<figure><img src="image_21.png" /><figcaption>**Fig. 4.20** Concentrations of the major forms of sulfur, including the radical ions, in two typical types of fluids as a function of temperature, (a) magmatic-hydrothermal fluid and (b) metamorphic fluid both in equilibrium with the quartz-muscovite-potassic feldspar assemblage. The sulfur species concentrations were predicted using the stability constants of sulfur forms discussed in this chapter. The concentration of S₂⁻ is tentative (see text). The S₃⁻, and potentially S₂⁻, ions may represent a significant part of dissolved sulfur content over a wide T-P range.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>**Fig. 4.21** In situ fluid/melt partition coefficients of sulfate, sulfide, S₃⁻ and S₂⁻, derived from in situ measurements for felsic melts at 700 °C and 3–15 kbar as a function of fO₂. Error bars are 1 s.d.; only upper vertical error bars for the radical ions could be estimated (shown by arrows), because their concentrations in the melt were close to the detection limit. Blue area outlines the sulfate-sulfide boundary in water saturated melt (estimated according to Moretti and Baker 2008); horizontal dashed line shows partition coefficients of sulfide extrapolated to the more reduced conditions. Note that a partition coefficient of an individual sulfur species is independent of redox conditions (modified after Colin et al. 2020).</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>**Fig. 4.22** Sulfidation states of hydrothermal fluids, in sulfur fugacity-temperature space, based on natural sulfide mineral assemblages. Lines represent the indicated mineral equilibria estimated at 1 bar pressure (from Einaudi et al. 2003). Different types of hydrothermal ore deposits are shown (colors for visualization aids only; modified from Fontboté et al. 2017). Abbreviations: IOCG = iron oxide copper gold; MVT = Mississippi Valley type, SMS = sedimentary-hosted massive sulfide; VMS = volcanic-hosted massive sulfide. Mineral abbreviations (according to Warr 2021): Apy = arsenopyrite; Bn = bornite; Ccp = chalcopyrite; Cv = covellite; Dg = digenite; Fe = iron; Lö = löllingite; Py = pyrite; Pyh = pyrrhotite.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>**Fig. 4.23** Sulfur speciation in the fluid phase at different sulfidation states shown in Fig. 22. Concentrations of aqueous sulfur species in hydrothermal saline fluid (KCl+NaCl, 10 wt% NaCl eq.) are shown as a function of temperature, along a typical pressure gradient (from 10 bar at 100 °C to 1000 bar at 600 °C) of hydrothermal ore deposit formation, in equilibrium with (a) quartz-faylite-magnetite-pyrrhotite, (b) pyrite-pyrrhotite-magnetite, and (c) liquid sulfur-pyrite, which are relevant to low, intermediate, and high sulfidation states, respectively. In (a) and (b), the fluid acidity is buffered by the quartz-muscovite-potassic feldspar assemblage (pH ~5–6), whereas in (c) the acidity is imposed by protonation reactions of sulfate and sulfite forming by dissolution of sulfur (pH ~2–4). Sulfur and oxygen fugacity values are also plotted as S₂(g) and O₂(g) (in bars) to the left and right Y axes, respectively. Solubility of Fe (as Fe²⁺, FeCl⁺ and FeCl₂⁰⁻) and Au (dominantly Au(HS)₂⁻ and Au(HS)S₃⁻) is also shown. In (b) the curves are drawn to 550 °C, above which pyrite is unstable at the chosen pressure conditions (<1 kbar).</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>**Fig. 4.24** Hard-soft classification of chemical elements for their naturally representative oxidation states (modified from Pokrovski 2025a).</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Fig. 4.25** Solubility of metals in hydrothermal fluids in equilibrium (i.e. saturated) with major sulfide minerals as a function of four parameters (a) temperature, (b) fluid salinity, (c) fluid pH, and (d) H₂S concentration. In each case, the other physical-chemical parameters of the fluid are fixed. Galena solubility, not shown, is slightly lower than that of sphalerite. Abbreviations: hem = hematite, py = pyrite, mag = magnetite. Gold solubility in (a) increases with temperature mainly due to the growing abundance of hydrosulfide (and trisulfur ion) ligands due to enhanced solubility of the Py-Mag-Hem assemblage with temperature. Note that predictions for Mo are tentative and given for illustration purposes only, in light of poor constraints on the stability of its chloride, sulfide and alkali complexes (see section 4.4.10). Modified from Kouzmanov and Pokrovski (2012) and Fontboté et al. (2017).</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>**Fig. 4.26** Decimal logarithms of the constants of the $Cl^-$ vs $HS^-$ ligand exchange reactions (4.68) and (4.69) indicated in the figure for the major Zn and Pb complexes as a function of temperature (at $P_{sat}$), according to the available model equations discussed in the text. Sv97 = Sverjensky et al. (1997) from the SUPCRT92 database, TS10 = Tagirov and Seward (2010), AT14 = Akinfiev and Tagirov (2014), Me15 = Mei et al. (2015a), Me16 = Mei et al. (2016). First reference in the legend corresponds to the datasource for the chloride complex versus the second reference for its sulfide counterpart.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>**Fig. 4.27** Decimal logarithms of the reaction constants of formation of the major Cu<sup>I</sup> (a, b) and Ag<sup>I</sup> (c, d) hydrosulfide complexes, according to the thermodynamic data sources discussed in the text. Sv97 = Sverjensky et al. (1997) from the SUPCRT92 database, AZ01 = Akinfiev and Zotov (2001), AZ10 = Akinfiev and Zotov (2010), MS03 = Mountain and Seward (2003), SS03 = Stefansson and Seward (2003a), Me13 = Mei et al. (2013), La22 = Lai et al. (2022), Tr23 = Trofimov et al. (2023). RB model = SS03 data were regressed, in this study for comparison, using the RB model and thermodynamic properties of the Ag<sup>+</sup> ion from AZ01 (AgHS<sup>0</sup> = Ag<sup>+</sup> + HS<sup>-</sup>, pK<sub>298</sub> = 14.98, A = -0.194; Ag(HS)<sub>2</sub><sup>-</sup> = Ag<sup>+</sup> + 2HS<sup>-</sup>, pK<sub>298</sub> = 17.08, A = 0.39).</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>**Fig. 4.28** Decimal logarithms of the solubility constants at 1 kbar (unless indicated) of the key Au aqueous species, AuOH⁰ (a), AuCl₂⁻ (b), Au(HS)₂⁻ (c), and AuHS⁰ (d), according to the major indicated thermodynamic datasources, discussed in the text: Sv97 = Sverjensky et al. (1997) from the SUPCRT92 database, AZ01 = Akinfiev and Zotov (2001), AZ10 = Akinfiev and Zotov (2010), Ra14 = Rauchenstein-Martinek et al. (2014), SS03b = Stefánsson and Seward (2003b), SS04 = Stefánsson and Seward (2004), Ta05 = Tagirov et al. (2005), Zo18 = Zotov et al. (2018).</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>**Fig. 4.29** Gold-trisulfur ion complexes in model hydrothermal fluids revealed by a combination of in situ spectroscopy and solubility measurements (modified from Pokrovski et al. 2022b). (a) Comparison between measured and calculated Au L<sub>3</sub>-edge HERFD-XANES spectra of the two major aqueous Au species with sulfur ligands. Measured spectra (solid curves) are from the two experiments in acidic and slightly alkaline thiosulfate solutions (pH of the neutrality point of water is 5.5 at 350 °C and 600 bar). The solution detailed sulfur (b) and gold (c) speciation is calculated, using the thermodynamic datasources discussed in the text, as a function of pH and corresponding redox (indicated in log<sub>10</sub>f<sub>O<sub>2</sub></sub> relative to the conventional hematite-magnetite buffer, HM). Simulated XANES spectra in (a) are obtained by quantum-chemistry calculations (FDMNES program) using the species structures shown in ball-and-stick style (Au = pink, S = yellow, S<sub>3</sub> = blue, H = grey) from static DFT (dotted curves) and dynamic MD (dashed curves) simulations. Grey arrows in (a) indicate differences in the experimental spectra, also apparent in the corresponding calculated spectra, supporting the predicted change in Au speciation from Au(HS)<sub>2</sub><sup>-</sup> to Au(HS)S<sub>3</sub><sup>-</sup>.</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>**Fig. 4.30** Gold, copper, iron and sulfur solubility and speciation in the hydrothermal fluid phase during its evolution in a generic context of porphyry-epithermal Cu-Au-Mo deposits (modified from Pokrovski et al. 2015). An initial magmatic fluid has the following typical composition as inferred from fluid inclusions and geochemical studies: 10 wt% NaCl equivalent, 2 wt% S, H₂S:SO₂ molal ratio = 1, 0.75 wt% Fe as FeCl₃, 0.30 wt% as CuCl. This fluid degasses from magma at 700 °C and 1.5 kbar and cools and decompresses in the liquid phase in equilibrium with native Au and alkali aluminosilicate rocks (quartz-muscovite-potassic feldspar assemblage, QMK, pH of 5–6 at all temperatures); this is a common scenario of fluid evolution in a porphyry-epithermal setting (see Kouzmanov and Pokrovski 2012 for details). Curves show the concentrations of the major indicated sulfur forms (in ppm S), Au total solubility (ΣAu, red curve) which is the sum of the major di-hydrosulfide and subordinate mono-hydrosulfide and di-chloride complexes (green curve) and the dominant Au(HS)S₃⁻ complex (pink curve), and total Fe and Cu solubility (ΣFe and ΣCu, as dominantly chloride complexes, **Table 4.6**). Gray horizontal bars show the temperature range of stability of the indicated minerals that precipitate on fluid cooling.</figcaption></figure>
<figure><img src="image_32.png" /></figure>

**Fig. 4.31** (a) Comparison of the solubility of PtS<sub>(s)</sub>, and native Pt and Au in an aqueous fluid of 2 m NaCl and 0.1 m H<sub>2</sub>S at the oxygen fugacity of the conventional nickel-nickel oxide buffer (NNO, log f<sub>O<sub>2</sub></sub> = -33.9) as a function of pH at 300 °C and 500 bar. The thermodynamic data of all Au species, PtCl<sub>4</sub><sup>2-</sup>, and Pt(HS)<sub>4</sub><sup>2-</sup> are, respectively, from Pokrovski et al. (2014), Tagirov et al. (2019), and Laskar et al. (2022). Adopted and modified from Laskar et al. (2022). (b) Comparison of the equilibrium constant values of the indicated Cl<sup>-</sup> vs HS<sup>-</sup> ligand exchange reaction between di-chloride and di-hydrosulfide complexes of Cu<sup>I</sup>, Ag<sup>I</sup>, Zn<sup>II</sup>, Pb<sup>II</sup>, Fe<sup>II</sup>, Au<sup>I</sup>, and Pt<sup>II</sup>, as a function of temperature and at 500 bar pressure for all metals (and at 1 kbar for Au). Note that the Pt<sup>II</sup> reaction constant between tetrachloride and tetrahydrosulfide complexes (reaction 4.80) was scaled to 2 exchanging ligands in the reaction to allow more direct comparisons with the other metals. The following datasources were used, as discussed in the text: Cu and Ag - Akinfiev and Zotov (2001, 2010); Au - Pokrovski et al. (2014) and Zotov et al. (2018); Zn - Akinfiev and Tagirov (2014); Pb - Sverjensky et al. (1997), Fe - Laskar (2022), Pt - Laskar et al. (2022).
<figure><img src="image_33.png" /><figcaption>**Fig. 4.32** The effect of the trisulfur ion on platinum solubility in hydrothermal fluids. Platinum dissolved concentration in equilibrium with PtS<sub>(s)</sub> in hydrothermal fluid at 300°C and 500 bar and its comparison with gold as a function of (a) total dissolved S concentration at pH ~5 and f<sub>O2</sub> buffered by the sulfide-sulfate equilibrium with (H<sub>2</sub>S)<sub>tot</sub>:(SO<sub>4</sub>)<sub>tot</sub> molal ratio of 4:1 corresponding to the maximum of S<sub>3</sub><sup>-</sup> abundance (see reaction 4.45); (b) oxygen fugacity corresponding to common redox buffers, QFM – quartz-fayalite-magnetite, NNO – nickel-nickel oxide, PPM – pyrite-pyrrhotite-magnetite, and HM – hematite-magnetite; (c) fluid acidity, pH = -log a(H<sup>+</sup>) at f<sub>O2</sub> buffered by sulfide-sulfate equilibrium (H<sub>2</sub>S:SO<sub>4</sub> = 4:1); (d) in equilibrium with gold metal as a function of pH at the conditions identical to (c). The curves denote the concentrations of S<sub>3</sub><sup>-</sup> (blue, in ppm of S, same scale as for Pt and Au), sum of known Pt/Au-Cl, Pt/Au-HS, Pt-SO<sub>4</sub> and Au-OH species (green) and the total Pt or Au solubility (red) including Pt(HS)<sub>2</sub>(S<sub>3</sub>)<sub>2</sub><sup>-</sup> and Pt(HS)<sub>3</sub>(H<sub>2</sub>O)(S<sub>3</sub>)<sub>2</sub><sup>-</sup> or Au(HS)S<sub>3</sub><sup>-</sup>. The difference between the two latter curves (vertical pink arrows) corresponds to the contribution of Pt-S<sub>3</sub> or Au-S<sub>3</sub> types of complexes. The thermodynamic properties of Au and Pt species and other fluid constituents are from datasources of **Tables 4.5 and 4.6**.</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>**Fig. 4.33** Two-step mechanism of pyrite formation and equilibration between the mineral and hydrothermal fluid controlled by [Fe<sup>II</sup>-HS-S<sub>3</sub>]-type aqueous species, as revealed using Fe isotopes (Pokrovski et al. 2021c). The first, both short and fast (&lt;10 days), step of pyrite precipitation occurs via aqueous Fe<sup>II</sup> (poly)sulfide species precursors exemplified here, forming in reaction between the dominant Fe-bearing complex, FeCl<sub>2</sub><sup>0</sup>, and hydrosulfide and polysulfide anions. The second, much slower and longer (100s to 1000 days), step of Fe isotope equilibration with the fluid occurs through slower pyrite recrystallization and re-equilibration with the fluid and requires about 1 year to reach 90% of Fe isotope equilibrium even at such high temperatures as 300–450 °C. The kinetic law established may be used for estimating, using Fe isotope signatures, the dynamic of relatively short (&lt;year-scale) mineralizing events in ancient hydrothermal metal sulfide deposits that cannot be assessed using traditional dating approaches.</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>**Fig. 4.34** Comparison of the equilibrium constants of the dissolution reaction of the major As, Sb and Bi sulfide minerals (orpiment, stibnite and bithmutite) with formation of aqueous trihydroxide complexes as a function of temperature at 300 bar, according to the available thermodynamic data sources discussed in the text.</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>**Fig. 4.35** Speciation of Mo<sup>VI</sup> in aqueous fluid at 25 °C, 1 bar (a) and 300 °C, P<sub>sat</sub> (b) as a function of pH with 0.01 m total H<sub>2</sub>S and 0.15 m total salt concentration (NaCl+HCl+NaOH). The fractions of H<sub>2</sub>MoO<sub>4</sub><sup>0</sup> and HMoO<sub>4</sub><sup>-</sup> in (a) and of H<sub>2</sub>MoO<sub>4</sub><sup>0</sup> in (b) are <1% (not shown).</figcaption></figure>
<figure><img src="image_37.png" /></figure>

**Fig. 4.36** Equilibrium thermodynamic formation constants for the 1:1 metal sulfate complexes plotted versus their corresponding first hydrolysis constants, at 25 °C and 1 bar and zero ionic strength, for the three groups of cations – hard, intermediate and soft, shown in green, blue and red, respectively. The straight lines are least-square linear regressions of data for each corresponding metal group. Data are from compilations of Baes and Mesmer (1976), Turner et al. (1981), Johnson et al. (1992), Smith et al. (2004).
<figure><img src="image_38.png" /></figure>

**Fig. 4.37** Mineral saturation state for anhydrite (a) and dissolved sulfide buffers (b) in reservoir hydrothermal fluids. The curves represent the equilibrium solubility of anhydrite and PPM (pyrite, pyrrhotite and magnetite) and PPPE (pyrite, pyrrhotite, prehnite and epidote) mineral buffers calculated with the aid of the SUPCRT92 program (Johnson et al. 1992). The symbols indicate reaction quotients for hydrothermal reservoir fluids for geothermal system sourced by seawater in basalts (Reykjanes and Svarstengi) and sourced by meteoric water in basalts (Námafjall and Krafla), trachyte (Olkaria) and andesite (Taupo). Data on natural hydrothermal fluids are from Stefánsson et al. (2016), Kleine et al. (2021) and Ricci et al. (2022).
<figure><img src="image_39.png" /></figure>

**Fig. 4.38** The relationship between the sulfate/chloride mole ratio and pH for hydrothermal waters at surface. Included are data from Yellowstone (USA) (McCleskey et al. 2022) and various geothermal fields in Iceland (Kaasalanen and Stefánsson 2012; Markússon and Stefánsson 2011; Björke et al. 2015; Stefánsson et al. 2016). Alkaline hot springs represent boiled reservoir hydrothermal water at surface and are characterized by similar $SO_4^{2-}/Cl^-$ ratios as the reservoir fluid and pH >8. Steam heated waters are produced upon condensation at surface of H$_2$S-enriched vapor formed upon boiling of reservoir hydrothermal fluids, followed by oxidation to form waters enriched in sulfuric acid resulting in the low pH and elevated $SO_4^{2-}/Cl^-$ ratios. Waters with mildly acid to mildly alkaline pH values can often be mixtures of hydrothermal water and cold or non-thermal water.
<figure><img src="image_40.png" /></figure>

**Fig. 4.39** Concentration of sulfur (in ppm) in various fluid inclusion types from magmatic-hydrothermal systems (a, b), metamorphic fluids (c, d) and basinal brines (e, f), as a function of temperature of homogenization (in °C) and apparent fluid salinity (in wt% NaCl eq.). See **Table 4.2** and Supplementary **Table 4.S1** for data sources. Abbreviations for fluid inclusion types in magmatic-hydrothermal systems: A – aqueous; B – hypersaline aqueous (brine); S – supercritical fluid; V – vapor.
<figure><img src="image_41.png" /><figcaption>**Fig. 4.40** Concentration of selected metals in fluid inclusions from magmatic-hydrothermal systems as a function of sulfur concentration (in ppm). See Tables 4.2 and S1 for data sources. Abbreviations for fluid inclusion types in magmatic-hydrothermal systems: A – aqueous; B – hypersaline aqueous (brine); S – supercritical; V – vapor. Dashed lines indicate the 1:1 atomic concentration ratio of metal to sulfur.</figcaption></figure>
<figure><img src="image_42.png" /><figcaption>**Fig. 4.41** Concentration of metals in fluid inclusions from metamorphic environments as a function of sulfur concentration (in ppm). See the Fig. 4.40 caption and Table 4.2 for details and data sources.</figcaption></figure>
<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

**Fig. 4.42** Concentration of metals in fluid inclusions entrapping basinal brine-type fluids as a function of sulfur concentration (in ppm). See Fig. 4.40 and Table 4.2 for details and data sources.
<figure><img src="image_49.png" /></figure>

**Fig. 4.43** Comparison between sulfur concentrations from natural fluid inclusions from major types of fluids indicated in the legend and predicted S concentrations in equilibrium with the common *f*<sub>S2</sub> and *f*<sub>O2</sub> iron oxide-sulfide mineral buffers, pyrite-pyrrhotite-magnetite (PPM) and pyrite-magnetite-hematite (PMH), calculated as a function of temperature at 1 kbar pressure for a typical 10 wt% NaCl eq. fluid whose pH is buffered by equilibrium with a common silicate rock (quartz-muscovite-feldspar, pH 4.5–5.5 at all temperatures). Note that fluid inclusion homogenization temperatures (T<sub>h</sub>) must be shifted by ~100–300 °C to the right, to account for true entrapment temperatures (T<sub>t</sub>) for metamorphic and sedimentary fluids (dashed horizontal arrows).
Tables

<table><caption>**Table 4.1** Concentrations of sulfur aqueous forms (in mmol/kg S equivalent) in modern natural hydrothermal fluids.</caption><thead><tr><th>Location</th><th>t °C</th><th>pH<sub>T</sub></th><th>Cl</th><th>SO<sub>4</sub></th><th>S<sub>2</sub>O<sub>3</sub></th><th>SO<sub>3</sub></th><th>S<sub>n</sub>O<sub>6</sub></th><th>H<sub>2</sub>S</th></tr></thead><tbody><tr><td colspan="9"><em>Reservoir hydrothermal fluids</em></td></tr><tr><td>Ohaaki, New Zealand<sup>a</sup></td><td>268</td><td>6.61</td><td>19.9</td><td>0.25</td><td>—</td><td>—</td><td>—</td><td>1.60</td></tr><tr><td>Rotokawa, New Zealand<sup>a</sup></td><td>300</td><td>6.16</td><td>30.4</td><td>0.01</td><td>—</td><td>—</td><td>—</td><td>4.28</td></tr><tr><td>Reykjanes, Iceland<sup>a</sup></td><td>299</td><td>4.88</td><td>498</td><td>0.76</td><td>—</td><td>—</td><td>—</td><td>2.38</td></tr><tr><td>Krafla, Iceland<sup>a</sup></td><td>258</td><td>6.89</td><td>0.24</td><td>0.09</td><td>—</td><td>—</td><td>—</td><td>5.58</td></tr><tr><td>Kizildere, Turkey<sup>a</sup></td><td>243</td><td>6.86</td><td>2.8</td><td>8.49</td><td>—</td><td>—</td><td>—</td><td>0.13</td></tr><tr><td>Olkaria, Kenya<sup>b</sup></td><td>295</td><td>7.19</td><td>10.0</td><td>0.05</td><td>—</td><td>—</td><td>—</td><td>2.81</td></tr><tr><td>Momotombo, Nicaragua<sup>c</sup></td><td>250</td><td>5.61</td><td>75.9</td><td>0.31</td><td>—</td><td>—</td><td>—</td><td>0.86</td></tr><tr><td>Los Humeros, Mexico<sup>d</sup></td><td>300</td><td>6.63</td><td>1.8</td><td>1.67</td><td>—</td><td>—</td><td>—</td><td>2.49</td></tr><tr><td>Wayang Windu, Indonesia<sup>e</sup></td><td>290</td><td>4.88</td><td>410</td><td>0.12</td><td>—</td><td>—</td><td>—</td><td>2.62</td></tr><tr><td>Fusime, Japan<sup>c</sup></td><td>272</td><td>4.37</td><td>563</td><td>0.24</td><td>—</td><td>—</td><td>—</td><td>3.46</td></tr><tr><td>Palinpinon, Philippines<sup>f</sup></td><td>240</td><td>5.50</td><td>202</td><td>0.14</td><td>—</td><td>—</td><td>—</td><td>2.53</td></tr><tr><td colspan="9"><em>Surface springs and ponds</em></td></tr><tr><td>Geysir, Iceland<sup>g</sup></td><td>82</td><td>8.85</td><td>3.72</td><td>1.02</td><td>0.089</td><td>0.003</td><td>—</td><td>0.038</td></tr><tr><td>Laugarvatn, Iceland<sup>g</sup></td><td>100</td><td>8.63</td><td>1.01</td><td>0.37</td><td>0.022</td><td>0.002</td><td>—</td><td>0.27</td></tr><tr><td>Krýsúvík, Iceland<sup>g</sup></td><td>98</td><td>2.20</td><td>0.037</td><td>52.7</td><td>0.017</td><td>—</td><td>—</td><td>1.16</td></tr><tr><td>Cinder Pool, YNP, USA<sup>h</sup></td><td>92</td><td>4.22</td><td>16.9</td><td>1.00</td><td>0.038</td><td>—</td><td>0.008</td><td>0.047</td></tr><tr><td>Azure Spring, YNP, USA<sup>h</sup></td><td>84</td><td>8.70</td><td>8.62</td><td>0.43</td><td>0.055</td><td>—</td><td>—</td><td>0.011</td></tr><tr><td>Acid Inkpot, Yellowstone USA<sup>h</sup></td><td>76</td><td>2.92</td><td>0.28</td><td>33.4</td><td>0.001</td><td>—</td><td>&lt;0.001</td><td>0.24</td></tr><tr><td>Champagne Pool, New Zealand<sup>i</sup></td><td>76</td><td>5.5</td><td>1.36</td><td>0.68</td><td>0.37</td><td>—</td><td>—</td><td>0.16</td></tr><tr><td>Champagne Pool, New Zealand<sup>i</sup></td><td>22</td><td>2.5</td><td>1.07</td><td>1.12</td><td>0.003</td><td>—</td><td>—</td><td>0.003</td></tr><tr><td colspan="9"><em>Fumaroles</em></td></tr><tr><td>Nisyros, Greece<sup>a</sup></td><td>97-102</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>90-340</td></tr><tr><td>Krafla, Iceland<sup>i</sup></td><td>100</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>46.3</td></tr><tr><td>Norris Canyon, YNP, USA<sup>k</sup></td><td>93</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>18.9</td></tr><tr><td>By Inkpot, YNP, USA<sup>k</sup></td><td>92</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>42.6</td></tr><tr><td colspan="9"><em>Hydrothermal vent fluids</em></td></tr><tr><td>Lost City<sup>l</sup></td><td>94</td><td>12.1</td><td>545-570</td><td>&lt;4.2</td><td>—</td><td>—</td><td>—</td><td>0.1</td></tr><tr><td>Logatchev<sup>l</sup></td><td>346-352</td><td>3.3-3.9</td><td>511-515</td><td>&lt;2.3</td><td>—</td><td>—</td><td>—</td><td>1.1-1.4</td></tr><tr><td>Juan de Fuca<sup>m</sup></td><td>224-285</td><td>3.2</td><td>896-1090</td><td>&lt;1.0</td><td>—</td><td>—</td><td>—</td><td>3.0-4.4</td></tr><tr><td>Rainbow<sup>l</sup></td><td>360-365</td><td>2.8-3.0</td><td>750-796</td><td>—</td><td>—</td><td>—</td><td>—</td><td>1.2-1.4</td></tr><tr><td>Borken Spur<sup>l</sup></td><td>356-360</td><td>—</td><td>469</td><td>—</td><td>—</td><td>—</td><td>—</td><td>8.5-11.0</td></tr></tbody></table>

'-)' means not available; pH<sub>T</sub> is at the fluid temperature; pH is measured at lower temperature and then slid to higher temperatures applying a mass balance equation for H<sup>+</sup>; this procedure is often called conservation of alkalinity or charge balance.

<footnote><sup>a</sup> Ricci et al. (2022); <sup>b</sup> Kleine et al. (2021); <sup>c</sup> Stefánsson and Arnórsson (2000); <sup>d</sup> Tello et al. (2000); <sup>e</sup> Prasetio et al. (2020); <sup>f</sup> Rae et al. (2011); Kaasalainen and Stefánsson (2011a,b); <sup>h</sup> Xu et al. (1998); <sup>i</sup> Ulrich et al. (2013); <sup>j</sup> Stefánsson (2017); <sup>k</sup> Chiodini et al. (2012); <sup>l</sup> Charlou et al. (2010) and references therein; <sup>m</sup> Von Damm and Bischoff (1987).</footnote>
<table><caption>**Table 4.2** Typical ranges of temperature, salinity, sulfur and selected metal concentrations (range and median value) in major types of fluids from magmatic-hydrothermal systems, metamorphic terrains and basinal continental brines, based on analyses of individual fluid inclusions by microthermometry and LA-ICPMS (please use the Table 4.2 native xlxx file for production).</caption><thead><tr><th>Hydrothermal fluid type</th><th>Environment</th><th>Fluid inclusion types</th><th>Temperature of hom. (°C)</th><th>Salinity (wt% NaCl eq.)</th><th>Density (g/cm³)</th><th>S (ppm)</th><th>Fe (ppm)</th><th>Cu (ppm)</th><th>Mo (ppm)</th><th>Au (ppm)</th><th>Ag (ppm)</th><th>As (ppm)</th><th>Sb (ppm)</th><th>Zn (ppm)</th><th>Pb (ppm)</th></tr></thead><tbody><tr><td rowspan="10">Magmatic-hydrothermal*</td><td>Deep barren and deep central and peripheral Cu-Au (Mo) ore zones in porphyry copper deposits; porphyry-associated skarns</td><td>S<br>Supercritical inclusions (S) are intermediate-density aqueous inclusions containing equal proportions of liquid and vapor; many contain small opaque daughter crystals of constant relative size.</td><td>300 - 650</td><td>2 - 16</td><td>0.4 - 0.7</td><td>70 - 96000<br>10500</td><td>10 - 47000<br>3900</td><td>5 - 90000<br>3800</td><td>&lt;1 - 1200<br>50</td><td>&lt;1 - 20<br>1.6</td><td>&lt;1 - 600<br>20</td><td>3 - 2000<br>210</td><td>1 - 30<br>10</td><td>2 - 6500<br>600</td><td>&lt;1 - 4500<br>330</td></tr><tr><td>Stockwork mineralization at moderate to shallow depth in central parts of Cu-Au (Mo) ore zones and upper parts of Cu-rich periphery; porphyry-associated skarns; IOCG; Sn-W deposits.</td><td>V &amp; B<br>Vapor-rich inclusions (V) can be high- (60-90% vapor) or low-density (&gt;90% vapor) and commonly contain small opaque daughter crystals.<br>Hypersaline liquid inclusions (brines - B) always contain a vapor bubble, a saline aqueous liquid and halite, additionally polyphase inclusions contain a few other transparent and opaque daughter phases. In many cases vapor-rich and hypersaline liquid inclusions form boiling assemblages.</td><td>260 - 650,<br>rarely up to 800</td><td>vapor: 0.2 - 20</td><td>vapor: 0.01 - 0.4</td><td>385 - 26000<br>5000</td><td>2 - 31000<br>6000</td><td>&lt;1 - 33000<br>4300</td><td>1 - 1025<br>20</td><td>0.05 - 11<br>1.9</td><td>&lt;1 - 600<br>45</td><td>2 - 1200<br>175</td><td>1 - 150<br>35</td><td>&lt;1 - 6800<br>660</td><td>&lt;1 - 4000<br>340</td></tr><tr><td>Late-stage porphyry veining (quartz-sericite-pyrite); IOCG; Sn-W deposits; base and porous metal mineralization in skarns, carbonate-replacement and epithermal ore bodies.</td><td>V &amp; A<br>Aqueous (A) low- to intermediate-salinity inclusions with predominantly liquid water and smaller vapor bubbles ranging from 20 to 40 vol % may occur together or not with low-density vapor-rich (V) inclusions (&gt;90% vapor). Aqueous inclusions are usually free of daughter crystals, however some may contain accidentally trapped sericite crystals. Coexistence of aqueous and low-density vapor inclusions is indicative of fluid boiling at low pressure.</td><td>150 - 450</td><td>hypersaline liquid: 26 - 75</td><td>hypersaline liquid: 0.8 - &gt;1</td><td>120 - 120000<br>8800</td><td>15 - 221000<br>51000</td><td>10 - 86000<br>3300</td><td>1 - 9300<br>70</td><td>0.03 - 90<br>0.7</td><td>&lt;1 - 184<br>95</td><td>2 - 6600<br>230</td><td>1 - 1200<br>95</td><td>90 - 40000<br>3200</td><td>5 - 60000<br>3000</td></tr><tr><td>Metamorphic fluids trapped in late-metamorphic quartz veins and Alpine fissure veins hosted by metamorphic rocks formed from subgreenschist-to-amphi-bolite-facies conditions.</td><td>A &amp; AC<br>Aqueous (A) inclusions are common for veins in subgreenschist- and greenschist-facies rocks, and aqueous-carbonic (AC) inclusions in amphibolite-facies rocks. Volatile content (CO₂, sulfur) increases systematically with the metamorphic grade.</td><td>80 - 300</td><td>vapor: &lt;0.5<br>aqueous: 0.5 - 22</td><td>vapor: &lt;0.02<br>aqueous: 0.1 - 0.6</td><td>100 - 57000<br>1750</td><td>6 - 33600<br>915</td><td>&lt;1 - 9700<br>85</td><td>&lt;1 - 270<br>15</td><td>0.08 - 54<br>2.1</td><td>&lt;1 - 250<br>10</td><td>2 - 5300<br>330</td><td>&lt;1 - 950<br>30</td><td>&lt;1 - 9200<br>215</td><td>&lt;1 - 5600<br>30</td></tr><tr><td>Basinal brines***</td><td>Basement-hosted Pb-Zn deposits formed by complex fluid process at the interface between sedimentary cover rocks and crystalline basement.</td><td>B &amp; A<br>High- (B), moderate- to low-salinity (A) fluid inclusions, sulfate and/or CO₂-bearing. Complex composition within the Na-Ca-Cl-SO₄-HCO₃ system, produced by mixing of fluids with different origin.</td><td>100 - 180</td><td>2 - 26</td><td>0.1 - 0.8</td><td>2 - 3400<br>290</td><td>3 - 180<br>85</td><td>&lt;0.1 - 410<br>5</td><td>no data<br>available</td><td>&lt;0.1 - 2.2<br>0.05</td><td>&lt;0.1 - 2.5<br>0.5</td><td>&lt;1 - 470<br>15</td><td>&lt;0.1 - 95<br>5</td><td>&lt;0.1 - 200<br>10</td><td>&lt;0.1 - 420<br>0.5</td></tr></tbody></table>

<footnote>*Data from: Kouzmanov and Pokrovski (2012) and references therein; Audétat (2015); Catchpole et al. (2015); Li et al. (2015); Marquez-Zavalia and Heinrich (2016); Chang et al. (2018); Berni et al. (2020); Schirra et al. (2022); Han et al. (2023).</footnote>

<footnote>**Data from: Marsala et al. (2013); Miron et al. (2013); Rauchenstein-Martinek et al. (2014); Rauchenstein-Martinek et al. (2016)</footnote>

<footnote>***Data from: Fusswinkel et al. (2013); Burisch et al. (2016); Walter et al. (2018); Walter et al. (2019).</footnote>
<table><caption>**Table 4.3** Major band Raman spectral frequencies and characteristic X-ray absorption energy positions at ambient conditions of the key aqueous inorganic species of sulfur that may be used for in situ detection of S species in fluid inclusions and hydrothermal fluids in laboratory experiments.</caption><thead><tr><th>Sulfur species (aqueous, unless indicated)</th><th>Raman shift (at max intensity and at ambient T, P) wavenumber, cm<sup>-1</sup></th><th>Nature of Raman band</th><th>Integrated intensity relative to SO<sub>4</sub><sup>2-</sup> (=1)</th><th>S K-edge energy (at max intensity, main edge, unless indicated), eV</th></tr></thead><tbody><tr><td>SO<sub>4</sub><sup>2-</sup></td><td>980</td><td>SO ss</td><td>1</td><td>2481.5</td></tr><tr><td>HSO<sub>4</sub><sup>-</sup> = (HO)SO<sub>3</sub><sup>-</sup></td><td>1050</td><td>SO ss</td><td>1</td><td>2181.5±0.5</td></tr><tr><td>H<sub>2</sub>SO<sub>4</sub> = (HO)<sub>2</sub>SO<sub>2</sub></td><td>970, 1140, 1370, 1220</td><td>SO<sub>2</sub> ss,as, SO<sub>4</sub> as</td><td>-</td><td>-</td></tr><tr><td>SO<sub>2</sub></td><td>1150</td><td>SO ss</td><td>0.5</td><td>2473.0<sup>c</sup>; 2478.0</td></tr><tr><td>(HS)O<sub>3</sub><sup>-</sup></td><td>1050, 2520</td><td>SO ss, SH ss</td><td>0.6</td><td>2477.5</td></tr><tr><td>SO<sub>2</sub>(OH)<sup>-</sup></td><td>1020</td><td>SO s</td><td>0.7</td><td>2476.3</td></tr><tr><td>SO<sub>3</sub><sup>2-</sup></td><td>930, 965</td><td>SO as,ss</td><td>0.5</td><td>2477.2</td></tr><tr><td>S<sub>2</sub>O<sub>3</sub><sup>2-</sup></td><td>450<br>672, 1002, 1125</td><td>SS s<br>SO b,s,as</td><td>1<br>0.3–0.5</td><td>2470.7<br>2479.7</td></tr><tr><td>HS<sub>2</sub>O<sub>3</sub><sup>-</sup>(s)</td><td>403, 642, 1027, 2486</td><td>SS s, SO b,s, SH s</td><td>-</td><td>-</td></tr><tr><td>COS<sub>(g)</sub></td><td>857</td><td>SO s</td><td>-</td><td>2471.0<sup>d</sup></td></tr><tr><td>SCN<sup>-</sup></td><td>745, 2068</td><td>SC ss, CN ss</td><td>-</td><td>-</td></tr><tr><td>S<sub>8</sub>(s,l,aq)</td><td>150, 215, 470</td><td>SS b,b,s</td><td>-</td><td>2471.5</td></tr><tr><td>S<sub>n</sub><sup>0</sup>, S<sub>n</sub><sup>2-</sup></td><td>400, 450</td><td>SS ss,as</td><td>-</td><td>2470–2473</td></tr><tr><td>H<sub>2</sub>S</td><td>2590 (aq), 2610 (g)</td><td>SH ss</td><td>1–3</td><td>2469</td></tr><tr><td>HS<sup>-</sup></td><td>2570</td><td>SH ss</td><td>1–3</td><td>2469</td></tr><tr><td>H<sub>2</sub>S<sub>2</sub></td><td>2500</td><td>SH s</td><td>-</td><td>-</td></tr><tr><td>S<sub>3</sub><sup>•-</sup></td><td>535, 1070</td><td>SS ss (v<sub>1</sub>, 2v<sub>1</sub>)</td><td>10<sup>a</sup>, 30–1000<sup>b</sup></td><td>2467.9<sup>c</sup></td></tr><tr><td>S<sub>2</sub><sup>•-</sup></td><td>590, 1180</td><td>SS ss (v<sub>1</sub>, 2v<sub>1</sub>)</td><td>10<sup>a</sup></td><td>2467.5<sup>c</sup></td></tr></tbody></table>

Relative integrated intensities are indicative; they vary depending on laser frequency, Raman setup, fluid color, and temperature and pressure; see Meyer et al. (1980), Burke (2001), Risberg et al. (2007), Ni and Keppler (2012), Pokrovski and Dubessy (2015), Huang et al. (2021); Schmidt and Seward (2017), Eldridge et al. (2018), Schmidt and Jahn (2024) for details and more references. S K-edge energy positions are corrected relative to sulfate, set to 2481.5 eV in this study. Raman band types: s = stretch with no indication of particular mode; ss = symmetric stretch; as = asymmetric stretch, b = bend; v<sub>n</sub> = particular vibrational mode as per molecular geometry; a = for 458 and 473 nm laser; b = for 515 and 532 nm laser; c = pre-edge; d = tentative estimation; ‘–’ = not available.
<table><caption>**Table 4.4** Sulfur species/minerals identified in natural fluid inclusions by Raman spectroscopy.</caption><thead><tr><th>Species</th><th>Geological setting, rock type</th><th>Host mineral/inclusion type, major composition</th><th>Associated species</th><th>Representative references</th></tr></thead><tbody><tr><td>H<sub>2</sub>S (HS<sup>-</sup>)</td><td>magmatic, porphyry-epithermal, sedimentary-hosted, metamorphic, shallow-mantle settings</td><td>large range of fluid compositions trapped in quartz, topaz, calcite, fluorite, garnet, pyroxene</td><td>S<sub>8</sub>, SO<sub>4</sub><sup>2-</sup></td><td>Dubessy et al. 1984, 1989, 1992; Bény et al. 1982; Burke 2001; Frezzotti et al. 2012 and references therein</td></tr><tr><td>SO<sub>4</sub><sup>2-</sup>, HSO<sub>4</sub><sup>-</sup></td><td>metamorphic, magmatic, volcanic settings</td><td>quartz</td><td>H<sub>2</sub>S</td><td>Rosasco and Roedder 1979; Dubessy et al. 1983, 1992; Boiron et al. 1999; Borisova et al. 2014</td></tr><tr><td>SO<sub>2</sub></td><td>magmatic, carbonatites in mantle xenoliths</td><td>CO<sub>2</sub>-rich inclusions in pyroxene</td><td>CO<sub>2</sub></td><td>Frezzotti et al. 2002</td></tr><tr><td>S<sub>8</sub><sup>0</sup></td><td>evaporites, oil-field sediments, metamorphic rocks</td><td>quartz, fluorite</td><td>H<sub>2</sub>S, SO<sub>4</sub><sup>2-</sup></td><td>Bény et al. 1982; Giuliani et al. 2003; Barré et al. 2017</td></tr><tr><td>COS</td><td>metamorphic rocks</td><td>quartz</td><td>S<sub>8</sub>, H<sub>2</sub>S</td><td>Grishina et al. 1992; Giuliani et al. 2003</td></tr><tr><td>H<sub>2</sub>S<sub>n</sub></td><td>metamorphic quartzite, corundum-bearing marble</td><td>H<sub>2</sub>S-CH<sub>4</sub>-CO<sub>2</sub> quartz and ruby hosted</td><td>S<sub>8</sub>, H<sub>2</sub>S, COS</td><td>Hurai et al. 2019; Huang et al. 2021</td></tr><tr><td>S<sub>3</sub><sup>-</sup>, S<sub>n</sub><sup>2-</sup></td><td>Carnian evaporites, French Alps</td><td>quartz, fluorite, saline (~25 wt% NaCl eq.), heated to 300°C</td><td>H<sub>2</sub>S, S<sub>8</sub>, SO<sub>4</sub><sup>2-</sup></td><td>Barré et al. 2017</td></tr><tr><td>α,β,γ-H<sub>2</sub>S(s)</td><td>organic-rich carbonates hosting fluorite, Southern Permian basin, Germany</td><td>fluorite, gas-rich, H<sub>2</sub>S-CO<sub>2</sub>-N<sub>2</sub>-CH<sub>4</sub>, cooled to -190°C</td><td>H<sub>2</sub>S-clatrates, CO<sub>2</sub>, CH<sub>4</sub></td><td>Sośnicka and Lüders 2021</td></tr><tr><td>Sulfide minerals</td><td>magmatic, sedimentary, metamorphic</td><td>e.g., pyrite, pyrrhotite, chalcopyrite hosted in quartz</td><td>—</td><td>Frezzotti et al. 2012; Mernagh and Mavrogenes 2019; Schiavi et al. 2020</td></tr><tr><td>Sulfate minerals</td><td>magmatic, sedimentary, metamorphic</td><td>e.g., anhydrite, gypsum, barite hosted in quartz</td><td>—</td><td>Frezzotti et al. 2012</td></tr></tbody></table>

“-” = not reported.
<table><caption>**Table 4.5** Recommended sources of thermodynamic data for major sulfur aqueous and gaseous species and mineral phases considered in this work at hydrothermal conditions.</caption><thead><tr><th>Chemical species <sup>a</sup></th><th>Data source</th></tr></thead><tbody><tr><td colspan="2"><strong>Aqueous species</strong></td></tr><tr><td>H<sub>2</sub>O, H<sup>+</sup>, OH<sup>-</sup>, Cl<sup>-</sup>, Na<sup>+</sup>, NaCl<sup>0</sup>, NaOH<sup>0</sup>, KCl<sup>0</sup>, K<sup>+</sup>, KOH<sup>0</sup>, HSO<sub>4</sub><sup>-</sup>, SO<sub>4</sub><sup>2-</sup>, KSO<sub>4</sub><sup>-</sup>, KHSO<sub>4</sub><sup>0</sup>, HS<sup>-</sup>, S<sub>2</sub>O<sub>3</sub><sup>2-</sup>, HSO<sub>3</sub><sup>-</sup>, SO<sub>3</sub><sup>2-</sup></td><td>Johnson et al. 1992 (SUPCRT);<br>Zimmer et al. 2016 (SUPCRTBL)<sup>b</sup></td></tr><tr><td>H<sub>2</sub>S<sup>0</sup>, SO<sub>2</sub><sup>0</sup>, H<sub>2</sub><sup>0</sup>, O<sub>2</sub><sup>0</sup></td><td>&lt;1-2 kbar; ρ<sub>H2O</sub>&lt;0.45 g/cm<sup>3</sup>: Akinfiev and Diamond 2003;<br>≥2 kbar, ρ<sub>H2O</sub>≥0.45 g/cm<sup>3</sup>: Schulte et al. 2001</td></tr><tr><td>HCl<sup>0</sup></td><td>&lt;1-2 kbar: Akinfiev and Diamond 2003;<br>≥2 kbar: Tagirov et al. 1997</td></tr><tr><td>NaSO<sub>4</sub><sup>-</sup></td><td>Pokrovski et al. 1995</td></tr><tr><td>S<sub>(2-8)</sub><sup>2-</sup></td><td>Barré et al. 2017</td></tr><tr><td>NaHS<sup>0</sup>, KHS<sup>0</sup>, NaHSO<sub>4</sub><sup>0</sup></td><td>Pokrovski and Dubessy 2015<sup>c</sup></td></tr><tr><td>S<sub>3</sub><sup>•-</sup></td><td>Pokrovski and Dubessy 2015</td></tr><tr><td>S<sub>2</sub><sup>•-</sup></td><td>Pokrovski et al. 2019<sup>d</sup></td></tr><tr><td>S<sub>8</sub><sup>0</sup> (possibly including other S<sub>n</sub><sup>0</sup>)</td><td>Pokrovski and Dubessy 2015<sup>e</sup></td></tr><tr><td>S<sub>8</sub><sup>0</sup></td><td>this study<sup>f</sup></td></tr><tr><td colspan="2"><strong>Pure solids and liquids</strong></td></tr><tr><td>S<sub>(s)</sub>, S<sub>(l)</sub>, K<sub>2</sub>SO<sub>4</sub>(s), Na<sub>2</sub>SO<sub>4</sub>(s)</td><td>Chase 1998 (JANAF database)</td></tr><tr><td>gold, pyrite, pyrrhotite, magnetite, hematite, quartz,<br>muscovite, microcline, sanidine, andalusite, albite,<br>chalcopyrite, bornite, argentite, galena, molybdenite</td><td>Robie and Hemingway 1995</td></tr><tr><td colspan="2"><strong>Gases</strong></td></tr><tr><td>O<sub>2</sub>, H<sub>2</sub>, H<sub>2</sub>S, SO<sub>2</sub></td><td>Robie and Hemingway 1995</td></tr><tr><td>S<sub>(2-8)</sub></td><td>Chase 1998</td></tr><tr><td>H<sub>2</sub>S<sub>(2-5)</sub></td><td>Suleimenov and Ha 1998</td></tr><tr><td colspan="2"><strong>Activity coefficient models for aqueous solution</strong></td></tr><tr><td>log γ<sub>i</sub> = -A z<sub>i</sub><sup>2</sup>√l/(1+B â<sub>i</sub>√l) + Γ<sub>γ</sub>, for charged species</td><td>Helgeson et al. 1974, 1981<sup>g</sup></td></tr><tr><td>log γ<sub>1</sub> = Γ<sub>γ</sub> + b<sub>i</sub> l, for neutral species</td><td></td></tr></tbody></table>

<footnote><sup>a</sup> Thermodynamic properties of H⁺ are equal to 0 at all *T* and *P*; the standard states for the solid phases and H₂O are unit activity for the pure phase at all *T* and *P*; for gases - unit fugacity of the ideal gas at 1 bar and all *T*; for aqueous species, the standard state convention corresponds to unit activity coefficient for a hypothetical one molal solution whose behavior is ideal. Note that other thermodynamic datasets for the OH⁻ ion are available from the Unitherm database (Shvarov 2008) and the DEW model (Sverjensky et al. 2014), which yield differences of a few to 10s kJ/mol for the Gibbs energy value of OH⁻ in particular near the water isochore of 0.4±0.05 g/cm³.</footnote>

<footnote><sup>b</sup> The updated version of the original SUPCRT database (2007) based on a series of subsequent papers reporting HKF parameters for most ions and aqueous complexes is available on line at http://geopig.asu.edu/index.html#_ These data were transferred and complemented with additional aqueous species and minerals in a more recent SUPCRTBL database available on line at https://models.earth.indiana.edu/supcrtbl.php. This database takes into account the expansivity and compressibility of the major mineral phases from Holland and Powell (2011). Note that for a given aqueous species the thermodynamic coefficients and the *T-P* allowed ranges of calculations are identical in both databases.</footnote>

<footnote><sup>c</sup> Formation constant [cation + ligand = ion pair] at any *T* and *P* is assumed to be equal, respectively, to those of NaCl<sup>0</sup>, KCl<sup>0</sup> and KHSO<sub>4</sub><sup>0</sup> from the SUPCRT database, for consistency.</footnote>

<footnote><sup>d</sup> The apparent molal Gibbs energy values (G°<sub>T,p</sub>) of S<sub>2</sub><sup>•-</sup> at 450 °C, 700 bar (16±5 kJ/mol) and 500 °C, 700-1400 bar (19±9 kJ/mol) were derived from the S<sub>2</sub><sup>•-</sup> concentrations estimated from Raman spectra in thiosulfate and sulfide-sulfate solutions reported by Pokrovski and Dubessy (2015). These values correspond, respectively, to stability constant values, log<sub>10</sub>K, of -16.2±0.5 and -18.4±3.7, for the reaction: 13 H<sub>2</sub>S(aq) + 3 SO<sub>4</sub><sup>2-</sup> = 8 S<sub>2</sub><sup>•-</sup> + 2H<sup>+</sup> + 12 H<sub>2</sub>O(liq).</footnote>

<footnote><sup>e</sup> HKF parameters were obtained by regression of both Kamyshny (2009) low-temperature and Dadze and Sorokin (1993) high-temperature solubility data to optimize c₁ and c₂, and using HKF parameter correlations from Sverjensky et al. (2014) and Shvarov (2015): Δ<sub>f</sub>G°<sub>T,p</sub> = 10.26 kcal/mol, S°<sub>298</sub> = 64.87 cal/mol K, C<sub>p</sub>°<sub>298</sub> = 43.40 cal/mol K, V°<sub>298</sub> = 124.08 cm³/mol, a₁×10 = 25.6 cal/mol bar, a₂×10⁻² = 20.2 cal/mol, a₃ = -11.7 cal/K/mol bar, a₄×10⁻⁴ = -3.6 cal/K/mol, c₁ = 84.8 cal/mol K, c₂×10⁻⁴ = -20.0 cal/K/mol, ω×10⁻⁵ = 0.08 cal/mol.</footnote>

<footnote><sup>f</sup> HKF parameters were obtained based on Kamyshny (2009) sulfur solubility data to 80 °C only and using the HKF correlations (see also Fig. 4.17): Δ<sub>f</sub>G°<sub>T,p</sub> = 10.26 kcal/mol, S°<sub>298</sub> = 64.87 cal/mol K, C<sub>p</sub>°<sub>298</sub> = 43.40 cal/mol K, V°<sub>298</sub> = 124.08 cm³/mol, a₁×10 = 25.6 cal/mol bar, a₂×10⁻² = 20.2 cal/mol, a₃ = -12.0 cal/K/mol bar, a₄×10⁻⁴ = -3.6 cal/K/mol, c₁ = 31.6 cal/mol K, c₂×10⁻⁴ = 5.8 cal/K/mol, ω×10⁻⁵ = 0 cal/mol.</footnote>

<footnote><sup>g</sup> A and B are the Debye-Hückel electrostatic parameters; *I* is the effective molal ionic strength (*I* = 0.5 Σzᵢ² mᵢ); *zᵢ* and *āᵢ* are the ionic charge and the distance of the closest approach for *i*th species, respectively; Γ<sub>γ</sub> is the mole fraction to molality conversion factor, Γ<sub>γ</sub></footnote>
= log(1+0.018m*), where m* is the sum of the molalities of all solute species. We adopted a value for ði of 4.5 Å for all charged species. For neutral species, bi is the empirical Setchenov coefficient, which may be assumed, in the first approximation, to be close to zero for all neutral species, which yields activity coefficients close to one.
<table><caption>**Table 4.6** Chemical speciation of major gangue and ore metals in saline hydrothermal fluids (T = 150–500 °C, P <2 kbar, fluid density >0.35 g/cm<fnref n="3" />,) and their major solubility-controlling solid phases at conditions relevant to magmatic-hydrothermal deposit formation.</caption><thead><tr><th>Element</th><th>Solubility-controlling solid phases</th><th>Major species in aqueous fluid <sup>1</sup></th><th>Uncertainty in log units<sup>2</sup></th><th>Key recommended references <sup>3</sup></th></tr></thead><tbody><tr><td>As</td><td>arsenopyrite, arsenian pyrite</td><td>As(OH)<sub>3</sub><sup>0</sup></td><td>&lt;0.5</td><td>Pokrovski et al. 2002a,b; Perfetti et al. 2008; Xing et al. 2019</td></tr><tr><td>Sb</td><td>stibnite, Cu-Fe-Sn sulfosalts</td><td>Sb(OH)<sub>3</sub><sup>0</sup>, Sb(OH)<sub>2</sub>Cl<sup>0</sup>, HSb<sub>2</sub>S<sub>4</sub><sup>-</sup>, Sb<sub>2</sub>S<sub>4</sub><sup>2-</sup></td><td>1</td><td>Zotov et al. 2003; Pokrovski et al. 2006; Olsen et al. 2019</td></tr><tr><td>Zn</td><td>sphalerite</td><td>ZnCl<sub>2</sub><sup>0</sup>, ZnCl<sub>3</sub><sup>-</sup>, ZnCl<sub>4</sub><sup>2-</sup>, Zn(HS)<sub>2</sub><sup>0</sup>, Zn(HS)<sub>3</sub><sup>-</sup></td><td>1</td><td>Sverjensky et al. 1997; Tagirov and Seward 2010; Akinfiev and Tagirov 2014</td></tr><tr><td>Pb</td><td>galena</td><td>PbCl<sub>2</sub><sup>0</sup>, PbCl<sub>3</sub><sup>-</sup>, PbCl<sub>4</sub><sup>2-</sup>, Pb(HS)<sub>2</sub><sup>0</sup>, Pb(HS)<sub>3</sub><sup>-</sup></td><td>1</td><td>Sverjensky et al. 1997</td></tr><tr><td>Fe</td><td>pyrite, magnetite, hematite, pyrrhotite</td><td>Fe<sup>II</sup>Cl<sub>2</sub><sup>0</sup>, Fe<sup>II</sup>Cl<sub>4</sub><sup>2-</sup>, Fe<sup>III</sup>Cl<sub>4</sub><sup>-</sup></td><td>0.5 (&gt;2) (&gt;3)</td><td>Sverjensky et al. 1997; Testemale et al. 2009; Saunier et al. 2011; Gammons and Allin 2022</td></tr><tr><td>Cu</td><td>chalcopyrite, bornite, enargite</td><td>CuCl<sup>0</sup>, CuCl<sub>2</sub><sup>-</sup>, CuCl<sub>3</sub><sup>2-</sup>, CuHS<sup>0</sup>, Cu(HS)<sub>2</sub><sup>-</sup></td><td>0.5</td><td>Akinfiev and Zotov 2001; Liu and McPhail 2005; Trofimov et al. 2023</td></tr><tr><td>Ag</td><td>argentite, sulfosalts</td><td>AgCl<sub>2</sub><sup>-</sup>, AgCl<sub>3</sub><sup>2-</sup></td><td>0.5</td><td>Pokrovski et al. 2013b</td></tr><tr><td>Au</td><td>native gold, invisible gold in arsenian pyrite and arsenopyrite as AuAs<sub>n</sub>S<sub>6-n</sub></td><td>Au(HS)<sub>2</sub><sup>-</sup>, Au(HS)<sub>3</sub><sup>-</sup>, AuHS<sup>0</sup>, AuCl<sub>2</sub><sup>-</sup></td><td>0.5-1.0 1.5</td><td>Stefánsson and Seward 2003c, 2004; Pokrovski et al. 2014, 2015; Zotov et al. 2018</td></tr><tr><td>Mo</td><td>molybdenite</td><td>HMoO<sub>4</sub><sup>-</sup>, MoO<sub>4</sub><sup>2-</sup>, MoS<sub>4</sub><sup>2-</sup>, oxysulfides, oxychlorides, alkali ion pairs, polysulfides</td><td>&gt;1 (&gt;3)</td><td>Dadze et al. 2018a; Liu et al. 2020</td></tr><tr><td>Pt</td><td>cooperite, sperrylite; chemically bound in pyrite, pyrrhotite, chalcopyrite</td><td>Pt(HS)<sub>4</sub><sup>2-</sup>, Pt(HS)<sub>2</sub>(S<sub>3</sub>)<sub>2</sub><sup>2-</sup>, PtCl<sub>4</sub><sup>2-</sup>, Pt(HS)<sub>2</sub><sup>0</sup></td><td>&gt;1</td><td>Kokh et al. 2017; Tagirov et al. 2019b; Filimonova et al. 2021; Pokrovski et al. 2021b; Laskar et al. 2022</td></tr><tr><td>Pd</td><td>braggite; chemically bound in pyrite, pyrrhotite, chalcopyrite</td><td>Pd(HS)<sub>4</sub><sup>2-</sup>, Pd(HS)<sub>2</sub>(S<sub>3</sub>)<sub>2</sub><sup>2-</sup>, PdCl<sub>3</sub><sup>-</sup>, PdCl<sub>4</sub><sup>2-</sup>, Pd(HS)<sub>2</sub><sup>0</sup></td><td>&gt;2</td><td>Bazarkina et al. 2014; Laskar 2022; Laskar et al. 2025</td></tr><tr><td>Si</td><td>quartz, silicate minerals</td><td>Si(OH)<sub>4</sub><sup>0</sup>, Si<sub>2</sub>O(OH)<sub>6</sub><sup>0</sup></td><td>&lt;0.5</td><td>Sverjensky et al. 2014</td></tr><tr><td>Al</td><td>muscovite, boehmite, corundum</td><td>Al(OH)<sub>3</sub><sup>0</sup>, Al(OH)<sub>4</sub><sup>-</sup>, (Na,K)Al(OH)<sub>4</sub><sup>0</sup></td><td>&lt;0.5</td><td>Tagirov and Schott 2001; Sverjensky et al. 2014</td></tr><tr><td>REE</td><td>monazite, bastnäsite, fluocerite</td><td>REECl<sup>2+</sup>, REECl<sup>2+</sup>, REE(SO<sub>4</sub>)<sub>2</sub><sup>-</sup>, REEF<sup>+</sup>, REE(OH)<sub>3</sub><sup>0</sup></td><td>&gt;1</td><td>Migdisov et al. 2016</td></tr><tr><td>Ca, Ba</td><td>calcite, gypsum, barite</td><td>(Ca,Ba)<sup>2+</sup>, (Ca,Ba)Cl<sup>+</sup>, (Ca,Ba)Cl<sub>2</sub><sup>0</sup></td><td>&lt;1</td><td>Sverjensky et al. 1997</td></tr></tbody></table>

<footnote n="1">¹ Species shown in italic are either subordinate in typical hydrothermal fluids or unconstrained.</footnote>

<footnote n="2">² Rough estimate, in terms of the variation of metal dissolved concentration in equilibrium with its solubility-controlling solid phase for typical porphyry-epithermal fluid compositions at a given T, P, pH and sulfur and oxygen fugacity, and using the range of published stability constants for the corresponding aqueous species from different studies. Values in brackets are for the case where the unconstrained species (shown in italic) are included in the calculations.</footnote>

<footnote n="3">³ Major recent experimental or theoretical studies explicitly reporting thermodynamic data, recommended in this article, for aqueous complexes and mineral phases, which can be used for mineral solubility predictions (numerous older references can be found therein).</footnote>