCl is soft pressure medium insuring good hydrostatic conditions and it is chemically inert in contact with iron alloys. X-ray angle dispersive diffraction measurements have been performed on ID27 High Pressure beamline at ESRF (Grenoble, France). The monochromatic X-ray beam was focused to 5 ⁎ 5 µm size for energy of 47 keV (Sm K edge: 0.26472 Å). More details are

To generate high temperatures, we used two 40 W single-mode (TEM 00) continuous YAG lasers with excellent power stability focused on each side of the sample. Temperature was equilibrated by tuning the lasers power while measuring on both sides of the sample by the spectroradiometric method using reflective collecting optics (Schultz et al., 2005). We achieved laser spots of more than ~20 µm diameter. Therefore, the X-ray spot is significantly smaller than the laser spot. The very high X-ray flux available on ID27 makes it very precise the alignment between X-ray spot and laser spot (Schultz et al., 2005), because diamond fluorescence (in the visible and UV range) is clearly visible on the CCD camera used for the optical alignments. During acquisition of the X-ray pattern, temperatures stability was checked by measurements on one sample side only. Time exposure of 30 s was required for diffraction pattern acquisition. Such short exposure time is necessary to avoid liquid migration in the sample. Despite our precautions, temperature gradients may remain in the laser-heated samples. The small size of the X-ray spot (5 ⁎ 5 µm) is the

Fig. 1. Diffraction patterns recorded with increasing temperature at a nominal pressure of 52 GPa and initial composition of Fe–20 at.% S. Dashed lines indicate the position of solid phases diffraction peaks (Fe ε, Fe3S and NaCl B2) at 1813 K. Progressive increase in intensity of diffuse scattering in the 7° to 9° 2θ region is related to the sample partial melting (Andrault et al., 2006).

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Fig. 2. Liquid signal obtained by summation of 10 diffraction patterns (P = 42 GPa; T = 2150 K; initial composition: Fe–20 at.% S). Baseline signal is obtained by subtracting manually diffraction peaks from quenched solid after heating cycle. In the inset, structure factor is shown with the corresponding fit. This fit is transformed in raw signal, before data treatment following Morard et al. (2007).

key to reduce both radial and axial gradients. It is particularly true for the radial temperature gradients in the analysed region that are clearly reduced when the size of the X-ray probe is significantly smaller than the laser spot. Concerning axial gradients, which were recently reported non non-negligible whatever is the temperature control on both sample sides, it is expected to be reduced to 100 K for a 5 ⁎ 5 µm X-ray spot, according to these simulations (Campbell et al., 2007). Additional temperature uncertainty comes from the pressure evolution of the sample emissivity, which was neglected in this study. A final source of error comes from the temperature fluctuations with time, which are measured lower than 50 K. In summary, we estimate that the total uncertainties are lower than 150 K for our experimental set-up. 3.1. Diffuse scattering of Fe–S liquid alloys When integrating the 2-dimensional image of angle dispersive diffraction, we took particular care to optimize the signal to noise ratio, in order to retrieve reliable information from the diffuse X-ray scattering contribution coming from the Fe–S liquid. Broad and intense spots of diamond diffraction can be masked. However, we found that this procedure is not ideal, because it produces discontinuities in the imaging plate surface to be integrated, which in return can affect the shape of the background in the integrated diffraction pattern. Instead, we preferred to integrate together radial portions of the image plate that are free of such contributions. The final signal used for liquid structure determination is an average of 10 diffraction patterns acquired at high temperature (Fig. 1). We checked that the shape of the liquid diffuse signal is not affected by the choice we made

concerning signal integration. Note that the signal of diffuse scattering coming from the liquid is expressed randomly in the reciprocal space and therefore choosing a particular area for the integrating is much less problematic than for X-ray diffraction of solids. Scarce diffraction spots from solid iron alloys in equilibrium with liquid were masked using fit2D software before the integration. Only remain peaks from NaCl pressure medium (Fig. 1) and two peaks of Fe hcp (101 and 103) in equilibrium with the liquid. In this figure, the background signal (reported as solid signal baseline) was derived from the X-ray diffraction pattern measured at the same sample location after shutting down the IR-lasers, after removal by hand of the diffraction peaks from solid iron alloy and NaCl pressure medium. Baseline signal was adjusted manually to account for the decrease with time of the ESRF storage ring (we adjust correspondence between the two signals in the low angle region). Coherent signal coming from Fe–S liquid at high temperature is obtained by differences between these two signals (Fig. 1, inset). This contribution can be used to discuss the local structure in the liquid. The liquid signal is interpolated using Igor Pro software on normalised signal, in order to intensify large Q signal. Then, the obtained fit is transformed in raw signal, before data analysis process, following method described in previous study (Morard et al., 2007). 3.2. Evolution of eutectic temperature up to 65 GPa At the lowest temperature, two phases Fe and Fe3S are coexisting with NaCl pressure medium, as determined from multi anvil experiments (Fei et al., 2000). This mixture is stable up to 65 GPa, in agreement with a previous study (Seagle et al., 2006). At higher temperatures, we observe a new growing diffuse contribution in the diffraction pattern (Fig. 2). This signal shows a main bump with a maximum located at 32 nm− 1, characteristic of the presence of a liquid Fe-alloy (Morard et al., 2007). It is clearly visible above the diffraction pattern background that comes from Compton diffusion of diamonds (see Fig. 1). It increases with increasing temperature, when the degree of melting increases, and thus, the first detection of a liquid signature upon heating indicate eutectic temperature (TEut). Using this methodology, we determined TEut at each experimental pressure investigated in this study (Table 1). It shows a uniform increase of eutectic temperature from 1450(150) K at 29 GPa to 1980(150) K at 65 GPa (Fig. 3). Our data points define a slope of about 15 K/GPa, which appears slightly higher to previous data set (Chudinovskikh and Boehler, 2007; Stewart et al., 2007), but agrees well with another recent work performed in a similar pressure range (Campbell et al., 2007). Previous experimental investigations at pressures below 25 GPa were performed using large volume apparatus (Fei et al., 2000; Morard et al., 2007). A decrease of TEut was reported up to 17 GPa, followed by an increase of TEut up to 1300 K at 21 GPa (Fei et al., 2000). This latter data point is in very good agreement with our data set.

Table 1 Cell parameters of solid phases in coexistence at high pressure and high temperature P (GPa)

T (K)

aNaCl B2 (Å)

aFe ε (Å)

cFe ε (Å)

aFe3S (Å)

cFe3S (Å)

aFe γ (Å)

aNaCl B1 (Å)

State

29.33 (−2;+ 3) 31.87 (− 2;+ 3) 32.17 (−2;+ 3) 43 (−2;+ 4) 43.09 (− 2;+ 4) 46.29 (− 2;+ 5) 47.38 (− 2;+ 5) 53.03 (− 2;+ 5) 52.63 (− 2;+5) 52.61 (−2;+ 5) 62.14 (−2;+ 6) 62.93 (− 2;+ 6) 64.85 (−2;+ 6)

1560 ± 150 1422 ± 150 1479 ± 150 1660 ± 150 1732 ± 150 1730 ± 150 1795 ± 150 1720 ± 150 1813 ± 150 1864 ± 150 1911 ± 150 1966 ± 150 1997 ± 150

3.1045(5) 3.0226(2) 3.0234(2) 2.9582(8) 2.9587(4) 2.9336(2) 2.9341(3) 2.9042(3) 2.8978(4) 2.9046(3) 2.8687(2) 2.8673(3) 2.8640(3)

2.4514(30) 2.4338(4) 2.4333(5) 2.4060(10) 2.4057(3) 2.4047(14) 2.4052(1) 2.3884(8) 2.3874(11) 2.3887(2) 2.3622(8) 2.3632(5) 2.3591(3)

3.9320(99) 3.9362(18) 3.9407(36) 3.9051(31) 3.9116(37) 3.8799(45) 3.8698(157) 3.8527(24) 3.8703(35) 3.8689(13) 3.8608(43) 3.8554(28) 2.8525(33)

8.5237(39) 8.7038(40) 8.7032(19) 8.5900(13) 8.5981(16) 8.5973(28) 8.5805(41) 8.5361(33) 8.5182(34) 8.5324(8) 8.4782(13) 8.4791(57) 8.4694(12)

4.2438(19) 4.3063(34) 4.3023(18) 4.2580(1) 4.2617(8) 4.2382(22) 4.2421(7) 4.1993(25) 4.2108(29) 4.2072(9) 4.1167(22) 4.1497(42) 4.0643(33)

3.4924(82) 3.4445(33) 3.4506(25)

4.9594(4)

LIQ SOL LIQ SOL LIQ SOL LIQ SOL SOL LIQ SOL SOL LIQ

Last column indicates the presence of diffuse X-ray scattering from the eutectic liquid in the diffraction patterns. Uncertainties for each pressure are shown and discussed in the text.

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Fig. 3. Pressure dependence of the eutectic temperature in the Fe–FeS system. Empty squares indicate the presence of melt, whereas filled squares indicate presence of Fe and Fe3S solid phases only. Solid line represents linear interpolation for this data set. Other melting data are coming from the following references: (Usselman, 1975; Boehler, 1993; Boehler, 1996; Fei et al., 1997; Shen et al., 1998; Fei et al., 2000; Alfè et al., 2002b; Campbell et al., 2007; Chudinovskikh and Boehler, 2007; Morard et al., 2007; Stewart et al., 2007).

Our experimental trend appears parallel to the melting curve of pure FeS (Boehler, 1992) and pure Fe (Boehler, 1993; Shen et al., 1998; Alfè et al., 2002b) in the pressure range investigated. Therefore, it is likely that the difference in melting temperature between Fe–S alloys and pure Fe and FeS remains significant with increasing pressures to the ICB conditions. This would mean, however, that the TEut profile is not linear, as we report for the experimental range investigated, but flattens at high pressure, in a similar manner than for melting curves of pure Fe and FeS, and more generally for melting curves of metals (Boehler et al., 2002). We note that phase transitions at high pressure, in FeS and/or in pure Fe, can potentially affect the pressure evolution of the Fe and FeS melting curves.

(Fig. 4). For our samples with 12.5 wt.% S, experiments performed above 48 GPa show coexistence of the Fe3S phase and liquid iron alloy, thus evidencing a eutectic liquid depleted in sulphur compared to the composition of the starting material (Fig. 5). We note that our observations of a stable Fe3S phase are compatible with a previous report performed up to 80 GPa (Seagle et al., 2006).

3.3. The Fe–Fe3S melting diagram at ~65 GPa In eutectic system, incongruent melting occurs exclusively for temperatures between solidus and liquidus. In this study, solid phases were observed to remain present even for temperatures above those expected for liquidus for our sample compositions, at ~ 200 K above TEut (Fig. 4). We can assess that this phenomena is due to convection, with rapid transit in the X-ray beam of solid grains involved in convection cells. Convection provoked by thermal gradients between border and centre of the laser hot spot is almost impossible to avoid in LH-DAC. An interesting feature is that it is likely that these grains were generated by recrystallisation at the border of the hot spot in chemical equilibrium with the eutectic liquid (Fig. 4). Thus, whether we observe Fe or Fe3S grains gives a straightforward information on the difference in chemical composition between the eutectic liquid and the 12.5 wt.% S (or 6.0 wt.% S) of the starting material. Observations in our diffraction patterns of Fe, or Fe3S, diffraction peaks suggest that the eutectic liquid is enriched, or depleted, in sulphur compared to the initial composition

Fig. 4. Time series of liquid diffraction spectra acquired at about 42 GPa and a constant temperature of 2150 K (initial composition Fe–20 at.% S). Stars correspond to diffraction peaks of the NaCl pressure medium. Blue dashed lines correspond to position expected for the ε-Fe diffraction peaks. The presence of solid Fe in coexistence with a liquid Fealloy indicates that the starting material is enriched in Fe compared to the eutectic composition. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 5. S content in eutectic liquid as a function of pressure. Solid arrows indicate if the eutectic liquid is found enriched or depleted in sulphur in regards to the 12.5 wt.% S (20 at.% S) starting composition. Dotted arrow represents the best trend extracted from our data set in the 30–70 GPa range, in agreement with previous studies performed at lower pressures (Chudinovskikh and Boehler, 2007). Other eutectic compositions are coming from the following references: (Fei et al., 1997, 2000; Chudinovskikh and Boehler, 2007; Stewart et al., 2007).

From the other hand, our sample with 10 at.% S (6 wt.% S) composition was compressed to 51 GPa and heated to 2500 K. Coexistence of solid Fe and Fe3S phases is observed for this temperature located just below the eutectic temperature. Interestingly, a large contribution to this pattern comes from the Fe3S compound, which indicates a low S solubility in pure solid Fe up to more than 50 GPa. This value of 10 at.% S provides an upper limit for S solubility at 51 GPa. We tentatively performed Rietveld analysis on these diffraction patterns in order to retrieve amounts of each of these phases. We obtained results compatible with about ~25 wt.% of Fe and ~ 75 wt.% of Fe3S; leading to solubility of S in pure Fe of ~3 at.% S (~ 1.7 wt.% S). In the literature, S solubility in solid Fe at high pressures and temperatures remains a controversial issue, as previous authors described it either quasi constant (from 1.6 wt.% S to 1.8 wt.% S between 23 and 40 GPa (Stewart et al., 2007)), or increasing largely (up to 3.1 wt.% S at 41 GPa (Chudinovskikh and Boehler, 2007)) with pressure. Such method needs to be applied under higher pressure conditions, to give unambiguous results on this issue. Using our experimental data set, we were able to reconstruct the Fe-rich side of Fe–Fe3S phase diagram at 65 GPa (Fig. 6). The fact that we observed coexistence of Fe and Fe3S solid phases at more than 50 GPa and up to the eutectic temperature for an initial composition with 10 at.% (6 wt.%) sulphur implies a limited solid solution between Fe and FeS. This finding is in disagreement with ab initio calculations performed on the Fe–FeS system suggesting the formation of a Fe–FeS solid solution (Sherman, 1995; Alfè et al., 2002a). However, general agreement remains concerning small partitioning of S between solid Fe and liquid phase for low S content (~ 8 at.% S) under core conditions and on the necessity to add other light elements to account for the core density deficit (Alfè et al., 2002a). But, according to our experimental results, the Fe–FeS phase diagram could remain significantly different than that observed in the Fe–FeSi system with a narrow melting loop and equal partitioning of Si between solid and liquid phases (Kuwayama and Hirose, 2004).

Fig. 6. Fe–FeS phase diagram extracted from measurements at 65 GPa. Arrows indicate possible evolution with pressure of eutectic composition from this study and S solubility in pure iron from previous studies (Chudinovskikh and Boehler, 2007; Stewart et al., 2007). Dotted line indicates starting composition used for this experiment.

agreement with previous results, showing that liquid Fe–S alloys adopt a compact structure for P N 15 GPa (Morard et al., 2007). Distance of first CS shows a strong decrease (r1 = 2.417 Å) compared to g(r) at 17 GPa (r1 = 2.477 Å, (Morard et al., 2007)). Ratio between second and first CS positions highlights a small contraction (r2/ r1 = 1.808 at 43 GPa; r2/r1 = 1.826 at 17 GPa). This suggests that the liquid structure is slightly modified by compression from 17 and 43 GPa. A method based on broad Gaussian distribution of atoms around atomic position in the solid state has been used to compare g(r) observed for the liquid phase with atomic arrangements in solid structures (Zeng et al., 1993). Partial atomic density functions ρij(r) between atoms i and j are calculated following atomic distribution in solid state as: ð ij Þ CN 4πr 2 ρij ðr Þ ¼ pffiffiffiffiffiffi e 2σ ij : 2π σ ij − r−r

2

Where r is the radial distance, CN the coordination number for the i–j atomic pair, rij distances between i–j atomic pairs following solid state structure and σij the standard deviation from the ideal atom

3.4. Liquid structural properties Structural information for Fe–S liquid alloy could be extracted from the diffraction patterns recorded at 42 (±5) GPa and 2150 (±200) K (Fig. 1). The obtained g(r) shows typical compact structure, with well defined coordinance sphere (CS) (Fig. 7). This structure is in

Fig. 7. Partial distribution function g(r) of liquid at 42 GPa and 2150 K compared with simulation based on Gaussian distribution around crystalline positions. Parameters for this simulation are shown in Table 2.

G. Morard et al. / Earth and Planetary Science Letters 272 (2008) 620–626 Table 2 Parameters used for Gaussian simulation Phase

P (GPa)

T (K)

a (Å)

c (Å)

kFeFe

kFeS

kSS

Shift (Å)

Fe3S Fe hcp

43.1 (−2;+ 4) 43.1 (−2;+ 4)

1732 (±150) 1732 (±150)

8.598 2.406

4.262 3.912

0.17 0.22

0.2

0.2

−0.012 0.135

Cell parameters of Fe3S and hcp Fe are from this study. Shifts indicated here have been adjusted in order to set the position of the first CS of simulated g(r) on the position of first CS of experimental spectrum.

positions. This latter parameter, denoting the structural disorder, is calculated, according to (Hosemann and Bagchi, 1962), as σ ij ðrÞ ¼ kij

pffiffiffiffiffi rij

Where kij is a parameter fixed for each type of i–j atoms (Table 2). Molecular atomic density function ρ(r) is calculated as   ρðr Þ ¼ ∑ Wij ρij ðr Þ=cj : ij

Where cj is the atomic proportion of element j and Wij are the weighting factors calculated following Faber–Ziman method (Faber and Ziman, 1965):   Wij ðQ Þ ¼ fi ðQ Þfj ðQ Þci cj =hf i2 hf i2 ¼ ∑ ∑ ci fi ðQ Þcj fj ðQ Þ i j

Wij ¼ hWij ðQ ÞiQmax : Where fi(Q) is the atomic form factor of element i and Qmax is the Q range where diffraction data are acquired. In this study, Qmax is equal to 70 nm− 1. Finally, g(r) is obtained by normalizing normalising ρ(r) to 1, using adequate density ρ0. g ðr Þ ¼

ρðr Þ : ρ0

We compared the experimental g(r) signal recorded at 42 GPa and 2150 K with those expected for hcp Fe and Fe3S model crystalline structures in this system (Fig. 7). As cell parameters, we used those refined for the two solid compounds at temperature just below melting. Experimental g(r) shows symmetric first and second CS peaks. In this figure, position of first CS from simulated g(r) is adjusted manually (shifted) to be superimposed on first CS of observed data (Table 2). Relative position between first and second CS positions is reproduced more accurately by the Fe hcp structure model rather than with Fe3S. The fact that the second CS contribution occurs at higher radial distance in the experimental Fe–20 at.% S liquid compared to the model iron hcp phase could be related to smaller compacity in the Fe–S alloy. The third CS position may appear closer to the Fe3S simulation, but the limited Q range of our experimental S(Q) (Fig. 1) prevents reliable discussion about the features at this position. In any cases, it seems clear that sulphur does not modify strongly the local structure of liquid Fe. It suggests that S behaves as an interstitial impurity in liquid Fe, with a good compatibility with compact structure, such as Si at ambient pressure (Kita et al., 1982). 4. Conclusion New constraints on the Fe–Fe3S phase diagram were derived from in situ X-ray diffraction analysis up to 65 GPa in LH-DAC. (1) By carefully tracking the first appearance of diffuse X-ray scattering of the liquid phase, we report progressive increase of eutectic temperature with a slope of 15 K/GPa. (2) Analysis of the nature of the solid phase (Fe or Fe3S) found in coexistence with the Fe–S liquid at all investigated

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pressure points out a decrease of S content in eutectic liquid with increasing pressure. (3) By Rietveld analysis of diffraction patterns recorded just before sample melting, we estimate that the S solubility in pure solid iron remains constant at around 3 at.% S up to 65 GPa, in good agreement with previous study (Stewart et al., 2007). (4) Therefore, we were able to construct Fe–Fe3S phase diagram for P ~ 65 GPa. (5) If extrapolating the observed trends in the megabar pressure range, our results appear to be incompatible with a large solid solution between Fe and S at ICB conditions, but rather with a classical eutectic system with a relatively low S content in the eutectic liquid. On the other hand, careful analysis of liquid diffraction data indicates compact structure for Fe–20 at.% S composition at 42 GPa and 2150 K. The local structure appears compatible with hcp iron, with large intensity of second CS contribution in the g(r). This suggests that S enters the Fe-liquid structure as an impurity, without disturbing strongly the local structure. Hence, differencing S and Si effects on liquid sound velocities at outer core conditions may remain very difficult if the two atoms adopt similar interstitial positions in the structure of liquid iron alloys.

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