Fabien Bernadou
email: fabien.bernadou@cnrs-orleans.fr

Fabrice Gaillard

Evelyn Füri

Yves Marrocchi

Aneta Slodczyk

Nitrogen solubility in basaltic silicate melt -Implications for degassing processes

Keywords: Nitrogen, Solubility, oxygen fugacity, IHPV, SIMS Nitrogen, solubility, degassing, oxygen fugacity, IHPV, SIMS

 to high pressure and higher C-O-H activities. It can be used to investigate the nitrogen degassing processes for different pressure, temperature and fO 2 conditions relevant to planetary accretion and modern volcanism.

Introduction

Whereas other volatile components such as H 2 O or CO 2 have been intensively studied, there is a lack of information and comprehension on the nitrogen (N) behaviour in Earth's interior during the various stages of its formation. Nitrogen, however, dominates the current Earth's atmosphere and its availability for life molecules like amino acids -as highlighted by the experiment of Miller and Urey [START_REF] Miller | A Production of Amino Acids Under Possible Primitive Earth Conditions[END_REF]-is probably an important prerequisite for habitability [START_REF] Catling | The Archean atmosphere[END_REF]). Earth's nitrogen shows isotopic compositions close to those of enstatite chondrites, suggesting it was probably delivered during the main accretion stage [START_REF] Marty | The origins and concentrations of water, carbon, nitrogen and noble gases on Earth[END_REF]. N must have been subsequently processed through the magma ocean stage and then possibly released via planetary magmatism during J o u r n a l P r e -p r o o f the Hadean and Archean eons. Understanding the timing of nitrogen degassing is of primordial importance to capture the evolution of Earth's atmosphere [START_REF] Zahnle | Earth's Earliest Atmospheres[END_REF].

Although N 2 partial pressure and isotopic composition of the Archean atmosphere have been reported based on N analyses of fluid inclusions trapped in quartz [START_REF] Marty | Nitrogen Isotopic Composition and Density of the Archean Atmosphere[END_REF], the N behaviour during the magma ocean and earliest terrestrial volcanism stages is still underconstrained.

According to the literature, the degassing of nitrogen from a silicate melt is enhanced by oxidizing conditions [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF]Boulliung et al., 2020). On the other hand, several recent studies of mantle-core differentiation [START_REF] Dalou | Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF] have highlighted that nitrogen can be moderately siderophile at oxygen fugacity closed to Iron-Wüstite redox buffer (IW-2), while it is magmatophile (ie. High affinity for the silicate melt phase) under more reduced conditions. This implies that from the most reduced to the most oxidizing conditions nitrogen behaviour must evolve from magmatophile to siderophile and then atmophile. Given this great diversity of possible N behaviour, tight and precise experimental constraints are needed to decipher the fate of nitrogen during these earliest differentiation events.

N solubility has been experimentally investigated in minerals [START_REF] Li | Nitrogen solubility in upper mantle minerals[END_REF][START_REF] Yoshioka | Nitrogen solubility in the deep mantle and the origin of Earth's primordial nitrogen budget[END_REF] as well as silicate melts, fluids and metal alloys [START_REF] Dalou | Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth[END_REF][START_REF] Kadik | Solubility of nitrogen, carbon, and hydrogen in FeO-Na2O-Al2O3-SiO2 melt and liquid iron alloy: Influence of oxygen fugacity[END_REF][START_REF] Roskosz | Nitrogen solubility in molten metal and silicate at high pressure and temperature[END_REF][START_REF] Speelmanns | Nitrogen Solubility in Core Materials[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF][START_REF] Grewal | The fate of nitrogen during core-mantle separation on Earth[END_REF]Dalou et al., 2019a;[START_REF] Mosenfelder | Nitrogen incorporation in silicates and metals: Results from SIMS, EPMA, FTIR, and laser-extraction mass spectrometry[END_REF]. In theory, all these data could be combined to address N magmatic degassing processes using thermodynamic modelling. Gaillard and Scaillet (2014) used the solubility model of [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF] to predict degassing in the C-H-O-N-S J o u r n a l P r e -p r o o f Journal Pre-proof system, but no experimental verification of the validity of this model at pressure superior then 1 bar and in H-bearing system exists. In this study, we thus focus on magmatic nitrogen in order to capture the fluid-melt equilibria governing nitrogen degassing at medium pressure (0.8 to 2.4 kbar) and medium temperature (1200 to 1300°C).

According to [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF], the nitrogen speciation in silicate melt can be split in two domains. For fO 2 more oxidizing than the Iron-Wüstite (IW) redox buffer, nitrogen is physically dissolved in the silicate melt and its concentration depends mainly on pressure (i.e., nitrogen partial pressure). Under these conditions, N 2 (N 0 valence) is the dominant nitrogen species and its concentration in the silicate melt is usually low (i.e., << 100 ppm; [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF]. For oxygen fugacity more reduced than the IW redox buffer, nitrogen is chemically dissolved in the silicate melt; its concentration is high (>>100 ppm) and strongly correlated with fO 2 variations. The dominant chemically dissolved species is described as N 3- in a hydrogen free system [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF], while NH 3 species (N 3-valence) have been identified in H-bearing system [START_REF] Kadik | Solubility of nitrogen, carbon, and hydrogen in FeO-Na2O-Al2O3-SiO2 melt and liquid iron alloy: Influence of oxygen fugacity[END_REF]Dalou et al., 2019b;[START_REF] Grewal | The speciation of carbon, nitrogen, and water in magma oceans and its effect on volatile partitioning between major reservoirs of the Solar System rocky bodies[END_REF][START_REF] Mosenfelder | Nitrogen incorporation in silicates and metals: Results from SIMS, EPMA, FTIR, and laser-extraction mass spectrometry[END_REF] at high pressure. Some other minor species have been suggested such as CN - (Dalou et al., 2019b) or NO - [START_REF] Roskosz | Dual speciation of nitrogen in silicate melts at high pressure and temperature: An experimental study[END_REF]. Therefore, in addition to N 3-, the potential role of CN -, NO -or NH 3 species in the solubility of nitrogen in basaltic system must be determined.

Considering the fluid phases at high pressure and high temperature, the nitrogen speciation in a N-H-O system mainly involves N 2 and NH 3 [START_REF] Chen | In situ Raman spectroscopic study of nitrogen speciation in aqueous fluids under pressure[END_REF][START_REF] Li | Nitrogen speciation in mantle and crustal fluids[END_REF]. The ratio between these two species depends on various parameters such as pressure, temperature, fO 2 and total nitrogen concentration in the fluid [START_REF] Chen | In situ Raman spectroscopic study of nitrogen speciation in aqueous fluids under pressure[END_REF]Li J o u r n a l P r e -p r o o f and Keppler, 2014). However, these studies report contrasting results, likely due to the different techniques used for characterizing the samples (in situ vs. post-mortem). According to [START_REF] Chen | In situ Raman spectroscopic study of nitrogen speciation in aqueous fluids under pressure[END_REF], it appears that post-mortem studies tend to overestimate the NH 3 stability domain, implying that at most magmatic conditions (low P, high T), N 2 should be the major N-species in the fluid (e.g P<5 kbar and T>1000°C).

Currently, the study by [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF] remains the reference when it comes to modeling the behavior of nitrogen between silicate melt and fluid phase as it links nitrogen fugacity in the fluid to N contents in the silicate melt. However, this model uses low pressure data (i.e. 1 atm) in a H-free system. The study by Li et al., 2015 at medium pressure (i.e.> 1kbar) is interesting because it provides data on Nsolubility in H-bearing systems but their interpretatation being based on empirical fluid-melt partition coefficient, prevents a link with N fugacity and does not permit of [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF] solubility model. There therefore remains a large shadow area concerning the medium and high pressure modeling.

In this study, we investigate nitrogen solubility in basaltic silicate melt, i.e., the nitrogen content in the quenched silicate melt at fluid saturation. We performed a series of experiments at intermediate pressure (0.8 to 10 kbar), high temperature (1200°C and 1300°C) and over a wide range of fO 2 (IW-4.72 to IW+4.91) in the C-H-O-N system with a starting material of basaltic composition. By combining our results and the available literature data, we calibrate a nitrogen solubility model operating from surficial to upper mantle conditions.

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Experimental and analytical techniques

Starting material

The starting product is a natural basalt of Monte Sagnolo (Etna, Sicily;[START_REF] Gennaro | Melt inclusions track melt evolution and degassing of Etnean magmas in the last 15 ka[END_REF].

The basalt was crushed in an agate mortar with ethanol. The obtained powder was melted at 1 bar and 1400°C for 1 hour in a Pt crucible. The obtained glass was crushed and melted a second time in order to get a homogenous chemical composition. After a last fine crushing, the powders were stored away from moisture at 120°C in a stove. Nitrogen was added using different sources in the experimental charges (Table 1): aqueous solution of ammonia (NH 3 32%), nitric acid (HNO 3 65%) and dry powder of silicon (Si 3 N 4 ) and iron nitride (Fe X N) were used. The exact stoichiometry of the iron nitride was not provided by the supplier, a range between Fe 2 N and Fe 4 N is indicated. We conducted X-Ray Diffraction (XRD) and elemental analyser analysis indicating an average stoichiometry of Fe 3,5 N. For the experimental charges where nitrogen was added as aqueous solution, we added graphite in order to dehydrate and buffer the carbon activity in the charges following the equilibria:

(1)

(2)

For the charges where we added nitrogen as solids, we used two nitride powders. Si 3 N 4 was used as reducing agent [START_REF] Dalou | Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth[END_REF] following the reaction:

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(3)

In our cases the reaction involves the following components (Dalou et al., 2017): (4) This resulted in glasses being depleted in FeO, enriched in SiO 2 and forming Fe metal alloys.

Experimental techniques

Samples were loaded in AuPd and Pt capsules. The various nitrogen sources were mixed with the basalt powders and graphite for the charges with aqueous solution. Palladium and iridium powders were also mixed with the starting products to create Fe-Pd and Fe-Ir alloys as fO 2 sensors in the capsules.

We investigated the nitrogen behaviour in silicate melt using two different experimental setups. We used the internally heated pressure vessel equipped with drop quench at the Earth Sciences Institute of Orleans (Iacono-Marziano et al., 2009). Within the furnace heated by molybdenum wires, the temperature is monitored by two Pt thermocouples. A platinum/rhenium quench wire was used as hanging wire. The temperature of most experiments was 1200°C, while for the experiment (AR5SiNFeN, AR5SiNFeNx2, PCR2SiNFeN), with nitrogen added as a mix of Fe 3,5 N and Si 3 N 4 , the temperature was 1300°C in order to avoid nucleation of olivine and clinopyroxene (Table 1). These experiments were conducted under gas pressure. The gas was composed of a mixture of J o u r n a l P r e -p r o o f argon and hydrogen. Between the different runs, we changed the hydrogen fraction of the mixed gas in order to control the oxygen fugacity following this reaction [START_REF] Gaillard | Rate of hydrogen-iron redox exchange in silicate melts and glasses[END_REF]:

(5) One experiment was carried out in a half-inch piston cylinder assembly at a pressure of 10 kbar (1 GPa) and a temperature of 1300°C (Table 1). The starting basalt was placed into a AuPd capsule and doped in nitrogen with a mix of Fe 3,5 N and Si 3 N 4 powders. The capsule was contained in an alumina sleeve and was sandwiched between a top and a bottom alumina plug. Temperature was monitored by two PtRh (platinum-rhodium) thermocouples. The alumina sleeve was placed in an assemblage composed of a succession of graphite pyrex and talc cylinders.

Analytical techniques

Electron microprobe analysis (EPMA)

EPMA analyses aimed at obtaining the chemical composition of silicate glass, minerals (olivines, clinopyroxenes) and metal alloys. Two different programs were used, one for analysis of the silicate glasses and the second one for the analysis of the iron alloys. The list of analysed elements of the two programs are listed in the Table 2. The setting for analysis was 15 kV and a current of 10 nA. Focused and defocused beams (5,10,20 µm) J o u r n a l P r e -p r o o f were used depending on the analysed phase (resp. alloy and glass). The counting time for each component varied with their concentrations, more the element was concentrated in the silicate glass least the counting time was (few seconds).

Infrared analysis

The H 2 O and CO 2 concentrations were determined by transmission Fourier Transform Infrared Spectroscopy [START_REF] Iacono-Marziano | New experimental data and semiempirical parameterization of H2O-CO2 solubility in mafic melts[END_REF][START_REF] Shishkina | Solubility of H2Oand CO2-bearing fluids in tholeiitic basalts at pressures up to 500MPa[END_REF] on doubly polished samples with the thicknesses varying between 80 to 130 µm. The micro-FTIR measurements were performed using a Nicolet Continuµm microscope coupled to a Nicolet 6700 FTIR spectrometer. The device is equipped with Globar light source, XT-KBr beamsplitter, liquid N 2 cooled MCT-A detector, 32x infinity corrected Schwarzschild objective matching to 32x condenser. The spectra were recorded between 6000-1200 cm -1 with CaF 2 support and 4000-650 cm -1 with NaCl support in order to detect H 2 O (3500, 4500 and 5200 cm -1 ) and CO 2 (1515-1430 cm -1 ) absorption bands, respectively.

fO 2 determination

Oxygen fugacity (fO 2 ) is an important parameter controlling the nitrogen behaviour in silicate melts (Boulliung et al., 2020;Dalou et al., 2019b;[START_REF] Grewal | The speciation of carbon, nitrogen, and water in magma oceans and its effect on volatile partitioning between major reservoirs of the Solar System rocky bodies[END_REF][START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF]. Here, we use three techniques to determine the experimental fO 2 conditions. The sensor technique [START_REF] Taylor | The calibration and application of accurate redox sensors[END_REF], measuring the fO 2 at water saturation, uses two pellets of a Nickel Palladium or Cobalt Palladium alloy with zircon J o u r n a l P r e -p r o o f powder and 10-20 mg of distilled water [START_REF] Gaillard | Rate of hydrogen-iron redox exchange in silicate melts and glasses[END_REF]. We call this parameter "external fO 2 " because it is measured in separate platinum capsule. This external fO 2 does not correspond to the fO 2 seen by each sample in their own capsule but it represents the fO 2 of a virtual sample in which water activity would be 1.

In order to account for the fact that water activity in our samples was less than 1, the fO 2 was calculated with the equilibrium (5). The law mass action for this equilibrium allows the fO 2 prevailing in each experimental charge to be related to the experimental fH 2 O and fH 2 .

(6) (7) Water fugacity (fH 2 O) is calculated using the model of [START_REF] Iacono-Marziano | New experimental data and semiempirical parameterization of H2O-CO2 solubility in mafic melts[END_REF] and the water content in silicate glasses (Table 3). We estimated the precision on fO 2 using this method as:

√ (8)
In order to directly probe the "internal fO 2 " specific to each sample, we used metal-silicate equilibria implying the fO 2 .

(9)

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Oxygen fugacity can be calculated from the equilibrium (9) involving the activity of FeO in the silicate melt, the activity of Fe in the alloy and the equilibrium constant K 9 [START_REF] Gaillard | Rate of hydrogen-iron redox exchange in silicate melts and glasses[END_REF].

(10)

From the equilibrium constant and with and the fO 2 is calculated with the equation [START_REF] Medard | Oxygen fugacity, temperature reproducibility, and H2O contents of nominally anhydrous piston-cylinder experiments using graphite capsules[END_REF].

( ) ( ) ( ) (11)
The alloys in our experiment were mainly iron palladium (Fe-Pd) and iron iridium (Fe-Ir), with iron concentrations higher than 90% for the most reduce samples (AR5SiNFeN, AR5SiNFeNx2, PCR2SiNFeN see Table 2). The activity coefficient (γ) of iron for the Fe-Ir alloy was determined using equation from [START_REF] Woodland | Thermodynamic data for Fe-bearing phases obtained using noble metal alloys as redox sensors[END_REF], for the Fe-Pd alloy, the activity coefficient of Fe was taken from [START_REF] Aukrust | Thermodynamic properties of Pd-Fe alloys in the Temperature range 1200-1460°C[END_REF]. The equation used for the propagation of uncertainties for the internal fO 2 calculations is:

√ (12)
2.3.4. Volatiles in the glasses and composition of the fluid phase Knowledge of the nitrogen pressure P(N 2 ) or fugacity fN 2 in the fluid phase during the experiment is fundamental. Conversely to the low-pressure experiments (1 bar; (Boulliung et al., 2020;[START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF], the nitrogen pressure in our experiment cannot be considered during the experiment as the fraction of N 2 injected in the gas mixture.

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Hence, we calculated the fluid phase P(N 2 ) in our high pressure experiments by quantifying the partial pressure of the other species composing the fluid phase. In our low pressure experiments (T>1200°C, P<2.5 kb), we assume the ideal mixing of ideal gaseous species of N 2 , H 2 O, CO 2 , CO, H 2 (see also [START_REF] Iacono-Marziano | New experimental data and semiempirical parameterization of H2O-CO2 solubility in mafic melts[END_REF].

The pressure of H 2 O and CO 2 was determined after FTIR analysis (Table 4). The intensity of the IR band was converted in concentration of these elements in the silicate glass following [START_REF] Shishkina | Solubility of H2Oand CO2-bearing fluids in tholeiitic basalts at pressures up to 500MPa[END_REF]. The calculated concentration was then converted into partial pressure of H 2 O and CO 2 using the numerical model taken from [START_REF] Iacono-Marziano | New experimental data and semiempirical parameterization of H2O-CO2 solubility in mafic melts[END_REF]. The P(CO) was determined using the activity of C (graphite) and the fO 2 of the experiment using the equilibrium: C + ½ O2 = CO. The P(N 2 ) was then calculated by subtracting the fugacity of the other species cited before to the "total pressure" of the experiment. The P(N 2 ) was then converted into nitrogen fugacity, fN 2 , applying a 1.5 fugacity coefficient for N2 at 2.4 kbar (calculated according to [START_REF] Belonoshko | A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures[END_REF]. For the high pressure piston cylinder experiment however, the N 2 -fugacity coefficient was significant γ N2 ≈5,6 (calculated according to [START_REF] Belonoshko | A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures[END_REF] for N 2 .

Secondary ion mass spectrometry (SIMS)

The nitrogen ( 14 N) concentration of the quenched glasses was measured by secondary ion mass spectrometry (SIMS) at the CRPG (Nancy, France), using the CAMECA 1280 HR2 ion microprobe [START_REF] Füri | Nitrogen abundance and isotope analysis of silicate glasses by secondary ionization mass spectrometry[END_REF]. Polished glass fragments were mounted in indium and coated with a thin layer of carbon. The sample mount was stored for 48h under vacuum in the airlock of the SIMS to remove any terrestrial adsorbed water before analysis.

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Spot analyses of 14 N 16 O -secondary ions were carried out at a nominal mass resolution m/m = 13'000 with a 10 kV Cs + primary ion beam, a current of ~10 nA, and a normal-incidence electron gun to compensate the charge at the surface of the sample. Basaltic, Fe-free glasses with N contents between <1 and 3906  188 ppm N (as determined by static mass spectrometry analysis at the CRPG noble gas facility; Humbert, 1998) were used as reference materials to calibrate the secondary ion intensity ratio 14 N 16 O -/ 16 O 2 -to the nitrogen abundances of the glasses. This method has been confirmed to yield nitrogen concentrations in silicate glasses of variable composition (synthesized at fO 2 = IW-8 to IW+4.1, T = 1425°C, P = 1 bar) that are in excellent agreement with static mass spectrometry measurements (Boulliung et al., 2020), for a wide range of N contents between 1 to ~6000 ppm; therefore, any matrix effects on the yields of secondary molecular ions ( 14 N 16 O -and 16 O 2 -) are considered to be negligible. To verify the homogeneity of the N distribution, three spot analyses were performed for each glass sample.

Results

Description of the run products

Most experimental products were crystal-free silicate glasses (Table 2). Only samples AR1FeN and AR1HNO3C showed a very small amount of olivine and pyroxene crystals.

These crystals were observed in run number 1, synthesised at 1200°C, while at 1300°C the experimental charge was crystal-free. The presence of bubbles was noticed in all samples J o u r n a l P r e -p r o o f (Table 3, Fig. 1). These bubbles prove the attainment of fluid saturation during the experiment.

Another important point was the presence of droplets of metal alloy in some samples (Fig. 1), i.e., the most reduced ones and the one with added palladium powders (Table 3).

These alloys were important for the fO 2 calculation of the samples. In agreement with previous work [START_REF] Kadik | Influence of oxygen fugacity on the solubility of nitrogen, carbon, and hydrogen in FeO-Na2O-SiO2-Al2O3 melts in equilibrium with metallic iron at 1.5 GPa and 1400[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF], we also observed metal micronuggets in the most reduced samples (AR5SiNFeNx2; fO 2 <IW-3.5). They were, however, too small to be analysed.

Composition of the experimental products and fluid phase

The glass compositions of our run products are reported in Table 2. Most of them were synthetized using internally heated pressure vessel experiments ('AR') and one using the piston cylinder experiment ('PCR'). In most cases, the chemical compositions of the silicate glasses were similar to the AR5HNO3C composition. Major compositional differences were however for the samples with Si 3 N 4 : those samples were enriched in SiO 2 with increase from 48 wt% to more than 54 wt%. For these extremely reduced samples, the FeO concentration is low (≈1 wt%) and we noticed many iron alloy nuggets (Table 3, e.g., samples AR4, AR5, PCR2). The volatile concentrations and oxygen fugacity of the different samples are reported in Table 3. In general, the samples were too CO 2 -poor to permit detection. Significant amounts of CO 2 were only measured in samples AR3HNO 3 C, AR4NH 3 FeSCIr, and AR4HNO 3 CPd that were graphite saturated, and in which nitrogen was added in the form of an aqueous solution (Table 3). The water concentration is strongly correlated with the fO 2 as

(1

)
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Journal Pre-proof expected from equilibrium (5). The highest H 2 O concentrations were measured in the samples doped in nitrogen as an aqueous solution (e.g., AR1NH 3 , AR3HNO 3 C, AR3HNO 3 AgCO, AR4NH 3 FeSCIr, AR4HNO 3 CPd). In addition to the volatile concentration of the samples, we also determined the composition of the fluid for each of them. Table 4 reports the fugacity of each component in the fluid in equilibrium with the silicate melt during the experiments. Samples with nitrogen added as an aqueous solution present the highest water and CO 2 fugacities. For these samples, the fluid phase was a multicomponent mixture, while the samples AR5SiNFeN and AR5SiNFeNx2 with addition of nitrogen as silicon nitride powders were mostly anhydrous and their fluid phase was essentially composed of nitrogen (N 2 ). The PC experiment has a fluid phase composed mainly of nitrogen species. The CO 2 concentration below the detection limit of the IR analysis (a few ppm) and the H 2 O concentration at 500 ppm indicates that in the fluid phase the fugacity of these elements is very low (<1 bar and fH 2 ≈ 3 bar) compared to the total pressure (10000 bar). We therefore consider that P(tot) = P(N 2 ) and the fugacity coefficient (see above) at P and T was used to calculate fN 2 . The uncertainty on the nitrogen pressure measurement hence corresponds to the uncertainty on the pressure measurement of the machine (±10%).

fO 2 (ΔIW) results

For the samples with fO 2 calculated using the two methods (i.e., Eqns. 7 and. 11), we compared the result to check the internal consistency and to validate the attainment of equilibrium (Table 5). In most cases, the difference between the log fO 2 values was very small and within the quoted uncertainties, i.e., between 0.1 and 0.4 log units.

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The biggest variation between the two internal fO 2 values was observed for the sample synthesized during run 5, which is characterized by the lowest water content (0.02 and 0.04 wt%, Table 3). For these samples, the treatment of IR spectra was difficult due to the very low intensity of the peak (0.041±0.017 Abs AR5SiNFeN, 0.054±0.011 Abs PCR2SiNFeN).

Nevertheless, for each sample, the differences between calculated fO 2 are within or close to the propagated uncertainties.

Experiments doped in nitrogen with a mix of Si 3 N 4 and Fe 3.5 N seems to be the best way to produce fO 2 conditions below the IW buffer [START_REF] Dalou | Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth[END_REF]. For the other experiments doped with other nitrogen sources such as aqueous solution, the fO 2 are more oxidised (+1.97<log fO 2 (ΔIW) <+4.91), consistent with the presence of large amounts of water.

When fO 2 constraints from both methods of calculations were available, we used the internal fO 2 value from Fe/FeO equilibrium in the following discussion (i.e., eq. 11).

Nitrogen concentration

Nitrogen concentrations at fluid saturation (Table 3) are shown in Figure 2 together with the results of previous studies supposed to be fluid saturated at low pressure (Boulliung et al., 2020;[START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF], medium pressure [START_REF] Li | Nitrogen distribution between aqueous fluids and silicate melts[END_REF] and high pressure [START_REF] Grewal | The fate of nitrogen during core-mantle separation on Earth[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF]. Nitrogen concentrations in our samples vary between 5 and >1000 ppm. The low N-concentration samples (3.6 ± 1.9 to 26.3 ± 5.3 ppm) were obtained for the most oxidizing condition (fO 2 >IW). In this fO 2 domain, N content weakly varies with fO 2 , because nitrogen is mainly dissolved physically as N 2 . For the reduced samples (fO 2 <IW-2), the N content in the glasses increases with decreasing fO 2 J o u r n a l P r e -p r o o f and attains, for the most reduced sample (AR5SiNFeNx2), 1737 ± 112 ppm at IW-4.5. These observations indicate that nitrogen concentrations are correlated with variation in fO 2 only for conditions below IW-1.5: under these conditions, if the fO 2 continue to decrease, the nitrogen concentration increases drastically.

Discussion

Attainment of equilibrium

To demonstrate that the equilibrium of our experiments was reached, the homogeneity of our samples was verified using different methods. Firstly, we check the homogeneity of the major elements through the chemical composition of our silicate glass (SiO 2 , Al 2 O 3 ,…), if the glass shows good homogeneity, this indicates that the latter was in equilibrium. The second important point to verify is the homogeneity of the nitrogen concentration within the sample in order to see if the nitrogen had sufficient time to diffuse in the sample in a homogeneous way. The third point is the convergence of the internal fO 2 value read with the two techniques explained in section 3.3. Only if these three elements are verified we validate the achievement of equilibrium during the experiment. In addition, a comparison with the equilibrium data taken in the literature is carried out to check consistency.

For our study, by referring to the different tables (

Nitrogen species and solubility as a function of fO 2 and pressure

Figure 2 shows that pressure has a major effect on the nitrogen solubility for all investigated conditions of oxygen fugacities. For fO 2 >ΔIW, no fO 2 -dependency is observed with similar trends observed at low pressure (1 bar; [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF] and in our experiments performed at medium pressures (i.e., 0.8 and 2.4 kbar). However, our data are shifted by two to three log-units upward in term of nitrogen concentration. At fO 2 >IW, our results show similar N-concentrations than those reported in previous study (Li et al., 2015, ~10 ppm), thus confirming the lack of fO 2 dependence. There is therefore a significant effect of pressure and independently of the nitrogen fugacity; with a general increase of one log unit in N-content as pressure increases by one order of magnitude. A similar trend can be J o u r n a l P r e -p r o o f observed in experiments performed at higher pressures [START_REF] Grewal | The fate of nitrogen during core-mantle separation on Earth[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF], with a comparable increase of N concentration at higher pressures (Fig. 2). Fig. 2 also shows the duality of N-solubility behaviour, reflecting most likely (i) a physical, fO 2independent, N 2 dissolution under oxidising conditions (> IW-1.5) and (ii) a chemical dissolution of N 3-that is strongly enhanced at the most reduced conditions. The hypothesis of a dual N-speciation, described first by [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF] at atmospheric pressure, seems to be confirmed at medium pressure within our experimental data.

Calibration of the solubility model

We have compiled a database containing nitrogen concentrations in melts of different experimental studies at different pressures, temperatures and fO 2 conditions. We only use the data of nitrogen concentration in basaltic melts that we assume to be equilibrated at fluid saturation (an assumption that could be verified for studies containing the relevant information). In addition to our experiments, the database contains data from low pressure [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF], medium pressure [START_REF] Li | Nitrogen distribution between aqueous fluids and silicate melts[END_REF] and high pressure experiments (≤1.5 GPa; [START_REF] Grewal | The fate of nitrogen during core-mantle separation on Earth[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF]. The parameters of the database were: nitrogen contents in the melt, temperature (°C, K), pressure (bar), oxygen fugacity (fO 2 , log fO 2 , log fO 2 (∆IW) and the nitrogen fugacity (fN 2 ).

We restricted the database to studies with similar starting material (≈basalt), in order to reduce the potential effect of the NBO/T on the nitrogen solubility [START_REF] Mysen | Amorphous materials: Properties, structure, and durability: Solubility and solution mechanisms of NOH volatiles in silicate melts at high pressure and temperature--amine groups and hydrogen fugacity[END_REF][START_REF] Roskosz | Dual speciation of nitrogen in silicate melts at high pressure and temperature: An experimental study[END_REF]Boulliung et al., 2020). We have also dismissed some studies that investigated nitrogen metal-silicate partitioning because they have no proof of fluid in the J o u r n a l P r e -p r o o f synthesized samples (such as bubbles trapped in the glass e.g Dalou et al., 2019b[START_REF] Dalou | Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth[END_REF].

Using this database, we can represent the effect of nitrogen pressure on nitrogen solubility (Fig. 3). The nitrogen concentration data used for figure 3 are for conditions more oxidizing than IW-2 in order to restrict the effect of fO 2 . In agreement with previous observations [START_REF] Roskosz | Dual speciation of nitrogen in silicate melts at high pressure and temperature: An experimental study[END_REF], the nitrogen concentration appears to increase as the pressure, and therefore the nitrogen fugacity increases. This observation is valid for reduced and oxidized conditions and suggests that N 2 remains the dominant N-species in the fluid for all these experimental studies. According to Chen et al. ( 2019), the N 2 species fraction in the fluid increases with fO 2 . In addition, an increase of the temperature and/or the total nitrogen concentration in the fluid phase appears to increase the N 2 fraction in the fluid at the expense of NH 3 . In contrast, a pressure rise will increase the NH 3 fraction in the fluid [START_REF] Chen | In situ Raman spectroscopic study of nitrogen speciation in aqueous fluids under pressure[END_REF]. When we extrapolate the result of [START_REF] Chen | In situ Raman spectroscopic study of nitrogen speciation in aqueous fluids under pressure[END_REF] to the conditions of the experimental data in Figure 3, the main species present in the fluid tends to be N 2 .

The two dissolution reactions used for the N-solubility model are:

(13) ( 14)

Reaction 13 corresponds to the physical dissolution of N 2 , whereas reaction 14 corresponds to the chemical dissolution of N 3-. The total nitrogen concentration in the silicate melt corresponds to the sum of the two species concentration.

J o u r n a l P r e -p r o o f

Journal Pre-proof [ ] [ ] [ ] (15)
From the eq. 13, we can calculate the N 2 concentration, which mainly depends on nitrogen fugacity:

[ ] (16)
From the eq. 14, we can calculate the N 3-concentration, which mainly depends on fO 2 and fN 2 :

[ ] (17)
The eq. 16 and 17 once replaced in eq. 15 allows us to propose the nitrogen concentration in silicate melt as:

[ ] (18)
The thermodynamic constants (K 13 , K 14 ) of the two reactions follow this form ( 19) where ∆rG P,T = ∆rH-T∆rS+P∆rV (20) P and T correspond to the pressure (bar) and temperature (K) of the system. In the eq. 20, ∆rG P,T corresponds to the Gibbs free energy of the reaction for given and variable P and T

J o u r n a l P r e -p r o o f values, calculated with, ∆rH the enthalpy, ∆rS the entropy and ∆rV the volume of the reaction at P and T. All the thermodynamic constants were adjusted using the low, medium and highpressure data and the result is given in Table 6.

We assumed that the enthalpy and entropy are constant over the T range, although this assumption was not applied to the volume changes of reaction ( 13) and ( 14). The following correction was applied in the P-range 0-1 GPa:

(21)

At P> 1GPa, the volume changes are considered constant.

The constants ∆H 13 , ∆S 13 and ∆V 13 were used for the calculation of the K 13 and characterise the physical dissolution of N 2 in the silicate melt. ∆H 14 , ∆S 14 and ∆V 14 were used for the calculation of K 14 and therefore characterise the chemical dissolution of N 3-. These two sets of constants were calibrated using two different functions F opti 13 for ∆H 13 , ∆S 13 , ∆V 13 and F opti 14 for ∆H 14 , ∆S 14 , ∆V 14 of the form:

∑ (22) ∑ (23)
F opti 13 was used to minimize the difference between the measured and the calculated N concentration for the most oxidised data (>IW-1.5). F opti 14 was used to minimize the difference in term of nitrogen concentration and oxygen fugacity for the most reduce data J o u r n a l P r e -p r o o f (<IW-1.5). This formalism allowed us to produce a model taking into account both uncertainties in N content and fO 2 .

The error estimation for the 6 constants presented in the Table 6 is calculated for an increase in the residue on the fitting function presented above of 30%. This threshold allows us to determine the range of variation (maximum and minimum values) for each of our constants.

This 30% threshold is comparable to the average value of the uncertainty in the measurement of nitrogen contents in glasses (31%) in the compiled database.

Results obtained experimentally and calculated by the model were then compared in two different ways. First, we compare the calculated data to the analysed nitrogen concentration in the silicate melt as a function of fO 2 (∆IW; Fig. 4).

The results of the model are in good agreement with experimental data (Fig. 4). If we compare the calculated nitrogen concentration to the measured data (Fig. 4), we obtain a data array aligned along a straight line of slope 1 (R2 = 0.96). These observations support the accuracy of the calculated data.

In details, we see that the solubility model captures well the trend. However, for some data points, the differences between the calculated and measured data exceed the uncertainties which is likely due to some uncertainties in the composition of the fluid phase of the experiments used for the calibration.

The 2-species model first presented by [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF] 13) is the partial molar volume of N 2 (being positive), while the volume change of reaction ( 14) is the difference between the volume of N 3-and 3/2 the volume of O 2-(being negative). In detail, we notice that the fitted partial molar volume of N 2 in the silicate melt is close to the partial molar volume of N 2 liquid at 1 atm. and its boiling point (i.e., 34.5 cc/mol. = 3.5 J/bar). Although the fluid phase of the model was assumed to be N 2 -dominated (it does not take into account the presence of NH 3 in the fluid phase), our model also adequately describes the N-solubility at low pressure to moderately high-pressure. A more complicated model including NH 3 in the fluid is not required at this stage, probably due to the fact that most experiments performed under reduced conditions are generally dry (Table 5), implying low fH 2 conditions. Since the NH 3 /N 2 speciation is ruled by the respective equilibria:

it clearly appears that low fH 2 (and low fH 2 O) strongly reduces the presence of NH 3 . NH 3 is also precluded by the high N-content of our fluid phase, the high temperature and the moderately high-pressure condition, in agreement with previous observations [START_REF] Chen | In situ Raman spectroscopic study of nitrogen speciation in aqueous fluids under pressure[END_REF].

A second working hypothesis concerns the nitrogen species in the silicate melt. We considered two main species: N 2 and N 3-. Several previous studies (Dalou et al., 2019b; J o u r n a l P r e -p r o o f [START_REF] Grewal | The speciation of carbon, nitrogen, and water in magma oceans and its effect on volatile partitioning between major reservoirs of the Solar System rocky bodies[END_REF][START_REF] Kadik | Solubility of nitrogen, carbon, and hydrogen in FeO-Na2O-Al2O3-SiO2 melt and liquid iron alloy: Influence of oxygen fugacity[END_REF][START_REF] Mosenfelder | Nitrogen incorporation in silicates and metals: Results from SIMS, EPMA, FTIR, and laser-extraction mass spectrometry[END_REF] suggested the presence of NH x species where N has the valence of N 3-. Here, a two-species model (N 2 and N 3-) adequately describes the fO 2 -P-T dependence of N-solubility. No attempt to parameterize an NBO/T parameter was considered though a significant effect of NBO/T on N-solubility was previously underlined [START_REF] Mysen | Nitrogen and hydrogen isotope compositions and solubility in silicate melts in equilibrium with reduced (N+H)-bearing fluids at high pressure and temperature: Effects of melt structure[END_REF]Boulliung et al., 2020). Here, this parameter has not been considered because in agreement with the observations of the articles Boulliung et al. ( 2020), for the fO 2 conditions of most of the points used by the database (i.e.

>IW -5,1), the NBO / T has an impact that is still difficult to define and requires more work.

For the time being, this model is accurate for describing the available database. However, this model will have to consider other melt and fluid species once their P-T-fO 2 domain will be better defined. In particular, data at low N-content or at least at low N/H and low N/C are needed.

Model application to melt degassing processes

Eq. 18 permits the prediction of nitrogen solubility in a basaltic melt in the P-fO 2 parameter space. For a constant temperature of 1200°C, we can make a series of isobars of nitrogen fugacity on a diagram nitrogen concentration as a function of fO 2 (Fig. 6). Fig. 6 shows that both N 2 and N 3-species have solubilities that increase with increasing nitrogen pressure. In details, the fO 2 at which speciation changes from N 2 to N 3-decreases as pressure increases.

At low pressure, the N 2 -N 3-transition occurs at IW, while at 3 GPa, it occurs at IW-3. There is therefore a shift of 1-log unit in fO 2 per GPa of the boundary separating the N 2 dominated J o u r n a l P r e -p r o o f from the N 3-dominated area. This shift can be explained by the dependence on P(N 2 ) of the solubility of both N 2 and N 3-species (Eqns. 16 & 17). N 2 dissolution mechanism has a +1 exponent on P(N 2 ) while N 3-dissolution mechanism has a 0.5 exponent dependence on P(N 2 ). This implies that the fO 2 domain where the N-speciation shifts from N 2 to N 3-must change with P(N 2 ) rather than total pressure.

Degassing of Earth's magma ocean is supposed to have occurred at fO 2 conditions ranging from IW-5, at the beginning of the magma ocean stage, to IW-2 for the lastest stages [START_REF] Wood | Accretion of the Earth and segregation of its core[END_REF]. This is deduced from metal partitioning during coremantle equilibration processes, but admittedly, after the core segregation, the magma ocean could have evolved more oxidized. At IW-5 and fluid saturation, the nitrogen content in the silicate melt is ca.

3000 ppm (0.3 wt%) for fN 2 of 100 bar (see Fig. 6). At IW-2, corresponding to the last stage of magma ocean-core equilibration, the nitrogen content in the silicate melt for a similar fN 2 decreases and attains 10 ppm (0.001 wt%). This implies a drastic change of the nitrogen behaviour during this period of core mantle segregation. According to [START_REF] Speelmanns | Nitrogen Solubility in Core Materials[END_REF], nitrogen became increasingly siderophile during the last stage of the core-magma ocean segregation (i.e., as the oxygen fugacity evolved from ΔIW-5 to IW-2). However, as the magma ocean went through this redox interval (from ΔIW-5 to ΔIW -2), nitrogen became also more atmophile as shown by Figure 6. This is because the oxidation state of N in metal and the gas phases is similar (zero). These two phenomena, N incorporation in metal vs. N degassing, thus entered in competition at the end of the core mantle equilibration at ca. IW-2.

This made more difficult the incorporation of N in the core. In summary, at very low fO 2 , N is neither siderophile nor atmophile, it is magmatophile, while at intermediate fO 2 (IW-2), N is J o u r n a l P r e -p r o o f

Journal Pre-proof siderophile and atmophile. We note that planetary systems experiencing very low fO 2 (ie. IW-5) during their magma ocean and post-magma ocean stages, such as Mercury, may accordingly contains high nitrogen content in their mantle. In contrast, planets like Earth and Mars, that experienced core-magma ocean equilibration close to IW-2, must have little N contents in their mantle.

4.5. Nitrogen impact on the volcanism of planets with reduced magmatic conditions As explained above, under reduced conditions nitrogen is magmatophile (not siderophile, nor atmophile), implying that reduced magma oceans must crystallize under high N-activity while oxidized magma oceans would solidify under low N-activity. No melt-crystal N-partitioning experiments exist. However, some studies, which focus on the nitrogen solubility in mantle minerals [START_REF] Li | Nitrogen solubility in upper mantle minerals[END_REF][START_REF] Yoshioka | Nitrogen solubility in the deep mantle and the origin of Earth's primordial nitrogen budget[END_REF], compare their solubility results for mantle minerals with data of nitrogen solubility in silicate melt of previous studies [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF][START_REF] Roskosz | Nitrogen solubility in molten metal and silicate at high pressure and temperature[END_REF]. From these comparisons, the two minerals studies deduce mineral-melt nitrogen partitioning, one of the important criteria for discussing nitrogen degassing.

Since nitrogen can be incorporated into mantle minerals [START_REF] Li | Nitrogen solubility in upper mantle minerals[END_REF][START_REF] Yoshioka | Nitrogen solubility in the deep mantle and the origin of Earth's primordial nitrogen budget[END_REF], we may assume that a solidifying magma ocean can sequester nitrogen in its mantle. In turn, assuming that N is incompatible upon partial melting (which is likely at fO 2 <IW-3), it can be incorporated into the liquid and transported to the surface. High N-content J o u r n a l P r e -p r o o f in the melt may impact the degassing process during the magma ascent and, in fine, the eruption. However, such features are not relevant for the current volcanism on Earth or Mars due to oxidising condition (≈IW to FMQ; [START_REF] Righter | Oxygen fugacity in the Martian mantle controlled by carbon: New constraints from the nakhlite MIL 03346[END_REF] yielding low nitrogen concentrations in their cooling magma oceans. For a planet with strongly reduced conditions like Mercury, where the fO 2 of its interior was estimated to be between ∆IW-6.3 to -2.6 (McCubbin et al., 2012) or ∆IW-7.3 to -4.5 [START_REF] Zolotov | The redox state, FeO content, and origin of sulfur-rich magmas on Mercury: SULFUR-RICH MAGMAS ON MERCURY[END_REF], nitrogen can be highly concentrated in the silicate melt with contents exceeding 1000 ppm. In addition, the low fO 2 conditions of Mercury do not allow the stability of species such as H 2 O or CO 2 but favour the stability of volatile species such as S 2 , CO and CH X by increasing the H 2 /H 2 O and C/O ratio [START_REF] Cartier | The Role of Reducing Conditions in Building Mercury[END_REF][START_REF] Ebel | Equilibrium condensation from chondritic porous IDP enriched vapor: Implications for Mercury and enstatite chondrite origins[END_REF][START_REF] Zolotov | On the chemistry of mantle and magmatic volatiles on Mercury[END_REF]. According to our data and previous formalism for reduced conditions (i.e., IW<-6, Zolotov, 2011) several wt% of N are lost by a pressure drop of 1kbar (red arrow fig. 6). It is therefore likely that, under these conditions, nitrogen was one of the main volatile species, which can impact the eruptive dynamics on Mercury similarly to water for Earth.

J o u r n a l P r e -p r o o f

Conclusion

This new experimental study provides constraints on the solubility of nitrogen in basaltic melts at fluid-saturation under lithospheric pressure. It indicates that for the most oxidised conditions, nitrogen solubility is low and depends mainly on the nitrogen pressure (N 2 dissolution). For the most reduced conditions (<IW), nitrogen solubility increases drastically and is correlated to the decrease in fO 2 (N 3-dissolution). These observations corroborate a previous studies at low pressure [START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF]Boulliung et al., 2020). A two species solubility model (N 2 , N 3-) of nitrogen in silicate melt was calibrated with our data and previous data for fluid saturated conditions [START_REF] Grewal | The fate of nitrogen during core-mantle separation on Earth[END_REF][START_REF] Li | Nitrogen distribution between aqueous fluids and silicate melts[END_REF][START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF][START_REF] Miyazaki | Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: implications for the origin and degassing history of nitrogen and noble gases in the earth[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF]. This model successfully reproduces most of the literature data at fluid saturation. However, we assumed some starting hypothesis (4.2.) that need to be verified against a larger set of experimental work. These results

(experimental and modelled) emphasize that nitrogen degassing from a magma ocean must predominantly occur in the fO 2 range IW-9 to IW. Pressure is also an important parameter. A decrease of the nitrogen pressure leads to a decrease of the nitrogen solubility in the silicate melt (see eq. 17), thus contributing to degassing. On reduced planets like Mercury, nitrogen can be a trigger for explosive eruptions.

The solubility model must evolve in the future with new data at low nitrogen activity in order to test the presence of NH 3 in both melt and fluid phases. More data at high pressure and fluid saturation are also needed.

J o u r n a l P r e -p r o o f

Nitrogen partitioning between the metal and the silicate melt is an additional important process to take into account. In most of the recent studies of the partitioning of nitrogen between silicate melt and liquid iron-alloy, nitrogen appears to be more siderophile when the condition become more oxidised (Dalou et al., 2019b;[START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF][START_REF] Speelmanns | Nitrogen Solubility in Core Materials[END_REF] and more lithophile at reduced conditions. We note a similar behaviour between silicate melt and fluid phase: when the condition becomes more oxidised, nitrogen becomes more atmophile.

Future efforts must consider this complex three-phase issue: chemical exchange of N between the metal, the silicate melt and the gas phases. For more reduced conditions than IW, we select only data at log fO 2 ≈IW-2 in order to limit the strong effect of the fO 2 and identify the real impact of the P(N 2 ).

J o u r n a l P r e -p r o o f

Journal Pre-proof Table 6. Thermodynamic constants of the model adjusted with the database ∆H 13 (J.mol -1 ) ∆S 13 (J.K.mol -1 ) ∆V 13 (J/bar) ∆H 14 (J.mol -1 ) ∆S 14 (J.K.mol -1 ) ∆V 14 (J/bar)

J o u r n a l P r e -p r o o f

  at a pressure of 1 bar is validated here to moderately high pressure in a C-H-O-N system. The temperature range covered by the database is from 1100 to 2000°C, the pressure from 1 bar to 10000 bar and the fO 2 from IW-8 to IW+8. The chemical composition is mainly basaltic. The volume J o u r n a l P r e -p r o o f changes of the two dissolution mechanisms are respectively positive and negative, which is consistent with fact that the volume change of reaction (

Figure. 1 .

 1 Figure. 1. Back scattered electron image (BSE) of (a) a part of the sample AR5SiNFeNx2 (Mag x177) with metal (white) and bubbles in the silicate glass (grey). (b) A part of the sample AR5SiNFeN (Mag x35) with metal droplets in silicate glass and bubbles. For the most reduced sample (AR5SiNFeNx2) with fO 2 <IW-3.5 the formation of micronuggets was observed (a).

  r n a l P r e -p r o o f

Figure. 2 .Figure. 3 .

 23 Figure. 2. Nitrogen concentration in basaltic silicate melt as a function of the fO 2 (ΔIW). Comparison of our experimental result (800 [blue square] to 10000 bar [blue circle]) with result of low-pressure study (ie. Libourel et al. 2003, Miyazaki et al. 2004, Boulliung et al. 2020; 1 bar) and high pressure study (ie. Grewal et al. 2019, Speelmanns et al. 2019 >10000 bar) J o u r n a l P r e -p r o o f

Figure. 4 .Figure. 5 .

 45 Figure. 4. Top diagram shows the difference between the measured nitrogen concentrations from different studies (full symbols) with the nitrogen concentration calculated by the model for identical conditions (open symbols) as a function of fO 2 . Second diagram at the bottom is a plot of measured versus calculated nitrogen concentration in the silicate melt. These two diagrams highlight the reproducibility of the data obtained experimentally by the model for identical conditions.

Table 2

 2 concentrations of volatile elements including nitrogen, the concentration only weakly varies between the different analysis points (Cf. Table3.). Regarding to the internal fO 2 values obtain by the two different calculation ways, i.e. water activity and Fe/FeO activities, the equilibrium seems to be reach due to the similar results of these two techniques (Cf. Table5.). Lastly when we compare our point with those of previous studies, we notice that our points are part of a logical trend of those already obtained by previous studies. Our nitrogen concentration evolves in a way similar to that of[START_REF] Libourel | Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity[END_REF], with higher

	, 3, 5) we can verify this attainment

sample shows a good spatial homogeneity, with minor compositional variation between the different analysis points

(Cf. Table 2.)

. This observation can also be made for the J o u r n a l P r e -p r o o f concentrations, linked to pressure and therefore nitrogen fugacity differences (i.e. 1 atm vs 800 bar). Our high-pressure anchor point (Cf. Figure

2

. blue circle) is also within the nitrogen concentration ranges observed by other high-pressure studies (i.e.

[START_REF] Grewal | The fate of nitrogen during core-mantle separation on Earth[END_REF][START_REF] Speelmanns | The almost lithophile character of nitrogen during core formation[END_REF]

.

Table 1 .

 1 Experimental conditions and starting mixtures of the runs presented in this study. 'A' stands for internally heated pressure vessel experiments and 'PC' for piston cylinder experiments. A Cobalt Palladium (CoPd) sensor was used for the experiments with the highest PH 2 pressure, whereas a Nickel Palladium (NiPd) sensor was used for low-PH 2 experiments.(1) Description of the starting material B=Basalt, G=Graphite, Ir=Iridium, Pd=Paladium

	Run	Sample ID	Starting material	(1)	Duration (hour)	N (wt%)	H2O (wt%)	C (wt%)	Type capsule	T (°C)	P (bar)	fH2 (bar)	External sensor
	A RUN 1	AR1FeN	B+Fe3,5N		1	0.67	-	-		AuPd	1200	800	10	CoPd
		AR1HNO3C	B+HNO3+G		1	1.44	3.5	10.0		AuPd	1200	800	10	CoPd
		AR1NH3	B+NH3		1	3.45	6.5	-		AuPd	1200	800	10	CoPd
	A RUN 3	AR3FeNFeS	B+Fe3,5N+FeS	1	0.33	-	-		Pt	1200	800	5	NiPd
	A RUN 4 A RUN 5 PC RUN 2	AR3HNO3C AR3HNO3AgCO AR4NH3FeSCIr AR4HNO3CPd AR5SiNFeN AR5SiNFeNx2 PCR2SiNFeN	B+HNO3+G B+HNO3+Ag2CO4 B+NH3+FeS+G+Ir B+HNO3+G+Pd B+Si3N4+Fe3,5N B+Si3N4+Fe3,5N B+Si3N4+Fe3,5N J o u r n a l P r e -p r o o f 1 1.44 3.5 7.0 1 1.44 3.5 0.8 1 3.45 6.5 7.0 1 1.44 3.5 7.0 1 1.78 --1 3.56 --1 1.78 --	AuPd AuPd Pt AuPd AuPd AuPd Pt	1200 1200 1200 1200 1300 1300 1300	800 800 2400 2400 900 900 10000	5 5 24 24 10 10 -	NiPd NiPd CoPd CoPd CoPd CoPd -

Table 2 .

 2 Chemical compositions (wt%) silicate glasses and alloys determined by EPMA.

				Journal Pre-proof
		AR1HNO3C	1-σ	AR4NH3FeSCIr	1-σ	AR4HNO3CPd	1-σ
	SiO2	48,36	0,09	45,99	0,26	47,13	1,02
	TiO2	1,67	0,12	1,46	0,13	1,40	0,12
	Al2O3	14,70	0,12	14,28	0,09	13,49	0,24
	FeO	6,40	0,43	7,48	0,16	8,23	0,23
	MnO	0,15	0,02	0,14	0,07	0,12	0,05
	MgO	8,37	0,13	8,55	0,05	8,24	0,11
	CaO	12,57	0,28	11,12	0,16	10,82	0,18
	Na2O	3,49	0,12	3,18	0,03	3,21	0,12
	K2O	1,22	0,08	1,25	0,08	1,31	0,06
	Total	96,91	0,40	94,08	0,41	93,97	0,70
	Si P S Fe Pd Pt Ir Total SiO2 TiO2 Al2O3 FeO MnO MgO CaO Na2O	AR1HNO3C 0,53 --22,29 77,02 --99,85 AR5SiNFeN 52,99 1,49 14,80 2,66 0,16 9,11 11,85 3,31 J o u r n a l P r e -p r o o f 1-σ AR4NH3FeSCIr 1-σ AR4HNO3CPd 0,57 0.01 0.01 0.52 ---0.01 -1.38 0.73 0.00 0,35 3.52 1.04 10.53 1,94 0.00 0.00 84.66 -0.00 0.00 0.22 -84.57 5.14 -1,54 89.47 3.37 95.94 1-σ AR5SiNFeNx2 1-σ PCR2SiNFeN 0,85 56,71 0,76 54,85 0,07 0,79 0,20 1,44 0,25 14,96 0,21 14,83 0,62 0,46 0,15 1,61 0,05 0,18 0,05 0,18 0,16 9,19 0,27 9,17 0,23 11,90 0,27 11,84 0,22 3,31 0,10 3,41	1-σ 0.54 0.01 0.00 0.21 2.05 0.32 -1.97 1-σ 0,38 0,05 0,15 0,35 0,07 0,14 0,19 0,09
	K2O	1,30	0,08	1,29	0,09	1,32	0,04
	Total	97,88	0,58	98,82	0,63	98,84	0,57
		AR5SiNFeN	1-σ	AR5SiNFeNx2	1-σ	PCR2SiNFeN	1-σ
	Si	0.01	0.01	0,01	0,01	0,01	0,01
	P	3.85	1.83	3,09	1,95	6,04	3,96
	S	0.01	0.01	0,01	0,01	0,01	0,01
	Fe	91.06	1.77	91,39	1,58	90,08	2,83
	Pd	0.01	0.02	0,01	0,01	0,00	0,00
	Pt	0.00	0.00	0,00	0,00	0,00	0,00
	Ir	-	-	-	-	-	-
	Total	94.95	0.45	94,51	0,67	96,15	1,23

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J o u r n a l P r e -p r o o f

Acknowledgements

This work is part of the PhD of Fabien Bernadou being supported by the university of Orleans. The authors acknowledge the GASTON project (ANR-18-CE31-0021). Chemical analyses at ISTO and CRPG were partly supported by the PLANEX investissement d'avenir project (ANR-11-EQPX-36). We thank Cécile Deligny and Johan Villeneuve (CRPG, Nancy) for providing help during SIMS analysis. David Sifré is thanked for his help on the piston cylinder experiment. We also thank Patricia Benoist (SEM, ISTO), Ida Di Carlo (EPMA, ISTO), Marielle Hatton (Elemental analyser, ISTO) and Emmanuel Véron (XRD, Cemhti) for the help with analysis. We would like to thank the anonymous reviewer for these comments and corrections.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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