A New Method for Measuring Infrared Band Strengths in H2O Ices: First Results for OCS, H2S, and SO2

Infrared (IR) band strengths are needed to extract accurate molecular abundances from astronomical observations of interstellar and solar system ices. However, laboratory measurements of such intensities often have required multiple assumptions about ice composition and thickness. Here we describe a method that circumvents most of the common assumptions and uncertainties in IR band-strength determinations. We have applied the method to measure IR band strengths of OCS, H2S, and SO2 in the absence and presence of H2O ice at 10 K, the first measurements of their type. Our results show for the first time that the presence of H2O makes little difference in IR intensities for these three sulfur-containing molecules’ strongest IR features. The immediate application will be to laboratory studies of low-temperature chemistry of interstellar and cometary ices.


Introduction
The accurate determination of molecular abundances in extraterrestrial solids using infrared (IR) spectroscopy is a longstanding challenge to both interstellar and planetary astronomers. The usual approach to the problem involves Equation (1), where N (in molecules cm −2 ) is the desired column density of a molecule or ion responsible for an IR absorption, the numerator on the right is the optical depth (τ) of an ice's absorbance feature integrated over wavenumber (ñ in cm −1 ), the ice being either extraterrestrial or a laboratory analog, and the denominator is a reference IR band strength A′ (in cm molecule −1 ) from laboratory measurements: Extensive financial and human resources have been devoted to observatory and spacecraft determinations of this fraction's numerator, but much less attention has been paid to the denominator's A′ on which the calculation of the column density N rests. In this brief paper, we describe our recent development and application of an apparently novel method for determining IR band strengths (A′) of molecules in mixed molecular ices, the method relying on laboratory data of the type (i.e., density, refractive index) we recently published here (Hudson et al. 2020). We have used results obtained with our method to address the applicability of IR band strengths of relatively simple ices to the more-complex solids expected in interstellar and planetary environments. More specifically, we compare spectral intensities for several strong IR features of the sulfurcontaining molecules OCS, H 2 S, and SO 2 in the absence and presence of H 2 O ice. The method we describe not only delivers accurate results, but it avoids many of the unchecked assumptions that often are made in such laboratory work.
The interest in sulfur among laboratory astronomers is easy to document from just our own work. One of our earliest papers concerned cometary S 2 , which was followed by a study of H 2 S and SO 2 on icy satellites (Moore et al. 1988(Moore et al. , 2007. Later work covered OCS formation in interstellar ices, Jovian NH 4 SH, and the solid-phase IR spectra of four thiols (Ferrante et al. 2008;Hudson 2016;Loeffler et al. 2016;Hudson & Gerakines 2018). Many other laboratory studies concerning extraterrestrial sulfur can be found in the publications referenced in the present paper.
Studies of sulfur in astronomical environments are just as easy to locate. Known interstellar molecules include OCS, H 2 S, and SO 2 , among others. For a summary and original references, see McGuire (2018). The only reasonably secure identification of sulfur in interstellar ice still seems to be that of OCS by Palumbo et al. (1997). Kama et al. (2019) published an extensive study of refractory sulfur in protoplanetary disks. Within the solar system, reports have been published about sulfur species in comets (A'Hearn et al. 1983), on Europa (Carlson et al. 1999), on Mars (Heinz & Schulze-Makuch 2020), in carbonaceous meteorites (Sephton 2002), and in atmospheres of the gas giants (e.g., Irwin et al. 2018). Among astrobiologists, sulfur is valued as a key bio-element in several amino acids (Brosnan & Brosnan 2006).
In this paper, the laboratory method we describe is aimed at experimental work on the chemistry of interstellar ices near 10 K in dense molecular clouds, although laboratory work on cometary-ice analogs at a similar temperature also will profit from quantification using the method we describe. We are particularly interested in the influence of H 2 O-dominated ices in each case as solid H 2 O is a dominant solid in cometary and interstellar ices.

Experimental Methods
Our laboratory work has three parts, (i) the measurement of two specific physical properties of a compound of astronomical relevance, (ii) the use of those results to determine one or more IR intensities of the same compound in the solid state, and (iii) the measurement of the intensities of the same IR band(s) when the compound is mixed with H 2 O ice. We have described the first two of these tasks in numerous papers, so only a brief summary is given here.
To determine IR band strengths of a neat (one-component) ice, we needed the ice's density (ρ) along with a reference index of refraction of the solid, both at the desired temperature and under vacuum. We used a quartz-crystal microbalance to determine densities and two-laser interferometry to measure refractive indices at 670 nm (n 670 ). In a separate measurement, we grew an ice by vapor-phase deposition onto a precooled CsI substrate, recording interference fringes during the process. The fringes and n 670 gave the ice sample's thickness (Groner et al. 1973). An IR absorbance spectrum of the ice was then recorded in the conventional transmission mode, the IR bands of interest were integrated (resolution = 1 cm −1 ), and the ice's density was used to calculate band strengths (Hollenberg & Dows 1961). Note that the integrated absorbance of an IR feature measured on a commercial spectrometer with a common-logarithmic (base10) scale must be multiplied by ln(10) ≈ 2.303 to convert it to the integrated optical depth (τ) of Equation (1). See Hudson et al. (2017) for examples, including thickness, n 670 , density calculations, and Beer's Law plots, as well as for details concerning the IR, vacuum, and cryogenic equipment used. Readers unfamiliar with the use of Beer's Law and the extinction of light might wish to consult Hollenberg & Dows (1961) or standard texts on molecular spectroscopy (e.g., Barrow 1962;Guillory 1977), astrophysics (e.g., Böhm-Vitense 1989; Ostlie & Carroll 1996), or physical chemistry (e.g., Atkins & de Paula 2006).
The third of our three tasks, the formation of a twocomponent solid with H 2 O ice being the more-abundant material, requires a more-detailed description. Two separate deposition lines and leak valves were connected to two glass bulbs, one holding H 2 O vapor and the other with the gas of interest, leading into our sample chamber with a CsI substrate precooled to 10 K. These separate valves and lines permitted simultaneous and independent deposition of the two ice components. Knowing n 670 and ρ for each compound allowed us to calibrate each deposition line and valve to determine the column density of each material condensing on the substrate, as outlined in the next section. No assumptions were necessary about either the flow of a gas and the quantity subsequently frozen on the substrate or about the composition in a gasmixing bulb compared to the composition of the resulting ice sample. No reliance was necessary on liquid-phase, or other, density and refractive index measurements found in the literature. It also was not necessary to determine band strengths by forming ratios with reference IR features whose IR intensities were known or assumed. The method we have described for comparing IR band strengths of single-and twocomponent ices is the only novelty we claim.
All reagents used were CP grade and higher H 2 S and SO 2 from Matheson and OCS from K&K Laboratories. All were used as received.

Band-strength Calculations
The determination of column densities is central to our method for preparing two-component ices with accurately known abundance ratios. We begin with a rearrangement of and then express the column density N as a product of the ice sample's number density ρ N (molecule cm −3 ) and thickness h to give The number density (ρ N ) can be calculated from the mass density (ρ) we measure for each compound as where N A is Avogadro's constant and M is the molar mass of the compound. Ice thickness is found from the number (N fr ) of laser interference fringes recorded during the ice's growth, knowing the laser's wavelength (λ = 670 nm) and having measured the ice refractive index (n) at that wavelength. The relevant equation for our equipment is (4) and (5) into Equation (3), and rearranging, gives (2) and (6) shows that the terms in the square brackets in Equation (6) are the column density of molecules (N). Finally, because τ = (ln 10) (absorbance), we have

Comparing Equations
where all terms in the square brackets are known and, again, their combination gives the ice's column density, N. The conclusion from Equation (7) is that a plot of integrated absorbance as a function of the terms in the brackets (column density) should be linear with a zero intercept and a slope A′/ (ln 10) from which the band strength A′ can be found. In practice, with ice mixtures, we first calibrate our deposition system so that we know the rate of fringe formation for a particular setting of the deposition valve for each of the two ice components, and when making an ice mixture, we simply multiply that rate and the deposition time to get the N fr used in Equation (7). We emphasize that ρ and n must be known for an accurate calculation of the column density and hence an accurate determination of A′ for an ice component. Note also that in a mixture it is still the ρ and n of each component that is needed to calculate A′ and not the density and refractive index of the resulting ice.

Results
Table 1 summarizes the n 670 and ρ values measured for our OCS, H 2 S, and SO 2 ices at 19 K, typically the base temperature of our UHV equipment, although occasionally values as low as 16 K were reached. Each n 670 and ρ value in Table 1 is the average of at least three determinations with standard errors on the order of 0.005 and 0.005 g cm −3 for n 670 and ρ, respectively. The values of Table 1 were critical for the measurement of the band strengths of our ices, as already described. A few measurements were carried out with an older system (Moore et al. 2010), at slightly lower temperatures (∼12 K), with essentially the same results (e.g., n 670 = 1.330 at ∼12 K versus n 670 = 1.332 for SO 2 at 19 K), so that a 10-19 K temperature difference is not particularly significant for our work. The decision to use our newer ultrahigh vacuum system and the higher temperature was based on the fact that that system's microbalance permitted density measurements.
Knowing n 670 and ρ for OCS, H 2 S, and SO 2 ices, we recorded IR spectra of each compound as a function of ice thickness. Conventional Beer's Law plots were constructed, based on Equation (7), and used to derive band strengths A′ for each compound at 10 K, with a focus on the stronger IR features that were unobscured by H 2 O ice. Again, see our earlier papers for additional background information and typical Beer's Law graphs (e.g., Hudson et al. 2017). Readers wishing to see IR spectra of amorphous OCS at 10 K should consult Hudgins et al. (1993). Spectra of solid H 2 S and SO 2 are found in Salama et al. (1990). See also our own work on OCS (Ferrante et al. 2008 Our final task was to prepare the two-component ices H 2 O+OCS, H 2 O+H 2 S, and H 2 O+SO 2 with known column densities for the sulfur molecule in each case and to again measure integrated absorbances in each ice's IR spectrum. Figure 1 shows representative IR spectra, which agree with those of Salama et al. (1990), Hudgins et al. (1993), Moore et al. (2007), and Ferrante et al. (2008). Plotting integrated absorbance (i.e., band area) as a function of column density N gave the results shown in Figure 2, each panel representing an IR feature in an H 2 O-rich ice sample. Each point in each plot is from a separate ice mixture, and three ice ratios were used in each plot. For example, in the panel for H 2 O+OCS, 15 ices were examined with H 2 O:OCS molar ratios of about 92:1, 9:1, and 4:1. A total of about 50 ices were used to generate  Table 2 summarizes the band strengths we obtained for OCS, H 2 S, and SO 2 in the absence and presence of H 2 O ice. Results from our recent study of HCN are included for comparison (Gerakines et al. 2022). Our goal in the present work was to measure IR intensities, leaving peak positions and band shapes for a future study.
Uncertainties in A′ values were estimated with both a propagation-of-error approach and a least-squares routine, taking into consideration uncertainties in both x and y quantities in the slopes of the Beer's Law plots. See both Irvin & Quickenden (1983) and Press et al. (1992). A conservative (upper) estimate for uncertainties is 5% for our A′ values, which could be reduced with additional measurements. Correlation coefficients for all regression lines, such as those in Figure 2, were above 0.990.

IR Band Strengths of Single-component Ices
We were motivated in our work by the question of how much band strengths might differ between one-and twocomponent ices, but the intensities of the single-component sulfur-containing ices, OCS, H 2 S, and SO 2 , are of interest in themselves.
For amorphous OCS, the only solid-phase band strengths we have located are from Hudgins et al. (1993), 1.5 × 10 −16 cm molecule −1 and 1.7 × 10 −16 cm molecule −1 for OCS and for an H 2 O+OCS (20:1) ice, respectively. These values are larger than those in our Table 2, mainly because of the ρ and n values used by Hudgins et al. (1993). Their ρ = 1 g cm −3 was assumed for convenience, and the n used, 1.24, was based on liquid OCS, although the method of calculation was not described. The A′(OCS) later used by Palumbo et al. (1997) in a study of solid OCS in dense molecular clouds was taken from Hudgins et al. (1993) and is about 25% higher than the value for neat OCS in our Table 2. This suggests that the OCS abundance in such interstellar objects is greater than the published value (i.e., a smaller value of A′ in the denominator of Equation (1) raises N). The published band strengths for amorphous H 2 S also have an interesting history, which we have described in a previous publication (Hudson & Gerakines 2018). There we explained how the paper of Chen et al. (2015) adopted an A′(H 2 S) value from Jiménez-Escobar & Muñoz Caro (2011), who rescaled a value from Smith (1991), who used crystalline H 2 S to derive a band strength that was applied to noncrystalline (amorphous) H 2 S but with no statement as to the values of n and ρ adopted. Given this situation, any agreement or disagreement with our work can be regarded as little more than fortuitous. As an aside, we note that a value of A′(H 2 S) published some years ago by Gibb et al. (2004) is not from the paper of Salama et al. (1990) cited, but from Smith (1991).
The literature trail for SO 2 is also problematic. The SO 2 studies of Bonfim et al. (2017) and Kaňuchová et al. (2017) both refer back to earlier work by Garozzo et al. (2008) for a band strength. However, none of these three papers have details of how A′(SO 2 ) was determined, and so any agreement or disagreement with our own work can be regarded, again, as little more than fortuitous. An earlier solid-phase study by  applied gas-phase A′(SO 2 ) values to amorphous SO 2 ices. Our conclusion is that, to our knowledge, the values we report for A′(SO 2 ) in Table 2 are the first direct measurements of this band strength.
Therefore, to the question of which similar published measurements match our own, the answer is simple: none. We are unaware of any similar direct IR band-strength measurements in the literature for OCS, H 2 S, and SO 2 . Each of the band-strength publications cited for these compounds lacks either a pair of measured n and ρ values or details of the calculation method adopted. Moreover, integration ranges are missing in most or all cases, hindering accurate comparisons of IR band areas over the same span of wavenumbers (or wavelengths). In short, our results in Tables 1 and 2 are the first of their type for OCS, H 2 S, and SO 2 .

IR Band Strengths in H 2 O-rich Ices-The Influence of Environment
The high degree of linearity for each panel in Figure 2 is striking and shows that the band strength A′ for each compound is essentially constant over a wide range of concentrations. Table 2 lists the band strengths for the ice mixtures examined, along with the A′ values for the same four compounds in the absence of H 2 O ice. It is readily seen that the presence of H 2 O ice in the solid sample makes relatively little difference in A′. We conclude that the A′ values we measured for these compounds as neat ices are safe to use when working with H 2 O-dominated mixtures.
By far the highest band strength in Table 2 is for OCS (∼2040 cm −1 ), either in the presence or absence of H 2 O ice, followed by the ν 3 mode of SO 2 (∼1330 cm −1 ), and then the stretching vibrations of H 2 S (∼2550 cm −1 ). The A′(ν 1 ) ≈ 1.2 × 10 −16 cm molecule −1 for OCS is essentially the same as that of the asymmetric stretch of amorphous CO 2 , a commonly reported intense feature near 2340 cm −1 (Gerakines & Hudson 2015b). The A′(ν 3 ) for SO 2 is higher than that of amorphous CH 4 (Gerakines & Hudson 2015b), which also is reported in interstellar ices. Such strong IR intensities for OCS and SO 2 are in contrast to the low abundances and nondetections of these molecules in interstellar ices. Our work suggests that such small abundances and nondetections are not caused by weak IR band strengths of OCS and SO 2 but are more likely from the smaller cosmic abundance of sulfur compared to carbon and to chemical reactions, such as radiolytic oxidation, that convert S-containing molecules into SO 4 2and other species that can be difficult to detect, partly due to the overlap of IR bands with other species (Moore et al. 2007). This situation resembles that of nitrogen in which cyanate (OCN -) has been reported in interstellar ices, but cyanide (CN -) has not (Hudson et al. 2001).

Assessment and Extensions
The method we have described for determining IR band strengths in H 2 O-rich ices has the advantage of measurements being made with minimal assumptions about the composition of the ice sample. The column densities of the non-H 2 O-ice and the H 2 O-ice components in the mixture are derived from n and ρ values (i.e., Table 1) for each solid compound at the desired temperature, avoiding the difficulties and assumptions listed earlier. The main spectroscopic obstacle to using our approach is the usual one of overlapping IR features. Accurate integration of an IR band is difficult when an IR feature of interest is located in a region of strong absorbance by H 2 O ice. This is, of course, a problem with astronomical IR spectroscopy whether laboratory or observatory based. As an example, see the extraction of a methanol abundance from the IR spectra of four protostars by Allamandola et al. (1992).
We should also mention possible laboratory complications to using the method described here. One is that vapor-phase deposition rates should be comparable in the calibration measurements on each ice component and in the two-component ices. Related to this is that too high a deposition rate can result in the heating of an ice and structural and spectroscopic changes, as we have documented in multiple papers (e.g., Gerakines & Hudson 2015a, 2015b. Also, the ices we have studied have been on the micrometer scale. Compositions of ices of much greater thickness could be different from those of thinner solids due to thermal conductivity changes. It also is not certain if more deposition lines than the two we have used for two-component ices would be needed for quantitative studies of ices with three or more components. Our results suggest several new lines of investigation. Perhaps first among these is the extension to other compounds. Each of the four triatomic molecules in Table 2 is polar, so experiments with NH 3 , amines, and alcohols in H 2 O-rich ices can also be expected to show the linearity of the plots in Figure 2. The trends for nonpolar guest molecules, such as acetylene (C 2 H 2 ) and ethane (C 2 H 6 ), are harder to predict. Another variation is to embed guest molecules in a nonpolar host matrix, such as solid carbon dioxide (CO 2 ), to see if the linear trends of Figure 2 are obtained. Finally, for applications to trans-Neptunian objects and icy satellites, our experiments should be repeated at higher temperatures, preferably after n 670 and ρ have been measured at those temperatures. For many applications, the n and ρ values we have already published will be useful (Hudson et al. 2020).

Summary and Conclusions
A method for accurate determinations of IR band strengths has been described and demonstrated with OCS, H 2 S, and SO 2 in amorphous H 2 O-rich ice mixtures. The method described circumvents the need for a reference refractive index and density of an ice mixture.
Our measurements show that the band strengths of the stronger IR features of OCS, H 2 S, and SO 2 ices hardly change when these compounds are mixed with H 2 O ice at 10 K. These are the first such measurements of IR band strengths for these three sulfur compounds in the solid state.