Measuring in situ CO2 and H2O in apatite via ATR-FTIR

We present a new approach to determine in situ CO2 and H2O concentrations in apatite via attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR). Absolute carbon and hydrogen measurements by nuclear reaction analysis (NRA) and elastic recoil detection (ERD) are used to calibrate ATR-FTIR spectra of CO2 and H2O in apatite. We show that CO2 and H2O contents in apatite can be determined via linear equations (r2 > 0.99) using the integrated area of CO2 and H2O IR absorption bands. The main benefits of this new approach are that ATR-FTIR analyses are non-destructive and can be conducted on polished sample material surfaces with a spatial resolution of ~ 35 μm. Furthermore, the wavenumber of the phosphate IR absorption band can be used to determine the crystallographic orientation of apatite, which allows for accurate quantification of CO2 and H2O in randomly orientated apatite grains. The limit of quantification of H2O in apatite is ~ 400 ppm and ~ 100 ppm for CO2. Via two examples, one from a carbonatite and one from a metasedimentary rock, we show that this new technique opens up new possibilities for determining volatile concentrations and behavior in a wide range of hydrothermal, igneous, and metamorphic systems.


Introduction
Volatiles, especially CO 2 and H 2 O, are key agents for igneous and metamorphic processes that impact the Earth's atmosphere and climate over millions of years. For example, they affect mineral stability and metamorphic reactions, and are, therefore, directly and indirectly controlling mass transfer (e.g., Phillips and Evans 2004;Williams-Jones and Heinrich 2005;Berkesi et al. 2012) as well as the melting and differentiation of the Earth's crust (e.g., Rubatto et al. 2009; see Weinberg and Hasalova 2015 for a review). However, given the fugitive behavior of CO 2 and H 2 O, measuring and quantifying these components in igneous, hydrothermal, and metamorphic systems is challenging. Nevertheless, due to the critical importance in global cycling of CO 2 and H 2 O for the evolution of the Earth and its climate, developing new techniques for tracing the geological distribution of these volatile components is essential (e.g., Kerrick and Caldeira 1998;Stewart and Ague 2018;Capriole et al. 2020). While fluid inclusions can provide useful insights into (Paleo)fluid compositions (e.g., Diamond 2001), their complexity is often a limiting factor for meaningful interpretations, and doubt has been cast over the preservation and reliability of (CO 2 -rich) fluid inclusions from high-grade metamorphic rocks for reconstructing fluid properties of the deep crust (e.g., Carvalho et al. 2020). An alternative approach to studying the role and presence of CO 2 and H 2 O in metamorphic, igneous, and hydrothermal systems is using minerals that incorporate CO 2 and H 2 O during their formation. While H 2 O is readily incorporated as a major or a trace component in many common igneous and metamorphic minerals, very few of them can incorporate both of these volatile components in their crystal structure to easily-detectable concentrations (well above the ppm level).
Apatite (Ca 5 (PO 4 ) 3 (F,Cl,OH)), is a ubiquitously present accessory phase in terrestrial and extra-terrestrial rocks that is able to incorporate significant amounts of H 2 O and CO 2 , reaching weight % concentrations of either component (Binder and Troll 1989;Santos and Clayton 1995;Boyce et al. 2010;Li et al. 2020;Pan and Fleet 2002 for a review). Note that despite C being incorporated in apatite in the form of carbonate (CO 3 2− ) and H as OH − , we follow the conventional reporting of C and H concentrations in their oxide component as CO 2 and H 2 O that would be released upon heating of apatite. Apatite has the general formula M 5 (ZO 4 ) 3 X, with H 2 O and CO 2 hosted in different crystallographic locations. Typically, the M site is mainly filled by Ca 2+ but can accommodate significant amounts of divalent Sr 2+ , as well as Ba 2+ , Pb 2+ , light rare earth elements (REEs), and also Na + . The Z site is mainly dominated by P 5+ , however, As 5+ , Si 4+ , C 4+ , and S 6+ can also be present in considerable quantities. F − , OH − , Cl − , and CO 3 2− share the channel anion X site (Pan and Fleet 2002 and references therein). The H 2 O content of apatite has been used in the past (e.g., Zhu and Sverjensky 1991) to estimate H 2 O contents in fluids and melts (Stock et al. 2018;Popa et al. 2021) and recent studies have also aimed at using CO 2 contents of apatite to gain insight into CO 2 contents of igneous systems (Riker et al. 2018).
One of the overarching goals of accurately measuring CO 2 and H 2 O in apatite is to determine partition coefficients of CO 2 and H 2 O between apatite, aqueous fluids, and melts to calculate CO 2 and H 2 O contents in igneous, hydrothermal, and metamorphic systems. One of the challenges for realizing this goal is the accurate, routine measurement of CO 2 and H 2 O on a (sub-) grain scale. For example, the H 2 O content of apatite is typically estimated via stoichiometric calculations based on electron probe microanalysis (EPMA) measurements (e.g., Deer et al. 2013;Ketcham 2015) but meaningful calculation of H 2 O in apatite in this way is notoriously problematic. One of the reasons is that the accurate quantification of Cl, and especially F, is difficult (Stormer et al. 1993;Goldoff et al. 2012;Stock et al. 2018), yet paramount, since Cl, F, and OH share the same site in apatite crystals. Other, less routine, in situ methods, such as secondary ionization mass spectrometry (SIMS) have also been employed for absolute H 2 O quantification in apatite with a high spatial resolution (Barnes et al. 2014;Hu et al. 2015). A recent comparison of H 2 O contents measured by SIMS with H 2 O concentrations determined stoichiometrically based on EPMA measurements illustrates the challenge of accurately determining H 2 O, as the two methods produced H 2 O values differing by a factor of two in some cases (Riker et al. 2018). Furthermore, the incorporation of CO 2 at the same (anion) site (see above) further complicates accurate H 2 O constraints via stoichiometric approaches. While the presence of CO 2 in natural apatite has been recognized for some time (e.g., Gulbrandsen et al. 1966;Elliott 1994;Fleet et al. 2004;Deer et al. 2013 and references therein), the quantitative (in situ) measurement of CO 2 remains difficult despite recent developments to quantify CO 2 contents in apatite via SIMS (Riker et al. 2018;Li et al. 2020). In addition to SIMS, one promising avenue for CO 2 and H 2 O detection and quantification in apatite on a sub-grain level is transmission Fourier transform infrared spectroscopy (FTIR) on sample wafers polished on both sides (e.g., Tacker 2004Tacker , 2008. Recent work by Wang et al. (2011) andClark et al. (2016) have shown that in situ transmission FTIR measurements and the resulting spectra can be calibrated and used for absolute H 2 O and CO 2 quantification down to ppm levels in individual apatite grains. However, for the in situ transmission FTIR method, samples need to be prepared as doubled-sided polished wafers, which can be challenging for minute grains (< 200 μm), which is the most common form of apatite occurrence in crustal rocks.
In this study, we explore the potential of in situ attenuated total reflection (ATR)-FTIR analyses of polished apatite grains (i.e., in polished thin sections or grain mounts) to determine absolute H 2 O and CO 2 concentrations. We have calibrated the ATR-FTIR method for measuring H 2 O and CO 2 concentrations in apatite minerals with absolute hydrogen and carbon concentrations determined by elastic recoil detection (ERD) and nuclear reaction analysis (NRA). Crucially, the ATR-FTIR technique does not require double polishing and hence has the potential to be applied to a far greater array of natural apatites. Our data, produced by ATR-FTIR, show that H 2 O and CO 2 contents in apatite as low as ~ 400 ppm and ~ 100 ppm, respectively, can be quantified accurately. Furthermore, based on FTIR spectra we show that the crystallographic orientation of apatite can be resolved, which is critical for accurate H 2 O and CO 2 quantification in randomly orientated apatite grains. Our study presents a new, effective and broadly applicable approach to accurately measure CO 2 and H 2 O in apatite via ATR-FTIR, contributing to the further development of using CO 2 and H 2 O concentrations in apatite as a tool to estimate the concentration of these volatiles in igneous, hydrothermal, and metamorphic systems.

Sample material and preparation
A total of eight apatite specimens, most of them between 1 and 2 cm in length, were used to develop the analytical technique for CO 2 and H 2 O quantification by ATR-FTIR. Samples used in this study include apatite from the High Atlas Mountains (HAM), Morocco, purchased from an online vendor and apatite from the Mud Tank (MT) carbonatite, Northern Territory, Australia, collected by J. Hermann. We also used apatite from Hormuz Island (HRZ), Iran (NMBE B6634), procured from the Natural History Museum Bern, Switzerland (NMBE) and apatite crystals named "SAP3" and "VOH", both originating from Madagascar. However, while VOH (NMBE 40865) originates from Milanoa in the Vohémar province and was provided by the NMBE, the exact location of SAP3 is unknown as it was purchased from an online vendor (see also Hammerli et al. 2021). Apatite specimen "GL", which comes from a large apatite crystal from a carbonatitic vein in Greenland, was obtained from K. Thrane of the Geological Survey of Denmark and Greenland. "YAM" apatite is a euhedral apatite embedded in a pink calcite matrix from the Yates Mine, Otter Lake, Canada. A smaller grain (~ 5 mm) "HOI" from the Hohe Ilmen mountains near Miass, Russia, provided by the NMBE, was also used for method development, however, the crystal chip was too small for Nuclear Reaction Analysis (NRA) or Elastic Recoil Detection (ERD) analyses.
NRA required the preparation of sample wafers (~ 4 mm × 4 mm), which were polished stepwise from 6 to 0.5 μm with diamond paste on both sides. Larger sample wafers (~ 8 mm × 5 mm) were prepared for ERD analyses following the same procedure as for NRA. For ATR-FTIR analyses, apatite specimens with euhedral crystal habits were cut parallel and perpendicular to the optical c-axis, embedded in 1-inch epoxy mounts, and subsequently stepwise polished from 6 to 1 μm with diamond paste. For each sample, randomly orientated pieces of the same wafers prepared for NRA and ERD analyses were embedded in epoxy to check sample homogeneity and to assess crystallographic effects on ATR-FTIR analyses.

Nuclear reaction analysis
NRA via the 1.7 MV tandem accelerator at the Michigan Ion Beam Laboratory (MIBL) of the University of Michigan was used to determine absolute carbon concentrations in apatite (Mathez et al. 1987;Proust et al. 1994;Cherniak et al. 2010;Clark et al. 2016). A high-energy beam (1.4 MeV) of deuteron ( 2 H) particles was used to bombard the polished apatite surface to activate the 12 C (d,p) 13 C nuclear reaction ( 12 C + 2 H → 13 C + 1 H, Proust et al. 1994;Wang and Nastasi 2009;Csedreki et al. 2014). As the deuteron beam interacts with the sample, 2 H particles react with the target nucleus of carbon ( 12 C), converting the target nucleus to a new nucleus ( 13 C), while releasing 1 H as a reaction product with a specific amount of energy. The liberated 1 H ions are subsequently detected in the Si charged-particle detector, set at a scattering angle of 160° with a 15 keV energy resolution. No filter foil was used in front of the detector; thus, the same detector detected the Rutherford Backscattered deuterons and the products of the nuclear reaction.
The estimated sampling depth is ~ 6 μm as determined by the SIMNRA software (Mayer 1999). The SIMNRA program was also used for NRA spectrum modeling to determine absolute atomic carbon concentration. Being an absolute method, no independent calibration is necessary for NRA, however, we verified the procedure by analyzing a calcite (CaCO 3 ). The obtained carbon concentration of 19.3 ± 1.3 at.%, agrees with the stoichiometric concentration of carbon (20 at.%) in calcite.

Elastic recoil detection
All ERD measurements were carried out at the Michigan Ion Beam Laboratory (University of Michigan). We used the 1.7 MV tandem accelerator with a similar setup as discussed in previous studies Bureau et al. 2009;Wang et al. 2011). A 2.5 MeV He++ ion beam was used to impact the polished apatite surface from which H ions are released. This beam energy permits the analysis of the H content in the sample to a depth of ~ 500 nm, while two detectors simultaneously collect the ERD and Rutherford back-scattering (RBS) spectra. The number of particle incidents on the sample during the acquisition of the ERD spectrum was measured via the RBS spectrum. A 12.5 μm Kapton film was used in front of the ERD detector to filter out ions heavier than H. Also, a Kapton polyimide (H 10 C 22 N 2 O 5 ) foil was used as the H standard to determine the ERD detector solid angle relative to the RBS detector solid angle (Wang 2004). No standards or additional calibration are required to determine absolute H concentration via the ERD method (Tirira et al. 1991;Aubaud et al. 2009;Bureau et al. 2009). Atomic H concentrations in the apatite samples were determined via ERD and RBS spectrum modeling using the SIMNRA program (Mayer 1999).

EPMA
Concentrations of the major elements Ca, P, Si, F, and Cl, as well as the minor element contents (Mn, Mg, Fe, Na, S) in the apatite samples were obtained via EPMA using a JEOL JXA 8200 superprobe housed at the Institute of Geological Sciences, University of Bern, Switzerland. The analytical potential was set at 15 kV and 4 nA beam current. The beam diameter was set at 15 μm and counting times were 20 s on peak and 10 s on background for each element, besides for S, which was counted for 30 s on peak and 60 s on background. Na, F, Ca, and Cl were measured first, followed by the other elements. All apatite grains were measured perpendicular to their c-axis as suggested by Goldoff et al. (2012) to avoid time-dependent X-ray intensity variations of F and Cl. The data were processed using ZAF corrections and standardized via in-house standards (apatite for P 2 O 5 and CaO, magnetite for FeO, celestine for SO 3 , topaz for F, orthoclase for SiO 2 , tugtupite for Cl, forsterite for Mg, albite for Na, and spessartine for MnO). The stoichiometry of the unknowns was calculated following the method of Ketchman (2015).

FTIR
We used a Bruker Tensor II spectrometer coupled to a Bruker Hyperion 3000 microscope housed at the Institute of Geological Sciences, University of Bern, to acquire FTIR spectra. The setup includes a fully automated sample stage and a dry air-purged analytical chamber to minimize atmospheric interferences. FTIR spectra of apatite were acquired using an ATR objective coupled with a single-spot mercury cadmium telluride (MCT) detector. The objective is composed of a germanium (Ge) two-reflection ATR element with internal and external incidence angles of 21.5° and 37°, which is placed in contact with the sample surface. The infrared light, emitted from a SiC globar source, is internally-reflected through the Ge crystal resulting in the generation of an evanescent wave which transmits into the uppermost portion of the sample (spot diameter of ~ 35 µm). The penetration depth of the evanescent wave is wavenumber-and incident angle-dependent, but is < 1 μm for the wavenumbers of interest in this study. Spectra were acquired using unpolarized light, 128 scans and a wavenumber resolution of 4 cm −1 . The pressure of the Ge crystal was set at 2, which corresponds to 2.6 N of force. A background measurement of (dry-purged) air was collected before each measurement. Subsequently, the spectra of the unknown were baseline corrected using the concave rubber band algorithm of OPUS® with 64 points and three iterations. The area of the bands in the spectra representing the absorption of the "H 2 O" and "CO 2 " vibration bands in the wavenumber regions 3600 cm −1 to 3400 cm −1 and 1600 cm −1 to 1300 cm −1 , respectively, were integrated using the OPUS ® program. Since the CO 2 and H 2 O absorption bands in apatite can be located at slightly different wavenumbers, a separate integration window was defined for each sample. The band areas were then used to calibrate the FTIR signal to absolute CO 2 and H 2 O contents of apatite (see below).

NRA and ERD data
Nuclear reaction analyses of the five apatite specimens (HAM, MT, SAP3, YAM, and GL) were performed on both sides of each wafer and the obtained C contents (in at.%) range from ~ 0.07 to ~ 0.62, which translates to mean CO 2 wt% values of 0.14 ± 0.03 (2SD) for HAM, 0.39 ± 0.03 (2SD) for MT, 0.46 ± 0.06 (2SD) for SAP3, 1.05 ± 0.28 (2SD) for YAM, and 1.12 ± 0.18 (2SD) for GL (Table 1).  Table 2 Mean values of EPMA measurements of apatite Uncertainties are show as the 2SD of the performed analyses of each sample. The stoichiometries are calculated following the method of Ketcham (2015). The OH content was calculated assuming that the anion site is filled with F, Cl, OH, and CO 2 and that the Z-site consisting of P, Si, S, and C, is 6 APFU. The  All analyses of the individual apatite specimens are within their analytical uncertainty, which is estimated at ~ 10%. Elastic recoil detection analyses were performed on the apatite specimens for which a H 2 O signal was detected by ATR-FTIR and a large enough sample material was available (8 mm × 5 mm). The front-and back-side of three MT apatite wafers were analyzed and the resulting H contents range from ~ 2.5 to 3.1 at.%, which means that all analyses are within the analytical uncertainty of ~ 10%. The resulting mean H 2 O concentration in MT apatite is 1.06 ± 0.17 wt% (2SD). VOH apatite returned H at.% contents of 2.49 and 2.60, which is the equivalent of 0.96 and 1.01 wt% H 2 O and a mean of 0.99 ± 0.06 (2SD). The two ERD measurements of HRZ apatite returned H at.% values of 0.58 and 0.60, which equals a mean of 0.23 ± 0.01 wt% H 2 O (2SD) ( Table 1).

Electron probe microanalysis (EPMA)
The composition of the eight apatite specimens used for the method development are given in Table 2. Their stoichiometries were calculated following the method by Ketcham (2015), based on 25 oxygens. CaO contents of the measured specimens range from ~ 54.8 to 56.1 wt% and P 2 O 5 contents vary from ~ 40.3 to 42.3 wt%. Fluorine is the most important anion in all the analyzed specimens, ranging from ~ 1.80 to ~ 3.94 wt%, while chlorine contents vary between ~ 0.04 and 0.55 wt%. MnO and MgO contents are ≤ 0.11 wt% in all measured samples and the highest FeO was found in the GL apatite with ~ 0.15 wt%. GL apatite also contains the highest SiO 2 concentration at ~ 0.91 wt%, while SAP3 apatite contains the most SO 3 (~ 0.63 wt%). In addition to elevated Cl contents (~ 0.55 wt%), HRZ also contains ~ 0.56 wt% Na 2 O, which is, together with GL apatite, the highest concentration of all analyzed apatite specimens (Table 2). Using the above concentrations, stoichiometric calculations, which also consider the CO 2 content on the anion site (1-C-F-Cl), reveal the highest OH concentrations in VOH and MT apatite, of ~ 1.71 and 1.62 wt%, respectively, followed by HAM (~ 1.15 wt%), GL (~ 0.88 wt%), and HRZ (~ 0.21 wt%). According to the stoichiometric constraints based on EPMA data, apatite specimens YAM, SAP3, and HOI are devoid of OH.

IR absorption of phosphate in apatite
The phosphate (PO 4 ) absorption band in apatite is typically located at wavenumbers around ~ 1000 cm −1 (e.g., Regnier et al. 1994) and is the most intense (i.e., highest) signal in the spectra (Fig. 1). ATR-FTIR measurements of the apatite specimens in this study typically produce absorption PO 4 bands between the wavenumbers ~ 1022 cm −1 and ~ 1013 cm −1 . Lower wavenumber absorption bands for PO 4 (e.g., 1013 cm −1 bands) are produced by analyzing apatite perpendicular to the c-axis (red section in Fig. 2), whereas a rotation of the apatite crystal leads to a shift of  the PO 4 absorption peak to higher wavenumbers (blue section; Fig. 2). Please note that we use the terms "parallel to c-axis" and "perpendicular to c-axis" as the orientation of the crystal with respect to the ATR alignment. ATR measurements are all done using unpolarized light and thus this notation does not refer to a polarized absorbance of apatite as might be used in polarized transmission measurements. To avoid confusion, all measurement directions are indicated in the figures. Consequently, a PO 4 band shift of ~ 6 to 8 cm −1 wavenumbers to a band position of ~ 1019 cm −1 or 1022 cm −1 is typically observed when apatite is analyzed parallel to the c-axis (i.e., 90° rotation of the crystal). In some cases, the phosphate absorption band heights in the FTIR spectra are positively correlated with the band wavenumbers (Fig. 2). However, this is not universally the case and appears to depend on the individual apatite specimen. Further investigation is required to determine if there is a link between the phosphate absorption band height, the crystallographic orientation, and the composition of the analyzed sample.

IR absorption of CO 2 bands in apatite
The incorporation of C in apatite results in multiple distinct bands in FTIR spectra due to a range of absorption bands caused by different vibration modes (e.g., Fleet et al. 2004Fleet et al. , 2011Gunaskeran et al. 2006;Tacker 2008;Clark et al. 2016). Several distinct bands in the wavenumber region between 1570 and 1360 cm −1 have been associated with CO 2 (CO 3 2− ) in apatite (e.g., Comodi and Liu 2000;Fleet and Liu 2003;Fleet et al. 2004;Tacker 2008) and these absorption bands are the most promising for directly quantifying the CO 2 content of apatite due to their clear separation from other absorption bands ( Fig. 1 and see Grunenwald et al. 2014;Clark et al. 2016). The CO 2 absorption bands generated by ATR-FTIR analysis are typically an order of magnitude smaller than the absorption bands of PO 4 (Fig. 1). Furthermore, similar to previous studies (e.g., Clark et al. 2016), we found that different crystallographic orientations of apatite affect the IR absorption of CO 2 , which results in different CO 2 band heights in some of the studied specimens. In general, the CO 2 absorption bands in the wavenumber region from 1570 to 1360 cm −1 reach their maximum heights when apatite is analyzed perpendicular to its c-axis (Fig. 3). Conversely, analysis parallel to the c-axis can lead to smaller CO 2 absorption bands, which confirms the findings of previous studies (e.g., Clark et al. 2016). Accordingly, integrated CO 2 absorption band areas of analyses conducted perpendicular to the c-axis are by a factor of ~ 1.25 larger compared to CO 2 absorption band areas of analyses conducted parallel to the c-axis of apatite (Fig. 3). However, while this observation is true for apatite specimens that produce two distinct bands at wavenumbers of ~ 1455 cm −1 and ~ 1430 cm −1 (Fig. 3), for some apatite, such as specimens GL or MT, the CO 2 absorption bands do not change to the same extent in response to different crystallographic orientations (see GL and MT in Fig. 3). It is noteworthy that apatite specimens GL and MT produce broader CO 2 absorption bands compared to, for example, YAM or HOI apatite specimens, with an additional "CO 2 " band between the two main absorption bands (Fig. 3). Importantly, this third band at, for example, ~ 1438 cm −1 in MT, increases when analyzed parallel to the crystal's c-axis. Thus, the integrated CO 2 absorption bands of such apatite samples are indistinguishable and independent of the sample's crystallographic orientation (Fig. 3).
ATR-FTIR analyses of randomly orientated fragments of apatite YAT, SAP3, and HOI show that CO 2 band heights and their corresponding integrated absorption areas do not change linearly when apatite fragments with different crystallographic orientations are analyzed (see above). Figure 4 shows that the integrated absorption band area only changes when the apatite grains are analyzed (sub) parallel to their c-axis as determined by the phosphate band shifts to wavenumbers ≤ 1019 cm −1 . However, the reason for this apparent "step-change" in the absorption of CO 2 has to be further explored, especially since a continuous change in the H 2 O absorption is observed (see below).

IR absorbance of H 2 O bands
The most prominent IR H 2 O (OH) absorption bands of apatite typically produce bands at wavenumbers between ~ 3600 and 3400 cm −1 (Fowler 1974;Freund and Knobel 1977;Tacker 2004 and reference therein), with the major band typically located around ~ 3540 cm −1 (Fig. 1). Similar to the CO 2 signals, absorption band heights of H 2 O acquired in the ATR-FTIR mode are one order of magnitude smaller than the main PO 4 absorption band (Fig. 1). Compared to the CO 2 absorption bands, the degree of H 2 O absorption in apatite and the corresponding band height is much more dependent on the crystallographic orientation of the sample-an observation also reported in previous studies (see Wang et al. 2011;Clark et al. 2016). Unlike the CO 2 absorption bands, IR H 2 O absorption in apatite changes continuously when a sample is analyzed along different crystallographic orientations (i.e., being rotated around an axis perpendicular to the c-axis). Most IR is absorbed by "H 2 O" when apatite is measured parallel to the c-axis (Fig. 5A), along the channels of the crystal, where the majority of H 2 O and halogens are typically located (see above). The integrated H 2 O absorption area of ATR-FTIR analyses parallel to the c-axis is ~ 4 times larger than the integrated H 2 O absorption area obtained from measurements perpendicular to the c-axis of apatite. This crystallographic control on the H 2 O absorption leads to a linear correlation between the crystallographic orientation and the H 2 O absorbance (Fig. 5B). While most of the H 2 O-bearing apatite specimens contain one major H 2 O absorption band in an IR spectrum, apatite specimen HRZ contains two main bands in the non-deconvoluted IR spectrum of H 2 O, located at wavenumbers of ~ 3582 cm −1 and ~ 3470 cm −1 (see below).

Reproducibility and limit of quantification
To test the reproducibility of ATR-FTIR analyses of CO 2 and H 2 O in apatite, we conducted repeat analyses of the same analytical spot (i.e., same location in the apatite specimen) of CO 2 and H 2 O bearing apatite specimens. All spectra were Fig. 3 CO 2 absorption spectra of apatite specimens YAM, SAP3, GL, MT, HAM, and HOI. Blue spectra represent analyses parallel to the c-axis and red spectra show analyses perpendicular to the c-axis. Wavenumbers of the main bands are assigned to measurements parallel to the c-axis (blue spectra). The integrated area under the curves are given for both analyses parallel (blue) and perpendicular (red) to the c-axis (see main text for a detailed discussion on band positions). The intergraded absorption areas of samples YAM, SAP3, GL, MT, and HAM were used for the calibration of the FTIR (see main text). The 2SD uncertainty of the individual absorption areas is estimated to be ± 5% (see main text for more information) ◂ Fig. 4 Absorption area of CO 2 bands in apatite when measured on differently orientated apatite grains. Integrated absorption area of CO 2 bands (vertical axis) in apatite specimens YAM, SAP3, and HOI vs. wavenumber of the phosphate bands (horizontal axis). The highest wavenumber of the phosphate band for each sample represents analyses parallel to c-axis and the lowest wavenumbers represent analyses of apatite perpendicular to c-axis (see Fig. 2). The dotted line at wavenumber 1019 cm −1 marks the change of CO 2 absorption in respect to the crystallographic orientation, illustrating that lower absorption areas are obtained when the phosphate absorption band sits at ≤ 1019 cm −1 acquired under the same analytical conditions and corrected identically for background noise and the same absorption band areas were integrated. Figure 6 shows 14 analyses of a YAM apatite grain (1.05 wt% CO 2 ) and 6 analyses of a VOH apatite grain (0.99 wt% H 2 O). The standard deviation for sets of repeated CO 2 and H 2 O analyses is < 2% and standard errors are < 1%. For individual measurements of sample material, we suggest to consider a conservative uncertainty of 5% for H 2 O and CO 2 quantification at the 95% confidence interval.
Limit of quantification (LOQ) of ATR-FITR analyses is typically estimated as the combination of the average background signal (BG) summed with the tenfold standard deviation (SD) of the background signal. In the case of the two examples with low CO 2 and H 2 O concentrations, as shown in Fig. 7, the calculated LOQ, via the above method, is similar to the approximation of LOD using signal to noise ratio (SNR), for which a ratio of 3 is typically considered as a threshold. It has to be kept in mind that the integrated absorption area is not only dependent on the absorption band height, but also on the band width. Therefore, an exact estimate of the LOQ in ppm is difficult. However, based on our data we estimate a LOQ for CO 2 of ~ 100 ppm and ~ 400 ppm for H 2 O (Fig. 7). The limit of detection, constrained by the average of the BG signal summed with the threefold SD, is significantly lower and might be in the ppm range for CO 2 (Fig. 7).
For the absolute CO 2 (in wt%) determination by ATR-FTIR, we constructed two calibration lines (parallel and perpendicular to the c-axis), both forced through the zero intercept of the vertical and horizontal axes (Fig. 8). The horizontal axis shows the integrated absorption bands of CO 2 in the wavenumber region ~ 1560 to 1360 cm −1 obtained by ATR-FTIR (see above), and plotted along the vertical axis is the absolute CO 2 (wt%) content determined by NRA measurements (see Table 1). The linear calibration line for analyses perpendicular to the c-axis is constructed via NRA and ATR-FTIR analyses of apatite specimens GL, YAM, HAM, MT, and SAP3 (Fig. 8). The data are fit by the following equation: where A CO2 is the integrated area of the CO 2 bands between wavenumbers ~ 1560 to 1360 cm −1 (Fig. 3). The calibration line for ATR-FTIR analyses parallel to the c-axis is defined by apatite specimen YAM and SAP3 (Fig. 8) (note that ATR-FTIR analyses of HAM apatite were not used for the calibration as analyses of the prepared sample returned slightly heterogeneous A CO2 values), both of which exhibit two main CO 2 bands, whose heights are related to the crystallographic orientation (Fig. 3). For such apatite specimens, when measured parallel to their c-axis, the following equation can be employed to calculate their CO 2 contents: where A CO2 is the integrated CO 2 absorption band area. Our data suggest that the CO 2 band heights and the corresponding integrated absorption areas only change when (1) CO 2 (wt%) = 0.32 × A CO2 , (2) CO 2 (wt%) = 0.40 × A CO2 , apatite is analyzed parallel to its c-axis, with wavenumbers ≤ 1019 cm −1 for their phosphate band (see above and Fig. 4).

H 2 O calibration
To calibrate the ATR-FTIR technique for the measurement of H 2 O contents in apatite, we used H 2 O measurements by ERD of several apatite specimens (HRZ, VOH, and MT), which we then compared with ATR-FTIR analyses. Similar to the  CO 2 calibration (see section above), ATR-FTIR analyses were performed along transects across the different apatite specimens, orientated parallel and perpendicular to the c-axis to test their homogeneity. The integrated H 2 O absorbance bands for analyses parallel to the c-axis are 0.22 ± 0.01 (2SD) (n = 12) for HRZ, 1.19 ± 0.06 (n = 11) for VOH, and 1.22 ± 0.06 (n = 13) for MT. The integrated H 2 O absorbance bands measured perpendicular to the c-axis are 0.34 ± 0.02 (2SD) (n = 13) and 0.33 ± 0.02 (2SD) (n = 10) for MT and VOH, respectively. Our data show that absolute H 2 O values in apatite are linearly correlated with the integrated absorption area of the H 2 O bands ( Fig. 9) (FTIR spectra can be found in supplementary Fig. A-1). Similar to the approach by Wang et al. (2011), we integrated all absorbance bands between wavenumbers 3400 and 3600 cm −1 , accounting for all OH bonds, such as OH-F, OH-Cl, and others (see e.g., Tacker 2004;Fleet 2017). The calibration was forced through the zero intercept of the horizontal and vertical axis. Absolute H 2 O concentration in apatite for analyses parallel to the c-axis can be calculated via the following equation: where A H2O is the integrated absorption area of H 2 O in the wavenumber region between 3470 and 3590 cm −1 (Fig. 9). The absorption bands of H 2 O in apatite, when measured perpendicular to the c-axis, are less pronounced compared to measurements parallel to the c-axis (see above and Fig. 5). Accordingly, the slope of the calibration line for calculating absolute H 2 O contents in apatite becomes significantly steeper (Fig. 9) resulting in the equation: Fig. 7 A CO 2 IR absorption bands in an apatite grain of sample 19JH-03 (see main text for details on sample) analyzed perpendicular to its c-axis. The signal to noise ratio (SNR) of the background corrected wavenumber region is ~ 3.5 and the repeated analysis (green spectrum) produces indistinguishable absorption bands and SNR. Limit of quantification (LOQ) is defined as the average of the background signal (BG) plus ten times the standard deviation of the back-ground signal in the wavenumber region 1600-1300 cm −1 . The limit of detection (LOD) is calculated as the average BG signal plus three times its standard deviation. B H 2 O IR absorption band of HOI apatite (analyzed parallel to c-axis). SNR of the background corrected wavenumber region is ~ 3.7 and the repeated analyses (green spectrum) produces the same absorption and SNR. LOQ and LOD are calculated in the same way as for CO 2 in A   Fig. 8 Calibration lines for ATR-FTIR measurements of CO 2 in apatite. The vertical axis displays the CO 2 (wt%) content of apatite determined by NRA and the horizontal axis shows the area of the integrated IR absorption bands of CO 2 in the wavenumber region 1600-1300 cm −1 , when measured parallel (diamond symbols and corresponding blue regression line forced through the origin) and perpendicular (round symbols and corresponding red regression line forced through the origin) to their c-axis. Uncertainties are shown at the 95% CI where A H2O is the integrated IR absorption area of H 2 O in apatite. Note that this calibration line (Eq. 4) is anchored by two apatite specimens (MT and VOH) and the zero intercept of the vertical and horizontal axes, since the H 2 O content of HRZ is too low to produce H 2 O absorption bands when measured perpendicular to the c-axis (see discussion). In contrast to the absorption of the CO 2 bands, the H 2 O absorption is consistently (and to a greater degree) affected when measured along different crystallographic orientations (see also sections above and Fig. 5).
The corrected H 2 O absorption (A H2Ocorr ), for randomly orientated apatite grains can be calculated based on the phosphate absorption band position. Figure 5B shows that there is a linear relationship of absorption with wavenumber of the phosphate peak. The best approach for measuring a sample where the crystallographic orientation of apatite is not clear is to measure multiple grains in random orientation, fit a linear line through the data points and obtain an absorption value at the high wavenumber of 1019 cm −1 to 1022 cm −1 , representing the phosphate absorption band parallel the c-axis. For rare cases, where only a single measurement is possible, a corrected absorption parallel the c-axis can be retrieved from a random orientation via the following equation: where A H2Omeas is the measured integrated peak area of H 2 O of the unknown in the random orientation and v Phos is the (5) A H2Ocorr = A H2Omeas × 8∕ v phos − 1011.13 , wavenumber of the phosphate band in the random orientation. The value of 1011.3 derives from the x-axis intercept of the best fit regression of the random grains shown in Fig. 5B, while the scaling factor 8 is the difference between the 1019 cm −1 of the phosphate absorption band position parallel the c-axis and the intercept at 1011 cm −1 . A H2Ocorr can then be taken to calculate the absolute H 2 O content via Eq. 3 used for H 2 O quantification parallel to the c-axis. However, it has to be considered that the wavenumbers of the PO 4 band can be slightly dissimilar in different samples. For example, measurements perpendicular to c-axis can result in a phosphate band at ~ 1013 cm −1 to ~ 1016 cm −1 , and 1019 cm −1 to 1022 cm −1 for analysis parallel to their c-axis. Given this uncertainty we, therefore, recommend, if possible, analyzing apatite either parallel or perpendicular to their crystallographic orientations and using equation five only in cases where no other measurements are possible.

Absorption bands of CO 2
Previous studies assigned IR absorption bands in the wavenumber region ~ 1560 cm −1 to ~ 1360 cm −1 to different CO 3 2− substitutions in apatite. CO 3 2− type A substitutions are located in the c-axis structural channel (the anion site), while type B CO 3 2− substitutes for PO 4 (e.g., Fleet and Liu 2003;Fleet et al. 2004;Tacker 2008 for a summary). Type-A CO 3 2− substitutions can be subdivided into type A1 and type A2, which produce IR absorption bands at ~ 1540 cm −1 and ~ 1450 cm −1 (type A1) and ~ 1563 cm −1 and 1506 cm −1 (Type A2) (Fleet et al. 2004). Both types sit in the channel position, however, type A2 is suggested to charge compensate the substitution of CO 3 2− for PO 4 and sits in a stuffed channel position (Fleet et al. 2004). A main IR absorption band for type B (termed type B2 in Tacker 2008) PO 4 is present at wavenumbers ~ 1455 cm −1 to 1450 cm −1 (Fleet et al. 2004) and a second type B band exists between wavenumbers 1430 cm −1 and 1405 cm −1 , however, its exact position is likely controlled by the composition of apatite (Tacker 2008 and references therein). The latter band, in the wavenumber region between 1430 and 1405 cm −1 , can be further subdivided into type B1 and type B2 substitutions with wavenumbers of ~ 1427 and ~ 1408 cm −1 , respectively, as elucidated in the example by Tacker (2008). These two subtypes of type B substitutions likely represent different crystallographic positions of carbonate at the PO 4 site (Fleet et al. 2004;Tacker 2008;Fleet and Liu 2003).
While it is outside the scope of this study to assign all of the individual absorption bands to different CO 2 bonds and vibration modes, we suggest that some of the bands can be assigned to specific (sub-) type carbonate substitutions. Peak deconvolution (e.g., Tollan and Hermann 2019) of the ATR-FTIR spectra show that the IR absorption of CO 2 in the wavenumber region 1560 to 1360 cm −1 is the result of an estimated ten different absorption peaks (Fig. 10A'-C'). For example, Band 1, with a peak position at 1497 cm −1 , likely represents type A2 substitution and Bands 7 (1432 cm −1 ) and 8 (1429 cm −1 ) are type B2 carbonate substitutions, while Band 10 (1406 cm −1 ) represents a type B1 carbonate substitution. The complexity of the CO 2 IR spectrum of apatite shows that many different substitutions are possible, which likely produce several absorption bands, some of which may need further experiments in combination with spectroscopy analyses to be better understood. Below we give a first order interpretation of the measured spectra.
Apatite specimen SAP3 and YAM (Fig. 3) show distinct type B2 doublet CO 3 2− absorption bands (Fig. 10A,  B). However, the apparent type B2 absorption band (using the nomenclature by Tacker 2008) at ~ 1456 cm −1 likely overlaps with the absorption of CO 3 2− type A1 substitution (c.f., Tacker 2008 and references therein and band 3 in Fig. 10A'). HOI apatite shows a shoulder on the B2 peak (1430.5 cm −1 ), likely caused by a B1 absorption band (band 10 in Fig. 10b', c.f., Tacker 2008). The HOI spectra also show a broad peak at higher wavenumbers (~ 1500 cm −1 ), which can be assigned to type A2 CO 3 2− substitution (band 1 in Fig. 10B'). CO 3 2− IR spectra of apatite specimens MT and GL (Figs. 3 and 10C) are more complex. The absorption band at ~ 1438 cm −1 is difficult to assign to a certain CO 3 2− type substitution, however, the absorption band at ~ 1419 cm −1 likely represents type B1 CO 3 2− substitution. CO 3 2− type A1 substitution absorption bands form a distinct peak at ~ 1470 cm −1 (band 3 in Fig. 10C'), with absorption peaks on its shoulders, potentially representing type B2 and type A2 CO 3 2− substitutions (Fig. 10C). In all specimens, IR absorption of type B2 (and type A) CO 3 2− substitutions increase when apatite is analyzed perpendicular to the c-axis. The only IR absorption band that increases when apatite is analyzed parallel to the c-axis is located at a wavenumber of ~ 1438 cm −1 in the MT and GL apatite (Fig. 10C).

Absorption bands of H 2 O
The IR absorption bands of H 2 O in apatite are less complex than those for CO 2 . Nevertheless, multiple absorption bands related to OH vibration are routinely observed, with the absorption of OH-F vibration bands (~ 3533 cm −1 ) typically resulting in the most significant peak ( Fig. 1 and see Tacker 2004). The deconvoluted spectra suggest that the main "OH-F" band in the IR spectra is composed of at least three absorption peaks (bands 3-5, see legend of Figs. 11A', B'), and we speculate that all of them are related to OH-F bonds in apatite, since all samples contain these three bands that make up the main peak. Based on previous studies (e.g., Tacker 2004 and references therein), peak 2 can be assigned to OH-OH vibration at ~ 3566 cm −1 , as for example observed in VOH apatite (Fig. 11A). Peak 6 is attributed to OH-Cl bonds, (Fig. 11A', B'). The absence of peak 6 in VOH apatite agrees with EPMA results suggesting a low Cl content, whereas HRZ apatite contains ~ 0.6 wt% Cl (Table 2), which likely leads to the absorption peak 6. According to Tacker (2004) the absorption peak 7 at a wavelength of ~ 3470 cm −1 most likely reflects OH-REE bonds (Fig. 11B). Indeed, HRZ apatite contains several wt% REEs (Hammerli, unpublished data).

Quantification of CO 2 and H 2 O by ATR-FTIR
For the quantification of CO 2 and H 2 O in apatite we followed a similar approach as described in the transmission FTIR studies by Clark et al. (2016) and Wang et al. (2011), in which the absorption areas of the H 2 O and CO 2 peaks in the wavenumber regions of ~ 3600 cm −1 to 3500 cm −1 and 1500 cm −1 to 1350 cm −1 are calibrated against ERD and NRA CO 2 and H 2 O measurements, respectively. The ATR-FTIR method for measuring CO 2 and H 2 O, described in this study, bears two main advantages over transmission FTIR techniques. First, samples are not required to be prepared as wafers polished on both sides. FTIR analyses in ATR mode can be directly conducted on polished surfaces, for example on apatite in polished thin sections or in epoxy mounts. Second, the PO 4 peak does not lead to total absorbance in apatite spectra generated by ATR-FTIR measurements (Fig. 1) and can, therefore, be used to determine the crystallographic orientation of the analyzed sample. This means that the CO 2 and H 2 O absorption bands of randomly orientated apatite can be corrected for crystallographic effects (see sections above).
Conversely, the main advantage of transmission FTIR is that lower concentrations can be measured, which can be in the ppm and sub-ppm range for H 2 O and CO 2 , respectively (Wang et al. 2011;Clark et al. 2016), while the limit of quantification for ATR-FTIR analysis is estimated to be ~ 400 ppm for H 2 O, when measured parallel to the c-axis and ~ 100 ppm for CO 2 , when measured perpendicular to the c-axis (see above). However, minimum detection and quantification limits, especially for H 2 O, are likely to some degree governed by the H 2 O absorbance band shape. The signal to background ratio from narrow H 2 O absorbance bands is higher than for wider or separated absorbance bands, even if the H 2 O content in all three scenarios are the same, hence a lower limit of quantification can be achieved in the former case. If no absorption is detected with the ATR-FTIR analysis, this gives valuable information for the sample preparation for transmission measurements in terms of sample thickness of the doubly polished wavers.

Comparison of H 2 O determination by EPMA vs. ATR-FTIR
As discussed before, measuring and calculating H 2 O concentrations of apatite is challenging, with the most routine approach for constraining H 2 O being the stoichiometric method based on EPMA measurements (see above and Ketcham 2015). Conducting ATR-FTIR H 2 O analysis at the same location as EPMA measurements allows for an assessment of the accuracy of EPMA-derived H 2 O concentrations (see Table 2). Figure 12 shows H 2 O (wt%) determined by ERD and FTIR vs. H 2 O calculated via stoichiometric constraints based on EPMA measurements. Note that all apatite grains were measured perpendicular to their c-axis as  Goldoff et al. (2012). Our data (Fig. 12) show that the calculation of H 2 O in apatite when following the methods by Goldoff et al. (2012) and Ketcham (2015), and by accounting for CO 2 on the anion site, leads to an overall good agreement between absolute methods (NRA and FTIR) and the EPMA approach (i.e., data of the different approaches are within ~ 20%, Fig. 11) for all studies apatite specimens with variable compositions. When the CO 2 content of apatite is not known, the stoichiometric calculation of H 2 O can in some cases lead to an overestimation of the H 2 O content. The reason is that the CO 2 at the anion site is not accounted for and hence the calculated H 2 O content at this site is too high (see Fig. 12).

CO 2 and H 2 O content in apatite of carbonatitic rocks
CO 2 and H 2 O play a major role in carbonatitic systems (Jones et al. 2013 for a review). For example, experiments have revealed that the solidus of carbonatitic melt is lowered by water (Poli 2015) and Martin et al. (2013) have shown that H 2 O is key for the immiscibility of parental magma of carbonatitic melt and also for enriching carbonatitic melt in REE. However, recognizing conjugate silicate and carbonatite melt, due to immiscibility is often challenging in natural settings due to post emplacement modifications of the intrusions (e.g., Martin et al. 2012). Besides melt inclusions, apatite, typically a major REE phase in carbonatitic rocks and igneous rocks in general, is a promising mineral to record CO 2 and H 2 O contents of carbonatitic melt (see, e.g., Chakhmourandian et al. 2017;Santos and Clayton 1995;Broom-Fendley et al. 2020). Measuring the volatile content of apatite via combined EPMA (Cl, F) and ATR-FTIR (CO 2 , H 2 O) analyses might be a helpful tool for further understanding the formation of carbonatites, and especially the immiscibility of carbonatite and silicate melt, as well as post emplacement alteration and element redistribution (Broom-Fendley et al. 2016. For example, the composition of apatite of the Mud Tank (MT) carbonatite in the Strangway Ranges, Northern Territory, Australia, suggests that MT apatite formed from a hydrous melt, as MT apatite contains ~ 1 wt% H 2 O and ~ 0.4 wt% CO 2 (Tables 1 and  2). While the CO 2 content of MT apatite is very similar to other published CO 2 concentrations of carbonatitic apatite (Binder and Troll;1989;Santos and Clayton 1995), the H 2 O content of MT apatite is significantly higher (by a factor 4) than in "typical" carbonatite apatite (Binder and Troll 1989). By assuming that the MT apatite retained its original geochemical fingerprint, a hypothesis supported by the mantlelike oxygen isotope signatures and the absence of alteration zones (Yang et al. 2020), we speculate that the Mud Tank carbonatite did not exsolve significant amounts of hydrous fluids, at least at the currently-exposed stratigraphic level. This would also explain the lack of significant alteration of the gneissic host rocks in agreement with earlier interpretations by Crohn and Moore (1984). Future studies of CO 2 and H 2 O contents in apatite at different stratigraphic levels of (carbonatitic) intrusions, might be useful to trace degassing and fluid exsolution processes during the emplacement of igneous rocks to trace, for example, proximal hydrothermal alteration and ore genesis by hydrothermal fluids. In addition, and given the seemingly universal elevated CO 2 in apatite of alkaline and carbonatitic rocks (e.g., Binder and Troll 1989;Santos and Clayton 1995;Broom-Fendley et al. 2020, this study), quantifying CO 2 via FTIR might be a useful tool for REE deposit exploration following a similar approach as described in Mao et al. (2016).

CO 2 and H 2 O in apatite of metamorphic rocks
Fluids and their compositions play a central role during prograde metamorphism. Metamorphic degassing in collisional orogens likely contributes significantly to the atmosphere's CO 2 budget (e.g., Kerrick and Caldeira 1998;Perrier et al. 2009;Skleton 2011;Groppo et al. 2017 Table 2) and round symbols show H 2 O determination when CO 2 contents are ignored. Uncertainties are 2SD of multiple ERD (Table 1) measurements or FTIR analyses perpendicular to the c-axis across a grain of the respective sample (2SD are the same for both symbol types). Note that for apatite SAP3, the uncertainty for stoichiometric H 2 O quantification based on EPMA measurements by ignoring its CO 2 content is ± 0.12 wt%. H 2 O. HOI values determined by FTIR are based on the spectra shown in Fig. 7 and 19JH-03 values are taken from Fig. 13  Fig. 13 A IR CO 2 absorption bands of apatite in sample 19JH-03 (including typical apatite morphologies and analytical sites of their cores) and B IR H 2 O absorption bands of the same apatite grains as shown in A. Dotted blue lines in A and B represent analyses parallel to the c-axis of apatite grains (n = 5) and red lines show analyses per-pendicular to the c-axis of different apatite grains (n = 5). C H 2 O and CO 2 concentrations of the analyzed apatite grains of sample 19JH-03. Blue circles represent analyses parallel to the c-axis and red circles are H 2 O and CO 2 concentrations of apatite grains measured perpendicular to the c-axis 2018). Modeling fluid compositions is challenging in heterogeneous rock types, such as in metasedimentary lithologies, as compositional changes on the thin section-scale lead to a range of attempted local equilibrium reactions between fluids and minerals. An alternative and complementary approach to geochemical modeling of fluid compositions is probing minerals, such as apatite, which can act as an archive of fluid compositions. To test the feasibility of our method in metamorphic rocks we analyzed a metasedimentary sample of the Bündnerschiefer Formation (BdsF) of the Central Alps. Rocks of the BdsF are typically formed during prograde Alpine metamorphism of marine sediments. Our sample (19JH-03) comes from metamorphosed Bündnerschiefer at Campolungo that underwent peak pressure and temperature conditions of 620 °C and 6.5 kbar at peak temperature (Todd and Engi 1997). It contains large (~ 1 cm) garnet porphyroblasts within fine-grained layers composed of quartz, plagioclase, zoisite, rutile, biotite, and minor sulfides alternating with predominantly calcite bearing layers. Sample 19JH-03 shows no indications of significant alteration or regression and hence the mineral assemblage likely represents peak metamorphic conditions. We analyzed the cores of apatite from mineral separates parallel and perpendicular to their c-axis by ATR-FTIR to test if apatite minerals record CO 2 and H 2 O during metamorphism (Fig. 13).
The results show that the H 2 O content in apatite is relatively uniform at ~ 0.30-0.33 wt%, which suggests that apatite attempted to reach equilibrium in the presence of a fluid at ~ 620 °C, which agrees with the findings of Hammerli et al. (2014). CO 2 contents in 19JH-03 apatite vary between ~ 100 and ~ 600 ppm (Fig. 13C) and in light of the uniform H 2 O content, variability of CO 2 concentrations likely suggests variable aCO 2 in metamorphic fluids on a cm-scale. While we are unable to quantify aCO 2 in the metamorphic fluid during metamorphism based on apatite compositions, mainly due to the lack of established CO 2 partition coefficients, this example illustrates that H 2 O and CO 2 contents in metamorphic rocks can be systematically and qualitatively studied via ATR-FTIR, which is useful to probe the enigmatic CO 2 release during metamorphism (e.g., Ramos et al. 2020;Stewart and Ague 2020) via the presence of CO 2 in metamorphic apatite.

Summary and future implications
We calibrated the CO 2 and H 2 O ATR-FTIR spectra of polished apatite specimens to absolute CO 2 and H 2 O concentrations. The apatite compositions used for the calibration of the ATR spectra varied from F-rich specimens (YAM, SAP3) to hydroxy-rich samples (MT, VOH), covering most common apatite compositions in igneous and metamorphic rocks (e.g., Piccoli and Candela 2002;Spear and Pyle 2002). However, it would be useful to develop further standards for H 2 O and CO 2 measurements by ATR-FTIR of Cl-rich apatite, with significantly higher Cl contents than those analyzed in the current study (~ 0.6 wt%, Table 2).
Importantly, all ATR-FTIR spectra in this study were produced using a Ge crystal in the ATR module with an internal reflection angle of 21.5°-37° (see methods). Therefore, using different ATR modules and crystal-types with different internal reflection angles will likely require recalibration of the absorbance areas of the spectra to absolute CO 2 and H 2 O values. Our data show a linear relationship between the integrated area of the CO 2 and H 2 O absorption bands and the absolute CO 2 and H 2 O concentrations determined by NRA and ERD, respectively, which can be used to directly calculate CO 2 and H 2 O contents in apatite from their FTIR spectra. The crystallographic orientation of apatite can be determined via the Funding Open access funding provided by University of Bern.
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