P Faure

M Boyet
email: maud.boyet@uca.fr

M A Bouhifd

G Manthilake

T Hammouda

J.-L Devidal

Determination of the refractory enrichment factor of the bulk silicate Earth from metal-silicate experiments on Rare Earth Elements

This study investigates the partitioning of rare earth elements (REE) from La to Gd between molten metal and silicate to evaluate potential fractionation occurring during core-mantle differentiation. We report molten metal-silicate liquid partition coefficients from 24 multi-anvil experiments, extending the range of pressure, previously ranging from 1 to 8 GPa, up to 14 GPa. Experiments were performed at temperatures of between 2300 and 2560 K, and for oxygen fugacities ranging from the IW (Iron-Wüstite buffer) to IW -4. Metal-silicate partition coefficients for the studied REE vary with the oxygen fugacity and S concentration in the metallic phase of the system. These elements were all lithophile during the Earth's accretion. By compiling all existing data on molten metal-silicate liquid partitioning, REE partitioning between the mantle and core during the Earth's accretion can be determined for a wide range of P, T and fo 2 conditions representing the early evolution of planetary bodies from planetesimals to planets. REE concentrations of the bulk silicate Earth (BSE) are calculated from accretion scenarios using varying proportions and compositions of chondritic building blocks. The models selected are those that reproduce the Earth's nucleosynthetic isotope signature and the Ni/Co, Th/U and Nb/Ta ratios of the BSE. The BSE refractory element enrichment factor determined from REE data is equal to 2.88 (relative to CI chondrites). This calculation takes into account the depletion in volatile elements in the Earth compared to chondrites. This new estimate is in good agreement with previous determinations based on analysis of the upper mantle rocks, which supports the idea of a chemically homogeneous mantle. We also confirm that the formation of the core, with or without segregation of a sulfide phase, does not fractionate Sm/Nd and cannot be responsible for the 142 Nd excess measured in modern terrestrial samples relative to chondrites.

Introduction

The planets of our Solar System result from the accretion of smaller objects including differentiated protoplanetary bodies and primitive objects formed in the early Sun's protoplanetary disk. The bulk chemical compositions of differentiated objects, which are composed of a metallic core surrounded by a silicate reservoir, are difficult to estimate because we do not have access to all the different reservoirs. Core-mantle differentiation processes concentrate chemical elements in the different reservoirs according to their partition coefficients. Siderophile elements are preferentially drawn into the metallic core whereas lithophile elements remain in the silicate portion.

Chondrites, which escaped planetary differentiation, are commonly used as a reference for elements characterized by a high condensation temperature called refractory elements. Unlike volatile elements, they must not have been partially lost during the accretion stage. Then planetary bodies should retain chondritic ratios of refractory lithophile elements (RLE) in their silicate parts. Ratios of two elements characterized by a high condensation temperature (e.g. Ca, Al, rare earth elements) are similar in the different chondrite groups (Wasson and Kallemeyn, 1988). This observation forms the basis for many geochemical models used for reconstructing the composition of the bulk silicate Earth (BSE). Proposed BSE compositions have chondritic RLE ratios, and the absolute concentrations in the BSE for these elements are commonly expressed in the literature using the enrichment factor (EF), which is the BSE to CI concentration ratio (EF=[RLE] BSE /[RLE] CI ). This enrichment factor is usually determined from the concentrations measured for highly refractory elements (e.g. Al, Ti) in the most fertile upper mantle rocks. Once determined, it is applied to all RLE to calculate the BSE composition. Enrichment factors are in the range of 1.7 to 2.8 in the literature explaining the differences in published BSE compositions [START_REF] Lyubetskaya | Chemical composition of Earth's primitive mantle and its variance[END_REF][START_REF] Mcdonough | The composition of the Earth[END_REF][START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF]. Concentrations in heatproducing elements vary by ~20% in the different BSE models with important implications on the geodynamics and habitability of Earth [START_REF] Jellinek | Connections between the bulk composition, geodynamics and habitability of Earth[END_REF].

The absence of RLE fractionation during the early phase of the Earth's evolution has been challenged, due to the presence of small 142 Nd/ 144 Nd excesses in modern terrestrial samples relative to chondrites (up to 30 parts per million in the 142 Nd/ 144 Nd ratio depending of the chondrite group; [START_REF] Boyet | 142Nd Evidence for Early (>4.53 Ga) Global Differentiation of the Silicate Earth[END_REF]. Since 142 Nd is a radiogenic isotope partly produced by the decay of 146 Sm (T 1/2 =103 Ma), a very early differentiation event of the silicate Earth had been proposed to explain this offset [START_REF] Boyet | 142Nd Evidence for Early (>4.53 Ga) Global Differentiation of the Silicate Earth[END_REF]. Variation in the 142 Nd/ 144 Nd ratio measured between the different groups of chondrites reflects nucleosynthetic heterogeneities in the protoplanetary disk during the accretion stage (Boyet et al., 2018). However, variations in mass-independent stable isotope ratios for Nd ( 145 Nd/ 144 Nd, 148 Nd/ 144 Nd and 150 Nd/ 144 Nd) are too small to be clearly resolved, with the exception of carbonaceous chondrites [START_REF] Saji | Ultra-high-precision Ndisotope measurements of geological materials by MC-ICPMS[END_REF].

The smallest difference in 142 Nd between chondrite and terrestrial samples is for the enstatite chondrite group (average value -10 ppm, Boyet et al., 2018). Enstatite chondrites (EC) display nucleosynthetic isotope signature similar to BSE for a large number of isotope systematics suggesting that they represent a large fraction of the material accreted to form the Earth (e.g. [START_REF] Dauphas | The isotopic nature of the Earth's accreting material through time[END_REF]). Because the analytical precision is not sufficient to detect significant variations in other Nd isotope ratios in EC relative to the terrestrial reference, a radiogenic origin of the 142 Nd excess measured in modern terrestrial samples cannot be totally disproved. In this case the small excess of 142 Nd in modern terrestrial samples relative to chondrites could be the result of Sm/Nd fractionation produced during the lifetime of the parent isotope, i.e. during the first 500 Ma of Solar System history. The Earth's core was proposed by [START_REF] Andreasen | Where on Earth is the enriched Hadean reservoir?[END_REF] as a potential enriched reservoir (early-formed low Sm/Nd reservoir characterized by deficit in 142 Nd), even though no REE partition coefficients were available then for core-forming conditions.

While experimental data suggest that Sm and Nd remain lithophile and behave in a similar fashion during liquid metal -liquid silicate partitioning [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF], it has been proposed that the addition of a significant amount of S into the core would fractionate Sm and Nd enough to explain the small 142 Nd excess in modern terrestrial samples relative to chondrites (Wohlers and Wood, 2015). A small number of recent experiments performed at higher temperature (2100°C), more compatible with core formation conditions, seems to rebut elemental fractionation between Sm and Nd in a sulfur-rich environment [START_REF] Wohlers | Uranium, thorium and REE partitioning into sulfide liquids: Implications for reduced S-rich bodies[END_REF]. To further constrain the behaviour of REE during core-mantle differentiation processes, we report molten metal-silicate liquid partition coefficients (D) determined from 24 multi-anvil experiments. We extended the range of pressure to 14 GPa, as previous measurements had only been carried out between 1.5 and 8 GPa. Experiments were performed from 2300 to 2560 K, and for oxygen fugacity conditions ranging from IW (Iron-Wüstite buffer) to IW-4. Partition coefficients were determined for REE from La to Gd in a liquid metal-liquid silicate system with various amounts of S. Our new data set, combined with all existing experimental results, give a consistent parameterisation of the behaviour of these elements during magma ocean episodes for planetary bodies of different sizes (planetesimals to planets) and for compositions representing the diversity found in the inner Solar System.

Experimental methods

Starting materials

The starting material for the silicate consisted of a natural equilibrated EC from the EL6 subgroup (Hvittis, composition given by [START_REF] Rubin | Impact melt-rock clasts in the Hvittis enstatite chondrite breccia-Implications for a genetic relationship between EL chondrites and aubrites[END_REF]. Once finely ground, the powder was doped with the studied elements, at a level ranging from 1500 ppm to 1 wt% per REE. Since the field of application of Henry's law is not well defined for REE, we decided to split the studied REE into two different doping solutions , synthesized from AAS standard solutions, in order to minimize the amount of trace elements in the starting materials. Type A solution contained La, Ce, Pr, Nd and Sm, while type B solution contained Nd, Sm, Eu and Gd. For sulfur-rich experiments, a type C solution containing all 7 REE from La to Gd at a level of 1500 ppm each was synthesized. All solutions contained Nd and Sm in order to compare our experiments with previous studies [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF][START_REF] Wohlers | Uranium, thorium and REE partitioning into sulfide liquids: Implications for reduced S-rich bodies[END_REF].

Various amounts of Fe-rich alloys (in the Fe-Ni-Si-S system) were then added in a weight proportion of 50:50. Control of the fo 2 between IW to IW-4 was obtained by addition of metallic Si to the starting material, resulting in the reduction of the FeO present in the silicate phase from about 20 wt% to ~0.2 wt% in some run-products. Each composition was mixed and ground in ethanol, before being dried and stored in a vacuum sealed dessicator for at least 48 h.

High-pressure and high-temperature syntheses

High-pressure and high-temperature experiments were carried out using the 1000-ton and 1500-ton multi-anvil apparatuses installed at the French National High-Pressure facility of Laboratoire Magmas et Volcans (LMV) in Clermont-Ferrand. Experimental conditions are summarised in Table 1, based on pressure calibrations similar to those already described in Boujibar et al., (2014) and [START_REF] Hammouda | High-pressure melting of carbonated eclogite and experimental constraints on carbon recycling and storage in the mantle[END_REF]. The pressure assemblies consisted of Cr-doped MgO octahedra, 18 or 14 mm edge length, containing a stepped graphite or LaCrO 3 heater, respectively. Octahedra were compressed using 32 mm tungsten carbide anvils with truncation edge lengths of 11 and 8 mm (with 18 and 14 mm octahedra, respectively) and pyrophyllite gaskets. The samples were contained either in graphite for 6 GPa experiments or in MgO single crystal capsules for 14 GPa experiments. The assembled octahedra were dried in an oven at 500 K overnight before each experiment. The samples were first compressed to the target pressure at room temperature and then heated to the desired temperature (between 2300 and 2560 K) for durations of 2 to 4 min. These durations are sufficient to achieve equilibrium between silicate melt and metallic liquid (e.g. Boujibar et al., 2014;[START_REF] Faure | Uranium and thorium partitioning in the bulk silicate Earth and the oxygen content of Earth's core[END_REF][START_REF] Siebert | Systematics of metal-silicate partitioning for many siderophile elements applied to Earth's core formation[END_REF] while preventing excessive reaction between the capsule and the silicate or metallic phases. Textural and chemical evidences (uniformed quenched silicate melts, well-formed metal blobs, chemically homogeneous metallic and silicate phases) confirmed that equilibrium was achieved in the sample. Temperatures were monitored with a thin axial W 5 Re/W 26 Re thermocouple whose junction was in direct contact with the top of the capsule. In the event that the thermocouple was lost, the temperature was determined using the power/temperature relation determined in previous experiments.

The pressure and temperature uncertainties are estimated to be ±1 GPa and ± 100 K respectively, since no pressure correction was made for the emf of the thermocouple (e.g. [START_REF] Li | Behavior of thermocouples under high pressure in a multi-anvil apparatus[END_REF]. The samples were quenched by shutting off the power, which resulted in a quench rate of approximately 800 K/s. The samples were then decompressed over a period of about 12h. After the experiment, the run-product was mounted in epoxy, polished and carbon coated for the chemical analyses.

Electron Microprobe

Major and minor elements in the metal and silicate phases were analyzed using the LMV CAMECA SX100 electron microprobe using a 20 kV accelerating voltage. Major elements analyses in the silicate phase were performed at 50 nA with a 5-20 µm defocused beam, counting times on the peak ranging from 5 to 80 seconds depending on element concentrations and detection limit requirements. The standards for silicates were natural minerals and synthetic oxides (Si, Ca: wollastonite; Mg: forsterite; Al: Al 2 O 3 ; Fe: fayalite; Na: albite; K: orthoclase; Ti, Mn: MnTiO 3 ; Cr: Cr 2 O 3 ; Ni: NiO). For metallic and sulfide phase analyses, we used a defocused beam (10-20 µm), beam currents of 15 nA for the major elements (Fe, Ni, S and Si) and 150 nA for the trace elements, and counting times on the peak ranging from 5 to 60 s. Standards were pyrite for Fe and S in sulfides, and pure metal (Fe, Mn, Si, Mg, Ni, Cr) for metallic alloys. For samples embedded in graphite capsules, the carbon content in Fe-alloys was estimated from the deviation of the analyses totals from 100%.

Laser Ablation ICP-MS

Trace element concentrations were determined using the LMV Elements XR laserinduced coupled plasma-mass spectrometer (LA ICP-MS) coupled with a 193 nm ArF excimer type laser (Resonetics M-50). The laser was fired at selected sample regions at a repetition rate of 2 to 4 Hz with 4 mJ output energy beam, with a spot size diameter of 15-44 µm in the silicate, and 80-130 µm in the metal. Ablation duration lasted usually around 80 s and was done in a pure He atmosphere. Reference material glasses NIST SRM 610, NIST 612 and BCR2-G were used for external calibration [START_REF] Gagnon | Quantitative analysis of silicate certified reference materials by LA-ICPMS with and without an internal standard[END_REF], and 29 Si, 57 Fe and 60 Ni were used as internal calibrators. All data were processed using the GLITTER software package [START_REF] Achterberg | Data reduction software for LA-ICP-MS[END_REF]. Ca signal was monitored during metal analyses and Fe and Ni signals during silicate analyses. Any sudden variation in their content was considered as indicative of phase contamination (metal contamination during the silicate phase analysis, or vice versa) and the corresponding analyses were rejected.

Oxygen fugacity determination

Oxygen fugacity was calculated using the Fe and FeO contents of the metal and silicate quenched phases, using the equilibrium reaction:

Fe metal + ½ O 2 ↔ FeO silicate (1)
The fo 2 was estimated relative to the Iron-Wüstite buffer (IW) from the activities of Fe and FeO in the metal and silicate following the equation:

log fo 2 (ΔIW) = 2×log ! !"# !"# ! !" !"# (2)
where

𝑎 !"# !"# = 𝛾 !"# !"# × 𝑋 !"# !"# and 𝑎 !" !"# = 𝛾 !" !"# × 𝑋 !"
!"# represent the activity of FeO in the silicate liquid and Fe in the metal phase, respectively. 𝑋 !" !"# and 𝑋 !"# !"# are the molar fractions of Fe in the metallic phase and FeO in the silicate liquid. 𝛾 !"# !"# and 𝛾 !" !"# represent the activity coefficient of FeO in the silicate liquid, and the activity of Fe in the metallic phase, respectively.

The Fe activity coefficient in Fe-rich alloys was calculated from the formula of [START_REF] Ma | Thermodynamic description for concentrated metallic solutions using interaction parameters[END_REF], using the interaction parameters ε provided [START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF] and the activity calculator (http://www.earth.ox.ac.uk/~expet/metalact/) provided by the University of Oxford.

We used the average gamma value derived from studies at 1 bar by O' Neill and Eggins (2002) for several melt compositions in the CaO-MgO-Al 2 O 3 -SiO 2 system, and by [START_REF] Holzheid | The activities of NiO, CoO and FeO in silicate melts[END_REF] for melts in the anorthite-diopside system and komatiitic basalt, assuming no pressure effect on the activity coefficients in silicate melts [START_REF] Toplis | The thermodynamics of iron and magnesium partitioning between olivine and liquid: criteria for assessing and predicting equilibrium in natural and experimental systems[END_REF].

Results

Phase assemblages and compositions

Typical run products consisted of quenched silicate melts and liquid metal blobs (Figure 1). [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF][START_REF] Wohlers | Uranium, thorium and REE partitioning into sulfide liquids: Implications for reduced S-rich bodies[END_REF] showed that these interactions do not have a significant effect on the partitioning of REE. In addition, we observed no noticeable difference in REE molten metal-silicate liquid partition coefficients between 14 GPa (MgO single crystal capsule) and 6 GPa (graphite capsule) experiments for a similar range of temperature, fo 2 and chemical composition,

showing no significant impact of the nature of the capsule or pressure in our experiments (Appendix B).

Experimental partition coefficients

Overall, 24 experiments were performed, resulting in 24 new partition coefficients for Sm and Nd and 15 for La, Ce, Pr, Eu and Gd (Table 1). Molten metal -silicate liquid partitioning are always low, ranging from 10 -3 to 10 -6 , in agreement with results obtained in previous studies for experiments performed at similar conditions (see Appendix C). The two main parameters influencing liquid metal -liquid silicate partition coefficients are the oxygen fugacity and the sulfur content of the metallic phase. Changing the oxygen fugacity conditions from IW-4 to IW-1 leads to a decrease in the partition coefficient by two to three orders of magnitude (Figure 2 and Appendix D.1). On the other hand, the transition from pure Fe metal to pure FeS increases the partition coefficient of all studied REE by up to three orders of magnitude (Figure 3 and Appendix D.2).

Europium behaves slightly differently to other studied REE in our experimental conditions (Figures 234). Around the Iron-Wüstite buffer, more than 50 % Eu is divalent in a basaltic melt [START_REF] Burnham | The oxidation state of europium in silicate melts as a function of oxygen fugacity, composition and temperature[END_REF]. Thus, in the redox conditions of the present study, Eu is mainly in a +2 valence state. Eu 2+ is more stable in a sulfide phase than all the other trivalent REE, as shown in all the FeS-bearing experiments in this study (Figure 4). In all sulfur-rich samples, the sulfide phase is enriched in Eu, leading to a mean D Eu 2.5 times higher than the partition coefficients for the other REE. Values from the literature are also plotted in Figure 4. Results obtained from experiments performed in evacuated silica tubes at temperatures of between 1200 and 1400 °C [START_REF] Ingrao | Rare Earth Element Partitioning Between Sulphides and Melt: Evidence for Yb2+ and Sm2+ in EH Chondrites[END_REF][START_REF] Lodders | An experimental and theoretical study of rare earth element partitioning between sulfides (FeS, CaS) and silicate and application to enstatite achondrites[END_REF] are in agreement with our results. These similarities strongly suggest that pressure and temperature have a negligible effect on molten Fe-rich alloysilicate liquid partitioning of the studied REE (D REE ). That D REE is little dependent on temperature can be can be shown by the fact that the free energy of the exchange reactions for REE are not sensitive to the variation of the temperature in the likely range during core formation (details are reported in Appendix D.3).

By including experiments from previous studies, it is also possible to analyze the impact of the nature of the silicate phase on the behavior of the studied REE. The NBO/T (Non-Bridging Oxygen per Tetrahedral cations) value is an indicator of melt polymerization, with zero corresponding to a completely polymerized melt (SiO 2 melt) and a value of 4 corresponding to a completely depolymerized melt (Mg 2 SiO 4 melt). For roughly similar experimental conditions and metallic compositions, and for a large difference in silicate composition (NBO/T from 0.5 to 3.7, see Appendix A and C), the D REE coefficients are similar within the analytical uncertainties. Furthermore, besides

FeO that is directly related to the oxygen fugacity of experiments, we find no significant impact of any of the major oxides that compose the silicate phase on the partition coefficient of the studied REE, for the available dataset. Therefore, data suggest that the silicate melt composition has no significant influence on the REE metal-silicate partition coefficients.

Parameterisation of the results

Partitioning of an element between metal and silicate phases can be considered as an exchange reaction involving Fe, FeO and the oxidized and reduced components of element M, of valence n:

𝑀𝑂 !/! + ! ! Fe = ! ! FeO + M (4)
By considering the equilibrium for this exchange reaction, it is possible to write the following relationship between log(D M ) and log(fo 2 ) [START_REF] Righter | Partitioning of Mo, P and other siderophile elements (Cu, Ga, Sn, Ni, Co, Cr, Mn, V, and W) between metal and silicate melt as a function of temperature and silicate melt composition[END_REF]:

log 𝐷 ! = 𝑎 log 𝑓𝑜 ! + 𝑏 ! ! + 𝑐 ! ! + 𝑑 log 1 -𝑋 ! !"#$% + 𝑒 (5)
The a, b, c, and e terms relate to valence n 𝑎 = -! ! , enthalpy

∆!°! " , volume !∆!°! " ,
and entropy ∆!°! , respectively. The empirical term d takes into account the effect of sulfur in a metallic liquid (X Smetal is the wt.% of S into the metallic phase), as discussed previously.

In order to refine the values of a and d for La, Ce, Nd, Sm, Eu, and Gd, we used all existing data sets for which the partitioning behavior, phase compositions and experimental conditions (temperature, pressure, oxygen fugacity) had been accurately determined. We considered solid silicate for experiments performed at T < melting temperature of the silicate phase (liquidus). The references as well as the conditions (P, T, fo 2 ) available for each experiment are listed in Appendices A and C. We used a multiple linear regression (approach used by [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF][START_REF] Faure | Uranium and thorium partitioning in the bulk silicate Earth and the oxygen content of Earth's core[END_REF][START_REF] Righter | Partitioning of Mo, P and other siderophile elements (Cu, Ga, Sn, Ni, Co, Cr, Mn, V, and W) between metal and silicate melt as a function of temperature and silicate melt composition[END_REF] for each element of interest. For every regression, the robustness of each overall model significance was determined using a Fisher-Snedecor test, and a

Student test was run to assess the significance of every variable. Results of the twovariable parameterisation for La, Ce, Pr, Nd, Sm, Eu and Gd are summarized in Table 2 with their respective standard deviations and determination coefficients. The p-values determined for each variable are also reported. As seen above, only a and d are relevant

to REE partitioning behavior. The parameters b and c, corresponding respectively to the effect of T and P are found here of no statistical significance, and are therefore set equal to 0. This result reflects the negligible impact that T and P have on D REE (Appendix B), in comparison to the effect displayed by X Smetal and fo 2 , within a dataset containing experiments performed up to 14 GPa and 2560 K. While this observation is in agreement and validate previous studies based on a smaller range of P and T [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF][START_REF] Wohlers | Uranium, thorium and REE partitioning into sulfide liquids: Implications for reduced S-rich bodies[END_REF], a dependence on pressure or temperature might be resolved when data obtained from higher pressure experiments will be collected.

The value of parameter a being proportional to the valence of one element (equations 5 and 6), the parameterisations proposed here are consistent with all REE being in a +3

valence state within the studied range of oxygen fugacity conditions, with the exception of Eu, which is essentially +2 below the IW buffer. In an S-free system, an oxygen fugacity from IW-5 to IW-2 will lead to a decrease in D Nd from 2.32×10 -3 to 3.76×10 -5 and a decrease in D Eu from 3.71×10 -4 to 2.34×10 -5 (Figure 2). The effect of the sulfur content of the metal is also noticeable in our parameterisation, leading to an increase of all REE partition coefficients by about three orders of magnitude when the S content in the metallic phase increases from 0 to ~35 wt% at constant oxygen fugacity. For example, at IW-2, D Eu increases from 2.34×10 -5 to 2.45×10 -2 and D Nd increases from 3.31×10 -5 to 2.56×10 -2 (Figure 3). No noticeable difference is found between Eu and the other REE with respect to the effect of the sulfur content in metal. In the discussion, we will use parameterisations obtained in the range of conditions of the available dataset, in order to establish the partitioning of REE in the conditions of Earth's core formation.

Discussion

Absence of Sm-Nd fractionation during planetary core formation

Previous high pressure -high temperature experiments led to different conclusions concerning the role of core formation on the Sm/Nd ratio of the BSE. Elemental fractionation between Sm and Nd was reported from sulfide-silicate partitioning data in experiments performed at 1.5 GPa and temperatures between 1400 and 1650°C (Wohlers and Wood, 2015). However, when both phases are molten, this fractionation is no longer observed. This is shown in our study and from published high pressure -high temperature experiment datasets (Figure 5, [START_REF] Bouhifd | Superchondritic Sm/Nd ratio of the Earth: Impact of Earth's core formation[END_REF][START_REF] Wohlers | Uranium, thorium and REE partitioning into sulfide liquids: Implications for reduced S-rich bodies[END_REF]. Sulfide-silicate and metal-silicate partition coefficients for Sm and Nd vary with two parameters: fo 2 conditions and sulfur content. They must be taken into account when calculating Sm and Nd concentrations in bulk planetary silicate reservoirs. A late addition of sulfide (FeS) to the segregating core, as proposed by Wohlers and Wood (2015), would change the final Sm and Nd concentrations of the BSE since the partition coefficients increase by three orders of magnitude from pure Fe metal to pure FeS.

However, Sm and Nd cannot be fractionated during core formation in a Solar System planetary body of any size. commonly defined using the RLE enrichment factor (EF), which is applied to all refractory lithophile elements considered to be present in the BSE (similar to primitive mantle) in chondritic proportions. When expressed relative to the concentration measured in CI chondrites, this RLE factor lies within the range of 1.7 to 2.8 (Table 3).

Refractory Lithophile

The determination of this EF is a key feature of most BSE model since non-refractory and non-lithophile element concentrations in the BSE are determined via their observed mantle ratio with RLE. Therefore, the enrichment of the BSE in RLE will dictate the concentration of the BSE in all elements.

Here we propose a new approach where the RLE enrichment factor is calculated from the experimental molten metal -silicate liquid REE partitioning results. We have developed a model of planetary accretion focusing on the partitioning of REE between the mantle and the core throughout Earth's formation. In this model, the Earth accreted from impactors with a given chemical composition, which then equilibrate (fully or partially) with the magma ocean of the proto-Earth, until the planet obtains its final mass (M E = 5.97.10 24 kg). All the scenarios result in a fully formed Earth, with a primitive mantle representing 68% of its mass, the core representing the last 32%. The model takes into account the composition of various building blocks potentially involved over the entire history of the Earth's accretion and metal/silicate partitioning data which evolve with core formation conditions (fo 2 , pressure, temperature, composition). The accretion model is described in detail in Appendix E.

The measurement of small variations in mass-independent stable isotope ratios for a large number of elements, also called nucleosynthetic anomalies, provides a real opportunity to investigate the genetic relationship between the different planetesimals and planets. Several mixtures of different building blocks (which differ in nature and proportions) have been proposed in previous studies to match the terrestrial isotopic signature (e.g. [START_REF] Dauphas | Calcium-48 isotopic anomalies in bulk chondrites and achondrites: Evidence for a uniform isotopic reservoir in the inner protoplanetary disk[END_REF][START_REF] Lodders | An Oxygen Isotope Mixing Model for the Accretion and Composition of Rocky Planets[END_REF]. Results vary mainly because different studies focused on different elements. However, most of the studies which integrate a large database of isotopic ratios agree on a major contribution of enstatite chondrites in the mixture with a smaller contribution of carbonaceous chondrites and/or ordinary chondrites [START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF][START_REF] Dauphas | The isotopic nature of the Earth's accreting material through time[END_REF][START_REF] Liebske | On the principal building blocks of Mars and Earth[END_REF]. We assume that Earth accreted materials with bulk chondrite composition from known type of meteorites and potential effects of collisional erosion on the chemical composition are not considered (see [START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF].

Among the available models, only those with a mixture of different building blocks (of chondritic composition) that succeed in reproducing the Earth's isotopic signature are considered (e.g. [START_REF] Dauphas | The isotopic nature of the Earth's accreting material through time[END_REF][START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF]. In order to further test the validity of the accretion scenarios, we also studied the evolution of certain element ratios whose elemental ratios are considered in the following discussion [START_REF] Dauphas | The isotopic nature of the Earth's accreting material through time[END_REF][START_REF] Dauphas | Calcium-48 isotopic anomalies in bulk chondrites and achondrites: Evidence for a uniform isotopic reservoir in the inner protoplanetary disk[END_REF][START_REF] Lodders | An Oxygen Isotope Mixing Model for the Accretion and Composition of Rocky Planets[END_REF][START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF]. These four accepted scenarios contain for the building blocks between 70 and 91% of EC, the rest being made more oxidized (CC or OC) materials (Table 4). Several models involving different building blocks mixture fail at reproducing the BSE elementary ratios (Javoy, 1995;[START_REF] Burbine | Determining the possible building blocks of the Earth and Mars[END_REF][START_REF] Javoy | The chemical composition of the Earth: enstatite chondrite models[END_REF][START_REF] Fitoussi | Silicon Isotope Evidence Against an Enstatite Chondrite Earth[END_REF].

Rare earth element concentrations in the BSE for these four accepted scenarios are reported in Table 4. Enrichment factors (EF) can be calculated from the comparison of these BSE compositions with CI chondrites concentrations. However, it must be noted that none of the measured chondrite compositions have so far succeeded in reproducing the Earth's depletion in volatile elements compared to CI, as the Earth is more depleted in those elements than any known chondrite [START_REF] Allègre | Chemical composition of the Earth and the volatility control on planetary genetics[END_REF][START_REF] Braukmüller | Earth's volatile element depletion pattern inherited from a carbonaceous chondrite-like source[END_REF][START_REF] Wang | Earth's moderately volatile element composition may not be chondritic: Evidence from In, Cd and Zn[END_REF]. While it has been suggested that the Earth's depletion in volatile elements could be the result of erosion following a giant impact during late accretion [START_REF] Halliday | Mixing, volatile loss and compositional change during impactdriven accretion of the Earth[END_REF][START_REF] Hubbard | Protoplanetary dust porosity and FU Orionis outbursts: Solving the mystery of Earth's missing volatiles[END_REF], it has also been proposed that this depletion pattern was already present in the Earth's building blocks [START_REF] Birck | 53Mn-53Cr evolution of the early solar system[END_REF]Siebert et al., 2018, and references therein). The depletion of the Earth in volatiles elements, no matter its occurrence in the planet history, would have a direct impact on the concentration of RLE within the BSE. In order to take the impact of volatile depletion on RLE concentrations in the resulting BSE into account, the concentration of volatile elements in chondrites has been recalculated in order to fit the Earth's volatileelement depletion pattern. This concerns volatile and moderately volatile elements, i.e.

those with 50% condensation temperatures below 1230 K [START_REF] Lodders | Solar System Abundances and Condensation Temperatures of the Elements[END_REF]. The composition of non-refractory elements for each chondrite group has been recalculated, by applying the primitive mantle (BSE) ratios when normalized to Mg [START_REF] Lyubetskaya | Chemical composition of Earth's primitive mantle and its variance[END_REF][START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF]. Then, concentrations of all elements were recalculated to reach 100% weight total. The resulting compositions are found to be enriched in RLE compared to measured chondrite compositions by a factor f dry ranging from 1.6 for EH chondrites, to 2.0 for CM chondrites (Appendix E). A weighted average of these f dry factors, depending on the respective proportion of each chondrite composition in the Earth's building blocks (Table 4), was applied to our calculations.

Calculated enrichment factors are reported in Table 4 for the four accepted scenarios corresponding to those proposed by Dauphas, (2017), [START_REF] Dauphas | Calcium-48 isotopic anomalies in bulk chondrites and achondrites: Evidence for a uniform isotopic reservoir in the inner protoplanetary disk[END_REF][START_REF] Lodders | An Oxygen Isotope Mixing Model for the Accretion and Composition of Rocky Planets[END_REF] and [START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF]. Values are identical within error and the average EF dry value is 2.88 (Figure 6). The effect of volatile depletion shown in the figure is significant, increasing the enrichment factor by a value of about 1. Compared to the concentrations given by previous authors (Table 3, Figure 6

Generalisation of the enrichment factor to all RLE?

Most BSE models assume fixed chondrite-normalized RLE ratios. While we show that this hypothesis is relevant for REE from La to Gd (except Eu under specific conditions), some elements usually classified as RLE may change their behavior at core-forming conditions (P, T, fo 2 ). For example, Nb and Ta are both siderophile elements in reduced conditions. Heterogeneous accretion models in which conditions evolve from reduced to oxidized during the Earth's accretion explain the superchondritic Nb/Ta ratio of the BSE [START_REF] Cartier | Redox control of the fractionation of niobium and tantalum during planetary accretion and core formation[END_REF]. Therefore, the RLE enrichment factor presented here should only be used to calculate the abundances of elements that are known to remain lithophile under Earth accretion conditions. Within the REE group, two elements are likely to behave differently: Eu and Yb. Data on heavy REE are available in the study of [START_REF] Ingrao | Rare Earth Element Partitioning Between Sulphides and Melt: Evidence for Yb2+ and Sm2+ in EH Chondrites[END_REF] and [START_REF] Wohlers | Uranium, thorium and REE partitioning into sulfide liquids: Implications for reduced S-rich bodies[END_REF]. In a similar fashion to Eu in a sulfur rich environment, Yb fractionation occurs in very reduced conditions (IW -5 to -7) and the partial reduction to a +2 valence state has been identified using X-ray Absorption Near Edge Structure measurements [START_REF] Ingrao | Rare Earth Element Partitioning Between Sulphides and Melt: Evidence for Yb2+ and Sm2+ in EH Chondrites[END_REF]. However, since Eu is more sensitive than Yb to a valence change under reduced conditions, and no significant fractionation between Eu and other studied REE is observed, we do not anticipate that core formation would cause an Yb anomaly in the calculated BSE REE pattern.

Furthermore, the S content of the Earth's core is considered to be about 2 wt% from geophysical, geochemical and cosmochemical constraints (e.g. [START_REF] Allègre | Chemical composition of the Earth and the volatility control on planetary genetics[END_REF]Boujibar et al., 2014). There is still debate as to whether the Earth's core acquired its sulfur signature over the entire accretion history, or exclusively in the last 10-20 % of the Earth's accretion (e.g. [START_REF] Wood | Cooling of the Earth and core formation after the giant impact[END_REF]. In order to consider the impact of the accretion of sulfur-rich bodies on the concentration of REE in the different reservoirs, we ran models representing several scenarios involving impactors containing iron sulfide instead of metallic iron, in various proportions (up to 20% of the Earth's mass). No significant variation in REE concentrations or ratios within the BSE is observed. The addition of sulfide to the Earth's core, at any time during the Earth's accretion, leaves no noticeable trace on the resulting REE concentrations of the BSE.

Chemical uniformity of present day mantle?

BSE composition models based on the analysis of the upper mantle rocks consider samples from the upper mantle to be chemically representative of the mantle as a whole.

However, it has been proposed that a substantial difference exists between a pyrolitic upper mantle and the lower mantle, below the 660 km seismic discontinuity, particularly in terms of Mg/Si and Mg/Fe [START_REF] Ringwood | Significance of the terrestrial Mg/Si ratio[END_REF]. Various evidences have been used to infer a lower mantle chemically distinct from the upper mantle in terms of major and trace elements. Among them, the isotopic and chemical heterogeneities measured in mantle-derived basalts. Measured isotopic ratios support the existence of early-formed chemical heterogeneities that could be preserved in the deepest part of the mantle.

Furthermore, the apparent mismatch between laboratory-measured properties in upper mantle composition assemblage and the seismic and other geophysical properties observed in the lower mantle, coupled with the identification of a global seismic discontinuity at 660 km depth and early interpretations of the density of the lower mantle led to the design of a two chemically distinct layers model of Earth's mantle (see Hofmann, 2014 for a review).

However, one compelling observation in favor of a homogeneous mantle is tomographic images showing slabs of oceanic lithosphere descending through the lower mantle [START_REF] Fukao | Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity: subducted slabs in the transitions zone[END_REF]. Furthermore, recent studies combining mineral physics data with seismological constraints support the idea that the lower mantle is most likely pyrolytic and that there is no need for a chemically stratified mantle [START_REF] Hyung | Is the mantle chemically stratified? Insights from sound velocity modeling and isotope evolution of an early magma ocean[END_REF][START_REF] Zhang | Elastic properties of MgSiO3perovskite under lower mantle conditions and the composition of the deep Earth[END_REF]. While it has been suggested that the Earth's layers could affect just the bulk mantle trace element budget [START_REF] Campbell | Evidence against a chondritic Earth[END_REF], our models show that REE abundances estimated for upper mantle samples are well reproduced by the resulting BSE using accretion models with isotopically-supported building block mixing. This supports the argument in favor of a chemically uniform mantle.

Conclusion

Molten metal -silicate liquid partitioning data have been obtained from 24 multi-anvil experiments on rare earth elements from La to Gd. These elements are lithophile under the conditions of Earth accretion, with molten metal -silicate liquid partition coefficients ranging from 10 -2 to 10 -6 . Their partitioning behaviour is mainly constrained by the oxygen fugacity and the S concentration in the metallic phase of the system.

Using our data, together with previously published results, we obtain a two-variable parameterisation for these elements. They are trivalent during the Earth's accretion, even at low oxygen fugacity conditions, with the exception of Eu, which is divalent.

Our results show that Sm and Nd are not significantly fractionated by core formation processes over a large range of fo 2 conditions, even in the presence of a large quantity of sulfur. The main impact of core formation is to concentrate the REE within the BSE.

The absolute REE concentration in the BSE depends on the nature of the building blocks involved in the accretion scenario. -11.91 ±1.17 1.01 .10 -12 -5.13 ±0.21 9.24 .10 -26 Eu 25 0.9 -0.40 ±0.11 9.64 .10 -5 -15.12 ±1.24 3.02 .10 -11 -5.10 ±0.23 1.30 .10 -16 Gd 20 0.89 -0.63 ±0.14 3.82 .10 -5 -11.59 ±1.17 1.07 .10 -8 -5.24 ±0.21 2.43 .10 -15 Table 3. Concentration of REE (La to Gd), in ppb, along with the enrichment factor (EF) in RLE compared to CI for the BSE proposed in the literature, based on cosmochemichal and/or petrological approaches. All EF are taken from the original papers, with the exception of [START_REF] Allègre | Chemical composition of the Earth and the volatility control on planetary genetics[END_REF], for which the EF is calculated using REE concentrations in the BSE normalized to CI chondrite concentrations given by Barrat et al. (2012). Uncertainties on EF presented here are taken from the original papers for [START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF] and [START_REF] Lyubetskaya | Chemical composition of Earth's primitive mantle and its variance[END_REF], and extrapolated from the uncertainties on the REE concentrations given in the BSE in [START_REF] Allègre | Chemical composition of the Earth and the volatility control on planetary genetics[END_REF] and [START_REF] Mcdonough | The composition of the Earth[END_REF]. Uncertainty (1σ) on the enrichment factor takes into account the uncertainties on the BSE and the CI compositions. b) Resulting REE concentrations (ppb) in the BSE, along with their 1 sigma uncertainty.

Where no precision relative to the chondritic subgroup is given, an average concentration of every subgroup is used to define the building block compositions. Concentrations used for chondrites are reported in Appendix E. Two enrichment factors based on these REE concentrations are reported for each model. EF is obtained using the measured composition of chondrites, whereas EF dry is based on chondritic compositions depleted in volatile elements to match the terrestrial depletion (see text for more details). The resulting enrichment factors are calculated for each REE based on the composition of CI chondrite given by Barrat et al. (2012). Uncertainty (1σ) on the enrichment factor takes into account the uncertainties on the calculated BSE and the CI composition. Table S1. Chemical analysis of the run products. Totals in silicate consider only major oxides, and only S-rich phase for the metallic phase when demixion in the Fe-S-Ni-C system occurs (see Appendix A2). All the reported experiments were performed using the Hvittis based composition. Pressure uncertainties are estimated to be ±0.5 GPa of the reported values and temperature uncertainties are within ±100 K. Oxygen fugacities relative to Iron-Wüstite buffer assuming that γFeO = 1.5, and γFe is calculated using the interaction parameters approach. Gr: Graphite; MgO: MgO single crystal. * For samples embedded in graphite capsules, the maximum C contents in Fe-alloys is estimated from the deviation of the analyses totals from 100%.

±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0 0 ±0
Appendix A2.

Role of graphite and MgO single-crystal capsules

For experiments with graphite capsules, and for S-rich experiments, we observed the coexistence of two immiscible liquids in the run products for the experimental conditions investigated here (see Figure below). For instance, the experiment performed at 6±1 GPa (run #699) shows the coexistence of a S-rich liquid and a S-poor liquid. The presence of carbon into the metallic phase is due to C diffusion from the graphite capsule into the sample. Observations of a demixion in the Fe-S-Ni-C system are consistent with an immiscibility gap in the Fe-C-S system reported previously for pressures below 5.5 GPa (e.g. [START_REF] Corgne | C-and S-rich molten alloy immiscibility and core formation of planetesimals[END_REF][START_REF] Dasgupta | High pressure melting relations in Fe-C-S systems: implications for formation, evolution, and structure of metallic cores in planetary bodies[END_REF].

By reporting the C content (for experiment with low Si content < 1 wt%) versus the S content in the metallic phase for all the experiments in the present study (we estimated the C content as the deviation of the analyses totals from 100%). We found that our semi-quantitative Canalyses are compatible with a decrease of the C-solubility with increasing S-content in the metallic liquid.

Also C and Si contents of the metallic phase appear inversely correlated. These trends are consistent with previous experimental studies [START_REF] Wang | Phase equilibria of liquid Fe-S-C ternary system[END_REF][START_REF] Corgne | C-and S-rich molten alloy immiscibility and core formation of planetesimals[END_REF][START_REF] Dasgupta | Carbon solubility in core melts in a shallow magma ocean environment and distribution of carbon between the Earth's core and the mantle[END_REF][START_REF] Mann | Evidence for high pressure core-mantle differentiation from the metal-silicate partitioning of lithophile and weakly-siderophile elements[END_REF] and thermodynamic models at 1 bar [START_REF] Bouchard | Simultaneous optimization of thermochemical data for liquid iron alloys containing C[END_REF].

Figure A2-2. C (wt%) vs S (wt%) and C (wt%) vs Si (wt%) for run-products with low Si content, and with low S content, respectively.

Low totals for the run-products with MgO single-crystal capsules

For two experiments with MgO capsules, we performed more than 20 chemical analyses and the Total in average is 97.33 ± 0.25. As reported in the back-scattered electron image below this is related to the state of the surface of the run-product that shows high level of porosity.

  photosphere, except for the most volatile elements. REE concentrations in the BSE are

  molten metal-silicate liquid partitioning behaviour is well constrained in the literature: Ni/Co, Nb/Ta, and Th/U. Accretion scenarios must be able to reproduced these elementary ratios already well established for the BSE (Nb/Ta = 14.0±0.60; Th/U = 3.78±0.12; Ni/Co = 18.90±0.30,[START_REF] Munker | Evolution of Planetary Cores and the Earth-Moon System from Nb/Ta Systematics[END_REF][START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF][START_REF] Wipperfurth | Earth's chondritic Th/U: Negligible fractionation during accretion, core formation, and crust-mantle differentiation[END_REF]. The parameterisations used to constrain the behavior of these elements during metal-silicate partitioning are taken fromFischer et al. (2015) for Ni and Co,[START_REF] Cartier | Redox control of the fractionation of niobium and tantalum during planetary accretion and core formation[END_REF] for Nb and Ta and[START_REF] Faure | Uranium and thorium partitioning in the bulk silicate Earth and the oxygen content of Earth's core[END_REF] for U and Th. Of all the accretion scenarios tested, only those reproducing (within 2σ uncertainties) the BSE

  Figure6yield lower enrichment factors.[START_REF] Lyubetskaya | Chemical composition of Earth's primitive mantle and its variance[END_REF], by

Figure 4 .

 4 Figure 4. Sulfur-silicate partition coefficients for REE (normalized to D Nd ) determined

Figure 5 .

 5 Figure 5. Ratio of metal-silicate partition coefficients determined for Sm and Nd

Figure 6 .

 6 Figure 6. RLE enrichment factors of the BSE calculated from accretion scenarios using

  Figure 1 .

  Figure 2 .

  Figure 5.

Figure

  Figure A2-1. Back-scattered electron image of a run-product recovered from 6±1 GPa and 2439 K showing a coexistence in the metallic phase of S-rich and S-poor molten alloys.

Figure

  Figure A2-3. Back-scattered electron image of the metallic phase for a run-product recovered from 14±1 GPa, 2560 K, and using MgO as capsule.

  Our estimate is in good agreement with those of[START_REF] Mcdonough | The composition of the Earth[END_REF] and[START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF], and in favor of a chemically homogeneous present day mantle. This enrichment factor can be extended to other elements which remain strictly lithophile during Earth core formation. The formation of the core, with or without segregation of a sulfide phase, cannot be responsible for the small 142 Nd excess measured in modern terrestrial samples relative to chondrites.

	Figure Captions
	Figure 1. Backscattered electron image of the sample #1322, recovered from a 6 GPa
	and 2503 K experiment in a graphite capsule.
	Figure 2. Evolution of metal-silicate partition coeffcients for neodymium and europium
	(D Nd and D Eu ) with log fo 2 . Datapoints are from this study (Appendix A) and from the

Accretion scenarios using mixtures of chondrites that match the nucleosynthetic signature of the Earth give an average enrichment factor of 2.88 relative to CI. This result takes into account the RLE enrichment of the BSE due to the Earth's depletion in volatile elements compared to chondrites. litterature (Apprendix B). Data are corrected for the effect of metalic sulfur using the parametrization presented in equation 6 and Table 2. Similar binary plots for other studied REE are given in Appendix D.1. Dashed line represents fitted linear regression, in agreement with equation 6 and parameters values displayed in Table 2.

Figure 3. Evolution of metal-silicate partition coefficients for neodymium and europium (D Nd and D Eu ) with the S concentration in the metal. Datapoints are from this study (Appendix A) and from the litterature (Apprendix C). Data are corrected for the effect of oxygen fugacity using the parametrization presented in equation 6 and

Table 2. Similar binary plots for other studied REE are given in Appendix D.1. Dashed line represents fitted linear regression, in agreement with equation 6 and parameters values displayed in Table 2.

Table 1 .

 1 Experimental conditions (P, T, fo 2 ) and metal-silicate partition coefficients of REE (La to Gd) for the different samples. Given uncertainties are 1 sigma. For this work, different doping solutions were synthesized. Type A solution contained La, Ce, Pr, Nd and Sm, while type B solution contained Nd, Sm, Eu and Gd. For sulphur-rich experiments, a type C solution containing all 7 REE from La to Gd was prepared. * Temperature determined using the power/temperature relation deduced from previous experiments.

	Run	Capsule	Doping solution P (GPa)	T (K)	log fo2 (∆IW)	DLa	DCe	DPr	DNd	DSm	DEu	DGd
	509	Graphite	C	6	2361	-0.60	6.19×10 -4 ± 1.63×10 -4	1.01×10 -3 ±1.33×10 -4	9.28×10 -4 ±1.23×10 -4	9.98×10 -4 ±1.67×10 -4	9.49×10 -4 ±1.88×10 -4	1.31×10 -3 ±1.86×10 -4	7.16×10 -4 ±2.09×10 -4
	536	Graphite	C	6	2386	-0.47	1.40×10 -3 ±8.24×10 -5	2.35×10 -3 ±3.70×10 -4	1.98×10 -3 ±1.55×10 -4	1.86×10 -3 ±5.95×10 -5	1.49×10 -3 ±1.85×10 -4	4.95×10 -3 ±3.14×10 -4	8.33×10 -4 ±5.88×10 -5
	581	Graphite	C	6	2563 *	-0.86	4.24×10 -4 ±8.44×10 -5	5.86×10 -4 ±1.16×10 -4	5.41×10 -4 ±8.95×10 -5	4.81×10 -4 ±9.93×10 -5	3.56×10 -4 ±5.16×10 -5	1.01×10 -3 ±1.44×10 -4	2.10×10 -4 ±2.16×10 -4
	594	Graphite	B	6	2388	-3.18				1.76×10 -4 ±1.48×10 -5	1.40×10 -4 ±1.99×10 -5	2.19×10 -4 ±1.77×10 -5	1.00×10 -4 ±6.96×10 -6
	596	Graphite	B	6	2499	-3.40				3.38×10 -5 ±1.04×10 -5	3.50×10 -5 ±5.11×10 -7	2.46×10 -5 ±5.02×10 -7	2.61×10 -5 ±9.61×10 -7
	598	Graphite	A	6	2543	-1.47	1.92×10 -5 ±4.96×10 -6	1.79×10 -5 ±1.71×10 -6	1.11×10 -5 ±4.01×10 -6	1.10×10 -5 ±1.77×10 -6	1.07×10 -5 ±1.55×10 -6
	599	Graphite	A	6	2532	-3.26	5.99×10 -5 ±2.89×10 -5	8.24×10 -5 ±1.42×10 -6	5.97×10 -5 ±3.95×10 -6	6.76×10 -5 ±5.17×10 -6	7.22×10 -5 ±1.66×10 -5
	600	Graphite	A	6	2536	-2.81	1.25×10 -5 ±9.85×10 -6	2.22×10 -5 ±9.56×10 -6	1.39×10 -5 ±3.47×10 -6	2.09×10 -5 ±4.65×10 -6	1.94×10 -5 ±1.53×10 -6
	601	Graphite	A	6	2517	-3.58	2.19×10 -5 ±1.44×10 -5	4.87×10 -5 ±1.82×10 -5	4.40×10 -5 ±1.23×10 -5	5.00×10 -5 ±1.70×10 -5	6.96×10 -5 ±1.43×10 -5
	603	Graphite	B	6	2500	-3.48				2.66×10 -5 ±4.41×10 -6	2.62×10 -5 ±2.69×10 -6	2.21×10 -5 ±3.12×10 -6	1.61×10 -5 ±2.22×10 -6
	685	Graphite	C	6	2529 *	-0.68	1.02×10 -3 ±3.73×10 -4	1.42×10 -3 ±5.23×10 -4	1.33×10 -3 ±4.68×10 -4	1.21×10 -3 ±4.54×10 -4	1.02×10 -3 ±4.01×10 -4	2.30×10 -3 ±7.54×10 -4	6.40×10 -4 ±2.70×10 -4
	693	MgO single crystal	B	14	2560	-1.51				1.25×10 -5 ±5.70×10 -6	1.18×10 -5 ±2.64×10 -6	1.34×10 -5 ±5.31×10 -6	8.47×10-06 ±3.43×10 -6
	694	Graphite	B	6	2365	-0.59				1.83×10 -5 ±2.35×10 -6	1.77×10 -5 ±2.22×10 -6	1.29×10 -5 ±6.03×10 -6	4.59×10 -5 ±3.79×10 -5
	696	MgO single crystal	A	14	2560 *	-1.51	2.61×10 -6 ±1.26×10 -6	6.30×10 -6 ±2.91×10 -6	4.88×10 -6 ±2.17×10 -6	5.36×10 -6 ±1.84×10 -6	6.17×10 -6 ±2.57×10 -6
	698	Graphite	C	6	2429	-0.63	2.74×10 -3 ±5.05×10 -4	3.44×10 -3 ±5.44×10 -4	3.24×10 -3 ±4.87×10 -4	3.04×10 -3 ±3.76×10 -4	2.74×10 -3 ±3.12×10 -4	5.21×10 -3 ±6.54×10 -4	2.06×10 -3 ±2.80×10 -4
	699	Graphite	C	6	2439	-0.20	4.01×10 -3 ±3.42×10 -4	4.85×10 -3 ±4.24×10 -4	4.93×10 -3 ±4.49×10 -4	4.46×10 -3 ±3.34×10 -4	4.15×10 -3 ±3.69×10 -4	7.75×10 -3 ±1.28×10 -3	3.27×10 -3 ±4.72×10 -4
	1320	Graphite	A	6	2450	-1.38	8.09×10 -5 ±1.12×10 -4	1.89×10 -5 ±9.66×10 -6	1.31×10 -5 ±3.09×10 -6	9.36×10 -6 ±1.85×10 -6	2.31×10 -5 ±3.75×10 -6
	1321	Graphite	A	6	2543 *	-2.67	1.56×10 -4 ±4.82×10 -6	2.21×10 -4 ±7.30×10 -6	2.24×10 -4 ±8.93×10 -6	2.29×10 -4 ±1.25×10 -5	2.98×10 -4 ±1.47×10 -5
	1322	Graphite	A	6	2486 *	-3.16	1.71×10 -4 ±3.98×10 -6	3.10×10 -4 ±3.33×10 -6	3.26×10 -4 ±4.45×10 -6	3.54×10 -4 ±5.58×10 -6	4.70×10 -4 ±9.25×10 -6
	1323	Graphite	A	6	2503	-3.42	3.27×10 -4 ±1.15×10 -4	5.11×10 -4 ±1.09×10 -4	6.04×10 -4 ±1.03×10 -4	6.55×10 -4 ±8.62×10 -5	7.65×10 -4 ±1.22×10 -4
	1324	Graphite	B	6	2499 *	-0.82				4.86×10 -5 ±3.71×10 -5	7.60×10 -5 ±4.17×10 -5	7.45×10 -5 ±5.94×10 -5	6.97×10 -5 ±2.12×10 -5
	1325	Graphite	B	6	2517	-3.11				2.80×10 -5 ±9.16×10 -6	4.42×10 -5 ±1.22×10 -5	5.54×10 -5 ±1.07×10 -5	4.34×10 -5 ±3.68×10 -5
	1326	Graphite	B	6	2536	-3.95				1.10×10 -3 ±5.73×10 -5	1.37×10 -3 ±1.12×10 -4	8.30×10 -4 ±5.95×10 -5	1.02×10 -3 ±1.37×10 -4
	1327	Graphite	B	6	2519	-3.46				1.88×10 -4 ±1.73×10 -4	2.96×10 -4 ±1.51×10 -4	1.71×10 -4 ±1.27×10 -4	3.21×10 -4 ±4.06×10 -6

Table 2 .

 2 Results of the multi-variable linear regression based on Equation 6 using experimental data from this study and those from literature listed in Appendix B. Twovariable parametrizations regressed the variables related to log fo 2 (a), the metallic concentration of S (d), along with the equation constant (e). The p-value for each variable used is also shown, with a significance level of 5%.

	Element N°	R 2	a	p-value	d	p-value	e	p-value
	La	25	0.86	-0.61 ±0.12 1.90 .10 -5	-14.20 ±1.5 3.41 .10 -9	-5.34 ±0.27 2.90 .10 -15
	Ce	24	0.87	-0.60 ±0.10 6.66 .10 -5	-13.45 ±1.40 4.23 .10 -9	-5.23 ±0.26 4.37 .10 -15
	Pr	21	0.88	-0.61 ±0.08 6.50 .10 -5	-12.65 ±1.30 1.31 .10 -8	-5.24 ±0.23 1.63 .10 -14
	Nd	42	0.81	-0.62 ±0.09 7.00 .10 -8	-12.45 ±1.16 2.47 .10 -13	-5.19 ±0.21 5.17 .10 -26
	Sm	42	0.8	-0.61 ±0.08 5.14 .10 -8

Table 4 .

 4 Presentation of the accretion models considered in this study. a) Building block mixing proposed by several authors (in %) in order to create the BSE nucleosynthetic composition, which also reproduce several elemental ratios of the BSE (see text for details).

		La	Ce	Pr	Nd	Sm	Eu	Gd	EF compared to CI
	Palme and O'Neill, 2014	683 ±68 1753 ±175 265 ±39 1341 ±134 434 ±43	166 ±17	585 ±29	2.83 ± 0.23
	Lyubetskaya
	and Korenaga,	508 ±87 1340 ±230 203 ±35 994 ±170 324 ±55	123 ±21	432 ±74	2.16 ± 0.37
	2007
	Allègre et al., 2001	415 ±42 1088 ±218 165 ±8	814 ±81	259 ±8	97.9 ±3	348 ±28	1.70 ± 0.24
	McDonough and Sun, 1995	648 ±65 1675 ±168 254 ±25 1250 ±125 406 ±41	154 ±15	544 ±54	2.75 ± 0.27

Graphite capsule MgO single crystal capsule Appendix C.

  Compilation of experimental data

	Appendix C. (continued)
	Run	Capsule	P (GPa)	T (K)	log fO 2 (∆IW)	NBO/T	X S metal (wt%)	D La	D Ce	D Pr	D Nd	D Sm	D Eu	D Gd
							Bouhifd et al., 2015
	969	Gr	4		-1.43	3.61	0.00				4.13×10 -5 4.43×10 -5
	975	Gr	4		-1.56	2.30	0.00				5.05×10 -5 5.38×10 -5
	1026	Gr	5		-0.82	2.29	23.79				1.08×10 -3 1.12×10 -3
	1027	Gr	5		-4.42	2.30	0.00				1.60×10 -3 2.06×10 -3
	986	MgO	6		-1.64	2.08	0.00				5.12×10 -5 6.14×10 -5
	1021	MgO	6		-1.44	2.35	21.53				2.69×10 -4 3.75×10 -4
	1028	MgO	8		-1.45	2.16	19.10				3.00×10 -4 2.75×10 -4
	1029	MgO	8		-4.67	2.14	0.00				4.79×10 -3 5.44×10 -3
	1082	Gr	5		-4.60	0.52	0.00				2.52×10 -2 3.01×10 -2
	1137	Gr	5		0.90	1.73	35.31				1.18×10 -3 7.73×10 -4
							Wohlers and Wood., 2017
	701	Gr	1.5		-0.78	0.80	28.94	1.06×10 -2			1.10×10 -2 9.92×10 -3	1.87×10 -2
	700	Gr	1.5		-3.73	0.24	34.50	3.94×10 -1	5.00×10 -1		4.81×10 -1 4.75×10 -1	2.19×10 -1
	699	Gr	1.5		-3.89	0.43	35.49	2.02×10 -1	1.43×10 -1		2.35×10 -1 2.45×10 -1	2.29×10 -1
	697	Gr	1.5		-3.95	0.25	35.73	3.28×10 -1	5.00×10 -1		3.80×10 -1 3.78E×10 -1 2.17×10 -1
							Ingrao et al., 2019
	1266		8.50E-06		-4.10		36.88	1.70 ×10 -2 2.40×10 -2	3.00×10 -2	2.80×10 -2 4.50×10 -2	9.00×10 -2	2.40×10 -2
	1282		7.00E-08		-4.50		36.56	3.40×10 -2	3.20×10 -2	4.30×10 -2	3.10×10 -2 4.10×10 -2	1.22×10 -1	2.00×10 -2
	1207		9.00E-07		-4.80		38.23	3.86×10 -1	4.81×10 -1	4.25×10 -1	3.99×10 -1 3.27×10 -1	6.58×10 -1	1.52×10 -1
	1239		8.50E-07		-4.80		36.48	5.50×10 -2	5.70×10 -2	4.80×10 -2	5.30×10 -2 5.10×10 -2	7.40×10 -2	3.00×10 -2
	1284		7.00E-08		-5.80		36.66	2.40×10 -2	2.80×10 -2	2.60×10 -2	2.40×10 -2 1.90×10 -2	2.70×10 -2	9.00×10 -3
	1252		1.00E-06		-5.80		36.56	2.72×10 -1	3.68×10 -1	4.06×10 -1	3.34×10 -1 2.96×10 -1	5.98×10 -1	1.40×10 -1

Table S2 .

 S2 Compilation of the experimental data used to derive the coefficients of equation (4) for all studied REE. The uncertainties on the reported data can be found in the original papers.Appendix D. Effect of experimental conditions on REE metal-silicate partition coefficients. Evolution of D REE with log fo 2 . Presented results are from this study (Appendix A) and from literature (Apprendix B). Data are corrected from the effect of metalic sulphur, using the parametrization presented in equation 6 and Table2.

	Run	Capsule	P (Gpa)	T (K)	log fO 2 (∆IW)	NBO/T	X S metal (wt%)	D La	D Ce	D Pr	D Nd	D Sm	D Eu	D Gd
							Lodders (1996)
	EQ6	Gr		1473	2.36		43.7	1.00×10 -2		1.00×10 -2		9.00×10 -3	6.50×10 -2	5.00×10 -3
	EQ1	Gr		1483	2.46		43.6	9.00×10 -3		9.00×10 -3	7.50×10 -3	5.50×10 -3	4.40×10 -2	5.80×10 -3
	VQ1	Gr		1473	2.26		43.56	1.50×10 -2		1.60×10 -2	1.70×10 -2	1.40×10 -2	6.60×10 -2	1.40×10 -2
	VQ2	Gr		1473	2.36		39.5	5.60×10 -3		6.00×10 -3	8.00×10 -3	4.60×10 -3	3.90×10 -2	3.00×10 -3
	VQ4	Gr		1473	0.26		36	4.10×10 -3		3.50×10 -3		3.70×10 -3	6.00×10 -3	2.80×10 -3
	VQ3	Gr		1473	-1.44		33.6	1.30×10 -3		1.20×10 -3		1.30×10 -3	7.00×10 -3
	EQ9	Gr		1473	-2.74		37.65	2.90×10 -1		3.30×10 -1	2.50×10 -1	1.70×10 -1	8.50×10 -1	8.10×10 -2
	EQ10	Gr		1473	-2.84		14.71	4.80×10 -1		5.10×10 -1	3.80×10 -1	2.00×10 -1	1.08	1.40×10 -1
	EQ4	Gr		1473	0		33.9	1.40×10 -3		1.00×10 -3		7.00×10 -4	3.50×10 -3
	EQ3	Gr		1473	-0.34		35	6.00×10 -4					3.00×10 -3
	QR1	Gr		1473	1.76		44.45	3.10×10 -2				1.60×10 -2	1.15×10 -1
	QR2	Gr		1473	2.16		40.42	3.80×10 -2				2.50×10 -2	1.64×10 -1

D.1

Acknowledgments

Detailed reviews by two anonymous reviewers are much appreciated as are the editorial comments and handling by James Badro. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 682778 -ISOREE). The multi-anvil apparatus of Laboratoire Magmas et Volcans is financially supported by the CNRS (Instrument national de l'INSU). This is also the French Government Laboratory of Excellence Initiative N° ANR-10_LABX-006, the Région Auvergne and the European Regional Development Fund. This is Laboratory of Excellence ClerVolc contribution N° xxx.

Appendix A1. Chemical analysis of all run products

Appendix D.2 Evolution of D REE with the S concentration in the metal. Presented results are from this study (Appendix A) and from literature (Apprendix B). Data are corrected for the effect of oxygen fugacity, using the parametrization presented in equation 6 and Table 2. In the following, we will use Nd as an example to determine the effect of temperature on metal-silicate partitioning of the REE.

The metal -silicate partitioning of Nd is shown relative to that of Fe in terms of an exchange reaction:

The free energy of the reaction ∆G reaction = ∆H reaction -T∆S reaction where ∆H reaction and ∆S reaction are the enthalpy and the entropy of the reaction, respectively.

Using tabulated values of H formation (FeO) from [START_REF] Robie | Thermodynamic properties of minerals and relied substances at 298.15 K and 1 bar (10 5 Pascals) pressure and at higher temperatures[END_REF]; and those of [START_REF] Gschneidner | Thermochemistry of the rare Earths[END_REF] and [START_REF] Barin | Thermochemical Data of Pure Substances, Part I and Part II[END_REF] for Nd 2 O 3 , a value of approximately 1000 kJ/mol is obtained for ∆H reaction at 2000 K.

In addition, ∆S reaction = 2 S (Nd) + 3 S (FeO) -S (Nd 2 O 3 ) -3 S (Fe).

Using tabulated values of [START_REF] Barin | Thermochemical Data of Pure Substances, Part I and Part II[END_REF] for Nd, of [START_REF] Gschneidner | Thermochemistry of the rare Earths[END_REF] and [START_REF] Barin | Thermochemical Data of Pure Substances, Part I and Part II[END_REF] for Nd 2 O 3 , and of [START_REF] Robie | Thermodynamic properties of minerals and relied substances at 298.15 K and 1 bar (10 5 Pascals) pressure and at higher temperatures[END_REF] for Fe and FeO, a value of approximately 100 J/mol K is obtained for ∆S reaction at 2000 K.

Therefore, the term T∆S reaction is about one order of magnitude lower than the term ∆H reaction .

Varying the temperature in the likely range during core formation (2500 to 3500 K), will result in a small change on ∆G reaction . From this, and considering that the effect of temperature on ∆H reaction is negligible, we conclude that temperature should not affect metal-silicate partitioning of Nd, and, by extension, all REE.

Appendix E. Accretion model.

We present here models of planetary accretion focusing on the evolution of the REE (La to Gd) content of the different reservoirs (core, bulk silicate Earth) during metal-silicate differentiation.

At each step of accretion (1% M E ), the impactor's metal and silicate equilibrate within the proto-mantle, which represents 68% of planet's mass throughout the entire accretion.

Equilibration pressure is set at a pressure of 50% of the core-mantle boundary at each step.

This fraction is derived from previous studies on the partitioning of siderophile elements sensitive to pressure (e.g. Boujibar et al., 2014;Fischer et al., 2015), leading to a final equilibration pressure set at 60 GPa [START_REF] Siebert | Metal-silicate partitioning of Ni and Co in a deep magma ocean[END_REF]. Temperature is fixed at the liquidus of chondritic melts given in [START_REF] Andrault | Solidus and liquidus profiles of chondritic mantle: Implication for melting of the Earth across its history[END_REF], evolving from 1900 K when the proto-Earth is at 1% of its final mass up to 3500 K in the final stage of accretion. The oxygen fugacity is constrained to the fo 2 paths defined in [START_REF] Clesi | Effect of H 2 O on metal-silicate partitioning of Ni, Co, V, Cr, Mn and Fe: Implications for the oxidation state of the Earth and Mars[END_REF], into a range going from IW-5 to IW-2. All scenarios studied here reproduced within error, the Earth primitive mantle

Each increment of the model represent the growth of the proto-Earth of 1% of its final mass, by the arrival of impactors already differentiated into silicate mantles and metallic cores [START_REF] Taylor | Accretion of differentiated planetesimals to the Earth[END_REF]. The initial chemical compositions of impactors are those measured on various types of chondrites, depending of the studied scenarios chondrites mixtures (Wasson and Kallemeyn, 1988; see below for REE). The compositions of both metal and silicate reservoirs are calculated at 1 GPa and 2000 K for every element studied here, using their respective partition coefficients. The metal silicate equilibration takes place at fo 2 conditions coherent with the type of chondrites attributed to each accretion step, ranging from ∼ IW -4 to IW [START_REF] Brett | Intrinsic oxygen fugacity measurements on seven chondrites, a pallasite, and a tektite and the redox state of meteorite parent bodies[END_REF]. In any way, the silicate reservoir of the impactor contains the near total of all REE because the differentiation leads to a maximum of a few ppb of the studied REE in the metallic phase.

Partitioning is determined using our parameterizations from Table 2. Following the approach of [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF], we take into account the effect of partial metal-silicate equilibration on element partitioning, which is mainly effective during the final 40% of Earth's accretion.

We apply here the method detailed in [START_REF] Rubie | Heterogeneous accretion, composition and core-mantle differentiation of the Earth[END_REF] in order to reproduce the metalsilicate partial equilibration by modeling an exponential decrease of the equilibration rates during the last stage of accretion (see equation 4 of [START_REF] Rubie | Heterogeneous accretion, composition and core-mantle differentiation of the Earth[END_REF]. We consider that the equilibration between the proto-Earth's mantle and the metal of the impactor becomes less efficient as the accretion progresses (e.g. [START_REF] Deguen | Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans[END_REF][START_REF] Rubie | Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed Solar System bodies and accretion of water[END_REF]. For the last giant impact that formed the Moon (M I =0.1M E ), the impactor's core merges almost completely with the Earth's proto-core, with less than 5 % of its mass equilibrating with the silicate mantle. Due to the lithophile behavior of REE, the impact of equilibration on our results is very limited, in agreement with [START_REF] Rudge | Broad bounds on Earth's accretion and core formation constrained by geochemical models[END_REF]. At each step of accretion, the content of the metallic core in Ni, O and Si is defined using the parametrisations of Fischer et al. (2015). The C content of the core remains constant at 0.2 wt% during accretion (Wood et al., 2006), and a late addition of sulfur-rich material increases the S content of the core to 2 wt% to fit geophysical, geochemical, and experimental estimates (e.g., Allègre et al., 1995;Boujibar et al., 2014;Dreibus and Palme, 1996;Palme andO'Neill, 2003, Suer et al., 2017).

Variations of the O and Si contents in the metal are related to the proportion of reduced and oxidized building blocks, which influence the fo 2 path. In models that consider a fully accreted Earth built from a major proportion (80%) of reduced materials, the Earth's core contains 0.2 wt% C, 2 wt% S, 6.75 ± 0.75 wt% Si, and 2.8 ± 0.7 wt% O. However the incorporation of these light elements into the core lead to a negligible enrichment (no more than 1.3%) of the silicate reservoir in REE.

In order to use the most precise and up-to-date REE concentrations for the various types of chondrites proposed as building blocks for the Earth, we compiled data from the most recent publications. The lowest concentrations in REE among the different groups of chondrites are measured in CI and enstatite chondrites whereas the most enriched are those of the CV group (factor 2). For the EL subgroup, data on EL3 from [START_REF] Barrat | The lithophile trace elements in enstatite chondrites[END_REF] are considered. Most EL samples belong to the EL6 subgroup and show depletion in light REE relative to heavy REE due to melting and thermal metamorphism events [START_REF] Barrat | The lithophile trace elements in enstatite chondrites[END_REF]Boyet et al., 2018;[START_REF] Rubin | Possible impact-induced refractorylithophile fractionations in EL chondrites[END_REF]. Concentrations used in this model are presented in the table below (Table S3), along with the enrichment factor f dry which is applied to the REE concentrations in order to take volatile depletion observed on Earth compared to chondrites into account (for details see text). 2.39 Barrat et al., 2012Braukmuller et al., 2018Pourmand and Dauphas., 2012Dauphas and Pourmand., 2015


S Mouaci

N Saidi-Amroun

V Griseri

L Berquez

G Teyssèdre

N Belkahla

M Saidi

Effect of Gamma Irradiation Dose on Space Charge in e-Beam Irradiated PET Films

Keywords: Poly(ethylene terephthalate), gamma radiation, space charge, e-Beam

Investigating radiation-induced effects in synthetic polymers makes sense for nuclear power and aerospace industries. We propose in this work to investigate the effect of the dose pre-deposited by gamma rays on the behavior of the charges implanted by electron beam in PET (polyethylene terephthalate) samples. The samples used in this study are PET films of 25 µm in thickness. The samples were first irradiated by gamma rays, at different doses (0.1 to 2 MGy). Then, they were exposed to 20 keV energy electron beam, during 5 min, with the purpose to implant electrons near the surface. Materials were characterized by different techniques, notably Light Intensity Modulation Method (LIMM) for space charge measurements and FTIR as physicochemical analysis. The results show that the electrons implanted in the PET irradiated at high dose do not stay close to the surface for a long time, which could be associated with significant material modifications at the scale of the molecules.

I. INTRODUCTION

The synthetic polymers have an important place in the nuclear power industry and aerospace. They are sensitive to ionizing radiation, which induces polymer chains excitation and ionization leading, eventually, to the formation of new groups called the radiation defects. The defects can be created in the chain (macromolecular defects) or emitted as small molecules (gas emission). The behavior of polymeric materials face to the irradiation remains a very delicate subject and under the study. In order to reproduce in the laboratory, at least partially, the effects of an "aggressive" environment on polymers and thus to better understand the problems that may occur, the combination of two kinds of irradiation has been studied. Indeed, at present the effects of electron beam (EB) bombardment [START_REF] Vasiljeva | Electron beam induced modification of poly(ethylene terephthalate) films[END_REF][START_REF] Nguyen | Post-Electronic Irradiation Measurements by PEA and FLIMM Methods on Dielectric Films[END_REF] or gamma rays (GR) [START_REF] Mariani | Gamma irradiation of PolyEthyleneTerephthalate and PolyEthyleneNaphthalate[END_REF][START_REF] Belkahla | Space charge, conduction and photoluminescence measurements in gamma irradiated poly(ethylene-2,6-naphthalate)[END_REF] on polymers have been studied separately. An important difference between the two irradiation means is that gamma irradiation produces mainly electron-hole pairs when e-beam can provide in addition primary electron deposition, breaking electrical neutrality. This can make a substantial difference when dealing with irradiation effects on the dielectric properties.

Based on the previous work on the combined effect of gamma ray and electron beam on the electrical properties of polyethylene terephthalate films [5], we present in this work the study of the behavior of the charges implanted by the electron beam on samples previously irradiated by gamma rays. Space charges in irradiated samples were probed by Light Intensity Modulation Method (LIMM) and this was complemented by Fourier Transform Infrared (FTIR) spectroscopy.

II. EXPERIMENTAL

A. Material and irradiation

Polyethylene-terephthalate (PET) films, 25 µm thick were used in this study. The chemical structure of PET is presented in Fig. 1. The particular chemical composition of this polymer, which comprises an aromatic ring, provide it with a set of remarkable chemical, physical and dielectric properties. The samples were first subjected to ionizing radiation ( rays), then bombarded with a dose of electrons. The samples were irradiated in air, at ambient temperature, using 1.25 MeV GR radiation source of 60 Co with a dose rate of 22 Gy/min. The samples were irradiated homogeneously in the dose range of 0.1 to 2 MGy using a facility available at the Nuclear Research Center of Algiers, Algeria.

EB with 20 keV energy at a flux of a 1 nA/cm² was used as post irradiation means to deposit charges. The irradiation time was 5 min. It was realized under secondary vacuum using the Matspace facility [START_REF] Belkahla | Space charge, conduction and photoluminescence measurements in gamma irradiated poly(ethylene-2,6-naphthalate)[END_REF]. It can be considered to be homogeneous over sample surface of several cm². With this energy, electrons are deposited within a few µm from the surface. Fig. 2 shows the maximum penetration depth of electrons predicted using the ESTAR software for PET.

B. Measurement methods

For the relatively thin films probed in this work, only thermal methods like thermal pulse or Light Intensity Modulation Method (LIMM) can provide space charge data with good spatial resolution [START_REF] Fleming | Space charge profile measurement techniques: recent advances and future directions[END_REF]. The LIMM method was selected and used in air in postirradiation conditions. It gives access to the distribution of space charge in the volume of the irradiated films, after the end of the irradiation. It is based on a perturbation of the electrostatic equilibrium consisting in a non-uniform thermal gradient created inside the material. A laser beam modulated in intensity and focused on the surface of the sample provides such thermal perturbation at frequencies in the range 10 2 -10 4 Hz. The interaction between the thermal wave with the charge and / or the spatial polarization produces a pyroelectric current. This current is converted into a voltage and extracted from the noise by a synchronous detector that provides the real and the imaginary part of the pyroelectric current. A mathematical deconvolution then makes it possible to determine the space charge profiles [START_REF] Fleming | Space charge profile measurement techniques: recent advances and future directions[END_REF]. The microcomputer manages the modulation frequency of the laser beam, the acquisition of the useful signal and the laser beam position on the surface of the sample.

The FTIR spectra of our polymer films were recorded in transmission mode from a Thermo-Nicolet spectrometer of a range of 400 to 4000 cm -1 with a resolution of 2 cm -1 . The information extracted from the infrared absorption spectrum is qualitative and quantitative.

III. RESULTS AND DISCUSSION

A. Physicochemical analysis

Generally, the most obvious chemical and physical changes that occur when polymers are exposed to ionizing radiation are formation of the volatile products, the loss of mass, the appearance of unsaturated structures, the chains scission and the crosslinking [START_REF] Mariani | Gamma irradiation of PolyEthyleneTerephthalate and PolyEthyleneNaphthalate[END_REF].

The overall FTIR spectra recorded for the irradiated GR + EB PET films with different GR doses are shown in Fig. 2 and compared to the reference PET. It should be noted that the baseline has been subtracted from the spectra for a better comparison. The peaks observed in the spectral region 500 -1100 cm -1 are those reported in the literature [8-10]. The CH 2 rotation in trans conformation gives the 728 cm -1 band. The bands between 847-880 cm -1 are related to the group C = C-H (aromatic ring) and the phenol group (OH). In addition, the broad bands located between 1100 and 1300 cm -1 are attributed mainly to a C-O stretch of the ester group. The evolution of the area of the peaks at 728 and 1018 cm -1 as a function of the absorbed doses of GR + EB is shown in Fig. 3. The peaks area shows a slight rise for 100 kGy GR dose and then it continuously decreases with a substantial for larger doses. As for the other peaks (793, 849, 873 and 972 cm -1 ), their intensities remain only slightly affected during the irradiation. The peaks positioned between 1471-1680 cm -1 are assigned to carboxylic acid groups. The most intense bands at 1723 cm - 1 are attributed to the C = O carbonyl groups. To better visualize the degradation of PET after radiation exposure, we plotted the area of the peaks at 1340, 1410 and 1725 cm -1 (the representation is given in Fig. 4). We find that the intensity of the peaks decreases very strongly with the absorbed dose of GR + EB. Also, the oxidation plays an important role in the degradation of the material as is has already been reported [START_REF] Kormunda | Characterization of oxygen and argon ion flux interaction with PET surfaces by in-situ XPS and ex-situ FTIR[END_REF]. From the analysis of the FTIR spectra, we can deduce that there is a major structural evolution between the irradiated sample and virgin one, especially at high doses (2 MGy + 20 keV). A reduction in peak intensity indicates a decrease in the concentration of the original bands and / or the change in the chemical environment of the band. This decrease is related to the degradation of the material by a scission of macromolecular chains, and consequently a decrease in the average molecular weight.

B. Profiles of charges density and electric field

The space charge measurements were performed directly after electron beam irradiation. The sample was placed in the cell, with the irradiated surface placed facing the laser beam. In such a way, the region with implanted electron is probed with improved spatial resolution. To obtain the charge density and electric field profiles, the real and imaginary parts of the pyroelectric currents are recorded then deconvolution is applied.

Fig. 6 shows the charge density profiles obtained by the LIMM method for the irradiated samples. It should be noted that the samples irradiated only with GR showed no workable signal. The charge density profiles shows the existence of two peaks, a negative charge peak near the surface and positive charge one deeper in the bulk. The positive charge detected at the very surface is probably due to artefacts in the LIMM signal conditioning [START_REF] Bouchareb | Etude de matériaux irradiés sous faisceau d'électrons[END_REF].

The peak of negative charges is most probably due to electrons implanted by the beam. It is detected at around 2 μm for the irradiated samples GR + EB. For the sample irradiated only with electrons beam, the peak is positioned at 4 μm. Indeed, the charges are implanted near the irradiated surface and this penetration depth is consistent with that predicted (maximum penetration 6 µm) by the model (Fig. 2).

The positive charge peak is present in the bulk for all the samples. Its origin is not clear. As PET is a polar material, one possibility is the build-up of orientation polarization under the field produced by the deposited electrons. Charge profiles with stable double peak in the bulk were observed in a similar way when homocharges were generated under high DC field and the features were observed using different techniques [START_REF] Teyssedre | High electric field behavior and energetic processes in Poly(ethylene naphthalate)[END_REF].

The detected charge amount is very large, implying very large residual fields, of the order of 100-200kV/mm, induced by space charges, see Fig. 7. These very large fields produced by electron implantation may indeed drive very specific charging processes into the bulk of polar materials. The internal electric field profiles of irradiated samples GR + EB are shown in Fig. 7. We find that the electric field is positive between 0-3 μm and negative in the region 3-10 μm. Therefore, the negative charges will tend to migrate to the nonirradiated region of the sample over time. In addition, we noticed that a positive peak of field related to the positive charges is located at around 12 μm. This peak, observed for all moderate doses, has a larger amplitude than the one related to negative charges. This peak, observed for all moderate doses, has a larger amplitude than the one related to negative charges. An important information is the evolution of the response with the dose. For moderate GR doses, 0 to 300 MGy, the shape of the charge or field profiles does not evolve much with the dose. Also, at low dose the charge amount does not evolve in the same way as FTIR data. It means that main effects at the origin of charge build-up as double peak with combined irradiation sources are presumably not due to the post gamma irradiation effects (as could be the case if electron-holes pair generated would be stabilized in deep traps).

For larger GR dose (2 MGy), a much lower charge density is obtained. The signal is practically uniform and the material cannot anymore retain the charge generated by the e-beam.

In summary, the strongly irradiated sample by gamma radiation retains very little charge injected by the electrons beam (the peak of 2 MGy + 20 keV is ten times less intense than that of the virgin).

IV. CONCLUSION

In this paper we have presented the space charge distribution profiles recorded by LIMM technique and the physicochemical modification of PET samples irradiated by combined gamma-ray and electron beam sources. These results show that very high internal field can be generated into PET by e-beam irradiation and this electron implantation induced complex space charge profiles. For doses up to 300kGy under GR, the behavior of the samples does not depend much on the on the irradiation dose whereas FTIR spectra show noticeable evolution.

The electrons implanted in the strongly irradiated sample do not stay trapped close to the surface for a long time, which could be associated with significant modifications at the scale of the PET molecules.

Fig. 1 .

 1 Fig. 1. The chemical structure of PET

Fig. 2 .

 2 Fig. 2. Maximum electron penetration depth versus energy according to ESTAR software.

Fig. 3 .

 3 Fig.3. FTIR spectra of irradiated PET

Fig. 4 .

 4 Fig.[START_REF] Belkahla | Space charge, conduction and photoluminescence measurements in gamma irradiated poly(ethylene-2,6-naphthalate)[END_REF]. The areas of the peaks at 728 cm -1 and 1018 cm-1 versus the absorbed dose.

Fig. 5 .

 5 Fig. 5. The areas of the peaks at 1340, 1410 and 1725 cm -1 versus the absorbed doses.

Fig. 6 .

 6 Fig. 6. Evolution of charge distribution profile as a function of the gamma doses

Fig. 7 .

 7 Fig. 7. Evolution of electric field distribution profile as a function of the gamma doses (Energy of electron beam : 20 keV during 5 min)

ACKNOWLEDGMENT

The authors are thankful to Mansouri, Mahlous, Arib and the Director of the Nuclear Research Center of Algiers for the irradiation of the samples.