Keywords: sulfur, core formation, metal-silicate partitioning, diamond anvil cell, quantitative NanoSIMS analyses core-mantle equilibration, magma ocean, LH-DAC, NanoSIMS

. On the other hand the mantle's sulfur content is matched if sulfur is delivered with large bodies (3 to 10 % Earth mass) during the last 20 % of Earth's accretion, combined with a chondritic late veneer of 0.5 % Earth mass. These results are conditional on the lowered equilibration efficiency of large impactor cores in a terrestrial magma ocean. In each accretion scenario, the core sulfur content remains below ∼ 2 wt.% in close agreement with cosmochemical estimates and is a further indication that sulfur is not a dominant light element in the core.

Introduction

Investigating metal-silicate partitioning behaviors at magma ocean conditions is important for deciphering the mantle's geochemical record. Recent works on the partitioning of siderophile elements carried out in laser heated diamond anvil cells (LH-DAC) have shown that equilibration at pressures and temperatures expected in a deep magma ocean played a key role in core-mantle differentiation and in establishing the mantle's geochemical signatures. In order to further understand the consequences of core-mantle equilibration it is necessary to study the metal-silicate partitioning behavior of other elements such as highly siderophiles and volatiles at magma ocean conditions. The recovery of samples from LH-DAC experiments with a focused ion beam allows micron sized samples to be prepared for petrological analysis. Chemical analysis techniques including focused electron -energy dispersive x-rays (FE-EDX) and Nanoscale secondary ion mass spectrometry (NanoSIMS) are now capable of measuring low elemental concentrations at the small spatial scales of samples produced from DAC experiments.

In this work, metal-silicate partitioning experiments were carried out in a LH-DAC to measure the partitioning coefficients of sulfur and platinum between liquid iron and silicate melts at pressures and temperatures directly relevant to core mantle differentiation. Understanding the effect of P-T on the partitioning behaviors of these elements is important for investigating their behaviors during core formation. The diverse properties of the elements chosen for this study, sulfur a moderately volatile and platinum a highly siderophile element allows constraints to be placed on core formation and the accretionary mechanism that delivered volatiles to the Earth. This work also explores the implications of the measured partitioning on the distribution of elements between the mantle and the core by means of core formation and Earth accretion models.

The results shows that the partitioning of sulfur is strongly affected by temperature but slightly modified by pressure over the conditions explored in the study. Sulfur's behavior is closer to that of a moderately siderophile element and is unlikely to be present in the core in abundances greater than ∼2 wt.%. The results also imply that volatiles including sulfur were delivered during the last stages of Earth's accretion. The measured platinum partitioning behavior suggests that it becomes less siderophile with increased temperatures and that core-mantle equilibration could explain a substantial fraction of its observed mantle abundance. These findings imply that inefficient core formation could be an important factor in setting mantle abundances. This thesis is organized as follows: A description of the properties of sulfur and platinum in the context of the primitive Earth and the thermodynamic parameterization necessary to characterize the metal-silicate partitioning experiments are presented in Chapter 1. Chapter 2 discusses the experimental procedures which include synthesis of starting material and standards; the methods used to probe the chemical properties of the experimental materials and the techniques used to carry out experiments at high temperatures and pressures. A description of the models that were used to apply the experimental results to core formation are presented in Chapter 3. Chapter 4 and 5 present the results obtained from the metal-silicate partitioning experiments done ii on sulfur and platinum respectively at temperatures of 3000 to 4000 K and pressures between 40 to 110 GPa. Chapter 6 concludes with a summary of the experimental work, the main results and their implications for core-mantle differentiation.

Chapter 1

General Context 1.1 Accretion and core formation

The setting for this work is the primitive Earth while metal-silicate segregation or core formation was ongoing. This process probably took place within roughly 100 Myr after the solar system formed [START_REF] Touboul | [END_REF], Lee 1997]. Impact generated heat, release of gravitational potential energy and decay of radioactive elements in the early Earth raised the temperature of the mantle enough to cause widespread melting [Melosh 1990, Canup 2004, Urey 1955, Rubie 2007[START_REF] Solomatov | Magma oceans and primordial mantle differentiation[END_REF]]. This partial or fully molten state is often referred to as a magma ocean. Immiscible iron-rich liquids from impactor cores migrated downwards through the magma ocean under the effect of gravity to form the Earth's core [Stevenson 1990]. Some degree of chemical equilibration occurred between the metal and the silicate. At the depth of the magma ocean base temperatures were close to the liquidus of the mantle silicate [Wood 2006] and pressures were between 40 to 65 GPa [Wood 2006, Siebert 2012]. To understand the implications of metal-silicate partitioning in the primitive Earth, measurements must be obtained over this P-T range. It is this environment and its imprint on the geological record that is probed by carrying out metal-silicate partitioning studies at high pressures and temperatures.

After the last giant impact, core formation ceased and the magma ocean eventually 2 Chapter 1. General Context crystallized [Elkins-Tanton 2012] but material continued to impact the Earth. A small mass of chondritic material (of primitive undifferentiated origin), referred to as the "late veneer"is assumed to have impacted the Earth during a prolonged period and is thought to account for ∼ 0.5 -0.7 % of the Earth's mass [Kimura 1974, Chou 1978, Dauphas 2002a[START_REF] James Md Day | Highly siderophile element constraints on accretion and differentiation of the Earth-Moon system[END_REF], Walker 2009]. This hypothesis has important implications for the results of this work since it represents material that was homogenized with the residue of core-mantle differentiation. Earth is thought to have acquired atleast some of it volatile inventory (including some sulfur) with this late flux of material which originated from further out in the solar system [Chyba 1992[START_REF] Dauphas | [END_REF]]. One key piece of evidence for this late veneer lies in the presence of the highly siderophile elements (HSE -e.g., platinum) in the mantle in near chondritic proportions. Therefore identifying the contribution of core-mantle differentiation to the mantle's volatile and HSE contents could help to further constrain the Earth's accretionary history. Interpretation of the mantle's chemical signatures must consider the main stages in the evolution of the Earth, summarized in Figure 1.1.

Elements have interesting tales to tell about nature and in this thesis, we follow the stories told by sulfur and platinum about the early Earth.

Sulfur

As a volatile element sulfur would have been depleted in the inner solar system during the early stages of the terrestrial planet's accretion. Volatile elements mainly condensed beyond the snow line. But sulfur also has siderophile properties which allows it to be used as a tracer of core formation. Volatility is a useful metric for quantifying the behavior of elements in the solar nebula and during accretion. Figure 1.2 shows the relative abundance of elements in the silicate Earth, with respect to chondrites, as a function of condensation temperature from a gas of solar nebula composition [Lodders 2003]. While the refractory lithophile elements are present in the Earth in chondritic proportions, the volatile elements are depleted due to nebular processes. However, the more refractory siderophile elements (including the HSE) are depleted due to core formation. The volatile siderophile elements such as the chalcogens show more depletion than elements of the same volatilities. The remaining complement of these elements are assumed to reside in the core [McDonough 2003].

Sulfur in particular has attracted much attention as a potential light element in the core [Murthy 1970, Ahrens 1979, Poirier 1994, Huang 2011, Morard 2013].

There are two main schools of thought regarding the delivery of volatiles (eg. C, H, N, S and water) to the primitive Earth: (i) Volatiles were delivered homogenously throughout the Earth's accretion by partially de-volatilized building blocks [Halliday 2004, Wood 2008]. This idea is supported by the mantle's depletion signature of the siderophile volatile elements, see Figure 1.2. (ii) Volatiles accreted after core formation with a volatile rich late veneer predominantly composed of carbonaceous chondrites [Wang 2013[START_REF] Albarede | Volatile accretion history of the terrestrial planets and dynamic implications[END_REF]. This is supported by the relative chondritic proportions of some volatiles such as chalcogen elements S, Se, and Te in the Earth's mantle [Wang 2013]. The relative abundance of other volatiles, H, C, N as well as the Earth's nobel gas inventory and some isotopic systems (e.g. Ag and Cu) are not as readily explained by a chondritic late veneer which imply other 1.2. Sulfur 5 sources or delivery mechanisms were in play. (iii) There is an intermediate view or heterogeneous accretion, in which both volatile depleted and volatile rich material were delivered throughout the Earth's accretion including some with a late veneer [Schönbächler 2010, Dauphas 2002a, Halliday 2013].

The effect of core-mantle equilibration on the mantle's sulfur signature could give further clues into these processes. However, the metal-silicate partitioning behavior of sulfur has only been quantified at pressures below 25 GPa and temperatures below 2500 K. By measuring sulfur partitioning at core formation conditions, this work seeks to constrain the sulfur content of the core, the residual sulfur content of the mantle and attempts to discriminate among the main scenarios for the delivery of volatile elements.

Figure 1.2: Earth's mantle elemental abundances normalized to CI chondrites and Mg, as a function of volatility. From [Siebert 2015] with data from the works of [McDonough 2003, Palme 2003, Becker 2006]. Depletion of lithophile elements are related to their volatilities. Depletion of siderophile elements are determined by core formation.

Platinum

Platinum is interesting for this study because of its highly siderophile property. Elements partitioning into the core based on their affinity for iron [Goldschmidt 1937].

The cumulative effect of metal-silicate partitioning during core-mantle equilibration is reflected in the primitive upper mantle (PUM) abundances as measured from fertile peridotites [Ringwood 1966, Ringwood 1979, Becker 2006, Lorand 2013]. Figure 1.3 shows the depletion pattern of elements observed in the mantle relative to carbonaceous chondrites, as a function of siderophility. Slightly siderophile elements such as Mn, V, Cr are present in near-chondritic proportions due to their low affinities for Fe, while, platinum, along with the other HSE (Ru, Rh, Pd, Os, Ir, Pt, Re, Au) are significantly depleted [Lorand 2008]. However, the HSE are present in the mantle in near chondritic abundances and therefore they appear to be mostly unfractionated by core formation. Figure 1.4 shows the relative abundance of the HSE in the mantle and three types of chondrites. The quantity of HSE present in the mantle is also at odds with experimental partitioning data which alludes that the HSE should have been completely sequestered to the core. The absolute HSE abundances are more than five orders of magnitude higher than predicted from metal-silicate partitioning experiments [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], Cottrell 2006, Ertel 2008]. This discrepancy is highlighted in Figure 1.3.

Though the provenance of the Earth volatiles are probably not wholly from the late veneer, the HSE being present in near-chondritic proportions [Dauphas 2002a, Becker 2006] is considered as strong evidence for the late veneer. Infact, the mantle's HSE abundance is used as a constraint on the mass of the late accreted material [Kimura 1974, Wanke 1981[START_REF] O'neill | [END_REF][START_REF] Albarede | Volatile accretion history of the terrestrial planets and dynamic implications[END_REF]. There is also additional evidence for a late veneer on the moon and Mars [START_REF] James Md Day | Highly siderophile element constraints on accretion and differentiation of the Earth-Moon system[END_REF], Dale 2012, Walker 2009]. However, since the mantle signatures of siderophile elements Ni, Co, W, and Mo can be explained by core-mantle equilibration at magma ocean pressures and temperatures e.g.

Magma ocean equilibration

7 [Li 1996, Siebert 2012], it has been hypothesized that the HSE could follow a similar trend [Murthy 1991, Righter 1997]. Alternative explanations for the mantle's HSE abundance have developed around a superimposition of the late veneer signature onto the pre-existing HSE from core formation [Dauphas 2002b, Walker 1997, O'Neill 1998].

So far, metal-silicate partitioning of the HSE has been quantified only up to pressures of 25 GPa and temperatures of up to 2500 K [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], Cottrell 2006, Ertel 2008, Righter 2008, Bennett 2014, Mann 2012]. Extrapolations of these partitioning data to magma ocean conditions do not necessarily capture the true effects of core-mantle equilibration. One of the main objectives of this work is to extend the range of this dataset by measuring platinum partitioning at magma ocean conditions.

Magma ocean equilibration

Early models of core-mantle differentiation proposed that the metal segregated by aggregating into large diapirs which accumulated at bottom of a magma ocean before descending to the core [Stevenson 1981, Stevenson 1990, Karato 1997[START_REF] Solomatov | Magma oceans and primordial mantle differentiation[END_REF]]. primitive magma ocean, it is necessary to reproduce these high temperatures and pressures in the laboratory. The laser-heated diamond anvil cell (LH-DAC) is a tool that permits us to explore the pressures and temperatures of the full range of conditions for the core-mantle differentiation in a magma ocean, eg. [Bouhifd 2003, Jephcoat 2008, Bouhifd 2011, Siebert 2012]. The experiments carried out in this study utilized Mid oceanic ridge basalt (MORB) and a peridotite glass (KLB-1) and as the starting silicate and alloys of iron with either sulfur or platinum as the starting metal. The metal alloy is pressed between two silicate platelets in a DAC and an IR-laser is used to heat the sample to melting temperatures. The phases anneal into well defined regions which can capture the exchange or partitioning processes in a magma ocean. The results of partitioning experiments in the LH-DAC have been shown to be consistent with partitioning experiments carried out in multi-anvil apparatus, e.g. [Bouhifd 2003, Chabot 2005, Chabot 2003, Siebert 2012, Siebert 2013], making this a reliable technique to study equilibrium partitioning at magma ocean conditions.

Chapter 1. General Context

The pressure range of the experiments was from 45 to 100 GPa while the temperatures were between 3100 and 4200 K, Figure 1.6. Due to the low solubility of these elements in the silicate melts and the small sizes of the samples, the chemical composition of the run products, necessary to assess partitioning behavior were acquired by ex-situ analysis techniques: wavelength dispersive X-ray (WDX) and energy dispersive X-ray (EDX). In addition, a protocol was developed to use Nanoscale secondary ion mass spectrometry (NanoSIMS), which has high spatial resolution and elemental sensitivity, to probe the trace element compositions of the quenched silicate melts from the small run products obtained from DAC experiments.

Another aspect of this work is to understand the implications of partial equilibrium on core-formation and the possible effects, on the elemental budgets of the two main terrestrial reservoirs. The 182 Hf -182 W of the Earth and the moon alludes to incomplete metal-silicate partitioning during giant impacts [Dahl 2010, Kleine 2009, Rudge 2010, Schönbächler 2010]. A likely outcome of this process is that a portion of the impactor core is sequestered into the Earth's core without equilibrating with the mantle. Continuous core formation modeling following the approach of [Rudge 2010] is used to understand the implication of this process for the net flux of elements to the core and mantle. The effect of turbulent mixing parameters during giant impacts following the work of [Deguen 2014] are also considered.

Parameterizing Metal-Silicate Partitioning

As the Earth accreted mass, the depth and hence pressure, temperature and composition of the magma ocean evolved. Likewise the partitioning behaviors of elements which are dependent on intensive thermodynamic variables, P-T-f O 2 -X evolved. Thermodynamic parameterization of partitioning reactions allows the derivation of empirical relationships in terms of intensive variables (e.g., P, T, f O 2 ). The expressions obtained can be used to understand the partitioning behaviors at conditions relevant to core formation. It has been shown that pressure can have a strong effect on partitioning of some siderophile elements e.g., [Li 1996, Li 2001, Righter 1997, Chabot 2005]. Previous works have also shown strong pressure and temperature dependencies for the partitioning behaviors of HSE eg., [Bennett 2014, Righter 2008, Mann 2012]. Metal and silicate composition, X and oxygen fugacity, f O 2 have also been shown to affect partitioning behavior [Drake 1989, Schmitt 1989].

Partitioning during core mantle equilibration is controlled by a redox reaction between the oxide of the silicate and the metal. The reactions of interest are exchange reactions in which the cation M changes oxidation state when it goes from the silicate to metal and vice versa.

M O silicate n/2 + n 2 F e metal ⇋ M metal + n 2 F eO silicate (1.5.1)
Where n is the valence. Chemical thermodynamics and phase equilibria parameterization can help us understand and quantify this process. A partition coefficient D M describes the distribution of an element between two immiscible phases. In these experiments, the phases of interest are the metal and silicate:

D M = [X] metal M [X] silicate M (1.5.2)
The energetics of such a reaction can be most adequately described by one of the thermodynamic potentials. At a given temperature and pressure, the equilibrium state can be determined by the Gibbs free energy. This is useful since we conduct experiments at known T and P.

G = U -T S + P V (1.5.3)
Where G is the Gibbs free energy, U is internal energy, T temperature, S entropy P pressure and V volume. As the system evolves the Gibbs free energy also changes: dG = dU -T dS -SdT + P dV + V dP (1.5.4) from knowing that: dU = T dS -P dV + µdN (1.5.5) where µ is the chemical potential and N is the number of particles in the system, dG can be expanded further to give:

dG = T dS -P dV + µdN -T dS -SdT + P dV + V dP (1.5.6)
Which simplifies to the thermodynamic identity for G. dG = µdN -SdT + V dP (1.5.7) dG can also be expressed interms of the change of the enthalpy of the reaction, dH , which can provide useful information on the evolution of the chemical reaction. But following from Eqn 1.5.8. G can also be written as G = µ N at constant P, T and V and ∆ G = ∆ µ (equivalent to the work done by the system or the difference in energy between the products and reactants).

For the reaction in equation 1.5.1.

∆µ = µ M O silicate n 2 + n 2 µ F e metal -µ M metal - n 2 µ F eO silicate (1.5.9)
The chemical potentials can be written interms of activity, a which define effective concentrations and are a more accurate way of determining chemical potential of a reaction. a = e µ-µ 0

RT , where R is the gas constant. µ -µ 0 = RT ln a i . µ being the chemical potential defined by the Gibbs energy, µ 0 the standard chemical potential.

With this, Eq. 1.5.9, can be rewritten:

∆µ = µ 0 M O silicate n 2 + RT lna M O silicate n 2 + n 2 µ 0 F e metal + RT lna metal F e -µ 0 M metal + RT lna metal M - n 2 µ 0 F eO silicate + RT lna silicate F eO (1.5.10)
At equilibrium, ∆ µ = 0 and ∆ µ 0 = ∆ G 0 . Which gives: .5.11) The ratios of activities are defined as a constant K, or the equilibrium constant,

∆G 0 = -RT ln [a metal M ][a silicate F eO ] [a metal F e ] n/2 [a silicate M O n/2 ] ( 1
Chapter 1. General Context then: lnK = - ∆G 0 (P, T ) RT (1.5.12) ∆G 0 (P, T ) = ∆H 0 -T ∆S 0 + P ∆V 0 (1.5.13)
So that:

lnK = - ∆G 0 RT = - ∆H 0 RT + ∆S 0 - P ∆V 0 RT (1.5.14)
A partially empirical relationship can be derived to describe K in terms of thermodynamic variables which affect partitioning, eg:

logK = a + b T + c.P T (1.5.15)
Where a is related to the entropy, b to the enthalpy and c to the volume change of reaction.

If activities are written interms of molar fraction of the components, from 1.5.11, K can be written as:

K = [γX metal M ][γX silicate F eO ] n/2 [γX silicate M O n/2 ][γX metal F e
] n/2 (1.5.16) where X is molar fraction and γ is the activity coefficient. Log K then decomposes as:

logK = log   [X metal M ][X silicate F eO ] n/2 [X silicate M O n/2 ][X metal F e ] n/2   + log γ metal M (γ metal F e ) n 2 + log   (γ silicate F eO ) n 2 γ silicate M O n 2   (1.5.17)
The first expression on the R.H.S can be measured experimentally. By combining Equations: 1.5.2, 1.5.15 and 1.5.17, the molar partition coefficient D M , can be defined

Parameterizing Metal-Silicate Partitioning

as:

logD M = a + b/T + cP/T - n 2 log X silicate F eO X silicate F e -log γ metal M (γ metal F e ) n 2
(1.5.18) (Derivations are similar to those of [Wade 2005, Siebert 2011, Mann 2012, Blanchard 2015]).

The constants a, b, c, d are obtained from regressing the results of experiments carried out at different conditions of P and T. But these terms are not necessarily constant over the entire range of core formation conditions. For example, structural transitions in metals and silicates at 5 GPa and 35 GPa could lead to volume changes which would vary the c term [Sanloup 2013]. Non-linear effects of pressure on partitioning have also been reported [Kegler 2008]. Therefore, extrapolation to conditions outside the range of measured data may not accurately capture the relevant behaviors and can lead to large errors in predictions of partitioning. By measuring partitioning at the pressures and temperature directly relevant to core formation, this work seeks to provide a more accurate description of the behaviors of the elements of interest across a wider range of P and T than previously available.

The expressions obtained for partitioning from regression of the measurements are then used to evaluate the distribution of elements in the core and mantle by metal-silicate partitioning during the accretion of the Earth. These calculations are constrained by geochemical and geophysical observations, such as the measured concentration of these elements in the mantle, the current mantle FeO content, and the light element concentration of the core inferred from seismology. These models further contribute to the understanding of core formation and the interpretation of the elemental abundances of the mantle.

Chapter 2

Materials and Methods

Measurement Objectives

The experimental objective of this project was to measure the concentration of HSE the NanoSIMS measurements to be accurate, nugget free glasses were required for the standard calibration to avoid issues with the ambiguities of micro and nanonuggets e.g., [Mann 2012, Bennett 2014[START_REF] Médard | [END_REF]].

Materials and Syntheses

Materials synthesized included NanoSIMS standards, starting material for DAC experiments and the quench products obtained from DAC experiments. Certified standard glasses (NIST 612 and 610) [Sylvester 1997[START_REF] Rocholl | [END_REF]] and a pillow basalt, CLDR1-05V [Chaussidon 1991] were used as silicate standards. Metals were obtained from Alfa Aesar, in the form of 99.99 % pure powders and 1000 µg/ml plasma solutions. Some metal powders were prepared as pure metal standards for the NanoSIMS, see Figure 2.6.

Silicate synthesis

The in-house silicate standards were of an average MORB (Mid Oceanic Ridge Basalt) composition. Natural MORB (NMORB) was mixed with the relevant trace elements (Pt, Pd, Au) in different concentrations. Homogenous mixtures were prepared in an agate mortar and were then melted with either a hydrodynamic gas laser levitation device at temperatures between 1600 and 2000 • C or in a convention furnace at temperatures up to 1700 • C. With the laser levitation apparatus (Figure 2.1), a CO 2 laser is used to quickly heat the sample up to its melting temperatures while the sample is kept buoyant by gas from a brass nozzle [Auzende 2011]. The temperature of the sample was monitored from its back body radiation. With this apparatus, the quench from high temperature is almost instantaneous as seen in Figure 2.2 and the resulting glass is homogenous. A mixture of argon and hydrogen gas was used in the first set of NMORB syntheses while air was used later to vary the oxidation condition during the synthesis. Synthetic MORB, FMORB (Fake MORB) samples were made from oxide starting materials. These mixtures were placed inside a platinum crucible in a convection oven and left at temperatures from 1500 to 1700 samples. The measurements on the first two samples are mostly zero (thick red lines on the x axis) with some noise being recorded from the laser ablation process. Trace elements were absent in measurable amounts in these samples and they were considered blanks. Small amounts of platinum (red cross) 7 ppm were detected in the third sample. The small variability is due to the laser ablation process and the signal is averaged to calculate concentrations. The third sample shows concentration spikes due to heterogeneities and nuggets. The latter was not used as a standard.

Alloy Synthesis

Metal-silicate partitioning experiments were carried out in an end-loaded piston cylinder apparatus with the aim of synthesizing alloys to be used as starting materials for DAC experiments. Powdered mixtures of MORB samples and mixtures of iron and each trace elements were packed into a MgO capsule and placed inside an insulated pressure vessel. Pressure was applied vertically by two hydraulic rams to between 1.5 to 2 GPa. Temperature was increased with resistive heating up to between 1200 and 1500 • C. A summary of these synthesis are in 2.3. The samples were held at superliquidus conditions for about 2 minutes. After quench, the capsule was opened and the

The Nanonugget Issue

Nanonuggets of platinum group elements in silicate glasses are a widespread issue in the study of PGE solubility and partitioning [Brenan 2015]. The formation of metal inclusions in silicate solubility experiments has been well documented [START_REF] Borisov | Solubility of palladium in silicate melts: Implications for core formation in the Earth[END_REF][START_REF] Borisov | Experimental determination of the solubility of platinum in silicate melts[END_REF][START_REF] Médard | [END_REF], Mann 2012, Ertel 2008, Bennett 2014]. Nuggets have also been observed in natural samples such as mantle peridotites [Lorand 2012] and in me-teoritic samples [Hewins 2014]. Interpretation of nuggets is critical to quantifying PGE behaviors in silicate melts. Studies have shown that redox conditions play a role in the formation of nuggets which have been observed to form more readily under reducing conditions [START_REF] Borisov | Solubility of palladium in silicate melts: Implications for core formation in the Earth[END_REF][START_REF] Borisov | Experimental determination of the solubility of platinum in silicate melts[END_REF], Ertel 1999, Farges 1999]. It has been argued

by [Cottrell 2006] that nuggets of platinum observed in the silicate quench during metal-silicate partitioning experiments are quench features and should be integrated with measurements of PGE partitioning. However, [Ertel 2006] and [START_REF] Médard | [END_REF] demonstrated that mechanical mixing centrifuging can reduce the formation of nuggets which supports the idea that they are stable during experiments and must be avoided in determining partitioning. Whether these nuggets are a quench products or whether they nucleate in melts due to saturation at high temperature is still a matter of debate [Ertel 2008, Malavergne 2016].

In this work a systematic study of nugget formation was not attempted. We instead endeavored to obtain nugget free glasses by varying the synthesis conditions, eg

High pressure-temperature experiments

Diamond Anvil Cells

High pressure experiments were carried out by means of a diamond anvil cell. The static diamond anvil cell technique can cover the full range of pressures necessary for the study of core-mantle differentiation (45 to 65 GPa). The cells used in this study were the symmetric piston cylinder type in which two aligned diamonds are used to compress materials. The diamonds used in this study were flat with culet sizes 200 and 250 µm, which can achieve pressures up to 100 GPa. Once the cell is closed, pressure is increased hydrostatically by turning four left and right handed screws, see Figure 2.9.

An indented rhenium gasket which sits between the two diamonds, serves as a sample chamber. Gaskets are prepared by first squeezing a piece of rhenium between the diamonds to achieve a very light pre-indentation to define the location of the sample chamber. The top diamond (piston) is then removed leaving the gasket on the bottom diamond. A ruby is placed in the middle of the indented region. The cell is closed again and the screws tightened slightly until the required gasket thickness is achieved.

After decompressing, the gasket is removed and cleaned with ethanol and the thickness of the indented section measured with a micrometer. The relationship between indentation pressure and gasket thickness depends on the compressibility of the gasket material and the culet size of the diamond. The optimal thickness for the gaskets used in these experiments were between 35 and 25 µm in order to achieve pressures between 40 and 100 GPa. A circular centered hole of 60 to 80 µm which served as an experimental chamber was cut into the indented gasket with a femtosecond laser drill.

Once the gaskets were prepared, the sample assembly consisting of a metal alloy (Fe,S or Fe,Pt) pressed between two silicate platelets (of either natural MORB or KLB-1 peridotite composition), was loaded into the sample chamber with a tungsten needle. A ruby was placed close to the edge of the chamber. The screws of the cells were tightened slowly to increase the pressure on the sample by reducing the volume of the sample chamber. with a measurable pressure dependent red shift [Eggert 1989]. Eq. 2.2.1 shows ruby pressure as a function of redshift [Mao 1978]. Uncertainties in the pressure measurements using this methods are ∼ ± 5 to 10 GPa and experiments carried out at high temperatures require a further thermal pressure correction.

P = a b [( ∆λ λ 0 + 1) b -1] (2.2.1)
where P is the pressure in GPa, a and b are dimensionless parameters (1904 and 7.665), ∆λ is the shift of the ruby wavelength with respect to wavelength at ambient pressure and temperature, λ 0 .

Materials and Syntheses

Laser Heating

The optical transparency of the diamond window allows lasers to be used to generate high temperatures in diamond anvil cells [Ming 1974, Williams 1991, Shen 2000, Boehler 2000]. IR lasers are commonly used to achieve controlled heating of samples in petrological studies. High temperatures were achieved for these experiments with a double-sided 200 W fiber laser (peak λ = 1070 nm). The optical set up used for these experiments is similar in principle to the schematic shown in The laser spot size is 10 to 20 µ m in diameter on each side and is focused at the contact between the alloy and silicate platelets from both sides of the cell, see Figure 2.12. Once the laser was focused, the temperature on the sample was raised by increasing the laser power. Stability of the laser and the ability to vary the power enabled control of the sample temperature environment. Spectra of the radiation emitted from the heated region were recorded from the two sides of the experiments simultaneously. The temperature was determined by fitting the thermal emission with the Planck radiation function [Boehler 2000], Eq. 2.2.2.

I(λ) = ǫc1λ -5 e c2/λT -1 (2.2.2)
where I is intensity, c1 and c2 are constants. ǫ is the sample emissivity (1 for a black body and less than one for a gray body), λ is wavelength of the emitted light [Boehler 2000]. The uncertainty in the temperature fits are approximately ± 150 K and temperature gradients in the laser heated volume are typically less than a few hundred Kelvins [Shen 2000].

During laser heating experiments, the temperature was ramped quickly until the sample region at the laser focus is molten, at which point the measured temperature plateaus. Prolonged exposure to the IR heating laser eventually anneals the silicate and metal phases into well-defined regions [Jephcoat 2008]. The experiments are designed to follow the silicate (peridotite or basalt) liquidus with increasing pressure maintaining melt-melt partitioning. Temperature plateaus observed during laser heating (see Figure 2.12) are due to the presence of significant liquid fraction in the volume of the heated region [Andrault 2011, Fiquet 2010, Lord 2009]. [Siebert 2012] reports similar observations in temperature behavior while carrying out superliquidus metal silicate partitioning experiments.

The experiments were kept at superliquidus conditions for 45 seconds to 2 minutes which has been shown in previous work to be much longer than the few seconds sufficient to reach chemical equilibrium at the length scales of diamond anvil cell experiments [START_REF] Corgne | [END_REF]]. Though the sample in the inner region is completely molten, it is insulated from the diamonds by the surrounding unmelted silicate. Turning off the laser rapidly quenches the experiments. The post quench pressures are determined by ruby fluorescence and are corrected for thermal pressure with a value of ∆P th ∼ 2.5.10 -3

GPa/K similar to the one used in previous works e.g., [Andrault 1998, Fiquet 2010, Siebert 2012]. Given that the diffusion coefficients are 10µm 2 /s, and the size of the region at superliquidus conditions is roughly 30 µm eg. see Figure 2.13, species could attain equilibrium interaction in less than 30 seconds.

Analytic Methods

Scanning Electron Microscope

Electron Images of the standards and DAC samples in this study obtained with a Zeiss

Cross-Beam Field Emission (FE) -SEM (and a Tescan Vega II for some standards) at Typical operating conditions included a 15 to 20 KeV accelerating voltage (EHT) for imaging and EDX.

Electron Microprobe Analysis

Quantitative chemical information for standards and some DAC samples were obtained with a Cameca SX100 at CAMParis. This instrument is similar in principle to an SEM but in addition, wavelength dispersive spectrometry (WDS) is performed on X-ray photons emitted from the sample. The use of standards combined with Bragg's law provide accurate elemental information on the sample. Typical operating conditions were 15 keV with a 10 nA beam current. Integration times ranged from 10 to

Analytic Methods

quency of 5 Hz and a beam energy of 83 mJ/pulse.

NIST 612 was used as a standard and was measured after every 2-3 sample analysis.

Measurements were obtained for silicon in addition to the trace elements of interest (Pt, Au, Pd). Several hundreds to thousands of data points were collected for each sample analysis. The first few hundreds of measurements points are collected without the laser and are averaged as background counts. The background was subtracted from the signal which were then normalized to silicon. The elemental concentration, X, in the samples, were calculated using the known silicon concentrations in NIST 612 glass standard.

X ppm = ( X Si ) cts sample ( X Si ) cts N IST * ( X Si ) ppm N IST * Si) ppm sample (2.3.1) X ppm = X W eight% * 10000 (2.3.2)

NanoSIMS

The CAMECA NanoSIMS 50 was the main analytic tool used to measure trace elements S and Pt in the silicate glasses used for this study and in the samples recovered from our experiments. The NanoSIMS was developed over the last 20 years by CAMECA [Hoppe 2013]. The probe uses a finely focused primary beam to erode the top few atomic layers of the target material and produce secondary ions that are analyzed by a high-resolution multi-collection mass spectrometer. The instrument uses a 16 keV primary ion beam (Cs + or O -) to sputter small volumes of sample material from the surface of which is then analyzed by a mass spectrometer. The small spot size of the primary current can focus at 50 nm to 400 nm. Five movable detectors allow the collection of measurements from five species simultaneously. Some of the main NanoSIMS calibration measurements for platinum and sulfur were obtained over three sessions. Measurements were obtained in isotope mode for standards on areas of 10 x 10 µ m in size and 64 square pixels resolution. During calibration sessions, the method of [Thomen 2014] and [START_REF] Thonnard | Confidence intervals and inverse regression[END_REF]], was used to determine the calibration curves and calculate detection limits for both Pt and S. The detection limit of ∼ 30 ppm was determined for sulfur and 2 ppm for Platinum. Figures 2.17 (piston cylinder syntheses) which had been previously quantified by EMP, table 2.1.

Table 2.6 shows the predicted sulfur content of the silicate glass of ELMO 151 and 145 based on the calibrations. The predictions agreed very well with measurements obtained from the microprobe. DAC Samples were then measured in an additional 3 session.

Before analysis of each DAC sample a large area of each sample is pre-sputtered for up to 10 minutes with a high primary current to clean the surface and implant primary ions of Cs + into the sample matrix [Hoppe 2013]. A 10 pA primary current of Cs + accelerated at 16 keV with a spot size of 300 nm is then used for imaging. During the analysis, the beam was rastered over a square region which ranged from 8 x 8 to 20

x 20 µm. These corresponded to images that were 256 x 256 pixel resolution. These image sizes and resolution were sufficient to covered the interesting regions in each sample. Integration times ranged from 30 minutes to 90 minutes during which several tens of data frames (up to 60), which recorded accumulated counts per second, were collected. Standards used to quantify sulfur in the 8 DAC samples were CLDR1-05V, NBS610 and NMORB-blank1 and the primary current for these measurements was 10 pA. The masses measured were 12 C, 28 Si, 32 S and 47 AlO. Standards used to quantify platinum in 7 DAC samples were NBS 610, NBS 612, FMORB-Pt1, FMORB-Pt2 and NMORB-blank1 and primary currents range from 23-26 pA. Masses measure were 24 C 2 , 28 Si, 32 S, 43 AlO and 194 P t.

The DAC samples posed an additional complication in that the standard mounting technique for these types of samples, welded to a TEM half grid, led to charge effects in the NanoSIMS which would render measurements of the samples unusable. To overcome this difficulty, a transfer protocol was developed at the FIB to mount thin sections extracted from DAC samples onto a silicon wafer, see section 2.3.6.

Transmission Electron Microscopy (TEM)

The microstructure of one quenched DAC experiment was observed by TEM. The operating principles of the TEM are similar to that of the SEM but electrons pass instead through the sample before being focused by an electromagnetic objective lens to produce an image. Chemical information can be obtained by EDX and the diffracting properties of electrons can be used to obtained crystallographic information. The TEM analysis was carried out with the JEOL 2100F at IMPMC, operating at 200 keV. This instrument has a field emission gun and is capable of point-to-point resolution of 1.8 Ä.

Slice thickness is crucial to obtaining high quality analysis and a thin section of ∼ 50 nm thick had to be prepared from the quench region of the sample for analysis.

The sample was placed in the column with a single tilt specimen holder. High angle annular dark field (HAADF) imaging mode was used to examine quench features and EDX chemical analysis mode was used to map the chemical composition. Electron diffraction patterns were also collected to identify crystallographic structures of the features in quench zone.

Focused Ion Beam

The focused ion beam (FIB) is used to prepare DAC samples for ex-situ analysis.

This technique has been successfully used to recover samples from DAC experiments [Siebert 2013, Fischer 2015, Pradhan 2015]. After experiments, gaskets were removed from the cells with the samples still in the sample chamber. These were placed on carbon tape and mounted on aluminum stubs for placement inside the FIB, Figure 2.13 b. The region that was laser heated usually has a small depression or bump.

With a large current, 10 nA, the sample is opened in an area close to the heated spot.

Once the region where melting occurred is found, a lamellae can be shaped with the beam, Figure 2.19 a. to d. The lamellae is clean with a low current, 200 pA and the sides cut in preparation for lift out. The lamellae are usually 3 to 5 µm in thickness, and 20 to 30 µm in length and width and is a slice of the region where metal silicate superliquidus equilibrium partitioning occurred.

Analyses by the NanoSIMS require samples to be placed flat and away from edges.

Samples placed close to edges such as those glued to TEM half grids had charging problems in the NanoSIMS and those measurements were unusable. To overcome this difficulty, a transfer protocol was developed to place each lamella flat on a silicon wafer, A silicon wafer was placed in the FIB on a vertical mount. The stage was rotated until the surface of the silicon wafer was roughly parallel with the surface of the lamellae containing the SEM glue. The stage and wafer were carefully moved closer together.

Small adjustments of the stage and the needle were made to bring the two surfaces Chapter 2. Materials and Methods perfectly parallel. Retracting the gas injection system (GIS) nozzle from the chamber during this stage allowed more range of motion for the micro-manipulator. The side of the lamella with the glue was gently touched onto the silicon wafer well away from the edges. A 50 pA current was then used to cure the glue and the needle was milled from the lamella with a stronger current. A low current was used to remove debris accumulated during the transfer process and to do a final polishing of the sample. Chapter 3

Accretion Model

Continuous Accretion Model

Continuous accretion models were proposed as a more likely scenario to explain the mantle's moderately siderophile abundances [Li 1996, Righter 1997, Wade 2005, Wood 2006, Wood 2008] than single stage accretion model [Stevenson 1990]. In these models there is continuous exchange of material between the core and the mantle as the Earth accretes new material. The relative compositions of the two reservoirs are then a result of the integrated metal-silicate partitioning at the base of a deep magma ocean as a function of P, T, X, and fO 2 . The primary metrics are (i) that final silicate mantle composition coincides with the observed present-day mantle compositions, and (ii) that the composition of the core is consistent with geophysical observations [Wood 2006].

Parameterization

The parameterizing for continuous accretion allows the determination of pressure and temperature at a given depth inside the accreting Earth. The effect of other properties such as redox state and light element composition can be integrated with these effects 53 based on empirical data. Partition coefficients can then be calculated as conditions at the base of the magma ocean evolve for the growing planet.

Growth Function

Growth functions of the Earth can be based on a linear or exponential function. Some exponential functions have similarities with the growth curves produced by n-body simulations [Raymond 2006, Morbidelli 2012]. For the model in this work the growth function for the Earth's mass is based on [Rudge 2010], Eqn 1 of that work.

M (t) = 1 -e -t/tα (3.2.1)
Where M, mass fraction of the Earth evolves over steps, t. τ α is a mean age for ac-

Parameterization 57

Pressure, temperature, redox and light element

The total energy of an an accreting planet can be considered as the sum of the gravitational binding energy and the planet's internal atomic energy. The radius, mass, density and pressure inside the growing planet are connected by the assumptions of hydrostatic equilibrium whereby, for the body to be in equilibrium, the force of gravitational compression must be balanced by the force of incompressibility of the material inside the planet [Cole 1984]. A direct consequence of hydrostatic equilibrium is the differentiation of planetary bodies as material of higher densities settles at greater depths. Assuming spherical symmetry, this idea can be expressed by the following set of equations:

ρg = ∆p (3.2.2) dp dR = -ρg = -ρGM R dM dR = 4πR 2 ρ (3.2.3)
Where ρ is the average density, G is the gravitational constant, g is the gravitational acceleration and p is pressure, M is mass and R radius of the planet. A relationship between radius and mass can be derived.

R = 3M g 4πGρ avg 1/3 (3.2.4)
where g is gravitational acceleration, ρ avg is the assumed average density of the Earth. This leads to:

M = 4 3 πρR 3 (3.2.5)
The pressure difference dp between two layers (R and R+dR) inside the planet is proportional to their separation dR.

58

Chapter 3. Accretion Model

dp = ρ(R)g(R)dR (3.2.6)
Using the relationship, g(R) = GM (R)/R 2 , where M(R) is the mass contained in sphere of radius R, dp can be re-expressed:

dp = 4πG R 2 R 0 ρ(r)r 2 dr (3.2.7)
combining Eq. 3.2.6 and 3.2.7

dp dR = -(4πG/R 2 )ρ R 0 ρ(r)r 2 dr (3.2.8)
Then at constant density and temperature:

dp dr = - 4 3 πGρ 2 R (3.2.9)
p at center of the planet.

p c = 2 3 πGρ 2 avg R 2
For a stratified body the density is more accurately derived as a function of radius by use of the bulk modulus K = ρ∂p ∂ρ , which can be determined as a function of pressure. The pressure gradient can be re-written in terms of the density gradient:

dp dr = - dp dρ dρ dr (3.2.10) ∂ρ dR = - 4πG K ρ 2 R 2 R 0 ρ(r)r 2 dr (3.2.11)
The density at a given depth dR below the surface:

ρ(R -dR) = ρRp + dρ dR | Rp dR (3.2.12)
The above formalisms can be used to calculate pressures inside the growing Earth.

In addition, constraints from Ni and Co partitioning provide estimates for the pressures

Parameterization

59

of core-mantle equilibration. From these experimental constraints it was determined that the base of the magma ocean was roughly 40 % of the radius of the growing Earth.

Estimates for the pressure at the magma ocean base can also be estimated as a fraction of the pressure at the Earth's core-mantle boundary which is well constrained. Figure 3.2 b shows pressure evolution at the magma ocean base as accretion proceeded.

Temperature also increases with compression. In this case the temperature at base of the magma ocean is estimated to follow the peridotite liquidus which has been determined experimentally [Fiquet 2010], Eq. 3.2.13. The average liquidus of [Fiquet 2010] and [Andrault 2011] is used in the model, see Figure 3.2 c:

T = 1 2 2022 + 54.21(P ) -0.34P 2 + 9.0747x10 -4 P 3 + 1940 P 29 + 1 1 1.9 (3.2.13)
Another factor affecting the exchange of material between core and mantle is the redox conditions. Redox conditions are vary according to changes in the amount of FeO in the mantle as it evolves. The mantle redox state is characterized by the equilibrium between Fe and FeO.

F e + 1 2 O 2 = F eO (3.2.14)
whose equilibrium constant that can be expressed in terms of activities, a:

K = a F eO (aF eO)(a 1 2 O 2 ) (3.2.15)
This can be expressed relative to the Iron-Wustite buffer.

∆IW = 2log

XF eO XF e mantle + 2log γF eO γF e (3.2.16)

where X is molar fraction and γ is activity coefficient, assumed to be 1 in the ideal case.

The light element composition of the metal can also have a strong effect on partitioning. Using oxygen as an example, partitioning of oxygen into the metal is describe by the reaction:

F eO silicate = F e metal + O metal (3.2.17)
With an equilibrium constant, the effect of oxygen as a light element in the core can be determined at varying conditions of P and T from empirical data e.g:

K O = a met F e a met O a sil F eO = X met F e X met O X sil F eO = (1 -X met O )X met O X sil F eO (3.2.18)
which rearranges to give: With the parameters P, T, and X determined as a function of the growth of the Earth, the partitioning can be then be calculated over all these conditions. For example, development of the parameterization for sulfur partitioning is discussed in Chapter 4

1 -X met O = 1 2 - 1 -4K O X sil F eO 2 (3.2.19) logK O = a + b T (3.
and the resulting expression is shown below as a function of several variables.

log[D m/s (S)] = a + b T + c P T + logX silicate F eO -logC s + dlog(1 -X O ) (3.2.21)
where a, b, d, d are regression constants, C s is the sulfide capacity, X is mole fractions.

Parameterization 61

Mass Balance

The partitioning expression is applied to the calculation of the mass balance of a specie in the accreting Earth which is implemented following the method of [Rudge 2010],

where embryos are added until the Earth attains mass fraction of 1. The embryo's mass balance in the specie, c, is defined as:

c b = F c ce + (1 -F )c me (3.2.22)
where c me is the concentration in the mantle embryo, c ce is the concentration in the core of the embryo and c b is its bulk composition. F is the mass fraction of the body's core which is assumed to be 0.323, as for Earth.

The effective partitioning of the specie in embryo is assumed to stay constant defined as:

c ce c me = D c (3.2.23)
The mass conservation of an element, c, into the accreting Earth's core and mantle are integrated numerically from the equations, A3 and A4 from [Rudge 2010]:

d dt ((1 -F )M c m ) = [(1 -F )c me + kF (c ce -D c c m )] dM dt (3.2.24) d dt (F M c c ) = [kF D c c m + (1 -k)F c ce ] dM dt (3.2.25)
where c m and c c are the concentration of chemical species in the mantle and in the core of the Earth. D c is the partitioning coefficient of the specie in the Earth which in our case, evolves as the planet accretes through collisions of embryos (Figure 3.1).

Partial re-equilibration is introduced in this model by the parameter k, the fraction of an embryo's core which equilibrates with the Earth's mantle. The expressions in the right hand side of Eq. 3.2.25 represent the two paths that the metal can take to the core: (1 -k)Fc ce is the fraction of the embryo's core that is added directly to the Earth's core while the other fraction kFD c c m experienced equilibration with the Earth's mantle and has a composition in equilibrium with the Earth's mantle. The first term in Eq. 3.2.24 is material from the embryo's mantle which is added to the Earth's mantle while the second term represents the mantle that re-equilibrated with the impactor core. Mass conservation of the species in the accreting Earth is obeyed since the sum of these two equations is equivalent to the bulk compositions of the embryos, Eq.3.2.22. [Rudge 2010].

Efficiency

Large impacts can affect the efficiency of core-mantle equilibration [Dahl 2010, Kleine 2009, Rudge 2010] because the impactors do not disperse to scales small enough to allow full metal-silicate equilibration with the magma ocean [Rubie 2003]. Figure 3.3 illustrate some of the main differences between the behaviors of large and small impacts in a magma ocean. Fluid dynamics experiments have shown that metal blobs mix mostly through turbulent entrainment in the magma ocean [Deguen 2014]. Though equilibration does occur for large impactors, this is significantly reduced as the impactor core diameter approaches the magma ocean thickness. The infinite dilution assumption is not sufficient to describe mixing in this situation.

In addition to the relative size of the impactor to the Earth, the efficiency of equilibration could also be element dependent, i.e. depends on partitioning behavior.

[ Deguen 2014] showed that the effect of equilibration is significant only if the metal re-equilibrates with a mass of silicates about D c times larger. This ratio is difficult to achieve for the more siderophile elements delivered by large impactors. A parameterization for mixing efficiency was implemented by [Deguen 2014] which considers relative size of metal and silicate which undergoes equilibration and the partitioning dependence. The implementation is identical interms of conservation to the approach of [Rudge 2010] but instead of k as a single fraction that describes partial equilibration, a parameter E is introduced, to describe the equilibration efficiency.

E = k 1 + Dc ∆ (3.3.1)
where D c is the partitioning function of the specie which evolves as the Earth accretes; k is the fraction of the embryo core which equilibrates with the Earth's mantle; ∆ the ratio of equilibrated silicate to equilibrated metal (dilution ratio) can be expressed at each step of accretion following [Deguen 2014] and [Badro 2016] as:

∆ = ρ silicate ρ metal 1 + 0.25 δ 1/3 3 -1 (3.3.2)
In which ρ silicate and ρ metal are the densities of silicate and metal respectively, and δ is the ratio of the impactor mass to Earth mass.

One consequence of this reduced equilibration efficiency during giant impacts is that more metal is likely to sink to the core before chemical equilibration can occur leaving no record in the mantle. Chapter 4

Sulfur partitioning during core formation

This chapter presents a manuscript in preparation on the results and implications of the metal-silicate partitioning experiments carried out on sulfur. We found that sulfur behaves as a moderately siderophile at the putative conditions of core formation. This result along with its low cosmochemical abundance, imply that sulfur cannot be a major light element component of the Earth's core. The sulfur contents of the bulk Earth and mantle can be best explained by heterogenous accretion scenario in which volatiles were delivered towards the end of main stage of Earth's accretion by a few large planetisimals such as the moon forming impactor. This does not exclude sulfur contribution from a late veneer.

A sulfur-poor terrestrial core inferred from metal-silicate partitioning experiments

Terry-Ann Suer1 , Julien Siebert2 , Laurent Remusat 1 , Nicolas Menguy 1 , Guillaume Fiquet 1

Abstract

As a siderophile and a volatile element, sulfur's partitioning behavior allows constraints to be placed on processes in the primitive Earth. Sulfur's core-mantle distribution during Earth's accretion has consequences for core content and implications for volatile accretion. In this study, metal-silicate partitioning experiments of sulfur were conducted in a diamond anvil cell at pressures between 46 and 91 GPa and temperatures between 3100 and 4100 K, conditions that are directly relevant to core segregation in a deep magma ocean. The sulfur partition coefficients measured from these experiments are an order of magnitude less than those obtained from extrapolation of previous results to core formation conditions (eg., [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014). These measurements challenge the idea that sulfur becomes a highly siderophile element at high pressures and temperatures. A relationship was derived that describes sulfur's partitioning behavior at the pressure-temperature range of core formation. This relationship combined with an accretion model was used to explore the effects of varying impactor sizes and volatile compositions on the sulfur contents of the Earth's core and mantle. The results show that homogenous delivery of sulfur throughout accretion would over enrich the mantle in sulfur relative to the present day observations of 200 ± 80 ppm (Lorand et al., 2013) unless the bulk Earth sulfur content is lower than its cosmochemical estimate of ∼ 6400 ppm (eg.,

Introduction

Metal-silicate partitioning studies provide constraints on the relative proportion of elements that entered the Earth's core and mantle during differentiation (eg., Li andAgee, 1996, 2001;Righter et al., 1997;[START_REF] Gessmann | The origin of the depletions of v, cr and mn in the mantles of the earth and moon[END_REF][START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF]Siebert et al., 2011). The relatively low abundance of sulfur in the bulk silicate Earth (200±80 ppm, Lorand et al. ( 2013)) is commonly attributed to its strong partitioning into liquid iron during core formation [START_REF] Li | Element partitioning constraints on the light element composition of the Earth's core[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]. This deduction also provides a convenient solution to the core density deficit problem and several works have explored the possibility of sulfur as a light element in the core (eg., [START_REF] Rama | The chemical composition of the Earth's core: Possibility of sulphur in the core[END_REF]Ahrens, 1979;Poirier, 1994;Huang et al., 2011).

Estimates for the core sulfur content are derived from either cosmochemical mass balance considerations (McDonough and Sun, 1995;[START_REF] Dreibus | Cosmochemical constraints on the sulfur content in the Earth's core[END_REF][START_REF] Allègre | The chemical composition of the Earth[END_REF]Mahan et al., 2017) or or from comparison of the physical properties of (Fe, S) alloys at high pressure and high temperature with geophysical models of the core (e.g, [START_REF] Badro | A seismologically consistent compositional model of Earth's core[END_REF][START_REF] Badro | Core formation and core composition from coupled geochemical and geophysical constraints[END_REF]Morard et al., 2011Morard et al., , 2013). Sulfur's depletion in the mantle with respect to lithophile elements of comparable volatilities such as Zn argues for a maximum of 2 wt.% sulfur in the core [START_REF] Dreibus | Cosmochemical constraints on the sulfur content in the Earth's core[END_REF]McDonough, 2003). However, a sulfur-rich core was proposed by Seagle et al. ( 2006) (up to 15 wt.%) with Fe 3 S equation of state measurements while Morard et al. (2013) reports a core containing 6 wt.% sulfur from direct liquid-metal density measurements at megabar pressures. Reassessment of the siderophile behavior of Zn also leads to a higher sulfur content in the core (Mahan et al., 2017). In contrast [START_REF] Badro | A seismologically consistent compositional model of Earth's core[END_REF][START_REF] Badro | Core formation and core composition from coupled geochemical and geophysical constraints[END_REF] predicted from experiments and ab initio calculations that a core deprived of sulfur is a better match for geophysical observations (i.e. sound velocity, density). In addition several studies have shown that the presence of silicon and oxygen better explain the core's density deficit and are more likely than sulfur to be light elements in the core (e.g., [START_REF] Kilburn | Metal-silicate partitioning and the incompatibility of S and Si during core formation[END_REF][START_REF] Alfe | Constraints on the composition of the Earth's core from ab initio calculations[END_REF]Siebert et al., 2013;[START_REF] Badro | Core formation and core composition from coupled geochemical and geophysical constraints[END_REF].

The near chondritic proportions of the chalcogens (S, Te, Se) in the Earth's mantle indicates a chondritic origin for these elements [START_REF] Wang | Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer[END_REF]. The mantle's sulfur content is generally assumed to have been delivered along with other volatiles with an oxidized late veneer [START_REF] Dauphas | Treatise on Geochemistry[END_REF][START_REF] Albarede | Volatile accretion history of the terrestrial planets and dynamic implications[END_REF]Halliday, 2004;[START_REF] Wang | Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer[END_REF]. However, in order to explain the depletion of the chalcogens relative to other moderately volatiles such as Zn and Pb (Halliday, 2004(Halliday, , 2013;;Wood, 2008), these elements must have been present to some extent during the main stages of Earth's accretion. A pre-late veneer presence of volatiles is also required to explain the isotopic signatures of S, Ag and Cu and the mantle abundances of siderophile elements W and Mo which are attributed to core-mantle equilibrium (e.g., [START_REF] Labidi | Non-chondritic sulphur isotope composition of the terrestrial mantle[END_REF][START_REF] Christopher W Dale | Late accretion on the earliest planetesimals revealed by the highly siderophile elements[END_REF]Schönbächler et al., 2010;Savage et al., 2015). The partially de-volatilized early building blocks of the Earth could have delivered minor amounts of sulfur but it has also been suggested that large impactors towards the end of accretion would have brought sulfur and other volatiles (eg., Wohlers and Wood, 2015;Li et al., 2016). Dynamical models have suggested that volatile-rich material derived from the outer solar system was added to the Earth during late accretion, (Raymond et al., 2006;Morbidelli et al., 2012). Models which explore the outcome of different possible histories for volatile delivery to the Earth can place broad constraints on the timing and origin of volatile accretion. But in order to evaluating the core-mantle distribution of volatile sulfur during accretion, accurate knowledge of its partitioning behavior during core formation is required.

Several studies have been conducted with large volume presses to quantify sulfur's partitioning behavior (e.g., [START_REF] Li | Element partitioning constraints on the light element composition of the Earth's core[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014). There is a general agreement that sulfur becomes more siderophile with increasing pressure while temperature is shown to have the opposite effect (Li andAgee, 1996, 2001;Mavrogenes and O'Neill, 1999;[START_REF] Holzheid | Sulfur saturation limits in silicate melts and their implications for core formation scenarios for terrestrial planets[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014). But estimates of the magnitude of pressure and temperature effects on sulfur partitioning strongly vary from one study to the other. Sulfur's increasing affinity for iron with depth (by two to three orders of magnitude from zero to 25 GPa) argues for it being present in the core as a dominant light element [START_REF] Li | Element partitioning constraints on the light element composition of the Earth's core[END_REF] and for a late accretion origin of sulfur in the silicate Earth from chondritic materials [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF][START_REF] Wang | Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer[END_REF]. Sulfur has also been shown to become more lithophile at low oxygen fugacities [START_REF] Holzheid | The activities of nio, coo and feo in silicate melts[END_REF]Siebert et al., 2004;[START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014), an effect that is adequately modeled from the FeO activity in the silicate. Consequently, heterogeneous accretion models involving very reduced conditions in the earliest phases of accretion (e.g. [START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF]Schönbächler et al., 2010) yield final mantle sulfur content higher than observed (Boujibar et al., 2014). Addition of sulfur in the later stages of accretion provides a possible solution to this issue while raising the abundances of some siderophile elements like W in the mantle to their current levels through a large effect of sulfur on metal-silicate partitioning [START_REF] Christopher W Dale | Late accretion on the earliest planetesimals revealed by the highly siderophile elements[END_REF]. So far, no systematic study has been done on sulfur partitioning at pressures above 25 GPa or temperatures higher than 2400 K. Yet estimates of core formation conditions include pressures from 45 to 65 GPa and temperatures up to 4000 K (e.g., [START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF]Rubie et al., 2003Rubie et al., , 2011;;Siebert et al., 2012;[START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF].

In this work, metal-silicate partitioning experiments of sulfur were conducted at pressures from 46 to 91 GPa and temperatures between 3100 and 4100 K. Sulfur partitioning was quantified as a function of pressure, temperature and liquid metal composition. A general partition function was obtained from fitting a multiple linear regression model to a dataset which combines the results of this study with those of previous works. This partitioning function was applied to a core formation model to constrain the cumulative amount of sulfur which partitioned into the core and the mantle throughout accretion. The model takes into account different impactor sizes, changes in volatile compositions of impactor material over time and varying equilibration efficiency between impactor core and the Earth's mantle. The challenge of precisely quantifying the chemical composition in diamond anvil cell run products for such supposedly highly siderophile element at conditions of our experiments is addressed by the use of Nanoscale Secondary Ion Mass Spectroscopy (NanoSIMS). NanoSIMS provides both the spatial resolution (∼ 300 nm) and analytical resolution suitable for measuring the low sulfur content dissolved in the silicate quenched melt region of the run products. Transmission electron microscopy (TEM) was also used to determine the structure and composition of the quenched features in the metallic and silicate melts.

Methods

Starting Material

The metallic starting material consisted of a thin foil of iron alloyed with 3 to 6 wt.% sulfur. These alloys were synthesized by either the planar flow casting technique (Morard et al., 2011) or by low pressure metal-silicate partitioning experiments done in a piston cylinder at superliquidus conditions (in which case a 1 mm diameter (Fe,S) alloy was manually separated from the silicate in the quenched run product). Two starting silicate compositions were used as magma ocean analogs: A natural MORB (Mid Oceanic Ridge Basalt) from the East Pacific Rise in seven experiments, and a peridotite glass of KLB-1 composition synthesized by aerodynamic levitation laser furnace (e.g., [START_REF] Auzende | Synthesis of amorphous MgO-rich peridotitic starting material for laser-heated diamond anvil cell experiments application to iron partitioning in the mantle[END_REF] was used in two experiments. The composition and homogeneity of the starting alloy and silicates were checked using FEG-SEM imaging, SEM-EDX and electron microprobe analyses. Table A.4 reports their respective compositions.

Silicate starting materials were polished down to a thickness of 15-20 µm and the (Fe,S) alloys to ∼10 µm. These were machined with a femtosecond laser micromachining instrument to cut small disks of various diameters. Each experiment was prepared by the placement of a piece of alloy, 10 to 15 µm in diameter, between two silicate platelets of 60 to 80 µm in diameter inside a laser drilled rhenium sample chamber that was pre-indented to 30 to 40 µm. The silicate acts as a pressure medium and a chemical and thermal insulator (Fiquet et al., 2010). A small ruby is placed at the edge of the sample chamber to obtain pressure readings by ruby fluorescence before and after the experiment.

Laser heated diamond anvil cell experiments

The experiments were performed in diamond anvil cells equipped with culet anvils of 200 or 250 µm in diameter, coupled with a double-sided 200 W fiber laser (λ = 1070 nm). The laser (spot size10 to 20 µm) was focused on the contact between the alloy and the silicate from both sides. Spectra of the radiation emitted (range 500 to 750 nm) from the heated region were recorded from the two sides of the DAC simultaneously and temperatures determined by fitting the emission with a Planck function (Boehler, 2000). The temperature was ramped up quickly until a significant fraction of material in the region of the laser focus was molten at which point the temperature stabilizes 1 (Andrault et al., 2011;Siebert et al., 2012;Fiquet et al., 2010;Pradhan et al., 2015). All experiments were carried out at superliquidus conditions at run times between 45 seconds to two minutes, much longer than the few seconds required to reach chemical equilibrium at the length scales of DAC experiments (Siebert et al., 2012). Though the inner region of the sample is completely molten, the surrounding silicate provides thermal and chemical insulation from the diamonds. The experiments were quenched by cutting the laser power. The post quench pressures were determined by ruby fluorescence and were corrected for thermal pressure with a value of ∆P th ∼ 2.5.10 -3 GPa/K as used in previous works (Andrault et al., 1998;Fiquet et al., 2010;Siebert et al., 2012).

Sample Recovery

A focus ion beam (FIB) was used to recover thin sections of 3 to 5 µm in thickness, and 20 to 30 µm in length and width, from the experimental run products. Each section, sampled from the quenched molten region, is characterized by a metallic blob 5 to 10 µm in diameter, surrounded by a quenched liquid silicate pocket of several microns in extent (see Figure 2). The melt region is surrounded by rims of crystals and unreacted silicate. The sections were deposited onto a 5 cm 2 silicon wafer by a tungsten needle attached to a micromanipulator.

Compositional Analysis

The measurement objective of this study was to quantify the concentrations of sulfur in the metal and silicate phases of the quenched products. Several probes were used to obtain concentrations of major, minor and trace elements compositions of the samples.

EDX and Microprobe

The major element composition of the samples was characterized by energy dispersive X-ray analysis (EDX) with a Zeiss Crossbeam field emission gun (FEG) -Scanning electron microscopy (SEM). Typical operating conditions include accelerating voltage of 15 keV. The spectra were measured from regions of interests that are several µm 2 in size from both the silicate and metal during 60 seconds integrations. The major and minor element compositions were cross-checked with a CAMECA SX 100 electron microprobe. Operating conditions included an accelerating voltage of 15 keV, beam current of 10 nA, a spot size of 1 to 5 µm and counting times of 10-20 s on peak and background. Several oxides and pure metals were used as internal standards for the measurements: diopside (Si, Mg Ca), Fe 2 O 3 (Fe), orthoclase (K, Al), albite (Na), MnTiO 3 (Ti, Mn), Cr 2 O 3 (Cr), and pyrite FeS 2 (Fe, S).

NanoSIMS

The quenched silicates liquid in these experiments can have complicated fine structures, examples seen in Figure 2. Obtaining high precision, spatially resolved measurements of trace species from these small areas is challenging with standard petrologic tools. Previous works (e.g., Siebert et al., 2013;[START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF], studying metal-silicate partitioning from LH-DAC experiments, have used WDX or EDX spectroscopy with an electron microprobe (EMP) or a transmission electron microscope (TEM) to quantify compositions in quench products. Considering that sulfur was predicted to be highly siderophile at high pressure, neither of these techniques are capable of achieving the required analytical and spatial resolutions to quantify sulfur at a few tens of ppm at the micrometer scale. We address this challenge by measuring sulfur concentration in the silicate regions with a CAMECA NanoSIMS 50 installed at the Museum National d'Histoire Naturelle (IMPMC-MNHN), Paris.

The NanoSIMS is a new-generation SIMS(Secondary Ion Mass Spectroscopy) instrument developed by CAMECA (Hoppe et al., 2013). The probe uses a finely focused primary beam to erode the top atomic layers of the target material and produce secondary ions which are analyzed by a high-resolution multi-collection mass spectrometer. NanoSIMS measurements of the DAC samples were obtained in three sessions during which secondary ions of 16 O -, 28 Si -, 32 S -, 56 F e -and 43 AlO -were recorded for each sample. The mass resolving power (MRP) of the instrument was sufficient to resolve the species of interest from major interferences, for example 32 S -and 16 O - 2 . Precisely controlled raster of the primary beam across the sample surface are re-projected to produce high-resolution ion maps. As many as five maps were recorded simultaneously from the same sputtered volume.

Before the analysis, a large area of each samples is pre-sputtered for up to 10 minutes with a high primary current in order to implant primary ions of Cs + into the sample matrix (Hoppe et al., 2013). A 10 pA primary current of Cs + accelerated at 16 keV with a spot size of 300 nm was then used for the analysis. During the analysis, the beam was rastered over a square region which ranged from 8 x 8 to 20 x 20 µm. These areas corresponded to images that were 256 x 256 pixels. These image sizes and resolution were sufficient to cover the interesting regions in each sample. Integration times ranged from 30 minutes to 90 minutes during which several tens of data frames (up to 60), which recorded accumulated counts, were collected.

The data from the NanoSIMS ion images were analyzed with the analysis software L'image (Larry Nittler, Carnegie Institution for Science). All data frames obtained during the acquisitions were deadtime-corrected and aligned to produce a map of the total counts over all cycles, in each specie measured. Maps of the ratio between the species sulfur and silicon were then calculated. Regions of interest (ROIs), typically 1 to 2 µm 2 in area, were defined and measurements of the sulfur/silicon ratio extracted. The high resolution of the NanoSIMS maps, allowed small zones to be selected for analysis (see Figure 3).

Converting the NanoSIMS measurements from ratio of sulfur/silicon counts per second to sulfur composition relied on the linear dynamic range of the NanoSIMS and standard calibrations carried out during each session. Several glass standards with known sulfur and silicon compositions were used during each NanoSIMS session: NIST610 [START_REF] Sylvester | Analysis of Re, Au, Pd, Pt and Rh in NIST Glass Certified Reference Materials and Natural Basalt Glasses by Laser Ablation ICP-MS[END_REF], 456 ppm, CLDR01-5V (Chaussidon et al., 1991) 950 ppm, NMORB-blank1, internally synthesized, measured by EMP, containing 0 to 10 ppm (see Table B.5. The sulfur/silicon measurements obtained for the DAC thin sections were then compared to those obtained for the standards (see sulfur calibration curve Figure B.8). Sulfur concentration in the DAC samples were obtained by inverse regression following the method of Thomen et al. (2014).

Transmission Electron Microscopy (TEM)

To further understand the sub-micron structure of the samples, one sample (experiment # 9) which displayed features observed in other run products, was further prepared by FIB for analysis by TEM. This analysis was carried out with a JEOL 2100F field emission gun scanning TEM operating at 200 kV in several modes. High angle annular dark field (HAADF) imaging mode was used to examine quench features, e.g. Figure 4 a and d. Energy Dispersive X-ray (STEM-EDX) mode was used to map the chemical composition of quench features and to examine the superposition among different chemical species, for example, Figure 4 b,c,e, andf. Electron diffraction patterns were also collected from some features in the quenched region.

Results

General Appearance

The co-existence of a central metallic blob and a surrounding quenched silicate liquid pocket is evident in all of the experimental run products (See examples in Figure 2). The quenched silicate liquid is surrounded by unmelted starting silicate glass some of which has recrystallized. In some samples cracks are seen in the silicate phases. A space can be seen at interface between metal and silicate in some samples. These cracks and spaces are likely due to mechanical stresses incurred during decompression of the cell. The general appearance of these samples are consistent with previous superliquidus metal-silicate partitioning experiments performed on siderophile elements in diamond anvil cells (e.g., Siebert et al., 2012Siebert et al., , 2013;;[START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF].

Three distinct populations of metals are observed in the run products: the central larger blob which can vary in diameter from 4 to roughly up to 15 µm; smaller blobs that are a hundreds of nanometers in diameter; ∼50 nm sized grains that are ubiquitous in the quenched silicate liquids. The larger metal blob is the main reservoir of iron and siderophile elements while the medium sized blobs are metal fragments that did not coalesce before the experiment was quenched. The ∼50 nm metallic grains are interpreted as exsolutions from the molten silicate during quench and are discussed further in Section 3.2. Similar coupled metal-silicate morphologies, though at larger scales, have been observed in the run products of metal-silicate partitioning experiments of sulfur and siderophile elements done in large volume presses (e.g., [START_REF] Kilburn | Metal-silicate partitioning and the incompatibility of S and Si during core formation[END_REF]Corgne et al., 2008;[START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014).

Quench Texture

Several petrological textures consistent with rapid quench of metal and silicate melts from high temperatures are expressed in the experimental run products. The main metal blobs can exhibit two distinct textures; circular exsolutions of several tens of nanometers in diameter and larger, irregularly shaped exsolutions. Figure 2 shows this diversity of metal textures which have also been seen in previous studies (e.g., Siebert et al., 2012). EDX mapping under TEM of one irregularly textured region (from experiment # 9) shows that these features are predominantly composed of silicon and oxygen (Figure 5). It has been shown in previous work that these elements are increasingly soluble in liquid iron at higher temperatures and pressures (Siebert et al., 2012). These TEM observation supports the hypothesis that these textures in the metal correspond to Si-O rich phases that exsolved during the quench of the liquid metal. The silicate quench displays elongated textures on submicron scales when examined by TEM EDX, for silicon, magnesium, titanium, sodium, potassium (see Figure 4f). Similar textures, on a larger scale have been identified in quenched molten silicates of large volume experiments (e.g., [START_REF] Chabot | Core formation in the Earth and Moon: new experimental constraints from V, Cr, and Mn[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014). Such textures are generally interpreted as the result of rapid cooling of a silicate liquid from high temperatures (e.g., [START_REF] Chabot | Core formation in the Earth and Moon: new experimental constraints from V, Cr, and Mn[END_REF]Siebert et al., 2011;Boujibar et al., 2014).

The quenched molten silicate regions are also pervaded by spherical metal rich grains that are about 50 nm in diameter. High resolution TEM imaging and EDX mapping of experiment #9 (see Figure5) show that the grains are iron rich and contains significant amounts of sulfur. Some of these grains were further analyzed by TEM selected area electron diffraction (SAED). Due to the small size of these grains which are embedded in the surrounding by silicate phases, analysis of the diffraction patterns was not conclusive. However, some of the largest d-spacings measured were consistent with those of pyrrotite, a monoclinic (FeS) compound which has hexagonal polytypes and that has been observed in high temperature quench studies (Liles and de Villiers, 2012). This composition of the grains is also different from that of the main (Fe, S) blob of experiment #9 which contains less than 2 wt.% S. These observations therefore support a quench origin for the smallest metal grains in the silicate quench.

Inclusions similar in appearance have been observed in the silicate quench of previous metal-silicate partitioning studies, carried out in both large volume experiments on sulfur partitioning (Boujibar et al., 2014) and diamond anvil cell studies of siderophile elements [START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF]. Boujibar et al. (2014) investigated the sizes of similar grains found in the silicate quench of sulfur partitioning experiments as a function of quench rate and observed that their sizes decreased significantly at higher quench rates. Using XANES and EDX analyses, Boujibar et al. (2014) concluded that these exsolutions, consisting of FeS troilite had a very different composition than that of the main coalesced metallic pool. Their observations strongly argued for FeS exsolution upon quenching and higher solubility of sulfur in the silicate melt at high temperatures (Boujibar et al., 2014). The small sizes ( 50 nm), homogeneous distribution and inferred chemical composition of the smallest metal grains in the silicate quench of our experiments are consistent with exsolutions that would have formed during rapid quench when the laser power was cut. The occurrence of these grains are consistent with relatively high amounts of sulfur dissolved in the silicate melt at high temperatures in our experiments prior to their exsolution from the molten silicate phase during quench. This interpretation is consistent with the interpretation proposed by Boujibar et al. (2014) from lower P-T experiments on sulfur partitioning conducted in multi-anvil press and critical for the measurements of sulfur partitioning in metal-silicate experiments. Moreover, such inclusions enriched in siderophile elements with respect to the main metal blob were similarly observed in previous DAC experiments [START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF] and argue strongly for the quench origin of such features.

Composition

The compositions of the quenched silicate and main metal components of all the samples in this study (See Table 2) were obtained from a combination of SEM-EDX, EMP-WDX analyses for major and minor elements and NanoSIMS analyses for sulfur in the silicate. After melting, the main metal blob (which had a starting composition of Fe alloyed with 3-6 wt.% S) is still predominantly iron, 70 to 90 wt.% but now consist of 3-8 wt.% oxygen and up to 3 wt.% silicon which diffused from the silicate phase during melting.

The metal is also sometimes enriched in sulfur due to partitioning from the natural MORB and some S-rich heterogeneities in the DAC from the Fe,S starting material. The metal of some experiments also contains traces of carbon carbon (<1 wt.%) which most likely diffused from the molten silicate or possibly from the diamond anvils during the experiments. As previously observed (e.g., Siebert et al., 2012Siebert et al., , 2013;;[START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF], the quenched liquid silicate is enriched in FeO by a factor of 2-3 due to preferential partitioning of FeO into the melt from the unmelted silicate. Increased silicon partitioning into the metal at high temperatures could also increase the FeO content of the silicate melt through the exchange of oxygen between SiO 2 and Fe. The enrichment of FeO leads to the high oxygen fugacities in the experiments. The oxygen fugacity, expressed relative to the iron-wüstite (IW) redox buffer, is quantified with the ratio of the activity of FeO in the molten silicate and Fe in the molten metal, assuming an ideal mixing behavior (i.e. IW = 2Log [X F eO /X F e ]). The oxygen fugacity range of these experiments is -1.7 <∆IW <-1.0. Previous sulfur partitioning experiments were carried out at oxygen fugacities that were slightly lower than or similar to the current study (Boujibar et al., 2014;[START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]. No compositional gradients for major elements were detected within the metallic or silicate melts demonstrating that these experiments reached equilibrium. Diffusion rates of S 2-in silicate melts at temperature of 1400 • C (Watson, 1994) indicate that diffusive equilibration of sulfur is expected to occur in less than a minute over the typical 20 µm size of our experiments. This further supports that our experiments reached equilibrium since they were carried out at much higher temperatures (above 3000 K) and under superliquidus conditions.

In addition to composition obtained by EDX and EMP, compositional information were derived from the NanoSIMS maps. Figure 3 shows that there is a correlation between the metal rich areas and sulfur rich regions while the presence of AlO 3 corresponds to the silicate regions. As seen in the SEM images (Figure 2), the silicate regions of the sample can have a complicated structure and the high resolution of the NanoSIMS allows sulfur concentrations to be extracted from localized regions and from the top few atomic layers. This approach allows a more careful characterization of the silicate than is afforded by the EMP technique which is limited in spatial resolution. EMP measurements are usually averaged over a region of several cubic microns in volume. This leads to the possibility of contamination from the larger metal rich inclusions, which could be under the surface or even from the unmelted silicate. Thus the average of such measurements would not necessarily be reflective of the true composition of the quench silicate liquid.

The sulfur composition obtained by NanoSIMS from the quench silicate liquids is heterogenous at the submicron scale. In some cases, variability of a few thousands of ppm can be seen in a small region. For instances sulfur is enriched in the silicate at the edge of the main metal blob. Sulfur enrichment can sometimes due to uncoalesced metal fragments present in the measured areas, though these artifacts are not always evident in regions with enhanced concentrations. The conclusion from these observations is that sulfur is not homogeneously distributed in the silicate despite the experiments being fully equilibrated at high pressures and temperatures. Enrichment observed along cracks and boundaries are probably due to edge effects in the NanoSIMS measurements and these areas were not used to calculate compositions. Compositions are instead extracted from clean regions that are roughly in the middle of the melted silicate region, i.e. halfway between the edge of the metal blob and the edge of the quenched silicate. An average composition is obtained for each sample from several such regions. The partitioning coefficient is then quantified as the ratio of the average sulfur content in the metal blob and the average sulfur content in the silicate.

Parameterizing sulfur metal-silicate partitioning

Partition coefficients, which describe the distribution of an element between two immiscible phases, are functions of thermodynamic variables. Sulfur partitioning is known to vary with pressure, temperature, oxygen fugacity, silicate melt composition, and metallic melt composition [START_REF] Li | Element partitioning constraints on the light element composition of the Earth's core[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014). The partition coefficient of sulfur between metal and silicate D S can be expressed as:

D S = X metal S X silicate S ( 1
)
Where X metal S and X silicate S are the molar fractions of sulfur in the metal and silicate respectively. Sulfur is likely present as S 2-anions in silicate melts at oxygen fugacities relevant to core formation, below the iron-wüstite buffer (IW) (Boujibar et al., 2014). Therefore, it has been proposed by Mavrogenes and O'Neill (1999) that sulfur substitutes for oxygen in silicate melts under reducing conditions following the exchange reaction:

O 2-+ 1 2 S 2 = S 2-+ 1 2 O 2 (2)
Assuming the large majority of anions are O 2-, Mavrogenes and O'Neill (1999) considered the activity of O 2-to be constant and defined C s the sulfide capacity which can be seen as the equilibrium constant of reaction in Eqn. 2:

C S = X silicate S . f o 2 f S 2 1/2 (3)
where f S 2 and f O 2 are the sulfur fugacity and oxygen fugacity. The equilibrium between a silicate melt and liquid metal has been previously described (e.g. [START_REF] Kilburn | Metal-silicate partitioning and the incompatibility of S and Si during core formation[END_REF]Mavrogenes and O'Neill, 1999) following:

F eO silicate + 1 2 S 2 = F eS metal + 1 2 O 2 (4)
The Gibbs free energy of this reaction can be expressed using Eqn. 5 as:

- ∆ r G 0 (4) 2.303RT = log a metal F eS -log a silicate F eO + logC S -logX silicate S ( 5
)
Following [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF] and Boujibar et al. (2014) where a metal F eS is approximated as the product of X metal S , molar fraction of FeS and the activity coefficient γ of FeS in the metal, sulfur partitioning is expressed by the relation: the molar fraction of FeO in the silicate melt and a constant a that also accounts for other invariable contributions. Sulfide capacity value C S is calculated with respect to silicate melt composition following [START_REF] Haughton | Solubility of sulfur in mafic magmas[END_REF]. At conditions of high pressure and high temperature experiments, metallic liquids can accommodate light elements other than sulfur, mainly silicon and oxygen (Siebert et al., 2012). The effect of silicon on sulfur partitioning is difficult to quan-tify as suitable experiments containing significant amounts of these elements simultaneously in the metal phase are scarce.

logD S = log a silicate F eO -log γ metal F eS -log C S - ∆ r G 0 (4) 2.303RT (
However, this effect is assumed to be negligible considering that above 15 GPa structures of (Fe, Si) and (Fe, S) liquids are very similar which favors ideal mixing of silicon and sulfur in Fe-S-Si ternary system (Morard and Katsura, 2010). Additionally, no significant effect of sulfur on silicon partitioning has been previously reported (Siebert et al., 2004). Therefore, only one empirical term log(1-X O ) is added to account for the effect of oxygen on partitioning and is used as a proxy to describe activity coefficient of sulfur in the metal γ metal F eS . Finally, ∆G 0 (4) can be described by pressure and temperature dependent entropy, enthalpy and volume terms, which yield the form expected for the variation in metal-silicate partitioning with pressure, temperature and composition [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014):

log D m/s (S) = a + b T + c P T + logX silicate F eO -logC s + dlog(1 -X O ) (7)
Although f O 2 has been shown to have a significant effect on S partitioning (e.g. [START_REF] Kilburn | Metal-silicate partitioning and the incompatibility of S and Si during core formation[END_REF], its partitioning as described from Eqn. 6 is independent of f O 2 . Under reducing conditions (below IW-3) sulfur partitioning strongly decreases and sulfur even behaves as a lithophile element below roughly IW-4 [START_REF] Kilburn | Metal-silicate partitioning and the incompatibility of S and Si during core formation[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]; while under more oxidizing conditions between IW-1 and IW-3, covering the range of f O 2 of this work, partitioning likely remains constant [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]. However, the effect of f O 2 on partitioning is well captured by the model (i.e. Eqn. 7) through compositional changes with f O 2 represented notably by the FeO content of the silicate melt X silicate F eO and the sulfide capacity C S [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF].

The measured partitioning coefficients of sulfur in this study range from 8 to 55, (Table 1), with all but one point having partitioning below 25. No significant difference was observed in the partitioning between the two different starting silicate composition. The results of this study were combined with results from previous works [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF][START_REF] Chabot | Core formation in the Earth and Moon: new experimental constraints from V, Cr, and Mn[END_REF][START_REF] Li | Geochemistry of mantle-core differentiation at high pressure[END_REF] in order to obtain constants a, b, c, d from least square multivariable regression of the model shown in Eqn. 7. Note that the results of Boujibar et al. (2014) are not included due to the high carbon content of the quench metal in their experiments. A single regression provides an adequate fit to the full set of selected data, including pressures from 1 to 91 GPa and temperatures from 1873 to 4100 K, with the relation:

log D S = -3.30 (± 0.47) + 3000(±1023) T + 33(± 11) P T +ln X silicate F eO -ln C S + 14 (± 2) ln(1-X 0 ) (8)
Figure 6 reports sulfur partitioning from a combined dataset. Various interpolation of the data using the regression model, (Eqn. 8) as well as predictions from the regression model of [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF] are shown. Tabulated coefficients of the regressions constants from this study and two previous studies are shown in Table 3 for comparison. As with previous works [START_REF] Li | Element partitioning constraints on the light element composition of the Earth's core[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014) both b and c are positive indicating an increasing siderophile behavior with increasing pressure and decreasing siderophile behavior with increasing temperature. However, the constant b which is related to the enthalpy change of reaction ( 4) and effect of temperature is smaller than that of [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF] and larger than that of Boujibar et al. (2014). The constant c which is related to the volume change of reaction (4), is smaller than that obtained in those two previous works. This shows that pressure effect on sulfur partitioning has been previously over estimated using data from a smaller P-T range than this work. Finally, the d constant which is related to the oxygen content of the metal is about a factor of two less than the value obtained by Boujibar et al. (2014). Again, this difference may be explained by the regression of a dataset with a smaller range of oxygen contents in the metal (oxygen contents in the metal are below 0.5 wt.% in the other datasets) than in the present work where much higher temperatures greatly enhance oxygen solubility in metal (up to 8 wt.%). The regression models from previous works [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014) predicted that sulfur partitioning would increase strongly at higher pressures and decrease at higher temperatures. For instance, Rose-Weston et al. ( 2009) predicted sulfur partitioning to be above 5000 at pressures of 50 GPa and 3000 K, at least two orders of magnitude higher than the values that are directly measured in our study.

Discussion

Single stage core formation

Analyses of upper mantle samples yield a bulk silicate Earth with 200± 80 ppm (e.g. McDonough and Sun, 1995;[START_REF] Palme | Cosmochemical estimates of mantle composition[END_REF]Lorand and Alard, 2010;[START_REF] Wang | Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer[END_REF]Lorand et al., 2013). Using this estimate and composition of carbonaceous chondrites, a value of core-mantle sulfur distribution, D S ∼ 100± 30, is obtained (e.g. [START_REF] Wang | Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer[END_REF]Siebert and Shahar, 2015). In other words, if the record of core formation is still preserved in the mantle then similar values of metal-silicate partitioning for sulfur is required. On the other hand, the addition of ∼ 0.5±0.2 % Earth mass of volatile rich late accretion (constituted predominantly of carbonaceous-chondrite-like material such as CM) after core formation, has been proposed to account for a large fraction of the budget of sulfur in the present mantle (e.g. [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]. Using the new partitioning data for sulfur combined with a core formation model, new constraints are provided on ( 1) the amount of sulfur in the core, ( 2) the proportion of late accreted sulfur in the mantle, and (3) the relative timing for the origin of moderately volatile elements such as sulfur in the Earth.

The main result from these experiments is that sulfur is much less siderophile than expected from previous works [START_REF] Li | Element partitioning constraints on the light element composition of the Earth's core[END_REF][START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014) at the putative conditions of the base of the magma-ocean (∼ 55 ± 10 GPa; ∼ 3500 ± 500 K; (Siebert et al., 2012(Siebert et al., , 2013;;[START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF]. Partitioning measurements of sulfur at these direct coremantle equilibrium conditions range from 8 to 55 while Boujibar et al. (2014) and [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF] predicted partitioning coefficients which are at least an order of magnitude higher at these conditions. This is notably explained by the relatively lower positive pressure effect on partitioning found in this work. Accordingly, sulfur is more likely to behave as a moderately siderophile element such as nickel or cobalt rather than a highly siderophile element during Earth's differentiation. Using our new parameterization for sulfur partitioning (Eq. 8; Figure 6), a single stage core formation event (Stevenson, 1990) occurring between 45 and 65 GPa and 3500 and 4000 K (mantle liquidus from the mean of Fiquet et al. (2010) and Andrault et al. (2011)) at the present-day oxygen fugacity of core-mantle equilibrium (IW-2.3; X F eO =0.057; X F e =0.8) could not generate a core containing more than ∼ 1.2 wt.% sulfur to account for a maximum of 280 ppm sulfur in the man-tle; A low upper bound value considering previous geochemical estimates of sulfur in the core of approximately 2 wt.% (e.g. [START_REF] Dreibus | Cosmochemical constraints on the sulfur content in the Earth's core[END_REF]McDonough, 2003). However, single stage core formation models do not integrate the disparity of P-T-f O 2 -X conditions of equilibration over the course of accretion.

Multi-stage core formation model

Continuous core formation [START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF] or multistage core formation (Rubie et al., 2011) in which P-T-X conditions at the base of the magma ocean, the locus of final core-mantle equilibrium, change with time as the Earth grows has been proposed as a more physically plausible process.

The parameterized values of sulfur partitioning measured in this study are used to determine the behavior of sulfur in a similar scenario.

In the present model, the Earth accretes mass according to a linear growth function. Mass contributions of the impactors (embryos) to the Earth's mass were varied in order to investigate the effects of the delivery of sulfur by bodies with a large range of masses. The first ∼ 80 % of Earth's mass is delivered by small planetary embryos of roughly 0.1% Earth mass. The final ∼ 20 % of the Earth's mass is added by several embryos of 3 to 4% Earth mass followed by a larger body of 10 % the Earth mass, the approximate size of the proposed last giant impactor (eg., [START_REF] Canup | Forming a moon with an earth-like composition via a giant impact[END_REF]. The impactors that accreted to form the Earth are assumed to have been already differentiated into silicate mantles and metallic cores with similar core mantle fractions as the Earth (i.e. 68 wt.% mantle and 32 wt.% core). Minor amounts of chondritic material, 0.5 % Earth mass is added (as a single body) following the cessation of core formation to assess the effect of a "late veneer"(eg., Walker, 2009) on the sulfur abundance in the silicate Earth.

For each step of accretion, the metal and silicate equilibrate at the base of the magma ocean fixed at 40% of the growing Earth's core-mantle boundary pressure (Siebert et al., 2012) and at the temperature of the pyrolite liquidus at that pressure (estimated from Fiquet et al. (2010) and Andrault et al. (2011)). Evolution equations for the concentrations of sulfur in the core and sulfur in the mantle are derived from mass balance considerations in the accreting Earth following the approach of Rudge et al. (2010):

d dt (1 -F )M c m = [(1 -F )c me + kF (c ce -D s c m )] dM dt (9) d dt (F M c c ) = [kD s c m + (1 -k) F c ce ] dM dt ( 10
)
Where c m and c me are the concentrations of sulfur in the Earth's mantle and embryo's mantle respectively; c c and c ce are the concentrations of sulfur in the Earth's core and embryo's core respectively; F represents the mass fraction of metal (the same as Earth's current core mass fraction F=0.32); D s is the metal-silicate partitioning for sulfur calculated from Eq. 8 and k is the fraction of the embryo's that equilibrates with the Earth's mantle. This approach allows the investigation of the effect of partial equilibration of impactor cores with the Earth's mantle, for large differentiated embryos (eg. [START_REF] Dahl | Turbulent mixing of metal and silicate during planet accretion -And interpretation of the Hf-W chronometer[END_REF][START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF]. Complete equilibration is assumed (k=1, memory of differentiation in the embryo is lost) during the accretion of the first 80 % of the Earth as emulsification of metallic cores from the small embryos into ∼ 1 cm size droplets allow full metal-silicate equilibrium (Rubie et al., 2003). Partial equilibration is included in the model only during the addition of the final larger bodies as complete emulsification of large cores is unlikely. Only a fraction k (which varies from 0.1 to 1) of the large impactor cores re-equilibrates with the Earth's mantle while the remaining fraction (1-k) is added directly to the Earth's core (See Eq. 9 and Eq. 10).

The evolution of sulfur concentration in core and metal also depends on the quantity of silicates that equilibrates with the metal. According to hydrodynamic model from [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF], a parameter for the equilibrium efficiency of sulfur E s is defined to express the mass exchange between the segregating core and mantle normalized by the maximum possible mass exchange (i.e. k=1 and metal infinitely diluted into the mantle; See [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF] for further details):

E s = k 1 + Ds ∆ (11)
Where ∆ the ratio of equilibrated silicate to equilibrated metal (dilution ratio) can be expressed at each step of accretion following [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF] and Badro et al. (2016) as:

∆ = ρ silicate ρ metal 1 + 0.25 δ 1/3 3 -1 (12)
In which ρ silicate and ρ metal are the densities of silicate and metal respectively, and δ is the ratio of the impactor mass to Earth mass. Then, as discussed in [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF], using the equilibration efficiency E s in place of k in Eq. 9 and Eq. 10 yields the following expressions for the compositional evolution of sulfur in the mantle and core:

d dt (M c m ) = c me + E S F 1 -F (c ce -D s c m ) dM dt (13) d dt (M c c ) = [E S D s c m + (1 -E)c ce )] dM dt (14)
(Notations modified from [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF] to be consistent with those of Rudge et al. (2010)).

The stage of growth at which sulfur was added to the Earth can have strong implications for the distribution of sulfur in the core and mantle. Two different accretionary scenarios were considered. In the first referred as the "homogeneous"scenario, sulfur is added continuously by embryos containing a bulk sulfur content similar to that estimated for the Earth of 6400 ppm (Mc-Donough, 2003). In the second case referred as the "heterogenous"scenario, sulfur is added only in the last 20 % of accretion by larger planetary embryos containing a bulk sulfur content of roughly 2.5 wt.% in order to obtain the bulk Earth sulfur content of 6400 ppm at the end of accretion.

Results of the modeling are reported in Figure 7. The main result of the "homogeneous"case is that it yields higher sulfur content (above 500 ppm) than the observed bulk silicate Earth values (200 ± 80 ppm). The mantle concentration reaches quickly high sulfur content (above 400 ppm) as the magma ocean depth allows for efficient re-equilibration of the small cores of accreting embryos with the mantle (E S up to around 0.3). Strong decrease of sulfur partitioning at the high temperature of the base of the deepening magma ocean quickly drives the sulfur mantle content toward a value around 450 ppm. The sulfur content of the mantle drops to lower values (below 400 ppm) during the last 20% of accretion as equilibrium efficiency is significantly lowered for large impacts where impactor core diameters approach the magma ocean depth [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF]. Finally, a late veneer consisting of 0.5 % Earth mass (Walker, 2009;[START_REF] Brenan | Core formation and metalsilicate fractionation of osmium and iridium from gold[END_REF] and average carbonaceous composition (calculated after [START_REF] Fegley | Planetary scientist's companion[END_REF]) is added to obtain a final mantle sulfur budget slightly above 500 ppm. This is at least two times more than the observed sulfur content of the mantle. As moderately siderophile elements such as Ni and Co require that a significant fraction of metal must have undergone re-equilibration with the mantle (Rudge et al., 2010), our results thus rule out the possibility of continuous accretion of volatile elements such as sulfur during the process of accretion and core formation of the Earth. Additionally, for any considered oxygen fugacity variation during accretion, either starting from highly reduced components (Wood and Halliday, 2005) or oxidized components (Siebert et al., 2013), a model (with continuous addition of sulfur) leading to the 200 ± 80 ppm sulfur in the present-day Earth's mantle was not obtained. In agreement with the conclusion raised for the single stage core formation model, only a bulk Earth containing lower amounts of sulfur could account for the observed mantle composition. However, this seems at odds with lower bound cosmochemical estimates of bulk Earth sulfur content (eg., McDonough and Sun, 1995;[START_REF] Dreibus | Cosmochemical constraints on the sulfur content in the Earth's core[END_REF][START_REF] Allègre | Chemical composition of the earth and the volatility control on planetary genetics[END_REF][START_REF] Palme | Cosmochemical estimates of mantle composition[END_REF]. Such change in the bulk Earth sulfur content would imply that the order of element volatility calculated for solar nebula condensation is not applicable to planetary composition which is a controversial issue (O'Neill and [START_REF] Kegler | New Ni and Co metal-silicate partitioning data and their relevance for an early terrestrial magma ocean[END_REF]Wang et al., 2016).

Over enrichment of sulfur in the mantle has been reported in recent work by [START_REF] Schubert | [END_REF] using N-body accretion simulations. Strong decrease of sulfur solubility in silicate melt with decreasing temperature at high pressure has been predicted by Laurenz et al. (2016). Therefore, exsolution of FeS from the magma ocean upon cooling at high pressure and segregation by sinking to the core is proposed as a potential mechanism to reduce the mantle's sulfur content [START_REF] Schubert | [END_REF]. The present dataset does not report sulfide saturation experiments and is not directly applicable for estimating sulfur solubility at HP-HT. However, sulfur partitioning between FeS and silicate predicted from sulfide saturation experiments at P-T conditions of the magma ocean (Laurenz et al., 2016) is at least an order of magnitude higher than sulfur metal-silicate partitioning obtained directly at these conditions from our work. The very strong negative pressure effect on sulfur solubility reported by Laurenz et al. (2016) likely explains such discrepancy. Additionally, a correction for sulfur activity in metal is missing, which would be necessary for a proper comparison of this work and solubility measurements (Laurenz et al., 2016). FeS saturation experiments at direct conditions of the bottom of the magma ocean are required to precisely quantify the relevance of such mechanism to strip the excess sulfur of the mantle to the core.

In contrast with the "homogeneous"case, "heterogenous"accretion can match the observed mantle sulfur content of 200 ± 80 ppm (Fig. 7). Late addition of sulfur in roughly the last 20 % of accretion from large planetary embryos (from 3 to 10 % of Earth's mass) implies much lower re-equilibration efficiency of the metal which results in more sulfur being added to the core (∼1.9 wt.%). This scenario allows for a bulk Earth sulfur content of roughly 6000 ± 1000 ppm as implied by the volatility trend of elements in the Earth (eg., McDonough and Sun, 1995;[START_REF] Dreibus | Cosmochemical constraints on the sulfur content in the Earth's core[END_REF][START_REF] Allègre | Chemical composition of the earth and the volatility control on planetary genetics[END_REF][START_REF] Palme | Cosmochemical estimates of mantle composition[END_REF]. However, core formation model involving higher mass fraction of silicate mantle that re-equilibrates with accreted metal than the present model (from 3 to 10 % for the final impacts) would lead to an excess of sulfur in the mantle. The heterogeneous scenario including late volatile addition and sulfur-rich iron liquid segregation to the core, often referred as the "Hadean Matte", has been invoked to explain numerous observations: (1) a low density layer at the top of the core (eg., [START_REF] Helffrich | Causes and consequences of outer core stratification[END_REF]; (2) the mismatch of various core formation chronometers (Wood and Halliday, 2005); (3) the abundance of moderately siderophile elements such as W and Mo in the mantle [START_REF] Christopher W Dale | Late accretion on the earliest planetesimals revealed by the highly siderophile elements[END_REF]; ( 4) the suprachondritic Ru/Ir and Pd/Ir ratios in the Earth's mantle (Laurenz et al., 2016); ( 5) dynamical models such as N-body simulations showing late accretion of materials derived from further out in the solar system (Raymond et al., 2006;Morbidelli et al., 2012) or ( 6) isotopic composition of the bulk silicate Earth and chondrites in Ag or Cu (Schönbächler et al., 2010;Savage et al., 2015). If the ability of incomplete equilibration to produce the above mentioned geochemical signatures needs to be explored, the heterogeneous model is compatible with a major fraction of the sulfur in the mantle being inherited from core-mantle differentiation as was proposed to explain sulfur isotopic composition of the BSE [START_REF] Labidi | Non-chondritic sulphur isotope composition of the terrestrial mantle[END_REF].

Conclusion

Laser heated diamond anvil cell experiments have been performed to study the metal-silicate partitioning behavior of sulfur at pressures and temperatures relevant to core formation in a deep magma ocean (above 40 GPa and 3500K). At these conditions, sulfur is less siderophile than previous estimates based on thermodynamic extrapolations from lower P-T experiments [START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]Boujibar et al., 2014). Direct application of these partitioning results to a single stage core formation model shows that Earth's core cannot contain more than 1.2 wt.% sulfur to account for the present sulfur content of the mantle. More complete modeling including changes in P-T-Xf O 2 conditions during the growth of the Earth, partial equilibration of both metal and silicate and the relative timing of sulfur delivery during accretion have been performed. A model of continuous delivery of volatile elements, the "homogeneous"case, yields an excess of sulfur in the mantle and could only be reconciled with a lower bulk Earth content and Earth's core sulfur content (∼ 3000 ppm and ∼ 1 wt.% respectively) than proposed from geochemical estimates (roughly 6000 ± 1000 ppm and 2 wt.%). Late addition of sulfur during the last 20% of Earth accretion, the "heterogenous"case, from large differentiated planetary embryos provides a possible mechanism to obtain 2 wt.% sulfur in the core and to match the observed sulfur content of the mantle due to significantly lowered metal-silicate equilibrium efficiency. The potential presence of volatile elements as core formation proceeds requires low degree of core-mantle equilibration to explain the mantle abundance of these elements. This implies that a major fraction of sulfur in the present mantle records the imprint of core-mantle equilibrium.

For any accretion and core formation scenarios, the low partitioning values of sulfur between metal and silicate at P-T conditions of the base of the magma ocean rule out sulfur as a major light element for Earth's core (i.e. there is less than 2 wt.% sulfur in the core). In contrast with recent works [START_REF] Jacobson | Highly siderophile elements in Earth/'s mantle as a clock for the Moon-forming impact[END_REF][START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O[END_REF][START_REF] Schubert | [END_REF], we argue that sulfur and by analogy other volatiles were not accreted continuously during Earth's accretion. Models favoring later addition of volatiles and sulfur, either during the last 10-20% of accretion similar to our heterogeneous model (eg., O'Neill, 1991;[START_REF] Christopher W Dale | Late accretion on the earliest planetesimals revealed by the highly siderophile elements[END_REF]Wood et al., 2014;Wohlers and Wood, 2015), or by the late veneer only [START_REF] Albarede | Volatile accretion history of the terrestrial planets and dynamic implications[END_REF]Marty, 2012;[START_REF] Ballhaus | The u/pb ratio of the earth's mantle-a signature of late volatile addition[END_REF][START_REF] Wang | Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer[END_REF] are promoted.

Tables

Run # Pressure (GPa) 2009) for 3000 K is also shown (grey line). The shaded region is the pressure range of coremantle equilibration proposed by previous works (Siebert et al., 2012).

Temperature (K) D m/s ∆ IW X FeO sil X Fe met X S met X O met X Si met †1 3100
Figure 7: Sulfur accreted to the mantle for two accretionary scenarios, "homogeneous"and "heterogenous"accretion. In the "homogeneous"case bodies contain the same amount of sulfur throughout accretion. During "heterogenous"accretion sulfur is only added after the Earth has accreted to ∼ 0.8 of its mass fraction and bodies richer in S are added. 1995, Borisov 2000, Brenan 2009, Ertel 2008]. Even more intriguing is that these elements are present in the PUM in broadly chondritic relative proportions [Morgan 1981, Lorand 1999, Becker 2006]. These observations support the "late veneer"hypothesis which postulates that chondritic material was delivered to the Earth after it had fully differentiated [Chou 1978[START_REF] Chou | [END_REF][START_REF] O'neill | [END_REF], Drake 2000]. Following from this is the assumption that the mantle's HSE content reflects the mass of carbonaceous chondrite material that was delivered during the last stage of the Earth's accretion. The inferred mass contribution of the late veneer (0.5 to 0.7 % mass of the that the HSE might have a similar tendency at elevated pressures and temperatures [Murthy 1991, Righter 1997, Yokoyama 2009] and several recent works have been carried out in large volume presses to test this hypothesis [Danielson 2005, Cottrell 2006, Ertel 2006, Righter 2008, Mann 2012, Bennett 2014]. [Righter 2008] showed that the metal-silicate partitioning of palladium decreased substantially with increased pressure and temperatures to values that could explain its PUM abundance. [Mann 2012] showed that all the HSE become less siderophile at high temperatures and pressures though they do not converge to the values required to explain their relative chondritic abundances. [Bennett 2014] predicted that at temperatures >3500 K, the PUM abundance of platinum could be explained by metal-silicate partitioning alone. However, the partitioning behavior of the HSE have not been characterized at pressures above 25 GPa and temperatures above 2400 K. The main goal of this work is to investigate the metal-silicate partitioning behavior of platinum at pressures and temperatures directly relevant to core formation. The partitioning of platinum is relevant to the other HSE particularly the platinum groups elements (PGE) -Ru, Rh, Pd, Os, Ir, due to the similarities in their bulk chemical and physical properties.

Figures

Formation of nanonuggets and micronuggets of platinum and the other PGE in silicate melts has retarded the acquisition of accurate measurements of solubility and partitioning for these elements [Ertel 1999, Cottrell 2006[START_REF] Fortenfant | Temperature dependence of Pt and Rh solubilities in a haplobasaltic melt[END_REF], Mann 2012]. This is a controversial topic with ambiguous experimental evidence for the origin: quench vs. stable inclusions, for these features [Brenan 2015]. [Cottrell 2006] presented evidence of the quench origins of these inclusions and reported partitioning coefficients which incorporated inclusions in the Pt composition of the silicate melts. Other stud-ies have put forth evidence that these inclusions are stable at high pressures and temperatures and should be avoided in determining solubilities and partitioning coefficients [Ertel 2008, Médard 2010[START_REF] Médard | [END_REF], Malavergne 2016]. Whether nuggets are averaged with composition or not can significantly affect the partitioning values and this has resulted in very different partitioning coefficients being reported for the same set of conditions [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], Cottrell 2006, Ertel 2006, Bennett 2014]. Additional factors that have affected the interpretation of measurements of partitioning for these elements include the common use of synthetic silicate melts which are of haplobasaltic diopside-anorthite compositions [eg.,] [START_REF] Fortenfant | Temperature dependence of Pt and Rh solubilities in a haplobasaltic melt[END_REF], Ertel 2006]. Some studies have also shown that melt composition can have a large impact on solubility e.g., [O'Neill 2002[START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF]. Solubilities in these melts would not necessarily be reflective of the bonding networks present in peridotite melts. [Borisov 2011] showed that SiO 2 content of the melt has an effect on solubilities. The metal compositions used in some studies is also often times pure PGE, i.e. Fe free melts. The presence of Fe will have an effect on the redox state of the experiments and hence the partitioning behavior [Laurenz 2010]. Thus some previous studies might not have been representative of or relevant to core formation in a magma ocean.

This chapter presents the first metal-silicate partitioning data of platinum at the putative pressures and temperatures of core-mantle equilibration. Seven experiments were carried out in a laser-heated diamond anvil cell (DAC) at pressures from 33 to 110 GPa and temperatures from 3600 to 4300 K. Nanoscale Secondary Ion Mass Spectroscopy (NanoSIMS) with a spatial resolution of ∼ 300 nm and high elemental sensitivity, is used to measure the platinum concentration in the quenched silicate of the experimental run products. This approach overcomes the analytic challenge of reliably measuring trace element concentrations in micron sized DAC run products. The partition coefficients obtained from this study are combined with those from previous studies on platinum partitioning in order to assess temperature, pressure and oxygen fugacity

Methods and Materials

111 dependencies in the range of conditions relevant to core formation. The results are applied to a core formation model in order to assess the effect of equilibration in a magma ocean on the mantle's platinum content.

Methods and Materials

The 5.2. After the quench, a thin section of 3 to 5 µm in thickness and 20 to 30 µm in length and width is recovered from the molten region of each sample with a focused ion beam (FIB).

The sections are then placed flat on a silicon wafer and prepared by ion polishing for compositional analysis. The major element composition of the samples was characterized by energy dispersive X-ray analysis (EDX) with a Zeiss Crossbeam field emission gun (FEG) -Scanning electron microscopy (SEM). Quantitative information was derived using the PhiRhoZ method. The platinum concentration of the quenched silicate portion of the samples was measured by means of NanoSIMS ion images with the procedures described in Chapter 2.

Before imaging, an area of each sample of about 15x 15 µm was first cleaned with a beam of 330 pA for about 10 minutes. A primary current of 23 to 26 pA was used for imaging. Images covered an areas of about 9 x 9 µm (128 square pixels). The species measured were 24 C 2 , 28 Si, 32 S, 27 Al 16 O and 194 P t. Figure 5.2 shows the maps obtained in 4 of these species. The mass resolving power was 5000 for 28 Si at 300 cps. To compensate for low signal in platinum, smaller areas were imaged for longer integration times.

Results

General Appearance

The coexistence of liquid metal and a quenched silicate surrounded by rims of recrystallized silicate is seen in all the experimental run products. Metal blobs can be up to 15 µm in diameter, while the quenched silicate region is several microns in width.

As with other metal-silicate partitioning experiments carried out in DAC, the silicate melt quenches to a homogenous phase, see Figures 5.1. No significant differences were noted between the appearance of these run products and those from partitioning experiments of other elements carried out in DAC [Siebert 2012, Siebert 2013, Fischer 2015].

As with the aforementioned studies, the quench silicate portions of these sample from this study display a population of metallic inclusions that are ∼ 50 nm in size that are dispersed uniformly throughout the silicate. Figure 5.1 a. shows a high resolu-

Results

113

tion image of the silicate region of one sample. These features have been attributed

to rapid quench from high temperatures [Siebert 2012, Siebert 2013, Fischer 2015].

Transmission electron microscopy (TEM) studies of similar features from sulfur partitioning experiments are reported in Chapter 3, where their quench origin were ascertained. These features are notably different in appearance from the nanonuggets that have been observed in previous partitioning or solubility experiments on platinum [Malavergne 2016, Ertel 2008]. At very high experimental temperatures, such as those of our experiments, the contribution of stable inclusions to the measured concentrations is likely to be small [Brenan 2015].

Composition Analysis

The compositions of the quenched metal and silicate components obtained from SEM-EDX and NanoSIMS are reported in [Siebert 2012, Siebert 2013, Fischer 2015]. This enrichment has been attributed to preferential partitioning of FeO from unmelted silicate phases or a reaction involving the exchange of oxygen between SiO 2 and Fe in the silicate melt. These FeO compositions result in oxygen fugacities of -0.75 to -1.50 calculated relative to the iron-wüstite redox buffer quantified with the ratio of the activity of FeO in the molten silicate and Fe in the molten metal, assuming ideal mixing behavior (i.e. IW = 2Log X F eO /X F e ). Overall, the major element composition of the quenched metal and silicate are homogeneously distributed which implies strongly that equilibrium was attained during the experiments.

NanoSIMS

NanoSIMS ion maps covering areas of up to 20 x 20 µm were obtained of each sample for the species measured.

Parameterization

Metal silicate partitioning of highly siderophile elements have been shown to be functions of thermodynamic variables, pressure (P), temperature (T), oxygen fugacity (fO 2 ), liquid metal and silicate compositions e.g., [START_REF] Borisov | Solubility of palladium in silicate melts: Implications for core formation in the Earth[END_REF][START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], Mann 2012, Bennett 2014]. The equilibrium partitioning of platinum between metal and silicate can be described by a redox reaction:

P tO n/2 = P t n+ + (n/4)O 2 (5.4.1)
At equilibrium, the Gibbs free energy, G 0 of this reaction is related to the equilibrium constant, K by the equation:

∆G 0 r -RT = lnK = ln[ aP t n+ O n/2 (aP t)(f O 2 ) n/4 ] (5.4.2)
Where a is the activity of the partitioning species, Pt. Replacing the activity terms, a i with X i γ i and rearranging gives:

ln   X P t X P tO n 2   = ∆G 0 r -RT - n 2 lnf O 2 + ln γP tO n 2 γ P t (5.4.3)
Expanding the free energy term, (∆ G 0 r = ∆ H 0 r -T∆ S 0 r + P ∆ V 0 r ) and substituting the partition coefficient X P t X P tO n 2 gives: (5.4.4) (Derivation followed from [Brenan 2015] and [Bennett 2014]).

lnD met sil = ∆H 0 r RT - ∆S 0 r R + P ∆V 0 r RT - n 4 lnf O 2 + ln γ P tO n 2 γ P t
For our experimental data, we do not consider the activity coefficients. The model used for the regression is:

lnD met sil P t = a + b T + c P T + dlnf O 2 (5.4.5)

Results

119

The term a is related to the valence of the metal (platinum) in the silicate melt, b to the enthalpy and c to the volume change of reaction. The partitioning measurements at specific temperature, pressure, oxygen fugacity are then used to regress for these constants by multiple linear regression.

Partition coefficients are calculated as the ratio of platinum in the metal and the silicate, D P t =

X metal P t X silicate P t
, where X is molar fractions .

Regression Analysis

The partitioning data obtained in this study are combined with results from the works of [Mann 2012[START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF]] and [Bennett 2014] in order to assess the temperature, pressure and oxygen fugacity effects on partitioning. Figure 5.3 shows the temperature dependencies with the data sets of [Bennett 2014] and [Mann 2012]. Our data is in good agreement with the temperature and oxygen fugacity dependence predicted [Bennett 2014] from the expression log[D m/s (Pt)] = a + b T + d ∆ IW. A regression of the combined dataset leads also to similar values for the constants a, b and d, summarized in Table 5.3. Data selected from previous works for the regression are of similar oxygen fugacities to our experiments and were also obtained at pressures of 2 GPa or above. Compositional terms were not included in the regression as previous studies did not report trace elements Si or O in the metal which were either absent or below the detection limit of those measurements.

The combined effect of temperature, pressure and oxygen fugacity is also assessed for the same dataset with a regression model that incorporates the three quantities log[D m/s (Pt)] = a + b T + c P T + d ∆ IW. The effect of pressure is small though the value of the c term is slightly higher than those reported by previous works. Pre-122 Chapter 5. Platinum partitioning at core formation conditions vious work reported a strong pressure effect between 1 to 6 GPa [Mann 2012] while no significant change in partitioning was seen at pressures between 6 and 18 GPa [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF]]. Though [Ertel 2006] reported a strong pressure effect up to 14 GPa.

The pressure dependent regression is shown in figure 5.4. The results of this study and previous work have shown that P is unlikely to have a substantial effect on partitioning for Pt, Re and Au (Danielson et al., 2005;Bennett and Brenan, 2013).

Discussion

In order to explain the PUM platinum abundance by core-mantle equilibration, a metal-silicate partitioning value of ∼ 400 to 950 is required [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], Mann 2012] to yield a final mantle of 6 ppb of Pt as observed by [Lorand 2008, Becker 2006]. Some of the partitioning values measured in this study are within an order of magnitude of the required value, see Table 5.2 contrary to the values reported by [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF]] and [Ertel 2006]. The values reported here are also several orders of magnitude lower than those measured in previous experiments [START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], Ertel 1999]. This difference can be due to several factors including different silicate melt compositions as well as the lower pressure and temperature regime of those measurements. Our measurements however provide confirmation that extrapolations of platinum partitioning to high P-T conditions of some previous works are accurate eg., [Bennett 2014], see Figure 5.3. The partitioning of other HSE have shown this general trend, as metal-silicate partitioning of palladium measured by [Righter 2008] decreased significantly with pressure and temperature. [Mann 2012] also showed that the partition coefficient of all the HSE decrease significantly with P and T.

Values of partitioning obtained using our new regression model for pressure of ∼ 60

GPa, temperatures of ∼ 3800 which are considered as the effective P and T of a final core-mantle equilibration are used to calculate the mantle's platinum content with a Chapter 5. Platinum partitioning at core formation conditions mass balance argument. The oxygen fugacity is assumed to be between IW between -1 and -2. A bulk Earth of chondritic composition is assumed. The resulting mantle has a platinum content of 1 to 5 ppb which is a substantial amount of the value reported for the PUM of about ∼ 8 ppb [Becker 2006]. The result of this model implies that core-mantle equilibration did not entirely strip the mantle of platinum. A similar conclusion was made from the study of palladium partitioning by [Righter 2008] who reported a partitioning values of ∼ 500, which adequately accounts for the mantle's between HSE and sulfides in mantle samples [Alard 2000, Lorand 2001, Lorand 2008].

[ Laurenz 2016] and [START_REF] Schubert | [END_REF]] have proposed that due to the lowered sulfides solubility in silicate at decreasing temperatures and high pressures, sulfur could exsolve as FeS and potentially segregate to the core. This process could also potentially strip the mantle of its HSEs and in this case a mostly chondritic late veneer could still have supplied the HSE observed in the mantle. Testing these hypotheses requires experiments on sulfide-silicate partitioning and sulfide saturation experiments at conditions relevant to core formation and a cooling magma ocean.

Conclusion

Metal-silicate partitioning coefficients were measured for platinum at pressures and temperatures directly relevant to core formation in a LH-DAC. These experiments were carried out between a natural MORB composition silicate melt and an alloy of Pt and Fe. The experimental results confirm the predictions of previous works that partitioning of platinum decreases with increasing temperatures. Regression models of combined datasets were used to derive an expression for platinum partitioning over a large range of P-T conditions. The accumulated platinum in the mantle based on modeling with the new partitioning result is close to its observed PUM abundance.

Magma ocean equilibration could therefore have played a role in establishing the mantle's platinum signature though a late veneer probably imprinted a chondritic signature on the mantle's HSE. If the mantle's HSE content is sourced from both endogenous and meteoritic origins then a model which considers partial equilibration during giant impacts or late sulfide segregation could reconcile these measurements with the observed HSE content of the mantle.

Chapter 6

General conclusion

Metal-silicate partitioning of sulfur and platinum have been investigated at pressures and temperatures directly relevant to core formation. High pressures and temperatures were achieve with a laser heated diamond anvil cell setup. Experiments were carried out at pressures from 40 to 110 GPa and temperatures between 3000 and 4300.

The fO 2 conditions ranged between IW -1 and -2. The use of NanoSIMS to analyze compositions in the DAC run products provided high fidelity measurements and revealed previously unexplored fine structures in such samples. TEM observations also provided further evidence that some features in the silicate melts were of quench origin.

The main experimental result for sulfur is that it becomes less siderophile at high pres- Mots clés : core-mantle équilibration, océan de magma, LH-DAC, NanoSIMS

Subject : The metal-silicate partitioning of sulfur and platinum during formation of the terrestrial core Résumé : Measurements of the metal-silicate partitioning behavior of siderophile and volatile elements at the conditions of the deep primitive Earth can provide constraints on the mechanisms of terrestrial core formation. Experiments were conducted in a laser-heated diamond anvil cell to investigate the metal-silicate partitioning of sulfur and platinum at high pressures and temperatures. The partitioning behaviors were quantified post-experiment by high resolution NanoSIMS imaging. Sulfur was found to be moderately siderophile at core formation conditions and this, together with cosmochemical estimates, argue that it cannot be a major light element in the core. Accretion modeling with this new partitioning data implies that a heterogeneous accretion scenario can best explain the mantle and bulk Earth sulfur contents. The measured partitioning values for platinum are such that the mantle's platinum abundance can be sufficiently explained by coremantle equilibration. Overall these results support the hypothesis that the cores of large impactors did not equilibrate fully with the magma ocean and metal could have sequestered to the Earth's core without leaving a record in the mantle. A late sulfide segregation event also likely played a role in establishing the observed mantle compositions. These findings help to further elucidate the accretion history of the Earth and core-mantle differentiation processes.

Figure 1 . 3 :

 13 Figure 1.3: Mantle Elemental Abundances showing the depletion of siderophile elements with respect to chondrites. Figure modified from [Drake 2002].

1. 4 .Figure 1 . 5 :

 415 Figure 1.5: Cobalt and nickel partitioning place constraints on the pressures and temperatures of core-mantle equilibrium [Siebert 2012, Siebert 2015] as compared to previous studies.

1. 5 .

 5 Figure 1.6: Pressure and temperature of the metal-silicate partitioning experiments in LH-DAC carried out in this work. The peridotite and MORB liquidii are shown for comparison and the P-T range for core-mantle equilibration constrained by Ni-Co partitioning.

1. 5 .

 5 Parameterizing Metal-Silicate Partitioning 13 = TdS + µdN + VdP, such that dG = dH -TdS + PdV, at constant pressures and temperatures.In the case of unchanging P and T: Eqn 1.5.7 reduces to,

Chapter 2 .

 2 and sulfur in quenched silicate glass after metal-silicate equilibration partitioning experiment at high pressures and temperatures in a diamond anvil cell (DAC). The samples extracted from the DAC experiments are small and delicate, typical dimensions are 20 µm x 4 µm x 10 µm. The standard techniques for measuring HSE concentrations, laser ablation inductively coupled mass spectrometer (LA-ICPMS) and secondary ion mass spectroscopy (SIMS), have spatial resolutions of ∼ 50 µm and 10 µm respectively. These would not provide spatially resolved compositional measurements on DAC samples. The predicted concentrations of HSE and sulfur in silicate melts, at the pressures and temperatures of this study (based on previous works [Cottrell 2006, Mann 2012, Bennett 2014, Boujibar 2014]) were quite low, ∼ 2 to 20 ppm for platinum and ∼50 to 200 ppm for sulfur. These values were close to or below detection limits of the other standard petrologic probes, the Electron Microprobe (detection limits for Pt Pd and Au being 60, 20, 70 ppm respectively). The high spatial resolution and elemental sensitivity of the NanoSIMS therefore made it the best choice for probing DAC samples in this study.Figure 2.16 .b and .c show a comparison be-18 Materials and Methods tween the LA-ICPMS and NanoSIMS footprints. Measurements with the NanoSIMS are reliant upon standard calibrations which required standards similar in structure and composition to the expected quenched silicate from DAC experiments. Silicate standards were synthesized in-house, purchased or obtained from previous study. These standards contained varying amounts of the elements Pt, Pd and Au. In order for

Figure 2 . 3 :

 23 Figure 2.3: Time resolved LA-ICPMS spectra for Pt, Pd and Au in doped natural MORB

Figure 2 . 4 :

 24 Figure 2.4: Time resolved LA-ICPMS spectra for Pt in synthetic MORB samples. The first two samples contain uniform concentrations of platinum (11 and 16 ppm respectively).The small variability is due to the laser ablation process and the signal is averaged to calculate concentrations. The third sample shows concentration spikes due to heterogeneities and nuggets. The latter was not used as a standard.

Figure 2 . 5 :

 25 Figure 2.5: SEM images of piston Cylinder synthesis experiments. a. ELMO 145 with central metal blob surrounded by silicate glass and an MgO capsule. b. Quench silicate region with typical quench features from ELMO 139. c. FeS alloy with small droplets due to liquid immiscibilities upon quench. d. ELMO169 EDX map of silicates next to the capsule.

Figure 2 . 6 :

 26 Figure 2.6: Optical images of pure metal standards.

Figure 2 . 7 :

 27 Figure 2.7: SEM images of a. and b. Pd nuggets in NMORB from levitation furnace with Ar-H 2 gas. c. Pt nugget from an NMORB sample from air levitation synthesis. d. polyhedral Pt nuggets in an FMORB sample synthesized in furnace.

Chapter 2 .

 2 Figure 2.9: A symmetric Diamond Anvil Cell with cutaway illustration of the diamonds (from [Dong 2009]).

Figure 2 .

 2 10 shows a typical loaded cell. Pressure in the DAC was measured by using the ruby pressure scale. Ruby or Al 2 O 3 contains Cr (III) impurities which induce fluorescence emissions (at 694.25 and 692.74 nm at ambient conditions)

Figure 2 .

 2 Figure 2.10: A loaded cell before heating as view by an optical microscope through the diamond window.

Figure 2 .

 2 11. The light from the laser is split into two branches by a non-polarized cube beamsplitter and guided to the sample from both sides of the DAC via mirrors and lenses which direct and focus the beam. Changing the alignment of the mirror can change the angle at which the beam enters the cell. Mirrors between the objective lenses and DAC receive sample images and thermal radiation signals. The images are collected and focused by lenses. A 50/50 beamsplitter transmits light for viewing by a CCD camera and reflects to a spectrograph. Images and thermal signals are recorded by a spectro-radiometric system which consists of an air-cooled CCD detector and monochronometer spectrograph.

Figure 2 .

 2 Figure 2.12: Temperature as a function of time measured from the two sides of the cell during laser heating. Time increment correspond to the laser power delivered to the sample. The plateau corresponds to the silicate solidus.

Figure 2 .

 2 Figure 2.13: Appearance of the sample after laser heating. a. Transmission optical image of a cell after laser heating. Dark region in the middle is the main metal pool which is embedded in the silicate. Rings around the metal pool represent the molten silicate volume. The ruby can be seen at the upper slight left. Cracks are induced by decompression. b. SEM image of a sample showing the hotspot.

  IPGP and IMPMC. The operating principles of the SEM is the use of a high energy electrons to raster a sample providing morphological and chemical information. Electrons are accelerated by a source (Shottky field emitter for the Zeiss and a W filament for the Tescan) and focused by electromagnetic lenses onto the samples inside a vacuum chamber, eg., Figure2.14. Secondary electrons from the sample contain information about sample morphology while back-scattered electrons give chemical contrast information. Energy dispersive X-ray (EDX) analysis was also done on samples with the SEM. Photons emitted from the sample due to electron interactions have energies and intensities characteristic of the emitting atoms. Measuring the energies of these photons gives semi-quantitative chemical information. The EDX at IPGP has also been cross-correlated with the EMP and provides accurate compositional measurements.

Chapter 2 .

 2 Materials and Methods components of the device are are summarized in Figure 2.15. Figure 2.16 a. shows a holder used to place samples inside the instrument.

Figure 2 .

 2 Figure 2.15: Some of the main components of the NanoSIMS.

  and 2.18 and table2.5 summarizes the calibrations for the two elements. Tests were carried out on the detection limits and the calibration accuracy on the silicate of ELMO 151 and 145

Figure 2 .

 2 Figure 2.20 a. to d. The lamella was first glued to a tungsten needle (attached to the micro-manipulator) with a deposit of platinum. One side of the lamellae was then touched onto a stub containing SEM glue. SEM glue is an adhesive made by Kleindiek which hardens under an electron beam (http://www.nanotechnik.com/semglu.html).

Figure 2 .

 2 Figure 2.16: a. Sample holder for NanoSIMS with 8 5 cm slots containing various standards. The surface of the samples have to be flush with or lower than the holder. b. SEM image of glass standard showing the LA-ICPMS footprints. c. SEM image showing NanoSIMS footprints on a MORB sample after measurements were taken in isotope mode. The shape of the footprints resulted from beam distortion and would otherwise be square. d. SEM image of one NanoSIMS footprint in isotope mode on a MORB sample. The erosion of the sample over several cycles is represented by the terraces of the pit wall.

Figure 2 .

 2 Figure 2.19: Ion milling of a DAC sample. (a) DAC sample in rhenium gasket after removal from cell. Laser heated spot in middle (b) Removal of material around the laser heated spot. (c) Polished surface showing the region of melting. (d) Lamella ready to be extracted.

Figure 2 .

 2 Figure 2.20: Liftout procedure for DAC samples. (a) Liftout of ion polished lamellae with a tungsten needle. The needle is attached with glued with with Kleindiek SEM glue to the lamella and material is milled away from the opposite end to free the lamella (b) Placement on a silicon wafer with SEM glue holding the lamellae in place.(c) Top view of needle and lamellae before the needle tip is removed by ion milling. (d) Sample towards the middle of the silicon wafer.

Figure 3 . 1 :

 31 Figure 3.1: An illustration of the Earth accreting from embryos through interplanetary collisions.

  occur, which is derived from isotopic chronometry with the Hf-W and U-Pb systems and was determined to be between 30 and 60 Myr[Rudge 2010]. Figure3.2 a shows this growth function for different values of τ α . M is 0 at t = 0 and 1 at the end of accretion. The function can be modified to allow bodies of variable masses to be added. Specifically, the effect of large impacts are included towards the end (last 80 % of growth) of the accretion by fixing mass fractions contributions to account for larger bodies (∼ 0.04 for intermediate bodies and 0.1 for the moon forming giant impactor).

Figure 3 . 2 :

 32 Figure 3.2: a. Earth growth functions as defined by [Rudge 2010] for different mean ages of accretion. b. Pressure at 40 % depth of planet which correspond to the base of magma ocean as the Earth accretes. c. Temperature determined by the average of peridotite liquidus from [Fiquet 2010] and [Andrault 2011]. d. Evolution of the oxygen content of the core. χ is molar fraction.

  Figure 3.2 d shows the evolution of oxygen in the core over accretion.

Figure 3

 3 Figure 3.3: The effect of impactor sizes on mixing in the magma ocean, from [Nimmo 2015].

  Figure 3.4 shows how the efficiency of sulfur partitioning (the subject of the next chapter) evolves over accretion. The first ∼ 700 impactors in the model are small, ∼ 0.001 the mass fraction of the Earth. At first the Earth is small too and the efficiency is low but as the Earth grows relative to the bodies, efficiency increases. This efficiency however plummets drastically for the giant impactors (mass fraction 0.03 to 0.1 Earth mass) during the last 20 % of accretion. If giant impactor cores underwent such inefficient equilibration then the mantle record in terms of elemental abundances, might not tell the full story.

Figure 3 . 4 :

 34 Figure 3.4: Evolution of efficiency of sulfur partitioning as embryos accrete to the Earth.

Figure 1 :

 1 Figure 1: Temperature as a function of time measured from the two sides of the cell during laser heating. The laser power is increased rapidly during the first 10 seconds to increase the temperature and induce melting of the sample at the laser focus. The plateau corresponds to the silicate solidus. Samples are kept molten for between 45 seconds to 2 minutes.

Figure 2 :

 2 Figure 2: SEM image of four thin sections for experimental run products #3, #2, #6, #9. All samples show the morphology typical of quench metalsilicate partitioning experiments. A metallic blob in a quench silicate liquid pocket surrounded by unreacted starting material. Light grey areas around the lamellae are platinum deposited to protect sample during ion milling.

Figure 3 :

 3 Figure 3: NanoSIMS chemical maps in greyscale. Samples are shown in the same order as Figure 3 but with each sample being rotated. Yellow box shows the typical size of ROI from which compositions are extracted. Sulfur map shows the metallic blob as white due to saturation in the scaling of measurements for display.

Figure 4 :

 4 Figure 4: TEM observations of the interface between metallic blob and quench silicate liquid for run #9. a. Dark field image, b. EDX Fe c. EDX S d. Dark field image e. EDX Fe f. EDX Mg. There is a correlation between the occurrence of iron and sulfur. Elongated crystals evident in magnesium map are due to the quench from high temperatures.

Figure 5 :

 5 Figure 5: TEM observations of an irregular quench feature present in the metal blob of one experiment (Run #9). Brighter colors indicate higher concentrations. The feature is enriched in oxygen and silicon. a. STEM HAADF image, b. STEM EDX Fe c. STEM EDX O d. STEM Si.

Figure 6 :

 6 Figure 6: Partition coefficient as a function of pressure showing data from this study (red dots), previous studies (blue dots) and the temperature dependent extrapolations (purple lines) from multivariable regression of the combined data set. The extrapolation of Rose-Weston et al. (2009) for 3000 K is also shown (grey line). The shaded region is the pressure range of coremantle equilibration proposed by previous works(Siebert et al., 2012).

Figure 1 :

 1 Figure 1:

  Figure 3:

Figure 5 :

 5 Figure 5:

5. 2 Introduction

 2 Figure 7:

  Earth[Morgan 2001]) combined with N-body simulations, has been used indirectly as a basis to date the moon forming giant impact[Jacobson 2014]. The dynamical consequences of a late veneer has also provided an explanation for the lunar inclination problem[Pahlevan 2015]. Understanding the source of mantle's HSE content can therefore resolve important geochemical and dynamical observations. Despite general acceptance of the "late veneer"hypothesis, other explanations have been sought to explain the anomalous presence of HSEs in the mantle. One of the most viable alternatives includes core-mantle equilibration at magma ocean conditions. It has been shown that equilibration at pressures and temperatures of a deep magma ocean can explain the mantle abundance of moderately siderophile elements Ni, Co, Mo, W[Wade 2005, Siebert 2012, Fischer 2015]. It has also been suggested

Figure 5 . 1 :

 51 Figure 5.1: SEM images showing an area of the lamella from run # 1(a.) and 7(b.). A main metal blob is surrounded by a glassy quenched silicate. Re-crystallized starting silicate form rings around the molten region. The quenched silicate appears to be relatively nugget free. The features are consistent with the appearance of other partitioning experiments carried out in DAC. Lamellae are glued to a silicon wafer, after being extracted by focused ion beam and polished. Quench features typical of DAC experiments are evident.

Figure 5 .

 5 2 shows that there is homogeneity in the 28 Si and 27 Al 16 O maps. The platinum map displays heterogeneities in the quenched silicate on the sub-micron scale. There is enrichment of platinum observed especially close to boundaries and cracks. Regions with these features were avoided for extraction of platinum composition. Composition of platinum is averaged from several regions which are free of heterogeneities and towards the middle of the molten silicate region. Because the NanoSIMS samples only the top layers of atoms from the sample, embedded contaminations that might be present are avoided. Therefore, the values we report for the platinum composition in the silicate are presumed nugget free.

Figure 5 . 3 :

 53 Figure 5.3: Regression for T and fO 2 from the study of [Bennett 2014] and the regression from this study for a combined dataset for both T and fO 2 . The two regressions are calculated for IW -2.

Figure 5 . 4 :

 54 Figure 5.4: Regression from this study for P,T, fO 2 for a combined dataset with [Mann 2012, Bennett 2014].

  Pd abundance through core-mantle equilibration. Experiments on the other HSE at HP-HT in LH-DAC would be needed to determine if all the required HSE partitioning coefficients can be matched for a given set of P-T-f O 2 conditions. The modeling which incorporates the effect of T and f O 2 gives a closer match to the required partitioning at IW -2 while slightly more oxidizing conditions would lead to higher partitioning and a more Pt depleted mantle. A model which incorporates P-T and f O 2 provides a better match for the mantle's platinum content at f O 2 of IW -1 while more reducing conditions would over enrich the mantle in Pt. Accretion is generally assumed to have proceeded under f O 2 conditions of between IW -4 to -2 e.g.[Wade 2005] while work on V and Cr partitioning[Siebert 2013] showed that higher f O 2 conditions are viable.Since the partitioning evolves as a function of P and T as the Earth accretes, a continuous accretion model is used to provide a more realistic value for the cumulative amount of platinum that would be retained in the mantle from core-formation. In this model, the Earth accretes mass by increments of 1 % over 100 steps and is assumed to have a bulk chondritic concentration of platinum at each step. The pressure of equilibration is estimated at the base of a magma ocean (40 % the radius of the Earth) and temperature is estimated from the peridotite liquidus. The continuous exchange of platinum between the core and the mantle is then evaluated. The model predicts platinum in the mantle in similar abundance to the single stage model above. Therefore, equilibration could plausibly explain the mantle abundance of platinum. However since there5.5. Discussion125 is very strong evidence for the late veneer, perhaps there is a mechanism which could reconcile the observations with the measurement. Incomplete core formation during giant impacts could potentially provide a mechanism to lower the platinum content in the mantle, which would then be replenished by a late veneer. Further modeling are required to investigate this idea.Another mechanism which could potentially convey excess platinum and other HSE to the mantle is the "Hadean Matte", an event which involved a wholesale removal of sulfide rich liquids to the core towards the end of core formation[START_REF] O'neill | [END_REF]. Experimental evidence for such an event was revealed by Cu isotopic fractionation during high pressure partitioning experiments[Savage 2015]. This mechanism could have siphoned HSE to the core due to their chalcophile nature. Strong relationships have been noted

Figure 5 . 5 :Figure 5 . 6 :

 5556 Figure 5.5: Evolution of platinum partitioning as the Earth accretes. From the T, FO2 regression.

  sures and temperatures contrary to predictions of previous work[START_REF] Rose-Weston | Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation[END_REF], Boujibar 2014]. It appears that the pressure effect was overestimated by these previous works compared to our measurements. A model of sulfur distribution in the core and mantle during accretion was implemented. The bulk Earth sulfur content as estimated from its depletion signature with respect to volatility[McDonough 2003] and its observed mantle abundance were used as constraints on the model. A homogeneous delivery of sulfur to the Earth throughout accretion overmatched the observed mantle's sulfur content. A delivery of sulfur with large impactors towards the end of accretion, 130 Chapter 6. General conclusion fulfilled the mantle's sulfur abundance due to the decrease in efficiency of metal-silicate partitioning during large impacts. In both scenarios, the core sulfur content is below ∼ 2.0 wt. % which is consistent with geophysical estimates and the conclusion that sulfur is not a dominant light element. The difficulty of the homogenous model in matching the observed mantle sulfur could originate in an overestimating in the Earth's bulk sulfur. When the bulk composition of the Earth was lowered to ∼ 3000 ppm, the homogenous model gave a good match for the mantle's sulfur content. However, the late veneer contribution would then over enrich the mantle in sulfur relative to observations. It does give pause to question whether the bulk Earth's sulfur is fully described by the chondrite model of theEarth [McDonough 2003]. Other mechanism such as a Hadean Matte[O'Neill 1991] could have sequestered sulfur to the core in a late sulfide segregation event, which could reconcile the result of the homogenous model. Though a mechanism for this process is unclear given the low partitioning measured in this study. It could also be that exsolution of sulfur as FeS in a crystallizing magma ocean might have removed sulfur from the mantle to the core[START_REF] Schubert | [END_REF], Laurenz 2016] or perhaps the lower mantle. This idea requires further experiments on the sulfide saturation limits at the conditions of the deep mantle.Measurements of metal-silicate partitioning of HSE at core formation pressures and temperatures, and with relevant compositions, have been obtained for platinum. The partitioning behavior is very close to what had been predicted by previous work[Mann 2012, Bennett 2014]. Instead of a mantle with too little HSE to match the mantle observations, as had been the case with many of the previous studies [O'Neill 1995[START_REF] Borisov | Experimental determination of the solubility of platinum in silicate melts[END_REF][START_REF] Holzheid | Evidence for a late chondritic veneer in the Earth's mantle from highpressure partitioning of palladium and platinum[END_REF], we are now faced with a mantle with a possible excess of platinum from core-mantle equilibration. Caution must be taken in interpreting these results. First, partitioning for the other highly siderophile elements should be obtained at core-formation pressures and temperatures to determine if their partitioning behaviors converge. Second, the effect of sulfur on the behavior of the HSE at high pressures and temperatures should also be considered. The mechanisms invoked to reconcile the sulfur results, the Hadean Matte and sulfide saturation in a crystallizing magma ocean could also be relevant to reconciling the partitioning behavior of platinum with the observation. Inefficient core formation during late stage giant impacts could also have depleted HSE from the mantle as was shown for sulfur. It could be that the mantle's HSE are the net sum of core formation residue and the late veneer.These experiments have shed new light on the consequences of core-mantle equilibration for the behavior of sulfur and platinum. Both elements become less siderophile at core formation pressures and temperatures and models show potential over-enrichment in these elements relative to mantle observations. It would appear that the stories told by sulfur and platinum partitioning are incomplete and mechanisms which can further remove these elements to the core during the late stages of the Earth's accretion are the missing chapters. N-body simulations of different accretion scenarios coupled with core-formation models might be one avenue that can add insights. But further understanding of the nature of the Earth building blocks and a reassessment of the Earth bulk composition could also bring clarity.

Table 2 .

 2 • C over several hours. Some of these FMORB samples were doped with trace elements while in the furnace. Others were crushed, doped and re-melted with the laser levitation. The quenched product of 2: Trace element composition of standards in ppm, measured by LA-ICPMS.

	Sample	SiO 2	FeO	MgO	Al 2 O 3 CaO Na 2 O	K 2 O	TiO 2	MnO	Cr 2 O 3	SO 2	Total
	NMORB-0	49.7	9.7	8.5	15.9	11.7	2.7	0.1	1.3	0.2	-	0.1	100.1
	NMORB-blank1	46.47	8.70	9.50	19.37 12.20 0.013 0.0037	2.09	0.17	0.015	-	98.55
	NMORB-blank1b 50.65	8.84	7.84	15.66	9.82	2.85	0.61	1.72	0.157	0.034	-	98.18
	NMORB-Pd3	49.41	8.76	-8.13	15.94 13.04	3.1	1.3	1.8	-	-	-	100.67
	NMORB-Pd4	51.8	8.6	7.9	16.06 12.11	1.64	0.5	1.86	-	-	-	101.61
	NMORB-Pd2	50.75	8.33	8.07	16.03 12.46	1.85	0.6	1.84	-	-	-	100.13
	NMORB-Pt2	50.29	9.0	8.12	15.93 12.23	3.07	1.17	1.82	-	-	-	101.75
	NMORB-Au2	49.4	8.9	8.1	15.8	11.97	3.17	1.31	1.81	-	-	-	100.69
	FMORB-Pt2	59.98 10.532 17.01	5.04	4.51	2.59	0.039	0.023	0.035	0.022	0.003	99.79
	FMORB-Pt1	60.34 11.12	17.58	5.21	4.58	2.54	0.04	0.009	0.033	0.007	0.006	101.47
	FMORB-N1	54.6	18.17	15.17	5.34	3.93	2.72	0.06	0.023	0.045	0.01	0.005	100.07
	FMORB-5	57.87 10.25	16.54	5.567	4.38	3.228	0.047	0.012	0.028	0.0071	0.001	97.94
	FLMORB-Pd-X1 54.55	8.42	16.20	5.22	3.87	3.18	0.032	0.016 0.01518	-	-	91.51
	FLMORB-Pd-X2 55.57 8.760	16.41	5.32	4.01	2.96	0.034 0.0135 0.0184	-	0.00028 93.09
	FLMORB-Pd-X3 54.71 8.495	16.20	5.26	3.91	3.09	0.032 0.0122	0.020	0.012		91.74
	Sample	SiO 2	FeO	MgO	Al 2 O 3 CaO Na 2 O	K 2 O	TiO 2	MnO	Cr 2 O 3	SO 2	Total
	ELMO 151 glass 43.59 14.30 13.658 13.50 8.370 2.921	0.61	1.43	0.149	0.037	0.21	98.79
	ELMO 145 glass 44.84 13.01 11.813 13.86	8.86	3.016	0.64	1.53	0.157	0.040	0.21	97.97
	Table 2.1: Major and minor element compositions in oxide weight % as measured by electron microprobe of the natural and synthetic
	glasses. NMORB -natural MORB; FMORB and FLMORB-synthetic MORB; ELMO -piston cylinder synthesis.

these syntheses were recovered, mounted in epoxy and polished for chemical composition analyses. Major and minor compositions are reported in table 2.1. Some volatile loss occurred for some high temperature syntheses as is seen in lowered amounts of Na and Mg. Table

2

.2 shows the trace element compositions: There is one nugget free NMORB sample with 7 ppm of platinum; One NMORB sample with 4.2 ppm of Pd; Two samples are true blanks for Pt, Pd and Au; 1 of 3 FMORB samples that were doped in platinum have nuggets; The other two contained 11 ppm and 17 ppm of Pt and were nugget free.

Figures 2.3 and 2.4

shows the time resolved LA-ICPMS spectra of trace elements for some of these samples.

Homogenous glasses of of natural MORB and KLB-1 peridotite were produced in the laser levitation furnace for use as silicate starting material for DAC experiments.

Table 2 . 4 :

 24 Nugget statistics from some doped natural and synthetic silicates.

	., tem-

Table 2 .

 2 5: Summary of trace element concentrations (ppm) in the internal and reference standards used for analysis of DAC samples at the NanoSIMS.

	Standard name	Pt	Pd	Au	S	Comment
	NMORB Pt1a	7	-	-	-	MORB doped
	NMORB-Pd1a	-	4.66	-	-	MORB doped
	NMORB-blank1	0	-	-	0.4 MORB re-melted
	FMORB-Pt1	11	-	-	0	Synthetic MORB
	FMORB-Pt2	16	-	-	0	Synthetic MORB
	NBS 610	3	-	15 456	NIST glass
	NIST 612	2.51 1.05 4.7 200	NIST glass
	CLDR1-05V	-	-	-	950	Pillow Basalt

Table 2 .

 2 6: Inversion of NanoSIMS measurements for ELMO glasses.

	Sample name 32S/30Si Predicted S (ppm) Measured S (ppm) EMP
	ELMO 151	5.58E-02	1110	1063
	ELMO 145	4.93E-02	979	1031

Table 1 :

 1 Experimental summary of the sulfur partitioning experiments. D m/s = metalsilicate partitioning coefficients, calculated from NanoSIMS measurements of sulfur in the silicate except for run # 3; quantities used in the calculation are in moles. ∆ IW = Oxygen fugacity, calculated relative to the iron-wüstite (IW) redox buffer. X = molar fractions. †

			20.94 ± 3.75 -1.66	0.10	0.70	0.13	0.11	0.03
	2	3700	13.59 ± 3.27 -1.30	0.14	0.61	0.15	0.19	0.03
	†3	3600	10.34 ± 1.24 -1.45	0.13	0.70	0.07	0.14	0.06
	4	3500	22.12 ± 3.96 -1.08	0.21	0.73	0.12	0.13	0.01
	5	3300	54.47 ± 4.22 -1.31	0.17	0.78	0.07	0.13	0.04
	6	3600	13.60 ± 1.94 -1.00	0.17	0.55	0.16	0.21	0.05
	7	3700	17.04 ± 2.01 -1.06	0.02	0.68	0.14	0.14	0.02
	8	4000	15.30 ± 2.12 -1.47	0.14	0.74	0.04	0.17	0.04
	9	4100	7.96 ± 1.83	-1.55	0.12	0.71	0.03	0.17	0.06
		KLB-1 starting silicate composition.

Table 2 :

 2 Silicate and metallic composition in weight % of run products. Measured by EDX, †EPM and ⋆NanoSIMS. Minor elements included in total.

	Study	a (intercept)	b (1/T )	c ( P/T) d (log(1-X 0 ))
	This work	-3.50 ± 0.47 3000 ± 1023 33 ± 11	14 ± 2
	Rose-Weston et al. (2009)	-4.37	13686	217.49	-
	Boujibar et al. (2014)	-3.72 ± 0.07	405 ± 150	136 ± 25	32 ± 5.5

  silicate starting material consisted of silicate glass platelets of natural MORB (Mid Oceanic Ridge Basalt) composition. The metal is a FePt alloy (Pt 45%, Fe 55%) synthesized by metal-silicate partitioning experiments in piston cylinder experiments at superliquidus conditions. Details of the alloy synthesis can be found in Chapter 2, Section 2.2. The compositions of the silicate and alloy are reported in Table2.1 and 2.2. The starting silicate was polished down or micro-machined into discs of about 15 to 20 µm in thickness and 60 to 80 µm in diameter. Foils of alloy of about 10 µm in thickness was sandwiched between two silicate platelets and the assembly then placed into a pre-indented rhenium gasket in a diamond anvil cell (DAC).The sample preparation and experimental procedures for carrying out Laser heated DAC experiments is described in Chapter 2. The DAC is coupled to double sided 200 Watt fiber laser with a spot size of 20 µm in diameter. Experiments are carried out above the silicate liquidus which results in the region of sample at the focus of the laser being fully molten. At the conditions of the experiments, the metal is expected to equilibrate fully with the surrounding silicate. A summary of the experimental conditions are presented in Table

Table 5 .

 5 1. The metal blobs have Fe compositions which ranges from 31 to 82 wt % and Pt compositions of 7 to 61 wt %. O and Si which diffused from the silicate are present in small amounts in the central metal blob while S is present in variable amounts from 1 to ∼ 9 wt %. The solubility of O and Si in the metal, increases with pressure and temperature. The sulfur present in the blob mostly likely partitioned from the natural MORB.

	The quenched silicate in these experiments is enriched in FeO by a factor of 2 to
	3 as it has been observed in other metal-silicate partitioning experiments under sim-
	ilar conditions

Table 5 .

 5 2 summarizes the partition coefficients which range from 14 to 502. These partitioning values are not corrected for the infinite dilution of Pt in liquid metal Fe. This correction is less critical for these experiments since the starting alloy is a mixture of Fe ∼55% and ∼45% Pt and the activity of Pt in the alloy is lowered. Previous partitioning experiments which consisted of pure HSE interacting with the silicate are corrected for infinite dilution with the Margules mixing models, for example, see[Mann 2012] annex. This correction will be done in future work.

	Run #	1	2	3	5	4	6	7
	Pressure (GPa)	43	54	65	75	85	85	110
	Temperature (K)	4000	3600	3900	4100	3800	3900	4300
				Silicate Composition
	MgO	6.93 ± 0.02	7.09 ± 0.44	7.85 ± 0.49	6.75 ± 0.08	4.84 ± 0.3	9.44 ± 0.59	4.51± 0.28
	SiO 2	36.955 ± 0.105	37.95 ± 0.30	35.3 ± 0.28	33.46± 0.05	28.37± 0.22	21.59± 0.17	32.31 ±0.26
	Al 2 O 3	19.235 ± 0.025	19.92 ±	22.73± 0.58	24.02 ± 0.05	25.59 ± 0.65	17.53± 0.44	18.18 ± 0.46
	CaO	2.925 ± 0.015	4.27 ± 0.19	3.05± 0.13	2.93±0.01	2.53± 0.11	3.8± 0.17	3.68 ±0.16
	Na 2 O	3.335 ± 0.055	2.98 ± 0.07	3.94 ± 0.09	4.0 ± 0.04	2.84 ± 0.06	7.48 ± 0.17	1.35 ±0.03
	K 2 O	1.56 ± 0.09	1.25 ± 0.08	1.73± 0.11	1.75 ± 0.02	2.09± 0.13	4.62± 0.17	0.93 ±0.06
	FeO	26.25 ± 0.03	21.53 ± 0.80	20.33± 0.76	22.07± 0.14	26.59± 1.0	21.29± 0.80	30.7 ±1.15
	MnO	0.245 ± 0.075	0.44± 0.01	0.23± 0.04	0.37 ± 0.05	-	0.86±	-
	TiO 2	2.225 ± 0.065	3.94± 0.05	2.66± 0.01	3.32 ± 0.05	5.32 ± 0.07	9.03± 0.11	6.15 ± 0.08
	S	-	⋆0.1364±	⋆0.21±	⋆0.26±	⋆0.54 ±	⋆0.07 ±	⋆0.08 ±
	Pt	⋆ 0.3175 ± 0.0219 ⋆ 0.2 ±0.01 ⋆ 0.2331±0.04 ⋆ 0.3961 ±0.04 ⋆ 0.1501 ± 0.01 ⋆ 0.2284± 0.06 ⋆ 0.72 ±0.04
	Total	100	100	98	99	99	100	99
				Metal Composition
	O	4.675 ± 0.055	4.80 ±0.15	3.86 ±0.33	5.39 ± 0.23	5.57 ± 0.23	0.80 ± 0.03	1.190 ±0.1
	Fe	53.860 ± 0.050	45.94± 0.14	31.11 ± 5.24	34.10 ± 0.10	73.50±0.30	82.14 ±0.25	81.085± 0.04
	Si	1.720 ± 0.020	1.13 ± 0.05	0.76± 0.01	0.51 ± 0.02	0.76 ± 0.01	0.19 ± 0.01	3.020 ± 0.16
	S	0.575 ±0.005	4.70± 0.01	3.21± 0.03	7.81 ± 0.02	8.60 ± 0.02	1.67 ±0.1	1.670 ± 0.46
	Pt	39.165 ± 0.015	42.15± 0.5	61.06 ±0.50	52.00 ± 0.5	11.30 ±	7.65 ± 0.1	11.540 ±0.03
	Total	99.995	98.720	100.000	99.81	99.73	92.45	98.51

Table 5 .

 5 1: Silicate and metal compositions of platinum partitioning experiments. ⋆ NanoSIMS measurements. Other measurements obtained by EDX.

	Run #	Pressure (GPa)	Temperature (K)	D m/s	∆ IW X FeO sil X Fe met X S met X O met X Pt met
	1	43	4000	162 ± 0.89 -1.07	0.21	0.72	0.013	0.135	0.150
	2	54	3600	275 ± 60	-1.11	0.17	0.61	0.108	0.218	0.160
	3	65	3900	502 ± 25	-1.15	0.16	0.60	0.108	0.223	0.338
	4	75	4100	157 ± 16	-0.75	0.17	0.41	0.164	0.261	0.018
	5	85	3800	65 ± 8	-0.97	0.21	0.65	0.133	0.173	0.029
	6	85	3900	37 ± 1.8	-1.50	0.16	0.88	0.031	0.030	0.023
	7	111	4300	14 ± 0.78	-1.00	0.26	0.82	0.030	0.042	0.033

Table 5 .

 5 2: Experimental summary of the platinum partitioning experiments. D m/s = metal-silicate partitioning coefficients, calculated from NanoSIMS measurements of platinum in the quench silicate; quantities used in the calculation are in moles. ∆ IW = Oxygen fugacity, calculated relative to the iron-wüstite buffer. X = molar fractions.

Table 5 .

 5 3: Comparison of regression constants for this study with previous works.

Terry-Ann Suer 01/12/2016 Sujet : Partage du soufre et du platine entre un réservoir métallique et un réservoir silicaté lors de la formation du noyau terrestre Résumé

  : La détermination du partage des éléments sidérophiles et volatils entre métal et silicates aux conditions du manteau profond de la Terre primitive peut fournir des contraintes relatives au mécanisme de formation du noyau terrestre. Des expériences ont été réalisées dans des cellules à enclumes de diamant (DAC) chauffées par laser afin d'étudier l'évolution du partage métal-silicate du soufre et du platine à haute température et haute pression. Le partage est déterminé grâce à la mesure sur échantillons trempés des concentrations par NanoSIMS et sonde électronique. L'affinité du soufre avec le métal, mesurée aux conditions de formation du noyau terrestre, est moins grande qu'attendue. En accord avec les observables cosmochimiques (météorites), il semble que la quantité de soufre dans le noyau ne peut excéder 2 poids %. Les modéles dccrétion de la Terre, combinés à nos mesures du coefficient de partage du soufre en fonction de la pression et la température, indiquent que la concentration globale de soufre du manteau terrestre doit être le résultat d'une accrétion hétérogène. Ces données indiquent également un apport tardif des éléments volatils au cours de lccrétion et de la formation du noyau. Les valeurs de partage du platine suggèrent que son abondance dans le manteau terrestre peut être expliquée simplement par la formation du noyau. De manière générale, ces résultats supportent les hypothèses selon lesquelles les noyaux des gros impacteurs n'ont pas pu s'équilibrer entièrement avec le manteau terrestre. Certaines fractions métalliques ont donc pu atteindre le noyau terrestre sans affecter le manteau. L'hypothèse d'un évènement tardif de ségrégation de sulfure durant la formation de la terre pourrait aussi expliquer les compositions du manteau terrestre observées. Ces résultats permettent de caractériser les processus de diffrenciation du manteau et du noyau et de mieux comprendre la formation de la Terre.

Institut de Minéralogie, de Physique des Matériaux, et de Cosmochimie (IMPMC) Sorbonne Universités -UPMC Univ Paris 06, UMR, CNRS 7590, Museum National d'Histoire Naturelle, IRD, 4 Place Jussieu, F-75005 Paris, France

2 Institut de Physique du Globe de Paris, Sorbonne Paris Cité -Université Paris Diderot, UMR CNRS 7154, F-75005 Paris, France submitted to Earth and Planetary Science Letters

Table 3: Regression Parameters from this study, Rose-Weston et al. (2009) and Boujibar et al. (2014)

Acknowledgements

This work was supported by French state funds managed by ANR within the Investissements d'Avenir program under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE led by Sorbonne Universités. J.S. acknowledges support from the French National Research Agency (ANR project VolTerre, grant no. ANR-14-CE33-0017-01). The authors are grateful for the use of the the National NanoSIMS facility at the MNHN which was established by funds from the CNRS, Region Île de France, Ministère déléagué à l'Enseignement súperieur et là Recherche. We are also grateful for the use of the FIB/MEB platforms at IPGP and IMPMC and the EMP at CAMParis. The authors acknowledge Stephan Borensztajn's and Imène Esteve's FIB preparation work, Gilles Le Marchand for help with sample recovery, Adriana Gonzalez for providing assistance with the NanoSIMS measurements, Guillaume Morard for providing starting materials and Michele Fialin for help with sample characterization. T-A.S acknowledges communication with John Rudge.

Appendix B .1 NanoSIMS Sulfur Extractions

Appendix C .2 Electron Diffraction Analysis

Using a JEOL 2100F field emission gun TEM, diffraction patterns were recorded from small grains of about 50 nm in diameter which were present in the silicate quench regions of all the DAC run products. These features were quantified in one sample, run # 9 from the sulfur partitioning experiments, Figure .3. The patterns indicated that several symmetries present in the grains but do not seem consistent with a single phase. The d-spacings and their ratios are reported here but identification of zone axes and a structure for the small grains proved elusive. The angles were measured with the Crystalbox software and the d-spacings d h i extracted in Image J using the relationships:

where L is the camera constant (effective length between the sample and CCD).

Using the Bragg condition λ

d-spacings are then quantified from a known camera constant, L (10980 pixels), the wavelength of the electron at 200 keV, 0.0025 nm, and R, the length in pixels measured from the diffraction patterns.