Maria Rita Cicconi

Eric Pili

Lucie Grousset

Daniel R Neuville

The Influence of Glass Composition on Iodine Solubility

Two glass series in the ternary systems and were studied in order to identify the main factors influencing the solubility of iodine. We established that iodine incorporation is strongly linked to the bulk chemistry, i.e. the SiO2/(B2O3+SiO2) molar ratio, and to the physical properties of the glasses, and we assessed three different solubility limits. Iodine in Si-rich glasses has a low solubility (≤1 mol% I) regardless of the alkali ion present. On the contrary, in B-rich glasses, the solubility is five times higher than in Si-rich glasses for Na-glasses, and more than six times higher for K-glasses. The strong dependence of iodine solubility on the bulk chemistry is related to the adaptability of the glass network. Furthermore, our data suggest that iodine is stable with different redox states in the glasses here analysed.

INTRODUCTION

Iodine, the heaviest stable halogen element, benefitted from relatively few studies on its solubility in glass matrices compared to the lighter halogens [START_REF] Grousset | Incorporation et rôle des halogènes dans les silicates vitreux et fondus[END_REF]. However, the incorporation, dissolution and mobility of this ion is very important in many fields, ranging from Materials and Earth Sciences to Waste management. Iodine occurs in nature as iodide (I -), as the oxyanion iodate (IO3 -) and rarely as elemental I (I2), respectively with oxidation states -I, +V and 0.

The radioisotope 129 I is of particular concern because it will be the main contributor to the radioactivity released by a geological repository site for nuclear wastes [START_REF] Hou | A review on speciation of iodine-129 in the environmental and biological samples[END_REF]. Furthermore, the iodine-xenon 131, 133, 135 decay chains are particularly important in the framework of the verification of the Comprehensive nuclear-Test-Ban Treaty (CTBT). Indeed, atmospheric radioxenon monitoring constitutes an important mean for the detection of underground nuclear explosions after transport to the subsurface [START_REF] Ringbom | Radioxenon detections the CTBT international monitoring system likely related to the announced nuclear test in North Korea on February 12, 2013[END_REF][START_REF] Kalinowski | Discrimination of Nuclear Explosions against Civilian Sources Based on Atmospheric Xenon Isotopic Activity Ratios[END_REF][START_REF] Sun | Radioxenon Production and Transport from an Underground Nuclear Detonation to Ground Surface[END_REF]. While the xenon source term in the nuclear cavity can be calculated, uncertainties persist regarding to what extend iodine may be trapped in magma inside the nuclear cavity [START_REF] Pili | Gas-Magma Interactions in Nuclear Cavities and Their Effects on the Xenon Isotope Ratios[END_REF].

Previous studies of iodine were mainly focused on the determination of iodine oxidation state and local surrounding in borosilicate waste glasses, and in cementitious wasteforms e.g. [START_REF] Riley | Iodine solubility in a low-activity waste borosilicate glass at 1000°C[END_REF][START_REF] Fuhrmann | Sorption of iodine on minerals investigated by X-ray absorption near edge structure (XANES) and 125I tracer sorption experiments[END_REF][START_REF] Riley | Materials and processes for the effective capture and immobilization of radioiodine: A review[END_REF] because the assessment of the valence state is quite important when dealing with radionuclide. Indeed, beside the redox state of the environment, also physical and chemical form of the elements (e.g. valence) could influence their mobilisation, diffusion and (re)distribution [START_REF] Ojovan | An introduction to nuclear waste immobilisation[END_REF]. In order to understand the main factors influencing the solubility of iodine, we investigated glasses in the ternary system K2O-B2O3-SiO2 (KBS), where the SiO2/(B2O3+SiO2) molar ratio was varied from 1 to 0. Data on I-bearing Na2O-B2O3-SiO2 (NBS) glasses are reported for comparison. The influence of iodine incorporation on glass physical properties, and glass network is here investigated by Raman spectroscopy.

EXPERIMENTAL

The borosilicate glasses here investigated have a constant amount (20 mol%) of potassium (or sodium) and a SiO2/(B2O3+SiO2) molar ratio ranging from 1 to 0, i.e., from K(Na)-silicate to K(Na)-borate glasses. All pristine glasses were synthesised in large batches from the appropriate amounts of oxide (SiO2), carbonate (K2CO3, or Na2CO3,) and acid (H3BO3), and melted between 950 and 1400 °C (as a function of the SiO2/(B2O3+SiO2) molar ratio) for a few hours to obtain bubble-free glasses. Powdered pristine glass and iodine compounds (I2 or alkali-I salts) were mixed by hand in an agate mortar. Batch of 300 mg of the powdered mixtures were inserted in platinum capsules and welded to avoid iodine leakage during experiments. Syntheses were carried out in a hot isostatic press (HIP) at Institut de Physique du Globe de Paris. The HIP is a medium-pressure (up to 2000 bars) high-temperature (up to 2000 °C) device. Experimental details are provided in [START_REF] Cicconi | Iodine dissolution and speciation in glasses: the effect of the glass-forming system fragility[END_REF]. Synthesis with solid I2 as starting material were all carried out at 1200 C and 1500 bar. Synthesis with alkali-I salts (KIO3 or NaIO3) as starting salts were carried out at different conditions of pressure and temperature, and for different holding times. Chemical compositions of both pristine and I-bearing glasses have been analysed with a Cameca SX100 electron microprobe (Table 1). Boron nitride (BN) and copper iodide were used as boron and iodine standards respectively. Ten measurements per sample (at 15keV and 40 nA) were performed to obtain more representative values of boron and iodine contents. The average compositions, of KBS glasses, are reported in Table 1. Boron calibration was achieved with BN as a standard and boron's Kα absorption coefficients by the other elements were adjusted on the analysis of several borosilicate glasses with variable B2O3 content from 80 to 0 mol%. Raman spectra were recorded at room temperature using a T64000 Jobin-Yvon® Triple-spectrometer set up with a confocal system, and a 1024 CCD detector cooled by liquid nitrogen. A Coherent® laser 70C Argon, with a wavelength of 488.1 nm, was used as excitation source providing 100mW on the sample. All spectra were recorded between 16 and 1700 cm -1 with an integration time of 300 s. Linear baseline subtraction and normalization to the total area were performed with LabSpec® software. Density measurements (Table 1) were done at room temperature by Archimedean method, using toluene as the immersion fluid. Glass transition temperatures (Tg) were determined by Differential Thermal Analysis (DTA) with a Setaram 96 Line Evo apparatus. A blank analysis was performed before sample analysis to corrected data from background signal. Temperature was increased with a rate of 5 °C/min and Tg was quantified by tangential method. All samples are labelled according the composition and iodine contents: NBSx and KBSx refer to pristine sodium/potassium borosilicate glasses where x represents the SiO2 molar content. KBSx.y refers to iodine-bearing glasses doped with K(Na)IO3, where x represents the SiO2 molar content, and y the iodine molar content.

RESULTS AND DISCUSSION

Physical and thermal properties have been determined for all pristine glasses. Figures 1A andB show the evolutions of the volumetric mass density (density for short) and glass transition temperature (Tg), in relation with the SiO2/(B2O3+SiO2) molar ratio for the pristine glasses synthetized under pressure. Density and Tg increase smoothly until 60 mol% of Si is substituted for B, with differences up to 20-22% in both properties, in agreement with published data in the NBS system [START_REF] Lenoir | The influence of Si,B substitution and of the nature of network-modifying cations on the properties and structure of borosilicate glasses and melts[END_REF]. When Si is substituted for B, the properties of KBS glasses follow a similar trend, although more irregularly.

The addition of iodine, in the two ternary systems, does not change the general trend, with both Tg and density increasing until a SiO2/(B2O3+SiO2) molar ratio equal to 0.75 for NBS glasses, and 0.87 for KBS glasses. I-bearing glasses have values with the B-rich ones being ~2% denser. Glass transition temperature values for the I-bearing NBS glasses are reported in Figure 1B, and they are always lower compared to the I-free glasses with variations of Tg up to 10% (data from [START_REF] Cicconi | Iodine dissolution and speciation in glasses: the effect of the glass-forming system fragility[END_REF]). Sample KBS60 has an anomalous higher Tg, and is partially out of trend. This glass has a lower potassium content, and a K2O/(SiO2+B2O3) molar ratio of 0.13, thus providing a glass transition temperature higher than 900 K.

Figure 1 -A, B) Volumetric mass density (g/cm 3 ) and glass transition temperature (Tg, K) vs. the SiO2/(B2O3+SiO2) molar ratios, for pristine KBS and NBS compositions, and iodine-bearing glasses (+I). Errors within the points. Lines are guide for the eyes.

The influence of synthesis conditions (pressure P, temperature T) on iodine solubility is shown in Figure 2. Glasses doped with KIO3 were synthesised under various P, T conditions and for different holding times to verify the attainment of equilibria, and the influence of pressure on iodine solubility. Glasses in the NBS system synthesised at 1500 ºC and 1500 bar are reported for comparison (black solid symbols; data from [START_REF] Cicconi | Iodine dissolution and speciation in glasses: the effect of the glass-forming system fragility[END_REF]).

Synthesis at the lowest T and P were held for almost 19 hours, whereas the synthesis at 1500 ºC and 1500 bar were held for 7 hours. For all I-bearing KBS glasses there is a general trend, with higher iodine solubility in boron-rich compositions (dashed line in Figure 2). The iodine content dissolved into the glasses did not vary too much between the different conditions of pressure, temperature and holding time, indicating that equilibrium was attained for all experiments. Depending on the SiO2/(B2O3+SiO2) molar ratio the amount of iodine incorporated within the KBS glass network varies from 0.27(1) to 1.97 [START_REF] Ojovan | An introduction to nuclear waste immobilisation[END_REF] In order to establish the solubility limit of iodine in glasses, the two glass series were doped with increasing amounts of solid I2 in the Pt capsules. In Figure 3, the nominal (starting) amount of iodine added is reported for the different compositions, either in the KBS or in the NBS systems, against the I content measured in the final synthesised glasses. Regardless the starting amount, iodine content for B2O3-rich samples is always higher than for the SiO2-rich ones. Furthermore, Na SiO2-rich glasses, with iodine contents greater than 5 mol%, were frequently partially crystallised and/or heterogeneous.

The highest amount of iodine is incorporated in glasses with SiO2/(B2O3+SiO2) molar ratio ~ 0.20 (NBS20, and KBS20). Potassium-glasses have higher ability to dissolve iodine, with a solubility limit established around 6.5mol%. The B-end member (KBS00) in the potassium series retained up to 10mol% I, but the lack of further experiments does not allow to establish the solubility limit. 5 mol% I represents the solubility limit for sodium B-rich glasses (NBS20) since higher doping levels did not produce any increase of iodine in the glass. SiO2-rich glasses were not able to incorporate more than 1 mol% I, either in the KBS or in the NBS system (Figure 3).

Glasses with KBS60 composition are depleted in K2O and have extremely low content of dissolved iodine (<0.3mol%), suggesting that alkali cations play a crucial role in enhancing iodine solubility. Raman spectra for KBS glasses with 20 mol% SiO2 are shown in Figure 4, along with the corresponding iodine-bearing glasses. Spectra for NBS20 glasses are reported for comparison. All bands are broad and are typical of B-rich alkali-silicate glasses [START_REF] Lenoir | The influence of Si,B substitution and of the nature of network-modifying cations on the properties and structure of borosilicate glasses and melts[END_REF][START_REF] Möncke | On the connectivity of borate tetrahedra in borate and borosilicate glasses[END_REF]. The vibrations related to Si-O-Si bending and Si-O stretching modes are weak and are, respectively, in the frequency regions below 600 cm -1 and between 850 cm -1 and 1250 cm -1 . Iodine incorporation in those glasses induces three main variations (Figure 4): in the very low (< 250 cm -1 ), in the intermediate (650 -900 cm -1 ), and in the high (1200 -1600 cm -1 ) frequency regions. The latter region contains vibrations associated to stretching of B-O -bonds of both tri-fold and four-fold coordinated boron (respectively, BO3 and BO4 units). Upon iodine incorporation the integrated area of this region decreases by ~ 17% (KBS20 sample containing 2.56( 14) mol% I). The relatively narrow bands in the 650-900 cm -1 frequency region represent breathing vibrations of pentaborate rings (~ 770 cm -1 ), and three corner-sharing BO3 rings (boroxol rings, ~805 cm -1 ). Iodine incorporation induces a decrease of the bands associated with pentaborate rings (770 and 732 cm -1 ), and a net increase of the boroxol at ~805 cm -1 both in Na and K borosilicate glasses (Figure 4, vertical dashed line at 805 cm -1 ). In the very low frequency region (< 250 cm -1 ) the rise of a broad shoulder around 110 cm -1 for I-bearing KBS samples, and a shift of the Boson peak toward lower frequencies can be observed. This additional contribution is clearly visible in the NBS20 glass containing ~5 mol% I (Figure 4, dashed line at 109 cm -1 ). Iodine incorporation in borosilicate glasses induces higher amounts of [BO3]-ring units compared to [BO4]. Usually, in alkali-B glasses, the stabilization of 4-fold coordinated boron units is due to an electron taken from K + (or Na + ) ions. Therefore, the alkali cation provides local charge neutrality being adjacent to the negative BO4 -units [START_REF] Griscom | Borate Glass Structure[END_REF].

Raman spectra of I-crystals identified the occurring of two main vibrational regions [START_REF] Cicconi | Iodine dissolution and speciation in glasses: the effect of the glass-forming system fragility[END_REF]: iodide crystalline compounds have the strongest bands in the very low frequency region (25-250 cm -1 ), whereas iodate crystalline compounds have their main vibrations in the region 650-850 cm -1 . In iodine-bearing glasses, the increase of [BO3] units, and the occurrence of the shoulder at very low frequencies, could be explained by considering K + ions being adjacent to I -ions. This implies the presence of iodide species, and, as previously suggested for NBS glasses and other borosilicate compositions [7-11-15] it likely results from the halogen local environment, where I - ions are surrounded by alkali cations. On the other hand, the particularly high increase of the peak around 805 cm -1 could be explained by the presence of extra contributions related to iodate vibrations <I 5+ -O>. Hence, the presence of additional contributions in the Raman spectra of I-bearing alkali borate glasses suggests the coexistence of iodine with different stable oxidation states. Based on the solubility study and on the Raman results we could speculatively say that the solubility of iodide species should be much higher than the solubility of iodate in borosilicate glasses. The stabilization of the reduced form is driven by the field strength of the alkali cation that will surround the halogen element in the first coordination shell, probably due to the larger continuous channels produced (percolation channels [START_REF] Le Losq | Percolation channels: a universal idea to describe the atomic structure and dynamics of glasses and melts[END_REF]).

CONCLUSIONS

Iodine incorporation in alkali borosilicate glasses is strongly affected by the bulk chemistry (SiO2/(B2O3+SiO2) ratio, alkali ion). Iodine solubility limits have been established for potassium borosilicate glasses and compared to that of sodium borosilicate glasses, as follows: -~5 mol% I and ~6.5 mol% I, respectively for B2O3-rich glasses in the NBS and KBS systems; -≤1 mol% I for Si-rich glasses, independently on the alkali cation.

Our results indicate that alkalis play a crucial role in enhancing iodine solubility. Most probably, elements with higher cation field strength (e.g. K) increases the incorporation of iodine because they induce larger continuous channels in the borosilicate glass network that might help iodine diffusion and dissolution.

Figure 3 -

 3 Figure 3 -Measured iodine content in the glasses as a function of the starting amount added, as solid I2. The solubility limits identified are reported as horizontal dashed lines.

Figure 4 -

 4 Figure 4 -Raman spectra of pristine glasses and I-bearing glasses. The dissolution of iodine in these glasses induces the appearance of two extra features, respectively around 109 cm -1 and 805 cm -1 (vertical dashed lines).

Table 1 -

 1 Analysed chemical composition (wt.%) and properties of KBS glasses. Some of the glasses in the NBSx+I2 series are reported for comparison (from[START_REF] Cicconi | Iodine dissolution and speciation in glasses: the effect of the glass-forming system fragility[END_REF]).

	Sample	salt used	starting amount I (mol%)	SiO2 (wt.%)	B2O3 (wt.%)	Na2O or K2O (wt.%)	I (wt%)	Density § (g/cm 3 )	Tg (K)
	pristine glasses
	KBS80			72.37	0.00	25.99		2.398(1) 718
	KBS60			68.89	15.14	16.80		2.442(2) 920
	KBS40			33.86	48.96	19.58		2.224(4) 578
	KBS20			14.76	66.86	22.66		2.189(3) 605
	KBS00			0.00	75.22	24.67		2.109(4) 536
	KIO3 series: KBSx.y (1500 ºC, 1500 bar)
	KBS80.1	KIO3	2	68.23	0.00	22.27	1.90	2.396(2)
	KBS60.03	KIO3	2	70.92	12.02	14.93	0.52	2.461(7)
	KBS40.2	KIO3	2	30.16	44.38	17.77	3.39	2.250(2)
	KBS20.1	KIO3	2	14.15	61.66	21.34	2.01	2.214(3) 592
	KBS00.1	KIO3	2	0	74.79	22.67	2.26	2.118(7)
	I2 series: KBSx+I2 (1200 ºC, 1500 bar)
	KBS80+ I2	I2	2	71.41	3.28	24.56	1.38	2.400(1)
	KBS80+ I2	I2	9	74.10	1.85	20.38	1.21	2.376(1)
	NBS80+ I2	I2	2	78.95	2.66	18.85	2.22	2.373(1) 730
	NBS80+ I2	I2	10	76.62	2.11	18.48	2.28	2.316(1)
	NBS80+ I2	I2	18.2	70.42	4.93	23.06	1.64	2.468(11)
	NBS60+ I2	I2	9.5	59.51	22.74	14.98	1.88	2.495(1)
	NBS60+ I2	I2	18.1	63.70	22.18	9.13	1.64	2.460(1)
	KBS20+ I2	I2	2.1	13.90	61.14	21.18	4.12	2.206(1) 593
	KBS20+ I2	I2	9.5	14.57	62.95	19.15	4.51	2.201(1) 675
	KBS20+ I2	I2	18.2	14.72	47.06	10.67	9.24	2.116(4)
	KBS20+ I2	I2	26.7	16.27	49.70	8.11	8.75	2.090(1)
	NBS20+ I2	I2	2	14.07	66.87	13.89	3.57	2.212(1) 697
	NBS20+ I2	I2	10.1	13.85	63.35	10.61	8.99	2.189(1) 590
	NBS20+ I2	I2	18	14.61	60.69	6.54	7.09	2.080(7) 513
	KBS80+ I2	I2	2	0.03	73.78	22.39	3.47	2.133(1)
	KBS80+ I2	I2	10	0.05	62.98	19.33	16.26	2.212(1)
	NBS00+ I2	I2	2	0.07	82.33	11.25	4.17	2.100(7) 499

§ volumetric mass density

SiO 2 /(B 2 O 3 + SiO 2 ) Figure 2

  -Iodine content (as mol%) incorporated in the different KBS glass compositions, depending on the synthesis conditions. I-bearing NBS glasses are reported for comparison (black solid line and symbols; data from[START_REF] Cicconi | Iodine dissolution and speciation in glasses: the effect of the glass-forming system fragility[END_REF]). Dashed line follows the general trend of KBS glasses. Lines are only guides for the eyes.

	Density (g/cm 3 )	2.1 2.2 2.3 2.4 2.5	A				KBS KBS+I NBS NBS+I
		0		0.2	0.4	0.6	0.8	1
	1000	B
	Tg (K)	600 800					KBS
							NBS
		400					NBS+I
			0	0.2	0.4	0.6	0.8	1
							mol% with a maximum for the glasses with
	SiO2/(B2O3+SiO2) ratio ~ 0.45. Interestingly, all samples with a nominal amount of 60mol% SiO2 (KBS60) have extremely low amount
	of iodine incorporated into the glasses.

ACKNOWLEDGMENTS

This work was funded in the framework of a CEA-IPG Paris collaboration.


Charles Le Losq

Andrew J Berry

Mark A Kendrick

Daniel R Neuville

Hugh C St

O'neill

The oxidation state of iron in Mid-Ocean Ridge basalt glasses determined by Raman spectroscopy

Synthetic Mid-Ocean Ridge Basalt (MORB) glasses, for which Fe 3+ /Fe TOT had been determined previously by Mössbauer spectroscopy and found to vary from 0 to 1, were used to test methods for determining Fe 3+ /Fe TOT by Raman spectroscopy. Six numerical data reduction methods were tested, based on conventional approaches and supervised and unsupervised machine learning algorithms. For the set of glass standards, with fixed composition, the precision of all methods is ≤ ± 0.04. This suggests that Raman spectroscopy may be a readily available method for determining the oxidation state of Fe in natural volcanic glasses with good precision and high spatial resolution. Raman spectra were recorded for 42 natural MORB glasses from a wide range of locations. There is a strong correlation between the Raman spectra and composition, despite relatively limited variability, such that the methods calibrated using the glass standards are not directly applicable to the natural samples. This compositional effect can be corrected by using a compositional term when linking spectral variations to the glass Fe 3+ /Fe TOT . The resulting Fe 3+ /Fe TOT value determined by Raman spectroscopy was of 0.090 ± 0.067 (n=42). This value agrees with the latest Fe K-edge XANES and wet-chemistry estimates of 0.10 ± 0.02. The larger uncertainty of the Raman determination reflects the sensitivity of Raman spectroscopy to small changes in glass composition and hence structure. This sensitivity allows Raman spectroscopy to be used to determine the major element composition of natural MORB glasses within 1 mol% through the use of a neural network. This suggests that Raman spectrometers may be used to determine the composition of samples in situ at difficult to access locations that are incompatible with X-ray spectrometry (e.g. Mid-Ocean Ridges or Mars).

Introduction

Mid-Ocean Ridge Basalts (MORB), derived from partial melting of the upper mantle, are of critical importance for understanding the geochemistry of the mantle and the formation of the oceanic crust (e.g. [START_REF] Langmuir | Petrological Systematics of Mid-Ocean Ridge Basalts: Constraints on Melt Generation Beneath Ocean Ridges, in: Mantle Flow and Melt Generation at Mid-Ocean Ridges[END_REF][START_REF] Asimow | A hydrous melting and fractionation model for mid-ocean ridge basalts: Application to the Mid-Atlantic Ridge near the Azores[END_REF][START_REF] Gale | The mean composition of ocean ridge basalts[END_REF]O'Neill et al., 2018). MORB glasses, formed by rapid cooling at the rim of pillow lavas enable the composition [START_REF] Jenner | Analysis of 60 elements in 616 ocean floor basaltic glasses: TECHNICAL BRIEF[END_REF][START_REF] O'neill | The global pattern of trace-element distributions in ocean floor basalts[END_REF], including volatile content [START_REF] Kendrick | Quantifying brine assimilation by submarine magmas: Examples from the Galápagos Spreading Centre and Lau Basin[END_REF], and oxidation state [START_REF] Christie | Oxidation states of mid-ocean ridge basalt glasses[END_REF][START_REF] Bézos | The Fe 3+ /ΣFe ratios of MORB glasses and their implications for mantle melting[END_REF]Cottrell andKelley, 2011, 2013;[START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF][START_REF] Zhang | Determination of Fe 3+ /ΣFe of XANES basaltic glass standards by Mössbauer spectroscopy and its application to the oxidation state of iron in MORB[END_REF] of the melts to be determined. This, in turn, allows the intensive and extensive thermodynamic conditions of the mantle source to be calculated (e.g. [START_REF] Asimow | A hydrous melting and fractionation model for mid-ocean ridge basalts: Application to the Mid-Atlantic Ridge near the Azores[END_REF]. In particular, the iron oxidation state of Fe in MORB, expressed as Fe 3+ /Fe TOT with Fe TOT = Fe 2+ + Fe 3+ , is important because it affects estimations of temperature, mineral assemblages, and the speciation of volatile elements, at both the surface and magmatic source.

The latest average Fe 3+ /Fe TOT values of natural MORB glasses from global sources have been determined to be 0.10 ± 0.02 [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF] or 0.14 ± 0.01 [START_REF] Zhang | Determination of Fe 3+ /ΣFe of XANES basaltic glass standards by Mössbauer spectroscopy and its application to the oxidation state of iron in MORB[END_REF] by Fe Kedge XANES spectroscopy, and 0.11 ± 0.02 by wet-chemistry (corrected for plagioclase phenocrysts, [START_REF] Bézos | The Fe 3+ /ΣFe ratios of MORB glasses and their implications for mantle melting[END_REF]. Wet chemistry is a destructive method that lacks spatial resolution and is unsuitable for inhomogeneous glasses or small samples such as melt inclusions (e.g. see [START_REF] Bézos | The Fe 3+ /ΣFe ratios of MORB glasses and their implications for mantle melting[END_REF]. Fe K-edge XANES spectroscopy has excellent precision and micron spatial resolution in two dimensions, but requires standards that are compositionally matched and for which Fe 3+ /Fe TOT is determined by another technique, such as 57 Fe Mössbauer spectroscopy (e.g. [START_REF] Berry | Oxidation state of iron in komatiitic melt inclusions indicates hot Archaean mantle[END_REF]. There are also questions concerning possible photo-oxidation during analysis of hydrous glasses (e.g. Cottrell et al., in press). A considerable drawback is that it also requires access to a synchrotron light source.

Raman spectroscopy is an alternative technique for determining Fe 3+ /Fe TOT that is easily accessible for most investigators, is non-destructive, has micron-scale spatial resolution, requires minimal sample preparation, is easy to perform, and spectra can be acquired within minutes. Previous studies have shown how Raman spectroscopy can be used for quantifying the concentration of H 2 O [START_REF] Thomas | Determination of water contents of granite melt inclusions by confocal laser Raman microprobe spectroscopy[END_REF][START_REF] Zajacz | A composition-independent quantitative determination of the water content in silicate glasses and silicate melt inclusions by confocal Raman spectroscopy[END_REF][START_REF] Behrens | Quantification of dissolved H₂ O in silicate glasses using confocal microRaman spectroscopy[END_REF][START_REF] Thomas | Determination of water in Fe-rich basalt glasses with confocal micro-Raman spectroscopy[END_REF][START_REF] Mercier | Influence of glass polymerisation and oxidation on micro-Raman water analysis in alumino-silicate glasses[END_REF][START_REF] Mercier | Spectroscopic analysis (FTIR, Raman) of water in mafic and intermediate glasses and glass inclusions[END_REF][START_REF] Losq | Determination of water content in silicate glasses using Raman spectrometry: Implications for the study of explosive volcanism[END_REF] and CO 2 [START_REF] Morizet | Quantification of dissolved CO 2 in silicate glasses using micro-Raman spectroscopy[END_REF] in glasses, with applications to pumices and melt inclusions [START_REF] Shea | Conduit-to Localized-scale Degassing during Plinian Eruptions: Insights from Major Element and Volatile (Cl and H 2 O) Analyses within Vesuvius AD 79 Pumice[END_REF][START_REF] Métrich | Magma transfer and degassing budget: Application to the 2009-2010 eruptive crisis of Mt Garet (Vanuatu arc)[END_REF]. The potential of Raman spectroscopy to determine Fe 3+ /Fe TOT in glasses has been demonstrated previously using various data treatment protocols [START_REF] Magnien | Kinetics of iron oxidation in silicate melts: a preliminary XANES study[END_REF][START_REF] Magnien | Kinetics of iron redox reactions in silicate liquids: A high-temperature X-ray absorption and Raman spectroscopy study[END_REF][START_REF] Magnien | Kinetics and mechanisms of iron redox reactions in silicate melts: The effects of temperature and alkali cations[END_REF][START_REF] Roskosz | Amorphous materials: Properties, structure, and durability: Quantification of the kinetics of iron oxidation in silicate melts using Raman spectroscopy and assessment of the role of oxygen diffusion[END_REF][START_REF] Muro | Micro-Raman determination of iron redox state in dry natural glasses: Application to peralkaline rhyolites and basalts[END_REF]Di Genova et al., 2016). The simplest method requires correlating changes in Fe 3+ /Fe TOT with changes in the intensity of the Raman spectra at given Raman shift [START_REF] Magnien | Kinetics of iron redox reactions in silicate liquids: A high-temperature X-ray absorption and Raman spectroscopy study[END_REF][START_REF] Roskosz | Amorphous materials: Properties, structure, and durability: Quantification of the kinetics of iron oxidation in silicate melts using Raman spectroscopy and assessment of the role of oxygen diffusion[END_REF]. A more complex method involves peak fitting the Raman signals assigned to stretching of tetrahedral SiO 4 and AlO 4 units in order to extract the Fe 3+ -O signal, which can be related to Fe 3+ /Fe TOT (Di Muro et al., 2009; Welsch et al., 2017). Recently, Di Genova et al. (2016) proposed another approach based on interpolation between two endmember spectra (e.g., one from a glass with oxidized iron and one from a glass with the same composition but reduced iron). Those different studies focused on demonstrating the ability of Raman spectroscopy to quantify Fe 3+ /Fe TOT in glasses of known composition. To date, no systematic use of Raman spectroscopy has been attempted to tackle a problem such as the quantification of Fe 3+ /Fe TOT in MORB glasses.

The existing methods for quantifying Fe 3+ /Fe TOT of glasses from Raman spectra rely on either simple treatments (e.g. the intensity of one or several peaks, mixing end-member spectra) or peak fitting. To our knowledge, machine learning algorithms, which remove subjectivity in the data reduction protocol, have not been used for determining Fe 3+ /Fe TOT of glasses. Here we compare existing data reduction methods (conventional methods), based on spectral intensity variations and mixing of spectra, with new supervised and unsupervised machine learning approaches. We avoided the peak fitting procedure (e.g. Di [START_REF] Muro | Micro-Raman determination of iron redox state in dry natural glasses: Application to peralkaline rhyolites and basalts[END_REF] because it is complex to perform and equivocal of interpretation [START_REF] Welsch | Fe-oxidation state in alkali-trisilicate glasses -A Raman spectroscopic study[END_REF], and thus may not be suited to a routine protocol. Conventional methods and supervised machine learning require the Fe 3+ /Fe TOT values of the glass standards to be known. Unsupervised machine learning methods, however, do not require prior knowledge of Fe 3+ /Fe TOT of the standards, such that they offer an independent way of determining Fe 3+ /Fe TOT for comparison with the results of other techniques. Those methods were assessed for a set of 13 synthetic glasses with a typical but simplified MORB composition and known Fe 3+ /Fe TOT [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF]. Following the proof of concept, the methods were used to determine Fe 3+ /Fe TOT of a representative set of 42 natural MORB glasses from the Atlantic, Indian and Pacific oceans, with known major and trace elements compositions [START_REF] Melson | A data brief on the Smithsonian Abyssal Volcanic Glass Data File[END_REF][START_REF] Jenner | Analysis of 60 elements in 616 ocean floor basaltic glasses: TECHNICAL BRIEF[END_REF][START_REF] Kendrick | Quantifying brine assimilation by submarine magmas: Examples from the Galápagos Spreading Centre and Lau Basin[END_REF] and Fe K-edge XANES Fe 3+ /Fe TOT values [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF].

Material and Methods

Starting Glasses

The MORB standards were prepared from mixtures of reagent grade SiO 2 (52.0 wt%), Al 2 O 3 (16.1 wt%), CaCO 3 = CaO (12.4 wt%), Fe 2 O 3 = FeO (10.0 wt%), MgO (8.2 wt%) andTiO 2 (1.3 wt%) that were equilibrated at 1400 ˚C and values of log fO 2 between 0 and -11 (-4.7 and 6.3 in log units relative to the quartz-fayalite-magnetite, QFM, buffer) for ~ 24 h before quenching in water. A sample was also prepared at logfO 2 = 4.8 (QFM + 11.2) using a pistoncylinder apparatus. The Fe 3+ /Fe TOT ratio of each glass was determined by Mössbauer spectroscopy, and found to vary from ~ 0 to 1 (Table 1). For further details see [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF].

Samples of natural MORB glass were obtained from the Department of Mineral Sciences, Smithsonian Institution, as polished chips mounted in epoxy resin and are listed by MNNH catalogue numbers in Supplementary Table 1. The sample details and major element composition are given in [START_REF] Melson | A data brief on the Smithsonian Abyssal Volcanic Glass Data File[END_REF], their trace element composition in [START_REF] Jenner | Analysis of 60 elements in 616 ocean floor basaltic glasses: TECHNICAL BRIEF[END_REF], and their Fe 3+ /Fe TOT values determined by Fe K-edge XANES spectroscopy in [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF]. From the set analysed by [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF], the Raman spectra of five glasses (NMNH No. 111235-85, 115083-41, 113828-5, 111241-1, 111237-67) were contaminated by contributions from crystals (see supplementary code) and were not considered during the data reduction. Five samples previously studied by [START_REF] Kendrick | Quantifying brine assimilation by submarine magmas: Examples from the Galápagos Spreading Centre and Lau Basin[END_REF] from Juan de Fuca (Alv 2262-8 and Alv 2269-2), the East Pacific Rise Clipperton (CL DR01) and Mid-Atlantic Ridge MAPCO (CH98 DR08 and CH98 DR11) were also analysed.

Raman Spectra Acquisition

Raman spectra of glasses were recorded using a Renishaw InVia spectrometer, equipped with a Peltier-cooled detector, a 2400 l/mm grating and a confocal system. Samples were excited using a 532 nm laser line focused ~ 3 m below the surface using a x100 Leica objective.

The laser power on the sample was ~ 1.2 mW. The spatial resolution was < 1 m, and the spectral resolution ~ 1.2 cm -1 . Five spectra were recorded from different points for each sample. They are treated separately during the data reduction process. The acquisition time varied between 120 and 180 s. For water-bearing natural MORB samples, oxidation of Fe by the laser has been reported at high laser power [START_REF] Genova | Effect of iron and nanolites on Raman spectra of volcanic glasses: A reassessment of existing strategies to estimate the water content[END_REF]. The combination of a laser power less than 5 mW [START_REF] Genova | Effect of iron and nanolites on Raman spectra of volcanic glasses: A reassessment of existing strategies to estimate the water content[END_REF] with a relatively short counting time of 120 s, and the analysis of five different spots, was used to prevent Fe oxidation during spectral acquisition. We checked this by recording Raman maps for six samples, by acquiring 120 spectra with an acquisition time of 1 s over an area of 10 m by 12 m. During the acquisition of these maps, the sample was continuously moved, such that the beam spent less than 1 s at a given location. The individual spectra were noisy, but their average produced a spectrum with a signal to noise ratio similar to that of a spectrum acquired in 120 s at a single point. No difference was observed between spectra obtained in these two ways, indicating that no variation of Fe 3+ /Fe TOT was induced the during acquisition.

Data pre-processing

The spectra (Fig. 1) were pre-processed in Python using the Rampy library (Le [START_REF] Losq | Rampy: a Python library for processing spectroscopic (IR, Raman[END_REF].

The data were corrected for temperature and excitation line effects following [START_REF] Galeener | Theory of the first-order vibrational spectra of disordered solids[END_REF]. We focus the data reduction methods on the 800-1300 cm -1 region of the spectra, which contains signals from Si-O, Al-O and Fe 3+ -O stretching in the glass structure (Brawer andWhite, 1975, 1977;[START_REF] Virgo | Anionic constitution of 1-Atmosphere silicate melts: implications for the structure of igneous melts[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Virgo | Speciation of Fe 3+ in 1-atm Na 2 O-SiO 2 -Fe-O Melts[END_REF]. This region also avoided signals due to nanolites (< 800 cm -1 ), which were observed in the spectra of some of the natural glasses (see supplementary materials). We chose to fit a linear baseline to subtract the background (Fig. 2A), with the aim of having only Si-O, Al-O and Fe 3+ -O stretching signals in the background-corrected spectra that will be used for Fe 3+ /Fe TOT determination. The low and high frequency anchors of the linear baseline were determined using a grid-search algorithm as those resulting in the lowest root mean square error (RMSE) between the Mössbauer Fe 3+ /Fe TOT values and those predicted by the intensity and mixing methods described in sections 2.4.1 and 2.4.2. This resulted in the subtraction of a linear baseline interpolated between the intensities at 850 and 1140 cm -1 (Fig. 2A). The baseline corrected spectra were smoothed using a Whittaker function to maximize the signal to noise ratio [START_REF] Eilers | A perfect smoother[END_REF]; see supplementary code for an example), and then the intensity normalised to vary between 0 and 1 (Fig 2B). The spectra resulting from this arbitrary baseline correction can not be used to infer the glass structure. However, the correction provides a simple method for isolating variations in the Raman signals related to changes in Fe oxidation state (Fig 2B). Furthermore, the arbitrary baseline correction was found to be beneficial because it avoids the introduction of random errors associated with variations in the real spectral background when the sample signal is low (e.g. near 1250 cm -1 ).

Determining the oxidation state of iron by Raman spectroscopy

In this study, six different methods were evaluated to determine the oxidation state of Fe in the suite of MORB glass standards (Table 1) from the background subtracted 850-1140 cm -1 region of the Raman spectra (Fig. 2B). The idea is to relate, for a set of glass standards with fixed major element composition, changes in the Raman spectra to changes in Fe 3+ /Fe TOT .

The six methods investigated are described below.

Intensity method

The intensity of the Raman spectra between 850 and 1140 cm -1 varies systematically with Fe 3+ /Fe TOT in the glass standards (Figs. 1,2B). In particular, the intensity at 930 cm -1 varies strongly with Fe 3+ /Fe TOT . This feature has contributions from Fe 3+ -O [START_REF] Virgo | Speciation of Fe 3+ in 1-atm Na 2 O-SiO 2 -Fe-O Melts[END_REF][START_REF] Magnien | Kinetics of iron redox reactions in silicate liquids: A high-temperature X-ray absorption and Raman spectroscopy study[END_REF][START_REF] Muro | Micro-Raman determination of iron redox state in dry natural glasses: Application to peralkaline rhyolites and basalts[END_REF], and thus should be ideal for determining Fe 3+ /Fe TOT . Two methods were tested to quantify the intensity at 930 cm -1 : direct measurement at fixed frequency (the average of values between 929 and 931 cm -1 ) and by peak fitting the 850-1140 cm -1 spectral envelop with arbitrary Gaussian components. Direct measurements of the intensity at 930 cm -1 (hereafter abbreviated I 930 ) provided the better precision and this approach was used.

Mixing method

The Mixing method is based on the bilinear model that describes the matrix dataset , of dimension n spectra times m features (i.e. Raman shifts), as:

,

where is the matrix of component fractions, the matrix of partial spectral components (endmember spectra), k the number of components and a noise term. In the present case, k = 2 (reduced and oxidised endmembers), as verified by a principal component analysis of the 13 standards, which revealed that two components account for more than 99.8% of the variance in the data. Using the notation S OX and S RED to designate the oxidised (Fe 3+ /Fe TOT = 1) and reduced (Fe 3+ /Fe TOT = 0) Raman spectral components, and F OX as the fraction of S OX , eq. ( 1) can be re-arrange as:

.

(2)

We used least absolute regression (LAD) to determine F OX , because LAD is more robust than least squares with respect to outliers or non-Gaussian distributions [START_REF] Tarantola | Inverse problem theory and methods for model parameter estimation[END_REF]. The optimised F OX values can then be related to the glass Fe 3+ /Fe TOT values (Di Genova et al., 2016).

Alternative Least Square Multivariate Curve Resolution (ALS MCR)

Solving eq. ( 1) usually requires either or . For example, are obtained from in the Mixing method (sec. 2.4.2). However, several techniques allow both and to be estimated from , as for example independent component analysis (e.g. [START_REF] Hyvärinen | Independent component analysis[END_REF], non-negative matrix factorisation (e.g. [START_REF] Lin | Projected Gradient Methods for Nonnegative Matrix Factorization[END_REF], and iterative optimisation (e.g. [START_REF] Zakaznova-Herzog | Quantitative Raman spectroscopy: Principles and application to potassium silicate glasses[END_REF]. For the present dataset of spectra, several conditions need to be satisfied: (i) ; (ii) = 1 -; and (iii) . Of the available methods, self-modelling curve resolution [START_REF] Jiang | Principles and methodologies in self-modeling curve resolution[END_REF][START_REF] De Juan | Multivariate Curve Resolution (MCR) from 2000: Progress in Concepts and Applications[END_REF], also known as multivariate curve resolution, can help solve the present problem. As they do not require prior knowledge of neither nor , those methods belong to the class of unsupervised machine learning algorithms.

Zakaznova

In this study, the Alternative Least Square Multivariate Curve Resolution (ALS MCR) method was used to iteratively optimise and . The PyMCR python library was used, starting the algorithm with estimations of obtained from mean spectra from our spectral dataset.

The algorithm was allowed to perform 50 iterations. After convergence, usually achieved in only a few iterations, optimised and matrices are available for the investigated dataset. The spectral endmembers stored in the optimised matrix (i.e. optimised F OX and F RED ) can then be used with the Mixing method for new samples.

Convergence of the ALS MCR algorithm is inherently dependent on the starting conditions (e.g. [START_REF] Valderrama | Independent components analysis as a means to have initial estimates for multivariate curve resolution-alternating least squares[END_REF]. The effects of the range of Fe 3+ /Fe TOT values included in , and the starting components, were tested using iterative protocols. The Fe 3+ /Fe TOT dataset range can be represented by two variables: (i)  Fe 3+ /Fe TOT of , which represents the difference of Fe 3+ /Fe TOT between the most reduced and the most oxidized samples in the dataset; and (ii) mean Fe 3+ /Fe TOT of , which is the mean value of Fe 3+ /Fe TOT of the dataset.

Similarly, variations in the initial components are represented using two parameters: (i)

 Fe 3+ /Fe TOT of represents the difference of Fe 3+ /Fe TOT between the two initial components; and (ii) mean Fe 3+ /Fe TOT of , which is the average value of the Fe 3+ /Fe TOT of the two initial components.

To determine how the root-mean-square deviations between the estimated and nominal Fe 3+ /Fe TOT values of the standard vary with  Fe 3+ /Fe TOT and mean Fe 3+ /Fe TOT of , and  Fe 3+ /Fe TOT and mean Fe 3+ /Fe TOT of , these values were varied by iteration, such that different subsets of and were generated. These subsets were provided to the ALS MCR algorithm to calculate optimised and matrices. These optimised matrices were then used to determine Fe 3+ /Fe TOT for the entire and datasets.

Neural Networks, Kernel Ridge and Support Vector regressions

The three other techniques that were investigated used the supervised machine learning regression algorithms Neural Networks, Kernel Ridge, and Support Vector from the Scikit Learn library [START_REF] Pedregosa | Scikit-learn: machine learning in python[END_REF]). An interface for using these algorithms for Raman data was implemented in the Rampy library (Le Losq, 2018) through the class mlregressor (see the Jupyter notebook in the supplementary materials as well as the rampy.mlregressor help).

The machine learning algorithms require the data to be divided into two subsets: a training subset to train the different algorithms, and a testing subset that are treated as unknowns to evaluate the predictive error of the algorithms. The train-test split was performed by randomly sorting the dataset according to their Fe 3+ /Fe TOT values (function chemical_splitting from the rampy library). The testing data subset was ~ 38 % of the total dataset.

The Neural Network technique uses a network of activation units, which are Rectifier functions [y = max(0,x)] [START_REF] Glorot | Deep sparse rectifier neural networks[END_REF] in the present study, to map the relationship between the Raman spectra and Fe 3+ /Fe TOT values of the glasses (see description in [START_REF] Bengio | Learning Deep Architectures for AI[END_REF] and references therein). The activation units have adjustable parameters, called weights and bias, that are optimised by least square regression. This method makes no assumptions about the linearity of variations in the Raman spectra with Fe 3+ /Fe TOT . The network was optimised by testing different architectures to minimize the training and testing errors, and to keep those two values as close as possible to each other. A simple architecture with three activation units in a single hidden layer provided the most robust fits. Adding more activations units or layers did not decrease the error metrics of the network, and hence this simple architecture was used. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (lbfgs) solver was chosen, as it performs better than others for the present small dataset.

Bagging, which consists of training multiple networks and returning the average of their outputs [START_REF] Breiman | Bagging Predictors[END_REF], was performed to avoid over-fitting and to promote the ability of the network to predict new values. A total of 100 networks were trained, and the results represent the average output of these 100 networks.

The Kernel Ridge and Support Vector techniques regress the data after their projection in a high-dimensionality space. This projection was done using a non-linear radial basis kernel function, such that the Raman intensity can non-linearly depend on Fe 3+ /Fe TOT . The difference between the Kernel Ridge and Support Vector regressions lies in the use of different loss functions: Kernel Ridge regression uses a penalized (l 2 normalisation) residual of the sum of squares, whereas Support Vector regression uses a -insensitive loss function ( is a deviation term in the loss function, i.e. the predictions are allowed to be as far from the calibration data as ). More information on these algorithms is available in Murphy (2012), [START_REF] Smola | A tutorial on support vector regression[END_REF] and [START_REF] Vapnik | The Nature of Statistical Learning Theory[END_REF]. The hyper-parameters of the Kernel Ridge and Support Vector algorithms were automatically tuned by performing a random 5-fold cross-validation on the training dataset.

A Jupyter notebook running under the Python language, together with all the spectra, are provided as supplementary materials to enable the results of this study, and the figures, to be reproduced.

Results

Raman spectra of MORB glass standards

The Raman spectra of the MORB glass standards exhibit peaks and shoulders at ~ 505, 570, 660, 735, 804, 930 and 1005 cm -1 (A to G markers in Fig. 1), with intensities that depend on Fe 3+ /Fe TOT . The intensity of the A, B, C and D Raman signals decreases with decreasing Fe 3+ /Fe TOT (Fig. 1, Table 1), whereas that of E and G increases (Figs. 1,2B). The intensity of F relative to that of G decreases with decreasing Fe 3+ /Fe TOT (Fig. 2B).

The changes in the Raman spectra of the glasses following changes in Fe 3+ /Fe TOT reflect changes in (i) the Fe 3+ contribution to the Raman signals, and (ii) the overall glass structure as Fe 3+ and Fe 2+ have different roles. The signals in the 810-1300 cm -1 region of the Raman spectra of MORB glasses can be assigned to symmetric and asymmetric stretching of Q n SiO 4 -AlO 4 units, where n is the number of bridging oxygens (Brawer andWhite, 1975, 1977;[START_REF] Furukawa | Vibrational spectra and glass structure[END_REF][START_REF] Furukawa | Raman spectroscopic investigation of the structure of silicate glasses. III. Raman intensities and structural units in sodium silicate glasses[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Mysen | Role of Al in depolymerized, peralkaline aluminosilicate melts in the systems Li₂ O-Al₂ O₃ -SiO₂ , Na₂ O-Al₂ O₃ -SiO₂ , and K₂ O-Al₂ O₃ -SiO₂[END_REF][START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF][START_REF] Losq | The role of Al 3+ on rheology and structural changes of sodium silicate and aluminosilicate glasses and melts[END_REF]. The intensity at F is assigned to the combination of signals from Fe 3+ -O stretching in the glass network (Virgo et al., 1982;[START_REF] Wang | In situ structural investigation of ironcontaining silicate liquids and glasses[END_REF][START_REF] Magnien | Kinetics of iron oxidation in silicate melts: a preliminary XANES study[END_REF][START_REF] Magnien | Kinetics of iron redox reactions in silicate liquids: A high-temperature X-ray absorption and Raman spectroscopy study[END_REF][START_REF] Magnien | Kinetics and mechanisms of iron redox reactions in silicate melts: The effects of temperature and alkali cations[END_REF][START_REF] Muro | Micro-Raman determination of iron redox state in dry natural glasses: Application to peralkaline rhyolites and basalts[END_REF][START_REF] Cochain | Effects of the iron content and redox state on the structure of sodium borosilicate glasses: A Raman, Mössbauer and boron K-Edge XANES spectroscopy study[END_REF] and Si-O stretching in Q 2 units [START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF][START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Virgo | Anionic constitution of 1-Atmosphere silicate melts: implications for the structure of igneous melts[END_REF]. This assignment agrees with (i) the decrease in the relative intensity of F with Fe reduction (Figs. 1,2B) and (ii) the presence of F as a shoulder in the most reduced spectra (Figs. 1,2B). The peak near 1005 cm -1 mainly comprises contributions from Si-O and Al-O stretching in Q 3 units. This signal usually occurs near 1100 cm -1 in Al-free silicate glasses (e.g. [START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF][START_REF] Mcmillan | Structural studies of silicate glasses and melts -Applications and limitations of Raman spectroscopy[END_REF] but shifts to lower frequencies in aluminosilicate glasses [START_REF] Neuville | Role of aluminium in the silicate network: In situ, hightemperature study of glasses and melts on the join SiO 2 -NaAlO 2[END_REF][START_REF] Mysen | The structural behavior of Al 3+ in peralkaline melts and glasses in the system Na₂ O-Al₂ O₃ -SiO₂[END_REF][START_REF] Losq | Effect of the Na/K mixing on the structure and the rheology of tectosilicate silica-rich melts[END_REF]. This assignment is consistent with the composition of MORB glasses; with NBO/T values ranging from ~ 0.5 to ~ 1.0 [START_REF] Mysen | Silicate glasses and melts -Properties and structure[END_REF], they are expected to be enriched in Q 3 units and to contain minor fractions of Q 2 and Q 4 (e.g. [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF].

3.2 Raman spectroscopy as a tool for determining Fe 3+ /Fe TOT of MORB glasses

The Intensity method

I 930 in the Raman spectra of the synthetic MORB glasses is linearly correlated with Fe 3+ /Fe TOT (Fig. 3), with a correlation coefficient of 0.9973. It is thus possible to determine Fe 3+ /Fe TOT of a glass from the I 930 scaled Raman intensity using the equation:

Fe 3+ /Fe TOT = 4.084(38)  I 930 -2.779( 29) .

(3)

The root-mean-square deviation between the Fe 3+ /Fe TOT values of the standards and those calculated with eq. 3 is 0.02 (1).

The Mixing method

Following a protocol similar to that described by Di Genova et al. (2016), we used the average of the five spectra recorded for the most oxidized and reduced glasses (log fO 2 = 4.8 and -11.0, Table 1) as endmembers. Then, F OX was adjusted by least absolute regression to obtain mixed spectra that matched the observed ones (Fig. 4A). The correlation between F OX and Fe 3+ /Fe TOT is shown in Figure 4B; the correlation coefficient is 0.9974. F OX is linearly proportional to Fe 3+ /Fe TOT . This result differs from the finding of Di Genova et al. (2016), who reported non-linear variations of F OX with Fe 3+ /Fe TOT for rhyolite and basalt glasses.

This may be due to the fact that these authors did not use endmember spectra with Fe 3+ /Fe TOT of 0 and 1, but of intermediate values. In the present case, F OX and Fe 3+ /Fe TOT are related by: Fe 3+ /Fe TOT = 1.02(1)  F OX -0.003(4) .

(4)

F OX directly gives Fe 3+ /Fe TOT of MORB glasses to within 0.03 (1).

The ALS MCR method

For a set of glasses with unknown but varying Fe 3+ /Fe TOT values, ALS MCR can determine the endmember spectra (i.e. spectra corresponding to Fe 3+ /Fe TOT = 0 and 1), and hence, Fe 3+ /Fe TOT for any MORB glass by linear combination fitting.

Figure 5 presents the results obtained from tests performed to evaluate the sensitivity of ALS MCR to the starting conditions (see sec. 2.4.3). The best results were obtained when the dataset covered the widest possible range of Fe 3+ /Fe TOT values, i.e. when  Fe 3+ /Fe TOT of 1 and mean Fe 3+ /Fe TOT of ~ 0.4 -0.5 (Fig. 5A). Fe 3+ /Fe TOT root-mean-square deviations < 0.06 were achieved using datasets with  Fe 3+ /Fe TOT of D ≥ 0.75 and mean Fe 3+ /Fe TOT of D [0.35,0.55]. The choice of the initial seems less critical, but still affects the accuracy of the ALS MCR method (Fig. 5B). Fe 3+ /Fe TOT root-mean-square deviations < 0.03 were obtained for initial with mean Fe 3+ /Fe TOT [0.4,0.6] and  Fe 3+ /Fe TOT [0.1,0.6].

The ALS MCR method was tested further by optimising using the full dataset .

From Figure 5B, initial S components with  Fe 3+ /Fe TOT and mean Fe 3+ /Fe TOT of ~ 0.5 and 0.4, respectively, should provide best results. Thus, the mean spectra at Fe 3+ /Fe TOT = 0.66 and 0.25 were selected as initial components. Selecting mean spectra with Fe 3+ /Fe TOT = 0 and 1 does not significantly change the results, but the present choice allows the effects of differences in the initial and optimised components to be illustrated, as shown in Figure 6A. The optimised spectra are clearly different from their initial values, demonstrating the ability of ALS MCR to identify the true endmembers. The optimised produce good fits to the observed spectra (Fig. 6B). The fraction of the oxidised endmember, C OX , is linearly related to the Fe 3+ /Fe TOT of the glass by (Fig. 6C):

Fe 3+ /Fe TOT = 1.07(1)  C OX -0.035( 5) .

(5)

Contrary to F OX , C OX is not directly equal to Fe 3+ /Fe TOT . This is because of small differences between the optimised endmembers and the mean Raman spectra at Fe 3+ /Fe TOT = 0 and 1 (residuals shown in Fig. 6A). These differences introduce a bias, such that using C OX as a direct estimate of Fe 3+ /Fe TOT leads to slightly (~ 0.02) under-and over-estimations of Fe 3+ /Fe TOT , depending on the glass Fe 3+ /Fe TOT . Because of that, the root-mean-square deviation between the Raman-determined and standard Fe 3+ /Fe TOT values is ± 0.04 when assuming F OX = C OX . Slightly better results were obtained using eq. 5, which allows Fe 3+ /Fe TOT of the glasses to be determined within ± 0.03 (Table 1).

Neural Networks, Kernel Ridge and Support Vector regression methods

The Neural Network, Kernel Ridge, and Support Vector methods performed very well on both the training and testing datasets (Fig. 7), with root-mean-square deviations between the measured and predicted Fe 3+ /Fe TOT values of ~ 0.01-0.03 (Table 1). For all methods, the rootmean-square deviations for the training dataset were slightly lower than that for the testing dataset, indicating that machine-learning algorithms tend to slightly over-fit the training dataset. Over-fitting is not desirable because it indicates that the generalisation ability of the algorithms (i.e. their ability to predict values for new samples) may not be optimal. However, in the present case, the difference between the training and testing standard deviations is small (≤ 0.02), and the over-fitting is considered to be negligible. Therefore, these algorithms can be used to predict Fe 3+ /Fe TOT of MORB glasses with an error ≤ ± 0.03 (1).

Is there a better method?

The root-mean-square deviations between the Fe 3+ /Fe TOT values determined by Mössbauer and Raman spectroscopy are < 0.04 for all six methods. The Intensity and Mixing methods are as accurate and precise as those using machine learning (ALS MCR, Neural Network, Kernel Ridge and Support Vector; Table 1).

The choice of method depends on the aims of the study and the dataset. If a single data reduction method was to be chosen, the simplicity of the Intensity and Mixing methods makes these appealing. In the case the Fe 3+ /Fe TOT of the standards are unknown, the ALS MCR method may allow components to be extracted and the Fe 3+ /Fe TOT to be determined, if the dataset covers a large range of Fe 3+ /Fe TOT values (Fig. 5). The Intensity, Mixing and ALS MCR methods all rely on linear variations between Raman signals and Fe 3+ /Fe TOT of the glasses. In contrast, the Neural Network, Kernel Ridge, and Support Vector methods do not assume linear variations and do not require the mathematical form of the variations to be known.

Ultimately, we recommend the use of multiple data reduction methods, as undertaken here, to test the consistency of results. This is desirable because each data reduction protocol may be differently sensitive to how differences in composition affect the Raman spectra (Fig. 2B). Therefore, following a Bayesian approach, the average of the results from all the methods should be more robust than any single estimate (e.g. [START_REF] Perrone | Improving regression estimation: Averaging methods for variance reduction with extensions to general convex measure optimization[END_REF]. In the present case, such an approach is easy to implement because all the methods presented in this study are simple to setup and cheap in terms of computing resources. For the present dataset, averaging the results of the six models to obtain an estimate of the Fe 3+ /Fe TOT from the Raman spectra of the glasses resulted in a root-mean-square deviation of 0.02 (1).

Application to natural MORB glasses

The baseline subtracted and normalised Raman spectra of natural MORB glasses are shown in Figure 8A (see supplementary Jupyter Notebook for full spectra). While their spectra are similar to that of the glass standard with Fe 3+ /Fe TOT = 0.106, non-negligible differences are apparent (8A). I 930 varies between 0.64 and 0.76, and is correlated with the concentration of MgO and CaO in the glass (Pearson correlation coefficient = 0.76, Fig. 8B). For the glass standards, a difference of ~ 0.2 in I 930 corresponds to a difference in Fe 3+ /Fe TOT of ~ 0.2 (Fig. 3). For these spectra, the methods described give an average Fe 3+ /Fe TOT of 0.16 with a large standard deviation of 0.12.

It is possible to refine this estimate by including a compositional term in the expressions relating Raman features to Fe 3+ /Fe TOT . We focused on the Intensity method and expressed I 930 as:

I 930 = (K0 + K1  Fe 3+ /Fe TOT ) + K2  X , ( 6
)
where X is a parameter reflecting the chemistry of the samples, and K0, K1 and K2 constants.

X could be chosen as either [MgO+CaO] or the number of non-bridging oxygen per tetrahedral units (NBO/T) in the glass. Increasing [MgO + CaO] favours the formation of non-bridging oxygens and thus depolymerised Q 2 units in basaltic glasses, which give signals near 950 cm -1 (e.g. [START_REF] Mysen | Curve-fitting of Raman spectra of silicate glasses[END_REF]. This is consistent with the positive trend observed between I 930 and [MgO + CaO] (Fig. 8B). However, while NBO/T parameterises the general effect of variations in the fractions of network formers (e.g. Si, Al) and network modifiers (e.g. Na, K, Ca, Mg) on the glass structure, it does not consider the effect of the ionic properties of network modifiers on the distribution of Q n units, which contribute to the Raman intensity between 850 and 1140 cm -1 . For example, at a constant NBO/T of 0.5, the fractions of Q 4 and Q 2 increase at the expense of that of Q 3 in alkali silicate glasses as the ionic field strength (Z/r 2 , where Z is the electric charge and r the ionic radius) of the alkali metal cation increases [START_REF] Maekawa | The structural groups of alkali silicate glasses determined from 29 Si MAS-NMR[END_REF]. The ionic field strength of metal cations also influences many other structural properties of silicate glasses and melts, including the fraction of highly-coordinated Al, excess NBO, and Si-Al disorder (see Le [START_REF] Losq | Silicate Glasses[END_REF] for a review). As a result, to capture changes in the Raman spectra due to variations in the sample chemistry, we used the mean ionic field strength (IFS) of network modifiers (M), IFS(M), as the X parameter in eq. ( 6):

,

where are the mol fractions of the oxide components , and IFS is the ionic field strength of the cation , calculated as Z/r 2 . The r values were taken from [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF], with coordination numbers (CN) of 6 for all M cations. For simplicity, we do not consider variations in CN although they will vary with glass composition (Le Losq et al., 2019 and references therein), but probably this effect is negligible due to limited range of compositional variability of MORB. We also consider FeO as equal to total Fe because the Fe 3+ /Fe TOT ratio of natural MORB is always low (~0.1) and constant (e.g. [START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF][START_REF] Zhang | Determination of Fe 3+ /ΣFe of XANES basaltic glass standards by Mössbauer spectroscopy and its application to the oxidation state of iron in MORB[END_REF], such that any influence of Fe on the glass structure will come from variations in .

The correlation between I 930 and IFS(M) is linear for natural MORB glasses (Fig. 9). The ordinate at the origin of this trend corresponds to K0 + K1 Fe 3+ /Fe TOT , and its slope to K2.

K1 is directly given by the linear trend between Fe 3+ /Fe TOT and I 930 (Fig. 3), and is equal to 0.2435(23), while K2 equals 0.00624(29). It then is trivial to determine K0 as 0.111(27).

Using these parameters, it is possible to plot iso-redox curves of IFS(M) versus I 930 , as shown in Fig. 9. A visual inspection indicates that the natural samples have a mean Fe 3+ /Fe TOT value ~ 0.1, although there is significant scatter. Manipulating eq. ( 7) to extract Fe 3+ /Fe TOT values for natural MORB from K0, K1, K2 and I 930 yields a mean Fe 3+ /Fe TOT of 0.090(67).

Discussion

Both conventional methods (Intensity, Mixing) and machine learning algorithms (ALS MCR, Kernel Ridge, Support Vector and Neural Network) allow Fe 3+ /Fe TOT to be determined from the Raman spectra of glasses, with fixed major element composition, with uncertainties < 0.04 ( The determination of Fe 3+ /Fe TOT in natural MORB glasses requires a correction for the effect of composition on the Raman spectra (Figs. 8B, 9, eq. 7). The corrected mean value of Fe 3+ /Fe TOT = 0.090( 67) is in agreement with the latest XANES and wet chemistry measurements [START_REF] Bézos | The Fe 3+ /ΣFe ratios of MORB glasses and their implications for mantle melting[END_REF][START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF][START_REF] Zhang | Determination of Fe 3+ /ΣFe of XANES basaltic glass standards by Mössbauer spectroscopy and its application to the oxidation state of iron in MORB[END_REF]. In particular, this estimate is in close agreement with the XANES estimate of 0.10(1) reported by Berry et al. (2018) for the same set of samples, which suggests an average fO 2 for MORB of 0.1 above the quart-fayalite-magnetite redox buffer.

Raman spectroscopy can thus provide reasonable estimates of Fe 3+ /Fe TOT in glasses, as long as the effect of glass chemistry is considered. However, the present results do not achieve the precision of Fe K-edge XANES, Mössbauer spectroscopy or wet chemistry for natural samples with variable chemical composition. While eq. ( 6) is valid for MORB glasses, it is probably not suitable for determining Fe 3+ /Fe TOT in other compositions. However, with a set of appropriate standards, Raman spectroscopy could be used to quantify Fe 3+ /Fe TOT in any composition through the use of a chemical correction similar to that of eq. ( 6).

Implications

Machine learning techniques do not seem to be advantageous relative to conventional approaches for quantifying Fe 3+ /Fe TOT in glasses with fixed standard composition by Raman spectroscopy. However, their ease of implementation and flexibility (the problem can be linear or not) make them preferable to other user-defined techniques when the functional form of the problem is unknown. In particular, the sensitivity of Raman spectra to glass structure can be used to determine glass composition. Di [START_REF] Genova | Approximate chemical analysis of volcanic glasses using Raman spectroscopy[END_REF]2016) proposed use of the mixing method to determine the composition of natural glasses from their Raman spectra. This required a post-analysis step in the data treatment as the mixing ratio of endmember spectra varied non-linearly with glass composition. In the present case, we trained a neural network to directly link the corrected 850-1140 cm -1 Raman signals ( [START_REF] Genova | Approximate chemical analysis of volcanic glasses using Raman spectroscopy[END_REF]2016). The approach could allow Raman spectroscopy to be used in situ to analyse erupting basalts forming pillow lavas with glassy rims at ocean ridges, using submersibles equipped with Raman spectrometers already developed for deep sea water analysis (e.g. [START_REF] Brewer | Development of a laser Raman spectrometer for deep-ocean science[END_REF][START_REF] White | Development and deployment of a precision underwater positioning system for in situ laser Raman spectroscopy in the deep ocean[END_REF][START_REF] Du | Feasibility investigation on deep ocean compact autonomous Raman spectrometer developed for in-situ detection of acid radical ions[END_REF], or for using Raman spectrometers as chemical probes during missions on planets or moons with dense atmospheres. The fact that all data processing performed in this study uses Python, a programming language that can be easily used in embedded systems would facilitate uptake.

The present approach should be easy to implement in any system operating a portable Raman spectrometer. S1). The red dotted line is the spectrum of the glass standard with Fe 3+ /Fe TOT = 0.10(1). B) I 930 as a function of the concentration (wt%) of MgO + CaO in the glasses.

  Fig. 8A) to the measured concentrations of major elements in the natural MORB glasses (supplementary materials), without any additional data manipulation. The results from one of the trained neural networks are shown in Figure 10. The network was able to predict the chemistry of MORB glasses with maximum errors of ~ 1 mol%. This result suggests that Raman spectroscopy may be developed as a chemical probe. It also demonstrates the usefulness of neural networks for such calculations, as the algorithm directly provides the glass composition without intermediate data analysis steps, as required by the method of Di

Figure 1 :

 1 Figure 1: Raman spectra of synthetic MORB basaltic glasses; the colors indicate Fe 3+ /Fe TOT . Each spectrum corresponds to the mean of five spectra acquired for each sample. The dashed lines labelled A-G mark the position of peaks and shoulders (see text).

Figure 2 :

 2 Figure 2: A) Example of the treatment of the 800-1300 cm -1 sections of the Raman spectra that was performed prior to any calculation. The linear cut-off baseline (red dotted line) joins the sample signals at 850 and 1140 cm -1 . Any intensity below this baseline is removed from the data. B) Intensity from 850-1140 cm -1 after baseline subtraction. This background subtracted region of the spectra was normalised between 0 and 1.

Figure 3 :

 3 Figure 3: Normalised intensity at 930 cm -1 in the Raman spectra of the glasses as a function of the oxidation state of Fe. The line is a linear fit to the data. If not visible, errors are smaller than the symbols.

Figure 4 :

 4 Figure 4: A) Comparison of the mean spectrum at Fe 3+ /Fe TOT = 0.41 (black line) and of fit (dotted red line) as a linear combination of the oxidised (S OX ) and reduced (S RED ) spectra (Mixing method); residuals between the data and fit are shown in the bottom panel. B) Fraction of the oxidised endmember spectrum, F OX , as a function of the oxidation state of Fe in the glasses. The line is a linear fit to the data. If not visible, errors are smaller than the symbols.

Figure 5 :

 5 Figure5: Results of the tests performed with the ALS MCR algorithm, using variable subsets of (A) D n,m and (B) initial S k,m spectra. In (A), the root-mean-square deviations between the predicted and measured Fe 3+ /Fe TOT for the entire dataset, RMSD Fe 3+ /Fe TOT , is represented as a function of the mean and range of the Fe 3+ /Fe TOT values of the subset of data. In (B), it is represented as a function the mean and difference of Fe 3+ /Fe TOT of the two initial S spectra. . Black points show where calculations were made; lines and colors were obtained by triangular interpolation.

Figure 8 :

 8 Figure 8: A) Normalised baseline-subtracted Raman spectra of 42 natural MORB glasses (see TableS1). The red dotted line is the spectrum of the glass standard with Fe 3+ /Fe TOT =

Figure 9 :

 9 Figure 9: I 930 as a function of the mean ionic field strength of modifier cations, IFS(M) for natural MORB glasses (open symbols) and MORB standards (solid symbols). Dotted lines represent the values of the model (eq. 7, see text) that links I 930 to IFS(M) and Fe 3+ /Fe TOT in MORB glasses. The colors reflect the Fe 3+ /Fe TOT ratio (see colorbar).

Figure 10 :

 10 Figure 10: Neural network predicted versus measured composition of natural MORB glasses. The standard deviations between the measured and predicted values for each subset are given for each compositional component.

  Table1). The combination of all six methods gives a precision of 0.02. The Intensity and Mixing methods are simple and provide accurate results. The machine learning methods performed well despite being trained with a limited set of samples. The ALS MCR method may be useful if the Fe 3+ /Fe TOT values of the glass standards are unknown, or if endmember spectra are not available. Kernel Ridge, Support Vector and Neural Network regression algorithms relate Fe 3+ /Fe TOT of the glasses to variations in their Raman spectra without any assumptions about the form of the variations. Pooling the results from multiple data reduction protocols is recommended for maximizing the robustness of Fe 3+ /Fe TOT determinations for glasses with fixed composition.

Table 1 :

 1 Synthesis oxygen fugacity at 1400 ˚C, and relative to the quartz-fayalite-magnetite (QFM) buffer, of MORB glass standards[START_REF] Berry | A reassessment of the oxidation state of iron in MORB glasses[END_REF], together with the Fe 3+ /Fe TOT values determined by Mössbauer spectroscopy (± 0.01), and by Raman spectroscopy using the Intensity (Int.), Mixing (Mix.), ALS MCR (A.M.), Neural Networks (N.N.), Kernel Ridge

	(K.R.) and Support Vector (S.V.) techniques. Root-mean-squared deviations (RMSD, 1) of
	the different Raman methods are indicated at the bottom; *calculated for the training data
	subset;  calculated for the testing data subset.
	log fO 2 QFM	Fe 3+ /Fe TOT Mössbauer Int. Mix. A.M. N.N. K.R. S.V.
	4.8	11.2	1.000	1.01 0.99 1.01 0.97 1.00 0.97
	0.00	6.38	0.773	0.75 0.73 0.75 0.77 0.77 0.75
	-1.00	5.40	0.661	0.66 0.63 0.65 0.66 0.66 0.66
	-2.00	4.40	0.537	0.53 0.51 0.53 0.54 0.54 0.54
	-3.07	3.32	0.414	0.43 0.42 0.43 0.43 0.42 0.44
	-4.00	2.39	0.250	0.26 0.25 0.27 0.23 0.27 0.28
	-5.00	1.39	0.167	0.16 0.15 0.16 0.14 0.16 0.17
	-6.00	0.39	0.103	0.11 0.10 0.11 0.09 0.10 0.10
	-7.00	-0.61	0.039	0.01 0.01 0.01 0.05 0.04 0.05
	-8.00	-1.61	0.024	0.04 0.04 0.05 0.04 0.03 0.02
	-9.00	-2.61	0.017	0.02 0.00 0.01 0.03 0.02 0.01
	-10.00 -3.61	0.000	0.00 0.00 -0.01 0.02 0.01 -0.01
	-11.00 -4.61	0.000	0.01 0.03 0.01 0.01 0.00 0.01
					0.01* 0.01* 0.02*
			RMSD:	0.02 0.03 0.03	0.04  0.02  0.03 

  Raman Fe 3+ /Fe TOT against 901 Mössbauer Fe 3+ /Fe TOT values for the 902 MORB glass standards. Raman values were 903 obtained from the A) Kernel Ridge, B) 904 Support Vector, and C) Neural Network 905 algorithms. See Table 1 for root-mean-906 square deviations of each dataset. If not 907 visible, errors are smaller than the symbols.

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	Figure 7: 908
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Acknowledgement

The Department of Mineral Sciences, Smithsonian Institution, of thanked for providing the samples of MORB glass. H.O.N thanks the Australian Research Council for the award of a Laureate Fellowship (FL130100066). C.L.L. thanks Guil Malmann for helpful discussions.