Coste Mawélé Loudy

Joachim Allouche

Antoine Bousquet

Hervé Martinez
email: herve.martinez@univ-pau.fr

Laurent Billon
email: laurent.billon@univ-pau.fr

Nanopatterned dual reactive surface-driven by block copolymer self-assembly

Keywords: thermoresponsive surface, patterned surface, click chemistry, gold nanoparticle, self-assembly, grafting

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The self-assembly of block copolymers (BCPs) at the nanoscale is attracting more and more research fields because of its various applications for emerging nanotechnologies such as sensors, organic optoelectronics, catalytic nanostamps, transistors and nanotemplating. [1] Among their various applications, the fabrication of patterned surfaces with a spatial resolution below 50 nm which cannot be reached by traditional lithographic means, has recently gained significant attention. [2,3] Moreover researchers have shown that BCP self-assembly could serve as a template for localized surface modification. Delaittre et al. have reported some examples of phase-segregating block copolymer systems to produce controlled nanopatterned platforms for further surface modification. [4,5] The authors synthesized derivatives of polystyrene-blockpolyisoprene bearing reactive functions towards Huisgen cycloaddition, or nucleophilic substitution reactions to produce a surface-reactive nanostructured films with 30 nm domains.

Billon et al. also reported the fabrication of a triple structured honeycomb film made with a polystyrene-block-poly(4-vinylbenzylchloride). The patterned surface was then modified by azidation and subsequent Huisgen cycloaddition with organic molecules to obtain a pHtriggered wettability. [6,7] This reactive patterning technology is getting even more interest in biological systems and medicine where the precise localization and the proximity of some proteins and enzymes are required for efficiency. [8] For example, the interaction between the cell and the extracellular matrix (ECM) is done through transmembrane cell adhesion proteins responsible of the signal transduction. [11] The principal receptors on animal cells for binding most extracellular matrix are integrins. The linkage of ECM to the cell is done through some specific sites called focal adhesions (FAs), by which the cell can recognize biochemical features, process and explore external stimuli. [12] The spatial organization and the spacing of integrins are key factors for the succesful recognition of biological systems and stimuli. Usually spacing below 100 nm is required, and can be achieved through the grafting of the receptors on gold nanoparticle patterns, obtained through block copolymers self-assembly. Arnold and co-workers proposed that the range between 58-73 nm was a universal ligand spacing for integrins. [13][14][15] They used polystyrene-block-poly(2-vinylpyridine) (PS-b-P2VP) micelle nanolithography to prepare surface patterned with gold nanodot of 8 nm diameters. This platform provided precise anchor point for integrin molecules that reacted through the cysteine groups of their beta subunits.

Using the self-assembly of various compositions of PS-b-P2VP, they were able to design the space between the gold mono-anchors from 28 nm to 85 nm. [13] Stimuli responsive surfaces are getting more and more attractive due to their ability to change their physical properties when subjected to different stimuli as temperature, light or pH.

Such surfaces can offer many applications in medicine [16,17] , bacterial biofilm [19] , tissue engineering [20] , cell culture [21] , mammalian cell release surfaces [22] and controlled delivery. [23] Since the first work of Heskins and al. [24] who showed that bulk poly(N-isopropylacrylamide) (PNIPAM) could express a lower critical solution temperature (LCST) close to the physiological temperature (32° C in water), many works have been done to investigate the thermoresponsive properties of surfaces modified by poly(N-isopropylacrylamide) (PNIPAM). [25,26] The aim of all those methods is to induce a switch of the surface wettability, from hydrophilic to hydrophobic when the temperature is increased above the LCST. When grafted onto the surfaces of cell culture dishes, PNIPAM can exhibit this behaviour allowing the proliferation and attachment of biological cells around 37° C (physiological temperature) and their removal from the surface around 20° C. [31] In this work we report the functionalisation of selective domains of a nanopatterned polymer thin film made of polystyrene-block-poly(4-vinylbenzyl azide) (PS-b-PVBN3). The polymer self-assembled into in-plane cylinders of poly(4-vinylbenzyl azide) that can be postmodified via Huisgen cycloaddition with both organic and inorganic materials, without modifying the surface structuration. Ethynyl-terminated PNIPAM and propargyl-capped-gold nanoparticles were covalently grafted to the surface of the film through click reaction with the azide group of the PVBN3 block (Scheme 1). The functionalized surface shows reversible thermoresponsive properties due to the presence of PNIPAM. Moreover, the spatial organization of gold nanoparticles patterned by the block copolymer self-assembly and separated by thermoswitchable PNIPAM could be a good candidate for single anchor points template for biochemical systems, as mentioned by Arnold et al., previously. [19][20][21] Scheme 1. Synthetic pathway for the dual grafting of PNIPAM and gold nanoparticles onto PVBN3 domains of a nanopatterned film of PS-b-PVBN3.

Results and Discussion

The polystyrene-block-poly(4-vinylbenzylazide) (PS-b-PVBN3) was synthesized in three steps via radical polymerization and nucleophilic substitution reaction (scheme SI1).

Styrene was first polymerized by NMP using Blockbuilder® as initiator and controlling agent.

The reaction was stopped at 50% conversion (followed by 1 H NMR) to ensure a high fraction of nitroxide end-functional chains. After purification the PS macro-initiator was used to SI1). The size exclusion chromatograms of both the macro-initiator (PS-SG1) and the final block copolymer (PS-b-PVBN3) in THF are reported in supporting information (Figure SI2). A narrow dispersity was observed for PS (Ð = 1.1) and PS-b-PVBN3 (Ð = 1.2) as reported in literature for PS and derivatives synthesized by Nitroxide-Mediated Polymerization. [6,32] The molar mass of PS-b-PVBN3 calculated from SEC analysis using PS calibration was found to be equal to 49 000 g.mol -1 .

The elaboration of a hybrid functional surface from self-assembled films of PS-b-PVBN3 studied in this work was done through a chemical grafting via Huisgen cycloaddition between azide groups at the surface of PS-b-PVBN3 film and alkyne functionalized materials.

For this reason, propargyl-terminated PNIPAM was synthesized by ATRP using propargyl 2bromoisobutyrate, an ATRP initiator with a carbon-carbon triple bond. For the same purpose, 5 nm gold nanoparticles were prepared in one step using a poly(ethyleneglycol) (PEG) ligand bearing a propargyl group and HAuCl4.6H2O salt. Details about the synthesis and characterization of those two materials can be found in supporting information (Figures SI3-8, Tables SI2-3).

Films were prepared through the drop-casting of a PS-b-PVBN3 solution in chloroform (10 g.L -1) on a glass slide. It is well known that linear diblock copolymer self-assembly depends on three parameters as predicted by the self-consistent mean-field theory: the volume fraction of the blocks (f), the total degree of polymerization (N) and the interaction between the two segments (χ, Fluory-Huggins parameter) [33] . Using the degree of polymerisation of the blocks (330 for styrene and 150 vinylbenzyl azide), the volume fraction of PS has been calculated and was equal to 0.63, characteristic value for a thermodynamic assembly into hexagonal-closepacked (hcp) cylinders. AFM images of the top surface of PS-b-PVBN3 film are depicted in Figure 1a. Parallel cylinders of PVBN3 (red colour) in a PS matrix (green colour) can clearly be observed. Such a structuration is in agreement with the previous calculated volume fractions and with PS-based block copolymers reported in the literature with similar composition. [33][34][35][36] It is worth noting that no thermal or solvent annealing were performed to reach the thermodynamic equilibrium of the hcp feature. From this image, we could also observe that PS has a higher adhesion value than PVBN3. After the click reaction with the alkyne modified particles, the AFM images showed black dots with a low adhesion value pertaining to the gold nanoparticles grafted at the top surface of the copolymer film (Figure 1b). It is clear that the nanoparticles are only grafted on the PVBN3 domains of the nanopatterned surface bearing the reactive azide anchor. When alkyne-functionalized PNIPAM was grafted onto PVBN3 domains (Figure 1c and1d), a significant shift of the adhesion value was observed (from 17.2 mV to 69 mV), indicating the successful anchoring of PNIPAM. 1e). N 1s high resolution spectrum is depicted in Figure 1i. The characteristic azide spectrum was best fitted with 2 components (intensity ratio 1:2, in agreement with the chemical formula of azide): the positively charged nitrogen (404.2 eV) and the neutral and negatively charged nitrogen peak (400.5 eV) [37] . The total contribution of nitrogen represented 1.8 % in atomic percentage (Table SI4). The success grafting of gold nanoparticles at the surface of PSb-PVBN3 can clearly be observed from both carbon and nitrogen spectra (Figure 1f,1j). Indeed, an increase of the intensity of the component at 286.2 eV is observed, due to C-O and C-S bonds from PEG-propargyl ligand at the surface of gold nanoparticles. Note that C-O, C-N and C-S have the same binding energy range and cannot be discriminated. A detailed quantification (Table SI5) from N 1s, O 1s and S 2p high resolution spectra showed that more than half of the intensity of that peak (2.8/4.1) comes from C-O and C-S bonds. The atomic percentage of nitrogen (azide peaks) slightly decreased (1.5 %) compared to PS-b-PVBN3 sample (1.8 %). Moreover, a new component is observed under the same area at 401 eV (labelled 2, figure 1j) with an intensity that is twice the one of the arising peak around 402.5 eV (labelled 1, figure 1j), in agreement with triazole binding energy as reported in literature. [START_REF] Savin | Writ. React. Mech. Org. Chem[END_REF][START_REF] Maalouli | [END_REF][40][41] The triazole environment (0.4 at. %) is only a fraction of the total amount of nitrogen detected by XPS (1.9 at. %), meaning that only 21% of the azide-anchors present at the surface of the film reacted with the ligands of gold nanoparticles. This quantitative XPS information is in line with the AFM observation where we can clearly observe black dots of gold nanoparticles between which the polymer is still visible. Thus the remaining azide-anchors can been used for further functionalization of the surface with PNIPAM polymer to create a thermoresponsive surface. Prior to this, PNIPAM was grafted on bare PS-b-PVBN3 film. Figure 1c shows the AFM image of the surface where the nanophase segregation is still visible. XPS was also used to confirm the anchoring of PNIPAM with the increase of C-N component at 286.2 compared to PS-b-PVBN3 sample (Figure 1k and1e). Moreover, a new component attributed to C=O can be observed, in agreement with the chemical formula of PNIPAM. The XPS N core peak (Figure 1k) presents a component located at 399 eV attributed to the secondary amide environment of PNIPAM.

The successful grafting of PNIPAM on PS-b-PVBN3 films modified with gold nanoparticles was finally proved by XPS with changes occurring on C 1s and N 1s spectra of the sample (Figure 1h,1l). First, an increase of C-N component at 286.4 eV (5.6 %) is noticeable compared with the sample of the film grafted with nanoparticles (4.0 %). Secondly, the apparition of C=O bond (288.3 eV) from the acrylamide group can be observed. The decrease of the intensity of the shake-up transition (291 eV) agrees with the addition of nonaromatic organic compound. The total amount of nitrogen increased from 1.9 % before grafting PNIPAM (Table SI5) to 2.9 % after reaction (Table 1). The intensity of azide positively charged peak at 404.2 eV decreased and triazole relative compounds (400.9 and 402 eV) increased due to the click reaction. Eventually, a strong intensity peak was observed at 399.9 eV, characteristic of nitrogen environment in PNIPAM [42] .

Table 1. XPS data of the final hybrid film after the dual grafting of GNPs@propargyl-PEG4thiol and propargyl-PNIPAM on PS-b-PVBN3 film. The wettability of the surfaces was studied using water contact angle measurements. No significant changes were observed for the contact angle value of PS-b-PVBN3 films before (92°) and after (90°) grafting gold nanoparticles (Figure SI9). Pure PNIPAM films, however, exhibited remarkable change of the water contact angle (CA) with temperature. As expected, at 25°C the CA was 31° whereas at 45°C it raised to 65° with a persistent reversible behaviour during at least 4 cycles, as shown in Figure 2. It is well known thast below its lower critical solution temperature (LCST, 32 °C), PNIPAM polymer chains are swollen, due to high interactions by hydrogen bonds with water that makes the polymer hydrophylic. [43,44] When the temperature is beyond its LCST, the hydrogen bonds weaken and the chains collapse into a hydrophobic state by water release. Finally, PNIPAM chains grafted specifically on PBVN3 domains exhibited the same thermoresponsive behaviour, with water angle contact switching from 78° at room temperature (25 °C) to 92° when heated at 45 °C (Figure 2). This amplitude, weaker than for the pure PNIPAM film, is in agreement with the surface fraction (40%) of the PS-b-PVBN3 film effectively grafted with PNIPAM. anchors to chemically bind both organic compounds and inorganic nanoparticles. A precise surface analysis by XPS, carried out under rigorous conditions like negative temperature, appeared to be a good tool to monitor quantitatively the reaction of likely unstable organic functions such as azide groups. The block copolymer surface grafted with PNIPAM exhibits thermoresponsive properties with significant changes of the contact angle at room temperature and above the LCST. Moreover, the grafting of PNIPAM in the inter-particle space to produce thermo-responsive surfaces can be a tool to trigger the cell adhesion. This property, combined with the chemical attachment of gold nanoparticles could offer a nanopatterned template for functionalization with integrins, allowing efficient interaction with living system through the so-called focal adhesion.

Orbitals

Experimental section

Materials Synthesis: See Synthesis section in the supporting information.

Chemicals, reagents: Propargyl-PEG4-thiol (90%) was brought from Brodpharm (USA). All other chemicals were purchased from Sigma Aldrich and used without further purification except copper bromide (CuBr) which was purified by stirring with acetic acid overnight, washing with acetic acid, absolute ethanol and diethyl ether before finally be dried in a vacuum oven.

Preparation of the hybrid film: Films were prepared through a drop-casting process. Contact Angle measurements were done using an instrument designed in the Lab. The apparatus was made of an optical bench equipped with a heat control unit that can reach till 200 °C, a humidity control system and an ethernet camera that can record 30 images per second. Angle angles were obtained through the analysis of the images using LabVIEW software.

References:

[1] H.

polymerize 4 -

 4 vinylbenzylchloride (VBC) to form PS-b-PVBC which, after reaction with NaN3, led to the formation of the final block copolymer (PS-b-PVBN3). 1 H NMR analysis have been carried out to determine the molar composition of the final block copolymer as PS330-b-(PVBN3)150 (see supporting information Figure SI1 and Table

Figure 1 .

 1 Figure 1. AFM images, C 1s and N 1s spectra from XPS analysis of bare PS-b-PVBN3 film (a,e,i) and PS-b-PVBN3 film grafted with: GNPs (b,f,j), PNIPAM (c,g,k) and both GNP and PNIPAM (d,h,l). X-ray photoelectron spectroscopy (XPS) was performed on the different films: PS-b-PVBN3, PS-b-PVBN3 grafted with both gold nanoparticles and PNIPAM and PS-b-PVBN3grafted with each separate materials. Note that XPS experiments were carried out at nitrogen temperature to avoid degradation effects under the X-ray beam. The C 1s spectrum (Figure1e)

Figure 2 .

 2 Figure 2. (a) Reversible wettability behaviour of pure PNIPAM film (grey) and PS-b-PVBN3 film grafted with PNIPAM (orange), observed through the measurement of water contact angle at 25 and 45 °C. (b) Pictures of the corresponding water droplets.

A 10 g

 10 .L -1 solution of PS-b-PVBN3 in chloroform was carefully drop-casted on a microscope glass slide to form a continuous film after the evaporation of the solvent. This led to a well-organized structure with distinct domains of PS and PVBN3 on which selective click reactions were performed were performed on the extreme surface of PS-b-PVBN3, allowing therefore to chemically bind successively both inorganic nanoparticles PNIPAM. Propargyl-PEG4-thiolcapped gold nanoparticles were first clicked on PVBN3 nanodomains. CuBr (4 mg), sodium ascorbate (4 mg) and PMDETA (5 mL) were added to a plastic tube containing 10 mL of ethanol. The mixture was stirred before adding 5 mL of the synthesized suspension of gold nanoparticles. Finally, the microscope slide containing the self-assembled film was dipped into the mixture for overnight. Then the glass was vigorously washed in ethanol several times and whether dried before the click reaction with Ethynyl terminated PNIPAM using the same procedure.Characterization: 1 H NMR experiments were carried out on a Bruker 400 MHz spectrometer in CDCl3 at 27 °C. XPS measurements were performed using an Escalab 250 Xi spectrometer using a monochromatized Al Kα radiation (hν = 1486.6 eV) at liquid nitrogen temperature. Atomic force microscopic (AFM) images were obtained using MultiMode® 8 Atomic Force Microscope (AFM) from Bruker in a PeakForce QNM (Quantitative NanoMechanics) mode. Transmission Electron Microscopy images of gold nanoparticles were performed on a Philips CM 200 (200 kV) TEM microscope equipped with a LaB6 source.

  -C. Kim, S.-M. Park, W. D. Hinsberg, Chem. Rev. 2010, 110, 146.

AUTHOR INFORMATION

Corresponding Authors e-mail: herve.martinez@univ-pau.fr; laurent.billon@univ-pau.fr;

Funding Sources

ACKNOWLEDGMENT

We thank Dr. A. Khoukh and Dominique FOIX are acknowledged for fruitful discussions on NMR and XPS analysis. We thank F. Portail, C. Bessibes, and F. Casbas of Arkema Industry for the TEM analysis realized on propargyl-PEG4-thiol-capped gold nanoparticles, Francis Ehrenfeld and Anthony Laffore for constructing and making available a well-equipped instrument for angle contact analysis in a controlled environment.


A D Rosa

M A Bouhifd

G Morard

R Briggs

G Garbarino

T Irifune

O Mathon

S Pascarelli

Krypton storage capacity of the Earth's lower mantle

Noble gases are important geochemical tracers allowing reconstructing global volatile cycles in Earth's reservoirs. To constrain these fundamental processes, precise data on their partitioning behavior at deep Earth conditions are needed. Such data are only available at moderate pressures up to 25 GPa due to experimental challenges. We have investigated the possibility of noble gas storage in the Earth's lower mantle up to 115 GPa. We studied the incorporation of krypton in the second most abundant lower mantle mineral (Mg1-x,Fex)O (ferropericlase) as well as in liquid metal-alloys by performing experiments up to 115 GPa and 3700 K using the laser-heated diamond anvil cell coupled to post-mortem EMPA analysis and X-ray absorption spectroscopy. The results reveal that, at these extreme conditions, up to 3 wt.% of krypton can be stored in (Mg1-x,Fex)O and 3000 ppm in the Fe-rich liquid metal. For both phases the storage capacities increase with pressure (between 40 GPa and 60 GPa) at a constant high temperature of 2300 K. Fpc has never been considered as a NG host, despite being the second most abundant mineral in the Earth's LM. Using recent accurate compressibility data, we demonstrate that a substitution of krypton into the anion site of (Mg1x,Fex)O in form of neutral oxygen Schottky defects at diluted lower mantle conditions is possible. This noble gas incorporation mechanism is in agreement with a previous study on bridgmanite. We show that (Mg1-x,Fex)O exhibits higher noble gas storage capacities than bridgmanite through the lower mantle using lattice strain modelling and including experimental solubility and thermoelastic data for neon, argon, krypton and xenon. We also demonstrate that both phases exhibit the highest solubilities for argon and krypton. We used the solubility data from lattice strain modelling to predict noble gas abundances stored in the solid lower mantle after magma ocean crystallization. The modelled abundances show apparent similarities with estimates for the deep noble gas reservoir that are based on either 3 He abundances in ocean island basalts or radiogenic 40 Ar abundances in the bulk Earth. This strongly indicates that the crystalline lower mantle may play an important role as deep noble gas storage reservoir. We propose, based on considerations on noble gas replenishment from the lower mantle to the atmosphere, that the lower mantle can only contribute to a small fraction of the present-day atmospheric noble gases. This suggests that the lower mantle is an un-degassed reservoir.

Highlights

1. Krypton storage capacities of (Mg,Fe)O and metal alloys up to 115 GPa and 3700 K 2. Storage capacities of lower mantle minerals are greater than those of metallic melts 3. Zero-charged krypton is incorporated in neutral oxygen defects of (Mg,Fe)O 4. The lower mantle could be a reservoir for noble gases through geologic times * Note: b and t denoted bottom and top, respectively.

Introduction

Noble gases (NGs) are important geochemical tracers allowing reconstructing atmospheric evolution processes over geological time scales (i.e., [START_REF] Moreira | Noble gas constrains on the origin and evolution of the Earth's volatiles[END_REF]. NG isotope patterns of oceanic island and mid oceanic ridge basalts (OIB and MORB) provide evidence for two different mantle NG reservoirs: the strongly degassed source of MORBs and a less degassed primordial reservoir sampled eventually by deeply originating mantle plumes of OIBs [START_REF] Allègre | Implications for a two-component marble-cake mantle[END_REF]Marty, 2012;Mukhopadhyay, 2012;[START_REF] Moreira | Noble gas constrains on the origin and evolution of the Earth's volatiles[END_REF]. The isotopic fingerprints for light NGs including He and Ne, indicate that the deep reservoir must have been created very early during Earth accretion (100 Myrs of solar system history) as it retained a fraction of the implanted proto-solar nebula. Moreover, because the deep reservoir inherits a higher fraction of fissogenic non-degassed xenon (Xe) isotopes than MORBs (formed by radioactive decay of U and Pu), it is assumed that the two reservoirs were decoupled early after Earth accretion (about 4.45 Gyrs ago) (e.g., Allègre et al., 1983;Pepin and Porcelli, 2006;Mukhopadhyay, 2012).

The size and location of the deep reservoir still remain subjects of debates because of the difficulties to constrain the exact sources and origins of OIBs. Possible candidates have been proposed including the entire lower mantle (LM), the D'' layer and the Earth's core [START_REF] Allègre | Implications for a two-component marble-cake mantle[END_REF]Marty, 2012;Mukhopadhyay, 2012;[START_REF] Bouhifd | Helium in the Early Earth core[END_REF]Moreira and Kunz, 2013).

The solubility data of NGs in different deep mantle and core phases (minerals and melts) could provide important information by identifying in which reservoir NGs have preferentially partitioned during the crystallization of the magma ocean (MO). Previous experimental studies on NG solubilities have revealed their preferential partitioning in silicate melts as compared to minerals at upper mantle (UM) conditions [START_REF] Carroll | Noble gas solubilities in silicate melts and glasses: New experimental results for argon and the relationship between solubility and ionic porosity[END_REF][START_REF] Matsuda | Noble gas partitioning between metal and silicate under pressure[END_REF]Brooker et al., 2003;[START_REF] Bouhifd | Aluminium control of argon solubility in silicate melts under pressure[END_REF][START_REF] Heber | Crystal-melt partitioning of noble gases (helium, neon, argon, krypton, and xenon) for olivine and clinopyroxene[END_REF][START_REF] Watson | 40Ar retention in the terrestrial planets[END_REF]. Because NGs exhibit also higher diffusivities in melts than in silicates at shallow mantle conditions [START_REF] Hofman | An assessment of local and regional isotopic equilibration in the mantle[END_REF], they are efficiently extracted from the mantle through partial melting and back-recycled into the atmosphere via volcanism.

In contrast to the observed NGs incompatibilities in silicates at shallow mantle conditions, Shcheka and Keppler (2012) reported high compatibilities of argon (Ar) and krypton (Kr) in the LM mineral bridgmanite (Bg). They reported solubilities of up to 1 wt.% for Ar, 3000 ppm for Kr and 300 ppm for Xe at 25 GPa and 2100 K and proposed that NGs are most likely incorporated in neutral oxygen vacancies. Interestingly, Ar solubilities measured in chondritic melts at similar conditions are below those of Bg [START_REF] Bouhifd | Aluminium control of argon solubility in silicate melts under pressure[END_REF], while those measured in pure SiO2 melts are in the same order of magnitude (~ 1 wt.% Ar) [START_REF] Niwa | Argon solubility in SiO2 melt under high pressures: A new experimental result using laser-heated diamond anvil cell[END_REF]. These discrepancies on NG solubilities in silicate melts might be related to compositional effects. Overall, previous observations suggest that LM minerals may exhibit higher NG solubilities and bear the capacity to store NGs over geological time scales. Shcheka and Keppler (2012) also proposed that the reinjection of these deeply stored NGs, predominantly composed of Ar and Kr, through mantle melting may explain the Xe depletion signature of the Earth atmosphere [START_REF] Pepin | Origin of noble gases in the terrestrial planets[END_REF]. However, the contribution of LM NGs to the present-day atmospheric signature may be only minor as the source of atmospheric xenon has been recently identified to be cometary (about 22 ± 5%), in addition to chondritic (or solar) xenon [START_REF] Avice | The origin and degassing history of the Earth's atmosphere revealed by Archean xenon[END_REF][START_REF] Marty | Xenon isotopes in 67P/Churyumov-Gerasimenko show that comets contributed to Earth's atmosphere[END_REF].

In the present study, we provide information on NG storage in LM minerals and melts by investigating experimentally the maximum solubility of Kr in ferropericlase (Mg,Fe)O and different metal alloys up to the conditions of the bottom of the LM (115 GPa and 3700 K). Our data reveal that ferropericlase can retain up to 3 wt.% of Kr. This is 5 to 10 times more than Bg in the Earth's LM and metallic melts of the outer Earth's core, respectively. Therefore, we propose that ferropericlase may play an important role in NG retention during magma ocean crystallization and that the LM could potentially be a deep NG reservoir.

Methods

Our experiments are aimed at constraining the Kr storage capacities of Fpc (Mg,Fe)O and different metal alloy melts up to the pressure and temperature (P/T) conditions of the bottom of the LM (115 GPa and 3700 K). We have performed laser-heated diamond anvil cell (LH-DAC) experiments at the X-ray absorption (XAS) beamline ID24 of the ESRF. Postmortem EMPA measurements and XAS analysis were used to precisely quantify and characterize the incorporation of NGs in the quenched samples.

Starting materials

We used synthetic metal-alloy foils of Fe88S12 and Fe85Ni5S10 which were produced by an ultra-rapid quench method at the ICMPE (Institut de Chimie et des Materiaux de Paris-Est, Paris, France) [START_REF] Morard | Melting of Fe-Ni-Si and Fe-Ni-S alloys at megabar pressures: implications for the coremantle boundary temperature[END_REF]. This technique guarantees a void free homogenous composition and a small sample thickness (5-7 μm). Nickel foils from Goodfellow (trace element basis 99.95%), MgO powder from Sigma Aldrich (catalogue number: 34279) and Kr gas having a purity of 99.99% from Air Products were used as high-purity starting materials.

The MgO powder was heated above 393 K to remove the moisture contamination from the air.

After heating, it was compressed under nitrogen atmosphere to produce thin pellets of 5-10 µm thickness using a diamond anvil cell without gasket. In such a device, the MgO powder is subjected to a high-pressure sintering process (up to 10 GPa) which leads to a highly compacted material with a very low porosity. The resulting metal foils and MgO pellets were stored in a dry atmosphere before sample loading.

High pressure and temperature experiments

Membrane driven diamond anvil cells (DAC) of the LeToullec design were used to generate high pressures. The DACs were equipped with single-crystal or nano-polycrystalline diamonds. The dimensions of diamond anvil culets varied between 150 and 400 μm depending on the target pressure . For all experiments, we have employed pre-indented Re gaskets. A hole drilled at the center of the gasket was used as sample chamber (Table 1).

In total seven samples were prepared and investigated (Table 1). Two samples were prepared using a 5 µm thick metal foil of Fe88S12 sandwiched between two MgO pellets (Cell_1-2, Table 1). The upper MgO pellet was placed such that it only partly covered the metal foil (Figure 1). These samples were used to investigate the different krypton storage capacities of MgO and Fe88S12 at identical T but different P conditions. We employed compacted MgO pellets because single-crystals of MgO have a high risk of breaking upon compression, especially in the present sample geometry.

Five other sample assemblies were prepared using Fe88S12, Fe85Ni5S10 or Ni placed on a KCl disc of 5-10 µm thickness (Cell_3-7, Table 1). These samples were used to study the Kr incorporation in metallic melts as a function of the composition and P/T conditions.

In all experiments a ruby sphere was loaded on the rim of the Re gasket hole for pressure monitoring. The remaining sample chamber cavity was then filled with supercritical Kr using the gas-loading device at the ESRF which was purged twice with Kr gas to avoid contamination from the air. The samples were stored and handled in dry nitrogen atmosphere or under vacuum during loading and after the laser heating runs.

At the target pressure, the samples were single-sided laser-heated using the laserheating system installed at ID24 (Supplementary Information). The metal foils sandwiched between two MgO pellets were heated at the contact surface of Kr and the metal (and MgO) (Figure 1). The metal foils placed only on a KCl disk were heated on the metal(-alloy) contact surface to Kr in several positions. The laser hot-spot diameter varied between 20 and 60 µm depending on the sample size and pressure. The temperature was raised up to 1800-3700(150) K by adjusting the laser power and maintained for 20-30 minutes to reach equilibrium conditions.

At the P/T conditions of the experiments, Kr and MgO remained solid (Jephcoat, 1998;[START_REF] Du | High-pressure melting of MgO from (Mg,Fe)O solid solutions[END_REF]. This excludes the formation of supercritical Kr or Kr gas during the experimental runs. In contrast, the experimental temperatures exceeded by several hundred degrees the liquidus temperature of metal foils (except for the heating spot 2 in Cell_7) [START_REF] Morard | In situ determination of Fe-Fe3S phase diagram and liquid structural properties up to 65 GPa[END_REF][START_REF] Morard | Melting of Fe-Ni-Si and Fe-Ni-S alloys at megabar pressures: implications for the coremantle boundary temperature[END_REF][START_REF] Lord | The melting curve of Ni to 1 Mbar[END_REF][START_REF] Mori | Melting experiments on Fe-Fe3S system to 254 GPa[END_REF].

Elemental concentration measurements

Scanning electron microscope (SEM) maps of recovered samples were acquired with a small beam size of 2 µm and at an acceleration voltage of 20 kV, except for Cell_7, to determine the distribution of Fe, Si, O, S, Mg and Ni, using the SEM microscope installed at the "Laboratoire Magmas et Volcans" in Clermont-Ferrand (France) (Figure S1). Precise quantitative concentrations of Kr, Fe, Ni, S, and Mg in the quenched samples were then determined from electron micro-probe analyzer (EMPA) measurements using a Cameca SX100 micro probe (Clermont-Ferrand, France) (Figure 2a). The signal intensity for Kr was calibrated following the procedure described in Shcheka and Keppler (2012) for three detector crystals using 7 different elemental standards adjacent to Kr (Figure S2). This calibration method resulted in a Kr detection limit of 100 ppm. For Fe, Ni, S, and Mg an EMPA electron beam current of 15 nA was employed while for Kr a current of 40 nA was used. The EMPA electron beam size was 1-2 µm, and after each analysis, the beam position was controlled to ensure the beam spot position stability. Those measurements for which the electron beam has moved were discarded. Measurements with analytical totals within 95% were included in the analysis in addition to few data with totals above 85%. Measurements with totals below 85% were excluded.

In two cases, the EMPA measurements of the laser-heated iron-alloy areas resulted in surface structure changes due to the impinging electron beam. This effect is most likely related to sample disproportions linked to the metastable nature of the quenched glasses. We therefore discarded these measurements. All Kr concentrations obtained from EMPA measurements in the samples and different phases are listed in Table S1, except for Cell_5 for which the measured concentrations fell below the detection limit and Cell_7 for which EMPA measurements have not been performed.

XRF and XAS experiments

X-ray absorption spectroscopy (XAS) is a powerful technique to probe the local structural environment of diluted elements embedded in crystalline or glass matrixes. XAS data acquired in transmission geometry present the sum of all contributions along the beam pathway. In the present study, the sample configuration was optimized to separate the signal from pure krypton loaded in the sample chamber cavity next to MgO and the one from the krypton incorporated in the crystal after laser-heating (Figure 1). At ID24 in-situ XAS transmission measurements on Kr retained in the oxide during heating were unfortunately not possible due to the low concentrations of Kr retained in the laser-heated hotspot and the large X-ray beam size at the Kr K-edge (50 μm at full width half maximum) which exceeded the laser hotspot size (Figure 1).

A much smaller beamsize (submicron) than presently available is required to conduct such experiments in-situ during heating or after heating and at high pressure. Therefore, only XAS data of pure Kr upon compression and after heating could be collected at ID24. The structural environments around Kr retained in the heating spot were therefore investigated only on quenched samples by XAS. These measurements were conducted in backscattered fluorescence geometry at the ESRF beamline BM23 using a highly focused beam of 5×5 μm 2 (Supplementary Information). The measurements were completed by full-multiple scattering calculations to derive the atomic environments around Kr in the quenched samples (Supplementary Information).

Results and discussion

Kr concentrations retained in Fpc and metallic melts

Detailed elemental concentrations obtained from EMPA measurements for each sample are listed in Table S1. For Cell_1-2, we observed that laser-heating of pure MgO in contact with the Fe88S12 alloy resulted in the diffusion of Fe into MgO forming Ferropericlase (Mg1x,Fex)O with x reaching up to 0.27. In the following, the resulting (Mg1-x,Fex)O phase will be referred to as Fpc.

The EMPA measurements and the XRF and SEM maps revealed that Kr concentrations in Fpc and the metal foils show variations with the distance from the laser hotspot (Figure 2 and S1, Cell_1, 2 and 6). Interestingly, the Kr contents measured for Fpc samples show a slight decrease with increasing distance from the hotspot (within a diameter of 20 μm). The observed concentration variations may be related to a partitioning or diffusion process that is sensitive to the temperature decrease with increasing distance from the laser hotspot.

Lateral temperature gradients in the LH-DAC depend on the laser beam shape, as well as the thermal conductivity of the sample and insulating material. We have maximized the laser-heating spot in all experiments in order to reduce the thermal gradients in its center and maximize the area where the concentration measurements were carried out. The measurement of the thermal gradients across the laser hotspot requires special LH-DAC setups [START_REF] Campbell | Measurement of temperature distributions across laser heated samples by multispectral imaging radiometry[END_REF]. The present measurements have been performed on a standard system that does not allow such measurements. We therefore assumed temperature gradients between 500-1200 K from the hotspot center to the hot-spot rim for measured hotspot temperatures ranging from 2300 -3700 K following the observations of [START_REF] Campbell | Measurement of temperature distributions across laser heated samples by multispectral imaging radiometry[END_REF] and [START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and[END_REF]. Due to the micrometric size of the samples, submicron beams would be necessary to better explore the effect of temperature gradients on Kr concentration variations. Such micro-beams are presently not available for standard EMPA instruments.

First order constrains on the relations between temperature, pressure as well as chemical composition and measured Kr contents in the different phases can be obtained by averaging those Kr concentrations measured in the hotspot center (within a diameter of 20 µm) and laserheating spot rim (within a diameter of 20-40 µm). This procedure allows separating regions in the laser hotspot that exhibit the most homogeneous temperature distributions from those that are subjected to higher T gradients. The P/T conditions of each cell and laser-heated spot together with the resulting averaged Kr concentrations of phases at different distances from the laser hotspot are listed in Table 1 together with the maximal Kr concentrations measured in each sample and averaged Kr concentrations using all measurements.

The Kr concentrations measured in Fpc in the hotspot center as a function of the pressure, the iron and sulfur content are shown in Figure 3. The most striking observations are the high Kr concentrations of almost 3 wt.% in Fpc (Table 1,Cell_2) and their increase with pressure (Figure 3). We also found that Kr concentrations in Fpc are strongly correlated with the Fe content (Figure 3a, taking only the data from the hotspot center). With increasing pressure from 40 to 60 GPa the average Kr and Fe contents in Fpc increases from 1.2(2) to 2.2(5) wt.% and 7(3) to 23(4) wt.%, respectively (Figure 3a). For sulfur, we observed the opposite trend: the averaged sulfur concentrations in Fpc are slightly higher at 40 GPa than at 60 GPa, decreasing from 2.1(4) down to 0.15(5) wt.% (Figure 3b).

We observed the highest Fe and Kr concentrations in the center of the laser heated hotspot in Fpc. This excludes a diffusion activated by the thermal gradients (Soret effect) which should normally result in a migration of heavy elements such as Fe or Kr towards the hotspot rim [START_REF] Auzende | Element partitioning between magnesium silicate perovskite and ferropericlase: New insights into bulk lower-mantle geochemistry[END_REF]. We considered instead that equilibrium conditions have been achieved during the long laser heating runs at least for Fe in the hotspot center [START_REF] Auzende | Element partitioning between magnesium silicate perovskite and ferropericlase: New insights into bulk lower-mantle geochemistry[END_REF]. To understand if the equilibrium conditions for Kr in the entire heating spot (max. 60 microns at 40 GPa) were also reached, the diffusion coefficients for Kr (DKr) in Fpc at the present experimental conditions are required. These coefficients are however not available. We therefore related the concentration variations of Fe and Kr in the hotspot center in Fpc to the temperature dependent partitioning behavior of Fe and Kr into Fpc.

Kr concentrations in quenched metallic melts as a function of the P/T conditions, distance to the laser-heated hotspot and composition are plotted in Figure 4. Molten Ni shows the highest Kr storage capacity, among all investigated metallic melts. It could retain a maximum of 0.77(1) wt.% of Kr at 62(1) GPa and 2800 K (Table 1). This value is much larger than for Fe88S12 and Fe85N5iS10 which respectively exhibit a maximum of 0.38(1) and 0.14(1) wt.% at similar conditions (Table 1). Interestingly, the averaged Kr storage capacities of the metallic melts are much lower than those of Fpc (Figure 3). Moreover, we did not observe a correlation between the Kr and S contents in Fe88S12 as in Fpc (Table S1).

Kr partitioning in the lower Earth's mantle

In-situ experiments at the relevant high dilution levels and extreme conditions remain challenging. The present experiments have been performed at Kr-saturated conditions similar to previous large-volume press studies on Bg (Shcheka and Keppler, 2012) or LH-DAC studies on silicate melts [START_REF] Chamorro-Perez | Argon solubility in silicate melts at very high pressures. Experimental set-up and preliminary results for silica and anorthite melts[END_REF][START_REF] Bouhifd | Aluminium control of argon solubility in silicate melts under pressure[END_REF][START_REF] Bouhifd | Helium in the Early Earth core[END_REF][START_REF] Niwa | Argon solubility in SiO2 melt under high pressures: A new experimental result using laser-heated diamond anvil cell[END_REF]. The derived concentrations in quenched samples of such studies present the upper limit of Kr solubilities in the different phases (Table 1).

We averaged the Kr concentrations from all EMPA measurements within the laserheated spot in each phase at a certain P/T point to estimate the maximum Kr solubilities as a function of pressure in the different phases (Table 1, column named: everything). We considered that this procedure provides a better statistical measure of Kr retained in the laser hotspot. The resulting maximal Kr solubilities in Fpc are 1.2 and 1.8 wt.% and 0.03 wt.% and 0.15 wt.% for Fe88S12 at 40 and 60 GPa and 2300 K, respectively. These estimated Kr solubilities are presented in Figure 5a and were used to assess the pressure dependent partitioning coefficients Dmetal/oxide shown in Figure 5b (black triangles). The resulting Dmetal/oxide values are below unity indicating that Kr preferentially partitions into Fpc. An extrapolation of Dmetal/oxide to the core mantle boundary reveals, that the preference for Kr to enter into Fpc prevails, while small amounts of Kr may still be present in the Earth's core.

The present results indicate that Kr is highly soluble in Fpc and to a lesser extent in metallic melts. The liquid Earth's core as well as liquid iron droplets descending within the magma ocean during Earth's core formation would therefore be rather poor in Kr (Figure 5).

Our data suggest that for both Fpc and metallic melts the solubility increases with depth. These observations strongly differ from the previously reported Ar solubility decrease in silicate melts beyond 15 GPa (i.e., [START_REF] Bouhifd | Aluminium control of argon solubility in silicate melts under pressure[END_REF][START_REF] Niwa | Argon solubility in SiO2 melt under high pressures: A new experimental result using laser-heated diamond anvil cell[END_REF]. According to [START_REF] Bouhifd | Aluminium control of argon solubility in silicate melts under pressure[END_REF], the Ar solubility in chondritic melts reduces at 25 GPa to 0.05 wt.%. This is a factor of 10 less than what we estimated for Kr in Fpc at such conditions (0.56 wt.% at 25 GPa). The extrapolation of the data from [START_REF] Niwa | Argon solubility in SiO2 melt under high pressures: A new experimental result using laser-heated diamond anvil cell[END_REF] in pure silicate beyond 20 GPa suggests an Ar solubility of 1 wt.% at 25 GPa and a decrease to 0.5 wt.% at 30 GPa. These observations may indicate that Kr is retained in crystalline phases especially at the bottom of the Earth's LM during mantle crystallization. This is due to the probable incompatibility of NGs in ultra-dense silicate melts. The solubilities in melts remain however still debated due to the few studies conducted so far. Therefore, a more elaborated discussion on crystal-melt partitioning behavior at LM conditions is not warranted. Shcheka and Keppler (2012) reported Kr solubilities in Fe-free and Al-bearing bridgmanite from 0.11 to 0.33 wt.% at 25 GPa and 1800 K that increase with the Al content.

Using their data, we obtained a partitioning coefficient between bridgmanite (Brg) and Fpc DFpc/Brg of 1.69 to 4.9 (9) at ~25 GPa. We found that Fpc can retain a maximum of 3.5 wt.% of Kr (Figure 5a) by extrapolating the maximal solubility of Kr in Fpc to the CMB. The lower storage capacity of Bg might be due to the absence of iron in the experiments of Shcheka and Keppler (2012). Iron could indeed play an important role for forming oxygen vacancies. Future studies on NG incorporation in iron-bearing bridgmanite are required to better understand partitioning of NGs between the two main crystalline constituents of the Earth's LM. Overall, Fpc exhibits a higher Kr solubility than Bg and despite Fpc is volumetrically inferior (Fpc:Bg = 20:80 vol.%), it can store up to 45% of the Kr present in the LM.

Kr incorporation mechanism

The understanding of the microscopic NGs incorporation mechanism in LM solid and liquid phases is fundamental for predicting their partitioning behaviors (Karato, 2016).

However, this mechanism remains largely unexplored except for Bg (Shcheka and Keppler, 2012). At moderate P/T conditions, NGs can substitute in open ring structures of hydrous phases [START_REF] Jackson | Noble gas transport into the mantle facilitated by high solubility in amphibole[END_REF], or cation positions in silicates [START_REF] Heber | Crystal-melt partitioning of noble gases (helium, neon, argon, krypton, and xenon) for olivine and clinopyroxene[END_REF]. Because pure Kr exhibits a high compressibility (Rosa et al., 2018), it may also be easily stored in defect vacancies or interstitial sites of phases present at Earth's LM and core conditions.

We calculated the size mismatch between atomic radii of zero charged Kr 0 , Mg 2+ , O 2- and metallic Fe at 2300 K and between 40 and 150 GPa (Figure 6, Supplementary Information) to understand if Kr atoms at Earth's LM conditions can fill vacancies or substitute for atoms in Fpc and/or metallic melts. Interestingly, the size mismatch between Kr 0 and the O 2-anion in Fpc is the lowest and remains below 10% (Figure 6b). This indicates that at diluted concentrations of the LM, Kr 0 can be incorporated into a neutral oxygen vacancy such as a Schottky defect. The size mismatch between Kr 0 and O 2-decreases with increasing pressure (Figure 6b). The proposed substitution of Kr in neutral oxygen Schottky defects can therefore explain the observed increase in solubility (Figure 3). It can also explain the increasing compatibility of Kr in Fpc with increasing iron content. In Fpc such neutral oxygen vacancies could be preferentially associated to iron defect clusters forming, upon increasing pressure, iron and Fe 3+ content [START_REF] Kantor | Shortrange order and Fe clustering in Mg1-xFexO under high pressure[END_REF].

If Kr solubility in Fpc is associated to the abundance of Fe 3+ related vacancies, then solubilities should be sensitive to the oxygen fugacity (fO2). In the present experiments, the fO2 can be estimated relatively to the iron-wüstite buffer (IW buffer) using the molar fractions of Fe in the metal phase and FeO in the mineral phase obtained from EMPA measurements (Table S1). We considered an ideal system and calculated fO2 using the equation:

log fO2(∆IW) = 2 log (XFeOsilicate / XFemetal)
where XFeOmineral and XFemetal are the molar fractions of FeO and Fe in the mineral and metallic phases, respectively. We have obtained logfO2 values ranging from -2.1(3) to -1.5(2) at pressures between 40 to 60 GPa and 2300 K. These values are consistent with those obtained in previous works conducted at comparable conditions [START_REF] Fischer | High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and[END_REF] and can explain the observed correlation of Kr solubility increase with Fe 3+ abundance. The redox conditions for the accreting mantle have been estimated to range between 4 and 2 log units below the IW buffer [START_REF] Rubie | Heterogeneous accretion, composition and core-mantle differentiation of the Earth[END_REF]. This confirms that the present experiments have been conducted at similar or slightly more oxidizing conditions than those of the early Earth.

Recently, an incorporation of single Kr atoms in neutral Schottky defects associated with oxygen vacancies has been also evidenced from XAS measurements of Kr-implanted UO2 for low Kr concentrations of 0.5 at.% and at ambient conditions (Martin et al., 2015). Oxygen vacancy substitution has been also proposed for the incorporation of Ar, Kr and Xe in Bg based on lattice strain modelling (Shcheka and Keppler, 2012;Karato, 2016).

For molten Fe88S12 our calculations have revealed a large radii mismatch between Fe 0 and Kr 0 in the pressure range of 60-150 GPa, with Kr being 30% smaller than Fe 0 (Figure 6b).

We propose that Kr is entrapped in interstitial voids of the metallic liquid structure because of the likely Kr diffusion in the low viscous metallic melt. Such an interstitial diffusion mechanism is consistent with the general concept of NG incorporation in silicate melts (Caroll and Stolper, 1993;Brooker et al., 2003;[START_REF] Heber | Crystal-melt partitioning of noble gases (helium, neon, argon, krypton, and xenon) for olivine and clinopyroxene[END_REF]. Detailed atomistic crystal and melt lattice calculations, that are beyond the scope of the present study, are required to better constrain the potential incorporation sites of NGs in these systems at lower Earth's mantle conditions.

Local atomic environment of Kr in quenched samples

The present study is the first attempt to characterize the incorporation mechanism of NGs in quenched LM minerals directly using XAS (Supplementary Information). The extended X-ray absorption fine structure (EXAFS) which corresponds to the X-ray energy domain located 1000 eV above the absorption edge, is highly sensitive to the distribution and sort of nearest-neighboring atoms. EXAFS data collected at the Kr K-edge demonstrate the existence of a highly disordered first coordination shell that is characterized by a large distribution of inter-atomic distances and different coordinating atomic species including Kr, Fe or Mg (Figure S3). The X-ray absorption near edge structure (XANES) which corresponds to the energy region that extends ~100 eV from the absorption edge, provides information on the local site symmetry of the absorbing atom and sort of neighbouring atoms on the medium range scale (second and third coordination shells). A clear similarity between the spectra of Kr retained in quenched samples and those of liquid and solid krypton is apparent (Figure S4). This suggests that Kr could partly have, as nearest neighbor, another Kr atom with a similar symmetrical arrangement as pure liquid or solid fcc Kr under pressure. A comparison of the experimental and calculated XANES spectra shows that Kr is most likely incorporated in 6fold coordinated vacancies surrounded by Fe, and Mg as next nearest neighbors (Figure S4-5). The potential substitution of Mg or Fe by Kr is a very unlikely scenario because, in this case, the calculated XANES spectra exhibit a significantly different shape of the white line (Figure S5). The local environment of Kr in quenched Fpc is disordered and composed of Mg, Fe and Kr with various amounts as nearest neighbors. The shift of the white line energy in the sample spectra relatively to those of Kr gas clearly demonstrates that Kr is retained under compressive strains in the quenched samples (of up to 8 GPa, see Supplementary Information).

An explanation for the observed highly distorted Kr environments could be the significant expansion of the previously homogeneously distributed Kr atoms during P/T quenching. Quenching from 40 GPa leads to a volume expansion of more than 50% for Kr (Rosa et al., 2018) resulting in the generation of large lattice strains in the host sites. These lattice strains can induce short range diffusion of Kr and lattice re-arrangement leading to the formation of defect clusters of sub-nanometric size. This type of cluster formation has been already reported for implanted samples such as MgO (Norton et al., 1992;Noordhuis and De Hosson, 1991). We do not consider that hydrous fluid inclusions containing Kr have formed in our samples. As outlined above in the methods section, we have employed pre-heated MgO powder as well as metal foils stored under vacuum in a desiccator to avoid moisture contamination. In addition, the sample was assembled and sealed in nitrogen atmosphere before loading with Kr in a gas-loading device.

We consider that it is very unlikely that Kr was substantially trapped on grain boundaries between (Mg,Fe)O crystals during the experiments, as we have employed precompressed (dried, water-free) MgO pellets. These pellets were made from a MgO powder that was highly compacted in a DAC. In such device, the MgO powder is subjected to a high pressure sintering process (up to 10 GPa) which leads to a highly densified material with low to negligible porosity. Also, similar XAS data of Kr were obtained with samples prepared using a very different synthesis method. Indeed, the iron-alloy foils have been obtained using sputtering methods, a technique that leads to compact foils without voids. Moreover, grain boundary contamination or formation of Kr blebs would lead to constant Kr concentrations in the samples independently of the experimental conditions while we observe an increase of the Kr concentrations with pressure that is consistent with the predictions of Shcheka and Keppler (2012).

TEM measurements could provide information about the Kr environment in the quenched samples. Such studies on Kr contained in MgO have been previously performed on thin ion-implanted MgO discs that did not require polishing (Norton et al., 1992). The samples produced in the present study would however require polishing due to the underlying iron foil.

We did not perform such measurements because this type of polishing procedure would lead to NG release. In addition, TEM measurements can be only performed on quenched samples that are altered by the significant expansion of Kr once released to room pressure (Tan et al., 1991;Norton et al., 1992;Martin et al., 2015).

In summary, based on the atomic radii mismatch calculations, we find that Kr incorporated in Fcp via a vacancy substitution mechanism at high P/T conditions is possible.

Moreover, as Kr remains solid at the high P/T conditions of the experiments and the starting materials employed are void free due to the pre-compressing treatment or used synthesis methods, it is unlikely that Kr blebs form inside Fpc and the metallic foils. The formation of Kr blebs at the surface of Fpc and the metallic foils can be excluded because the experimental XANES spectra clearly demonstrate that Kr is retained under a high compressive stress of up to 8 GPa (Figure S4, S6) that can only be sustained in the bulk and not on the surface of the samples. Therefore, we propose that the observed Kr concentrations are due to diffusion processes that took place at high P/T conditions. The precipitation of NG nano-impurity clusters related to Kr exsolution are induced during quenching. We note that sub-nanometric Kr clusters potentially formed in the quenched samples have a minor influence on the conducted EMPA measurements. The electron beam size for EMPA measurements was in the range of 2 μm. Therefore, the sampling was conducted on several sub-(nanometric) impurity clusters as well as on cluster free-areas during one measurement.

Implications

NGs solubilities in the lower mantle minerals

The present experimental results reveal that Fpc can retain 5 times more Kr than Fefree and Al-bearing Bg in the Earth's uppermost LM and 10 times more than the liquid Earth's outer core. Our results suggest that a larger proportion of the mantle's Kr is stored by Fpc than previously thought. In order to constrain the solubilities of Ne, Ar, Kr and Xe through the LM (25-120 GPa and 1900-2500 K), we performed lattice strain modelling (LSM) ( Blundy and Wood, 2003) assuming that NGs enter in neutral oxygen vacancies of Fpc and Bg.

This LSM allowed us predicting solubilities through the mantle for the suite of NGs.

NGs exhibit high compressibilities and it is therefore important to include their volumetric variations through the LM. The coordination number is another parameter that has a significant influence on the host site and noble gas radii (Zhang and Zhu, 1995). In the present LSM approach, the radii of NGs and those of the host sites were fixed to calculated values obtained using thermoelastic and crystal-chemistry data (coordination dependent atomic radii size).

Similarly, the host site flexibility was fixed to the calculated values extracted from thermoelastic data (Supplementary Information).

In our LSM, we only used the maximal solubility of the site as fitted parameter. This differs from the classical approach for which three parameters (the maximal solubility of the site, the site flexibility and the host site radius) are normally adjusted. We found that the solubility data of Shcheka and Keppler (2012) can be well reproduced with the present LSM (Figure 7). This suggests that the present approach is appropriate and can be used for predicting NG solubilities in a host lattice site at the extreme P/T conditions of the lower mantle and beyond.

The obtained NGs solubilities of the two major LM minerals exhibit different evolutions through the LM (Figure 7). For Fpc, the solubilities increase with depth for all NGs while, for Bg, the NGs solubilities decrease with depth except for Xe. This contrasting behavior can be explained by the difference in the mechanical properties of Fpc and Bg. Fpc is indeed softer than Bg and the radius of the oxygen site in Fpc exhibits a higher reduction with increasing depth. Moreover, in the investigated P/T conditions, the NGs exhibit a similarly high compressibility as Fpc.

NG retention in the lower mantle during magma ocean crystallization

Our lattice strain modelling results reveal that the LM phase assemblage Fpc and Bg retains efficiently Ar and Kr and to a lesser extend Ne and Xe. The present solubility data are representative for NG saturated conditions and can therefore be only applied to crystallization conditions in presence of a volatile saturated liquid or melt phase. Presently, two models describing the crystallization of the magma ocean (MO) in the deep primitive Earth have been reported: (1) the classical solidification model from the bottom to the top (Solomatov and Stevenson, 1993) and ( 2) the more recent model that propose the onset of solidification in the mid-mantle (Labrosse et al., 2007). For both models crystallization of LM minerals at NG saturated conditions may have occurred (Supplementary Information). Our model is independent of the type of lower mantle crystallization (either bottom-up or mid-mantle). We presumed in our model a first crystallization of volatile-free pheno-crystals of Bg, followed by a simultaneous eutectic crystallization of Fpc and Bg in volumetric ratios of 25:75 [START_REF] Baron | Experimental constraints on melting temperatures in the MgO-SiO2 system at lower mantle pressures[END_REF].

We estimated the relative abundance ratios of NGs (only stable isotopes normalized to Ar) retained in the solid LM using the solubilities extracted from the LSM (Figure 7). We compared the calculated normalized NG abundance patterns in the solid LM to those reported by Marty (2012) for the bulk mantle that are obtained by a global mass balance approach of radiogenic 40 Ar. We also compared them to those given by Moreira and Kurz (2013) which were evaluated from 3 He abundances in OIBs. The results are presented in Figure 8a for an initial NG MO composition similar to phase Q and an additional solar contribution of 10% for Ne and Ar as suggested by Marty (2012). Our estimated Ne/Ar ratio in the solid LM is slightly larger than the one reported by [START_REF] Moreira | Noble gases as tracers of mantle processes and magmatic degassing. Chapter 12[END_REF] but one order of magnitude larger than the one obtained by Marty (2012). The estimated Kr/Ar and Xe/Ar ratios of the solid LM agree well with those evaluated by Marty (2012). This suggests (especially for heavy NGs) that the solid LM could represent a deep NG reservoir that is not readily sampled by plumes.

NG replenishment from the LM to the atmosphere

In the following, we discuss the contribution of NG replenishment from the LM through partial melting and plume volcanism to the present-day atmosphere over geological times.

Stable Ne isotopes reveal that the present-day atmosphere has lost most of its primordial solarlike signature. This might be due to the moon-forming impact (MFI) that occurred 40-60 Myrs after Earth formation and that induced a massive erosion of primordial volatiles from the atmosphere and from the MO generated by the impact. One plausible scenario suggests that the impactor's (potentially Q-like) NG signature may have led to an overprint of the residual NGs. The 129 Xe abundances estimated from the 129 I/ 127 I ratio systematically constrain the loss of 129 Xe on Earth to 97% [START_REF] Avice | The iodine-plutonium-xenon age of the Moon-Earth system revisited[END_REF][START_REF] Schlichting | Atmosphere impact losses[END_REF]and references therein).

Xe isotopic compositions also imply that most of present-day atmospheric NGs might have been acquired during late accretion of chondritic and cometary materials. This is related to the origin of atmospheric Xe that is most likely cometary U-Xe [START_REF] Avice | The origin and degassing history of the Earth's atmosphere revealed by Archean xenon[END_REF]Marty et al., 2017). Such relatively small impacts may have not induced a re-melting and rehomogenization of the mantle but may have modified the atmospheric NG signature relatively to the one in the MORB and OIB sources. Overall, this suggests that replenishment of LM NGs has not played a major role for the composition of the present-day atmosphere [START_REF] Trieloff | The nature of pristine noble gases in mantle plumes[END_REF].

In the following, we evaluate the maximum contribution of replenished LM NGs to the present-day atmosphere. To this aim, we considered an extreme scenario which assumes that only the solid LM has captured solar-wind like Ne after the MFI and that the solar-like signature in the present-day atmosphere is entirely due to LM replenishment (Supplementary Information).

In this model, we considered an atmosphere of the Early Earth with chondritic NG abundances that has lost its primordial solar signature during the giant impact phase of planetary accretion. We took into account the element mass fractionation and volatile loss (no isotope fractionation) due to the impact that affect lighter NGs to a larger extend. Due to the lack of data on the effect of the impact loss for all NGs, we scaled the losses of Kr, Ar and Ne to the one of Xe (75%) [START_REF] Schlichting | Atmosphere impact losses[END_REF] using the relations reported by [START_REF] Pepin | Evolution of Earth's noble gases: consequences of assuming hydrodynamic loss driven by giant impact[END_REF] for hydrodynamic escapes. This leads to residual fractions of: 25% Xe, 10% Kr, 1.3% Ar and 0.7% Ne. We obtained an atmospheric Neon-B component of 30.4% and a remaining 68.9% cometary and chondritic contributions (see Supplementary Information for details). From the analysis of refractory comet grains, Marty et al. (2008) established that the cometary contribution could be Q-like. This was also assumed in our model. For Xe, an additional loss of 22% was considered to account for the progressive isotope fractionation due to the ionization of dominantly light Xe isotopes by enhanced EUV flux from the young sun [START_REF] Avice | The origin and degassing history of the Earth's atmosphere revealed by Archean xenon[END_REF].

The resulting modelled normalized NG abundances in the atmosphere are shown in Figure 8b. The obtained Kr/Ar and Xe/Ar ratios are close to those of the present-day atmosphere. The modelled Ne/Ar ratio is however much lower than the present-day one. In order to increase the Ne/Ar ratio, it is necessary to include solar contributions because the

Figures and Tables

Figure 1. Schematic view of a typical diamond anvil cell sample loading (Cell_2, Table 1 andFigure S1) designed for the present experiments. A diamond culet size of 300 µm allows reaching 60 GPa. A metal foil (gray) is sandwiched between two MgO pellets (light blue). On the laser-heated side, the metal foil is not fully covered by MgO. The remaining sample chamber was filled with supercritical Kr (250 bars). For the partitioning experiments, the sample was heated on one side at the contact surface of the three materials. In the experiments carried out up to 60 GPa, the laser was slightly defocused (yellow triangle) to provide a larger laser spot size of approximately 40-60 µm in diameter. At the K-edge energy of Kr (14.3 keV) the focused X-ray beam (blue dashed line) exhibited large tails of ~50 µm at full width half maximum adjacent to the focused X-ray beam (blue shaded area). These tails arise from the deep penetration of the X-ray beam in the bended polychromatic Si(111) crystal used for horizontal focusing. This effect becomes significant for X-ray beam energies above 10 keV. 1 andS1 1 andS1 Shcheka and Keppler (2012), the uncertainties on the solubilities are represented by gray bars. The models obtained from the classical lattice strain approach (gray dashed lines) are compared to those obtained with the extended approach developed in this study (dotted colored lines). Note that in the classical approach the experimentally determined solubilities are fitted to ambient condition NG radii (ri) by adjusting the host site flexibility (Em), the maximum solubility of the site (c0) and the host site radii (r0).

In the extended approach ri , r0 and Em are fixed to the calculated values derived from the thermoelastic data obtained at high P/T conditions. In this case, the only fitting parameter is c0.

Right panels: NG solubility trends from the top to the bottom of the LM indicated by arrows (black to red). Note that the differences in NG and oxygen vacancy site radii at equivalent conditions for Fpc and Bg arise from the differences in coordination environments that is [6]fold in Fpc and [4]-fold in Bg. Table 1. Experimental runs conducted in this study sorted by loadings (Cell 1-7). We provide the following details: the number of laser-heated spots per loading, the insulating and starting material (KCl, MgO, metal foil composition), the experimental conditions for each laser-heated spot including the maximal pressure P in GPa (the errors correspond to the standard deviation of pressures measured before and after laser-heating) and temperature T in K (errors are of the order of 100-200 K). Kr concentrations from EMPA measurements in wt.% are given for the different phases (Fpc or metallic melts) and include averages of measurements acquired only in the hotspot center (center: within a diameter of 20 µm), only in the rim of the laser-heated spot (rim: with a diameter range of 20-40 µm from the center), in the entire hotspot region (everything: within a diameter of 40 µm) and the maximum Kr content measured in a single analysis (maximum). A detailed list of all measurements is provided in the Supplementary Information Table S1.

Laser-heating experiments at ID24

The samples were single-sided laser-heated using the laser-heating system installed at ID24 [START_REF] Pascarelli | The Time-resolved and Extreme-conditions XAS (TEXAS) facility at the European Synchrotron Radiation Facility: the energy-dispersive X-ray absorption spectroscopy beamline ID24[END_REF][START_REF] Kantor | A laser heating facility for energydispersive X-ray absorption spectroscopy[END_REF]. The temperature was determined in-situ via spectroradiometry [START_REF] Giampaoli | Measurement of temperature in the laser heated diamond anvil cell: comparison between reflective and refractive optics[END_REF]. The pressure was measured before and after laserheating using the ruby fluorescence signal and the ruby pressure scale after Dewaele et al. (2008) or the Raman shift of the single-crystal diamonds at the centre of the culet [START_REF] Akawama | High-pressure Raman spectroscopy of diamond anvils to 250 GPa: Method for pressure determination in the multimegabar pressure range[END_REF].

XRF experiments at BM23

The X-ray energy was tuned to the Kr K-edge (14.2 keV) using a double-crystal fixed exit monochromator equipped with a pair of Si( 111) crystals. The X-ray beam was focused down to 5×5 µm 2 using a KirkPatrick-Baez mirror system [START_REF] Mathon | The time-resolved and extreme conditions XAS (TEXAS) facility at the European Synchrotron Radiation Facility: the general-purpose EXAFS bending-magnet beamline BM23[END_REF]. The quenched samples were oriented with the laser-heated surfaces towards the incoming X-ray beam. In order to avoid shadowing of the Re gasket, the samples were rotated by 15° from the incoming X-ray beam and towards the single-element silicon solid-state fluorescence detector (Vortex). The Vortex detector was positioned in backscattering geometry (rotated by 30˚ from the incoming X-ray beam).

In a first step, finely-meshed two-dimensional µXRF elemental distribution maps at a fixed X-ray energy of 14.5 keV were acquired for each sample with a step size of 5 µm. These maps enabled determining the Kr distribution around the laser-heating spot (Figure S1). In a second step, X-ray absorption spectra were collected in regions of high Kr concentrations by scanning the monochromator energy with a small mesh size of energy points (0.4 eV) around the edge region and up to a k-range of 14 Å -1 , respectively (Figure S3 and S4).

Cell_1

MgO and Fe88S12 40.0(5) GPa and 2300 K

Cell_2

MgO and Fe88S12 61.5(5) GPa and 2350 K

Cell_3

KCl and Fe83Ni5S12 65.0(5) GPa and 2700-3100 K

Cell_6

KCl and Fe88S12 110(1) GPa and 3150-3700 K

Cell_7

KCl and Fe88S12 115(1) GPa and 1900-3100 K

. SEM, EMPA and µXRF maps acquired on samples Cell_1, _2, _3, _6 and _7 (Table 1, main manuscript and Table S1).

EMPA calibration and measurment results

Size mismatch calculations

Zero-charged Kr 0 atomic radii were calculated using the equation of state of fcc Kr determined by Rosa et al. (2018) and the assumed thermal parameters reported by Jephcoat (1998).

For Fpc we calculated the anion and cation vacancy site radii using the thermal equation of state reported for Mg0.75Fe0.25O by [START_REF] Mao | Thermal equation of state of lower-mantle ferropericlase across the spin crossover[END_REF] and an assumed bond ratio between Mg 2+ and O 2- of 1/3 to 2/3, respectively. Such bond ratios are expected from the ion-radii values at ambient conditions (Zhang and Zhu, 1995). Average atomic radii for Fe 0 in the liquid were calculated using the density of liquid Fe88S12 reported from shock wave experiments at Earth's core conditions [START_REF] Huang | Shock compression of Fe-FeS mixture up to 204 GPa[END_REF]. For calculating the hard sphere diameter from the obtained densities, we used the Percus-Yevick equation assuming the arrangement of atoms in transition metal liquids can be described by the hard sphere model [START_REF] Ashcroft | Structure and Resistivity of Liquid Metals[END_REF] with a packing fraction of 0.44 as determined experimentally by [START_REF] Shen | Structure of Liquide Iron at Pressures up to 58 GPa[END_REF] for pure liquid iron. We further assumed a liquid structure consisting of zero-charged Fe 0 atoms with S atoms sitting in the interstitial sites as proposed by [START_REF] Posner | High P-T experiments and first principles calculations of the diffusion of Si and Cr in liquid iron[END_REF].

Kr incorporation in quenched samples

Information on the local bonding environment of Kr retained in the samples can be obtained from X-ray absorption spectroscopy (XAS). XAS is a local and element selective probe, sensitive to the sort and arrangement of neighbouring atoms. Several energy regions in a XAS spectrum are distinguished: The white line energy corresponds to the ionization energy of the core electron and is defined as the energy position of the first peak in the spectrums' derivative function.

The X-ray absorption near edge structure (XANES) region is defined in the energy domain between 50 and 100 eV from the white line energy. XANES provides information on the local site symmetry of the absorbing atom, bond distance distribution and sort of neighbouring atoms on the medium range scale. The extended X-ray absorption fine structure (EXAFS) corresponds to the energy region that extends ~1000 eV from the absorption edge. EXAFS is highly sensitive to the distribution and sort of nearest-neighboring atoms.

XANES and EXAFS spectra of Kr retained in quenched Fpc and Fe88S12 (blue spectra, Cell_1 and Cell_7 Table 1) are presented in Figure S3 and S4. Comparison of these two spectra reveals a well-structured first XANES peak region in both spectra, as well as an energy shift of the white line. Despite the absence of a simple theoretical interpretation of the XANES spectra, important information is commonly extracted through the comparison to reference spectra measured on known materials as well as from full multiple scattering calculations.

In a first step, we compared the XANES spectra acquired in quenched samples to reference spectra of pure Kr in the gaseous, liquid and solid state collected at different pressures (black spectra, Figure S4). We observed a clear similarity between the spectra of Kr retained in quenched samples with those of liquid and solid krypton. This suggests that Kr could partly be coordinated to another Kr in a similar symmetrical arrangement as pure liquid or solid fcc Kr under pressure.

To better interpret the experimental XANES data and constrain the structural incorporation mechanism of Kr, we conducted full multiple scattering calculations (FMS) using the Feff9 code [START_REF] Rehr | Parameter-free calculations of Xray spectra with FEFF9[END_REF]. FMS XANES spectra were computed at the Kr K-edge for a single Kr atom replacing the anion or cation in MgO and FeO. Calculations were performed on a sphere having a FMS radius of 6 Å. For the self-consistent loop, a cluster of 3.1 Å and a convergence after 30 iterations were chosen. The core hole was calculated after the final state rule and the scattering amplitude was fixed to unity for all calculations. The XANES spectra were calculated with a fine grid of 0.05 eV. The exchange-correlation potential for the fine structure and the atomic background were computed using the Hedin-Lundquist formalism and the ground state.

The resulting calculated XANES spectra for Kr incorporated in MgO in FeO and in (Mg,Fe)O are shown in Figure S5. It is worth noting that only those spectra calculated for Kr replacing the oxygen site in FeO show similarities to the experimental spectra. They indeed exhibit a comparable white line slope and first XANES peak shape (Figure S5). These similarities in the XANES data imply that Kr atoms in the quenched samples may be entrapped in oxygen vacancies of Fpc having Mg and Fe as next-nearest neighbor. Such Kr substitution for neutral Schottky oxygen vacancies has been previously suggested by Martin et al. (2015) from X-ray absorption data on ion-implanted UO2. In contrast, the calculated spectra of Kr replacing Mg and Fe do not match with the measured Kr K-edge XANES data. This discards this type of substitution mechanism in the quenched samples.

To estimate the Kr next nearest neighbor bond distances in the quenched samples, we used the energy shift of the first XANES peak in the acquired spectra following the approach of DiCicco et al. (1996). Calculated pressures are in the range of 0.5-5 GPa (Figure S6). This matches the experimental XANES measurements and suggests that the Kr impurity atoms are enclosed under a positive confinement pressure or stress. Similar pressures have been reported for Kr ionimplanted metal foils MgO and UO2 (Tan et al., 1991;Norton et al., 1992;Martin et al., 2015;).

Based on these observations, we propose that Kr impurity clusters may have formed during P/T quenching. The significant expansion of Kr (more than 50% during P quenching from 40-60

GPa (Rosa et al., 2018) may favor short range diffusion of initially homogenously distributed Kr atoms and their precipitation into NG nano-impurity clusters. This short range diffusion and lattice rearrangement may be driven by the lattice strains that Kr atoms exert on the host lattice at room conditions. It has been previously shown that structures hosting large impurity atoms tend to form impurity clusters by a point defect coalescence mechanism. This mechanism allows reducing the tensile stresses by transforming them in compressive ones that are energetically more favorable for the structure (Noordhuis and De Hosson, 1991). The general observation of low diffusivities of NGs at ambient pressure and high temperature in crystals (i.e., Kr: 1.92×10 -22 m 2 s -1 in UO2 at 1273 K; [START_REF] Michel | Etude Du Comportement Des Gaz de Fission Dans Le Dioxyde D'uranium : Mecanismes de Diffusion[END_REF] further supports a dissolution mechanism based on short range diffusion and lattice rearrangement. Such mechanism also operates for trace elements that tend to concentrate in defect structures in strained crystal [START_REF] Piazolo | Deformation-induced trace element redistribution in zircon revealed using atom probe tomography[END_REF]. coordination. The relative volume reduction of zero-charged radii at high P/T conditions were obtained from those of pure NGs using the thermal equation of states listed in Table S3. The resulting radii are also listed in Table S3.

We employed values of Em that have been calculated based on bulk elastic data corresponding to the high P/T conditions of the experiment using K0, G0 and their P/T derivatives reported by Wang et al. (2004) (see Table S2). However, this approach does not account for the small difference in stiffness between a filled host site and a vacant site (Karato, 2016), which in general should be slightly more flexible. This may only affect NGs that exhibit large differences between their ionic radii and the ones of the host sites (i.e., Ne, Xe in the present case). This could in turn lead to a slight underestimation of their solubilities, which is however not relevant in the present case as maximal solubilities are always used. This effect may become an important factor for solubility data obtained at high dilution levels.

Our lattice strain model approach contains only one fitting parameter that is the maximal site solubility c0. For the oxygen site in Fpc c0 was adjusted using the Kr solubility data obtained in the present study as anchoring points (Figure 5a). Solubilities of Ar, Kr and Xe obtained at 25

GPa and 1800 K were used to fit c0 for Bg. Due to the absence of solubility data at higher P/T conditions for NGs in Bg, the value of c0 obtained at 25 GPa and 1800 K was subsequently employed for the Bg lattice strain models at 50 and 120 GPa.

The combination of EP,T , r0,P,T and ri,P,T in our lattice strain model reproduces well the experimentally observed solubility trend from light to heavy NGs reported by Shcheka and Keppler (2012) (Figure 7, bold black dotted line for Mg(Si,Al)O3)). The fitted c0 value is in good agreement with the one obtained by Shcheka and Keppler (2012). Our approach takes into account the compressibility of NGs, the type of host site and change in stiffness of a site with P/T. This is important because these parameters change significantly at LM conditions. We therefore conclude that, for highly compressible NGs, the present approach is appropriate and can be used for predicting NG solubilities in a host lattice site at the extreme P/T conditions of the lower mantle and beyond. Table S3. Thermo-elastic parameters for Mie-Grüneisen equation of states after Jackson and Ridgen (1996) or Dewaele et al. (2008)

Figure 2 .

 2 Figure 2. (a) Back scattered electron image of the sample Cell_1 (Table1). The diamond

Figure 3 .

 3 Figure 3. Measured Kr concentrations in Fpc after quenching of laser heated samples subjected

  ). Uncertainties on the EMPA measurements are within the symbol size for Kr and Fe (103 and 816 ppm, respectively). The detection limits of S (642 ppm) exceed the measured quantities for most points and therefore plot (b) can only be used for evaluating chemical trends.

Figure 4 .

 4 Figure 4. Averaged Kr concentrations in metallic melts with different compositions after

Figure 5

 5 Figure 5 (a) Estimated maximal Kr solubilities in Fpc and metallic melts (red squares and

  ). The extrapolation of solubility data to the core mantle boundary (CMB) conditions is delineated by red and cyan dashed lines for Fpc and Fe88S12, respectively. The results of the Kr solubility in Fe-free and Al-bearing bridgmanite (Bg) fromShcheka and Keppler (2012) are shown for comparison as black and orange squares. They have been experimentally determined at 25 GPa and 1800 K and estimated from lattice strain modelling at 50 GPa. (b) Approximated partitioning coefficient Dmetal/oxide between (Mg1-x,Fex)O and Fe88S12 for Kr as a function of pressure at 2300 K (Cell_1-3, Table1). The black triangles, blue squares and red circles indicate the calculated D values using measurements from the entire heating spot (within a diameter of 40 µm), the central portion of the hotspot (within a diameter of 20 µm) and the outer rim of the hotspot (within a diameter range of 20-40 µm), respectively. The yellow shaded area indicates the extrapolation of the experimental Dmetal/oxide values to the Earth's outer core conditions and takes into account the uncertainties.

Figure 6

 6 Figure 6 (a) Calculated atomic radii of zero-charged Kr 0 in solid fcc Kr, Fe 0 in liquid Fe88S22 and O 2-and Mg 2+ in solid Mg0.75Fe0.25O as a function of pressure at 2300 K. The radii have

Figure 7 .

 7 Figure 7. Left panels: Solubility trend versus NG radius in oxygen vacancies of Fe-free Al-

Figure 8 . 7 .

 87 Figure 8. (a) Abundances of 20 Ne, 36 Ar, 84 Kr and 130 Xe (stable isotopes) normalized to 36 Ar

  Figure S1. SEM, EMPA and µXRF maps acquired on samples Cell_1, _2, _3, _6 and _7 (Table1, main manuscript and TableS1). The figures for each sample include a raw back scattered electron (BSE) image and the corresponding elemental distribution maps of Fe (red), S (orange), Ni (brown),Mg (pink) and O (green). The positions of acquired EMPA measurements are outlined as diamond symbols in a detailed BSE image on the right. The coloured symbols indicate the measured concentration of Kr as outlined in the legend below the detailed BSE images. The position of the laser spot is delineated in the detailed BSE images as yellow circles having an inner circle representing the central hot-spot region. The XRF image is shown on the right below the detailed BSE image. It represents the elemental distribution of Kr in red; Fe in blue and O in green. The colour intensity scales with the abundance of the element. The sample size is given on the µXRF image. Solid orange circles indicate the positions where X-ray absorption data were acquired.

Figure S2 .

 S2 Figure S2. The EMPA Kr counts to concentration calibration using 7 standards of elements adjacent to Kr (from atomic number 30 to 40) for the three crystal detectors SP1, SP2 and SP3. Linear fits to the data are shown as solid lines.

Figure S5 .

 S5 Figure S5. Calculated Kr K-edge XANES spectra for a single Kr atom incorporated in MgO, FeO and Mg0.5Fe0.5O. Green and blue spectra show the calculation results for Kr substituting in the anion site (O 2-) and in the cation site (Mg 2+ and Fe 2+ ), respectively. The black spectrum is the sum over all calculated Kr environments in Mg0.5Fe0.5O.

Table S1 .

 S1 EMPA concentration measurements (in wt.%) and their distance from the centre of the laser 878 heating spot. Averaged detection limits of elements are 530 ppm for Mg, 642 ppm for S, 816 ppm for Fe, 879 971 ppm for Ni and 103 ppm for Kr. Errors on temperature are in the order of 100-200 K. 880

	Sample, LH-spot	Mg	S	Fe	Ni	Kr	P (Gpa)	T (K)	Distance from centre of hotspot
	Cell_1, MgO	47.67	0.27	5.65	0	1.08	40.0(5)		~10 µm
		47.25	1.07	10.34	0.08	1.01			~10 µm
		49.84	0.25	3.26	0.08	1.24			~10 µm
		49.19	0.35	2.35	0.02	0.18			10 -20 µm
	Cell_1, Fe88S12	0.07	9.36	89.27	0.09	0.00	40.0(5)		~10 µm
		0.42	8.17	89.09	0.12	0.00			10 -20 µm
		0.14	8.50	90.11	0.17	0.00			10 -20 µm
		0.63	3.24	91.78	0.09	0.11			>20 µm
		0.17	13.1	84.04	0.08	0.03			>20 µm
		0.46	8.15	85.38	0.09	0.02			>20 µm
	Cell_2, MgO	40.56	0.06	15.88	0.00	1.473	61.5(5)		~10 µm
		35.23	0.21	26.43	0.02	2.9264			~10 µm
		41.21	0.13	22.59	0.01	1.8444			~10 µm
		38.64	0.16	25.67	0.01	2.4057			~10 µm
		38.51	0.18	26.46	0.03	2.266			~10 µm
		48.09	0.00	11.33	0.00	0.9489			10 -20 µm
		44.63	0.02	15.85	0.00	1.0297			10 -20 µm
	Cell_2, , Fe88S12	0.17	11.80	87.71	0.23	0.09	61.5(5)		< 10 µm
		0.25	10.37	88.79	0.20	0.39			< 10 µm
		0.07	13.38	86.31	0.17	0.07			~10 µm
		0.04	12.75	86.99	0.13	0.10			~10 µm
		0.02	2.87	96.94	0.12	0.05			~10 µm
		0.08	4.70	95.08	0.09	0.06			10 -20 µm
		0.09	4.12	95.56	0.09	0.14			10 -20 µm
		0.23	6.78	92.65	0.16	0.18			10 -20 µm
	Cell_3, Fe83Ni5S12, LH_1	0.00 0.00 0.01 0.00 0.00	12.96 7.67 13.04 15.99 11.89	78.17 82.49 78.97 79.86 84.73	8.87 9.70 7.98 4.14 3.38	0.00 0.14 0.00 0.00 0.00	65.0(5)		< 10 µm < 10 µm ~10 µm 10 -20 µm 10 -20 µm
	Cell_3, Fe83Ni5S12,, LH_2	0.01 0.01 0.04 0.01 0.00	8.95 8.92 5.25 7.37 10.71	80.55 76.99 80.55 75.06 78.91	10.49 14.05 14.15 17.56 10.37	0.00 0.03 0.01 0.00 0.00			< 10 µm ~10 µm ~10 µm ~10 µm 10 -20 µm
	Cell_3, Fe83Ni5S12,, LH_3	0.00 0.00 0.02	17.76 14.14 15.17	74.97 82.41 81.53	7.26 3.45 3.26	0.00 0.00 0.01	65.0(5)		< 10 µm ~10 µm ~10 µm
		0.00	15.41	81.22	3.36	0.00			~10 µm
	Cell_5, Ni, LH_1	0.02 0.00 0.01 0.01 0.03 0.00 0.00 0.00 0.01 0.01 0.00 0.01	0.02 0.03 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.01 0.00 0.01	0.02 0.03 0.01 0.02 0.00 0.02 0.01 0.01 0.03 0.00 0.00 0.03	99.91 99.92 99.97 99.93 99.95 99.77 99.29 99.62 99.19 99.81 99.85 99.68	0.03 0.02 0.01 0.04 0.03 0.21 0.70 0.35 0.77 0.17 0.15 0.26	62.0(5)		< 10 µm < 10 µm < 10 µm < 10 µm < 10 µm 10 -20 µm 10 -20 µm 10 -20 µm 10 -20 µm 10 -20 µm 10 -20 µm 10 -20 µm
	Cell_6, Fe88S12 ,LH_1 0.00 0.00 0.00 0.00 0.00	9.43 7.60 10.29 9.27 5.98	90.41 92.18 89.53 90.54 93.58	0.08 0.14 0.11 0.09 0.06	0.08 0.07 0.07 0.09 0.38	110(1)		< 10 µm < 10 µm ~10 µm 10 -20 µm 10 -20 µm
	Cell_6, Fe88S12, LH_2 0.00 0.01 0.03 0.02 0.03 0.00	11.21 9.13 8.37 11.45 9.72 8.53	88.54 90.60 91.41 88.27 90.08 91.36	0.25 0.25 0.13 0.12 0.16 0.09	0.00 0.01 0.06 0.14 0.01 0.02	110(1)		< 10 µm < 10 µm < 10 µm ~10 µm 10 -20 µm 10 -20 µm
	Cell_6, Fe88S12 ,LH_3 0.00 0.00 0.00 0.02 0.02 0.01	15.08 15.25 7.98 13.44 10.05 14.49	84.80 84.41 91.54 86.37 89.40 85.40	0.12 0.08 0.11 0.18 0.17 0.10	0.00 0.25 0.38 0.00 0.36 0.00	110(1)		< 10 µm ~10 µm 10 -20 µm 10 -20 µm 10 -20 µm 10 -20 µm

Table S2 .

 S2 Lattice strain model input parameters used to calculate NG solubilities at high P/T conditions in Fpc and Bg.

	P	T	Fpc			ri [6]					Bg			ri [4]
	GPa K	c0	r0,P,T Em	He	Ne	Ar	Kr	Xe	c0	r0,P,T Em	He	Ne	Ar	Kr	Xe
	0	298	1.53 1.4	18	1.08 1.21 1.64 1.78 1.96 0.9	1.37	25	0.9	1.18 1.51 1.69 1.89
	25	1900 1.1	1.26	306	1.04 1.10 1.31 1.33 1.50 0.54 1.21	440	0.86 1.07 1.20 1.27 1.44
	50	1900 1.9	1.19	440.2 1.04 1.09 1.22 1.25 1.40 0.54 1.19	552.5 0.86 1.06 1.12 1.19 1.35
	120	2500 2.6	1.12	777.5 1.00 1.06 1.13 1.15 1.29 0.54 1.17	866.5 0.84 1.03 1.04 1.10 1.24

  used to calculate NG radii at high P/T conditions.

		V0	K0	K'	ΘD	γ0	γ1
	Ne a	88.98	1.4	8.03	75.1	0.97	2.44
	Ar	149.8 b	2.b	7.59 b	93.3 c	0.5 fixed	2.2 c
	Kr	220.61 d	1.65 d	6.7 d	79.1 c	0.5 fixed	2.17 c
	Xe	270 e	2.18 e	6.26 e	57 c	0.5 fixed	2.36 c

a all parameters taken from Dewaele et al. (2008); b from Dewaele et al. (2018); c form Jephcoat (1998); d from Rosa et al. (2018); e from Rosa et al. (in prep.).

Acknowledgements

We thank the reviewers for their constructive comments that helped improve the manuscript. We also greatly appreciated the way the editor handled it. We thank the ESRF for allocating beamtime to this project, I. Kantor, R. Torchio and S. Boccato for their help in setting up the experiments, F. Perrin, S. Pasternak, J.-L Devidal and J. Jacobs for technical assistance.

MAB acknowledges the support of the Labex ClerVolc (This is laboratory of Excellence ClerVolc contribution number xxxx).

Ne/Ar ratios of the LM, comets and chondrites are below the atmospheric ratio. A solar-like Ne/Ar ratio could originate from the outgassing of the Earth's core or could have been captured in the early atmosphere due to solar-wind irradiation. The required addition of a high solar-like Ne/Ar ratio from another reservoir implies a significantly lower contribution of LM NGs to the present-day atmosphere. This conclusion is consistent with the study of [START_REF] Holland | Meteorite Kr in Earth's mantle suggests a late accretionary source for the atmosphere[END_REF] in which they found that Kr and Xe play only a minor role in determining the NG composition of the modern atmosphere. All these arguments thus suggest that the LM may not be fully outgassed and could be an available NG reservoir through geologic times.

Supplementary Information

Lattice strain model approach and parameters

We conducted lattice strain modelling following the established method of Blundy and Wood (2003) to estimate solubilities of Ne, Ar, Kr and Xe throughout the lower mantle from 25 to 120 GPa and 1800 to 2500 K:

Here, ci is the solubility of element i with radius ri, c0 is the maximal solubility of the host site, NA is the Avogadro's number, Em is the Young's modulus which provides the flexibility of the site and r0 is the host site radius. The elasticity of the host site, Em is expressed by the relation:

In previous studies that developed lattice strain models for noble gases, the high P/T experimental solubility data have been adjusted using ambient conditions NG radii (ri) (Brooker, 2003;Shcheka and Keppler, 2012). This approach results in unrealistically low values of the Young's moduli Em, that are much smaller than the values calculated from the bulk elastic moduli at the conditions of the experiment.

For example, Shcheka and Keppler (2012) obtained a fitted Em value of 35 GPa for the oxygen site in Bg, at 25 GPa and 1800 K. This value is close to the calculated Young's modulus of Bg at ambient condition (Em = 25 GPa), but differs significantly from its calculated value at the experimental conditions of the uppermost lower mantle (Em = 440 GPa). The host site at uppermost lower mantle conditions is significantly stiffer than at ambient conditions. This should be taken into account to fit and extrapolate solubility data to high P/T conditions.

We intended to establish lattice strain models to predict solubilities through the mantle for the suite of NGs. Therefore, we reduced the fitting parameters in the lattice strain models to c0 and constrained Em and r0,i to calculated values using thermoelastic and crystal-chemistry (coordination dependent atomic radii) data.

The oxygen host site radii in Fpc and Bg at ambient conditions were derived from [START_REF] Shannon | Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides[END_REF] by taking into account the coordination of the sites (Zhang and Zhu, 1995). In Fpc, oxygen is six-fold coordinated to cations and has an effective ionic radius of 1.4 Å. In Bg, oxygen is fourfold coordinated to cations but in two distinct crystallographic sites with different bond lengths, leading to an average site radius of 1.37(1) Å. Vacancy site radii (r0,P,T) at high P/T conditions were obtained by calculating the high P/T structures from the thermal equation of states reported by [START_REF] Mao | Thermal equation of state of lower-mantle ferropericlase across the spin crossover[END_REF] for Fpc and by [START_REF] Fiquet | Thermoelastic properties and crystal structure of MgSiO3 perovskite at lower mantle pressure and temperature conditions[END_REF] for Bg (Table S2). We noted that the solubility trends of Ar, Kr and Xe reported by Shcheka and Keppler (2012) at 25 GPa and 1800 K could not be reproduced with the ionic radius of oxygen in Bg and only with a crystal radius that is about 0.13 Å smaller. We therefore employed the crystal radii obtained at high P/T conditions for Bg.

Neutral atomic effective radii of NGs at ambient conditions from Ne to Xe were evaluated using the ionic radii reported by Zhang and Zhu (1995). For Ar, Kr and Xe, we extrapolated the ionic radii for the [4]-fold coordination using the available data for the [6]-and [8]-fold Supplementary Information 55

Formation of volatile saturated liquid/melt phase during magma ocean crystallization

Presently, two models describing the crystallization of the magma ocean (MO) in the deep primitive Earth have been reported: (1) the classical solidification model from the bottom to the top (Solomatov and Stevenson, 1993) and ( 2) the more recent model that proposes the onset of solidification in the mid-mantle (Labrosse et al., 2007). For both models crystallization of LM minerals at NG saturated conditions may have occurred.

In the classical bottom-up crystallization model of Solomatov and Stevenson (1993), volatiles are incorporated in solidifying minerals in small quantities. The majority of volatiles are enriched and saturate in solution in residual liquids as solidification proceeds. Then, volatile-rich liquids rise to the surface where they form bubbles. If the size of the bubbles remains below 1 mm, they are re-entrained in the flow of the convecting MO and resorbed at depth [START_REF] Elkins-Tanton | Linked magma ocean solidification and atmospheric growth for Earth and Mars[END_REF].

In the second model, buoyant crystals of the first forming solid phase (Fe-poor Bg) accumulate on the top of the LM and Fe-rich residual melt. This leads to an early chemical decoupling of the LM from the upper mantle (UM). Upon further crystallization and cooling, the basal Fe-rich melt saturates in volatiles. The early decoupling of the LM and UM is supported by geochemical observations on fissogenic Xe isotopes (Allègre et al., 1983;Pepin and Porcelli, 2006;Mukhopadhyay, 2012).

NG replenishment model and considered isotopic Ne signatures therein

In our model, we assumed that only the lower mantle has captured a solar-wind irradiated Ne isotope signature (Neon-B) after the moon-forming impact, with a 20 Ne/ 22 Ne ratio of 12.73 [START_REF] Eberhart | Trapped solar wind noble gases in Apollo 12 lunar fines 12001 and Apollo 11 breccia 10046[END_REF]. We also presumed that the atmosphere has entirely lost its Neon-B signature during the moon-forming impact and that the residual atmosphere (residual Ne comprises 0.7% of primordial atmosphere) is Q-like with a 20 Ne/ 22 Ne ratio of ~10.5. In our model, the present-day atmospheric 20 Ne/ 22 Ne ratio of ~9.8 is considered as a mix of Neon-B (30.4%), residual Q-like signature (0.7%) and planetary component with a 20 Ne/ 22 Ne ratio of 8.5 (68.9%) that was delivered during late-veneer by comets and meteorite (Marty, 2012). In our model, we supposed that the Ne signature of comets is Q-like, as it is for meteorites. This was proposed by Marty et al. (2008) based on measurements of refractory grains in comets. Measured Ne abundances in the comet 67P, revealed concentrations below the detection limit, showing that Ne was not trapped in cometary ice. In the present scenario, the solar Ne component found for MORBs and CO2 wells [START_REF] Eberhart | Trapped solar wind noble gases in Apollo 12 lunar fines 12001 and Apollo 11 breccia 10046[END_REF]) may then be explained by subduction of atmospheric Ne after lower mantle outgassing.

Supplementary Information

Supplementary Information