Celine Crepisson
email: celine.crepisson@upmc.fr

Chrystèle Sanloup

Laurent Cormier

Marc Blanchard

Jessica Hudspeth

Angelika D Rosa

Olivier Mathon

Tetsuo Irifune

Céline Crépisson

Kr environment in feldspathic glass and melt: A high pressure, high temperature X-ray absorption study

Keywords: Krypton, XAS, silicate glass, silicate melt, high pressure

Introduction

Due to their supposed chemical inertia, high volatility, and high dilution, noble gases have been intensively studied by geochemists to understand the formation of the Earth's atmosphere, and to study mantle dynamics. None of Kr stable isotopes ( 78,80,82,83,84,86 Kr) is purely radiogenic, and Pu and U fission yields are very low for Kr. Thus Kr cannot be used to constrain chronology of the atmosphere evolution, and as such has been less studied than He, Ne, Ar, and Xe. However, the small amount of radiogenic Kr makes it suitable to trace air component in fluid inclusions [START_REF] Böhlke | Brine history indicated by argon, krypton, chlorine, bromine, and iodine analyses of fluid inclusions from the Mississippi Valley type lead-fluorite-barite deposits at Hansonburg, New Mexico[END_REF]. Earth atmospheric Kr isotope composition, unchanged since at least 3.3 Ga [START_REF] Avice | The origin and degassing history of the Earth's atmosphere revealed by Archean xenon[END_REF], falls in-between solar and chondritic compositions [START_REF] Pepin | On the origin and early evolution of terrestrial planet atmospheres and meteoritic volatiles[END_REF]. Kr isotopic ratios in CO 2 magmatic well gases that probed the continental lithosphere, showed a significant enrichment in 84 Kr and 86 Kr compared to the atmosphere [START_REF] Holland | Meteorite Kr in Earth's Mantle Suggests a Late Accretionary Source for the Atmosphere[END_REF]. The discovery of Kr isotopic fractionation in these well gases, taken as a proxy of deep mantle gases, was interpreted as the signature of a primordial Kr chondritic component [START_REF] Holland | Meteorite Kr in Earth's Mantle Suggests a Late Accretionary Source for the Atmosphere[END_REF]. Nevertheless [START_REF] Holland | Meteorite Kr in Earth's Mantle Suggests a Late Accretionary Source for the Atmosphere[END_REF] argue that early degassing of an accreted primordial chondritic composition, followed by mass fractionation during atmosphere loss, fails to explain the composition of the modern atmosphere. Instead, late accretion of cometary material is assumed to explain Kr isotope signature of the atmosphere. Although very few samples have been analyzed for all Kr isotopes, mantle-derived basalts (MORBs, OIBs) have an atmospheric Kr isotopic composition [START_REF] Moreira | Rare gas systematics in popping rock: Isotopic and elemental compositions in the upper mantle[END_REF][START_REF] Trieloff | The nature of pristine noble gases in mantle plumes[END_REF][START_REF] Graham | Noble gas isotope geochemistry of Mid-Ocean Ridge Basalt and Ocean Island Basalts: characterization of mantle source reservoirs[END_REF]. This homogeneous composition could be due to atmospheric Kr recycling at subduction zones [START_REF] Holland | Seawater subduction controls the heavy noble gas composition of the mantle[END_REF].

To explain highly precise Kr isotopic data, geochemists need an understanding of Kr behavior in silicate melts, including Kr solubility value and mechanism, as well as Kr degree of compatibility.

Fractionated fission Kr has also been observed in the Okhlo natural nuclear reactor. In nuclear plants, 85 Kr is a common fission product. Nuclear waste confinement by vitrification in SiO 2 -rich glasses has been used for many years (Ojovan and Lee, 2011). Accumulation of Kr leads to the formation of nanobubbles where pressure may reach 2.6 GPa [START_REF] Martin | Behavior of fission gases in nuclear fuel: XAS characterization of Kr in UO 2[END_REF] under high temperature generated by irradiation. Understanding of Kr behavior in silicate glasses is thus crucial for long nuclear waste storage.

The majority of studies dedicated to noble gases solubility in melts are based on analyses of recovered glassy samples, and did not directly investigate the noble gas structural environment in the silicate network, as noble gases can escape from the silicate structure at ambient conditions. These studies showed that noble gas solubility decreases with increasing radius (from He to Xe) (Caroll and Stolper, 1993[START_REF] Lux | The behavior of noble gases in silicate liquids: Solution, diffusion, bubbles and surface effects, with applications to natural samples[END_REF][START_REF] Shibata | Solubility of neon, argon, krypton, and xenon in binary and ternary silicate systems: A new view on noble gas solubility[END_REF], and that this solubility strongly depends on the chemical composition of the melt. Noble gas solubility was first related to ionic porosity, i.e. the absolute volume of voids (Caroll and Stolper, 1993), whereas [START_REF] Shibata | Solubility of neon, argon, krypton, and xenon in binary and ternary silicate systems: A new view on noble gas solubility[END_REF] showed that it was better inversely correlated to the number of non-bridging oxygen per silicon, even if the presence of Al may modify this trend [START_REF] Bouhifd | Aluminium control of Argon solubility in silicate melts under pressure[END_REF]. Based on these findings and noble gas relative chemical inertia, noble gases were supposed to passively fill the voids of the silicate network.

In situ structural data on the environment of heavy noble gases in silicate melts and glasses are scarce. [START_REF] Wulf | Structural environment of krypton dissolved in vitreous silica[END_REF] performed an X-ray absorption study at the Kr K-edge in a SiO 2 glass (1.97 wt % Kr). They identified a Kr-O distance of 3.45±0.1 Å, interpreted as corresponding to a local rearrangement of the silicate network into a local clathrasil-type environment around the Kr atom. The supposed chemical inertia of Kr and Xe, the most reactive of the noble gases, has been questioned throughout the past 15 years, with the synthesis of numerous Kr and Xe compounds (see [START_REF] Grochala | Atypical compounds of gases, which have been called 'noble[END_REF] for a review). Bonding of Xe to O in compressed haplogranitic magmas had also been evidenced by in situ X-ray diffraction [START_REF] Sanloup | Bonding of xenon to oxygen in magmas at depth[END_REF]).

In the present study, we perform in situ X-ray absorption spectroscopy (XAS) at the Kr K-edge, to specifically access Kr structural environment in a feldspathic (sanidine) glass.

Starting (Na,K)AlSi 3 O 8 glass composition was chosen as representative of the chemistry of a major mineral of the continental crust, and proxy of silica-rich melts that can be generated at pressure reaching 2 GPa in orogenic contexts (Jimenez-Munt et al., 2008), and in subduction contexts from melting of hydrous basalt [START_REF] Prouteau | Evidence for mantle metasomatism by hydrous silicic melts derived from subducted oceanic crust[END_REF], or silica-rich sediments [START_REF] Turner | Recent contribution of sediments and fluids to the mantle's volatile budget[END_REF]. Experiments were conducted at pressures (P) and temperatures (T) up to 2.7 GPa and 1086°C, relevant for both continental crust melting and subduction zone contexts.

2.Material and Methods

Sample: synthesis and characterization

The starting glass of Kr/Xe-bearing sanidine was synthesized in a piston cylinder press at 3.5 GPa and 1400°C for 24 hours before quenching. For this purpose, Xe and Kr were loaded as a 1:1 gaseous mix along with sanidine powder in a Pt capsule [START_REF] Boettcher | A simple device for loading gases in highpressure experiments[END_REF]. Sanidine is a high-temperature feldspar, of atomic composition (K x Na 1-x )AlSi 3 O 8 with x higher than 0.32 [START_REF] Bendel | Raman spectroscopic characterisation of disordered alkali feldspars along the join KAlSi 3 O 8 -NaAlSi 3 O 8 : application to natural sanidine and anorthoclase[END_REF]. In our experiments, sanidine powder was obtained by grinding a natural sanidine mineral (K 0.52 Na 0.43 Al 1.05 Si 2.96 O 8 , formula unit retrieved from electron microprobe analysis) from the Sorbonne Université mineralogical collection.

Starting glass and recovered sample were mounted in epoxy, polished and C-coated.

They were observed by Scanning Electron Microscope (SEM) with a Zeiss Supra 55 (equipped with a field emission gun). Detection of Xe and Kr was optimized with an acceleration voltage of 20 keV and a working distance of 6.6 mm in backscatter mode.

Electron microprobe analyses (EMPA) were done on a CAMECA SX5, at CAMPARIS centre at Sorbonne Université. Operating conditions were 15 kV accelerating voltage, 10 nA beam current, and a focused beam for point analysis. We use the method from [START_REF] Montana | Xe and Ar in highpressure silicate liquids[END_REF] for Kr, which was calibrated by measuring the counts on neighboring elements (i.e. Rb). Xe was calibrated using a known standard analyzed by Particle-Induced X-ray Emission (data published in [START_REF] Sanloup | Bonding of xenon to oxygen in magmas at depth[END_REF].

The synthesized starting glass is chemically homogeneous (based on SEM and EMP analyses) with presence of Kr/Xe gas bubbles indicating that saturation was reached. Contents of 2.2 wt % Xe (0.36 at %) and 0.5 wt % Kr (0.13 at %) were measured by electron microprobe analyses from an average of seven points of analysis in areas free of micrometric gas bubbles. Average composition in wt % of the starting glass is given in Table 1. Recovered sample was quenched from 1040°C and 2.7 GPa, where it reequilibrated as partial melt and feldspar crystals (Figure 1), following cooling from fully molten state (1415°C and 3 GPa) which was reached with the initial purpose to collect XAS data at the Xe-edge. Kr and Xe are only observed in the glass, with striking alignments of Kr/Xe gas nanobubbles (Figure 1).

Average analyses of the recovered sample are given in Table 1, although degassing upon quenching prevents Xe and Kr contents to be determined by EMP analysis.

Experimental set-up

In-situ X-ray absorption spectroscopy (XAS) was performed on beamline BM23 at the ESRF, dedicated to general purpose XAS [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]. High pressure and temperature conditions up to 2.7 GPa and 1086°C (Table 2) were generated in a Paris Edinburgh Press [START_REF] Besson | A large volume pressure cell for high temperature[END_REF]. We used a cell assembly developed by [START_REF] Kono | Toward comprehensive studies of liquids at high pressures and high temperatures: Combined structure, elastic wave velocity, and viscosity measurements in the Paris-Edinburgh cell[END_REF] and adapted from [START_REF] Yamada | High-pressure x-ray diffraction studies on the structure of liquid silicate using a Paris-Edinburgh type large volume press[END_REF]. More details on the cell-assembly and experimental set-up can be found in [START_REF] Rosa | In-situ characterization of liquid network structures at high pressure and temperature using X-ray Absorption Spectroscopy coupled with the Paris-Edinburgh press[END_REF]. The sample (0.75 mm diameter and 1.5 mm height) was encapsulated in a synthetic nanopolycrystalline diamond (NPD) cylinder caped with Pt-Rh caps. The use of NPD prevents glitches from a single or polycrystalline diamond capsule, which deteriorate the XAS signal. Temperature was determined using calibration from [START_REF] Kono | Toward comprehensive studies of liquids at high pressures and high temperatures: Combined structure, elastic wave velocity, and viscosity measurements in the Paris-Edinburgh cell[END_REF], and pressure using unit cell volume of hBN from the cell assembly (based on X-ray diffraction measurements) and equation of state from Le [START_REF] Godec | situ X-ray diffraction studies of formation of cubic and hexagonal graphite-like boron nitride by the reaction of elemental boron with supercritical hydrazine[END_REF]. Error bars are ±50°C for temperature and ±0.2 GPa for pressure.

XRD and XAS measurements

Angle-resolved X-ray diffraction data were recorded on a MAR165 CCD at 15 keV.

Image plates were integrated using Fit 2D software [START_REF] Hammersley | FIT2D: An Introduction and Overview[END_REF]. Cell parameters of hBN were determined using POWDER CELL software [START_REF] Kraus | POWDER CELL -a program for the representation and manipulation of crystal structures and calculation of the resulting X-ray powder patterns[END_REF].

XAS transmission measurements were performed first at the Kr K-edge (14326 eV) up to 2.7 GPa, upon increase of temperature up to 1086°C, and upon decrease of temperature down to 505°C, before quenching to room temperature (Table 2). Xe K-edge spectra were recorded following measurement at the Kr K-edge upon increasing temperature up to 1415°C and 3 GPa, and upon cooling to 1040°C at 2.7 GPa followed by quenching. Xe K-edge spectra are however not of sufficient quality to allow fitting, given the very small absorption jump (0.09 compared to 0.25 at the Kr K-edge), and are thus not shown here. Energy calibration of the edge position was made by frequent analyses of Kr gaseous standards. The beam size on the sample was 300 x 80 μm². Transmitted X-ray intensity was recorded by ionization chambers filled with gaseous Ar-He mixed gas. Signal was collected from 14244 eV to 14971 eV at the Kr K-edge (451 points analysis). Counting times, number of scans, and P/T conditions are given in Table 2. Energy steps were adapted as a function of the edge position, each scan takes about 1 hour.

Processing of XAS data

The edge of the standard was fixed to 14326 eV, and the edge of each sample was recalibrated using the averaged edge value of two gaseous Kr standards taken before and after the sample measurement. For Kr standard, no significant shift of the Kr K-edge was noted (0.4 eV at the largest). After correction of edge position, data were cut at 14800 eV for better normalization.

Data processing was performed using ATHENA and ARTEMIS packages, based on the IFEFFIT programs [START_REF] Ravel | ATHENA, ARTEMIS, HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT[END_REF]. Each scan was corrected with a pre-edge and a post-edge baseline. Position of the edge was determined by the position of the first derivative of the absorption. The intensity of the jump at the edge was then normalized to one.

After merging of the scans collected at a given P/T condition, data were corrected using a background function. We used an automated background subtraction method (AUTOBKG) developed by Newville [START_REF] Newville | EXAFS analysis using FEFF and FEFFIT[END_REF] and implemented in the ATHENA software. This correction minimizes the features below the first atom-atom distance in the R-space. R bkg was fixed to 1.2 Å.

To fit the data at the Kr K-edge, we used a k-range of ~ 2.2-6.5 Å -1 (Table 3), due to low signal to noise ratio at higher k values. A small k-range ensures that all the different contributions to the Fourier transform are not artifacts but really arise from neighboring atoms. Real part of backward Fourier transform was exported to ARTEMIS software to be fitted using R-range ~ 1.1-3.8 Å (Table 3). Fitting made on real part of backward Fourier transform ensures that all XANES and noise contributions are removed from the EXAFS signal. Fit parameters include: amplitude reduction factor (S0), average distances of the neighboring atom to the central Kr atom, Debye Waller factor (σ²), and difference of edge position compared to standard value (ΔE 0 ). ΔE 0 values remain smaller than 7 eV, attesting consistency of the fits. It was necessary to add a third order anharmonic cumulant expansion fitting parameter (C3) for high pressure or high temperature measurements [START_REF] Stern | Thermal vibration and melting from a local perspective[END_REF][START_REF] Farges | Structural transformation in Ni-bearing Na 2 Si 2 O 5 glass and melt[END_REF]. C3 is a measure of the asymmetry of the signal disorder, which arises in glasses from configurational disorder associated to thermal vibration at high pressure and/or high temperature conditions. The absolute value of C3 remains smaller than 0.009 Å 3 , similar to values found by [START_REF] Cochain | Bromine speciation in hydrous silicate melts at high pressure[END_REF] on silicate glasses and melts at high pressure and temperature conditions. As no Kr standard was analyzed in the course of the experiment besides Kr gas, it is not possible to determine coordination numbers (CN). We therefore fixed S0 at a common value of 0.79, and fixed the value of CN. In total, seven parameters must be fitted (first interatomic distance, σ 2 and C3 for the two contributions and ΔE 0 ) whereas 𝑁, the number of variables to fit, cannot exceed (Teo, 1986):

𝑁 = 2∆𝑅∆𝑘 𝜋 (1)
In our case ∆𝑘 ≈ 4.3 Å -1 and ∆𝑅 ≈ 2.8 Å. Therefore maximum number of parameters 𝑁, which can be fitted is ~ 7.7, indicating that we can theoretically fit our data as exposed above.

3.Results and Discussion

XAS data at the Kr K-edge

XAS data were recorded at ambient conditions, at high pressure and high temperature, and after quenching (Table 2). Potassic sanidine (KAlSi 3 O 8 ) is expected to melt around 1500°C at 2.6-2.7 GPa [START_REF] Boettcher | Melting in feldspars-bearing systems to high pressures and the structures of aluminosilicate liquids[END_REF]. Reports on the KAlSi 3 O 8 -NaAlSi 3 O 8 join under anhydrous conditions at 1 atm showed that melting temperature of KAlSi 3 O 8 drops by 100°C for our starting composition (Na 0.43 K 0.52 Al 1.05 Si 2.96 O 8 , atomic formula retrieved from EMPA) [START_REF] Schairer | The alkali-feldspar join in the system NaAlSiO 4 -KAlSiO 4 -SiO 2[END_REF]. Glass transition temperature (Tg) of felspathic glass at 1 atm was found inbetween 907-948°C based on viscosity measurements (Petermann et al., 2008;[START_REF] Richet | Glass transitions and thermodynamic properties of amorphous SiO 2 , NaAlSi n O 2n+2 and KAlSi 3 O 8[END_REF]. Moreover, viscosity is shown to decrease from 0 GPa to 2.5 GPa for both sanidine melt [START_REF] White | The effect of H 2 O and CO 2 on the viscosity of sanidine liquid at high pressures[END_REF] and albite melt [START_REF] Kushiro | Viscosity and structural changes of albite (NaAlSi 3 O 8 ) melt at high pressures[END_REF]. Thus Tg is expected to be even lower than 907-948°C at our pressure conditions. Therefore our measurements at 1086°C (and potentially at 920°C) were recorded above Tg and before recrystallization, i.e. on the supercooled liquid, behaving like a melt. Well-defined oscillations are visible in the X-ray absorption signal, and clearly differ from the signature of Kr gas and Kr liquid under pressure (Di [START_REF] Cicco | High-pressure EXAFS measurements of solid and liquid Kr[END_REF] (Figures 2 and3).

Rapid damping of the EXAFS signal indicates disorder beyond the first shell. We compare in Figure 3 our data with the k²-weighted EXAFS function recorded at 27°C on UO 2 (8 at % Kr) previously implanted with Kr ions [START_REF] Martin | Behavior of fission gases in nuclear fuel: XAS characterization of Kr in UO 2[END_REF]. Oscillations observed after 4 Å -1 clearly differ from our data sets. The magnitude of the Fourier transform (k-range used is displayed in Table 3) clearly shows two peaks at all measurement conditions (Figure 4), indicating that two distances contribute to the signal, with the main distance at ~ 1.9 Å, while [START_REF] Martin | Behavior of fission gases in nuclear fuel: XAS characterization of Kr in UO 2[END_REF] reports a main distance at 3.44 Å. Kr environment in sanidine glass is therefore different from that observed by [START_REF] Martin | Behavior of fission gases in nuclear fuel: XAS characterization of Kr in UO 2[END_REF] in UO 2 , i.e. Kr nanoclusters.

There is no noticeable change in the room temperature glass with pressure: data at ambient pressure and after quenching at 1.4 GPa being similar (Figures 2, 3 and4). The relative intensity of the two peaks however varies with temperature, the magnitude of the Fourier transform (Figure 4) being different at ambient temperature, at 505°C and 706°C, and especially in the melt at 920°C and 1086°C.

Resolving Kr environment in sanidine glass and melt

Variations of fitted Kr-O distances over our experimental P/T range are within error (i.e. ±0.1 Å). We thus evaluate averaged Kr-O distances for the whole P/T range, two Kr-O distances are identified at 2.49±0.1 Å and 3.32±0.1 Å (Table 3, Fig. 5). No other neighboring atom than oxygen could fit the observed XAS signal, although we considered other atomic pairs such as Kr-Kr, Kr-Si, Kr-Na, or Kr-K. Identified distances confirm the absence of Kr neighbors. Indeed Kr-Kr distance in solid cubic Kr is 3.68 Å at 2 GPa and room temperature [START_REF] Cicco | High-pressure EXAFS measurements of solid and liquid Kr[END_REF]. We can interpret these results as two distinct populations of Kr located in two different sites of the silicate network. Results clearly differ from [START_REF] Wulf | Structural environment of krypton dissolved in vitreous silica[END_REF], who only reported a Kr-O distance at 3.45 Å, as shown in Figure 5.

At ambient condition, there is no non-bridging oxygen in sanidine glass (KAlSi 3 O 8 ), and Al coordination number is four for all Al atoms [START_REF] Thompson | Non-bridging oxygen and high-coordinated aluminum in metaluminous and peraluminous calcium and potassium aluminosilicate glasses: High-resolution 17 O and 27 Al MAS NMR results[END_REF]. Study of an albite glass (NaAlSi 3 O 8 ) quenched from the melt at 2.6 GPa showed that less than 3% of Al atoms present a coordination number of five, whereas all remaining Al atoms have a coordination number of 4 [START_REF] Gaudio | Linking high-pressure structure and density of albite liquid near the glass transition[END_REF]. Sanidine glass is thus fully polymerized, with all Na + /K + compensating the charge deficit created by the presence of Al 3+ in tetrahedral position. Molecular dynamic simulations showed that in soda aluminosilicate glass, for Na/Si=1, distribution of the aluminosilicate rings at ambient pressure varies from 2 to 13 membered-rings, with 6 or 7 membered-rings being the most present ring population [START_REF] Xiang | Structure and properties of sodium aluminosilicate glasses from molecular dynamics simulations[END_REF]. Similarly, at ambient pressure, a ring size distribution from 2 to 12-membered rings is predicted for silica glass with 6 to 7 membered-rings being the dominant ring population [START_REF] Kohara | Relationship between topological order and glass forming ability in densely packed enstatite and forsterite composition glasses[END_REF][START_REF] Guerette | Structure and Properties of Silica Glass Densified in Cold Compression and Hot Compression[END_REF]. To our knowledge, no pore size distribution data is available for our glass composition. Based on the similarity of ring size distribution between aluminosilicate and silica glass, we assume that size of cages within aluminosilicate rings range from 0.9 Å to 5.9 Å in diameter, like in silica glass [START_REF] Guerette | Structure and Properties of Silica Glass Densified in Cold Compression and Hot Compression[END_REF]. This size distribution indicates the presence of 5-5.9 Å-diameter voids, inside the largest (i.e. ~ 12-membered) aluminosilicate rings. The Kr-O distance of 2.49±0.1 Å is therefore compatible with a Kr atom located inside the largest observed rings of the silicate network. This Kr-O distance falls in-between the sum of covalent radii of Kr and O (1.16 Å and 0.66 Å respectively [START_REF] Cordero | Covalent radii revisited[END_REF]) and the sum of ionic radii of Kr 0 and O 2- (respectively 1.78 Å for a coordination number of 6 [START_REF] Zhang | Atomic radii of noble gas elements in condensed phases[END_REF] and 1.4 Å [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]). This result indicates that Kr is interacting closely with the neighboring oxygen atoms, suggesting an oxidation of Kr. Under pressure, the edge position shifts by + 0.6 eV (Figure 6). Shift of the edge can be related to change in the oxidation state as observed for Cu, Co, Fe, Mn (e.g. Klysubun et al., 2015). This observation further supports a change in Kr oxidation due to Kr-O bonding. Kr is in the oxidation state II in most of Kr compounds synthesized, such as KrF 2 , KrF + or Kr 2 F 3 + [START_REF] Grosse | Krypton Tetrafluoride: Preparation and Some Properties[END_REF][START_REF] Burbank | Crystal Structure of Krypton Difluoride at -80°C[END_REF][START_REF] Lehmann | X-ray Crystal Structures of alpha-KrF2[END_REF].

Kr oxidation number is expected to increase compared to gaseous Kr, if Kr is surrounded by several O atoms.

The Kr-O distance of 3.32±0.1 Å cannot correspond to the presence of Kr atoms inside aluminosilicate rings, as the size distribution is limited to 5.9 Å in diameter. This larger Kr-O distance is similar to the 3.45±0.1 Å distance reported in SiO 2 glass at ambient pressure and 5 K [START_REF] Wulf | Structural environment of krypton dissolved in vitreous silica[END_REF], and close to predictions from first principle molecular dynamics. [START_REF] Zhang | Effective radii of noble gas atoms in silicate from first principles molecular simulation[END_REF] indeed found Kr-O = 3.5 Å in liquid silica, with Kr coordination number varying from 10 to 15 depending on pressure. Similar result was found by [START_REF] Guillot | Noble gases in high-pressure silicate liquids: A computer simulation study[END_REF] using molecular dynamics with Kr-O = 3.45 Å in silica melt and 3.31 Å in rhyolite melt. This large distance can be explained by the formation of large cavities in the melt where noble gases are accommodated, in agreement with a passive filling of the void space, or with a clathrasil-like environment [START_REF] Wulf | Structural environment of krypton dissolved in vitreous silica[END_REF]. Contribution of Kr fluid to this longer distance cannot be ruled out if the few Kr bubbles observed on starting and quenched samples are not fully homogenized with the melt at high pressure and temperature.

Disappearance of the larger Kr-O distance at higher temperatures (Figure 4), indicates that smaller Kr-O distance is more favorable, possibly with the increase of Kr reactivity.

Moreover, the Debye Waller factor associated with the smallest Kr-O distance (σ²1), is twice larger at room temperature than at high temperature (Table 3), suggesting that ordering of the smaller Kr-O environment is higher. Measurements at high pressures and temperatures are all above Kr melting point, whereas measurement after quenching at 1.4 GPa is below Kr melting point [START_REF] Ferreira | The fusion curves of xenon, krypton, and argon[END_REF]. Kr reactivity therefore seems enhanced above Kr melting curve, suggesting that it is pressure-induced, i.e. it favors smaller volume, as observed for Xe incorporation in olivine [START_REF] Sanloup | Xenon and Argon: a contrasting behavior in olivine at depth[END_REF]. Besides, the larger Kr-O distance vanishes in the melt, i.e. at 920°C and 1086°C (Figure 4), indicating structural changes between the melt and the glass. A complementary explanation could be a contribution of Kr fluid to the longer Kr-O distance, which would diminish with temperature due to the increase of Kr solubility in the melt.

Current knowledge of glass and silicate melt structures therefore supports the hypothesis of two Kr populations, with one population of Kr, oxidized and possibly located in the largest aluminosilicate rings, and one population filling the large cavities available in the silicate network.

4.Conclusion

The present work provides evidence for the reactivity of Kr with silicate that adds up to the previously reported evidences of Kr reactivity [START_REF] Grochala | Atypical compounds of gases, which have been called 'noble[END_REF]. Kr oxidizes in feldspathic glass and melt at high P/T conditions as shown by creation of short Kr-O bonds (2.49±0.1 Å) and shift of the edge position. Kr behavior in compressed magmas thus appears to be intermediate between that of an inert noble gas (He, Ne, Ar) and that of the heavier Xe.

Indeed Xe is shown to fully oxidize in compressed haplogranitic melts with Xe in the most abundant 6-membered rings containing 12 nearest O, Xe-O distance of 2.05±0.05 Å is similar to distance reported for covalent Xe-O bond in crystalline silicates [START_REF] Probert | An ab initio study of xenon retention in α-quartz[END_REF][START_REF] Kalinowski | Chemically-bound xenon in fibrous silica[END_REF]Crépisson et al., 2018). Both results question the supposed passive filling of the void spaces by heavy noble gases (Caroll and Stolper, 1993;[START_REF] Shibata | Solubility of neon, argon, krypton, and xenon in binary and ternary silicate systems: A new view on noble gas solubility[END_REF], and the assumption that all noble gases can be considered as zero-charge cation (e.g. [START_REF] Brooker | The 'zero charge' partitioning behaviour of noble gases during mantle melting[END_REF].

Creation of short Kr-O bonds in sanidine melt at depth, supports the role of Kr recycling at subduction zones, proposed by [START_REF] Holland | Seawater subduction controls the heavy noble gas composition of the mantle[END_REF], as Kr will efficiently dissolve in the melt. Hydrated melts will now need to be studied to test the influence of water, which is thought to dramatically increase noble gases solubility [START_REF] Nuccio | Investigation of the noble gas solubility in H2O-CO2 bearing silicate liquids at moderate pressure II: the extended ionic porosity (EIP) model[END_REF].

The Earth's atmosphere is depleted in heavy Kr isotopes compared to chondrites [START_REF] Holland | Meteorite Kr in Earth's Mantle Suggests a Late Accretionary Source for the Atmosphere[END_REF]. Observation of short Kr-O bonds in silicate melt, implying Kr reactivity, suggests potential isotopic fractionation during partial-melting and melt percolation, as shown for instance for Cu [START_REF] Huang | Copper isotope fractionation during partial melting and melt percolation in the upper mantle: Evidence from massif peridotites in Ivrea-Verbano Zone, Italian Alps[END_REF], and / or during fluid / melt interactions either upon fluid injection at depth in subduction zones or degassing during magma ascent. This phenomenon could have contributed to enrichment of well gases from the continental lithosphere in heavy Kr isotopes, while most of the samples from the Earth's mantle (OIBs and MORBs) have an atmospheric Kr isotopic composition due to intense recycling. gaseous Kr at ambient conditions, and liquid Kr at 0.75 GPa [START_REF] Cicco | High-pressure EXAFS measurements of solid and liquid Kr[END_REF].

Figure 3: k 2 -weighted EXAFS function for sanidine glass and supercooled liquid (color coding: same as Figure 2), and for UO 2 at room conditions [START_REF] Martin | Behavior of fission gases in nuclear fuel: XAS characterization of Kr in UO 2[END_REF].

31 phase correction (same samples as Figure 3). The peak observed at ~1.9 Å corresponds to Kr-O = 2.49 Å, and the peak at ~2.9 Å corresponds to Kr-O = 3.32 Å. A general decrease of the amplitude is observed with increasing temperature (as noticed by [START_REF] Stern | Thermal vibration and melting from a local perspective[END_REF].

Figure 5: Real-part of backward Fourier transform (in dashed lines) and fit to the data (plain black line) for sanidine glass and supercooled liquid, and Kr-bearing SiO 2 glass [START_REF] Wulf | Structural environment of krypton dissolved in vitreous silica[END_REF].

Figure 6: Shift of the Kr K-edge from 1.4 to 2.7 GPa (cf Table 2) compared to the standard reference value (14326 eV).

Figure 2 :

 2 Figure 2: Normalized X-ray absorption spectra for sanidine glass and supercooled liquid,

Figure 4 :

 4 Figure 4: Magnitude of the Fourier transform of the k 2 -weighted Kr EXAFS function without

Table 1 :

 1 Average composition of the starting glass (7 data points) and recovered sample (20 data points both in the glassy and crystalline parts) in oxide wt %, in brackets: standard deviation.

		Na 2 O	SiO 2	Al 2 O 3	K 2 O	CaO	Xe	Kr	Total
	Starting material	4.80 (0.2)	63.6 (0.40)	19.2 (0.14)	8.70 (0.24) 0.78 (0.05) 2.18 (0.04) 0.52 (0.05) 99.7 (0.47)
	Recovered sample	2.9 (0.6)	65 (1)	19.8 (0.6)	11(1)	0.3 (0.2)	[0-1.3]*	[0-0.5]*	100(1)
	* due to degassing upon quenching Kr and Xe contents cannot be properly evaluated by
	EMPA. Ranges of analyzed contents are given as an indication.

Table 2 :

 2 P/T conditions and state of the sample for each XAS measurement. n.s = number of scans, count. time = counting time per point analysis (451 point analysis).

			Kr K-edge
	P (GPa)	T (°C)	state	n.s	count . time
	0	20	glass	7	2s
	2.6	920	melt	4	2s
	2.7	1086	melt	5	2s
	2	706	glass	5	2s
	2	505	glass	5	2s
	1.4	20	quench	4	2s

Table 3 :

 3 Pressure-Temperature conditions and EXAFS-derived structural parameters. Conservative error bars are ± 0.05 eV for ΔE 0 , ± 0.1 Å for Kr-O distances and ± 0.05 Ų for σ².Figure 1: SEM images in backscatter mode of recovered sample after XAS measurements. Feldspars recrystallized upon cooling to 1040°C at 2.7 GPa, coexisting with partial melt recovered as a glass upon quenching. Kr/Xe-nanobubbles (bright dots) are visible.

	P (GPa)	T (°C)	k-range (Å -1 )	R-range (Å)	ΔE 0 (eV)
	0	20	2.2 -6.5	1.1 -3.5	3.32
	2.6	920	2.3 -6.5	1.2 -4.0	6.09
	2.7	1086	2.3 -6.5	1.1 -3.8	7.00
	2	706	2.3 -6.5	1.1 -3.5	6.45
	2	505	2.3 -6.5	1.1 -3.8	5.84
	1.4	20	2.2 -6.5	1.1 -4.0	3.50
	P (GPa)	T (°C)	Kr-O1 (Å)	σ 2 1 (Å 2 )	C3 1 (Å 3 )
	0	20	2.42	0.025	-
	2.6	920	2.45	0.009	0.0021
	2.7	1086	2.51	0.014	0.0078
	2	706	2.53	0.009	0.0085
	2	505	2.53	0.012	0.0076
	1.4	20	2.49	0.021	0.0035
	P (GPa)	T (°C)	Kr-O2 (Å)	σ 2 2 (Å 2 )	C3 2 (Å 3 )
	0	20	3.38	0.048	-
	2.6	920	3.27	0.040	-0.0090
	2.7	1086	3.37	0.042	0.0090

Acknowledgements:

We thank Omar Boudouma for SEM analyses, the Sorbonne Université Mineralogical collection for providing the natural sanidine sample, and the European Synchrotron Radiation Facilities for allocating beamtime to this work. This work was supported by the European Community's Seventh Framework Programme (FP7/2007-2013), European Research Council starting grant to C. Sanloup [grant numbers 312284 and 259649].