Accounting for the species-dependence of the 3500 cm^–1 H₂O_t infrared molar absorptivity coefficient: Implications for hydrated volcanic glasses Open Access

The dissolved water content of a silicate melt affects a range of magmatic processes, since it exerts a strong influence on melt viscosity (e.g., Hess and Dingwell 1996; Giordano et al. 2008), volatile diffusivities (e.g., Baker et al. 2005; Baker and Alletti 2012), and crystallization (e.g., Hammer 2004; Gualda et al. 2012). Accurate measurement of the water content of silicate glasses is therefore crucial to a wide range of volcanological and petro-logical studies. Additionally, measuring water speciation, i.e., the amount of water present as molecular water (H₂O_m) vs. hydroxyl groups (OH), can provide information about the cooling rate and glass transition temperature (T_g) of a sample (e.g., Stolper 1989; Dingwell and Webb 1990; Xu and Zhang 2002), and whether a sample has been affected by hydration during bubble resorption, or crystallization during cooling (e.g., McIntosh et al. 2014; Nichols et al. 2014), or by secondary hydration at low temperature in the time following deposition (e.g., Dixon et al. 1995; Anovitz et al. 2008; Denton et al. 2009; Tuffen et al. 2010). Whereas most commonly used techniques [e.g., hydrogen manometry, thermogravimetric analysis (TGA), secondary ion mass spectrometry (SIMS)] can measure only total water (H₂O_t) contents, Fourier transform infrared spectroscopy (FTIR) is capable of measuring both total water and water species concentrations.

During transmission FTIR analysis, some infrared light passing through the sample is absorbed by molecules within the sample, with different species absorbing light at different, characteristic frequencies. The resulting FTIR spectrum thus exhibits absorbance bands at wavelengths (or wavenumbers, cm^–1) corresponding to these different absorbing species. There are four main absorbance bands associated with water dissolved in silicate glasses that can be seen in the near- and mid-IR range (Fig. 1), and their assignments are given in Table 1. The H₂O_m and OH bands at 5200 and 4500 cm^–1 have low absorption intensities and are often not detected in glasses that have low water contents or that require thin samples for analysis (e.g., to avoid bubbles or crystals in the beampath). Additionally, these bands can be difficult to measure accurately in intermediate glass compositions where absorptions by Fe cause curvature of the baseline at high wavenumbers (e.g., Stolper 1982b; Ohlhorst et al. 2001; Mandeville et al. 2002), or for samples where the absorptions creating the 4500 cm^–1 band may be complex (Malfait 2009; Le Losq et al. 2015). In many situations therefore the 3500 cm^–1 band is used to measure the total water (H₂O_t) concentration, and water speciation is obtained by measuring the 1630 cm^–1 H₂O_m band and then finding OH indirectly by difference (e.g., Wysoczanski and Tani 2006; Yokoyama et al. 2008; Nichols et al. 2009; McIntosh et al. 2014; Giachetti et al. 2015).

It has been previously noted that, because the 3500 cm^–1 absorbance band is the net result of absorptions by both H₂O_m and OH species (Table 1), the correct molar absorptivity coefficient for that band—termed ε3500—will vary with the ratio of the two species (Newman et al. 1986; Okumura et al. 2003). Since the equilibrium proportions of water species vary with temperature and total water concentration (e.g., Stolper 1982a, 1989), and can be altered by disequilibrium processes such as quench resorption (McIntosh et al. 2014), crystallization (e.g., Nichols et al. 2014), and secondary hydration (e.g., Dixon et al. 1995; Anovitz et al. 2008; Tuffen et al. 2010), the “true” ε3500 value will also vary accordingly, potentially even across the same sample. This accounts for the wide range in ε3500 values reported in the literature, even among glasses of the same composition. For example, rhyolites, which are the most studied composition to date, have reported ε3500 values ranging from 75 to 95 L/mol·cm (Table 2).

To test the accuracy of this new species-dependent ε3500 method we apply it to the published data set of Newman et al. (1986) from which they calculated their end-member ε3500 values for rhyolite. Their data set consists of samples of natural rhyolitic obsidian from tephra deposits, domes, and flows taken from a range of locations in the U.S.A. Thickness data and 5200, 4500, and 3500 cm^–1 absorbances are reported for 28 analyses of 24 different samples, containing 0.27–2.64 wt% H₂O_t as measured by manometry. For these samples, we calculate their H₂O_t and OH concentrations in the conventional way (Eq. 1) using the published 5200 cm^–1 (H₂O_m) and 4500 cm^–1 (OH) absorbance data together with the ε5200 and ε4500 values for rhyolite derived by Newman et al. in the same study (Table 2). These are then plotted against the H₂O_t and OH concentrations of the same samples calculated from the published 3500 cm^–1 (H₂O_t) and 1630 cm^–1 (H₂O_m) absorbances using our new species-dependent method with the values of ε3500_OH and ε3500_H2Om for rhyolite derived by Newman et al. (Fig. 2). We find that there is excellent agreement between H₂O_t and OH concentrations calculated by the two methods, as demonstrated by the excellent fit to the 1:1 line (R² = 0.993 for H₂O_t, and R² = 0.971 for OH). The “true” (species-dependent) ε3500 values for individual samples then calculated via Equation 2 range from 73.6 to 97.2 L/mol·cm, compared to the end-member values of ε3500_OH = 100 ± 2 and ε3500_H2Om = 56 ± 4 L/mol·cm.

Thus to calculate end-member ε3500 values for a given glass composition, it is necessary to have a data set containing 5200, 4500, and 3500 cm^–1 absorbance and thickness data for the same piece(s) of glass, for which the ε5200 and ε4500 values are also known. Since the absorbances are normalized to thickness it is possible to measure the weaker 5200 and 4500 cm^–1 absorbances on a thicker piece of glass and then subsequently thin it to measure the 3500 cm^–1 absorbance. Additionally, it would also be possible to use the 1630 cm^–1 H₂O_m absorbance and ε1630 value in place of the 5200 cm^–1 H₂O_m absorbance and ε5200 value, if necessary.

We demonstrate this procedure by using the published data set of Mandeville et al. (2002) to calculate new end-member ε3500 values for both their Fe-bearing and Fe-free andesite compositions. Their samples are hydrous glasses that were synthesized at high pressure and temperature from either a mixture of natural basaltic andesite and evolved andesite rock powders from Krakatau, or a mixture of pure oxide powders and carbonates; H₂O_t contents were measured by hydrogen manometry (see original study for further details). In their data set, glasses with data for all three bands (5200, 4500, and 3500 cm^–1) include two Fe-bearing andesite glasses, Run 9 (1030 °C, 200 MPa, 4.32 wt% H₂O_t, 28 analyses) and Run 101 (1100 °C, 50 MPa, 1.67 wt% H₂O_t, 13 analyses), and three Fe-free andesite glasses, Run 58 (1100 °C, 200 MPa, 5.68 wt% H₂O_t, 56 analyses), Run 68 (1100 °C, 150 MPa, 2.15 wt% H₂O_t, 11 analyses), and Run 106 (1050 °C, 65 MPa, 1.31 wt% H₂O_t, 9 analyses). From the normalized absorbances of these glasses we used the Linest function in Microsoft Excel to find values of ε3500_H2Om/ε5200 and ε3500_OH/ε4500, as per Equation 5, for each composition, from which the end-member ε3500_OH and ε3500_H2Om coefficients were calculated using the values of ε5200 and ε4500 previously derived and published in the original study (Table 2).

For the Fe-bearing andesite glass compositions reported in Mandeville et al. we thus calculate end-member ε3500 values of ε3500_OH = 79 ± 11 and ε3500_H2Om = 49 ± 6 L/mol·cm, while for their Fe-free andesite composition we calculate values of ε3500_OH = 76 ± 12 and ε3500_H2Om = 62 ± 7 L/mol·cm. Errors were calculated by propagating the standard error on the regression coefficients and the reported error on the ε5200 and ε4500 values used to derive them via Equation 5. Figure 3 compares the H₂O_t and OH concentrations calculated from the 5200 and 4500 cm^–1 bands with those calculated from the 3500 and 1630 cm^–1 bands using both the species-dependent ε3500 method (Eq. 4) with the new end-member ε3500 values (filled symbols) and the conventional method (Eq. 1) with the fixed ε3500 value derived by Mandeville et al. (open symbols). For both compositions, the H₂O_t concentrations calculated using the species-dependent ε3500 method are in slightly better agreement with the H₂O_t concentrations calculated from the 5200 and 4500 cm^–1 bands than the data calculated using the fixed ε3500 value (Figs. 3a and 3c). Meanwhile, the OH concentrations calculated using the species-dependent ε3500 method are in markedly better agreement with the OH concentrations calculated from the 4500 cm^–1 band than those calculated from the 3500 cm^–1 band using the conventional OH-by-difference method. For Fe-bearing andesite the OH-by-difference method gives no correlation with OH concentrations derived directly from the 4500 cm^–1 band (R² = 0.10), whereas the new method gives a much better fit (R² = 0.80; Fig. 3b). The OH data for Fe-free andesite are somewhat more scattered with regards to the 1:1 line, with most of the scatter corresponding to one glass (Run 58a), but the new method again is closer to the gradient of the 1:1 line and provides a better correlation than the OH-by-difference method, with R² values of 0.66 and 0.55, respectively (Fig. 3d).

A previous study by Silver and Stolper (1989) of H₂O in albitic glasses also followed the method of Newman et al. (1986) in determining end-member ε3500 values for the 3500 cm^–1 band, but since they were similar they elected to publish a single fixed ε3500 value instead. For completeness, we use the published Silver and Stolper data set (absorbance data for 5 glasses, synthesized at 1500–2000 MPa and 1400–1600 °C with 1.02–5.12 wt% H₂O_t) to calculate that the end-member ε3500 values would be ε3500_OH = 69 ± 17 and ε3500_H2Om = 71 ± 17 L/mol·cm, compared to the published fixed ε3500 value of 70 ± 2 L/mol·cm (Table 2).

To further test the accuracy of Equation 4 we performed transmission FTIR analyses of three glass standards with independently constrained water contents (NWC, KRA-045-2, Run 10). Chemical compositions and densities of these glasses are reported in Table 3. NWC is a rhyolitic obsidian from the Upper Dome of NW Coulee at Mono Craters, California. A piece of this glass was included in the data set of Hauri et al. (2002) (“NW Coulee”), whose manometry analysis found it to contain 0.297 wt% H₂O_t. KRA-045-2 is a rhyodacitic obsidian matrix glass from the pyroclastic flow deposit of the 1883 Krakatau eruption (Mandeville et al. 1998), which was analyzed by manometry and found to contain 0.48 wt% H₂O_t [C. Mandeville, published in Maria and Luhr (2008)]. Finally, Run 10 is an experimentally synthesized Fe-bearing andesite glass that was part of the data set of Mandeville et al. (2002), whose manometry analysis gives its total water content as 5.78 wt% H₂O_t.

All three glasses were prepared for transmission FTIR analysis as double-polished free-standing wafers. The glass thicknesses of the rhyolite standards (NWC and KRA-045-2) were measured using a digital micrometer with a precision of ±1 μm, with measurements taken at the location of each analysis. Run 10 was too thin, hence fragile, to measure with the micrometer and so thickness was instead calculated from fringes in reflectance spectra following the method of Wysoczanski and Tani (2006) and utilizing a refractive index of 1.55 for andesite (Wohletz and Heiken 1992), with an estimated accuracy of ±3 μm. FTIR spot analyses were performed at the Japan Agency for Marine-Earth Science and Technology, using a Varian FTS 7000 spectrometer and an attached UMA600 microscope. Mid-IR (6000–700 cm^–1) transmittance spectra were collected over 512 scans at a resolution of 8 cm^–1 using a heated ceramic IR source, a KBr beamsplitter and a liquid nitrogen-cooled HgCdTe₂ (MCT) detector. Apertures were used to reduce the beam spot size to 20 × 20 μm. Both the spectrometer bench and microscope were continuously purged with N₂ gas to minimize any interference from atmospheric H₂O. Obtained spectra were then processed using Win-IR Pro software. Band absorbances were determined by measuring the height of the peak above the baseline. For the 3500 cm^–1 band a linear baseline was used, while for the 4500 and 1630 cm^–1 bands baselines were drawn by hand using a flexicurve. H₂O_m concentration was calculated from the 1630 cm^–1 absorbance via the Beer-Lambert law (Eq. 1) using ε1630 values of 55 ± 2 L/mol·cm for rhyolite (Newman et al. 1986) and 42.34 ± 2.77 L/mol·cm for Fe-bearing andesite (Mandeville et al. 2002). OH concentration was then calculated according to Equation 4, utilizing the end-member ε3500 values of Newman et al. (1986) for rhyolite and the newly derived end-member ε3500 values for Fe-bearing andesite. H₂O_t was then calculated as C_H2Ot = C_OH + C_H2Om. For comparison, C_H2Ot and C_OH (using OH-by-difference) were also calculated from the 3500 cm^–1 band via Equation 1 using the range of published fixed ε3500 values (Table 2). For NWC and KRA-045-2 OH concentration was also calculated via Equation 1 from the 4500 cm^–1 band using appropriate values of ε4500 (Table 2).

Table 4 and Figures 4 and 5 show the results of the FTIR spot analyses of the two rhyolite standards, NWC and KRA-045-2, and the Fe-bearing andesite Run 10. Reported values for each sample are the mean value of 12 measurements made on the same wafer. Errors for the rhyolite standards are given as one standard deviation and for the Fe-bearing andesite are derived from the ±3 μm error on the thickness measurement, which becomes the dominant source of error for thin samples. For each glass, the H₂O_t concentration measured by FTIR using both the species-dependent ε3500 method and the conventional fixed ε3500 method is plotted against their known H₂O_t content previously measured by manometry (Figs. 4a and 5a). For all compositions, the species-dependent ε3500 method (filled squares) gives H₂O_t concentrations that are within 5% of the known value, whereas those calculated using fixed ε3500 values from the literature (open squares) span a wide range and differ from the known H₂O_t concentration by as much as 33%.

OH concentrations calculated using the species-dependent ε3500 method and the conventional OH-by-difference method are compared to the OH concentration obtained from the 4500 cm^–1 band (Figs. 4b and 5b). For each glass, H₂O_t concentrations determined by summing the 4500 cm^–1 OH and 1630 cm^–1 H₂O_m concentrations were compared to their manometry H₂O_t concentration (Fig. 4c), with the fit to the 1:1 line used to select the most appropriate ε4500 value from the literature (Table 2). Since the weak 4500 cm^–1 band could not be measured in our thin Run 10 standard we use instead the 4500 cm^–1 absorbance data reported by Mandeville et al. (2002) for the same glass, and the ε4500 value derived in the same study (Table 2). For the rhyolite standards (Fig. 4b) the OH concentrations calculated by the species-dependent ε3500 method (filled circles) are within 12% of the 4500 cm^–1 OH concentration for NWC and within 2% for KRA-045-2, whereas the OH-by-difference concentrations using fixed ε3500 values (open circles) differ by up to 45% and 27%, respectively. For the Fe-bearing andesite Run 10 (Fig. 5b), the species-dependent ε3500 method gives an OH concentration within 9% of that reported by Mandeville et al. (2002). Finding OH-by-difference using the fixed ε3500 value derived by Mandeville et al. (2002) (for the data set that contained Run 10) matches the 4500 cm^–1 value exactly, whereas the OH-by-difference derived using the King et al. (2002) fixed ε3500 coefficient is 39% lower than the 4500 cm^–1 value.

The new species-dependent ε3500 method is able to reproduce accurately the H₂O_t and OH concentrations of both the published rhyolite and andesite data sets (Figs. 2 and 3) and the hydrous glass standards (Figs. 4 and 5; Table 4). For the data sets, the H₂O_t and OH concentrations derived from the 5200 cm^–1 H₂O_m and 4500 cm^–1 OH absorbance bands are not strictly independent measurements since they need ε5200 and ε4500 values to find concentration via the Beer-Lambert law. However, by using the ε5200 and ε4500 values derived from these same data sets in the original studies of Newman et al. (1986) and Mandeville et al. (2002) the resulting concentrations are particularly reliable. The H₂O_t and OH concentrations from the new species-dependent ε3500 method have an excellent correlation with the values derived from the 5200 and 4500 cm^–1 bands, demonstrating the accuracy of this technique (Figs. 2 and 3). For the andesite data sets, the species-dependent ε3500 method gives a better fit than the conventional method using fixed ε3500 values. Although the improvement for H₂O_t is only slight, it is particularly marked for OH, where the species-dependent ε3500 method gives much better agreement with the 4500 cm^–1 OH concentrations than the conventional OH-by-difference method. In particular, the OH-by-difference values for Fe-bearing andesite (Fig. 3b) give no meaningful correlation to the 4500 cm^–1 OH concentrations (R² = 0.10) while the species-dependent method gives a much stronger correlation (R² = 0.79). We therefore strongly recommend the use of the species-dependent ε3500 method for finding the OH concentration when it is necessary to use the 3500 absorbance band to do so.

Similarly, FTIR analysis of the three glass standards using the species-dependent ε3500 method produces H₂O_t and OH concentrations that are within 11% of their independently determined concentrations. The absolute difference is greatest for the Fe-bearing andesite Run 10, where the species-dependent ε3500 method overestimates H₂O_t by 0.11 wt% (Fig. 5a). This discrepancy is most likely due to the need to analyze a thin glass wafer (to avoid saturation of the 3500 cm^–1 band in this water-rich sample), which increases the relative error owing to the thickness measurement and also creates interference fringes, which introduce uncertainty when picking the baseline. Since Run 10 is water-rich however, this error is <2% of the total H₂O_t concentration measured by manometry. By contrast, the H₂O_t concentration calculated for the rhyolite NWC (Fig. 4a) is only 0.015 wt% higher than the manometry value, but due to the low H₂O_t content of this sample the relative difference is higher (5%). Possible sources of error include slight heterogeneity in water content between the chip that was analyzed with manometry and the chip that was analyzed with FTIR, and differences in how the baseline was picked for the 1630 cm^–1 H₂O_m peak (see below). Despite these minor discrepancies, the H₂O_t and OH concentrations calculated using the species-dependent ε3500 method are markedly closer to the independently determined concentrations than some of the concentrations calculated using fixed ε3500 values from the literature, which may differ by up to 45% of the known values. Since using a fixed ε3500 value necessarily implies that OH concentration must be found as OH-by-difference, the resulting errors in H₂O_t concentration are also propagated through as errors in OH concentration.

Since the H₂O_m concentration is needed to calculate the species-dependent ε3500 value, any error in the H₂O_m concentration affects the calculated OH and H₂O_t concentrations. When using the 3500 cm^–1 band, the H₂O_m concentration will generally be determined from the 1630 cm^–1 band. The ε1630 value for rhyolite comes from Newman et al. (1986) (Table 2), who used the spectrum of an anhydrous equivalent of the glass to define the baseline when measuring 1630 cm^–1 absorbances, in recognition of the silicate peak at ~1600 cm^–1 that can interfere with the 1630 cm^–1 H₂O_m peak and may cause the 1630 cm^–1 absorbance to be overestimated if using a linear baseline. In lieu of an anhydrous piece of the same glass, we used a hand-drawn flexicurve baseline pinned to the baseline immediately adjacent to the 1630 cm^–1 peak to account for non-linearity of the baseline. This flexicurve baseline gives an H₂O_m concentration of 0.04 wt% (and subsequent H₂O_t concentration of 0.31 wt%), compared to 0.06 wt% H₂O_m (and 0.32 wt% H₂O_t) if a linear baseline is used. The good agreement of our flexicurve H₂O_m concentration measurement with the H₂O_m concentrations measured by Newman et al. (1986) for NWC (0.05 wt% using 1630 cm^–1 band and 0.03 wt% using 5200 cm^–1 band) validate our method of fitting the 1630 cm^–1 baseline, and the small difference between our FTIR H₂O_t concentration value and the manometry value (0.015 wt%) indicates that its impact is limited. The weak intensity of the ~1600 cm^–1 silicate peak means that significant absorbance is restricted to thick sample wafers, while the relative importance of its interference with the 1630 peak is greatest for samples with low H₂O_m concentrations (McIntosh et al. 2015). The error introduced by the 1630 cm^–1 baseline will therefore be greatest for water-poor samples, but since these samples should contain predominantly OH the ultimate error on the calculated OH and H₂O_t concentrations using the species-dependent ε3500 method will be limited.

The accuracy of the H₂O_m measurement will also necessarily rely on the accuracy of the ε1630 value used to obtain it. When using the 3500 and 1630 cm^–1 bands along with a fixed ε3500 value to find OH concentration as OH = H₂O_t – H₂O_m, the resulting error for the OH concentration may previously have been attributed to an inaccurate value of ε1630, rather than ε3500. We expect that the use of the species-dependent ε3500 method will reduce or remove such apparent discrepancies in H₂O species concentrations, and that the existing literature values for ε1630 in the compositions discussed in this paper will prove to be robust. It is worth noting that there is evidence that the ε values of the 5200 and 4500 cm^–1 bands can vary with H₂O_t concentration (Zhang et al. 1997b; Yamashita et al. 2008). The excellent fit of the H₂O_t and OH concentrations calculated using the species-dependent ε3500 method to the published Newman rhyolite and Mandeville andesite data sets, which span a wide range of H₂O_t concentrations, supports our assumption that the ε3500_H2Om and ε3500_OH values are true end-member values and do not themselves vary with H₂O_t concentration. It is possible however that in the future a similar H₂O_t-dependence will be found for ε1630 in some compositions, in which case we expect that our species-dependent ε3500 method can be adapted to account for it. As an example, we show that the H₂O_t-dependent relationship derived for the 5200 cm^–1 band by Zhang et al. (1997) can be successfully substituted into our method in place of the 1630 cm^–1 band (see Supplementary¹ spreadsheet). In cases where both the 5200 and 1630 cm^–1 bands can be measured for the same glass, we recommend using H₂O_m concentrations calculated from both as input into Equation 4 to check and quantify possible error stemming from the H₂O_m measurement.

The variation in published ε3500 values for a given glass composition therefore results from differences in both the water contents and temperature histories of the samples used in each calibration study. For Fe-bearing andesite, Mandeville et al. (2002) derived their fixed ε3500 value of 62.32 ± 0.42 from four glasses synthesized at 1030–1130 °C containing 0.21–4.32 wt% H₂O_t, with 39 of their 63 analyses stemming from their Run 9 glass (1030 °C, 4.32 wt% H₂O_t), while King et al. (2002) derived a fixed ε3500 value of 70.3 ± 6.86 using glasses synthesized at 1300 °C and containing 0–6.09 wt% H₂O_t, of which only three out of 43 analyses were made on glasses with >3.39 wt% H₂O_t. The higher ε3500 value of King et al. (2002) therefore likely reflects the lower average H₂O_t content of their samples and their use of a higher experimental temperature and rapid quench rate (with samples quenched to below the glass transition in ~4 s), all of which favor higher C_OH:C_H2Om. Applying the fixed ε3500 value of King et al. (2002) to our measurements of the Fe-bearing andesite standard Run 10 underestimates the true H₂O_t content of this glass by 0.72 wt% (Fig. 5a), highlighting the potential for large errors when applying a fixed ε3500 value to samples created under different conditions.

Our analyses of the rhyolite standards NWC and KRA-045-2 produced “true” ε3500 values of 94.7 and 93.1, respectively. These high ε3500 values reflect the dominance of OH at low H₂O_t concentrations (Fig. 6), and are close to the highest fixed ε3500 values reported in the literature: 90 (Hauri et al. 2002) and 95 ± 8 (Aubaud et al. 2009). The calibration of Hauri et al. (2002) was based on a wide range of samples, the majority of which had <0.8 wt% H₂O_t, while that of Aubaud et al. (2009) was based on two samples with <0.16 wt% H₂O_t. At such low H₂O_t contents only negligible H₂O_m would be expected (Fig. 6) and it is therefore reasonable that these fixed ε3500 values should approach the end-member ε3500_OH value of 100 ± 2 for rhyolite. Although Leschik et al. (2004) found that for glasses with >2 wt% H₂O_t the ε3500 value decreases with increasing H₂O_t concentration (as would be expected due to the increasing proportion of H₂O_m and corresponding shift toward the lower ε3500_H2Om end-member), it is unclear why their fixed ε3500 value of 80 ± 4.9 for water-poor, OH-dominated samples (like our standards) is so much lower than both the Newman et al. ε3500_OH end-member and other fixed ε3500 values.

By contrast the lowest published value for a fixed ε3500 value for rhyolite (75 ± 4) is that of Okumura et al. (2003), and is based on obsidian samples with 0.24–1.25 wt% H₂O_t that were either unheated or heated to 500–700 °C. The authors noted that ε3500 values derived for the same obsidian source and H₂O_t content (OBSW, 0.74 wt% H₂O_t) increased with the experimental temperature, being 73 for 500 °C, 76 for 600 °C, and 80 for 700 °C. As discussed by the authors, this variation can be explained by the temperature dependence of H₂O speciation that favors higher C_OH:C_H2Om, hence higher ε3500, at higher temperatures. Okumura et al. (2003) also derived an ε3500 value for the original unheated obsidian of 77 L/mol·cm. Based on their observed temperature dependence of ε3500, we suggest that this value implies that the original T_ae of this obsidian was ~620 °C. While this indicates that finding the true ε3500 of a sample could be a useful method of finding its T_ae (≈ T_g), we stress that it is only valid if the temperature dependence of ε3500 is known for samples with exactly the same H₂O_t content. Any derivation of a fixed value of ε3500 is effectively unique to samples with the exact same H₂O_t content and temperature history, hence water speciation, as the samples that were used in its original calibration. Provided that end-member ε3500 values exist for the glass composition of interest, the advantage of our species-dependent ε3500 method is that it is possible to obtain accurate H₂O_t and OH concentrations regardless of a sample's H₂O_t content or temperature history, and it can also account for changes in H₂O_t concentration across an individual sample.

Volcanic glasses are susceptible to secondary hydration, i.e., the addition of water at low temperature in the time following eruption (Friedman and Smith 1958). Hydration of obsidian in particular has a long history of study, not only by the geological, but also the archaeological community, since diffusion modeling of hydration profiles at glass margins could offer a way to date obsidian flows or tools (e.g., Friedman and Long 1976, 1984; Anovitz et al. 1999; Riciputi et al. 2002). Recent studies have also demonstrated that secondary hydration is widespread and has altered the glass water contents of many erupted pyroclasts, with the effect most pronounced for samples with greater surface area exposed to outside water, such as vesicular glasses (e.g., Giachetti and Gonnermann 2013; Dingwell et al. 2015). Determining the original eruptive H₂O_t content of hydrated glasses is therefore critical to volatile studies of erupted pyroclasts. Here we use an example of obsidian hydration from the literature to discuss how the species-dependent ε3500 method can be used to measure accurately the water species concentrations of hydrated glasses, with the potential to thereby reconstruct the original H₂O_t contents of hydrated glasses.

Yokoyama et al. (2008) used transmission FTIR to analyze hydration profiles at the margins of two obsidian flows from Kozushima, Japan, dated to 26 000 and 52 000 yr before present. Using the 3500 and 1630 cm^–1 bands (and thus finding OH-by-difference), their analyses showed that both H₂O_m and H₂O_t concentrations increase toward the hydrated boundary. The trend in OH concentration was less simple, however, with OH either increasing or decreasing toward the boundary depending on the choice of the fixed ε3500 value. To prevent negative OH concentrations, they had to use a fixed ε3500 value of 60; much lower than any of the published values of ε3500 for rhyolite (Table 2). We extracted the concentration data from their published profiles and used their stated values of thickness and density to back-calculate their original 3500 and 1630 cm^–1 absorbances using the Beer-Lambert law. We then applied our new species-dependent ε3500 method to their absorbances to recalculate the H₂O_t and OH concentrations of their hydration profiles, and to calculate the “true” ε3500 value for every point along the profile (Fig. 7). Doing so, we find that for both profiles the ε3500 value decreases toward the hydrated boundary. Accordingly, the OH concentration profiles no longer exhibit a fall to negative values and remain within 0.1 wt% of their non-hydrated values, while the increase in H₂O_t concentrations toward the boundary becomes more pronounced than in the original profiles.

Since the species interconversion reaction effectively stops at the glass transition temperature (e.g., Dingwell and Webb 1990; Nowak and Behrens 1995; Zhang 1999; Behrens and Nowak 2003; Behrens and Yamashita 2008), water added at ambient temperature during secondary hydration is added as H₂O_m and not interconverted to OH; this creates “disequilibrium” speciation similar to that which develops during quench resorption (McIntosh et al. 2014). Glass in the hydrated margin becomes enriched in H₂O_m, and the correct ε3500 value to use will shift toward the ε3500_H2Om end-member value (56 ± 2 for rhyolites). This explains why Yokoyama et al. (2008) had to use an ε3500 value of 60 to prevent negative OH concentrations when finding OH-by-difference. This value is much lower than the fixed ε3500 values in the literature, since the literature values were derived from samples with equilibrium rather than H₂O_m-rich disequilibrium speciation. When measuring H₂O_t and OH concentrations of hydrated samples using the 3500 cm^–1 band, it is therefore imperative that the species-dependence of the ε3500 coefficient is accounted for.

The study of Yokoyama et al. (2008) was limited by the spatial resolution of their FTIR apparatus (they used 15 × 50 μm spots at overlapping 5 μm steps) and we therefore truncate our recalculated profiles at the distance from the edge at which the authors calculated there would be no interference from the adjacent resin. FTIR apparatus with higher spatial resolution, such as those using a synchrotron source (e.g., von Aulock et al. 2014), may be able to investigate the concentration variations in hydrated margins in more detail. Nevertheless, it is clear from the data of Yokoyama et al. (2008) that OH concentration does not increase sharply in the hydration rim, whereas the H₂O_m concentration does, supporting their conclusion that the dominant species diffusing into the glass is H₂O_m. A recent study (Bindeman and Lowenstern 2016) on hydration of rhyolite during perlite formation at Yellowstone concluded that hydration occurred at temperatures <200 °C but greater than ambient temperature, over an expected cooling timescale of weeks to years. The authors observed that, although dominated by addition of H₂O_m, this hydration also added minor amounts of OH (~0.2 wt%) to hydrated rims. Our recalculated hydration profile of Yokoyama et al.'s Ohsawa lava (Fig. 7a) reveals a slight increase in OH concentration from ~0.1 to ~0.2 wt% toward the margin, raising the possibility that its hydration may have occurred under similar conditions to that of the Yellowstone perlite. However, for glasses that are quenched rapidly to ambient temperature and hydrated subsequently, it is expected that the OH content of a hydrated sample should remain the same as when that sample was first deposited. This is in keeping with observations of volcaniclastic glasses that contain hydrated regions. Those hydrated regions have elevated H₂O_m concentrations, but have similar OH concentrations to unhydrated regions of the same samples (e.g., Nichols et al. 2014). By using the new species-dependent ε3500 method to measure accurately the OH concentration of such hydrated glasses, it is now possible to estimate the original pre-hydration H₂O_t content by using speciation models (e.g., Nowak and Behrens 2001; Fig. 6) to find the H₂O_t concentration that corresponds to the measured OH concentration for the expected T_ae (≈ T_g) of the sample (e.g., Dingwell et al. 2015). Although the glass transition temperature can vary with cooling history and H₂O_t concentration, OH vs. H₂O_t curves for different values of T_g converge at low-H₂O_t concentrations (Fig. 6), making this an effective method for glasses with <1 wt% OH. Other proposed methodologies for reconstructing the original H₂O_t content of hydrated glasses involve thermogravimetric analysis (TGA) (e.g., Denton et al. 2009, 2012; Tuffen et al. 2010; Giachetti et al. 2015) or hydrogen isotope analysis (e.g., DeGroat-Nelson et al. 2001)—both of which produce bulk measurements and destroy the sample—in conjunction with modeling of diffusion, for which some of the parameters are not well constrained for ambient temperatures. This FTIR methodology is relatively cheap and simple to perform, and has the significant benefit of permitting spatial variations in both the original and subsequent H₂O_t concentration to be measured.

It has long been recognized that the values of FTIR molar absorptivity coefficients vary with glass composition (e.g., Silver et al. 1990; Dixon et al. 1995; Ohlhorst et al. 2001; Mandeville et al. 2002; Seaman et al. 2009; Mercier et al. 2010), hence it is unsurprising that the end-member ε3500 values also vary with glass composition. H₂O_t and OH contents derived using the rhyolite end-member coefficients agree well with the manometry data for both of the rhyolite glass standards (Fig. 4), suggesting that these end-member ε3500 values are not sensitive to minor compositional differences, such as a few wt% of SiO₂ (Table 3), and can be successfully applied to other glasses with similar major element compositions. However, glasses with greater compositional differences will require their own set of end-member coefficients, as seen in the variation between values for rhyolite, albite, and Fe-bearing and Fe-free andesite (Table 2).

Previous studies have suggested that the molar absorptivity coefficients of the H₂O absorption bands decrease with decreasing tetrahedral cation fraction (τ) of the melt, where τ = (Si⁴⁺+Al³⁺)/total cations (e.g., Dixon et al. 1995; Ohlhorst et al. 2001; Mandeville et al. 2002; Seaman et al. 2009; Mercier et al. 2010). Although our data are so far limited to only four glass compositions, our values of ε3500_OH and ε3500_H2Om do not show a trend with τ (Table 2), and neither do they show a trend with the ratio of non-bridging O atoms over tetrahedrally coordinated cations (NBO/T; Table 2). Although the end-member ε3500 values clearly vary with melt composition, it is not yet possible to simply link this variation with a particular structural parameter that describes the silicate melt.

Of the four compositions discussed here, the use of a species-dependent ε3500 is most important for the rhyolite and Fe-andesite compositions. These compositions have the greatest difference between the two end-member coefficients (56–100 and 49–79, respectively) hence the appropriate ε3500 value, and the calculated H₂O_t and OH concentrations, can vary widely. For Fe-free andesite the difference between the end-member coefficients is smaller (62–76) but is still sufficient to justify the use of species-dependent ε3500. On the other hand, the difference between end-member ε3500 values for albite is so small (69–71) that they are within error of each other, which enabled Silver and Stolper (1989) to conclude that there is no advantage in choosing a species-dependent ε3500 value over a fixed ε3500 value for this composition.

Dissolved H₂O content exerts a strong control on silicate melt properties such as viscosity, glass transition temperature, diffusivities of mobile species, and crystallization kinetics. Consequently, for many studies throughout the geological, archeological, and materials sciences, it is critical to know accurately the H₂O contents of silicate glasses, even when the behavior of H₂O is not the main focus of the study. The relative ease of sample preparation and low cost of FTIR analyses means that, in many studies of this sort, the H₂O data are obtained by FTIR, and often by analyzing the 3500 cm^–1 H₂O_t absorbance band. Our new species-dependent ε3500 method, which does not require a change in analytical procedure or expensive instrumentation, will improve the accuracy of these FTIR data, and remove systematic bias in samples that have undergone hydration. Previously published H₂O data that depend upon fixed ε3500 values will therefore need to be re-evaluated to identify and correct potential inaccuracies. This is particularly important given the common use of FTIR H₂O data to constrain glass standards used in the calibration of other analytical techniques such as SIMS (e.g., Hauri et al. 2002). We emphasize that this correction can be accomplished without the need for new instrumental analyses, by simply re-analyzing the raw absorbance, thickness, and density data that have already been collected, using the methodology developed in this work. We provide a simple spreadsheet, which accepts these data and performs the relevant calculations, in the supplementary information¹.

The clear advantage of FTIR analysis over other techniques is the ability to obtain quantitative H₂O speciation data, which can be used to investigate topics such as the mechanisms and rates of H₂O diffusion (e.g., Zhang et al. 1991), or the pressure and temperature histories of glasses (e.g., Zhang et al. 1997a; McIntosh et al. 2014). Many of these studies involve measuring the spatial variation in H₂O species along an H₂O diffusion profile, for example along a diffusion couple experiment or toward a crack, bubble or crystal in the glass (e.g., Zhang et al. 1991; Castro et al. 2008; Berlo et al. 2013; von Aulock et al. 2013; McIntosh et al. 2014; Saubin et al. 2016; Watkins et al. 2017). In such cases, where H₂O_t concentration varies systematically with spatial position, it is essential to account for the species-dependence of ε3500 when using the 3500 cm^–1 absorbance band, because otherwise errors will also vary systematically with spatial position, as illustrated by our reinterpretation of the Yokoyama et al. hydration profiles (Fig. 7). Removal of this systematic error will significantly improve the quality of interpretations of H₂O speciation data along such profiles.

As well as facilitating reanalysis and reinterpretation of existing studies of experimental and natural hydrous glasses, our new method also opens new avenues of research into glasses affected by secondary hydration. Secondary hydration has been shown to be a widespread phenomenon (e.g., Giachetti and Gonnermann 2013), and we recommend the use of FTIR analyses to identify (by their excess H₂O_m contents) glasses that have been hydrated; information that cannot be obtained by SIMS or Raman spectroscopy. Moreover, improved accuracy of H₂O speciation data along hydration profiles will benefit researchers investigating mechanisms of glass hydration, and the use of obsidian hydration profiles as a dating tool for volcanic and archeological glasses. Most exciting of all, however, is the prospect of estimating the pre-hydration H₂O_t contents of hydrated glasses based on accurate measurement of their OH contents. We propose that this will be a particularly important breakthrough for understanding the eruption processes and associated hazards of silicic submarine eruptions, for which pyroclast glasses are routinely found to be hydrated (e.g., Bryant et al. 2003; Kutterolf et al. 2014). In the same way that the pressure-dependence of H₂O solubility can be used to determine paleo-ice thicknesses from subglacially erupted and quenched glasses (e.g., Tuffen et al. 2010), reconstructed H₂O_t contents of submarine pyroclast glasses can be used to establish the quench depth of unobserved submarine eruption plumes and, in particular, to determine whether pyroclasts now resting on the deep sea floor may have originally reached the sea surface (e.g., Fiske et al. 2001; Tani et al. 2008; Allen et al. 2010; Rotella et al. 2013).

Although this paper has focused necessarily on rhyolitic and andesitic glasses, it is hoped that future FTIR studies of hydrous silicate glasses will enable further sets of end-member ε3500 values to be derived for more compositions (particularly basalt). This will allow the species-dependent ε3500 method to be applied more widely, and will also improve our understanding of the composition dependence of molar absorptivity coefficients. Such future studies may also improve upon the molar absorptivity coefficients that are available to us today. This study has benefited hugely from the previously published data sets of Newman et al. (1986) and Mandeville et al. (2002), which contained the absorbance, thickness, and density data necessary to test and develop our methodology. We therefore strongly advocate for researchers using FTIR data to publish, as we have done here, not only their concentration data but also the absorbance, thickness and density data that underpin them, with the aim of increasing the longevity and relevance of their hard-won data.

We are grateful to Madeleine Humphreys for providing the glass standards used in this study. We thank Jake Lowenstern and an anonymous reviewer for their thorough and insightful reviews. This research was supported by a Japan Society for the Promotion of Science Postdoctoral Fellowship for Foreign Researchers held by I.M., and a JSPS Grant-in-Aid for Scientific Research (Kakenhi grant number 00470120) awarded to A.R.L.N and I.M.; E.W.L. acknowledges support from the U.K. Natural Environment Research Council via grant NE/N002954/1. Data Access Statement: Underlying data can be obtained by contacting the corresponding author.