Synthetic fluid inclusions XIX. Experimental determination of the vapor-saturated liquidus of the system H2O–NaCl–FeCl2

Accepted Manuscript Synthetic fluid inclusions XIX. Experimental determination of the vapor-saturated liquidus of the system H2O-NaCl-FeCl2 Pilar Lecumberri-Sanchez, Matthew Steele-MacInnis, Robert J. Bodnar PII: DOI: Reference:

S0016-7037(14)00510-9 http://dx.doi.org/10.1016/j.gca.2014.08.015 GCA 8941

To appear in:

Geochimica et Cosmochimica Acta

Received Date: Accepted Date:

14 May 2014 12 August 2014

Please cite this article as: Lecumberri-Sanchez, P., Steele-MacInnis, M., Bodnar, R.J., Synthetic fluid inclusions XIX. Experimental determination of the vapor-saturated liquidus of the system H2O-NaCl-FeCl2, Geochimica et Cosmochimica Acta (2014), doi: http://dx.doi.org/10.1016/j.gca.2014.08.015

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Synthetic fluid inclusions XIX. Experimental determination of the vapor-saturated liquidus of the system H2O-NaCl-FeCl2 Pilar Lecumberri-Sanchez 1,2,*, Matthew Steele-MacInnis 1,2, Robert J. Bodnar1

1. Dept. of Geosciences, Virginia Tech, Blacksburg VA 24061 USA 2. Present address: Inst. for Geochemistry and Petrology, ETH Zürich, 8092 Zürich, Switzerland

*Corresponding author. Email: [email protected] Tel.: +41 44 632 3991 Fax: +41 44 632 1827

Email addresses: [email protected] (Lecumberri-Sanchez) [email protected] (Steele-MacInnis); [email protected] (Bodnar)

Abstract Magmatic-hydrothermal fluids associated with felsic to intermediate composition magmas are generally dominated by (Na±K)Cl, but often the fluids also contain significant concentrations of FeCl2. Previously, fluid inclusions containing such fluids were interpreted using the properties of H2O-NaCl because the effect of FeCl2 on the phase equilibrium and volumetric (PVTx) properties of aqueous fluids was essentially unknown. In this study, synthetic fluid inclusion experiments have been conducted to determine the vapor-saturated liquidus phase relations of the system H2O-NaCl-FeCl2. Microthermometric and microanalytical measurements on synthetic fluid inclusions have been combined with the limited existing data, as well as with predictions based on Pitzer's formalism, to determine the ternary cotectic and peritectic phase boundaries and liquidus fields. The liquidus is qualitatively similar to those of other ternary systems of 1

H2O-NaCl plus divalent-cation chlorides (MgCl2 and CaCl2) and has been characterized through empirical equations that represent the liquid salinity on the ice- and haliteliquidus surfaces. The ice and halite liquidi intersect at a metastable cotectic curve, which can be used to determine fluid compositions in this system if metastable behavior is observed. Furthermore, based on the experimentally determined liquidus, bulk salinities of natural fluid inclusions can be determined from the last dissolution temperatures of ice and/or halite using the new empirical equations.

Keywords: magmatic-hydrothermal systems; experimental petrology; microthermometry; LA-ICPMS analysis; ferrous chloride; daughter minerals; freezing-point depression; thermodynamics

1. INTRODUCTION Fluid inclusions (FI) in minerals commonly provide the best record of the pressuretemperature-volume-composition (PVTx) properties of geologic fluids (Roedder, 1984). The compositions of fluid inclusions can be estimated by microthermometry (measuring the temperature(s) of phase changes in the FI), as well as by chemical microanalysis (Roedder, 1984). Fluid inclusion major (and potentially minor) element compositions are commonly estimated from the last dissolution temperature(s) of one or more solid phases (including H2O-ice and/or various salts, salt hydrates or clathrates) according to the experimentally determined liquidus relations of model chemical systems (e.g., H2ONaCl±KCl±CaCl2±MgCl2) under vapor-saturated conditions (e.g., Sterner et al., 1988, Bodnar, 1993; Dubois and Marignac, 1997; Steele-MacInnis et al., 2011). The fluid total salinity, usually reported in mass (or weight) percent, thus determined may then be combined with element ratios obtained from laser ablation (LA)-ICPMS analyses to

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calculate the absolute concentrations of major and trace elements in the FI (e.g., Heinrich et al., 2003). Trace element concentrations obtained from combined microthermometry and LA-ICPMS analysis are optimized when the model system used to interpret the liquidus phase relations is a good approximation of the actual composition of the FI, as shown recently by Schlegel et al (2012). Vapor-saturated liquidus phase relations have been extensively characterized for binary H2O-NaCl fluids (see the reviews by Bodnar and Vityk, 1994, and Bodnar, 2003, and references therein), as well as ternary systems of H2O-NaCl plus KCl, CaCl2 or MgCl2 as the predominant chloride components (Chou, 1987; Sterner et al., 1988; Oakes et al., 1990; Vanko et al., 1992; Dubois and Marignac, 1997; Steele-MacInnis et al., 2011). In general, the liquidus relations for FI containing more than three major components (quaternary systems, etc.) have not been well characterized experimentally (Liebscher, 2007), although compositions of H2O-NaCl-KCl-CaCl2-MgCl2 FI may be estimated based on combined LA-ICPMS analysis and thermodynamic modeling using Pitzer's formalism (Pitzer, 1973; Pitzer and Mayorga, 1973; Leisen et al., 2012). Hydrothermal fluids in many geologic environments, particularly those with temperatures > 400°C and/or associated with intermediate composition magmas, commonly have iron concentrations of several mass percent (Yardley, 2005; Yardley and Bodnar, 2014). Thus, the review by Shepherd et al. (1985) listed iron chloride as one of the "ten most commonly reported" solid phases in aqueous fluid inclusions. Similarly, Roedder (1984) noted that Fe is one of the most abundant metals in aqueous FI from porphyry deposits, such that sometimes "the solutions must have held far more Fe than Na" (Roedder, 1984, p. 445). For example, Grant et al. (1977) described high-salinity FI

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from some Bolivian porphyry Sn deposits, containing hydrous iron chloride daughter minerals that occupy ~50 vol% of the inclusions. Based on a recent compilation of FI data from porphyry systems worldwide, Bodnar et al. (2014) noted that the iron concentration in the fluid is commonly comparable to or greater than the concentration of other major cations. Despite the apparent ubiquity and geochemical abundance of iron chloride in hydrothermal fluids (Yardley, 2005; Yardley and Bodnar, 2014), few experimental data are available on the PVTx properties of aqueous iron chloride-bearing systems (Liebscher, 2007). Compositional estimates based on microthermometric measurements of Fe-bearing fluids are currently limited, because the available experimental data on the vapor-saturated liquidus of iron chloride-bearing fluids does not cover the complete range of H2O-NaCl-FeCl2 compositions observed in natural fluids (Fig. 1). Most available data on the liquidus in the system H2O-NaCl-FeCl2 are for low-salinities (Fig. 1). Baldassaro (1998) studied the ice liquidus along two pseudobinary joins, and Chou and Phan (1985) investigated solubility relations along several pseudobinaries between 25 °C and 70 °C. Atbir et al. (2000) further studied the solubility relations between 0 °C and 70 °C and partially defined the halite-FeCl2·6H2O and halite-FeCl2·4H2O cotectic boundaries. In addition, the H2O-FeCl2 binary liquidus has been partially defined by the studies compiled by Linke (1958), and the anhydrous FeCl2-NaCl binary liquidus has been characterized by Ionov et al. (1960). These data are listed in Tables 1 and 2. In the present study, we used the synthetic fluid inclusion method (Sterner and Bodnar, 1984) to investigate and characterize the liquidus phase relations in the system H2O-NaCl-FeCl2, over the range of compositions reported for natural FI (Bodnar et al.,

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2014). Ferrous chloride (rather than ferric chloride) was chosen for these experiments because, over a five order of magnitude range of fO2 conditions appropriate for natural magmatic-hydrothermal systems, iron in aqueous fluids occurs predominately as Fe2+ (Simon et al., 2013). Moreover, iron is transported as the ferrous iron complex FeCl20 in magnetite-buffered, sulfur-absent fluids (Chou and Eugster, 1977). 2. METHODS 2.1 Experimental procedure Synthetic H2O-NaCl-FeCl2 FI were trapped in quartz at elevated pressure-temperature conditions (1-3 kbars; 500-700°C) using the procedures described by Sterner and Bodnar (1984), Bodnar and Sterner (1987) and Sterner et al. (1988). Starting solutions were prepared from reagent grade FeCl2·4H2O and NaCl (Alfa Aesar) and de-oxygenated, doubly distilled water. For experiments with bulk compositions below salt (halite or FeCl2·4H2O) saturation at room temperature, batch aqueous solutions were prepared. The solution (30-120 µL) was loaded into Pt or Au capsules using a microliter syringe, along with a pre-fractured quartz core that was ~5-10 mm long by ~3 mm in diameter. For experiments with bulk compositions greater than the room temperature salt solubility, we used a procedure similar to the one described above, but also added solid NaCl and/or FeCl2·4H2O to achieve the desired bulk composition, as described by Bodnar (1994). Fresh solutions were prepared as required, to prevent compositional modification by oxidation or precipitation of Fe3+ bearing solids. The capsules were sealed by welding and run at pressures of 1 to 3 kbar and temperatures of 500 to 700 °C in René 41 (Ni-CrMo-Co-Al-Ti alloy) cold-seal pressure vessels. The pressure medium was water, and the combination of the René 41 vessel and the water pressure medium buffered fO2 at nickel-

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nickel oxide (NNO) (Eugster and Skippen, 1967; Popp et al., 1984; Frank et al., 2001). Thus, the oxidation state of iron in solution would be fixed as Fe2+, and the speciation dominated by FeCl20 (aq), at the experimental conditions (Simon et al., 2004). Below we discuss tests that were conducted after the FI were synthesized to confirm that compositions did not change during the experiment or during quenching. The capsules were weighed before and after the experiment to check for any change in mass (which would indicate leakage during the experiment). Samples contained in capsules that leaked were discarded.

2.2 Analytical Protocols The quartz cores were sliced into 1 mm thick wafers, which were then doubly polished for petrographic examination. Synthetic FI samples were observed petrographically to identify the phases present and phase ratios at room temperature. These observations were made to determine the compositional range over which the solutions were halitesaturated, based on the presence of halite daughter minerals at room temperature, and to assess whether any of the experiments were at PTx conditions outside of the one-phase fluid field, which would be indicated by inconsistent phase ratios and/or coexisting liquid-rich and vapor-rich FI (which were not observed in any of our samples). Following petrographic characterization, the FI were analyzed by microthermometry and LAICPMS. Low-temperature microthermometric measurements were made using a USGStype gas-flow stage (Werre et al., 1979). Temperature measurements were calibrated according to the triple point of CO2 (-56.6 °C) and the triple point and critical point of

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H2O (0.01 °C and 374.1 °C, respectively) using synthetic FI standards (Sterner and Bodnar, 1984). The synthetic FI samples were first cooled to ~-196 °C by delivering liquid nitrogen into the fluid inclusion stage sample chamber, then heated to observe and record the temperatures of dissolution of solid phases in the FI. For temperatures below 0°C, the estimated reproducibility was ±0.1 °C, as previously noted by Sterner et al (1988) and Fall et al. (2009). High-temperature microthermometric measurements (i.e., for FI that contained a halite daughter mineral and/or iron chloride hydrates at room temperature), the dissolution temperature (Tm) was measured using a Linkam TS1400XY stage (Esposito et al., 2012), calibrated according to the 1-atm melting point of sulfur (115.2 °C), the critical point of H2O (374.1 °C) and the 1-atm α/β transition of quartz (574 °C). Reproducibility of the Tm,halite measurements was approximately ±0.5 °C. The iron-to-sodium (Fe/Na) elemental concentration ratios within the synthetic FI were measured by LA-ICPMS at Virginia Tech. The LA-ICPMS system consists of a 193 nm GeoLasPro Laser Ablation system coupled to an Agilent 7500ce inductively coupled plasma mass spectrometer. Synthetic FI were ablated with a laser beam diameter selected such that the inclusion was wholly encompassed within the ablation pit. A NIST610 glass standard was analyzed before and after each sample for calibration. The signals were processed using the AMS software (Mutchler et al., 2008). Thus, we compared the Fe/Na ratios in the FI with the starting compositions that were weighed into the capsules, in order to test for any modification of fluid composition during the experiment (Section 3).

2.3 Thermodynamic and empirical modeling of the vapor-saturated liquidus

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The ice liquidus Tx (temperature-composition) relations, as well as intersections of the ice liquidus with the hydrohalite and halite liquidi, were predicted using Pitzer's model (Pitzer, 1973) according to the algorithms described by Harvie and Weare (1980) and Spencer et al. (1990), using the Fe-Na, Fe-Cl and Fe-Na-Cl interaction parameters tabulated by Marion et al. (2003). Pitzer modeling was conducted for two purposes: Firstly, the predictions allowed us to assess whether the combined LA-ICPMS and Pitzermodeling approach described by Leisen et al. (2012; for H2O-NaCl-KCl-CaCl2-MgCl2 FI) could be extended to FeCl2-bearing systems. Secondly, the model allowed us to predict the vapor-saturated cotectic and peritectic curves between ice and hydrohalite, as well as (metastable) ice and halite. The model also allowed prediction of the ternary eutectic temperature and composition. We performed regression analysis using experimental data from this study supplemented by those for the ice and halite liquidus relations compiled from the literature. Equations were generated expressing bulk salinity in weight percent as a function of last dissolution temperature (Tm,x) and the ratio Φ= wFeCl2 / (wNaCl + wFeCl2), where wFeCl2 and wNaCl represent mass percent of FeCl2 and NaCl, respectively: wFeCl2 = 100 * mass FeCl2 / mass {NaCl+H2O+FeCl2} and wNaCl = 100 * mass NaCl / mass {NaCl+H2O+FeCl2}. Regression analyses were conducted using SAS JMP® 10 statistical software.

3. RESULTS Experimental conditions and microthermometric data for FI are reported in Table 3. Figure 2a shows a field of view of typical halite-bearing synthetic FI produced in our

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experiments. The eutectic dissolution could not be documented in most samples (as is common in FI studies; Roedder, 1984). Some samples exhibited metastable phenomena, such as incomplete solidification even at -196 °C (similar to CaCl2-bearing FI described by Vanko et al., 1988 and Baumgartner and Bakker, 2009) or the unambiguous occurrence of metastable liquid at temperatures below the eutectic temperature, which is 37 °C (Borisenko, 1977). In those cases, metastable ice melting commonly occurred at temperatures of approximately -60°C. Figure 2b shows a synthetic FI containing vapor, ice and metastable liquid at -47.5 °C (approximately 10°C below the eutectic temperature). Some FI exhibited metastable phase assemblages owing to the failure to nucleate salt hydrates. For example, Fig. 2c shows a synthetic FI in which hydrohalite did not nucleate and the FI contains the metastable assemblage ice+halite+liquid+vapor at 35 °C. In most of the halite-bearing FI, in which incongruent salt-hydrate dissolution should have been observed (according to equilibrium thermodynamics), salt hydrates did not nucleate. These types of metastable behavior are common in ternary (or more complex) systems where the eutectic temperature is rarely observed and cooling can lead to the formation of a saline, glass-like substance that recrystallizes upon heating (Dubois et al., 2000; Bakker, 2004). Such metastable behaviors have been described in detail in previous studies (e.g. Dubois et al. 2010, Bakker 2004), and can present difficulties in interpreting the composition of natural fluid inclusions from thermometric measurements. Compositions for which no solid phase dissolution was observed in the present study due to metastability are reported in Table 3, to provide a guideline of the range of compositions in which similar metastable behavior may be expected for natural FI. One example in which hydrous ferrous chloride daughter minerals were present during

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heating is shown in Fig. 2d. Owing to the metastable absence of hydrates in most of the FI, we were only able to measure the dissolution temperature of the second-to-last solid phase to dissolve (on a univariant curve) in a few cases (Table 4). In all other cases we measured only the temperature of dissolution of the last solid phase. 3.1 Assessment of potential modifications of the fluid during FI synthesis The few previous studies that have investigated PTx properties of FeCl2-bearing fluids identified several potential pitfalls associated with experiments involving Fe-bearing compositions (Bowen and Schairer, 1932; Chou and Eugster, 1977; Simon et al., 2004). Therefore, we performed several tests to ensure that the FI compositions that were trapped in the FI at experimental conditions and which were present in the FI after quenching were representative of the starting bulk composition, and were not influenced by Fe-Pt alloying with the capsule material (Bowen and Schairer, 1932), redox reactions, or precipitation of magnetite (Chou and Eugster, 1977; Simon et al., 2004). Firstly, the measured ice dissolution temperatures of binary FeCl2-H2O fluid inclusions of known composition were compared with the known binary liquidus relations tabulated by Linke (1958). Secondly, we compared the dissolution temperatures of the last phase to dissolve in FI of the same nominal composition synthesized at various temperatures and pressures, ranging from 500 to 700 °C and 1 to 3 kbar (Table 3), for several ternary bulk compositions within both the ice and halite stability fields. As such, we could assess whether the FI compositions showed any evidence of modification by alloying with the capsule, redox reactions, or magnetite precipitation (all of which are temperature- and/or pressure-dependent processes). Thirdly, after each experiment, and after

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microthermometric measurements were completed, FI were analyzed by LA-ICPMS to characterize the Fe/Na ratio and compare with the known starting composition. As a first qualitative assessment of the redox state of Fe after each experiment, we noted the color of the solution when the capsule was opened. Ferrous chloride solutions are green, whereas ferric chloride solutions are yellow to orange and rapidly precipitate a red-brown (ferric oxide) residue. In all of our experiments (excluding those in which the capsules leaked and were discarded), the fluid in the capsule after the run was either green or colorless, but never orange, suggesting that ferric iron was not present. The colorless appearance of the fluid after some experiments was likely due to the small fluid volume, because in those cases the fluid always left a greenish residue when absorbed in a paper tissue. We compared microthermometric measurements of synthetic H2O-FeCl2 FI with the known ice liquidus relations tabulated by Linke (1958) (Fig. 3a). For H2O-FeCl2 FI synthesized at 500 °C and 600 °C, the ice dissolution temperature was the same within ±1 °C, for FI of the same starting bulk composition (Table 3). Also, Tm,ice measurements are the same (within about ±1 °C) as dissolution temperatures predicted for those compositions according to the data from Linke (1958) (Fig. 3a). As noted above, it is well known that Fe can form an alloy with Pt at high temperatures. If alloying of Fe with the Pt capsule material occurred during the experiments, we would expect differences between experiments run in Pt versus Au capsules. Most of the experiments presented here were run in Pt capsules, but one of the H2O-FeCl2 experiments listed in Table 3 (experiment 120811-MI) was conducted using a Au capsule. The ice dissolution temperatures for the FI synthesized in Pt and Au capsules

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(120811-MXI and 120811-MI) agree within ±0.5 °C (Table 3), suggesting that the experiments run in Pt capsules were not affected by Fe-Pt alloying. [Note that the homogenization temperatures of the FI synthesized in Pt and Au were also consistent; not shown]. For ternary H2O-NaCl-FeCl2 fluids, the temperatures of ice dissolution in inclusions prepared with the same starting composition, but formed at different PT conditions, are consistent within ± 1 °C at all experimental conditions. For halite-bearing FI, the halite dissolution temperatures for FI with the same nominal composition are within ± 3°C at all experimental conditions. We did not observe any systematic variation in the ice or halite dissolution temperatures (for FI of a given starting composition) with either the trapping pressure or trapping temperature. The Na/Fe mass ratios of synthetic H2O-NaCl-FeCl2 FI determined by LAICPMS analysis are consistent with the Na/Fe mass ratios of the starting compositions, mostly within ~ ± 15% (Fig. 4). Note that we are not implying that the compositions of the fluid in the inclusions varied by ±15% from the starting composition, but that the variability in LA-ICPMS data was mostly less than ±15%. Allan et al. (2005) reported that the typical analytical precision for LA-ICPMS analysis of K, Rb and Cs is about ±15 %, while the relative standard deviation for Fe, as well as Li, Mg, Ca, Sr, Ba, Mn, Cu, Zn and Cl, is about ±30%. Allan et al. (2005) noted that the relatively poor precision of these elements is related to differences in the ablation and ionization behavior compared to the internal standard (sodium). Allan et al. (2005) also noted that iron signals from LAICPMS analysis tend to have more "noise" compared to those of other elements. The present results are within the analytical precision and accuracy range reported by Allan et

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al. (2005), but are inconclusive in terms of confirming or disproving whether the compositions loaded into the capsules are the same as those in the inclusions after the experiment. These results also highlight, however, that LA-ICPMS analysis of FI is typically not capable of resolving differences in Na/Fe mass ratios of less than about ±30 % (relative). Note that microthermometric measurements may detect variations in Na/Fe mass ratio with significantly better resolution, as has previously been noted for Na/Ca ratio by Schlegel et al. (2012). Taken together, all of the observations reported above indicate that the composition of the fluid originally loaded into the capsules is identical to the composition in the capsule following quenching at the end of the run, and is identical to the composition of the fluid trapped in the FI. 3.2 Vapor-saturated liquidus phase relations Figure 5 shows the available experimental data, categorized according to the solid phase(s) present on the vapor-saturated liquidus. Note that liquidus phase relations are pressure dependent, and in the present study the pressure is constrained by the presence of vapor. Therefore, all data shown on Figure 5 have pressures defined by the coexistence of liquid+vapor+solid(s). The pressure range along the H2O-NaCl binary is thus between about zero to 400 bar (see, e.g., Liebscher, 2007). No experimental data are available for the vapor-saturated liquidus pressure in the system H2O-FeCl2 but, based on the data for other aqueous chloride-salt systems, we would expect that the pressure range will be similar to that along the H2O-NaCl binary (see Liebscher, 2007, for a review of available data).

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In the H2O-rich part of the system, the vapor-saturated liquidus phase is ice. The ice liquidus surface is bordered by two cotectic curves that extend from the two binary eutectic points (-21.2 °C and 23.2 wt% NaCl on the H2O-NaCl binary (Hall et al., 1988); -36.5 °C and 30.4 wt% FeCl2 on the H2O-FeCl2 binary according to Schimmel, 1928, or 35.0 °C according to Borisenko, 1977) and intersect at the ternary eutectic point. Borisenko (1977) reported that the H2O-NaCl-FeCl2 ternary eutectic temperature is -37 °C, and that the solid phase assemblage at the eutectic is ice+hydrohalite+FeCl2·6H2O, although the eutectic liquid composition was not characterized. Modeling of the phase equilibria in this part of the system using Pitzer's equations (using parameters from Marion et al., 2003) predicts a eutectic liquid composition of 1.7 wt% NaCl and 29.2 wt% FeCl2. In the NaCl-rich part of the system, and over a wide range of composition, halite is the stable liquidus phase (Fig. 5). Thus, for saline fluids, even FI containing considerably greater concentrations of FeCl2 compared to NaCl may contain only a halite daughter mineral without hydrous ferrous chloride solids. This observation is again consistent with previous results for MgCl2- and CaCl2-rich fluids (Dubois and Marignac, 1997; Steele-MacInnis et al., 2011). This result also implies that FI containing hydrous ferrous chloride daughter minerals (e.g., Grant et al., 1977) generally represent fluids that are not only FeCl2-rich, but also NaCl-poor (containing at most ~10 mass% NaCl) – otherwise such FI would contain halite daughter minerals rather than iron chloride solids. Based on thermodynamic constraints, the halite liquidus surface must be separated from the ice liquidus surface by the stability field of hydrohalite. However, to our knowledge there are no existing data on the Tx relations for the hydrohalite field or

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the halite+hydrohalite peritectic curve in the H2O-NaCl-FeCl2 system (other than the endpoint on the H2O-NaCl binary at 26.2 wt% NaCl and +0.1°C; Sterner et al., 1988). In the present study, hydrohalite nucleation was uncommon in the FI, and thus we were only able to measure two dissolution temperatures along the ice+hydrohalite cotectic curve (Table 4), and none along the hydrohalite+halite peritectic curve. However, owing to the absence of hydrohalite in most of our synthetic FI, we were also able to observe several metastable ice dissolution events (phase changes) along the ice+halite metastable cotectic curve (the intersection of the metastable extensions of the ice and halite liquidi). Temperatures associated with these metastable univariant phase changes (Table 4) were incorporated into the empirical model as described in Section 3.4, to allow compositional estimates, including situations where hydrohalite dissolution was not observed. Throughout the high-salinity, NaCl-poor part of the system (close to the H2OFeCl2 binary), the liquidus phases are FeCl2 hydrates of decreasing hydration number with increasing salinity. The liquidus phases along the H2O-FeCl2 binary are: FeCl2·6H2O, from the binary eutectic to the first binary peritectic point at ~8 °C and 37 wt% FeCl2; FeCl2·4H2O, from the first to the second peritectic point at ~77 °C and 47 wt% FeCl2; FeCl2·2H2O (= rokuhnite), from the second peritectic to the inferred third peritectic point (temperature and liquid composition unknown); and FeCl2 (anhydrous; = lawrencite), from the third peritectic point to the FeCl2 apex. The occurrence or extent of a FeCl2·H2O field has not been reported in the literature or observed in these experiments, and no experimental data are available in the part of the system where this field might occur (near the FeCl2 apex). Cotectic lines separate the halite liquidus from the FeCl2hydrates, although experimental data exist only for the halite+FeCl2·6H2O and

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halite+FeCl2·4H2O cotectic curves (Atbir et al., 2000). From our experiments we were able to constrain only one additional point, along the halite+FeCl2·2H2O curve from the FeCl2·2H2O melting temperature in the presence of halite (Fig. 5, Table 4, Section 3.4). Extrapolation of the existing data suggests that the halite+FeCl2·2H2O and halite+FeCl2 cotectic lines may follow an approximately straight-line trajectory from the halite+FeCl2·4H2O+FeCl2·2H2O peritectic point (between ~70 to 77 °C; Atbir et al., 2000) to the halite+FeCl2 binary eutectic (370 °C, Ionov et al., 1960), although the existing data are too sparse to resolve this part of the system with confidence. The H2O-FeCl2 binary eutectic temperature is -36.5°C according to Schimmel (1928) and -35°C according to Borisenko (1977). In this study we have adopted the eutectic temperature from Schimmel (1928, (obtained by cryometry and tritation), because we could not evaluate the uncertainty associated with the value reported by Borisenko (1977). Our experimental results show that FI containing 9.99 wt% NaCl (relative to NaCl+H2O) and 25 wt% FeCl2 (relative to FeCl2+H2O) exhibit last ice dissolution at -37.6 °C (Table 3). Therefore, the ice+FeCl2·6H2O cotectic curve must lie subparallel to the -36 °C isotherm in the ice field, and the hydrohalite-ice peritectic curve must lie subparallel to the -36 °C isotherm in the hydrohalite field Based on equilibrium thermodynamics one would expect inclusions consisting only of crystalline FeCl2·4H2O (±vapor) for experiments in which the starting materials consisted only of solid FeCl2·4H2O (~63 wt % FeCl2). Such "fluid" inclusions would thus be expected to contain no liquid at room temperature, similar to natural "liquid-absent" CaCl2-rich FI described by Schiffries (1990) from the Bushveld complex. Instead, however, our samples from these experiments contained abundant liquid+vapor+solid

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inclusions. Mass balance constraints suggest that the solid is most likely FeCl2·2H2O (rokuhnite), coexisting with a metastable low-salinity liquid. These FI show last dissolution (via the reaction FeCl2·2H2O + L = L) at 220°C, thereby providing one point in the FeCl2-H2O binary liquidus for a liquid composition of ~63 wt% FeCl2.

3.3 Empirical models for the ice and halite vapor-saturated liquidus surfaces We have generated equations to calculate salinity through regression of the available experimental data combined with Pitzer modeling at low temperatures. Liquid salinity on the ice liquidus is given by the equation

(Eq. 1)

where w = salinity (wt%; = wNaCl + wFeCl2), Φ= wFeCl2 / (wNaCl + wFeCl2), and the coefficients agh are listed in Table 5. The root mean square error of Eq. 1 is 1.6 wt%, and the residuals from the equation are presented in Fig. 6a. Equation (1) is only applicable if the last solid phase to dissolve is ice. Liquid salinity on the halite liquidus is described by the equation

(Eq. 2).

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Coefficients of Eq. 2 are listed in Table 5. The root mean square error of equation (2) is 1.2 wt% and the residuals are presented in Fig. 6b. The H2O-FeCl2 and H2O-NaCl binary liquidi predicted using Eqs. 1 and 2 are presented in Fig 3. Equation (2) is only applicable if the last solid phase to dissolve is halite, and is only valid for mass ratio FeCl2/(FeCl2+H2O) < 0.64 (see limit of model in Fig. 7). Isotherms on the ice and halite liquidi are presented in Fig. 7. The data from Ionov et al. (1960) along the binary NaCl-FeCl2 were excluded from this regression analysis. Therefore, the equation for the halite liquidus surface is valid within the compositional region bounded by the NaCl-FeCl2·4H2O join and the halite-Fnh cotectics, and the equation should not be used for more saline or iron-rich compositions that lie to the high salinity or FeCl2-rich side of this join (Fig. 7). Initially, we attempted to include the data from Ionov et al. (1960) in the empirical model, which in principle could extend the model to very saline, FeCl2-rich compositions (up to anhydrous, NaCl-FeCl2 fluids). However, we found that including these data required an unacceptably large number of fitting coefficients in the equation, and this was not warranted given the limited data in this part of the system and the scarcity of natural FI of such compositions (Bodnar et al., 2014). We should note that recently Kodera et al. (2014) reported hydrous NaCl-FeCl2KCl salt-melt inclusions from the shallow Biely Vrch porphyry-Au deposit in Slovakia. The model described here is not suited for estimating the bulk compositions of such saltmelt inclusions, and additional experimental data are required to extend the model to such compositions.

3.4 Vapor-saturated cotectic and peritectic boundaries

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Experimental data along the vapor-saturated cotectic and peritectic boundaries are listed in Tables 2 (literature data) and 4 (from the present study). Note that in the present study no fluid inclusions were synthesized with compositions such that last dissolution occurred along a univariant boundary (which would be observed as last dissolution of two solids simultaneously). Rather, the temperature of dissolution of the second-to-last solid phase in the FI (listed in Table 4) was used to provide constraints on the Tx conditions of some of the univariant boundaries, as described below. Three experiments (010512-L, 052012-XXCI and 010412-IL; Table 4) produced FI in which ice completely dissolved in the presence of hydrohalite (via the reaction I+Hh+L+V = Hh+L+V) at Tm,ice. The liquid composition at Tm,ice from those experiments is constrained by the intersections of (1) the isotherm of Tm,ice in the ice field (Eq. 1) with (2) the extrapolation of the tie line connecting the composition of hydrohalite (NaCl·2H2O) and the FI bulk composition. These FI thus provide data along the ice+hydrohalite cotectic curve. Several experiments (see Table 4) produced fluid inclusions in which hydrohalite did not nucleate; rather ice dissolved completely in the presence of halite (via the metastable reaction H+I+L = H+L) at Tm,ice. From those experiments, the Tx conditions along the ice+halite metastable cotectic line can be determined from the intersection of any two of the following three features: (1) the isotherm of Tm,ice on the ice liquidus (Eq. 1), (2) the isotherm of Tm,halite on the halite liquidus (Eq. 2), and (3) the extrapolation of the tie line connecting the composition of halite (NaCl) and the FI bulk composition. In principle the ice+halite metastable boundary is thus over-constrained and the need to satisfy these three intersections simultaneously provides additional constraints on the ice

19

and halite liquidus surfaces. The resulting intersection of the ice and halite liquidus surfaces (Eqs. 1 and 2) is shown in Fig. 8. Two experiments (270812-VII and 270812-VIII; Table 4) produced fluid inclusions in which ferrous-chloride hydrates dissolved completely in the presence of halite (reaction H+Fnh+L = H+L) at Tm,Fnh. The tie lines connecting the FI bulk compositions and the NaCl apex projects into the stability field of FeCl2·2H2O, implying that the salt hydrate was FeCl2·2H2O. Thus, the intercept of the isotherm of Tm,Fnh on the halite liquidus with the tie line defined by the FI bulk composition and the composition of halite (NaCl) provides a point on the halite-FeCl2·2H2O cotectic curve. The two experiments that showed FeCl2·2H2O dissolution in the presence of halite both lie along the same NaCl-bulk-composition tie line, such that both projections yield the same point along this cotectic curve. Consistency of Tm,Fnh between these the two experiments was ±4 °C (Table 4). Data that lie along univariant boundaries (from this and previous studies) are plotted in Fig. 5. Note that the four data points that appear to lie along the hydrohalitehalite peritectic boundary actually represent the metastable ice+halite cotectic curve. Thus, in this system, the Hh+H and I+H curves appear to overlap almost perfectly in compositional space (albeit with the I+H curve at lower T), owing to the steep temperature gradient along the halite liquidus at these conditions. The cotectic and peritectic boundaries ice+hydrohalite, hydrohalite+halite and metastable ice+halite were modeled using Pitzer's formalism (Pitzer, 1973; Spencer et al., 1990; Marion et al., 2003) as further discussed in section 4.2. The resulting boundaries are consistent with the available experimental data from this and previous studies (Hall et

20

al., 1988). Note that no experimental data are available for the halite-hydrohalite boundary in the NaCl-FeCl2-H2O system. The eutectic composition (indicated by a star in Fig. 5) was also calculated using Pitzer's model (using parameters from Marion et al., 2003). 4. DISCUSSION 4.1. Behavior of ferrous iron in hydrothermal experiments The tests described in Section 3.1 (e.g., comparison of H2O-FeCl2 PTx properties based on FI microthermometric data with the known liquidus data (Linke, 1958); FI synthesis at various PT conditions for each bulk composition) indicate that the FI compositions are consistent with the starting compositions loaded into each capsule. Thus, our experiments indicate that PTx properties of Fe-bearing fluids can be successfully studied using the synthetic fluid inclusion method at hydrothermal conditions. It has long been known that Fe-Pt alloying at high P and T can modify the bulk compositions of experiments on silicate melt (Bowen and Schairer, 1932). However, our results suggest that little to no iron was lost to the capsule during these experiments. The lack of Fe-Pt alloying in these experiments may indicate either: (1) that Fe-Pt alloying at the PT conditions of the experiments proceeds at a rate that is significantly slower than the rate at which quartzfracture healing occurs, or (2) while the partitioning behavior of iron between platinum and melt favors the formation of Fe-Pt alloys at magmatic conditions, at hydrothermal conditions the partitioning behavior of iron between aqueous solution and platinum favors iron in solution. However, the present experiments are not designed to assess partitioning of iron between silicate melts, aqueous fluids and solids.

21

4.2. Application to FI from magmatic-hydrothermal systems. Iron-rich aqueous fluid inclusions are frequently reported in magmatic-hydrothermal systems (e.g. Mole Granite, Australia (Audétat et al. 2000); Bajo de la Alumbrera, Argentina (Ulrich et al., 2001); Industrianoe, Russia (Kamenetsky et al., 2002), Butte, Montana (Rusk et al., 2004), and El Teniente, Chile (Klemm et al., 2007). In such systems, the concentration of Fe is the same order of magnitude as that of K and Na (Bodnar et al., 2014). The data presented in this study provide a basis for interpreting microthermometric and microanalytical data from such Fe-bearing and Fe-rich FI. For compositions within the range reported for natural FI (Bodnar et al., 2014), the last solid phase to dissolve in FI approximated by the H2O-NaCl-FeCl2 system will most commonly be either halite or ice. Dissolution of hydrohalite as the last solid should in principle occur within this range of compositions, but failure of hydrohalite to nucleate commonly prevents observation of Tm,Hh (similar to what has been described for H2ONaCl FI; Bodnar et al., 2014; see Fig. 2). Based on the results of the present study, bulk composition (salinity and Fe/Na ratio) can be uniquely determined from the last dissolution temperature of ice or halite, combined with the second-to-last dissolution temperature of either hydrohalite (I+Hh cotectic) or ice (I+H metastable cotectic). For FI in which ice is the last solid phase to dissolve, the ratio Φdetermined from the hydrohalite dissolution temperature (Fig. 8) remains constant between Tm,Hh and Tm,ice, and this ratio can be input directly into Eq. 1 (along with Tm,ice) to determine the bulk composition. For FI in which halite is the last solid to dissolve, the liquid salinity and ratio Φon the metastable ice-halite cotectic can be determined from the intersection of Eqs. 1 and 2, or graphically from Fig. 8. In this case, the bulk composition lies at the intersection of the

22

Tm,halite isotherm with the tie line between the liquid composition on the I+H cotectic and the NaCl apex (see Steele-MacInnis et al., 2011). The bulk composition can thus be determined graphically from Fig. 7, or by iterative calculation (Eqs. 1 and 2). Note that LA-ICPMS analysis (which provides element mass ratios directly) can be used instead of the second-to-last dissolution temperature, because the ratio Φobtained from LA-ICPMS can be input directly into Eq. 1 or 2 to determine the bulk composition. Unfortunately, while thermometric measurements allow the major element concentrations to be calculated once the major elements have been identified, it is may not be possible to identify uniquely the major elements (i.e., the chemical system) from microthermometry alone. Eutectic melting is rarely observed in fluid inclusions, particularly in complex systems, owing to metastability issues (e.g., Dubois et al., 2000; Bakker 2004), prohibiting measurement of the eutectic temperature. Moreover, even in cases where eutectic melting can be unequivocally recognized in FI and the eutectic temperature determined, several ternary systems of H2O plus common chloride salts share similar eutectic temperatures and similar liquidus phase relations (see section 4.3). Therefore, the eutectic temperature may not uniquely define the system under study, unless additional constraints can be provided. The presence of daughter minerals can provide clues concerning the major elements in the fluid (e.g. Grant et al., 1977). When daughter minerals are not present at room temperature, careful combination of (cryogenic) Raman spectroscopic analysis and low-temperature microthermometry may provide insights, as described in detail by Bakker (2004) and Baumgartner and Bakker (2010). Other techniques that may provide insights concerning the major components in aqueous fluid inclusions have been described by Boiron and Dubessy (1994) and include LA-ICPMS

23

analysis, crush leach analyses, or decrepitate mound analysis by SEM (Haynes et al., 1988; Kontak, 2004). Major- and trace-element ratios (generally with respect to sodium) from LAICPMS analyses are commonly converted to absolute concentrations by applying an "empirical rule" from Heinrich et al. (2003). The empirical rule is a trigonometric approximation, based on the observation that isotherms in ternary H2O-NaCl-X (X = KCl, CaCl2, etc.) fluid systems commonly form approximately right angles with the H2ONaCl binary join. Results of the present study allow us to assess the validity of the empirical rule when applied to FeCl2-rich fluids. Compositions estimated from the empirical rule provide a reasonable approximation for concentrations of wFeCl2 < 20 wt% (Fig. 7). At wFeCl2 > 20 wt%, the empirical rule systematically overestimates the bulk salinity. The results of the present study provide a method to quantify major- and trace-element concentrations for FeCl2-rich fluids that avoids this potential error. From the last dissolution temperature (from microthermometry) and the Fe/Na ratio (from LAICPMS analysis), the "true" NaCl (wt% NaCl, rather than wt% NaCl eq.) concentration can be obtained from Eq. 1 or 2, and the concentrations of major and trace elements can be quantified based on this internal standard, obviating the need for the empirical rule for fluid inclusions dominated by NaCl+FeCl2. A similar procedure has been applied CaCl2rich fluid inclusions by Schlegel et al. (2012). As mentioned above, Leisen et al. (2012) described a method for reducing LAICPMS data by combining measured element ratios with the last ice dissolution temperature, according to the model of Pitzer (1973) and its subsequent additions. We calculated cotectic and peritectic boundaries using this model, with parameters from

24

Marion et al. (2003) and found excellent agreement with the experimentally determined I+Hh and (metastable) I+H boundaries. Moreover, isotherms calculated using this method are essentially indistinguishable from those based on the empirical model for the ice liquidus (Eq. 1). These results indicate that the Pitzer-modeling approach proposed by Leisen et al. (2012) can be directly extended to FeCl2-bearing fluid inclusions. Note that the predicted liquidus is in good agreement with our experiments despite the fact that few experimental data in the H2O-NaCl-FeCl2 ternary were included in the parameterization by Marion et al. (2003), thus demonstrating the excellent predictive power of this model for mixed electrolytes. 4.3.Comparison with other H2O-NaCl-XCl2 (X = Mg, Ca) systems We compared the experimental results from this study with the results from the systems H2O-NaCl-CaCl2 (Steele-MacInnis et al., 2011) and H2O-NaCl-MgCl2 (Dubois and Marignac, 1997) to assess similarities and differences in these ternary systems in terms of ice and halite liquidus phase relations. While the results from this study have been presented in terms of wt% units for practical reasons (most analytical data for salts in the FI literature are expressed this way), for comparison between systems it is more appropriate to use either molality or mole-fraction units, to remove the effect of the different molar masses between cations. Comparison between the three ternary diagrams, with Fe, Mg or Ca as the divalent cation, shows that there is little difference between the ice liquidi in the three systems (Fig. 9). In fact, the experimental salinity for each ternary system can be reproduced to within ±2 wt% using the regression equations derived for the other systems, provided all are corrected for differences in cation molar mass (i.e., expressed in

25

mole units). This result indicates that the empirical models for the ice liquidus Tx relations (Dubois and Marignac, 1997; Steele-MacInnis et al., 2011; this study) are generally transferrable among the various H2O-NaCl-XCl2 ternary systems. This further suggests that bulk compositions of FI containing significant H2O+NaCl plus chlorides of Ca2+, Fe2+ and Mg2+ (plus other divalent cations?) can be estimated based on ternary liquidus relations (expressed in mole fractions), provided that ice is the last solid to dissolve. The comparison of the halite liquidi for the three ternary systems is less comprehensive, because data for halite-bearing FI in the system H2O-NaCl-MgCl2 are scarce. Therefore, the halite liquidus has been compared only between the systems H2ONaCl-FeCl2 and H2O-NaCl-CaCl2. While the general topologies of the halite liquidi of both systems are similar, there are quantitative differences in the temperaturecomposition relations on the liquidi of the two systems that preclude direct transference of empirical models. Specifically, isotherms on the halite liquidi of H2O-NaCl-FeCl2 and H2O-NaCl-CaCl2 systems diverge systematically away from the H2O-NaCl binary, exhibiting up to several tens of mol% difference at high salinities. The differences between halite liquidi in the CaCl2-versus FeCl2-bearing systems are perhaps not surprising, given the constraints of the NaCl-CaCl2 (Seltveit and Flood, 1958) and NaClFeCl2 (Ionov et al., 1960) binary liquidi. The NaCl-FeCl2 system has a eutectic at ~370 °C and has no intermediate compounds (Ionov et al., 1960), whereas the NaCl-CaCl2 system has a eutectic at 500 °C and has the intermediate compound CaNa4Cl6 on the liquidus (Seltveit and Flood, 1958); thus, the halite liquidi in the CaCl2- versus FeCl2-

26

bearing ternaries must diverge as H2O concentration decreases, in order to satisfy these different anhydrous phase relations. 5. SUMMARY This study provides a comprehensive dataset for vapor-saturated liquidus phase equilibria of H2O-NaCl-FeCl2 fluids, covering the full range of compositions reported for natural fluids in magmatic-hydrothermal systems (c.f., Bodnar et al., 2014). This range of compositions is mostly covered by the ice and halite liquidus surfaces. The empirical model developed in the present study can be used to estimate FI bulk compositions based on ice and halite dissolution temperatures. The microthermometric data can also be combined with LA-ICPMS analyses to constrain FI major- and trace-element abundances. These data will allow improved interpretations of the compositions of magmatic-hydrothermal fluids, particularly in environments in which fluids are known to be iron-rich (e.g., Grant et al., 1977; Audétat et al., 2000; Kamenetsky et al., 2002; Yardley, 2005). 6. ACKNOWLEDGMENTS We are very grateful to Charles Farley, whose assistance was crucial for all aspects of the hydrothermal experiments. We thank Adam Simon, Brian Tattitch, Zoltan Zajacz, Bob Linnen, and Bruce Yardley for helpful discussions during the development of this project. We thank Larryn Diamond, Axel Liebscher, I-Ming Chou and an anonymous reviewer for insightful comments that greatly improved the quality of this manuscript. This material is based on work supported in part by the National Science Foundation under Grant No. EAR-1019770 to R.J.B. REFERENCES

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Klemm M.K., Pettke T., Heinrich C.A. (2007) Hydrothermal evolution of El Teniente deposit, Chile: porphyry Cu-Mo ore deposition from low-salinity magmatic fluids. Econ Geol 102, 1021-1045 Kodera P., Heinrich C.A., Wälle M., Lexa J. (2014) Magmatic salt melt and vapor: extreme fluids forming porphyry gold deposits in shallow subvolcanic settings. Geology 42, 495-498. Kontak, D. (2004) Analysis of evaporate mounds as a complement to fluid-inclusion thermometric data: case studies from granitic environments in Nova Scotia and Peru. Can Mineral 42, 1315-1329. Leisen M., Dubessy J., Boiron M.C., Lach P. (2012) Improvement of the determination of element concentrations in quartz-hosted fluid inclusions by LA-ICP-MS and Pitzer thermodynamic modeling of ice melting temperature. Geochim Cosmochim Acta 90, 110-125. Liebscher A. (2007) Experimental studies in model fluid systems. Rev Mineral Geochem 65, 15-48. Linke W. (1958) Solubilities, inorganic and metal organic compounds. D. Van Nostrand Company, Princeton, New Jersey, 3401 pp. Marion G.M., Catling D.C., Kargel J.S. (2003) Modeling aqueous ferrous iron chemistry at low temperatures with application to Mars. Geochim Cosmochim Acta 67, 4251-4266. Mutchler S.R., Fedele L., Bodnar R.J. (2008) Appendix A5; Analysis Management System (AMS) for reduction of laser ablation ICP-MS data. Short Course Series Mineral Assoc Canada 40, 318-327. Oakes C.S., Bodnar R.J., and Simonson J.M. (1990) The system NaCl-CaCl2-H2O; 1, The ice liquidus at 1 atm total pressure. Geochim Cosmochim Acta54, 603-610. Pitzer K.S. (1973) Thermodynamics of electrolytes. I. Theoretical basis and general equations. J Phys Chemy 77. 268-277. Pitzer K.S., Mayorga G. (1973) Thermodynamics of electrolytes, II. Activity and osmotic coefficients with one or both ions univalent. J Phys Chem 77, 2300-2308. Popp R.K., Nagy K.L., Hajash A. (1984) Semiquantitative control of hydrogen fugacity in rapid-quench hydrothermal vessels. Am Mineral 69, 557-562. 31

Roedder E. (1984) Fluid Inclusions. Rev Mineral 12, 644 pp. Rusk B.G., Reed M.H., Dilles J.H., Klemm L.M., Heinrich C.A. (2004) Compositions of magmatic hydrothermal fluids determined by LA-ICP-MS of fluid inclusions from the porphyry copper-molybdenum at Butte, MT. Chem Geol 210, 173-199 Schiffries C. (1990) Liquid-absent aqueous fluid inclusions and phase equilibria in the system CaCl2-NaCl-H2O. Geochim Cosmochim Acta 54, 611-619. Schimmel F. (1928) Löslichkeiten und Umwandlungspunkte der Eisenchlorürhydrate in wäßriger Lösung. Z anorg allg Chem 173, 285-288. Schlegel T.U., Wälle M., Steele-MacInnis M., Heinrich C.A. (2012) Accurate and precise quantification of major and trace element compositions of calcic-sodic fluid inclusions by combined microthermometry and LA-ICPMS analysis. Chem Geol 334, 144-153. Shepherd T.J., Rankin A.H., Alderton D.H.M. (1985) A practical guide to fluid inclusion studies. Blackie and Son Ltd., Glasgow, 239 pp. Seltveit A., Flood H. (1958) Determination of the solidus curve by a tracer technique. The system CaCl2-NaCl. Acta Chem Scand 12, 1030-1041. Simon A., Bilenker L., Bell A. (2013) The importance of iron mobility in magmatichydrothermal systems. Mineral Mag 77, 2215. Simon A.C., Pettke T., Candela P.A., Piccoli P.M., Heinrich C.A. (2004) Magnetite solubility and iron transport in magmatic-hydrothermal environments. Geochim Cosmochim Acta 68, 4905-4914. Spencer R.J., Møller N., Weare J.H. (1990) The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the Na-K-Ca-Mg-Cl-SO4-H2O system at temperatures below 25°C. Geochim Cosmochim Acta 54, 575-590. Steele-MacInnis M., Bodnar R.J. (2013) Effect of the vapor phase on the salinity of halite-bearing aqueous fluid inclusions estimated from the halite dissolution temperature. Geochim Cosmochim Acta 115, 205-216. Steele-MacInnis M., Bodnar R.J., Naden J. (2011) Numerical model to determine the composition of H2O-NaCl-CaCl2 fluid inclusions based on microthermometric and microanalytical data. Geochim Cosmochim Acta 75, 21-40.

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Sterner S.M., Bodnar R.J. (1984) Synthetic fluid inclusions in natural quartz I. Comopositional types synthesized and applications to experimental geochemistry. Geochim Cosmochim Acta 48, 2659-2668. Sterner S.M., Hall D.L., Bodnar R.J. (1988) Synthetic fluid inclusions. V. Solubility relations in the system NaCl-KCl-H2O under vapor-saturated conditions. Geochim Cosmochim Acta 52, 989-1006. Ulrich T., Günther D., Heinrich C. (2001) The evolution of a porphyry Cu-Au deposit, based on LA-ICP-MS analysis of fluid inclusions: Bajo de la Alumbrera, Argentina. Econ Geol 96, 1743-1774. Vanko D.A., Bodnar R.J., Sterner S.M. (1988) Synthetic fluid inclusions. VIII. Vaporsaturated halite solubility in part of the system NaCl-CaCl2-H2O, with application to fluid inclusions from oceanic hydrothermal systems. Geochim Cosmochim Acta 52, 2451-2456. Vanko D.A., Griffith J.D., Erickson C.L. (1992) Calcium-rich brines and other hydrothermal fluids in fluid inclusions from plutonic rocks, Oceanographer Transform, Mid-Atlantic Ridge. Geochim Cosmochim Acta 56, 35-47. Werre R.W., Bodnar R.J., Bethke P.M., Barton P.B. (1979) A novel gas-flow fluid inclusion heating/freezing stage. Geol Soc Am 11, p. 539. Yardley B.W.D. (2005) Metal concentrations in crustal fluids and their relationship to ore formation. Econ Geol 100, 613-632. Yardley B.W.D., Bodnar R.J. (2014) Fluids in the continental crust. Geochem. Perspec. 3 (1), 127pp.

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Figure captions

Figure 1. Data available for the halite and ice liquidi in the system H2O-NaCl-FeCl2 from the literature and from this study. L'58 = Linke (1958), I'60 = Ionov (1960), C&P'85 = Chou and Phan (1985), H et al '88 = Hall et al. (1988), S et al '88 = Sterner et al. (1988), B '98 = Baldassaro (1998), A et al '00 = Atbir et al. (2000), S-M&B '13 = SteeleMacInnis and Bodnar (2013). The shaded area represents the range of compositions of FI reported from porphyry systems (Bodnar et al., 2014).

Figure 2. (a) Photomicrograph of fluid inclusions from sample 051712-X at room temperature, typical of synthetic fluid inclusions from the present experiments. (b) Fluid inclusion from sample 051712-VI showing metastable ice melting at temperatures below the eutectic for the system H2O-NaCl-FeCl2 (-37 °C, according to Borisenko, 1977). (c) Fluid inclusion from sample 010412-XLVI showing the metastable phase assemblage ice+halite+liquid+vapor at -35°C. (d) Halite-bearing fluid inclusion from sample 270812VII with ferrous chloride hydrate (F2h= FeCl2·2H2O = rokuhnite) present at 100°C. I = ice; L = liquid; F6h = FeCl2·6H2O

Figure 3. Comparison of results predicted by Equations 1 and 2 with experimental data for the liquidus relations of the binary H2O-FeCl2 and H2O-NaCl systems. (a) H2O-FeCl2 system, experimental data from Linke (1958; L'58) and the present study, ice liquidus modeled by Eq. 1. (b) H2O-NaCl system, experimental data from Sterner et al. (1988; S et al. '88), Hall et al. (1988; H et al. '88) and Steele-MacInnis and Bodnar (2013; S-M&B

34

'13), ice and halite liquidi modeled with Eqs. 1 and 2, respectively. I = ice; L = liquid; H = halite; Hh = hydrohalite; F2h = FeCl2·2H2O; F4h = FeCl2·4H2O; F6h = FeCl2·6H2O.

Figure 4. Comparison of NaCl/FeCl2 mass ratios loaded into the capsule with NaCl/FeCl2 mass ratios measured by LA-ICPMS in the synthetic FI. Each data point represents an individual fluid inclusion. The diagonal line represents a one-to-one line, and the shaded regions represent ±15 % and ±30 % deviation respectively. See text for details.

Figure 5. Stability fields in the system H2O-NaCl-FeCl2. The symbols indicate which phase is present on the liquidus for a given bulk composition. “Metastable” indicates samples with FI that should have contained halite daughter minerals at room T or nucleated hydrohalite upon cooling (at equilibrium) but did not. “Cotectic” points represent experimental data on the stable cotectic boundaries. “Metastable ice-halite cotectic” points indicate experimental data on the metastable cotectic ice-halite boundary. Continuous indicate well-constrained phase boundaries, whereas dashed lines with question marks are inferred. See text for additional details. Salt/hydrate circles represent the compositions of salts or hydrates in the system H2O-NaCl-FeCl2.

Figure 6. Residuals for the regression equations representing salinity for (a) the ice liquidus (Eq. 1) and (b) the halite liquidus (Eq. 2).

35

Figure 7. Isotherms on the ice and halite liquidi predicted from Equations 1 and 2. Continuous lines represent the isotherms within the validity range of the empirical model, and discontinuous lines represent isotherms where experimental data are absent (or the data were not used in the regression analysis). Short-dashed lines represent cotectic and peritectic curves.

Figure 8. (a) Temperature-Φ , and (b) temperature-salinity relations for the ice-hydrohalite cotectic (dashed) and the ice-halite metastable cotectic (solid) curves in the ternary system NaCl-FeCl2-H2O. The ice-hydrohalite curve is predicted using Pitzer's equations (see text for details). The (metastable) ice-halite curve represents the intersection between Equations 1 and 2. Note that some of the data points in plots (a) and (b) overlap with one another (depending on the projection). .

Figure 9. Comparison of vapor-saturated ice liquidus isotherms in the systems H2ONaCl-CaCl2 (as predicted by Steele-MacInnis et al. 2011 (S-M et al '11)), H2O-NaClMgCl2 (as defined by Dubois and Marignac 1997 (D&M '97) and H2O-NaCl-FeCl2 (as defined in this study). Part of the -30°C isotherms are metastable extensions.

36

37

38

39

40

41

42

Table 1. Vapor-saturated halite and ice liquidi data compiled from literature. Source

LP

Tm

w (wt %)

Φ

Source

LP

Tm

w (wt %)

Φ

B’98

I

-33.5

26.0

0.8502

A et al’00

H

0

27.5

0.3688

B’98

I

-33.8

26.0

0.8502

A et al’00

H

0

29.3

0.5700

B’98

I

-33.0

26.0

0.8502

A et al’00

H

0

31.7

0.7646

B’98

I

-32.2

26.0

0.8502

A et al’00

H

0

32.7

0.8123

B’98

I

-11.1

15.0

0.7013

A et al’00

H

30

26.3

0.0000

B’98

I

-28.2

23.8

0.8314

A et al’00

H

30

27.7

0.2655

B’98

I

-21.3

21.7

0.8099

A et al’00

H

30

28.6

0.4197

B’98

I

-18.6

19.6

0.7835

A et al’00

H

30

32.0

0.7167

B’98

I

-7.5

11.0

0.5731

A et al’00

H

30

34.4

0.8127

B’98

I

-3.9

6.8

0.2794

A et al’00

H

30

38.4

0.8844

B’98

I

-20.0

21.4

0.8066

A et al’00

H

40

26.2

0.0000

B’98

I

-14.0

17.2

0.7462

A et al’00

H

40

27.3

0.2654

B’98

I

-10.3

14.3

0.6834

A et al’00

H

40

30.2

0.5202

B’98

I

-5.7

9.2

0.4781

A et al’00

H

40

31.9

0.6683

B’98

I

-34.7

25.5

0.8465

A et al’00

H

40

37.6

0.8125

B’98*

I

-14.5

23.5

0.8433

A et al’00

H

40

38.5

0.8601

B’98*

I

-12.9

21.8

0.8108

A et al’00

H

40

40.3

0.9071

B’98

I

-9.0

13.6

0.6661

A et al’00

H

70

27.9

0.0000

B’98

I

-5.3

10.3

0.6171

A et al’00

H

70

29.7

0.2653

B’98

I

-32.3

25.5

0.9066

A et al’00

H

70

33.1

0.5202

B’98

I

-22.5

20.9

0.8587

A et al’00

H

70

40.1

0.8127

B’98

I

-15.7

17.4

0.8123

A et al’00

H

70

42.8

0.8602

B’98

I

-11.6

13.0

0.7078

A et al’00

H

70

47.0

0.9071

B’98

I

-6.8

9.0

0.5112

C&P’85

H

25

38.0

0.8742

B’98

I

-5.6

7.6

0.3908

C&P’85

H

25

35.8

0.8374

B’98

I

-3.0

5.0

0.0000

C&P’85

H

25

33.1

0.7155

L’58

I

-9.0

14.5

1

C&P’85

H

25

29.8

0.4808

L’58

I

-11.6

17.0

1

C&P’85

H

25

27.2

0.1348

L’58

I

-13.3

17.7

1

C&P’85

H

50

40.9

0.8836

L’58

I

-22.5

23.3

1

C&P’85

H

50

36.1

0.7644

L’58

I

-29.0

26.6

1

C&P’85

H

50

32.0

0.5467

L’58

I

-35.0

29.8

1

C&P’85

H

50

28.3

0.1894

L’58

I

-36.5

30.4

1

C&P’85

H

70

40.3

0.8211

43

Table 1. Vapor-saturated halite and ice liquidi data compiled from literature. Source

LP

Tm

w (wt %)

Φ

Source

LP

Tm

w (wt %)

Φ

H et al’88

I

0.0

0.0

0.0000

C&P’85

H

70

34.5

0.6136

H et al’88

I

-1.7

3.0

0.0000

C&P’85

H

70

29.5

0.2532

H et al’88

I

-2.5

4.2

0.0000

I et al’60*

H

750

100.0

0.8933

H et al’88

I

-3.0

5.0

0.0000

I et al’60*

H

700

100.0

0.8201

H et al’88

I

-4.0

6.4

0.0000

I et al’60

H

651

100.0

0.7652

H et al’88

I

-5.0

7.8

0.0000

I et al’60

H

599

100.0

0.7165

H et al’88

I

-6.0

9.2

0.0000

I et al’60

H

549

100.0

0.6768

H et al’88

I

-7.0

10.5

0.0000

I et al’60

H

501

100.0

0.6402

H et al’88

I

-8.0

11.7

0.0000

I et al’60

H

451

100.0

0.6067

H et al’88

I

-9.0

12.9

0.0000

I et al’60

H

401

100.0

0.5793

H et al’88

I

-10.0

14.0

0.0000

S et al’88

H

298.6

37.6

0.0000

H et al’88

I

-11.0

15.0

0.0000

S et al’88

H

393.3

46.0

0.0000

H et al’88

I

-12.0

16.0

0.0000

S et al’88

H

481.2

57.0

0.0000

H et al’88

I

-13.0

16.9

0.0000

S et al’88

H

518.1

62.4

0.0000

H et al’88

I

-14.0

17.8

0.0000

S et al’88

H

518.0

62.4

0.0000

H et al’88

I

-15.0

18.6

0.0000

S et al’88

H

644.1

80.0

0.0000

H et al’88

I

-17.0

20.2

0.0000

S et al’88

H

713.9

90.0

0.0000

H et al’88

I

-18.2

21.2

0.0000

S&B’13

H

256.7

35.0

0.0000

H et al’88

I

-19.0

21.7

0.0000

S&B’13

H

378.9

43.9

0.0000

H et al’88

I

-20.0

22.4

0.0000

S&B’13

H

452.0

53.3

0.0000

H et al’88

I

-21.0

23.0

0.0000

S&B’13

H

463.7

54.4

0.0000

H et al’88

I

-21.2

23.2

0.0000

S&B’13

H

499.1

59.2

0.0000

A et al’00

H

15.0

26.0

0.0000

S&B’13

H

521.2

62.8

0.0000

A et al’00

H

15.0

27.3

0.2657

S&B’13

H

555.2

66.8

0.0000

A et al’00

H

15.0

30.2

0.5699

S&B’13

H

567.0

69.3

0.0000

A et al’00

H

15.0

32.2

0.7166

S&B’13

H

591.5

72.8

0.0000

A et al’00

H

15.0

33.2

0.7651

S&B’13

H

617.1

77.0

0.0000

A et al’00

H

15.0

35.5

0.8601

S&B’13

H

652.1

81.5

0.0000

A et al’00

H

15.0

37.2

0.9070

S&B’13

H

674.1

84.2

0.0000

A et al’00

H

0.0

26.2

0.0000

S&B’13

H

731.2

90.7

0.0000

A et al’00 H 0.0 26.1 0.1607 LP= Last melting phase; Tm= last dissolution temperature; w (wt%) = salinity (weight percent); Φ=mass FeCl2/(FeCl2+NaCl). B’98 = Baldassaro (1998); L’58 = Linke (1958); H et al.’88 = Hall et al. (1988); A et al.’00 = Atbir et al (2000); C&P’85 = Chou and Phan (1985); I et al’60 = Ionov et al. (1960); S&B’13= Steele-MacInnis and Bodnar (2013)

44

Table 2. Cotectic and peritectic points compiled from literature. Φc Source Boundarya Tb wd Atbir et al., 2000 F6h-Ice -36.5 1 30.4 Atbir et al., 2000 F4h-F6h 12.3 1 37.6 Atbir et al., 2000 F4h-F2h 76.5 1 47.4 Hall et al., 1988 Ice-Hh -21.2 0 23.15 Hall et al., 1988 Hh-H 0.1 0 26.3 Atbir et al., 2000 F4h-H 15 0.9258 39.08 Atbir et al., 2000 F4h-H 30 0.9164 41.87 Atbir et al., 2000 F4h-H 40 0.9071 42.62 Atbir et al., 2000 F4h-H 70 0.9212 48.98 Atbir et al., 2000 F6h-H 0 0.8742 35.05 Ionov et al., 1960 F-H 368 0.6293 100 Spencer et al. 1990 Ice-He -28.12 0 26.86 a cotectic/peritectic phases: F6h = FeCl2.6H2O; F4h = FeCl2.4H2O; F2h = FeCl2.2H2O; Hh = NaCl.2H2O; H = NaCl; F =FeCl2 b T = temperature (°C) c Φ= wFeCl2 / (wFeCl2 + wNaCl) where w is weight d w = salinity (wt%) e Metastable invariant point

45

Table 3. Summary of experimental data on halite and ice liquidi from this study.

Sample

a Ψ N

b Ψ F

w (wt%)

d

50.0 0 25.0 0 10.0 0 10.0 0 10.0 0 10.0 0 40.0 0 15.0 0 10.0 0

52.62

10.0 0 10.0 0 20.0 0 20.0 0 20.0 0 20.0 0 20.0 0 25.0 0 15.0 0 39.8 7 5.00

18.23

15.0 0 10.0

30.76 18.18 18.18 18.18 18.18 43.75 22.35 18.23

18.23 26.59 26.59 26.59 26.59 26.59 33.75 26.09 47.68 23.20 29.88 26.55

LPg # FIh

T (°C)

e

e

0.900 4 0.750 2 0.500 0 0.500 0 0.500 0 0.500 0 0.857 1 0.613 1 0.498 3

2000

700

M

2000

600

1000

0.498 3 0.498 3 0.690 2 0.690 2 0.690 2 0.690 2 0.690 2 0.654 2 0.500 0 0.727 6 0.174 2 0.414 1 0.308

c

270812 9.96 -VI 051712 9.99 -VI 012812 10.0 -LVI 0 012812 10.0 -LIV 0 011812 10.0 -LIII 0 012812 10.0 -LV 0 270812 10.0 -I 0 051712 10.0 -I 2 121311 10.0 6 XXVIII 121311 10.0 -XXVII 6 121311 10.0 -XXVI 6 121211 10.0 9 -XIIj 121211 10.0 -XXII 9 121211 10.0 -XV 9 121211 10.0 -XI 9 121211 10.0 -XVIII 9 051712 14.9 -VII 8 051712 15.0 -II 0 270812 19.8 -II 9 052012 19.9 -XXIV 7 151712 19.9 -IIIj 8 120911 19.9

PPRTf

P (bar)

Media n Tmi

STD V Tmi

I

N A 4

-37.6

0.1

500

I

4

-12.6

0.3

2000

500

I

4

-13.4

0

2000

600

I

4

-15.0

0.1

2000

700

I

5

-12.7

0.1

2000

700

M

2000

600

I

N A 4

-20.8

0.3

3000

500

I

5

-14.0

0.1

3000

600

I

4

-14.6

0

3000

700

I

5

-15.2

0.1

2000

500

I

5

-34.2

0.1

2000

600

I

5

-31.2

0.1

3000

500

I

5

-29.5

0

3000

600

I

4

-31.1

0.1

3000

700

I

8

-29.5

0.6

2000

600

M

2000

600

I

N A 6

-28.2

0.1

2000

700

M

3000

600

I

N A 6

-21.3

0.2

3000

600

I

15

-35.1

0.2

1000

500

I

2

-22.9

0.3

46

-IV 120911 -VI 120611 -VIII 120611 -V 120611 -VII 270812 -VIIj 012912 -LVIII 012912 -LX 051712 -VIII 270812 -XI 051712 -IX 270812 -VIII 010212 XXXV 010312 -XLIII 051712 -V 010312 -XLIVj 010312 -XLI 010312 -XLV 061813 -VIIIj 270812 -IXj 010412 -IL 010412 -XLVI 052012 -XXVI 010512 -L 051712 -X

9 19.9 9 19.9 9 19.9 9 19.9 9 19.9 9 20.0 0 20.0 0 20.0 7 20.1 9 25.0 3 30.3 3 39.9 1

4 10.0 4 10.0 4 10.0 4 10.0 4 50.0 0 10.0 0 10.0 0 25.0 0 29.9 6 25.0 0 50.0 1 20.0 0

39.9 1 39.9 4 39.9 4 39.9 6 39.9 6 39.9 8 39.9 8 40.0 1 40.0 2 40.0 4 40.0 4 40.0 4

20.0 0 15.0 0 20.0 0 20.0 0 20.0 0 30.0 2 49.7 4 10.0 0 10.0 0 5.00 10.0 0 25.0 0

26.55 26.55 26.55 26.55 55.55 26.53 26.53 36.89 40.50 40.02 58.94 47.76

47.76 45.70 47.78 47.80 47.80 52.27 62.35 43.76 43.77 41.87 43.79 50.03

8 0.308 8 0.308 8 0.308 8 0.308 8 0.800 1 0.307 7 0.307 7 0.570 4 0.628 4 0.499 6 0.696 8 0.273 5 0.273 5 0.209 7 0.273 2 0.273 1 0.273 1 0.391 7 0.597 7 0.142 8 0.142 8 0.073 1 0.142 7 0.333 0

2000

500

I

5

-23.0

0.2

2000

700

I

3

-23.9

0.1

3000

500

I

2

-23.1

0.1

3000

600

I

5

-22.8

0.1

2000

700

H

8

158.5

0

1000

600

I

4

-22.5

1

2000

600

I

3

-22.8

0.1

2000

600

M

2000

700

M

2000

600

M

2000

700

194.5

0.5

1000

N+FnH ?

H

600

H+FnH ? H

N A N A N A 6

H

3

318.0

0.5

3000

600

H

H

7

315.5

0.5

2000

600

H

H

6

322.5

0.5

2000

600

H

H

4

340.5

0.5

2000

700

H

H

3

318.0

1

3000

700

H

H

5

318.0

2

1400

700

H

H

7

315.0

3

2000

700

H

H

18

249.5

0.5

2000

600

H

H

3

330.0

2

2000

500

H

H

5

326.5

0.5

3000

600

H

H

6

331.5

0.5

3000

600

H

H

4

328.0

1

1500

600

H

H

7

305.5

0.5

47

270812 -IV 021413 -VII 021513 -VIII 061813 -VI 021413 -II 021413 -III 021413 -VI 021413 -I 021413 -V 021413 -IV 061813 -I 061713 -II 061713 -III 061713 -V 061713 -IV 032112 -MXIII 120811 -MXIV 012812 -MIX 012812 -MV 120911 MXXX 032512 -MVIX 012912 MXVII I 120811 -MXI 120811

40.4 2 50.0 3 50.0 3 50.3 1 60.0 2 60.0 4 60.0 8 60.1 1 60.1 7 69.9 9 70.0 6 70.2 7 70.3 5 71.7 8 72.2 5 0.00 0.00 0.00 0.00 0.00

0.00 0.00

0.00 0.00

39.8 6 10.0 0 20.0 2 30.0 7 20.0 0 10.0 1 50.0 1 30.0 4 40.0 5 39.9 9 50.2 1 10.0 1 19.9 8 40.0 9 30.0 1 10.0 0 10.0 0 15.0 0 15.0 0 20.0 0

57.29

20.0 0 25.0 0

20.00

30.0 0 30.0

30.00

52.66 55.59 59.06 63.65 61.74 71.47 65.94 68.54 74.99 77.00 71.22 72.39 76.26 75.20 10.00 10.00 15.00 15.00 20.00

25.00

30.00

0.494 2 0.099 9 0.200 0 0.298 1 0.142 8 0.068 9 0.399 3 0.221 8 0.306 6 0.222 2 0.301 2 0.044 9 0.095 2 0.208 3 0.141 4 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0

2000

700

H

H

11

274.5

0.5

1600

600

H

H

7

435.5

0.5

1600

600

H

H

8

428.5

0.5

1400

700

H

H

5

429.5

0.8

1600

600

H

H

8

505.5

0.5

1600

600

H

H

3

508.5

0.5

1600

600

H

H

5

465.0

0.5

1600

600

H

H

6

503.5

0.5

1600

600

H

H

7

490.5

0.5

1600

600

H

H

5

569.5

0.5

1400

700

H

H

6

551.5

0.5

1400

700

H

H

5

579.5

0.5

1400

700

H

H

6

579.5

0.5

1400

700

H

H

4

577.5

1.2

1400

700

H

H

6

587.5

0.5

750

500

I

5

-5.9

0.1

1500

600

I

3

-5.9

0.1

3000

500

I

2

-8.4

0.1

3000

500

I

3

-9.8

0.1

1500

500

I

4

-17.4

0.1

1.000 0 1.000 0

1000

600

I

2

-17.7

0.1

2000

400

I

2

-24.0

0.2

1.000 0 1.000

3000

500

I

3

-37.0

0.2

1000

600

I

4

-38.0

0.1

48

-MIk 0 0 012912 0.00 35.0 35.00 1.000 2000 500 M N -MXV 0 0 A 012912 0.00 35.0 35.00 1.000 2000 600 M N -MXIV 0 0 A 012912 0.00 35.0 35.00 1.000 2000 700 M N -MXIII 0 0 A 060312 0.00 63.8 63.8 1.000 750 553 F2h F2 4 220.0 -MLI 0 h 060312 0.00 63.8 63.8 1.000 500 508 F2h F2 3 219.0 -MLII 0 h a Ψ N = 100wNaCl/(wNaCl + wH2O) where wX = mass percent of component X (see section 2.3) b Ψ F = 100wFeCl2/(wFeCl2 + wH2O) c

0.1 0.3

w = 100(wFeCl2 + wNaCl)/(wNaCl + wFeCl2 + wH2O) Φ= wFeCl2/(wFeCl2 + wNaCl) e P & T = formation pressure and temperature of the experiment f PPRT = phases present at room temperature: H (halite), FnH (FeCl2 hydrate, where n = number of H2O's in formula unit) g LP = liquidus phase: I(ice), H (halite) or F2h (FeCl2·2H2O). M indicates metastable liquid, for FI that could not be solidified. h # FI = number of FI measured; NA = Not applicable i Tm = last dissolution temperature (°C); STDV = standard deviation (analytical precision is reported, in cases in which the standard deviation is less than the precision of the measurement) j excluded from regression analysis k experiment conducted in Au capsule d

Table 4. Experimental measurements on univariant curves. b Sample Boundary Median Tm STDVa Tm w 28.8 010312-XLV I+Hd -33.8 0.2 d I+H 28.9 010312-XLIII -34.1 0.5 d I+H 28.4 010312-XLI -32.9 0.1 d I+H 28.7 010212-XXXV -33.6 0.2 d I+H 28.9 010312-XLIV -34.1 0.1 d I+H 27.0 010412-IL -30.1 0.1 d I+H 27.0 010412-XLVI -29.9 0.3 d I+H 27.7 051712-V -31.5 0.1 23.8 010512-L I+Hh -22.6 2 23.8 052012-XXVI I+Hh -22.7 0 25.6 010412-IL I+Hh -26.5 NA 54.3 270812-VII FnH+H 127.9 0.2 53.8 270812-VIII FnH+H 120 1 49

Φc 0.62 0.61 0.63 0.62 0.61 0.30 0.30 0.46 0.55 0.24 0.49 0.84 0.86

30.8 0.94 I+Hh+F6He -38 NA a standard deviation b w = liquid salinity (wt%) c Φ= wFeCl2 / (wFeCl2 + wNaCl) on univariant curve. d metastable cotectic, ice+halite e eutectic T and composition predicted using Pitzer's equations (see text for details). Table 5. Coefficients agh for Eq. 1 (ice liquidus) and aij for Eq. 2 (halite liquidus) g=1 g=2 g=3 i=0 i=1 i=2 h = 0 -1.916 -5.169E-2 -5.903E-4 j = 0 26.43 1.278E-2 1.069E-4 0 h=1 0 -1.338E-5 j = 2 7.481 0.231 0 0 h=2 -1.144E-4 0

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