A Raman spectroscopic tool to estimate chemical composition of natural volcanic glasses

Abstract A correlation between Raman spectra of silicate glasses and their chemical composition is investigated using a collection of 31 natural multicomponent silicate glasses. The sample suite comprises the largest database of Raman spectra collected on natural volcanic materials and spans subalkaline to Na-rich and K-rich alkaline compositions. Raman spectra were acquired using an Ar/Ar source green laser having an excitation wavelength of 532 nm. The model was verified against an independent database of 8 additional samples (i.e. not used for calibration). Ratios of Raman peaks (R, Rn) retrieved from spectra are shown to have a strong covariance with concentrations of six oxides (SiO2, TiO2, Al2O3, FeOT, MgO and CaO) across the compositional range of the sample suite. The Raman ratios are also strongly correlated to pseudo-structural parameters (e.g., NBO/T, SM) calculated from oxide concentrations of SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O and K2O. The Raman ratios are relatively insensitive to variations in Na2O and K2O contents and, as a consequence, their concentrations can only be estimated if additional independent constraints on chemical content are available. This work constitutes the first generalized model for retrieving chemical compositions of natural glasses from corresponding Raman spectra. The model provides a rapid, robust and inexpensive way to retrieve compositions of volcanic glasses in both laboratory and field environments and thus represents a powerful new tool for earth and planetary, archaeological and glass sciences.


Introduction
Interest in the application of Raman spectroscopy to geosciences has increased substantially over the last decades. Raman spectroscopic analysis is non-destructive, and it is a relatively straightforward and flexible analytical technique for rapid characterization of geologic materials, including minerals, glasses, fluids, and organic materials (e.g., Mysen et al., 1982a;Roberts and Beattie, 1995;Zotov and Keppler, 1998;Dubessy et al., 2012;Giordano et al., 2019). The advantages of Raman spectroscopy include the following: (i) samples require little to no preparation; (ii) samples can be small (few microns), and (iii) a high spatial resolution allows detailed mapping of samples (Bernard et al., 2008;Giordano et al., 2020). In recent years, the possibility of deploying portable or remotely-operated Raman spectrometers has created the opportunity for exploration in inaccessible environments (e.g. hazardous areas, subsurface environments, oceans, space) (Pasteris et al., 2004;Jehlička et al., 2008;Wei et al., 2015;Rull et al., 2017). In such applications Raman spectroscopy is capable of working from distances up to 200 m, and some studies suggest the possibility of performing long range analysis (hundreds of km) of exposed land surfaces in orbital planetary surveys (Simon et al., 2003;Klein et al., 2004;Tarcea et al., 2008;Angel et al., 2012;Rossano and Mysen, 2012;Sharma et al., 2013). Raman spectral analysis has also been used successfully to obtain structural information during high temperature experiments involving melts or glasses (Mysen and Frantz, T by volcanic processes (Dingwell, 2003), by meteorite impact (Koeberl, 1986), or by lightning strikes (i.e., fulgurites, Carter et al., 2010;Pasek et al., 2012). Lunar glasses of both volcanic and impact origin, for example, were among the first materials collected during the Apollo missions and have provided important constraints on the composition of the lunar interior and the origin of the Earth-Moon system (Shearer et al., 1991). Commercial glasses are diverse in composition, properties and uses and are an ever more important industrial product for our modern society (Calas et al., 2006;Galoisy, 2006;Wadsworth et al., 2013).
Raman spectroscopy is sensitive to molecular vibrations in the target material which can reveal the structure and chemistry of glasses. Recent Raman-based studies of the molecular structure of glasses, melts and minerals and their correlations with the physical properties include Le , Giordano and Russell (2018), Giordano et al. (2019Giordano et al. ( , 2020. Recent efforts have provided specific baseline fitting and spectra treatment routines in support of estimating abundances of dissolved water (Thomas, 2000;Behrens et al., 2006;Mercier et al., 2009Mercier et al., , 2010Le Losq et al., 2012;Schiavi et al., 2018) and carbon dioxide contents (Morizet et al., 2013), determining sulfur speciation (Klimm and Botcharnikov, 2010), iron oxidation state (Di Genova et al., 2016a: Le Losq et al., 2019, and the detection of nanolites (Di Genova et al., 2017). Raman spectra have also been shown to be predictors of melt viscosity and fragility (Le Giordano and Russell, 2018;Giordano et al., 2019) and thermal history . For a review on the applications of Raman spectroscopy to natural silicate melts and glasses see Giordano et al. (2020).
The use of Raman spectroscopy for determining the compositions of natural silicate glasses is, in contrast, underdeveloped. Previous attempts to relate Raman spectra to glass composition have been limited to narrow ranges of composition. Di Genova et al. (2015) investigated the correlations of Raman spectra to composition along a single mixing line resulting from chemical diffusion in experimental melts. They used an ideal mixing equation to parameterize Raman spectra as a function of a Raman parameter R p , using the whole spectrum, modelled by simple 2nd to 4th order polynomials (Di Genova et al., 2015, 2016b. Their insights are valuable, but their results cannot be extended beyond their array of binary mixed compositions. More recently, Le Losq et al. (2019) implemented a machine learning approach to predict compositions of natural MORB basalt glasses, restricted to a range in SiO 2 from 50 to 56 wt%. The main challenge in estimating chemical compositions from Raman spectra is due to the fact that melt structure has a low sensitivity to small changes in composition whereas the spectra are highly sensitive to variations in structure. Raman spectra of glasses have only a few characteristic bands, and these commonly depend on several factors, making the separation of their effects a challenging task.
At present the current database for natural multicomponent glasses is sparse. Furthermore, there is no single standard protocol for the treatment of the raw Raman spectra. Several online, open access databases of Raman spectra (e.g., the RRUFF Project; Downs, 2006, available at http://rruff.info/ or The Handbook of Raman Spectra for Geology, http://www.geologie-lyon.fr/Raman/index. php) and machine learning tools for mineral recognition (Carey et al., 2015) are available or being developed and can potentially lead to a common protocol for the treatment of Raman spectra of glasses. For this purpose, a number of open source software libraries are available, such as Rampy in Python (github.com/charlesll, including machine learning algorithms) or Chemospec in R (https:// cran.r-project.org/web/packages/ChemoSpec/index.html).
Here, we explore the correlation of Raman spectra, obtained with a green laser source, to the chemical composition of silicate glasses. Our analysis is based on a database of remelted dry, multicomponent volcanic glasses of natural compositions covering a wide range of compositions. In our approach, we develop a series of empirical equations that relate the molar oxide contents to the intensity ratio of the low wavenumber band and the high wavenumber band associated with bonding in the silicate network (R) parameterized in terms of its normalized value (R n ). Values of R n are obtained by normalizing R to a reference glass. In our database normalization has been performed based on spectral features of an obsidian from Newberry volcano (NWB) (e.g. Giordano et al., 2019Giordano et al., , 2020Giordano and Russell, 2018;Mercier et al., 2009Mercier et al., , 2010. Our contribution constitutes the first attempt to provide a predictive model for the retrieval of silicate glass and melt chemistry from Raman spectroscopy over the whole range of natural volcanic glass compositions. The proposed protocol only requires a simple and quick spectral processing (a few minutes) and therefore is likely to find widespread use in the fields of Earth sciences, material science research and in industrial activity.

Raman spectroscopy
Raman spectra were collected using a confocal integrated macro/ micro Raman spectrometer LabRam HR800 spectrometer (manufactured by HORIBA JOBIN YVON), equipped with a Peltier-cooled CCD detector and edge filters, located at the Interdepartmental Centre "G. Scansetti" (Department of Earth Sciences, University of Turin). The solid-state Nd laser has a power of 80 mW and a wavelength of 532 nm (green light). A slit of 300 μm and a grating of 600 grooves/ mm were used, resulting in a spectral resolution of 1.7 cm −1 . Spectra were collected in confocal setting with a hole of 200 μm and the laser was focused on the sample through an Olympus BX41 microscope with an objective producing 20× (spot size resolution of ca. 5 × 5 × 15 μm; power at the sample surface of ca. 17.1 mW). Exposure times were of 5x30s. The calibration of the instrument was checked at the beginning of each analytical session using the 521 cm −1 silicon band. Laser power at the sample surface was checked using a COHERENT "LaserCheck" pen. Spectra were acquired in the 100-1800 cm −1 range (further details can be found in Giordano et al., 2019).

Spectra processing
The shape of Raman spectra of silicate glasses in the low frequency domain (20-1500 cm −1 ) is strongly controlled by the structure of silicate glasses at the molecular level, which in turn is defined by the bulk chemical composition of the glass. Two main Raman bands related to the aluminosilicate glass network are observed. The low wavenumber (LW) band is present at wavenumbers in the range 150-650 cm −1 , which has been attributed to low energy bending vibrations of bridging oxygens in a T-O-T configuration, or to angular deformation of TO 4 groups in a O-T-O configuration (Geissberger and Galeener, 1983;McMillan and Hess, 1990;Ruiz et al., 2002;Ardia et al., 2014). This domain shows a strong signal centred at ca. 500 cm −1 , and sometimes a shoulder at ca. 600 cm −1 . This shoulder, assigned to breathing vibrations of rings constituted by three tetrahedra, has been shown to increase with K + substitution for Na + in highly polymerized glasses . In addition, a high wavenumber (HW) region is visible in the range 850-1250 cm −1 , related to stretching vibrations of (Si, Al)-NBO and (Si, Al)-BO bonds (Mysen et al., 1982b;McMillan, 1984a), where NBO and BO denote non-bridging and bridging oxygens, respectively. The shape of the HW region results from the combined contributions of tetrahedral units with n bridging oxygens (Q n species).
Raman spectra shape and Q n -species distributions are strongly affected by the presence of ferric iron (Fe 3+ /Fe tot ratio) acting as a network former. Recently, Di Genova et al. (2016a) and Le Losq et al. (2019) have explored the effect of iron speciation in basaltic and rhyolitic glasses in the HW region. These authors showed that the intensity of the band at ca. 970 cm −1 rises to significantly higher values as the Fe 3+ /Fe tot ratio increases. This effect is much more intense in rhyolitic glasses but it is also noticeable in MORB basalt glasses (Di Genova et al., 2016a;Le Losq et al., 2019;Di Muro et al., 2009).
To date, different procedures for baseline correction have been used depending on the specific target of interest, (for a review, see Rossano and Mysen, 2012). Here, we employ the method utilized by Giordano et al. (2019) which was first introduced by Mercier et al. (2009Mercier et al. ( , 2010 for data processing and baseline subtraction. The reader is referred to those sources for additional details. Briefly, the method relies on correcting spectra through the employment of a third order polynomial baseline with four anchor points at 200-300 cm −1 , 650 cm −1 , 800 cm −1 and 1200-1300 cm −1 . Supplementary Fig. S3 shows that the correction of spectra proposed by Long (1977) for analytical conditions does not produce any observable difference in final data quality.
After baseline subtraction, the intensities of the peaks of the LW and HW domains of the spectrum were considered. We have chosen to use peak intensities of the broad bands over peak area on the basis of the high covariance between peak intensity and chemical parameters including NBO/T or SM. The covariance between peak area and chemical parameters are less strong because area measurements are less precise since they are more affected by spurious signals .
We use the Raman ratio (R) as the index to which chemical compositions can be related. R is defined as the ratio of intensities of the LW and HW regions of the silicate band in glass spectra (R = I LW / I HW ) (Rossano and Mysen, 2012;Mercier et al., 2009Mercier et al., , 2010Di Muro et al., 2009;Giordano et al., 2009). The LW region is sensitive to T-O-T bending, which becomes weaker in depolymerized glasses, while the HW increases its intensity in depolymerized glasses, making R a sensitive parameter for glass composition. However, the absolute value of R is not unique; it is sensitive to spectrometer type and even the analytical conditions. We therefore used a normalized ratio R n where R values are normalized to the value of a reference sample . Here, we use sample NWB which is a calcalkaline, slightly peraluminous rhyolite. Following this simple procedure, interlaboratory variations are erased, and comparison between spectra from different systems becomes possible .
A further advantage of this procedure is that the values of R n are independent of whether or not the Long correction is used (more details in Section 4.1). Further discussion on the use of the R n parameter is discussed in detail in Section 4.3.

The database
In this study we used a set of 31 multicomponent, dry glasses of natural compositions. The sample set is based on that published by Giordano et al. (2019). The selected glasses were prepared by remelting natural samples at high temperature in ambient pressure furnaces working on air. Compositional details of the investigated glasses are reported in Table 1. The materials investigated range from depolymerized, silica-poor, basaltic and tephritic glasses to highly polymerized, silica-rich, rhyolitic glasses and from subalkaline to peralkaline affinity.
Further compositional and volcanological details of all investigated compositions can be found in previous works (Davì et al., 2009;Piochi et al., 2009;Vetere et al., 2007Vetere et al., , 2015González-García et al., 2017;Giordano et al., 2019). Here we show (Fig. 1) the compositional variation of all investigated samples according to the Total Alkali Silica (TAS) grid (Le Bas et al., 1986). Samples were subdivided into three distinct groups belonging to the subalkaline and the alkaline series. The subalkaline series comprises eight specimens ranging from tholeiitic basalt to calk-alkaline andesite to rhyolite. The alkaline series includes eight transitional to alkaline glasses varying from trachybasalt to trachyte and a group of fourteen highly alkaline specimens that range in composition from basanite to phonolite. Based on their relative proportion of Na 2 O and K 2 O this group can be subdivided as a sodic-transitional series (4 specimens: SKHN418; R389_2511; NYI, Mercato, EIF), and a potassic-ultrapotassic series (10 specimens, mostly from Vesuvius and Campi Flegrei) ( Fig. 1b and Table 1), respectively. One clear outlier is NYI, an alkali-rich foiditic glass prepared from a sample of the 2002 Nyiragongo (DRC) eruption (Giordano et al., 2007). Most samples are metaluminous (Fig. 1c) except for NWB (peraluminous rhyolite) (P.I. > 1) and NYI, Td_ph and PVC, (peralkaline) (Best and Christiansen, 2001).

Table 1
Compositions and structural parameters of studied glasses and relationship with the Raman shift values (cm −1 ) associated to the main Raman bands. R n = normalized Raman Ratio; LW, MW and HW: intensities of the low wavenumber, medium wavenumber and high wavenumber, respectively. NBO/T: non-bridging oxygens per tetrahedron (Mysen, 1988); SM: sum of structural modifiers ; SCFM: empirical compositional parameter (Walter and Salisbury, 1989

Effect of Long correction on Rn
The correction proposed by Long (1977) is widely used in Raman spectroscopic analyses and allows to correct spectra for analytical conditions. It is expressed as follows where I obs is the measured intensity, ν 0 is the wavenumber (i.e. the frequency divided the speed of light) of the incident laser light, ν is the measured wavenumber (cm -1 ), h is the Planck constant (6.62607 x 10 -34 J·s), c is the speed of light (2.9979 x 10 10 cm/s), k is Boltzmann's constant (1.38065 x 10 -23 J/K) and T the sample temperature (in K). Its main advantage is that it eliminates the Rayleigh scattering peak, allowing to resolve features in the low frequency region, and in addition, baseline subtraction becomes easier. In order to clarify the influence of Long's correction in the calculation of Raman ratios as defined in the present work, we carried out a comparative study on 9 samples representative of the compositional spectrum covered by our database.
After application of the Long correction to the raw Raman spectra, a procedure analogous to that followed in the data treatment was followed. Fig. 2 allows to compare the Raman ratios obtained both with and without the implementation of the Long correction. The results show clearly that the relationships between Raman ratios calculated from Long-corrected and uncorrected spectra is linear, with an extremely high correlation (R 2 = 0.99). Moreover, the normalized Raman ratios (R n ) obtained from bot procedures are virtually identical, allowing us to conclude that the Long correction does not have any effect on the value of R n , strengthening the validity of our approach.

Raman spectra
To explore how the shape of Raman spectra varies with glass composition, we have compared selected representative spectra from samples covering the entire compositional range (Fig. 3). A systematic variation in the shape of spectra is observed with chemical composition, from silicic to mafic glasses. The LW band is most prominent in silicic glasses (e.g. NWB), consisting in one wide band with a main peak at ~480-490 cm −1 . A weak shoulder is visible at ~580 cm −1 . As compositions become more mafic, the LW band intensity decreases and the position of the main peak shifts towards higher wavenumbers, moving to ~520 cm −1 in the basaltic compositions (Fig. 4). Accompanying this shift, the LW domain evolves from a single peak in silicic glasses towards a mildly bimodal shape in mafic glasses. This transition is achieved by the progressive increase of the influence of the 580 cm −1 shoulder relative to the main LW peak. In the basaltic glasses, the shoulder becomes the most intense in LW region. However, the absolute intensity of the LW band diminishes from silicic to mafic glasses.
The HW domain experiences a similar but inverse evolution. Spectra of silicic glasses show a broad band shape, with two peaks at 960 cm −1 and 1100 cm −1 . This shape evolves towards a unimodal shape in the mafic glasses, reflecting the different contributions of the various Q n species (Fig. 3). The position of the main peak also shifts from 965 cm −1 in basaltic materials to ca. 1000 cm −1 in rhyolitic samples, but here the shift with respect to glass chemistry is much weaker than the LW peak (Fig. 4). Contrary to what happens in the LW domain, a correlation between peak intensity and glass composition is not observed.
Aside from these two main domains, an intermediate weaker band (MW) with wavenumbers varying from 690 to 800 cm −1 is also present in all our spectra. The MW domain is attributed to a SieO symmetric vibration with a Si motion against its oxygen cage (Matson et al., 1983;McMillan, 1984b;Kalampounias et al., 2006). As shown in Figs. 2 and 3, its position and intensity are strongly correlated to silica content: peak position shifts to higher wavenumbers (from 690 to 800 cm −1 ) and intensity increases when composition evolves from basaltic to rhyolitic. This behaviour is analogous  D. González-García, et al. Chemical Geology 556 (2020) González-García, et al. Chemical Geology 556 (2020) 119819 to that observed in alkali silicate glasses (Furukawa et al., 1981;McMillan, 1984b;Mysen et al., 1982b).

Correlations between oxides and spectral features
We use the Spearman correlation coefficient (ρ) for non-linear and monotonic correlations to explore the degree of covariance between oxide concentrations and the various spectral features discussed before. Table 2 shows the calculated Spearman coefficients, which can be calculated for monotonic trends. Among the spectral features, R n is invariably the parameter with the strongest covariance with most compositional parameters, and hence we use it as the main spectral proxy for glass composition. Aside from R n , the other spectral parameters discussed in the previous section show a diverse but always weaker correlation to glass composition. Among intensity-based parameters, only the low-wavenumber region (I LW ) seems to be sensitive to oxide concentrations and structural parameters, while I MW and I HW show very low correlations. The position of the LW and MW peak appears to be most sensitive to SiO 2 , FeO T and MgO, but Spearman coefficient are far from that of R n (|ρ| 0.81-0.83). The MW peak position is also sensitive to FeO T and MgO (ρ = 0.91). On the other hand, the HW peak position does not show good correlation with any of the individual oxides, oxide groups or compositional parameters (|ρ| < 0.62). Overall, alkalis do not correlate linearly with any of the considered parameters (Table 2).
In our dataset, R n varies between 0.08 and 1.20, with the lowest value corresponding to an Oceanic Island Basalt (OIB) (Piton de La Fournaise; Kolzenburg et al., 2019) and the highest value corresponding to a rhyolite (Lipari_RR; Gottsmann et al., 2002). Fig. 3 shows that R n values are low in mafic glasses and high in silicic glasses. Fig. 5 shows the Relationship between the normalized Raman ratio R n and major element concentration in mol%. Solid lines are exponential fits, and dashed lines represent uncertainties of ± 10% for SiO 2 and SiO 2 + Al 2 O 3 , ± 30% for FeO T , MgO and CaO, and ± 50% for TiO 2 , as a guide.
D. González-García, et al. Chemical Geology 556 (2020) 119819 relationships between R n and the main oxide components (expressed in mol%) ( Table 1). Values of R n can be correlated to and can track changes in the concentrations of most oxides and compositional indexes (Fig. 5). In all cases the alkaline and mildly alkaline samples associate with R n < ca 0.8, subalkaline samples span the entire spectrum of R n values. For our suite of glasses, chemical composition correlates strongly with R n values. Specifically, SiO 2 shows a strong positive covariation with R n values whereas the oxides TiO 2 , FeO T , MgO and CaO show a negative covariation (Figs. 4 and S1 in the Supplementary information). The corresponding Spearman correlation coefficients (ρ) (see Table 2) have absolute values above 0.93. For Al 2 O 3 contents, R n values define a concentration maximum at R n values of 0.4. This trend mirrors the behaviour already observed in Harker diagrams, where a maximum in Al 2 O 3 content is observed at 65 mol % (i.e. 54 wt%). R n also shows a poor positive correlation with total alkali content (ρ = 0.54) and in particular with Na 2 O, where only a very rough positive correlation is observed. As expected, different magma series follow diverse alkali trends, a consequence of the different evolutionary paths in different magma series and/or tectonic settings. Taken independently, samples of the comagmatic series of Vesuvius (e.g. Ves_W, Ves_G, 1906; Mercato, Pompei_TR, Pollena GM and Polena_TR) and Campi Flegrei (AMS, MNV, IGC, Fr_A, AS20, ATN) show good alkali correlations with R n values.
We have also explored the correlation of R n with common structuralrelated parameters. Here we use NBO/T (Rossano and Mysen, 2012), SM  and SCFM (Walter and Salisbury, 1989) as parameters reflecting the degree of polymerization of the melts. NBO/T is calculated as (2·O − 4·T)/T (where O are the mole of oxides and T the moles of cations in tetrahedral coordination). SM is defined as the sum (mol%) of all those oxide components which are considered structural modifiers. For both SM and NBO/T parameters, iron (in wt%) has been equally partitioned between FeO and Fe 2 O 3 , so that Fe 2 O 3 /FeO T = 0.5. Partitioning is required as iron plays a role of network modifier or network former as a function of redox state (FeO acting as network modifier, and Fe 2 O 3 as network former; Giordano and Dingwell, 2003). The applied partitioning fits reasonably well with the average iron oxidation state of most of the anhydrous glasses synthesized under atmospheric conditions Giordano et al., 2019). On the other hand, SCFM is an empirical parameter commonly used in spectroscopic surveys of planetary surfaces (Cooper et al., 2002;Pisello et al., 2019) and it is calculated as: where the oxides are expressed in wt%. The selected compositionally predicted structural parameters also provide high values of the Spearman coefficient, confirming their excellent correlation to most of Raman features analysed, especially R n (ρ = −0.97).

Raman models for glass composition
On the basis of the high covariance between Raman spectra and bulk glass compositions (Fig. 5, Table 2), we have developed a model for predicting glass composition (mol% oxide) from measured values of R n . The model comprises a series of six exponential functions (Fig. 5) that relate components SiO 2 , TiO 2 , FeO T , MgO, CaO and the sum SiO 2 + Al 2 O 3 to R n and have the form: where C is the concentration in mol% of the oxide or combination of oxides (Table 1), and C 0 is the base concentration where R n approaches infinity (i.e. for I HW ➔ 0 or high I LW ). The model parameters C 1 and C 2 are specific to each oxide. In particular, C 1 represents the maximum contribution (I LW ➔ 0 and high I HW ) of the structural modifier cations at R n = 0, whereas C 2 is the weighting of R n to concentration for each oxide. Fits were obtained in QtiPlot v. 1.0.0-rc9 software with Eq. (3) and using a statistically weighed Levenberg-Marquardt least-squares algorithm. Fit parameters for each single oxides or combination of oxides (e.g. SM, NBO/T, SCFM) are provided in Table 3.
The best fit is observed for SiO 2 , where the model fits most data with an RMSE of 2.75 mol% (ca ± 10% accuracy). For the remaining oxides, most data points fall within ± 30% (FeO T , MgO, CaO) to ca. ± 50% (TiO 2 ). The best observed fit corresponds to the SiO 2 + Al 2 O 3 value (RMSE = 2.68 mol %). Al 2 O 3 can be obtained by subtracting the SiO 2 model from the Al 2 O 3 + SiO 2 model, yielding an RMSE value of 1.08, with most data points being within a relative error of ± 15% of the model. Calculated RMSE values for each oxide are reported in the figure panels. Table 3 summarizes Table 3 Parameters of model fits for both the general model and the alkalis model. Exponential fits follow the equation C = C 0 + C 1 *exp(-C 2 *R n ), where C is the concentration in mol%, C 0 , C 1 and C 2 the fitting parameters, and R n the normalized Raman ratio. The alkalis linear fit of the subalkaline series was obtained using the equation C = C 0 + C 1 *R n . Unless specified, parameters are given in mol%.  González-García, et al. Chemical Geology 556 (2020) 119819 the function parameters obtained from fitting each function. The different degrees of accuracy reflect the fact that Raman spectroscopy is most sensitive to the molecular structure of glasses, which is dominated by vibrational contributions of SiO 2 and Al 2 O 3 . The remaining melt components have more subtle and diverse effects on melt structure resulting from their mutual interactions and their interaction with the main tetrahedrally coordinated cations. The quality of the fits increases substantially when components are grouped according their structural significance. Incorporating TiO 2 with SiO 2 and Al 2 O 3 produces a slightly improved exponential fit. A slightly improved model curve is also obtained by summing the alkaline earth oxides (CaO + MgO) ( Table 2, Supplementary Fig. S3).
Pseudostructural parameters have been shown before to correlate well to R n (Mercier et al., , 2010Giordano and Russell, 2018;Giordano et al., 2019). In our dataset, NBO/T, SM and SCFM produce well-defined trends increasing with the value of R n from mafic to silicic melts (Figs. 4 and  5). These simplified parameters can also be considered as first-order proxies to correlate the complexity of the physical properties of silicate and other spectroscopy techniques (Pisello et al., 2019). Modelling NBO/T and SM with Eq. (3) yields notably good accuracies, with R 2 values of 0.94 (Fig. 4, Table 2). Finally, despite working in weight percent, the SCMF parameter is also exceptionally well modelled by the exponential fit (Fig. 6).
The described chemical variation as a function of vibrational features constitutes a pioneering tool for determining approximate chemical compositions of natural glasses on Earth and terrestrial planets and moons. The model spans basalt to rhyolite and from subalkaline to highly alkaline magma series. In fact, the NYI sample is foiditic in composition and represents an extreme glass composition but is reasonably wellmodelled by the exponential decay equations adopted here.  Dashed lines represent uncertainties of ± 0.5 mol% (K 2 O) and ± 1.5 mol% (Na 2 O).

The case of alkalis
Contrary to the remaining oxides, a Raman model for alkali concentrations (Na 2 O, K 2 O and their combinations) is more complicated. The trends between concentrations and R n vary widely for the different magma series. Although there is no single trend, subgroups of samples show better correlations between K 2 O or Na 2 O + K 2 O and R n . Three main groups can be distinguished according to the amount of alkalis present: (1) subalkaline series; (2) mildly alkaline series, and (3) alkaline series of potassic affinity. Alkaline glasses with sodic affinity (i.e. Td_ph, Mercato and NYI) were not included in this scheme, since the paucity of samples does support a well-defined trend. Fig. 7 shows the same fitting procedure as above for the three subgroups. For this subset, fitting parameters are listed in Table 3.
This approach produces a good fit for K 2 O and Na 2 O + K 2 O for each of the magma series. K 2 O can be modelled to within ± 0.5 mol% for all magma series, a remarkable degree of accuracy (Fig. 8). RMSE is 0.33 for the potassic series, 0.34 for the mildly alkaline and 0.24 for the subalkaline series. The combined Na 2 O + K 2 O data is also well modelled having an RMSE value from 0.56 to 0.75. From these values, it is possible to retrieve the Na 2 O concentration by difference with reasonable RMSE values (0.40-0.70).

Validation dataset
In order to test the validity of the proposed models in an independent manner, we selected a series of eight external samples for which Raman spectra and glass composition are available. This validation dataset includes two widely available standards commonly used in Electron Microprobe or LA-ICP-MS laboratories, the natural glasses VG-2 (basalt) and VG-568 (rhyolite) (Jarosewich et al., 1980;Helz et al., 2014), as well as six remelted samples prepared from natural volcanic rocks from Rattlesnake Tuff (Oregon, U.S.A.), Campi Flegrei, El Hierro (Canary Islands), Merapi and Hawaii. Raman spectra were gathered with three different spectrometers and processed following the procedure explained above and in Giordano et al. (2019). The results of the validation process are summarized in Table 4. Fig. 9 shows that the results obtained are in good agreement with the observations in the calibration dataset and furthermore validate the applicability of the method to spectra obtained with different spectrometers by using the normalized Raman ratio R n . The five components used in the general model are well reproduced, with SiO 2 exhibiting the lowest error (in the order of 2-10%), followed by FeO T (10-15% error). The remaining oxides are reproduced with higher error of 15-40% (especially those showing low abundances). Al 2 O 3 has error of 20% and is slightly underestimated. As observed above, structural parameters NBO/T and SM are very well reproduced, with uncertainties in the order of 15% for SM and ca. 30% for NBO/T, lower than obtained during calibration. On the other hand, TiO 2 shows the largest uncertainty (error up to 50%) due to its low abundance in the investigated samples. Again, the accuracy of the model as a function of SMCF parameter is remarkable; the model predicts SMCF values with a ca. 5% accuracy. Although errors are larger than those obtained in the calibration step for some elements and parameters, the non-calibration samples confirm the validity of the model. It should be emphasised that these spectra were collected using two spectrometers different than the one used for calibration.

Table 4
Validation results using eight samples external to the calibration of the model and carried out in spectrometers at LMU Munich (LMU; Giordano et al., 2019) and CEA Saclay (Mercier et al., 2010;Giordano et al., 2019). Values given in parentheses are the deviation of the model results with respect to analysis. All values, unless otherwise indicated, are in mol%.  D. González-García, et al. Chemical Geology 556 (2020)

Discussion
The proposed model constitutes a first order attempt to predict the composition of natural multicomponent glasses from their corresponding Raman model. The model can be applied to the broad range of compositions found on Earth. However, it has some limitations inherent to the sensitivity of Raman spectra to bulk glass composition of multicomponent silicate glasses and melts, and, likely, to the sample database employed to calibrate the model. A logical extension to this work would be to expand the database to include other compositional suites.
This study utilizes the most diverse Raman database on natural, multicomponent silicate glasses available, but even this database is insufficient to accurately define how Raman spectra evolve with composition. In particular, our sample set has a bias towards K-rich alkaline compositions. Some compositions, such as those belonging to Na-rich alkaline series or subalkaline compositions, are underrepresented with the consequence that our model should be restricted to the range of compositions investigated here. Unusual compositions and those falling largely outside the scope of this work will have a low accuracy. A graphic way of visualizing the relationship between R n and bulk glass compositions can be obtained by a TAS diagram in which R n values are superposed as contour lines (Fig. 10), which can be useful to have a quick guide of glass composition based on Raman spectra. This diagram highlights the variation of R n across the SiO 2 versus Na 2 O + K 2 O field,  Table 3). with low R n for basaltic glasses and high R n for rhyolitic glasses. A single value of R n does not allow to discriminate alkali content, and previous constraints must be known to assign a sample to a particular alkali content (e.g., when the affinity of the studied sample is roughly known beforehand). We note that the SM parameter (the sum of all network modifier cations) shows, a remarkably good correlation with R n . This is in contrast to the behaviour of individual alkalis and alkaline earths, which show moderate to large uncertainty and some outliers are present (e.g. UNZ in MgO and CaO diagrams). It is evident that some kind of interplay exists in the role played by Ca, Mg, Na, K and Fe 2+ in the network modifiers framework, When these oxides are combined, the model trends show few outliers, while taken individually, the overall correlations are poorer (Figs. 5, S3 and S4 in the Supplementary information).
Another potential source of uncertainty is the effect of the oxidation state of iron on Raman spectra. As outlined above, the variation of the oxidation state results in notable variations in the shape of the HW region of the spectrum, notably increasing the intensity of the 970 cm −1 band with the Fe 3+ /Fe tot ratio of the glass (Di Genova et al., 2016a;Le Losq et al., 2019). These changes are most prominent in polymerized silicic glasses (e.g. peralkaline rhyolites), whereas the structure of depolymerized glasses (e.g. basalts) is much less sensitive to oxidation state, due to a complex interrelation between the peaks resulting from Fe 3+ -O stretching and Q 2 units at ca. 950 cm −1 (Di Le Losq et al., 2019). The effect is especially prominent in peralkaline, iron rich rhyolites and, thus, we do not recommend the present approach for this kind of glasses. Given that all glasses in this work were prepared at ambient conditions, and hence at mostly constant oxygen fugacity our calibration should be regarded as optimal in similar conditions, but this fact must be considered when studying natural glasses. Further work is necessary to clarify bulk chemical trends with different iron oxidation states.
The methods developed here should find application in the study of non-volcanic glasses (e.g. pseudotachylites, tektites and other impact glasses, maskelynite, fulgurites). However, for the reasons outlined above, we suggest that only SiO 2 , SiO 2 + Al 2 O 3 , NBO/T, SM, SCFM and other combinations of oxide components can be retrieved with a reasonable degree of certainty in these usually non-igneous derived glasses. The relationships outlined here for the other major oxides may not be applicable because the compositional range we have calibrated on derives from magmatic processes and other glass compositions may lie outside that restricted field.
The prediction of chemical composition from Raman spectra cannot provide the same accuracy as conventional chemical analysis. However, the prediction of glass compositions from Raman spectra is important in some situations and can support new avenues of research: (1) rapid estimation of compositions in the field using in-situ portable devices; (2) new applications where it is not possible to obtain a direct sample, such as planetary exploration, involving in situ analysis from form a rover/lander, or in the study of unexposed melt inclusions; (3) volcanic monitoring programs could use this approach to obtain fast estimates of melt composition during ongoing eruptions by using long-range Raman systems; or (4) direct, in-situ estimates of melt compositions in high pressure, high temperature experimental devices such as diamond cell or heating wire.
In summary, the methodology proposed here is a first and simple approximation to the problem of retrieving glass composition from Raman spectra, which can be easily put in practice. Yet Raman spectra of silicate glasses show a complex pattern, and their analyses can potentially shed more light on the issue. However, the use of whole spectra outside a single mixing line (e.g. Di Genova et al., 2015) is notably more complex to put into practice and would probably require deconvolution techniques, which would add a new level of uncertainty. In this regard Machine learning techniques such that proposed by Le Losq et al. (2019) for basaltic glasses, have a high potential of improving compositional estimations.
Compact portable Raman devices have become increasingly common, and these developments have made possible an entire new range of applications of Raman spectrometers (Hutchinson et al., 2014;Giordano et al., 2020). In fact, Raman spectrometers have been included among the scientific payload in some past and planned Mars rovers such as the Raman Laser Spectrometer (RLS) onboard ESA ExoMars rover, or the Micro-beam Raman Spectrometer onboard NASA Mars2020 rover (Rull et al., 2011(Rull et al., , 2017Wei et al., 2015;Lopez-Reyes et al., 2013), and the availability of a Raman calibration to determine compositions of natural glasses would greatly expand their possibilities.

Conclusions
Here we show that Raman spectroscopy can be used to obtain a quick and approximate chemical composition of natural volcanic multicomponent glasses. This allows us to construct the first general Raman model to derive their compositions, using the normalized Raman ratio R n , as index term. R n correlates best with five oxides (SiO 2 , TiO 2 , FeO T , MgO and CaO) and the sum SiO 2 + Al 2 O 3 , and this allows building a general compositional model covering a wide range of compositions. However, such general model is not possible for alkalis, and instead partial fits are given for different magma series. In consequence, some previous constraints on the chemistry of samples is necessary to obtain probable alkali concentrations. This work expands and complements earlier models available for more restricted glass compositions (Di Genova et al., 2015, 2016bLe Losq et al., 2019) and is of potential applicability in a wide variety of works, from quick exploratory method and monitoring of volcanic activity to planetary exploration.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.