magmatic-hydrothermal fluid in Fig. 4.20a. Combining reactions (4.45) and (4.46), the relative trends in the S₃⁻ vs S₂⁻ equilibrium distribution can be identified:

$$4 S_3^{-} + 4 H_2O = 4 S_2^{-} + 3 H_2S + SO_4^{2-} + 2 H^{+} \quad (4.47)$$

According to reaction (4.47), at given T-P, the disulfur ion would be favored over the trisulfur ion at i) more alkaline pH, ii) lesser total S concentrations dominated by sulfate and sulfide, and iii) slightly more reduced (i.e. more H₂S) fluids. The pH trend has been clearly confirmed by Colin et al. (2020) showing that S₂⁻ was more abundant in fluids that were in equilibrium with more alkaline silicate melts. The tentative S₂⁻ trend with T shown in Fig. 4.20a is supported by general entropy considerations that higher temperatures (i.e., more disorder) favor smaller and more compact species. Thus, S₂⁻ forming at the expense of S₃⁻ may become an important sulfur species at magmatic temperatures. Larger radical congeners, Sₙ⁻ with n = 4–8, have recently been envisioned by theoretical molecular modeling but await physical evidence (Chivers and Oakley 2023).

### 4.3.5 Sulfidation state concept and sulfur aqueous speciation

A long-standing simple concept in mineral deposit research uses the notion of sulfur fugacity, fS₂, to describe sulfide mineral reactions and associations found in hydrothermal ore deposits. Although S₂ is not a dominant sulfur species in the natural gas phase and is non-existent in aqueous solution, it is a useful species to portray mineral equilibria in the framework of a simple thermodynamic formalism, similar to the use of oxygen fugacity (fO₂). The quantitative use of fS₂ has been facilitated by the existence of robust thermodynamic data on sulfide mineral equilibria acquired in anhydrous systems since the 1950s. These data allowed quantifying mineral stability domains and equilibria in terms of temperature, fS₂ and fO₂ (Holland 1959, 1965; Barton 1970; Barton and Skinner 1979; references therein). They constitute the basis of the sulfidation state concept reviewed and further developed in the seminal paper of Einaudi et al. (2003). According to it, the different sulfide mineral associations observed in hydrothermal ore deposits are a function of the fS₂ value, i.e., sulfidation state, as pictured in Figure 4.22. It is commonly qualified being in between “very low” and “very high” by ore deposit geologists, according to the major Fe and Cu mineral assemblages present, as exemplified by the formal equilibria (Fig. 4.22):

$$Fe_{(iron)} + S_{2(g)} = FeS_{(pyrrhotite)}, \text{ very low} \quad (4.48)$$

$$FeS_{(pyrrhotite)} + FeAs_{2(löllingite)} + 1/2 S_{2(g)} = 2 FeAsS_{(arsenopyrite)}, \text{ low} \quad (4.49)$$

$$FeS_{(pyrrhotite)} + 1/2 S_{2(g)} = FeS_{2(pyrite)}, \text{ intermediate} \quad (4.50)$$

$$5 CuFeS_{2(chalcopyrite)} + S_{2(g)} = Cu_5FeS_{4(bornite)} + 4 FeS_{2(pyrite)}, \text{ high} \quad (4.51)$$

$$2 S_{(liquid)} = S_{2(g)}, \text{ very high} \quad (4.52)$$
Sulfidation state goes along with oxidation state, with lower *fS*₂ generally corresponding to lower *fO*₂ or higher *fH*₂ (both being in equilibrium with H₂O in the hydrothermal fluid or vapor), which led to the use of the redox parameter, RH = log (fH₂/fH₂O), and sulfidation parameter, RS = log (fH₂/fH₂S), as alternatives of *fS*₂ and *fO*₂, to interpret vapor compositions and mineral associations in active geothermal systems (Giggenbach 1987; Einaudi et al. 2003). Figure 4.22 pictures different types of hydrothermal deposits, illustrating the different fluid environments in terms of temperature and *fS*₂ parameters whose detailed evolution may be found in Einaudi et al. (2003).

However, the *fS*₂-*fO*₂ thermodynamic formalism has obvious limitations in interpreting the true sulfur chemical state and related mineral solubility in the fluid phase, which requires knowledge of major sulfur and metal aqueous species. Figure 4.23 shows the concentrations of major sulfur species and dissolved Fe and Au in the fluid as a function of temperature, along a typical pressure gradient in shallow-crust sulfide deposits, in equilibrium with iron mineral assemblages representative of low (quartz-fayalite-magnetite-pyrrhotite), intermediate (magnetite-pyrrhotite-pyrite), and high to very high (pyrite-sulfur) sulfidation states. These calculations use the thermodynamic data for sulfur discussed above and referenced in Table 4.5; those for metals will be detailed in the following section (see also Table 4.6). It can be seen in Fig. 4.23 that dissolved sulfur aqueous concentrations, dominated by H₂S, are similar between the low and intermediate sulfidation states as imposed by the mineral solubility. Aqueous H₂S increases by more than 10⁴ times from 100 to 600 °C, along with the increase at elevated temperatures of more oxidized S species such as sulfate (representing the sum of all sulfate and hydrosulfate species and their alkali ion pairs), SO₂ and S₃⁻, with sulfate and SO₂ becoming comparable to H₂S at the highest temperatures at intermediate sulfidation states. For the high sulfidation states, such as represented by native sulfur(+ pyrite), sulfur solubility is much greater, attaining mol/kg fluid levels above 400 °C, along with a growing abundance, at the expense of sulfate and sulfide, of intermediate valence sulfur species, SO₂ and S₃⁻. At all sulfidation states, Fe solubility (as chloride complexes) is comparable above 300–400 °C attaining ~1000 ppm levels, but the temperature dependence is different at high and lower sulfidation states, invoking different potential precipitation mechanisms (cooling vs fluid oxidation or sulfur scavenging by Fe-bearing rocks). Gold solubility (as hydrosulfide complexes), in contrast, is greatly favored by both temperature and sulfidation (and oxidation) state, because of the increasing H₂S ligand concentrations and, at high sulfidation state, by the growing abundance of S₃⁻ that is also a strong ligand for gold. Thus, full appreciation of the sulfidation state concept, based on mineral associations, may only be achieved by its combination
with detailed sulfur and metal chemistry in hydrothermal fluids. An in-depth account of metal speciation and mineral solubility is given in the next section.
## 4.4 Metal speciation and sulfur-metal relationships in hydrothermal fluids

### 4.4.1 General tendencies of metal-ligand complexation in aqueous solution

#### Fundamentals of metal speciation in the fluid phase

To appreciate the role of metal complexes with sulfur in hydrothermal fluids it is necessary to place the metal-sulfur interaction issues into a more general picture of mineral solubility and metal speciation in the fluid phase, with the simultaneous presence of other geologically ubiquitous non-sulfur ligands, in particular chloride, hydroxide and alkalis as well as some other compounds (e.g., carbonate, organic carbon, fluoride, bromide). In this section, we briefly outline the basics of metal-ligand complexation and general tendencies, before providing an in-depth account of complexes of different groups of metals with various sulfur ligands.

Chemical elements are dissolved in aqueous solution in the form of cations (electrically positively charged ions formed by most metals, e.g., Ag⁺, Fe²⁺, Zn²⁺, Al³⁺) and anions (negatively charged ions formed by nonmetals, usually called ligands, e.g., Cl⁻, SO₄²⁻, HS⁻). The ions are all coordinated by water molecules to some extent that can be directly “seen” by some spectroscopic methods (e.g., X-ray absorption or nuclear magnetic resonance spectroscopy). For example, Zn²⁺ has a clearly defined first-shell atomic sphere with 6 water molecules by forming Zn-OH₂ chemical bonds, Zn(H₂O)₆²⁺, along with more loosely bound outer-sphere H₂O molecules. Anions, like Cl⁻ or HS⁻, are much weaker solvated by H₂O with no clearly defined coordination spheres. Both types of ions associate together in some extent, usually by displacing a water molecule from the metal first coordination sphere and forming a direct chemical bond (e.g., Zn-Cl):

$$ \mathrm{Zn}(\mathrm{H}_2\mathrm{O})_6^{2+} + \mathrm{Cl}^- = \mathrm{ZnCl}(\mathrm{H}_2\mathrm{O})_5^{+} + \mathrm{H}_2\mathrm{O} \quad (4.53) $$

From a thermodynamic point of view, this reaction may be simplified to

$$ \mathrm{Zn}^{2+} + \mathrm{Cl}^- = \mathrm{ZnCl}^+ \quad (4.54) $$

by omitting water molecules in this reaction because water activity is close to one in an aqueous fluid phase.

With increasing salt content in the fluid and raising temperature, such associations become more abundant, and more ligands may be bound to the cation (e.g., forming ZnCl₂⁰ and higher-order chloride complexes, ZnCl₃⁻ and ZnCl₄²⁻). All cations, anions and their complexes are present simultaneously in the aqueous fluid phase, but at different concentrations (or activities). This fluid propery contrasts to pure mineral phases (e.g., pyrite, sphalerite, or hematite) whose thermodynamic activity is either 1 or 0 and their formation and disappearance in T-P-composition space is governed
by the phase rules. There is thus a fundamental physical-chemical difference between a phase and a species, often misunderstood and sometimes misinterpreted by geologists (e.g., Pokrovski 2014). The total metal content in the fluid phase is the sum of all species concentrations:

$$ \Sigma Zn_{(aq)} = Zn^{2+} + ZnCl^{+} + ZnCl_{2}^{0} + ZnCl_{3}^{-} + ZnCl_{4}^{2-} \quad (4.55) $$

To this equation should also be added other, non-chloride, species (e.g., such as hydrosulfides and sulfates, see sections below). However, among the multitude of possible aqueous species for a given metal, there is usually one or a couple that is dominant (i.e. most concentrated) within the given T-P and fluid composition range, whereas all other species are often much less abundant. Their contribution to the total metal amount transported by the fluid would be very small and may therefore be neglected. With the temperature rise, two general changes in the fluid properties occur such as i) the increase of thermal motion and, therefore, disorder, along with ii) the decrease of dielectric constant of the fluid phase. In many cases, these changes lead to a simplification of the metal speciation schemes in the high-temperature fluids compared to near-ambient aqueous solution. Thus, neutral and weakly charged complexes (e.g., ZnCl₂⁰, Zn(HS)₂⁰) are generally favored due to the weakening of Born solvation contribution to the species Gibbs energy when ε decreases (equation 18). Similarly, the increasing thermal disorder renders more favorable species of lower entropy (i.e. with more compact and more symmetrical geometries, such as ZnCl₂⁰ compared to ZnCl₃⁻). However, these solvent-controlled tendencies are complicated by other factors such as specific electronic structure of the chemical bond, metal coordination and steric constraints, and relativistic electron effects, inherent to particular metals as will be selectively discussed in the following subsections. For more extended general literature on the topic concerning different types of ligands the reader is referred to Seward (1981), Brimhall and Crerar (1987), Wood and Samson (1988), and Barnes (1997).

## Soft-hard relationships

What are the dominant complexes for a given metal in hydrothermal fluids? Their nature is governed by two factors: the metal chemical affinity for a particular ligand and the abundance of the ligand itself in the fluid. Metal-ligand affinities are fundamentally defined by the electronic structure of the complexing elements. These affinities may be predicted using the so called soft-hard classification of chemical elements (hard and soft acid and base theory, HSAB) appeared in chemistry in the 1960s (Pearson et al. 1963; Pearson 1997 and references therein). While behind this theory lie numerical functions such as ionization potential, bond dissociation energy and electronegativity, the concept in itself is simple and elegant. It is outlined below for a general reader who is also referred to Crerar et al. (1985), Brimhall and Crerar (1987), Wood and Samson (1988),
and Barnes (1997) for more detail and variations of presentation. According to the HSAB classification illustrated in Fig. 4.24, metal cations (called acids) are divided in three categories. The first, shown in red, is represented by either small and strongly charged ($Be^{2+}$, $B^{3+}$, $Zr^{4+}$, $Nb^{5+}$) or big and easily ionizable ($Cs^{+}$, $Ba^{2+}$). These properties make such elements "hard", with their electronic clouds hard to deform (i.e. polarize) to share electrons with ligands in a chemical bond. Such chemical bonds are termed ionic and are ensured by dominantly electrostatic attraction between the charged cation and anion spheres. The second category, shown in blue, is constituted by large, weakly charged, and strongly polarizable cations ($Ag^{+}$, $Au^{+}$, $Pt^{2+}$, $Cu^{+}$), with electronic clouds easy to deform to enable sharing electrons with a ligand in a chemical bond. Such bonds are termed covalent. The intermediate category of metal cations lies in between these two types (e.g., $Fe^{2+}$, $Zn^{2+}$, $Co^{2+}$, $As^{3+}$) and shown in yellow in Fig. 4.24. Analogous three types are applicable to non-metals (or ligands), with $O^{2-}$, $OH^{-}$, $F^{-}$, $C^{4+}$ (as carbonate $CO_3^{2-}$) being hard, $I^{-}$, $Te^{-}$, $Br^{-}$ – soft, and $Cl^{-}$ – intermediate. The fundamental rule is the following: a soft "loves" a soft and a hard "loves" a hard. It means that hard metals will preferably complex with hard ligands, and soft metals – with soft ligands. The degree of hardness (or softness) is also dependent of the element oxidation state, with higher oxidation states being harder. Sulfur is an excellent example of such dualism because it forms both very soft sulfide ($S^{2-}$) and very hard sulfate ($S^{6+}$). Similarly, arsenic and antimony in their highest oxidation state of +5 as arsenates and antimonates form almost exclusively oxyhydroxides both in aqueous solution and solid phase at the Earth's surface. In oxidation state +3, stable in reduced sedimentary settings and geothermal systems, both oxyhydroxide and sulfide types of complexes and minerals are known for those elements. The most reduced formal states –1 to –3, as arsenides and antimonides, are soft ligands similar to sulfide. Although qualitative, this classification not only elegantly explains the predominance of the different complexes in aqueous solution, but it also accounts for the general distribution of elements on Earth, since it is applicable to solid phases as well. Remarkably, the soft-hard classification strongly resembles the geochemical classification of elements into lithophiles (i.e. $SiO_2$-loving and, therefore, hard), chalcophiles (i.e. copper-loving meaning reduced sulfur-loving such as in the main copper ore chalcopyrite, $CuFeS_2$, and, therefore, soft), and siderophiles (iron-loving and, therefore, intermediate). Thus, a hard metal cation, like $La^{3+}$, representative of the REE group, forms the most stable complexes with the hardest ligand of the halogen group, $F^{-}$, while a moderately soft metal, $Ag^{+}$, forms the strongest complexes with $I^{-}$.

However, it does not mean that fluoride and iodide complexes, respectively, would be the dominant types transporting REE and Ag by most hydrothermal fluids. Another parameter, the ligand concentration itself must be taken into account. Aqueous fluoride is a relatively minor
component of most hydrothermal fluids because of poor solubility of its solid phases (e.g., fluorite, apatite), and its strong affinity for silicate minerals and melts rather than for aqueous fluids. Iodine concentrations are usually negligibly small in the fluids due to its very low natural abundance (average I concentration in the upper continental crust is only ~0.1 ppm; Rudnick and Gao 2014). Consequently, neither F⁻ nor I⁻ ligands are present in sufficient concentrations to complex the metals above. As a result, both types of metals are transported predominantly as chloride complexes due to the large abundance of Cl⁻ in most types of hydrothermal fluids. However, this general picture may be complicated by additional complexing with sulfate and sulfide for REE and Ag, respectively, in some types of hydrothermal fluids as will be discussed below.

An important advantage of the hard-soft classification is also the ability to qualitatively predict tendencies in metal speciation with temperature in light of the competition among the different ligands. This is because the thermodynamics of hard and soft types of bonding are different. For hard-hard interactions dominated by electrostatic attractions, the increase in temperature and concomitant decrease in dielectric constant generally reinforce bonding according to the Coulomb electrostatic law. This dielectric constant control results in the increase of stability constants with temperature for most hydroxide, chloride and sulfate metal complexes. In contrast, soft-soft interactions, being covalent and strongly steric-controlled, generally weaken with the increase of thermal disorder. Thus, compared to chloride and hydroxide complexes, hydrosulfide complexes of many intermediate and moderately soft metals (Zn, Cu, Ag, As, Sb) are generally significant only in low-temperature hydrothermal and sedimentary fluids, but become almost negligible in higher-temperature hydrothermal-magmatic fluids. However, it should not be forgotten that this general knowledge is based on hard-soft principles established using metal-ligand complexation data in aqueous solution at ambient conditions. The soft-hard properties of elements themselves may change with temperature and pressure. Recently, based on the revised and corrected scale of the electronegativity of chemical elements of Tantardini and Oganov (2021), Dong et al. (2022) theoretically evaluated the effect of very high pressures (up to 500 GPa) on the chemical hardness of elements. They found that the degree of hardness changed differently depending on the group of elements thereby leading to surprising changes in the element reactivity compared to ambient pressures. These theoretical predictions appear to be consistent with experimental studies relevant to planetary interiors (e.g., pressure induced metallization). The effect of temperature yet remains to be quantitatively assessed, which might challenge the traditional view outlined above.

*General overview of metal-transporting complexes in geological fluids*
Our current knowledge of the dominant complexes of different metals in typical liquid-type hydrothermal fluids is summarized in Table 4.6. This knowledge is the result of a large body of experimental, spectroscopic and theoretical studies since the 1950s that have established the stoichiometry of the dominant metal complexes and generated their stability constants. For details on the methods and complexation specificities depending of the element, the reader is referred to the representative papers cited in Table 4.6 as well as to more general reviews (Brimhall and Crerar 1987; Barnes 1997; Wood and Samson 1998; Kouzmanov and Pokrovski 2012; Pokrovski et al. 2014; Brugger et al. 2016; Migdisov et al. 2016). Studies of the chemical speciation of different metals in aqueous fluids at elevated temperatures and pressures benefiting of state-of-the-art approaches, such as solubility measurements, in situ spectroscopy and molecular modeling, regularly appear in the geochemical literature, and our vision of some elements hydrothermal chemistry and behavior continuously evolves as will be detailed for major ore metals in the following sections.

The current general situation is resumed below. In typical hydrothermal fluids within the T-P-density range of liquid-like to supercritical fluids, most metalloids (As, Sb, Si) dominantly form uncharged hydroxide complexes. The speciation of transition and base metals (Fe, Cu, Ag, Zn, Pb) is generally dominated by chloride species. “Hard” metals (Al, Zr, Nb, Ti, Cr) mostly form hydroxide complexes. For rare earth elements (REE), chlorides and sulfates are likely to be most important while hydroxide and fluoride are rather subordinate. “Soft” metals (Au, PGE) largely prefer the hydrosulfide (HS⁻) and trisulfur radical ion (S₃²⁻) ligands. In addition to the exact complex stoichiometry cited in Table 4.6, our ability to predict metal solubilities equally depends on the robustness of the values of stability constants for all these complexes. This parameter may be expressed in terms of the uncertainty associated with thermodynamic calculations of ore and gangue mineral solubilities within the typical T-P domain of hydrothermal fluids (<500 °C, <5 kbar). The solubility of the major solid phases of metals and metalloids like As, Au, Si, Al, Cu, Zn, and Pb in hydrothermal fluids may reasonably be predicted within 0.5–1 log units. The equilibrium predictions are much less precise for REE, which form different complexes depending on the context, and more importantly, different silicate, oxide and fluoride solid phases and solid solutions whose thermodynamic properties are poorly known, bringing additional uncertainty. The “worst” situation is probably for Mo (and its geochemical twin, Re, not shown) whose complexes with major ligands (such as Cl and S) are yet very poorly known. Modeling trace elements that do not usually form their pure mineral phases, but rather get incorporated into major minerals in chemically bound states is virtually non-existent to date because of the lack of a robust thermodynamic framework for such mineral-hosted trace elements. The uncertainty of thermodynamic predictions generally grows with
increasing *T* and *P*. Note that a typical error of 1 log unit intrinsic to best known metals and minerals may be considered as a fairly good precision in the face of much larger variability of natural metal concentrations that commonly display variations of several orders of magnitude as demonstrated by natural fluid inclusion studies (see section 4.5 and Yardley 2005; Kouzmanov and Pokrovski 2012; Pokrovski et al. 2014).

## Solubility-controlling reactions and the effect of sulfur

**Table 4.6** shows that the great majority of base metals and metalloids forming hydrothermal sulfide ore (As, Sb, Zn, Pb, Fe, Cu, Ag, Mo) do not predominantly form complexes with sulfur in the fluid phase under typical ore forming conditions in the Earth's crust, whereas sulfide minerals are omnipresent solid phases at such conditions. There is, therefore, an important divide between the hydrothermal fluid phase and the solid phase as to the global affinity of metals to sulfur. This difference is due to the presence of water as the major solvent on Earth that imposes controls on elements' state, hydration, bonding and ligand composition and activity as shown above. Thus, in addition to the intrinsic chemistry of the dominant dissolved species, the second key factor governing metal solubility in the fluid is the identity and stability of the metal-bearing solid phase as shown by the following reactions for selected ore metals:

$$ \mathrm{CuFeS_2(s)} + 3 \mathrm{H}^+ + 4 \mathrm{Cl}^- + \frac{1}{2} \mathrm{H_2(g)} = \mathrm{CuCl_2^-} + \mathrm{FeCl_2^0} + 2 \mathrm{H_2S(aq)} \quad (4.56) $$

$$ \mathrm{FeS_2(s)} + 2 \mathrm{H}^+ + 2 \mathrm{Cl}^- + \mathrm{H_2(g)} = \mathrm{FeCl_2^0} + 2 \mathrm{H_2S(aq)} \quad (4.57) $$

$$ \frac{1}{2} \mathrm{Ag_2S(s)} + \mathrm{H}^+ + 2 \mathrm{Cl}^- = \mathrm{AgCl_2^-} + \frac{1}{2} \mathrm{H_2S(aq)} \quad (4.58) $$

$$ \mathrm{ZnS(s)} + 2 \mathrm{H}^+ + n \mathrm{Cl}^- = \mathrm{ZnCl_n^{2-n}} + \mathrm{H_2S(aq)}, n = 2, 3, 4 \quad (4.59) $$

$$ \mathrm{PbS(s)} + 2 \mathrm{H}^+ + n \mathrm{Cl}^- = \mathrm{PbCl_n^{2-n}} + \mathrm{H_2S(aq)}, n = 2, 3, 4 \quad (4.60) $$

$$ \mathrm{MoS_2(s)} + 4 \mathrm{H_2O} = \mathrm{HMoO_4^-} + \mathrm{H}^+ + 2 \mathrm{H_2S(aq)} + \mathrm{H_2(g)}, \quad (4.61) $$

$$ \mathrm{MoS_2(s)} + 2 \mathrm{H_2O} + \mathrm{Na}^+ = \mathrm{NaHMoO_2S_2^0} + \mathrm{H}^+ + \mathrm{H_2(g)}, \textit{magmatic fluids, tentative} \quad (4.62) $$

$$ \mathrm{MoS_2(s)} + 2 \mathrm{H_2S(aq)} = \mathrm{MoS_4^{2-}} + 2 \mathrm{H}^+ + \mathrm{H_2(g)}, \textit{in sulfide-rich fluids below 300 °C} \quad (4.63) $$

$$ \mathrm{Au(s)} + \mathrm{H_2S(aq)} + \mathrm{HS}^- = \mathrm{Au(HS)_2^-} + \frac{1}{2} \mathrm{H_2(g)}, \textit{in near-neutral and alkaline fluids} \quad (4.64) $$

$$ \mathrm{Au(s)} + \mathrm{H_2S(aq)} + \mathrm{S_3^{\cdot -}} = \mathrm{Au(HS)S_3^-} + \frac{1}{2} \mathrm{H_2(g)}, \textit{in acidic-to-neutral S-rich fluids} \quad (4.65) $$

$$ \mathrm{Au(s)} + \mathrm{H_2S(aq)} = \mathrm{AuHS^0} + \frac{1}{2} \mathrm{H_2(g)}, \textit{in acidic S-poor fluids} \quad (4.66) $$

$$ \mathrm{Au(s)} + \mathrm{H}^+ + 2 \mathrm{Cl}^- = \mathrm{AuCl_2^-} + \frac{1}{2} \mathrm{H_2(g)}, \textit{in acidic, saline, H_2S-poor fluids above 500 °C} \quad (4.67) $$

In these reactions, all species are in aqueous state (unless indicated), H₂S(aq) is the dominant S aqueous form and H₂(g) is the conventional redox gaseous species related to oxygen fugacity by the chemical equilibrium with water: H₂(g) + ½ O₂(g) = H₂O(l).

It can be seen from these reactions, sulfur exhibits an important effect on the mobility of most metals, including those that do not form direct complexes with sulfur in the fluid phase but do
form sulfide minerals. Because dissolved H₂S is directly involved in these reactions, the solubility of all metals strongly depends on H₂S content of the fluid phase, with amplitudes comparable to those exerted by salt concentration, pH or redox, depending on the stoichiometric coefficients of these constituents in the solubility reaction. Figure 4.25 shows the solubility of major ore minerals as a function of four key parameters, temperature, acidity, salinity, and H₂S concentration, calculated using the available thermodynamic data for minerals and aqueous species cited in Table 4.6 (note that Mo solubility curves are tentative since the effect of chloride, alkalis and other sulfur ligands is currently poorly constrained (see section 4.4.10). The differences in aqueous speciation between base metals plus Ag (chlorides), Au (predominantly sulfides), and Mo (oxyhydroxides, alkali ion pairs and possibly sulfides in sulfur-rich moderate-temperature systems) yield contrasting solubility trends versus pH, H₂S, and salinity for these three groups of metals (Fig. 4.25). The only feature common to all metals is an increase in solubility with temperature, for sulfur-, redox-, and pH-buffered systems, typical for rock-dominated porphyry-epithermal environments (e.g., Giggenbach 1997; Kouzmanov and Pokrovski 2012). The metal concentrations are highly variable depending on salinity, pH, and S content. For acidic-to-neutral fluids (4 < pH < 6) of moderate salinity (10 wt% NaCl equivalent) and S contents (<0.5 wt%), the absolute dissolved concentrations of Cu, Fe, Zn (and Pb, not shown) in equilibrium with their respective sulfide minerals are generally higher than for Au and Mo. However, this trend may be inverted in S-rich, low-salinity and alkaline pH fluid compositions. For all metals except Au, solubility increases significantly with salinity, the largest increase being for Zn and Pb (not shown), which likely form tri- and tetrachloride species (Table 4.6, section 4.4.2). Fluid pH exerts a comparably strong negative effect on base metal solubility as H₂S content does. In contrast, both parameters (pH and H₂S) have a positive effect on Au solubility in near-neutral and S-rich fluids. Molybdenite solubility increases with increasing pH, but decreases with increasing H₂S; however Mo solubility predictions are affected by much larger uncertainties than the other metals because of poorly known contribution of chloride and sulfur-type complexes (see section 4.4.10).

The generalized trends shown in Fig. 4.25 illustrate the complexity of mineral solubility that is both dependent on the exact metal speciation that determines the controlling dissolution/precipitation reactions, and on the concentrations of other reaction constituents defined by the specific fluid composition. A few in-depth reviews of the identity and thermodynamic stability of complexes of metals and the solubility of their minerals in hydrothermal fluids were published in the 1970–1990s (e.g., Barnes 1979; Crerar et al. 1985; Wood and Samson 1998). The sections below provide an extended update of the speciation data for major ore metals obtained since then, in particular using cutting-edge methods and combined approaches that were unavailable in
the past. The role of sulfur cannot, of course, be regarded as standalone without assessment of the
role of other competing complexes, in particular chlorides and hydroxides, in the whole picture of
the aqueous speciation for a metal. That is why non-sulfur aqueous complexes will also be
overviewed and compared here for each selected metal.

4.4.2 Base metals - Zn, Pb, and Cu

Although this group of metals is believed to form dominantly chloride complexes in typical
liquid-like hydrothermal fluids (Table 4.6), the role of sulfur-bearing complexes remains a subject
of great controversy for some of those metals (Zn) and appears to be more important in high-
temperature fluids for others (Cu).

Zinc

Although zinc chloride and sulfide complexes in hydrothermal fluids have been extensively
studied experimentally since the 1960s, this metal provides a rather paradoxical example that the
more data are accumulated, the more discrepancy is added to the topic, in particular for sulfide
complexes. Chloride complexes in hydrothermal fluids have been investigated in numerous
solubility studies critically reviewed by Sverjensky et al. (1997), Wood and Samson (1998),
Bazarkina (2010), and Akinfiev and Tagirov (2014). To these works, have recently been added
studies that used X-ray absorption spectroscopy and molecular dynamics (e.g., Mei et al. 2015). The
major common outcome of those studies is the identification of four chloride species in saline
hydrothermal fluids (ZnCl⁺, ZnCl₂⁰, ZnCl₃⁻, ZnCl₄²⁻) and generation of their stability constants.
There currently exist two HKF model (Sverjensky et al. 1997; Akinfiev and Tagirov 2014) and one
RB model (Mei et al. 2015a) set of coefficients derived from different experimental studies and
allowing extrapolation of these stability constants over the hydrothermal T-P range. The resulting
distribution of Zn-Cl species is somewhat different in temperature-composition space, with the
Sverjensky et al. (1997) dataset predicting the predominance of ZnCl₂⁰ at temperatures >300-350
°C and salinities >1 wt% NaCl, whereas both Akinfiev and Tagirov (2014) and Mei (2015a) sets
favor ZnCl₄²⁻ at such conditions. Despite these discrepancies, the overall solubility of the major Zn-
bearing minerals (ZnS(s) and ZnO(s)) consistently shows a large increase with increasing temperature
and salinity (Fig. 4.25), with 100s to 1000s ppm of Zn that may be transported by moderate-
temperature fluids (~300 °C) and with close-to-wt% Zn concentration levels in magmatic fluids
(>500 °C).

The situation with sulfide complexes is less consistent. Numerous low-temperature studies
have reported a plethora of Zn-S(-OH) polymeric complexes that will not be discussed here (see
Wood and Samson 1998; Rickard and Luther 2006). In contrast, only a handful of studies is available at hydrothermal conditions, which is primarily due to intrinsic experimental difficulties for working in reduced sulfur systems and much lower ZnS solubility (<ppm level) posing analytical challenges. The most remarkable studies are those of Bourcier and Barnes (1987) and Hayashi et al. (1990) who measured ZnS(s) solubility to 350 and 240 °C, respectively ($P_{sat}$), in concentrated H₂S-NaHS solutions (to 3–4 m). They suggested Zn(HS)₂₀, Zn(HS)₃⁻, and Zn(HS)₄²⁻ to be the solubility-controlling complexes at acidic to neutral pH, whereas at alkaline pH and/or low temperatures, mixed Zn-HS-OH and deprotonated Zn-S species were inferred (e.g., Zn(OH)(HS)⁰, Zn(OH)(HS)₂⁻, and Zn(OH)(HS)₃²⁻). Almost 20 years after, Tagirov et al. (2007) and Tagirov and Seward (2010) measured sphalerite solubility in less concentrated H₂S-NaHS solutions (<0.2 m) to 250 °C and derived the same set of three major complexes, [Zn(HS)₂,₃,₄], along with a deprotonated sulfide complex, Zn(HS)S⁻, only significant in alkaline (pH>8–9) solutions. Note that in the absence of direct spectroscopic evidence, the Zn(HS)S⁻ species is thermodynamically equivalent to Zn(OH)(HS)₂⁻, proposed by Hayashi et al. (1990), since they differ by one H₂O molecule. Tagirov and Seward (2010) generated a RB equation coefficients for the four species derived that may be used with reasonable confidence to 300–350 °C. The absolute values of Tagirov’s stability constants for the three Zn-HS species at temperatures above 100 °C are, however, up to 2–3 orders of magnitude lower than in the previous work above, clearly reflecting the difficulties of measuring and interpreting ppb-level metal solubilities. Akinfiev and Tagirov (2014) re-fitted Tagirov data within the framework of the HKF model. To allow better constraints on the HKF coefficients, they assumed that the thermodynamic functions at 25 °C and 1 bar ($Δ_rS⁰, Δ_rCp⁰$, and $Δ_rV⁰$) of the isocoulombic reactions of ligand exchange with equivalent previously HKF-processed Zn-Cl complexes are equal to zero. This assumption should, however, be considered with caution because metal affinity for Cl⁻ vs HS⁻ ligands is very different (see below). A more recent word to the Zn-S complex issue has been added by Mei et al. (2016) who calculated, using ab-initio molecular dynamics in simulation boxes with Zn/HS ratios of 4 to 10, both geometry and energy of Zn-HS complexes with 1 to 4 HS⁻ ligands to 600 °C. Combining these data with limited XAS measurements in 2 m NaHS solutions to 500 °C, they concluded that Zn(HS)₃⁻ and Zn(HS)₄²⁻ are the dominant species at these conditions. They further fitted their MD-generated stability constants with the RB model. Their stability constants in moderate-temperature hydrothermal fluids (<400 °C) for the two complexes above appear, however, 3 to 4 orders of magnitude higher than those of Tagirov’s group. This discrepancy may be due to both intrinsically high uncertainties of the MD thermodynamic integration approach (e.g., see Laskar et al. 2022) and the limited-temperature range solubility dataset (<250 °C) which was used for HKF and RB models parameterization. Therefore, any
prediction for Zn-HS types of complexes at temperatures above 300–350 °C should be taken with extreme caution.

The existing data may further be rationalized using isocoulombic ligand exchange reactions between the major chloride and hydrosulfide complexes (Fig. 4.26):

$$ZnCl_n^{2-n} + n HS^- = Zn(HS)_n^{2-n} + n Cl^-, n=2, 3, 4 \qquad (4.68)$$

For consistency, the data for hydrosulfide complexes were taken from Tagirov and Seward (2010), Akinfiev and Tagirov (2014) and Mei et al. (2016), whereas the corresponding data for equivalent chloride complexes are from Akinfiev and Tagirov (2014) and Mei et al. (2015a), respectively. Three major features are apparent in Fig. 4.26. First, the chemical affinity of Zn for the HS⁻ ligand is much greater than for the Cl⁻ ligand (up to 4–5 log unit per ligand at ambient temperature, in terms of the exchange reaction constant whose absolute value is normalized to the number of ligands). Second, the Zn affinity for reduced sulfur decreases systematically with increasing temperature, in agreement with the general soft-hard relationships discussed above. Finally, there is large discrepancy in the ligand affinity between Tagirov and Mei groups’ data. Adopting a typical Cl⁻/HS⁻ ratio of 10³ to 10⁴ in near-neutral pH (pH 5–6) fluids around 300 °C (i.e. typical temperature of ZnS deposit formation), the K values reported in Fig. 4.26 imply that chloride complexes are thousands to millions times more abundant than their sulfide counterparts according to Tagirov’s data set, whereas the two types of complexes may have comparable abundances according to Mei’s data set.

Reconciling these discrepancies would require more systematic experimental data on both Zn sulfide and chloride types of complexes over a larger T-P range. In the meantime, we would recommend using Sverjensky et al. (1997) or Akinfiev and Tagirov (2014) HKF model parameters for Zn-Cl complexes because they are based on a large number of studies and more robust and validated HKF relationships than those of the RB model. For Zn-HS complexes, the solubility data of Tagirov and Seward (2010) should be privileged at present, being most direct and analytically accurate ones, with caution about the stability constant values extrapolation above 350 °C.

## Lead

Complexes of lead in hydrothermal fluids have received less in-depth investigations than those of its counterpart, zinc. The lower PbO(s) and PbS(s) solubility than that of the corresponding Zn solid phases might have contributed to discouraging more systematic experimental work. Like for Zn, the major Pb-bearing complexes in saline hydrothermal fluids are chlorides, investigated in the 1960s–1990s by solubility and UV-Vis spectroscopy, as reviewed in detail by Wood and Samson (1998). Sverjensky et al. (1997) have generated a consistent set of HKF coefficients for a series of
Pb-Cl complexes with 1 to 4 Cl⁻ ligands based on low-temperature studies and Seward (1984) UV-Vis work to 300 °C. The three species, PbCl⁺, PbCl₂⁰ and PbCl₃⁻, showed formation constant values consistent among those works, while the tetrachloride, PbCl₄²⁻, was much less certain. According to these and other limited higher-temperature solubility work (e.g., Hemley et al. 1992), PbCl₂⁰ and PbCl₃⁻ are the dominant species in a wide range of temperature and salinity. A more recent UV-Vis study of Luo and Millero (2007) to 40 °C demonstrated a good agreement for the mono-, di- and tri-chloride species, but did not detect PbCl₄²⁻. The latter complex was also rejected by Etschmann et al. (2018) on the basis of X-ray absorption spectroscopy measurements of saline solutions to 10 m NaCl and ~500 °C, supplemented by MD simulations. Their data indicate the predominance of PbCl₃⁻ with the possible presence of one or two H₂O molecules in the Pb first coordination sphere. Compared to Zn, for which ZnCl₄²⁻ is the major species, the absence of the Pb tetrachloride complex was explained by the presence of stereochemically active lone electron pair (6s²) hampering additional coordination by Cl⁻. Etschmann et al. (2018) further refitted HKF-model parameters for the first three Pb-Cl complexes based on previous work (Seward 1984; Hemley et al. 1992; Luo and Millero 2007). While the resulting stability constants for Pb-Cl complexes are very similar to those of the original HKF model of Sverjensky et al. (1997), which was partly based on the same data sources, some of the coefficients reported by Etschmann et al. (2018) appear to be unphysical. Those include, for example, large negative Born parameter values (ω) that contradict to the HKF model fundamentals that ω values for charged species must be positive (e.g., Pokrovseki et al. 2024), along with inconsistencies in *a*₃ and *a*₄ coefficients that show either zeroed values or anomalously large negative values for some complexes (e.g., ω = -0.83×10⁵ cal/mol, *a*₃ = -232 cal/(mol bar), and *a*₄ = 0 cal/mol for PbCl₂⁰). For these reasons, the Etschmann et al. (2018) HKF dataset cannot be recommended, and the HKF parameters of Sverjensky et al. (1997) for the mono-, di- and trichloride complexes should be used in Pb speciation and solubility modeling.

Much more limited data exist for lead sulfide complexes. Sverjensky et al. (1997) produced the first set of HKF coefficients for Pb(HS)₂⁰ and Pb(HS)₃⁻ based on the formation constants for those complexes from the solubility study of Hemley (1953) at ambient conditions. Remarkably, these HKF-model predictions are in good agreement, within 1 log unit, with the later solubility work of Giordano and Barnes (1979) who reported, from PbS(s) solubility measurements in NaHS-H₂S solutions the formation constants for Pb(HS)₂⁰ and Pb(HS)₃⁻ from 30 to 200 °C (*P*<sub>sat</sub>) along with a third complex of the tentative stoichiometry Pb(HS)₂(H₂S)⁰ at 200–300 °C. The latter species is, however, less certain, even though it has also been proposed in some low-temperature PbS(s) solubility work (Anderson 1962; Nriagu 1971) that might have been affected by analytical issues.
Wood et al. (1987) reported tabulated values for a single Pb(HS)₂⁰ formation constant from 200 to 350 °C on the basis of extrapolations of the Giordano and Barnes (1979) experimental values and other theoretical estimations (Naumov et al. 1971). The Wood et al. (1987) tabulated values have recently been used by Etschmann et al. (2018) to report another set of HKF coefficients for Pb(HS)₂⁰. However, their Born parameter had an unphysical, anomalously negative, value for a non-volatile and water-hydrated metal complex whose ω is expected to be close to zero and positive in sign (Plyasunov and Shock 2001; Perfetti et al. 2008; Tooth et al. 2013; Pokrovski et al. 2024).

This overview highlights the difficulty of extracting the origin of true experimental data used in generation of thermodynamic model coefficients and of assessing their errors. We recommend using the Sverjensky et al. (1997) dataset for Pb hydrosulfide complexes in speciation calculations to 300–350 °C, whereas any higher-temperature extrapolation should be taken with extreme caution. As for zinc, the affinity of Pb to HS⁻ is stronger than to Cl⁻ and decreases with temperature as shown by constants of ligand exchange reactions analogous to those for Zn (Fig. 4.26):

$$ \mathrm{PbCl}_{n}^{2-n} + n \mathrm{HS}^{-} = \mathrm{Pb(HS)}_{n}^{2-n} + n \mathrm{Cl}^{-}, n = 2 \text{ and } 3 \qquad (4.69) $$

It follows from the plot in Fig. 4.26 that, like for Zn, Pb-HS complexes may only be significant in alkaline, sulfur-rich and low-temperature fluids, whereas chloride complexes are largely responsible for the formation of most hydrothermal lead deposits characterized by saline acidic-to-neutral fluids with Cl/S ratios of >1000.

## Copper

Complexes of copper in hydrothermal fluids have been a subject of extensive studies in the 1970s–1990s, elegantly overviewed in detail by Wood and Samson (1998), and complemented by more recent work that will be briefly outlined here. Most studies employed the hydrothermal reactor solubility and synthetic fluid inclusion methods and, more recently, UV-Vis and XAS (both XANES and EXAFS) spectroscopy, complemented by quantum-chemistry and molecular dynamics (MD) simulations of complex structures and stabilities. Experimental studies span from low-temperature aquatic systems to silicate melt-fluid systems. In addition, Cu speciation in natural fluid inclusions from different magmatic-hydrothermal settings was also investigated using XAS and XRF (e.g., Mavrogenes et al. 2002; Cauzid et al. 2007; Berry et al. 2009). These and many other studies published in the chemical literature evidence a plethora of Cu¹¹ complexes, including hydroxides, chloride, sulfides and polysulfides that form in aqueous solution at circa-ambient conditions, whereas Cu¹ chlorides and hydrosulfides are the major Cu-transporting species in geological fluids at elevated temperatures. The two latter types will, therefore, be considered in more detail here.
*Chloride complexes of Cu*<sup>l</sup>* are believed to be dominant in most saline fluids (see Table 4.6).*

The number of specific experimental studies devoted to these complexes is too large to allow
reviewing here; instead, we evaluate the major thermodynamic compilations of those data that are
used by the geochemical community. There exist at least four sets of HKF-model parameters for
Cu¹ chloride species. The first set of Sverjensky et al. (1997) for Cu⁺, CuCl⁰, CuCl₂⁻ and CuCl₃²⁻,
included in the major thermodynamic databases of aqueous species (SUPCRT92, SUPCRTBL), has
been based on 25 °C stability constants and apparently involved no other, higher-temperature, data
source in the HKF-parameter derivation. Akinfiev and Zotov (2001) produced a second HKF set for
those Cu species, based on Cu(s), CuCl(s), and Cu₂O(s) solubility data mostly from Russian work to
450 °C and 1.5 kbar (overviewed by Zotov et al. 1995) and those of Xiao et al. (1998) to 300 °C at
P<sub>sat</sub>, and using isocoulombic reactions with analogous silver complexes to better constrain
thermodynamic values at 25 °C (S⁰, Cₚ⁰, V⁰), necessary for the HKF parameter derivation. A few
years later, Lui and McPhail (2005) produced another set of HKF coefficients for CuCl⁰, CuCl₂⁻,
CuCl₃²⁻, and CuCl₄³⁻, based on the Lui et al. (2002) UV-Vis spectroscopy study to 250 °C. Their
HKF set for CuCl⁰ and CuCl₂⁻ is in excellent agreement with that of Akinfiev and Zotov (2001),
despite differences in the choice of experimental data regressed and calculation algorithms, yielding
equilibrium constant values within <0.5 log units to at least 400–450°C and 1 kbar for the reaction

$$
\mathrm{Cu}^{+}+n \mathrm{Cl}^{-}=\mathrm{CuCl}_{n}^{1-n}, n=1 \text { or } 2
\qquad(4.70)
$$

However, in contrast to the Akinfiev and Zotov (2001) speciation scheme that ignored higher-order
complexes (n>2), the results of Liu and McPhail (2005) imply that CuCl₃²⁻ and CuCl₄³⁻ would be
the dominant species in high-temperature saline fluids (>400 °C, >2 m Cl). More recently, however,
Brugger et al. (2007) demonstrated by in situ X-ray absorption spectroscopy that the dominant
complex in high-temperature saline fluids is dichloride, CuCl₂⁻. Its dominant formation in high-
temperature fluids was also qualitatively confirmed by other XAS and MD studies (Fulton et al.
2000; Sherman 2007). The trichloride (CuCl₃²⁻) was only significant at temperatures <250 °C and
salinities above 4–8 m Cl. In light of the new XAS-derived speciation, Brugger et al. (2007) re-
interpreted previous UV-Vis measurements (Lui et al. 2002), rejected the tetrachloride species, and
produced a third set of HKF coefficients for CuCl₃²⁻. Finally, a fourth HKF dataset was recently
added by the IGEM team (Trofimov et al. 2023), who selectively re-analyzed previous experimental
and theoretical data in terms of CuCl₂⁻ and CuCl⁰ (Xiao et al. 1998; Archibald et al. 2002; Migdisov
et al. 2014), complemented by their own data and Russian work cited therein. These authors also
proposed an alternative set of AD model parameters for CuCl⁰ for vapor phase and low-density
supercritical fluids. This historical background demonstrates that caution should be given to
speciation interpretations and thermodynamic data derivation based on a single method or limited
datasets. To summarize, the present-date Cu speciation in saline hydrothermal fluids is believed to be dominated by dichloride (CuCl₂⁻) and either Akinfiev and Zotov (2001) or Lui and McPhail (2005) or Trofimov et al. (2023) sets of HKF coefficients for this species may be used with confidence in modeling Cu solubility in magmatic-hydrothermal fluids to at least 500 °C and 1–2 kbar (e.g., Kouzmanov and Pokrovski 2012). CuCl⁰ is a very minor species in saline liquid-type fluids, according to the above models. For lower-temperature epithermal-sedimentary brines, CuCl₃²⁻ may also be added to Cu speciation models.

At higher temperatures, closer to conditions of silicate melt - aqueous fluid separation, and in S-poor vapor phase produced by supercritical fluid unmixing, the low fluid dielectric constant favors ion association and uncharged species stability thereby changing Cu speciation. Indeed, Cu¹ species such as CuCl⁰, (Na,K)CuCl₂⁰, and/or CuCl(HCl)ₐ were inferred from solubility, partitioning, and molecular simulation studies at such conditions (e.g., Zajacz et al. 2011; Pokrovski et al. 2013a; Mei et al. 2014; Alex and Zajacz 2022; references therein), but quantitative assessment of their exact stoichiometries, abundances and thermodynamic properties over the magmatic *T-P*-density range is yet lacking. The role of sulfur in Cu speciation and transport, in particularly in high-temperature fluid systems, also remains poorly quantified, as will be overviewed below.

*Sulfide complexes.* Extensive geo-biochemical literature attests for the formation of a variety of Cu¹ complexes, both mono- and polymeric, with reduced sulfur ligands (sulfide, polysulfides, thiosulfate) in near-surface aquatic and biological systems (Rickard and Luther 2006; Pluth and Tonzetich 2020, for review). By contrast, only a handful of studies is available for hydrothermally relevant conditions. Among before-2000s studies (see Wood and Samson 1998 for review), the work of Crerar and Barnes (1976) is the rare one that reported thermodynamic values for Cu sulfide complexes. The authors measured the solubility of the chalcopyrite-pyrite-bornite assemblage in NaHS-H₂S fluids from 200 to 350 °C and reported the first values of stability constants for Cu(HS)₂⁻ and Cu(HS)₂(H₂S)⁻. Mountain and Seward (1999) measured the solubility of chalcocite (Cu₂S(s)) at 22 °C in NaHS-H₂S solutions over a wide pH range (4.0–11.5) using flow-through reactors, and produced an accurate set of stability constants for CuHS⁰, Cu(HS)₂⁻ and Cu₂S(HS)₂⁻, dominant in sulfide-bearing solutions at acidic, neutral, and alkaline pH, respectively. Mountain and Seward (1999) also re-assessed the high-temperature data of Crerar and Barnes (1976) in light of the speciation scheme above, and reported van't Hoff-type equations (e.g., equation 4.8) describing the temperature dependence (up to 350 °C) of *K* values of the formation reaction for the two monomeric complexes (Fig. 4.27a,b):

$$Cu^+ + n HS^- = Cu(HS)_n^{1-n}, n = 1, 2 \qquad (4.71)$$
Mountain and Seward (2003) further confirmed the data for Cu(HS)₂⁻ by extending Cu₂S(s) solubility measurements to 95 °C at near-neutral pH. Their reported set of logK₇₁ for Cu(HS)₂⁻ that also incorporated the data from the three studies above remains the most up-to-date one from 25 to 300 °C at Pₐt (Fig. 4.27b). However, because their logK vs T functions did not offer a possibility of extrapolating to supercritical conditions, two attempts have been made to place their data into the framework of the HKF equation of state. Akinfiev and Zotov (2001) used only the ambient-temperature data of Mountain and Seward (1999) and isocoulombic reactions with analogous Ag¹ complexes to produce a first set of HKF parameters for CuHS⁰ and Cu(HS)₂⁻. Their resulting logK₇₁ values are within 0.5 log units of those from Mountain and Seward (2003) empirical equations, lending credence to the HKF-model approach which was based exclusively on low-temperature data. Akinfiev and Zotov (2010) further refined the HKF parameters for Cu(HS)₂⁻ (notably the entropy and the related *a* and *c* parameters) by incorporating solubility data (<100 °C) of Mountain and Seward (2003). They rejected the higher-temperature data of Crerar and Barnes (1976) claiming that they were inconsistent. Paradoxically, the revised HKF parameters yield K₇₁ values 1 to 2 log units lower than the van't Hoff estimations above 200 °C (Mountain and Seward, 2003) (Fig. 4.27b).

The first in situ verification of Cu hydrosulfide speciation at supercritical conditions was made by Etschmann et al. (2010). They measured Cu₂S(s) solubility and local structure in concentrated NaHS solutions to 600 °C and 600 bar using in situ X-ray absorption spectroscopy. Their structural data clearly demonstrate the predominance of complexes with a linear S-Cu-S geometry, which would be consistent with Cu(HS)₂⁻ (note that XAS cannot “see” hydrogen atoms in most cases). Remarkably, their measured solubilities to 450 °C are in excellent agreement with the thermodynamic predictions using the HKF parameters of Cu(HS)₂⁻ from Akinfiev and Zotov (2001) further lending credence on their data, and confirming Cu(HS)₂⁻ to be the dominant CuI hydrosulfide complex in liquid-like fluids over a very large range of fluid acidity and sulfur concentration. This conclusion has recently been re-confirmed by new solubility data of Cu₂S(s) obtained in H₂S solutions at 350 and 450 °C at 500 and 1000 bar by a Russian team (Trofimov et al. 2023 and Russian references therein). The authors combined their few solubility datapoints with those of Mountain and Seward (1999, 2003), while rejecting Crerar and Barnes (1976) values, to propose another set of HKF parameters for CuHS⁰ and Cu(HS)₂⁻. Their set yields, however, virtually identical K values (within <1 log units, Fig. 4.27b) to those of Akinfiev and Zotov (2001) to at least 600 °C and 2 kbar.

Theoretical molecular simulations complemented the collection of Cu complexes. Mei et al. (2013a), using thermodynamic integration approach in MD simulations, were able to predict the Cu-Cl and Cu-HS complex stability constants between 22 and 327 °C to be within 1–4 log units of the
key experimental values (depending on the species and temperature). However, the MD uncertainties are yet too high compared with those of experimental measurements and corresponding thermodynamic models, even though they may provide qualitatively similar trends (Fig. 4.27a,b). In addition, these MD simulations indicate favorable formation of a mixed-ligand complex, Cu(HS)Cl⁻, that might potentially be dominant in hydrothermal fluids at Cl/S ratios of 10³ to 10⁴ at near-neutral pH around 300 °C. Complexes of Cu with sulfur of yet unknown stoichiometry have been hypothesized from in situ XRF-XANES spectra acquired on re-heated to 500 °C natural fluid inclusions from the Yankee Lode porphyry deposit (Cauzid et al. 2007). Mixed HS-Cl complexes for Cu and Au have also been inferred from experiments at magmatic temperatures and quantum-chemistry simulations (Zajacz et al. 2010, 2011), attesting a significant affinity of Cu¹ for reduced sulfur even at very high temperatures.

This affinity is further expressed in the S-rich hydrothermal-magmatic vapor phase in which Cu forms relatively volatile complexes with reduced sulfur. Such complexes promote Cu partitioning into the vapor compared to other transition metals such as Fe, Zn or Pb, as has been thoroughly demonstrated by laboratory measurements of vapor-liquid partition coefficients and natural fluid inclusion analyses in porphyry Cu systems. Note, however that natural fluid inclusions may be affected by post-entrapment enrichment through Cu⁺ diffusion into the inclusion from the external fluid, leading to an overestimation of Cu vapor-brine partitioning (see Kouzmanov and Pokrovski 2012; Pokrovski et al. 2013a, for extensive reviews on vapor-like geological fluids).

### 4.4.3 Silver

Like for copper, complexes with chloride and hydrosulfide ligands control silver transport by hydrothermal fluids. A set of four chloride complexes of Ag¹, AgCl⁰, AgCl₂⁻, AgCl₃²⁻ and AgCl₄³⁻, forms over a wide salinity range at low-to-moderate temperatures (<200 °C). With increasing temperature to 300–350 °C, the predominance domain of the dichloride species, AgCl₂⁻, widens significantly, covering salinities from ~0.01 m to at least 2 m NaCl. However, at supercritical temperatures and higher salinities, there is more discrepancy. Based on available data from AgCl(s) solubility experiments to 350 °C (Seward 1976), Sverjensky et al. (1997) generated a set of HKF parameters for the four chloride species. Their model implies a growing abundance of AgCl₄³⁻ at supercritical temperatures and salinities >2 m NaCl. However, their set is in disagreement with that of Akinfiev and Zotov (2001) who based their HKF-model for AgCl⁰ and AgCl₂⁻ on more extensive solubility studies (Zotov et al. 1995; Tagirov et al. 1997; Akinfiev and Zotov 1999) that do not show evidence of tri- and tetrachloride above 300–350 °C. Their data imply that AgCl₂⁻ is the major chloride species above 300°C and >2 m NaCl (>10 wt% salt). Thus, depending on the
chosen thermodynamic data set, Sverjensky et al. (1997) vs Akinfiev and Zotov (2001), solubility predictions of Ag₂S(s) in moderate-salinity fluids buffered by iron sulfide/oxide and alkali-aluminosilicate assemblages above 400 °C differ by a factor of 10–100 (see Pokrovski et al. 2013b for detailed discussion). This discrepancy is a consequence of both a lack of validation of a thermodynamic model (HKF) beyond the range of data covered by measurements and difficulties intrinsic to deriving species stoichiometry from regressions of bulk-solubility data.

In the 2010s, with the advent of spectroscopic and molecular modeling approaches, important constraints have been brought. Liu et al. (2012) showed by MD simulations that the only stable chloride species in hydrothermal range would be AgCl⁰ and AgCl₂⁻, while higher-order chloride complexes are unstable even at low temperatures. Pokrovski et al. (2013b) combined in situ X-ray absorption spectroscopy in supercritical fluids with MD simulations to demonstrate that AgCl₂⁻, of quasi-linear Cl-Ag-Cl geometry and without H₂O molecules in the first Ag atomic shell, is the only spectroscopically detectable species above >350 °C and salinities to at least 40 wt% NaCl. In addition, triangular AgCl₃²⁻ may account for a moderate part of total dissolved Ag (<30 %) below 300 °C and salinities above 10–15 wt% NaCl. These results are in very good agreement with the thermodynamic properties of AgCl₂⁻ of Akinfiev and Zotov (2001), and of AgCl₃²⁻ of Zotov et al. (1995). Their thermodynamic dataset, as compiled in Pokrovski et al. (2013b), is thus recommended for modeling Ag transport in saline fluids over the hydrothermal-magmatic range. Further support to this speciation scheme has recently been added by Zotov et al. (2020) from Ag(s) solubility measurements showing that the AgCl₂⁻ complex dominates up to remarkably high salinities at supercritical temperatures (425–475 °C, 0.1–18 m NaCl). These authors demonstrated that the traditional Debye-Hückel equation for activity coefficients (Helgeson et al. 1981) can be applied with confidence to very high salinities (at least for 1:1 electrolytes).

*The hydrosulfide complexes of silver* in hydrothermal fluids are dominatly AgHS⁰ and Ag(HS)₂⁻, at acidic and neutral pH, respectively, whereas at alkaline pH and low temperatures other, likely polynuclear, species exist (e.g., Ag₂S(HS)₂²⁻). In addition, complexes with polysulfides, thiosulfate and sulfite may form in more oxidizing environments (Wood and Samson 1998; Rickard and Luther 2007; references therein). The mono- and dihydrosulfide complexes (reaction 4.72 below) are the most relevant to hydrothermal fluids. Their stability has been derived from Ag₂S(s) solubility studies in H₂S-NaHS solutions, both at ambient and elevated temperatures (Schwarzenbach et al. 1958; Schwarzenbach and Widmer 1966; Renders and Seward 1989; Melent'yev et al. 1969; Sugaki et al. 1987; Gammons and Barnes 1989; Stefánsson and Seward 2003a), and more recently from theoretical MD simulations (e.g., He et al. 2016). Among the experimental studies that generated species stability constants, the solubility measurements of
Stefánsson and Seward (2003a) using flow-through reactors cover the widest T-P range, from ambient conditions to 400 °C and 500 bar. These data are in good agreement with previous work and significantly strengthen the robustness of the available experimental dataset. These data were regressed by the authors as polynomial equations of logK vs T, which are strictly valid within the experimental T-P range (see section 4.3.3). Consequently, there have been several attempts to place some of those experimental data into the HKF-model framework to enable predictions to higher temperatures and pressures. However, the data selection procedures were not sufficiently explicit or coherent in those attempts. Sverjensky et al. (1997) produced the first set of HKF parameters for Ag(HS)₂⁻ based of inter-parameter correlations and using the stability constant at 25 °C from Gammons and Barnes (1989). Akinfiev and Zotov (2001) regressed a more extended solubility dataset that included Ag₂S(s) solubility works at elevated temperatures and an improved description of H₂S(aq) thermodynamic properties (AD model, see section 4.3.3) to produce HKF-model parameters for Ag(HS)₂⁻ and AgHS⁰. Akinfiev and Zotov (2010) further revised the AgHS⁰ parameters based on the low-temperature solubility studies of Schwarzenbach et al. (1958) and Schwarzenbach and Widmer (1966). Those two studies reported the lowest Ag₂S(s) solubilities, which likely correspond to the well-crystalline sulfide phase, and were therefore judged to be most accurate. Fig. 4.27c,d compares the formation constants of both complexes for the reaction

$$Ag^+ + n HS^- = Ag(HS)_n^{1-n}, n = 1 \text{ or } 2 \qquad (4.72)$$

Despite the differences in data choice, the values from both HKF datasets, as well as the most recent solubility work of Stefánsson and Seward (2003a) not considered by those models, are all in decent agreement, with differences ≤1 log unit to 300 °C at Psat. It should be noted that this discrepancy is in part due to different choices of the thermodynamic properties of the other reaction constituents (Ag⁺, H₂S and HS⁻) adopted in data processing in different works. The agreement may be improved if similar basis data are used. For example, regressing Stefánsson and Seward (2003a) logK₇₂ values, using the RB equation and the HS⁻ and Ag⁺ thermodynamic properties used by Akinfiev and Zotov (2010), improves their agreement with the independent HKF predictions at elevated temperatures. The stability constants of the Ag hydrosulfide complexes extrapolated to 400–600 °C are likely to be uncertain within <2 log units. We recommend using Akinfiev and Zotov's (2001, 2010) HKF dataset for silver species for consistency, in particular if comparisons with Cu and Au complexes are to be made, because the three elements have been processed within the same thermodynamic framework. According to the available data overviewed above, silver hydrosulfide complexes dominate in sulfide solutions below 100 °C and in dilute hydrothermal fluids (<300 °C) of meteoric origin typically found in active geothermal systems (e.g., Otaki and Broadlands, New Zealand). The silver dichloride species usually dominate in high-temperature hydrothermal fluids of sea-water or
higher salinity (see Stefánsson and Seward 2003a for details of Ag species distribution at different solution compositions).

At magmatic temperatures, similarly to Cu¹, the ion pair between AgCl₂⁻ and Na⁺, NaAgCl₂⁰, becomes dominant in S-poor fluids. In S-bearing fluids over a typical fO₂ range of arc magmatism (NNO±2), another mixed-ligand ion pair, NaAg(HS)Cl⁰, predominantly forms, as has recently been inferred from elegant solubility measurements of Cu-Au-Ag alloys of a given metal activity using synthetic fluid-inclusion techniques for trapping the fluid phase at 900 °C and 2 kbar (Yin and Zajacz 2018; Alex and Zajacz 2022). Further qualitative evidence for another mixed-ligand complex, Ag(HS)Cl⁻, and its ion pair with Na⁺ has been provided by MD simulations (Lai et al. 2022) suggesting that these species may control Ag¹ speciation in hydrothermal fluids with H₂S concentrations >0.01 m and temperatures >300 °C. However, the realistic uncertainties on the stability constants of these and other chloride and hydrosulfide species that may now be calculated by MD methods yet remain rather high, and do not systematically reproduce the more robust experiment-based data trends (e.g., Fig. 4.27c). Nevertheless, in light of the recent work, mixed HS-Cl complexes could be important for chalcophile metals (Cu, Ag, Au). More data on their stability constants over wider T-P ranges are required to place such species, along with their more traditional chloride and hydrosulfide congeners, in a unified thermodynamic framework for hydrothermal-magmatic fluids.

#### 4.4.4 Gold

Among all metals, gold is definitely the “king” of hydrothermal ore-deposit research. As a result, it is the most studied metal in hydrothermal fluids as to its chemical speciation and solubility. Being notoriously soft, aurous gold, Au¹, has a much stronger chemical affinity to reduced sulfur in aqueous solution than Cu¹ and Ag¹ but, due to relativistic effects affecting its electronic structure, its affinity to the OH⁻ and Cl⁻ ligands is also much stronger. As a result, there is competition between those three types of ligands for Au¹. The speciation is further complicated by the existence of auric gold, Au³³, which has a strong affinity for both OH⁻ and Cl⁻. Tetrachloride, AuCl₄⁻, is the most popular Au³³ species in chemistry and may easily be prepared by gold metal dissolution in aqua regia. Auric gold species are only stable at strongly oxidizing conditions of the Earth’s surface. Aurous gold can also be stabilized at ambient conditions as very strong complexes with cyanide, Au(CN)₂⁻, famous for its use in heap leaching operations for gold recovery. The formation of strong Au¹ complexes with intermediate-valence sulfur ligands (S₂O₃²⁻, Sₙ²⁻, SCN⁻, organic thiols) occurs at conditions of sulfide ore oxidation in mine drainage sites (e.g., Vlassopoulos and Wood 1990), and is used in chemical engineering applications such as gold ore processing (Adams 2005) or gold
nanoparticle synthesis (Häkkinen 2012). These ligands are, however, generally present in much smaller concentrations than H₂S and HS⁻. As a result, the fate of gold in crustal fluids and silicate melts has been believed to be controlled by Au¹-OH-Cl-HS types of complexes. They have been the subject of a large number of experimental and thermodynamic studies, reviewed in detail in Wood and Samson (1998) and Pokrovski et al. (2014). More recently, tri- and disulfur radical ions have emerged as strong ligands for Au¹ in hydrothermal-magmatic fluids. Below we overview the available data on Au¹ hydroxide, chloride, sulfide and polysulfide species with an emphasis on >2010s work. Unfortunately, many thermodynamic databases of gold species, widely used in geochemical modeling of fluid-rock interactions and ore deposit formation, contain sometimes obsolete and confusing information on some of those species and do not take into account the more recent data. Another caveat of the thermodynamic properties of reaction constants of Au solubility the reader can face in the literature is the use of different thermodynamic data sources for the reaction constituents such as H₂S/HS⁻, Cl⁻/HCl⁰, H₂(aq)/H₂(g) that renders different datasets thermodynamically inconsistent and may lead to large uncertainties on gold solubility predictions at elevated temperatures.

*Au¹ aqua ion and its hydroxide complexes.* Aurous gold ion, Au⁺, often used in expressions of formation constants of Au complexes and is traditionally present in common databases (e.g., SUPCRT92, SUPCRTBL), is in reality virtually non-existent in aqueous solution at ambient conditions at any physical pH value because it undergoes hydrolysis to AuOH⁰.

$$Au^{+} + H_{2}O = AuOH^{0} + 0.5 H^{+} \qquad (4.73)$$

The reaction constant value, logK₇₃, is between 6 and 11 at ambient conditions according to available estimations (e.g., Akinfiev and Zotov 2001; Stefánsson and Seward 2003b; Rauchenstein-Martinek et al. 2014). This range of values means that Au⁺ can only form in significant fractions at pH < -6 in the best case, which is simply an unphysical condition in aqueous solution. Note that the instability of Au⁺ strongly contrasts with that of the Cu⁺ and Ag⁺ ions that are dominant in aqueous solution at pH <9-11 in the absence of complexing ligands (S, Cl, see above). Paradoxically, Au⁺ thermodynamic properties and HKF-model coefficients have been estimated and revised with some minor modifications by the HKF people in several papers over almost 20 years (Helgeson et al. 1981; Shock and Helgeson 1988; Shock et al. 1997) and used in some more recent work (e.g., Akinfiev and Zotov 2001; Stefánsson and Seward 2003c). However, it is hard to track the true original data source, and in particular the Gibbs energy of formation value of the Au⁺ aqua ion, since all the papers mentioned above just refer one to another for this value. A perseverant reader finally finds that it stemmed from the compilation of Latimer (1952) in which it has been tentatively estimated from the solubility product of Au¹ iodide (AuI(s)), which, in turn, has been very roughly
estimated using an analogy with CuI(s) and AgI(s). This example shows how unreliable thermodynamic data can be for some aqueous species, in particular those poorly stable within the range of experimentally realizable conditions. Needless to say that extrapolation of such data to elevated temperatures suffers from large uncertainties that may lead to unphysical results in speciation calculations for hydrothermal fluids. For example, the value of logK73 that may be calculated at 600 °C and 2 kbar using the HKF parameters of Rauchenstein-Martinek et al. (2014) is -2.2, which implies that Au+ would be the dominant AuI species in solution at realistic pH of 2-3. This result is unphysical, however, since it contradicts everything we know about the large increase of cation hydrolysis with temperature making most metal cations negligible in hydrothermal fluids in favor of their hydroxide counterparts (e.g., Wood and Samson 1998). As a result, no set of Au+ thermodynamic properties published so far could be recommended, and the use of Au+, for example in expressing cumulative complexation constants as commonly done for much more stable Ag+ and Cu+ (equations 4.70-4.72) should be avoided for Au species. The thermodynamic properties of AuI hydroxide, chloride, and sulfur-ligand complexes have been derived from solubility measurements of gold metal. Therefore, Au(s) solubility reactions, such as equations (4.64-4.67) and others given below, should be used to avoid the misleading Au+ issue.

The stability of monohydroxide complex, AuOH°, dominant over a geologically realistic range of pH (pH <10-12) in dilute S- and Cl-poor solutions, has been investigated by gold solubility measurements from 25 to 600 °C (Vlassopoulos and Wood 1990; Zotov et al. 1995 and references therein; Stefánsson and Seward 2003b) for the reaction:

$$Au(s) + H_2O = AuOH^0 + 0.5 H_2(g) \quad (4.74)$$

These data, are in good agreement, in particular at temperatures above 200 °C where Au solubilities approach the 100-ppb level and, therefore, become more easily measureable. They were regressed using the HKF model based on different approaches and solubility data sources by Akinfiev and Zotov (2001) and Rauchenstein-Martinek et al. (2014). Both sets of HKF parameters predict similar K74 values, within <0.5 log units between 200 and 600 °C and up to several kbars (Fig. 4.28a). Therefore, both datasets may be used in thermodynamic modeling studies. The AuOH° species is only significant for gold transport in Cl- and S-poor fluids in which its concentrations may attain 100s ppb Au. The Au(OH)2- complex, invoked in few studies in highly alkaline solutions at near-ambient temperature, is unlikely to be important in geological fluids. The tentative HKF parameters proposed so far for this species (Pokrovski et al. 2014 and references therein; Rauchenstein-Martinek et al. 2014) are not recommended for extrapolation to hydrothermal conditions.

Au¹ chloride complexes. Chloride complexes of Au¹ have received considerable attention given the common presence of salt in geological fluids. To the best of our knowledge, the first
quantitative estimations of Au-Cl complex stability and concentrations in hydrothermal fluids have been made by Helgeson and Garrels (1968). They combined rare available experimental data and thermodynamic extrapolations with estimations of gold budget in quartz veins based on geological observations to conclude that gold is transported as aurous chloride complexes and precipitated mostly in response to cooling. Their conclusions were, however, criticized by Boyle (1969) who, based on field observations and geochemistry of gold ore, argued that Au is primarily transported as complexes with S, As and Sb and deposited in response to boiling and fluid-rock interactions rather than cooling. These first debates have been followed by a substantial number of experimental solubility studies that quantified the equilibrium constant of reaction (4.67). Among the available experimental studies, those of Nikolaeva et al. (1972) to 90 °C, Zotov et al. (1991) to 500 °C and 1.5 kbar, Gammons and Williams-Jones (1995) to 300 °C and $P_{sat}$, and Stefánsson and Seward (2003c) to 600 °C and 1.8 kbar, are the most consistent ones (see Wood and Samson 1998; Pokrovski et al. 2014 for detailed assessment). They have been used in derivation of HKF-model parameter sets of variable degree of confidence for $AuCl_2^-$, considered as the main complex. The Sverjensky et al. (1997) set, included in the SUPCRT92 and SUPCRTBL databases, was based on low-temperature data (Nikolaeva et al. 1972) and HKF correlations, whereas the Akinfiev and Zotov (2001) set was derived by optimization of more extended solubility data mostly from Russian teams (Nikolaeva et al. 1972; Zotov et al. 1995 and references therein). In the range 400–600 °C and 0.5–2 kbar, both sets predict Au solubility to be 1 to >3 log units higher than Stefánsson and Seward's (2003c) extensive solubility measurements. The latter experimental work was apparently used in a third HKF dataset (Rauchenstein-Martinek et al. 2014) that, however, did not report explicit information on the parameter derivation procedure. Recently, Zotov et al. (2018) have performed additional gold solubility measurements at 450 °C and 0.5–1.5 kbar over a large $f_{H_2}$ range (>6 log units). They combined these data with those cited above, as well as more recent gold solubility measurements at magmatic temperatures (to 1000 °C and 2 kbar; Zajacz et al. 2010; Guo et al. 2018) reinterpreted in terms of a single species, $AuCl_2^-$, to propose a density-model equation for the thermodynamic constant of the following solubility reaction that was modified from reaction (4.67) to render it isocoulombic and allow a better linearization vs T:

$$Au(s) + HCl^{0}_{(aq)} + Cl^{-} = AuCl_{2}^{-} + 0.5 H_{2}(aq) \quad (4.75)$$

Their simple model allows the stability of $AuCl_2^-$ to be predicted with an uncertainty of <1 log units at hydrothermal temperatures (<600 °C), with $K_{75}$ values being in between Akinfiev and Zotov's (2010) and Stefansson and Seward's (2003c) results, thereby partly reconciling the two datasets (Fig. 4.28b). The data of Zotov et al. (2018) await to be incorporated in common thermodynamic databases, e.g., in the form of an HKF-parameter set, to enable its wider use in hydrothermal-
magmatic fluid models. The large T-P-salinity range of the AuCl₂⁻ stability has independently been confirmed by direct in situ XAS measurements at hydrothermal conditions that evidence a quasi-linear Au coordination with two Cl atoms (Pokrovski et al. 2009a; Tagirov et al. 2019a).

These in situ data, along with most solubility studies discussed above, do not provide any robust evidence for mono- and trichloride species, AuCl⁰ and AuCl₃²⁻, whose significance was also doubted in some previous studies (e.g., Gammons and Williams-Jones 1995). Despite the lack of evidence for both species, two theoretical HKF parameter sets for them have been suggested (Sverjensky et al. 1997; Akinfiev and Zotov 2001). Their values should be, however, regarded as highly unconstrained and their use in gold speciation modeling in hydrothermal fluids is not recommended.

*Au¹ hydrosulfide complexes.* This most important type of Au¹ species in hydrothermal fluids has been the subject of extensive solubility measurements since the pioneering work of Ogryzlo (1935) who reported elevated Au solubility in alkaline sulfide solutions. Since then, more than 40 studies have attempted to constrain Au (hydro)sulfide species stoichiometry and stability constants via the solubility method (see Pokrovski et al. 2014 for detailed review). Among early studies, those of Seward (1973), Renders and Seward (1989) and Shenberger and Barnes (1989) are probably the most constrained ones. It follows from these and other studies that Au¹ dihydrosulfide, Au(HS)₂⁻, is likely the major complex in the near-neutral pH range of H₂S-bearing geological fluids. In addition, other Au-S complexes of various stoichiometry have also been proposed in different studies dealing with acidic and alkaline pH regions and more oxidizing conditions (see below). Despite the common agreement on the Au(HS)₂⁻ stoichiometry, the absolute values of the solubility constants of reaction (4.64) diverged significantly among before-2000s studies (up to 3 log units at typical hydrothermal temperatures of 300 °C). Such discrepancies may be explained by difficulties in controlling or buffering the three key parameters, H₂S, H₂ and pH, on which Au solubility depends, as well as different choices of the thermodynamic datasets for H₂S(aq) and its dissociation constant, and H₂(aq)/H₂(g) equilibria, as well as the presence of other sulfur ligands (polysulfides, thiosulfates) which also form strong complexes with Au¹. Some data from these early studies have been used to produce first sets of HKF parameters of Au(HS)₂⁻ by Sverjensky et al. (1997) and Akinfiev and Zotov (2001) still being used in modeling studies. While the most available experimental data and these predictions are in good agreement at moderate temperatures (200–350 °C), the HKF predictions at supercritical temperatures likely overestimate Au solubility values by a few orders of magnitude, as was shown by 1990–2000s studies (e.g., Benning and Seward 1996; Gibert et al. 1998). Among them, gold solubility measurements of Stefansson and Seward (2004) and Tagirov et al. (2005, 2006) are the most extended and analytically elaborated ones, covering a large range
of *T* (25–500 °C) and *P* (*P*<sub>sat</sub>–1 kbar). These works are in good mutual agreement (Fig. 4.28c,d) and provide important constraints on Au speciation in supercritical liquid-like fluids. The data of these three studies have been processed by Akinfiev and Zotov (2010) (as overviewed and corrected in Pokrovski et al. 2014) to produce an improved set of HKF model coefficients. Another set of Au(HS)<sub>2</sub><sup>−</sup> HKF parameters has been proposed by Rauchenstein-Martinek et al. (2014) based on the solubility data of Stefansson and Seward (2004). The first direct molecular evidence for Au(HS)<sub>2</sub><sup>−</sup> in near-neutral hydrothermal fluids was provided by in situ X-ray absorption spectroscopy combined with molecular modeling (Pokrovski et al. 2009b), showing that Au is linearly coordinated by two [(H)S]<sup>−</sup> ligands. Gold bulk solubility measured from the spectrum absorption edge amplitude was in excellent agreement with gold solubility predictions using the thermodynamic properties of Au(HS)<sub>2</sub><sup>−</sup> (Akinfiev and Zotov 2010; Pokrovski et al. 2014). As a result, at present, the stability of Au(HS)<sub>2</sub><sup>−</sup> is well constrained in a wide *T* (20–500 °C) and *P* (<1.5 kbar) range of hydrothermal fluids.

The second “popular” Au sulfide species in hydrothermal fluids is *gold monohydrosulfide*, AuHS⁰, which is believed to dominate gold speciation at weak-to-moderate H₂S concentrations at acidic pH. Being much less soluble than Au(HS)₂⁻, it has been constrained less thoroughly experimentally based exclusively on solubility data. The low AuHS⁰ concentrations at most experimental conditions (typically below the ppm level) have not yet enabled direct spectroscopic proof of its existence. Moreover, MD calculations showed AuHS⁰ to be structurally a quasi-linear complex HS-Au-OH₂, coordinated by a water molecule that may easily be exchanged with a stronger ligand such as HS⁻ or H₂S (Liu et al. 2011). Solubility-derived reaction constants of AuHS⁰ (equation 4.66) from before-2000s works (e.g., Hayashi and Ohmoto 1991; Benning and Seward 1996; Gibert et al. 1998) were rather discrepant (e.g., >2 log units at 300 °C; see more detailed analyses in Stefánsson and Seward 2004, and Tagirov et al. 2005), due to numerous technical issues coupled with the complexity of experimental system compositions employed promoting the AuHS⁰ competition with Au chloride, hydroxide and other S-ligand complexes forming at acidic pH. The works of Stefánsson and Seward (2004) and Tagirov et al. (2005) prevail amongst the most accurate solubility studies to date for AuHS⁰, which are in mutual agreement (within ~0.5 unit of logK₆₆; Fig. 4.28d). HKF-model parameter sets derived by Akinfiev and Zotov (2010) and Rauchenstein-Martinek et al. (2014), based on those works, are in good agreement and may be used for quantitative modeling of Au solubility in sulfide-poor acidic fluids. The former HKF set of Akinfiev and Zotov (2001), yet used in some databases, should be considered as obsolete because was based on experiments in which both Au and S speciation was insufficiently constrained (e.g., Hayashi and Ohmoto 1991).
*Other Au (hydro)sulfide and polysulfide species* have also been invoked in some solubility and more recent X-ray spectroscopy studies in acidic-to-neutral sulfur-rich solutions to account for much higher measured Au solubility than predicted using the AuHS⁰ and Au(HS)₂⁻ complexes above. The additional complexes include AuHS(H₂S)⁰ (Hayashi and Ohmoto 1991), AuHS(H₂S)₃⁰ (Loucks and Mavrogenes 1999), or AuHS(H₂S)⁰ or AuHS(SO₂)⁰ (Pokrovski et al. 2009b). However, none of these species has been confirmed by more recent work. For example, the very popular in the 1990s AuHS(H₂S)₃⁰ complex in high-temperature metamorphic fluids, inferred from limited synthetic fluid inclusion analyses of Au concentrations in saline fluids at 550–725 °C and 1–4 kbar buffered by iron oxide/sulfide and alkali-aluminosilicate assemblages (Loucks and Mavrogenes 1999), has later been rejected for a number of reasons. First, these solubility data could equally be interpreted by traditional AuHS⁰ + Au(HS)₂⁻ + AuCl₂⁻ species (Stefánsson and Seward 2004). Moreover, its stability constants calculated using the HKF set proposed in the original study, significantly overestimate the in situ measured Au solubilities at 300–400 °C (Pokrovski et al. 2009b). Direct evidence against the tetra-hydrosulfide complex has been brought by in situ XAS measurements and MD simulations. Such species stoichiometry contradicts the linear S-Au¹-S geometry inherent to Au¹ coordination chemistry as directly shown by XAS in hydrothermal fluids (Pokrovski et al. 2009b, 2014). Recent MD simulations have demonstrated AuHS(H₂S)₃⁰ to be unstable, breaking down to the linear [L-Au-(SH)] (L = H₂O or H₂S/HS) and 2 H₂S molecules (Liu et al. 2011). The [HS-Au-SH₂]⁰ species, which is more consistent with Au¹ coordination chemistry, has been regarded as a possible alternative for acidic solutions as well as for S-rich hydrothermal-magmatic vapor phases (Pokrovski et al. 2008a, 2009b). However, there are rather disparate thermodynamic data for this species, and the direct determination of its stoichiometry faced the limitations of traditional XAS methods that are poorly sensitive to light atoms like hydrogen. Alkali ion pairs (e.g., NaAu(HS)₂⁰) have been proposed in magmatic vapors (e.g., Zajacz et al. 2010). Such ion pairs may easily account for Au transport in magmatic vapor-like fluids in contrast to recent claims that the traditional Au sulfide species, AuHS⁰ and Au(HS)₂⁻, dominant at lower-temperature hydrothermal conditions should be revised (Farsang and Zajacz 2025). In alkaline NaHS solutions, a binuclear species, Au₂(HS)₂S²⁻ in which two [(HS)Au-] moieties are linked together via an [-S-] bridge, has been inferred from analyses of pH and ligand concentration trends in Au(s) solubility data (Seward 1973). However, direct spectroscopic or molecular dynamics evidence for such bulky species in hydrothermal fluid is lacking. Polysulfide-ligand ((H)SₙS²⁻) Au¹ complexes of unconstrained stoichiometry and stability have equally been invoked in some Au solubility studies in S⁰/H₂S-bearing hydrothermal fluids both at relatively low and high temperatures (100–150 °C, Berndt et al. 1994; 600–800 °C, Hu et al. 2022) to explain the elevated measured gold concentrations
(100s ppm Au); however, their interpretation was complicated by poorly constrained sulfur speciation in such experiments with unknown or neglected contributions of the thiosulfate, sulfite or di- and trisulfur ion ligands to Au complexing.

**Complexes with sulfur radical ions.** From the dawn of ore-deposit research, the interpretation of Au speciation in S-rich fluids both at hydrothermal and magmatic conditions has been based on the assumption that the major sulfur forms are hydrogen sulfide and sulfate, the former being the ligand of choice and the latter having a negligible affinity for Au¹. This view was challenged in the 2010s by the discovery of the S₃⁻ ion (Pokrovski and Dubrovinsky 2011; Pokrovski and Dubessy 2015), which turned out to be abundant in acidic-to-neutral solutions in the redox range of the sulfate-sulfide coexistence (see section 4.3.4 and Figs. 18–20). This discovery has first inspired theoretical molecular modeling studies of S₃⁻ interactions with chalcophile metals. These works indicated that S₃⁻, similarly to HS⁻, might be able to form stable complexes with Cu¹ and Au¹ (Tossell 2012; Mei et al. 2013b). Direct quantitative experimental evidence has been brought by Pokrovski et al. (2015) who combined in situ solubility measurements with EXAFS spectroscopy and FPMD modeling in hydrothermal solutions in which sulfate and sulfide coexist, to demonstrate the formation of a mixed complex, Au(HS)S₃⁻, across a large T-P range of crustal fluids (equation 4.65). Its exact stoichiometry and structure have further been confirmed by Pokrovski et al. (2022b) using high-resolution XANES spectroscopy coupled with quantum-chemistry and molecular modeling that enabled its unambiguous spectroscopic distinction from its “rival” Au(HS)₂⁻ (Fig. 4.29) that was virtually unresolvable using classical XAS techniques (e.g., Pokrovski et al. 2009b, Trigub et al. 2017).

Based on the robust thermodynamic properties of Au(HS)₂⁻ and S₃⁻, Pokrovski et al. (2015) demonstrated that the equilibrium constant is equal to 1 over the entire T-P range investigated (300–500 °C, 0.1–1 kbar) for the ligand exchange reaction

$$Au(HS)_{2}^{-} + S_{3}^{\cdot -} = Au(HS)S_{3}^{-} + HS^{-} \qquad (4.76)$$

These data open new perspectives for our understanding of Au speciation in crustal fluids, allowing a more accurate assessment of gold transport and precipitation phenomena. Fig. 4.30 illustrates the effect of trisulfur ion complexing on gold solubility in a porphyry Cu-Au setting, predicted using the thermodynamic data for S and Au species discussed above. The Au(HS)S₃⁻ abundance closely follows that of S₃⁻ itself (e.g., Fig. 4.19, 4.20) and accounts for >90–95% of the total dissolved gold at temperatures ≥350 °C and pressures ≥Psat in S-rich (>0.5 wt% S) acidic-to-neutral (pH 4–6) fluids under redox conditions of the H₂S-SO₂ or sulfide-sulfate coexistence (Pokrovski et al. 2015). This gold complex therefore stands as a major gold carrier in porphyry environments, capable of extracting from magma and transporting 10s to 100s ppm of dissolved Au (Fig. 4.30), thus
accounting for natural Au concentrations analyzed in fluid inclusions from such settings (Kouzmanov and Pokrovski 2012). In can be seen in Fig. 4.30 that the other traditional Au species with Cl⁻, OH⁻ and HS⁻ ligands considered above represent only a minor fraction of dissolved gold in S-rich fluids at magmatic-hydrothermal temperatures. It is only upon fluid cooling below 300–350 °C and S₃⁻ decrease that Au hydrosulfide complexes, such as Au(HS)₂⁻ (and eventually AuHS⁰, at lower S concentrations and more acidic pH), take the lead in gold transport to epithermal deposits. In metamorphic fluids relevant to orogenic gold deposits (section 4.5.3), the generally lower sulfur concentrations and lower fO₂ render Au(HS)S₃⁻ less abundant compared to AuHS⁰ and Au(HS)₂⁻. It is only at hot stages of metamorphism corresponding to amphibolite facies (>550–600 °C) potentially favorable for large S release in the fluid due to breakdown of pyrite to pyrrhotite in some lithologies (e.g., Tomkins 2010; Schwarzenbach and Evans, 2025) that the gold-trisulfur complex might become important. However, thermodynamic predictions at temperatures above 500–600 °C are exclusively based on extrapolations and therefore become highly dependent on the choice of thermodynamic data sources for metal and sulfur species as well as other fluid constituents. The use of consistent thermodynamic datasets for the key species such as H₂S and Au(HS)₂⁻ (Pokrovski et al. 2014), based on which the reaction (4.76) constants have been derived, allows significantly reducing uncertainties of extrapolations above 500 °C. As a result, current realistic uncertainties of Au solubility predictions at 550–700 °C and 1–5 kbar for a given fluid composition are probably within 1 log unit (see Pokrovski et al. 2015 for detailed discussion). Note that the estimated Au solubilities above 500 °C in Fig. 4.30 are pessimistic in light of the possible existence of Au complexes with the disulfur radical ion that becomes more abundant at closer-to-magmatic temperatures (Fig. 4.20a; 4.21), as well as of mixed alkali-Cl-HS complexes whose stability remains to be quantified at the conditions of the magmatic-hydrothermal transition.

The findings of stable Au-trisulfur ion complexes help better constrain gold deposit
formation models (e.g., He et al. 2024) and, in the future, may open perspectives for improving
methods of gold recovery from ore or hydrothermal synthesis of gold nanomaterials (Pokrovski et
al. 2015, 2022b). Assuming similar affinities of S₃⁻ and HS⁻ for base metals (Cu¹, Zn¹¹) and Ag¹,
with equilibrium constants equal to one for exchange reactions of their dihydrosulfide complexes
(Cu(HS)₂⁻, Zn(HS)₂⁰, Ag(HS)₂⁻) analogous to reaction (4.76), the predicted effect of S₃⁻ on these
metals solubility was found to be almost negligible (Pokrovski et al. 2015). This result is in line
with the much lower affinity to HS⁻ of those metals than of Au¹ (Fig. 4.31b) and their dominantly
chloride-type speciation in most hydrothermal fluids. By contrast, the effect of S₃⁻ on Pt, Pd and,
potentially, Mo speciation appears to be much stronger as discussed in the following sections.
4.4.5. Platinum group elements (PGE)

This group of metals includes Pd, Pt, Rh, Ir, Ru and Os, which are notoriously chalcophile
being concentrated in (ultra)mafic magmatic settings along with Fe-Ni-Cu sulfide minerals and
melts, such as in the famous Bushveld, Norilsk and Sudbury deposits from which >95% of the
current PGE georessources are mined (e.g., Mungall and Naldrett 2008; Gunn 2014). The
mechanisms of PGE concentration in magmatic deposits are believed to be controlled by different
processes of fractional crystallization, fractionation and segregation of silicate and sulfide melts
amply discussed in the literature (e.g., Kerr and Leitch 2005; Brenan 2008; Lorand et al. 2008;
Barnes and Liu 2012; Mudd and Jowitt 2014; Barnes and Ripley 2016; Kiseeva et al. 2025; Simon
and Wilke 2025). However, the potential role of aqueous magmatic or post-magmatic fluids in PGE
ore formation processes has long been debated (e.g., Ballhaus and Stumpfl 1986;
Kanitpanyacharoen and Boudreau 2013; Le Vaillant et al., 2016a,b; Boudreau, 2019; Sullivan et al.,
2022a,b, to name a few). Furthermore, there are numerous instances of PGE (re)mobilization and
concentration in various hydrothermal settings such as porphyry Cu-Au-Mo deposits, black-shale
hosted gold deposits, and serpentinites from subduction zones (e.g., Ballhaus and Stumpfl 1986;
Rehkämper et al. 1997; Wood 2002; Hanley 2005; Mungall 2005; Luguet et al. 2008; Economou-
Eliopoulos 2010; Bazarkina et al. 2014; Arai and Miura 2016; Barnes and Ripley 2016; Holwell et
al. 2017; Boudreau 2019), with Pd and Pt concentrations locally reaching 1000 times their average
crustal abundance, thereby making such settings potentially exploitable for these metals. The
interest in aqueous, including hydrothermal, chemistry of PGE has been rapidly growing in the last
20 years, pushed by the increasing use of these critical metals in many high-technology fields
spanning from the automotive and petrochemical industries to pharmaceuticals and nanomaterials
(Brenan 2008; Yam 2010; Gunn 2014). However, compared to the base and precious metals
discussed above that all form nominally hydrothermal deposits (Zn, Pb, Cu, Ag, Au), only a small
number of studies is available in hydrothermal fluids for Pd and Pt whose aqueous speciation and
thermodynamic properties yet remain highly uncertain. Compared to the rest of the platinoids group,
Pd and Pt are more abundant in the Earth's continental crust (0.8 ppb vs 0.04–0.08 ppb for the other
PGE; Chen et al. 2016), more soluble and mobile in aqueous fluids, and more widely used by the
industry. These properties make Pd and Pt more available, cheaper and therefore more amenable to
scientific research. Their hydrothermal speciation and the role of sulfur in their fluid-phase transport
will be overviewed here. The other PGE remain virtually unknown in hydrothermal fluids and only
very scarce experimental data and thermodynamic estimations are available for some of them at
temperatures above ambient (e.g., see Sassani and Shock 1998; Wood 2002).
## Palladium

This element exists almost exclusively in PdII oxidation state with an electronic configuration enabling square planar complexes with most ligands. Among them, water, chloride and sulfur are most relevant to hydrothermal conditions. The Pd(H₂O)₄²⁺ ion, of square-planar coordination with 4 H₂O, undergoes hydrolysis at ambient conditions, by substitution of H₂O by OH⁻, by forming PdOH⁺ at pH~1, and Pd(OH)₂⁰ and Pd(OH)₃⁻ at higher pH (the coordinating water molecules are omitted in these complexes for more fluency). However, the available estimations of the HKF parameters of Pd²⁺ and high-temperature extrapolations of its hydrolysis constants (Sassani and Shock 1998; Tagirov et al. 2013, 2015) must be regarded with caution because the data are both very scattered and do not predict the expected increase in hydrolysis at elevated temperatures common for metal cations. Sulfate complexes of Pd were reported at ambient conditions; these data were used by Sassani and Shock (1998) to propose a set of HKF parameters for PdSO₄⁰, Pd(SO₄)₂²⁻, Pd(SO₄)₃⁴⁻. However, both hydroxide and sulfate complexes appear to be largely negligible at hydrothermal conditions dominated by chloride and sulfide ligands for which Pd has a much greater chemical affinity.

**Chloride complexes.** In acidic chloride solutions below 100 °C, stepwise chloride complex formation, with four square-planar complexes, from PdCl(H₂O)₃⁺ to PdCl₄²⁻, is evidenced by a plethora of solubility, spectroscopy, potentiometry and quantum-chemistry studies, with PdCl₄²⁻ being dominant at salinities above 0.1–0.3 m NaCl (see the reviews of Wood et al. 1992; Sassani and Shock 1998; Bazarkina et al. 2014). At typical hydrothermal conditions (<500 °C), the agreement on the dominant species and its thermodynamic stability is less good. First comprehensive theoretical estimations, based on low-temperature data and using the HKF model, predicted PdCl₂⁰ and PdCl₃⁻ as the dominant species (Sassani and Shock 1998), in contrast to earlier theoretical estimations (Wood et al. 1992) that privileged PdCl₃⁻ and PdCl₄²⁻. The latter speciation scheme, while being independent, appears in better agreement with pioneering solubility measurements of Gammons' group who used different Pd solid phases (Pd, Pd₄S, Pd₁₆S₇, PdS, and Ag-Pd alloy) to constrain the formation of PdCl₃⁻ and PdCl₄²⁻ to 300 °C (Gammons et al. 1992; Gammons and Bloom 1993a, Gammons 1995). More recent solubility measurements to higher temperatures (500 °C, 1 kbar) supported PdCl₄²⁻ as the dominant species at salinities above 0.1 m NaCl; they were coupled with an analysis of selected existing data to generate a second set of HKF parameters for Pd chloride complexes (Tagirov et al. 2013). First systematic in situ XAS measurements at hydrothermal conditions, combined with PdO(s) and PdS(s) solubility determinations in saline solutions to 450 °C and 600 bar (Bazarkina et al. 2014), demonstrate that PdCl₄²⁻ forms at the expense of PdCl₃(H₂O)⁻ at salinities above 0.1–0.3 m NaCl in a wide T range,
from ~100 to 450 °C. Molecular dynamics simulations at 300 °C, using a thermodynamic integration method, imply $PdCl_4^{2-}$ to be the most stable (i.e. most abundant) among the four chloride complexes (Mei et al. 2015b). Solubility measurements of $Pd(s)$ at magmatic temperatures in saline fluids (900 °C, 2 kbar, to 60 wt% NaCl), however, point to lower-order chloride complex stoichiometries, $PdCl_2^0$ and $PtCl_3^-$ (Sullivan et al. 2022a).

More importantly, the discrepancies in the thermodynamic stability of Pd chloride species among those studies are remarkably large for the same species, for example attaining 7 orders of magnitude for the $PdS(s)$ solubility reaction as $PdCl_4^{2-}$ at temperatures 300–450 °C (see Bazarkina et al. 2014 for detailed comparisons). This difference translates to an equivalent uncertainty of 7 orders of magnitude (!) in aqueous Pd concentrations in equilibrium with a Pd-bearing solid phase in typical hydrothermal fluids. For example, those of Sassani and Shock (1998) yield the lowest Pd concentration values (<1 ppt) and those of Tagirov et al. (2013) – the highest (~1 ppm) at salinities of 10 wt% NaCl at acidic (pH~4) and oxidizing (HM buffer) conditions. The discrepancy becomes even more spectacular at magmatic temperatures, up to 12 orders of magnitude between those two HKF-model predictions, with predicted solubilities of $Pd(s)$ of <10 ppt (Sassani and Shock 1998) and >10⁶ ppm (Tagirov et al. 2013) at 900 °C, 2 kbar, 10 wt% NaCl and $fO_2$ of the NNO buffer. Both predicted values seem unlikely to be realistic, compared to direct experimental measurements that report ~10 ppm Pd at such conditions (Sullivan et al. 2022a).

We are thus unable to recommend any of the thermodynamic datasets published so far for estimating the concentrations of Pd chloride complexes in hydrothermal-magmatic fluids. Based on the data from direct $PdS(s)$ and $Pd(s)$ solubility measurements as such conditions (Bazarkina et al. 2014; Sullivan et al. 2022a) as well as those extrapolated from lower temperatures (e.g., Gammons and Bloom 1993a), Pd transport as chloride complexes may only be significant (i.e. above 1–10 ppb) in acidic, sulfur-poor, and highly-saline fluids at temperatures above 400–450 °C. Therefore, to account for Pd mobilization by most types of sulfur-bearing near-neutral pH hydrothermal fluids, other types of complexes, in particular those with sulfur, are likely to be required.

*Sulfide complexes.* This type of Pd complexes has received far more limited experimental quantification than chlorides. This limitation is primarily due to intrinsically lower Pd dissolved concentrations that could be obtained in equilibrium with Pd sulfide solids, which are the stable phases in H₂S-bearing systems, in contrast to $PdO(s)$ and $Pd(s)$ commonly used in solubility studies in S-free Cl-bearing fluids discussed above. Furthermore, the Pd-S system is characterized by the existence of several sulfide phases (e.g., PdS, $Pd_4S$, $Pd_{16}S_7$) whose thermodynamic properties and the resulting stability regions are yet poorly quantified. For example, the value of the standard Gibbs energy of formation, $\Delta_Y G^0$ at 25 °C and 1 bar, of stoichiometric $PdS(s)$ varies over >15 kJ/mol in
different studies (see Bazarkina et al. 2014 for a recent compilation). This range of values corresponds to a PdS(s) solubility variation of >1.5 log units, bringing additional uncertainty to the stability constants of Pd complexes derived in different studies. However, this uncertainty is yet much smaller than that associated with the derivation of aqueous Pd-S complexes from solubility studies.

First systematic investigations of such complexes have been made by C. Gammons's and S. Wood's groups. Gammons and Bloom (1993) measured PdS(s) and PtS(s) solubility in reduced H₂S/HS⁻ solutions (pH = 0.5–8.4, 0.4–1.0 m S) from 200 to 300° C at Psat using fused silica tubes quenched at the end of experiment. Their interpretation suggests three Pd (Pd(HS)₂₀, Pd(HS)₃⁻ and Pd(HS)₄²⁻) and Pt (Pt(HS)₂₀, Pt(HS)₃⁻ and Pt(HS)₄²⁻) complexes, among which di- and trihydrosulfide would be the most abundant for both metals. However, their solubility-pH-H₂S trends were too scattered to allow robust constraints on the exact HS⁻ ligation numbers. Their study contrasts with that of Pan and Wood (1994) and Wood et al. (1994) who used H₂S/SO₄²⁻ solutions of comparable pH and sulfide concentration ranges (pH 5.9–9.4; 0.3–2.2 m S) to simultaneously measure PtS(s)/PtS₂(s) and PdS(s) solubility from 25 to 90 °C and from 200 to 350 °C at Psat using hydrothermal reactors allowing fluid sampling. The authors tentatively assumed Pd(HS)₂₀ and Pt(HS)₂₀ to be the major species. However, they failed to provide enough constraints on the stoichiometry and proposed to the reader a large choice of alternative complexes of different ligation numbers (from Pd(HS)⁺ to Pd(HS)₄²⁻ and from Pt(HS)⁺ to Pd(HS)₄²⁻) with their corresponding formation constants. Some of their tabulated constants were later identified to be in error (Pokrovski et al. 2021b). While the measured Pt and Pd concentrations in these two studies were comparable, the predicted absolute PdS(s) and PtS(s) solubility values using corrected Pan and Wood's (1994) stability constants are, however, 3 to 4 orders of magnitude higher than those from Gammons and Bloom (1993) at the same temperature and solution composition. This discrepancy has remained unresolved for more than 15 years. Tagirov and Baranova (2009) measured PdS(s) solubility in H₂S (up to 0.6 m)-NaOH-HCl solutions (2<pH<10) from 5 to 200 °C using ampoule- or batch-reactor quench-based methods. Despite a large solubility data scatter (over ~3 log units), the authors tentatively derived from the analyses of solubility trends 3 complexes, Pd(HS)₂₀, Pd(HS)₃⁻, and PdS(HS)₂²⁻, which were dominant at acidic, neutral, and alkaline pH, respectively. Their data and extrapolations to higher temperatures for Pd(HS)₂₀ appear to be strongly inconsistent with both Gammons' and Wood's works, with stability constants being from 4 to 8 log units lower, while for Pd(HS)₃⁻ discrepancies are somewhat smaller. Tagirov et al. (2013) further used their data and ligand exchange reactions with the analogous Pd-Cl species to generate a set of HKF parameters for those Pd-S complexes. However, in light of the discrepancies discussed above, their use cannot
currently be recommended. Additional caution as to the Pd-S complex stoichiometry was added by
MD calculations (Mei et al. 2015b), which predicted much lower constants (by 3 to 6 log units) for
Pd(HS)₂₀ and Pd(HS)₃⁻ and, instead, the dominant formation of Pd(HS)₄²⁻, rejected by Tagirov's
team. Very recently, Laskar (2022) and Laskar et al. (2022, 2024) reported PdS(s) and PtS(s)
solubility measurements in reduced H₂S-NaOH solutions at slightly acidic to alkaline pH with the
pyrrhotite-pyrite buffer from 50 to 300 °C and 100–500 bar. They used a flexible-cell reactor
equipped with an accurate sampling device and analytical setups allowing metal concentration
analyses down to ppb levels. The authors demonstrated the dominant formation of Pd(HS)₄²⁻ and
Pt(HS)₄²⁻ (see below), and reported a first set of HKF parameters for both complexes. The stability
constant of the Pd(HS)₄²⁻ complex derived in their work is in agreement with Mei et al.'s (2015b)
predictions, lending more credence to the high stability of the symmetrical tetra-hydrosulfide
species, rather than mixed [Pd(HS)ₙ(H₂O)₄⁻]²⁻ species that have chemically contrasting ligands (S
and O) in the metal coordination sphere. Such mixed-ligand complexes are generally expected to be
less stable, in agreement with the fundamental hard-soft relationships. Laskar (2022) further
measured PtS(s) and PdS(s) solubility in sulfate-sulfide solutions at 300 °C, 300–500 bar, and
revealed large solubility enhancements for both Pt and Pd (from ppb level in reduced H₂S solutions
to 1–10 ppm level), thereby confirming the formation of recently discovered stable complexes with
the S₃⁻ ion (Pokrovski et al. 2021b), as will be discussed below for the case of platinum.

Platinum

Platinum primarily distinguishes itself from palladium by the existence along with Pt<sup>II</sup> of another oxidation state, Pt<sup>IV</sup>. Both Pt<sup>II</sup> and Pt<sup>IV</sup> form oxide, chloride and sulfide solid phases and corresponding aqueous species within the range of terrestrial redox conditions. Divalent Pt<sup>II</sup> and its aqueous complexes and solid phases (e.g., PtS<sub>(s)</sub>) are more common in hydrothermal environments, even though Pt<sup>IV</sup>S<sub>2(s)</sub> also occurs, along with stable Pt<sup>IV</sup> complexes with hydrosulfide and polysulfide ligands, whereas Pt<sup>IV</sup>-O and Pt<sup>IV</sup>-Cl types of compounds and aqueous species are only stable in surficial oxygenated environments (e.g., see Reith et al. 2014 for a recent review). Similarly to Pd<sup>II</sup>, the great majority of Pt<sup>II</sup> aqueous complexes are square-planar, whereas those of Pt<sup>VI</sup> are octahedral (Pokrovski et al. 2021b).

The divalent Pt²⁺ cation is strongly hydrolyzed in water and may only be significant at extremely acidic negative pH (<-2.5) above which the PtOH⁺ and Pt(OH)₂⁰ complexes likely to form (Baes and Mesmer 1976; Wood 1991; Sassani and Shock, 1998). Because of the instability of Pt²⁺ in aqueous solution, published estimations of its Gibbs energy vary over more than 30 kJ/mol at ambient conditions and up to 50 kJ/mol at hydrothermal temperatures (Sassani and Shock 1998;
Tagirov et al. 2015). Like the Au⁺ ion, Pt²⁺ should be avoided in thermodynamic modeling in aqueous solution. Caution should be taken when deriving and reporting absolute values of stability constants of Pt¹¹ complexes from cumulative reactions of complex formation involving Pt²⁺ – the approach commonly used in MD theoretical studies; such data will be affected by at least the same uncertainty (see Laskar et al. 2022 for extended discussion). According to the HKF-model parameters reported by Sassani and Shock (1998), hydroxide and sulfate complexes of Pt¹¹ would represent a negligible contribution to Pt mobility in typical hydrothermal fluids, with less than 1 Pt atom per kg of water. Like for Pd and other metals overviewed above, the two major ligands for Pt considered so far in hydrothermal research are chloride and (hydro)sulfide.

**Chloride complexes.** Because of the much stronger Pt²⁺ (and Pt⁴⁺) hydrolysis, Pt¹¹ and Pt⁴⁵ chloride complexes in low-temperature aqueous solution (<100 °C) are less constrained than those of Pd¹¹. A series of PtClₙ²⁻ⁿ complexes with n from 1 to 4 has usually been considered in the chemical literature. The estimations of their formation constants from Pt²⁺ at ambient conditions, based on meagre existing data, most of them being measured at high ionic strength, are uncertain by at least 3 to 8 log units, with even greater uncertainties when extrapolated above 100 °C (see the review of Sassani and Shock 1998). Direct experimental data at hydrothermal temperatures are limited to a handful of studies. Gammons' group conducted first systematic solubility measurements of Pt(s) and AgCl(s) and in HCl-NaCl-SO₄ saline solutions to 300 °C at Pₐ₉₆ (Gammons et al. 1992; Gammons 1995, 1996). They identified PtCl₃⁻ and PtCl₄²⁻ for Pt¹¹ and PtCl₅⁻ and PtCl₆²⁻ for Pt⁴⁵ as the dominant complexes. Their results indicate that Pt⁴⁵ chlorides are restricted only to very acidic and oxidizing conditions corresponding to atmospheric O₂ pressures. Under hydrothermal conditions, Pt¹¹ chloride complexes may only be significant (> 1 ppb Pt) in unusually acidic (pH<4), highly saline (>15 wt% NaCl) and oxidizing (hematite stable) fluids. The interest for Cl complexes of Pt has therefore faded until a new generation of researchers coming with improved experimental and analytical methods. Tagirov et al. (2015) extended Gammons' data to supercritical conditions by measuring Pt(s) solubility in a narrow T range of 400–475 °C at 1 kbar, and interpreted the data as the PtCl₃⁻ complex. Based on these and some previous data the authors generated a new set of HKF parameters for Pt²⁺ and the four Pt¹¹-Cl complexes. However, in their following study of Pt(s) solubility aided by in situ XAS measurements to 575 °C and 5 kbar, Tagirov et al. (2019b) reconsidered their data in terms of the dominant PtCl₄²⁻ and proposed a density-model equation to describe, up to magmatic temperatures, the solubility constant of the reaction

$$Pt(s) + 2 HCl^{0}_{(aq)} + 2 Cl^{-} = PtCl_{4}^{2-} + H_{2}(aq) \quad (4.77)$$

Their equation reasonably matches the Pt(s) solubility data in the acidic NaCl brine phase at 800 °C in the system vapor-brine-rhyolite melt (Simon and Pettke 2009), whereas in the corresponding
vapor phase it significantly underestimates the measured solubilities, which were instead tentatively interpreted by the uncharged complex PtCl₂⁰. The tendency to form less chlorinated and less charged complexes with increasing temperature and decreasing salinity seems to be confirmed by the recent study of Sullivan et al. (2022b) who studied Pt(s) solubility as a function of NaCl (to ~30 m) and HCl (to ~3 m) concentrations in aqueous fluids at 800–1000 °C and 2 kbar and redox conditions of NNO±1. Their solubility dependences would be more consistent with PtCl₂⁰ and PtCl₃⁻ than with PtCl₄²⁻, but the absolute solubility values (10–100 ppm Pt) are also equally matched by PtCl₄²⁻ of Tagirov et al. (2019b). For comparison, older HKF predictions of Pt(s) solubility of Sassani and Shock (1998) and Tagirov et al. (2015), respectively, underestimate by 7 log units and overestimate by 4 log units the measured solubilities at the Sullivan et al. (2022b) experimental conditions. Thus, at present, Tagirov et al.’s (2019b) thermodynamic data for PtCl₄²⁻ are recommended for modeling Pt transport in saline fluids over a range of hydrothermal-magmatic conditions. The contribution of Pt-Cl complexes is very weak in the hydrothermal domain (<500 °C) being limited to oxidized, highly-saline, S-poor, and acidic conditions, but grows towards magmatic temperatures at which PtCl₂⁰ and/or PtCl₃⁻ may also contribute. Their thermodynamic quantification awaits more systematic data coupled with in situ approaches. Like for Pd, accounting for Pt mobility in sulfide-bearing, near-neutral pH and reduced hydrothermal-magmatic fluids requires the assessment of complexes with reduced sulfur ligands.

**Sulfide complexes.** Platinum sulfide (PtS(s) and PtS₂(s)) solubilities were investigated together with PdS(s) in H₂S-bearing fluids under hydrothermal conditions in early work of Gammons’ and Wood’s groups, as detailed above for the case of palladium. Whereas the measured Pt concentrations were similar in those works, the reported solubility constants for the same reactions (e.g., 4.78) presented similarly large discrepancies as for Pd-hydrosulfide complexes. It is only by the 2020s that some advance has been made towards resolution of these discrepancies. Kokh et al. (2017) used a flexible-cell reactor to measure PtS(s) solubility in supercritical H₂O-CO₂ fluids with pH and redox buffered by potassium aluminosilicate and sulfide/oxide iron mineral assemblages at 450 °C and ~700 bar (pH = 4–6, 0.02–0.06 m H₂S). The constancy of the solubility as a function of CO₂ content (up to 50 wt%) was consistent with the uncharged Pt(HS)₂⁰ complex with equilibrium concentrations of 1–2 ppb:

$$PtS_{(s)} + H_2S_{(aq)} = Pt(HS)_2^0 \qquad (4.78)$$

Such measured concentrations were, however, at least 100 times lower than those predicted by extrapolating the solubility constants for Pt(HS)₂⁰ of Pan and Wood (1994). Filimonova et al. (2021) measured PtS(s) solubility in H₂S/HS⁻ solutions (pH = 3–8, 0.01–0.2 m S) at 50–75 °C, 1 bar, and at 450 °C, 1000 bar, using batch reactors quenched at the run end. They tentatively interpreted their
data by Pt(HS)₂₀ as the dominant species, with PtS(s) solubility magnitudes matching those of Gammons and Bloom (1993) and Kokh et al. (2017). However, the ppb-level Pt concentrations found might have been subjected to significant uncertainties by the use of a quench technique that often suffers from elevated analytical backgrounds. Thus, the bulk-solubility approach alone for PGE in hydrothermal sulfur-bearing systems does not provide sufficient resolution that would allow unambiguous constraints on sulfide complex stoichiometry and stability. Very recently, Laskar et al. (2022) combined in a single study three complementary approaches – solubility measurements, in situ XAS experiments, and MD simulations – to demonstrate that the tetrahydrosulfide complex, Pt(HS)₄²⁻, is the dominant species, to at least 300 °C in H₂S-rich (0.2–2.0 m S) near-neutral to alkaline (5 ≤ pH ≤ 9) solutions. They derived a coherent set of constants of the dissolution reaction

$$PtS_{(s)} + 3 H_2S_{(aq)} = Pt(HS)_4^{2-} + 2 H^+ \quad (4.79)$$

over the temperature range 25–300 °C and pressure range Pₛₐt–600 bar, consistent with the results of the three independent methods employed. Furthermore, their MD estimations yield the solubility constants of lower-ligation number complexes, Pt(HS)₂₀ and Pt(HS)₃⁻ (analogous to reaction 4.79), to be 7 to 15 orders of magnitude lower than suggested in the previous solubility studies above. Such a difference is well beyond the errors associated with the determination of stability constants from MD, supporting the overwhelming predominance of Pt(HS)₄²⁻ over those complexes. Laskar et al. (2022) further re-analyzed Gammons’ and Wood’s solubility data in terms of Pt(HS)₄²⁻ and obtained stability constant values better matching those of logK₇₉ above thereby, at least partly, reconciling those previous data. Thus, it turns out that, similarly to Pd, the symmetrical, fully S-coordinated, tetrahydrosulfide species would be the dominant carrier of Pt at moderate temperatures in reduced sulfide-bearing hydrothermal fluids of near-neutral pH. However, in sulfur-poor fluids and at higher temperatures, lower HS⁻ ligation number complexes, such as Pt(HS)₂₀, may over compete Pt(HS)₄²⁻, as indicated by rare solubility data existing for supercritical fluids (Kokh et al. 2017; Filimonova et al. 2021). This tendency would be in line with the water dielectric constant decrease favoring ion association and uncharged or weakly charged species stability. From the other hand, the increasing ion pairing with alkalis, similar to Au and Cu chloride and hydrosulfide complexes (see above), coupled with the high species symmetry, might maintain the high stability of Pt tetrahydrosulfide up to magmatic temperatures.

It follows that PtCl₄²⁻ and Pt(HS)₄²⁻, which are the only Pt species directly evidenced by in situ spectroscopy, would be the major Pt-bearing complexes in most moderate-temperature hydrothermal fluids (<400 °C). At higher temperatures, PtCl₂₀, PtCl₃⁻, and Pt(HS)₂₀ may over compete those species, but their direct spectroscopic proof is yet lacking and more robust constraints are required on their stability constants over the large T-P range. The solubility of PtS(s) in
moderately-saline sulfur-bearing fluids of ~10 wt% NaCl equivalent and 0.1 m H₂S under redox conditions corresponding to those of the conventional Ni-NiO mineral oxygen buffer (NNO) is illustrated in Fig. 4.31a as a function of pH at 300 °C and 500 bar. The solubility is dominated by Pt(HS)₄²⁻ (thermodynamic data from Laskar et al. 2022) at moderately-acidic to alkaline pH, whereas the domain of predominance of PtCl₄²⁻ is limited to very acidic pH (pH<3). The contribution of hydroxide and sulfate complexes (Sassani and Shock 1998; not shown) is virtually negligible being <1 Pt atom per kg of fluid. The maximum solubility is attained at near-neutral pH (6–7) as Pt(HS)₄²⁻, but the total Pt dissolved concentrations remain too small (<0.1–1 ppb Pt at pH 5–7) to account for significant Pt transport in most epithermal environments. For example, such Pt dissolved concentrations would have required an amount of fluid equivalent to the global flux of water through all subduction zones operating for 1000 years (e.g., Wallace 2005) to form a modest deposit of 10 tons of Pt provided much focused fluid flow and 100% precipitation efficiency. Such a scenario would be geologically implausible. Therefore, it is unlikely that Pt-Cl or Pt-HS types of complexes may explain the multiple instances of PGE remobilization and concentration commonly observed in sulfide-dominated hydrothermal environments.

*Comparison with gold.* The behavior of PGE in hydrothermal fluids contrasts with that of gold, which is far more soluble and mobile than Pt and Pd in most epithermal systems (<300–350 °C) that host large gold deposits (10s to 100s tons). In epithermal fluids, the speciation of Au¹ is dominated by similar hydrosulfide complexes (Au(HS)₂⁻) easily attaining ppm-level concentrations (e.g., Fig. 4.30; Kouzmanov and Pokrovski 2012 and references therein), which is ~1000 times more than Pt. The chemical affinities of Pt¹¹ and Au¹ to the aqueous HS⁻ ligand compared with Cl⁻ are astonishingly similar as can be seen from the ligand exchange reactions:

$$PtCl_4^{2-} + 4 HS^{-} = Pt(HS)_4^{2-} + 4 Cl^{-} \qquad (4.80)$$

$$AuCl_2^{-} + 2 HS^{-} = Au(HS)_2^{-} + 2 Cl^{-} \qquad (4.81)$$

Their equilibrium constant values at 300 °C and 500 bar (logK₈₀ and logK₈₁ of 23.2 and 11.4, respectively), derived by combining the thermodynamic properties of Pt and Au complexes recommended in this study (Table 4.6), correspond, respectively, to 5.8 and 5.7 per HS⁻ ligand when normalized to the number of ligands in the Pt (/4) and Au (/2) complexes. Thus, the key difference between Au from one hand and Pt and Pd from the other hand in hydrothermal systems is the different solubility-controlling solid phases. The formation of poorly soluble Pt and Pd sulfide minerals is the major limiting factor for PGE mobility compared to Au whose solubility is largely controlled by the native metal. Had Pt (and Pd) metal been the stable phase in S-bearing environments, its solubility would have been comparable with that of Au metal (Fig. 4.31a). This difference in the solid-phase control of sulfur on the noble metal transport is the main cause of the
general scarcity of Pt and Pd (and by inference other PGE) compared to Au in epithermal deposits,
despite their similar Clarke values (~1 ppb) and almost identical chemical affinities for the
hydrosulfide ligand in aqueous solution.

**Comparison with base metals.** The gold and platinum affinity for HS⁻ versus Cl⁻ ligands may further be compared with that of base metals (Fe, Cu, Zn, Pb) and silver as illustrated in Fig. 4.31b in terms of symmetrical ligand exchange reactions (such as 4.68, 4.69, 4.80 and 4.81) for di-chloride and di-hydrosulfide complexes, which are the best constrained for all those metals. Two major tendencies emerge from this figure. First, the affinity of Au¹ and Pt¹¹ for HS⁻ vs Cl⁻ is almost 10 orders of magnitude greater (in terms of logK value) than that of the four base metals and silver at ambient temperature with differences slightly diminishing with temperature increase. Second, for all metals shown (note that there is only a single data point for Fe as will be discussed in the next section) the affinity for HS⁻ vs Cl⁻ systematically decreases with increasing temperature. The temperature trend directly reflects the general soft-hard metal-ligand relationships such as i) stronger soft metal (Au, Pt) - soft ligand (HS⁻) complexes and ii) weakening the stability of any soft ligand complexes in favor of harder ligand complexes with increasing temperature and thermal disorder and decreasing the water dielectric constant. As discussed in sections above, the uncertainties on the logK values are strongly temperature-dependent, with the best constrained data being around 300±50 °C. At such temperatures, the order of increasing metal affinity for reduced sulfur is the following: Cu¹≤Ag¹≈Zn¹¹≤Pb¹¹≈Fe¹¹<<Au¹≈Pt¹¹. At higher, supercritical, temperatures, the order among the base metals is more uncertain, both because of significant uncertainties on their logK values and the potential presence of higher-order chloride as well as mixed Cl-HS species as discussed above. Finally, an interesting trend with pressure can be seen for Au, which is the best studied metal as to its HS⁻ and Cl⁻ complexes. The affinity for reduced sulfur seems to slightly increase with decreasing pressure, which is also in line with greater volatility of sulfur-bearing Au and Pt complexes in the vapor phase (Pokrovski et al. 2013a), which is beyond the scope of this chapter. Among the considered metals, data for Pt¹¹ hydrosulfide complexes remain the least constrained to date; however, even within their large uncertainties, PGE sulfide solubilities as sulfide and chloride complexes appear to be negligibly small in typical hydrothermal fluids.

*Complexes with the trisulfur radical ion.* To account for Pt and Pd mobility in hydrothermal fluids, complexes with ligands other than HS⁻ or Cl⁻ would be required. The most plausible one is the trisulfur radical ion, stable in a wide range of temperature and capable of forming stable complexes with Au¹ (see section 4.4.4.) The first recognition of the role of the S₃⁺⁻ ion in PGE transport came from a recent study of Pokrovski et al. (2021b) who measured PtS₈ solubility in sulfate-sulfide solutions containing significant concentrations of S₃⁺⁻ within a narrow T-P and S
concentration range (275–300 °C, 500–700 bar, 1–2 m S), using different types of hydrothermal reactors (both quench- and sampling-based) and in situ X-ray absorption spectroscopy, coupled with quantum chemical modeling of the species structures and XANES spectra. Their data show that the presence of S₃⁻ enhances Pt solubility by 3 to 5 log units compared to H₂S-dominated solutions of similar sulfur concentrations (Laskar et al. 2022), due to the formation of mixed HS⁻/S₃⁻ complexes with both Pt¹¹ and Pt⁴⁻ according to the reactions

$$PtS_{(s)} + H_2S_{(aq)} + 2 S_3^{\cdot -} = Pt^{II}(HS)_2(S_3)_2^{2-} \quad (4.82)$$

$$PtS_{(s)} + 2 H_2S_{(aq)} + 2 S_3^{\cdot -} + H^+ + 0.5 O_{2(g)} = Pt^{IV}(HS)_3(H_2O)(S_3)_2^{\cdot -} \quad (4.83)$$

Laskar (2022) further confirmed the reaction (4.82) stoichiometry and equilibrium constant by additional solubility measurements at 300 °C. He reported an analogous complex for Pd with a similar stability constant value. The stability constants of reactions (4.82) and (4.83) enable predictions of Pt solubility in epithermal fluids as illustrated in Fig. 4.32. The solubility enhancement due to the formation of these complexes, apparent in this figure at sulfur concentrations above 0.1 wt% (Fig. 4.32a), fO₂ around the sulfate-sulfide transition (≈ HM±1; Fig. 4.32b) in the acidic-to-neutral pH range (Fig. 4.32c), appears to be much stronger than for Au¹ (Fig. 4.32d). Indeed, the ligand exchange reaction

$$Pt(HS)_4^{2-} + 2 S_3^{\cdot -} = Pt(HS)_2(S_3)_2^{2-} + 2 HS^{-} \quad (4.84)$$

has a K value of ~10,000 as calculated by combining the data of Pokrovski et al. (2021b) and Laskar et al. (2022), whereas the corresponding value for an analogous Au¹ exchange reaction (4.76) is 1. An equally high value was obtained by Laskar (2022) for the Pd¹¹ exchange reaction analogous to reaction (4.84). The much higher affinity of S₃⁻ than HS⁻ both for Pd¹¹ and Pt¹¹ is likely due to a combination of the PGE unfilled valence electron shells (4d⁸ and 5d⁸, respectively) and 4-coordinated Pd¹¹ and Pt¹¹ (as well as 6-coordinated for Pt⁴⁻) geometries, both offering more flexibility for binding with S₃⁻, compared with Au¹ that has its 5d shell filled (5d¹⁰) and almost exclusively linear coordination geometries.

The discovery of stable Pd and Pt complexes with the trisulfur ion might provide a plausible explanation for PGE enrichment cases observed in sulfide-dominated hydrothermal environments. It further emphasizes the potential role of aqueous S-bearing fluids in PGE magmatic deposit formation. This role would be consistent with the growing abundance of both S₃⁻ and S₂⁻ in magmatic-derived fluids (Figs. 20, 21). Selective complexing by the radical ions of Pt and Pd, compared to the other more refractory and less chalcophile PGE (Ru, Rh, Ir, Os), may induce fluid-mineral fractionations affecting PGE elemental and isotope signatures in mantle-derived rocks widely used as tracers of core-mantle evolution (Kiseeva et al. 2025 and references therein). The highly soluble S₃⁻ complexes with both Pd and Pt may open new routes for hydrothermal synthesis
of PGE-based nanomaterials as well as PGE ore processing. There is thus an urgent need to extend
these first findings over the wider hydrothermal-magmatic *T-P* range via more systematic studies
of PGE interactions with the sulfur radical ions.

4.4.6 Iron

Iron holds a particular place in metal-sulfur interactions as pyrite (FeS₂) is by far the most
abundant metal sulfide mineral in the Earth's crust. However, Fe-S relationships in the fluid phase
are quite different. Both FeII and FeIII oxidation states coexist in natural fluids and minerals, with
FeIII being thermodynamically stable in oxygenated Earth's surface environments. Increasing
temperature and depth generally makes FeII more abundant both in solid and fluid phases, but FeIII
still remains an important redox form in a wide range of oxygen fugacity, as manifested by
ubiquitous coexistence of both redox states in mineral assemblages (e.g., magnetite-hematite-pyrite,
with equilibrium fO₂ ~10⁻³⁰ bar at 300 °C), and by the presence of both FeII and FeIII in major silicate
minerals (e.g., serpentinite, garnet) and silicate glasses over a wide T-P-fO₂ range of metamorphic
and magmatic conditions. In sulfide-dominated aquatic environments, both near-surface and
hydrothermal, pyrite is notoriously stable, being transformed to pyrrhotite when going towards
magmatic and high-metamorphic (amphibolite facies) conditions. In aqueous solution, the Fe²⁺
cation is dominant to pH~9, whereas Fe³⁺, being chemically "harder", is hydrolyzed at pH>2 (Baes
and Mesmer 1976). Both cations form hydroxide and/or organic ligand complexes and sulfide
clusters in near surface aquatic environments, but in hydrothermal fluids their speciation is very
different. Both FeII and FeIII hydroxide species domains greatly widen with increasing temperature
at the expense of the cations. These species are reasonably well constrained to at least 350 °C by
solubility and spectroscopic experiments (e.g., Sweeton and Baes 1970; Tremaine and Leblanc
1980; Diakonov et al. 1999; Stefánsson and Seward 2008; references therein) and thermodynamic
predictions (Shock et al. 1997). Discrepancies among the stability constant values for the given
[Fe(OH)n] complex in different studies typically amount 1–3 log units.

Irrespective to the exact *K* values, the solubilities of iron oxides as hydroxide complexes are quite low in typical hydrothermal fluids (≤ ppm levels of Fe). The major Fe carrier is believed to be chloride. In near-ambient aqueous solution, both FeII and FeIII are known to form at least 4 chloride complexes, from mono- to tetrachloride. Yet, there are large discrepancies as to their stability and composition in hydrothermal fluids, despite a large amount of work on FeII-chloride complexation. Similarly to other base metals such as Zn and Pb (see above), most available solubility work tends to converge to the dominant presence of dichloride species stoichiometries, FeCl₂⁰, over a wide salinity range (see Wood and Samson 1998; Sverjensky et al. 1997; Simon et al. 2004; Testemale
et al. 2009; Saunier et al. 2011; references therein). In contrast, spectroscopy-based approaches
(UV-Vis, XAS and Raman) tend to favor higher-order, $FeCl_4^{2-}$ (and/or $FeCl_3^-$) species at similar
fluid salinities (Liu et al. 2006; Testemale et al. 2009; Scholten et al. 2019). Recent hematite and
pyrite solubility measurements at supercritical temperatures (e.g., Simon et al. 2004; Saunier et al.
2011; Syverson et al. 2013; Pokrovski et al. 2021c) are well accounted for by the predictions using
the thermodynamic properties of $FeCl_2^0$ available within the HKF model (Sverjensky et al. 1997).
In contrast, those of $FeCl_4^{2-}$ (Testemale et al. 2009) lead to significant overestimations of the
solubility results. Other recent solubility experiments also show $Fe^{II}$ dichloride to be the major
complex in low-density hydrothermal vapors and supercritical fluids (400–500 °C, $\rho<0.3$ g/cm$^3$)
produced by seawater boiling and fluid unmixing in active geothermal systems of mid-ocean ridges
(Xing et al. 2021). Therefore, higher-order $Fe^{II}$ chloride complexes still await more in-depth
experimental and thermodynamic efforts to be considered in quantitative modeling of iron transport
by hydrothermal-magmatic fluids.

Data on Fe<sup>III</sup> chloride species are less abundant under hydrothermal conditions. A handful
of solubility and spectroscopic studies (Liu et al. 2006; Saunier et al. 2011; Stefánsson et al. 2019;
Gammons and Allin 2022) demonstrates the dominant formation of Fe<sup>III</sup>Cl<sub>3</sub><sup>0</sup> and Fe<sup>III</sup>Cl<sub>4</sub><sup>-</sup> at
oxidizing conditions (hematite stable). However, the numerical thermodynamic data for those
complexes available so far are too disparate or available within too narrow temperature ranges to
allow reliable predictions of Fe(III) abundance at hydrothermal-magmatic conditions. For example,
the reported solubility constants of hematite with formation of the FeCl<sub>4</sub><sup>-</sup> complex differ as much
as 10 log units at 300 °C (e.g., Stefánsson et al. 2019 vs Gammons and Allin 2022). Given the
growing recognition that subduction-zone fluids may be quite oxidized, with f<sub>O2</sub> values sometimes
above that of the HM buffer (e.g., Debret et al. 2016; Debret and Sverjensky 2017; Pokrovski et al.
2022a; Schwarzenbach and Evans 2025; references therein), it is likely that Fe<sup>III</sup> chloride, and
possibly sulfate, complexes might be the major carriers of Fe in deep subduction zones.

Stable Fe<sup>II</sup>-(hydro)sulfide complexes are known at near-ambient conditions in the presence
of reduced sulfur, such as FeHS<sup>+</sup>, along with a number of polynuclear hydrosulfide (e.g., Fe<sub>3</sub>(HS)<sub>5</sub><sup>+</sup>),
polysulfide (e.g., FeS<sub>5</sub><sup>0</sup>, Fe<sub>2</sub>(S<sub>5</sub>)<sub>2</sub><sup>2+</sup>), and sulfide (Fe<sub>x</sub>S<sub>x</sub>, conventionally expressed as FeS<sup>0</sup>) clusters,
for which tentative stability constant values at ambient conditions and high ionic strength have been
reported in few studies (see Rickard and Luther 2006, 2007 for extensive reviews). Precursors of
[Fe<sub>x</sub>S<sub>y</sub>]-like stoichiometries, with short-range structures resembling those of mackinawite (FeS<sub>m</sub>) or
troilite (FeS), have traditionally been assumed to operate over a wide temperature range, from
ambient up to at least 300 °C during pyrite and marcasite precipitation (e.g., Murowchick and Barnes
1986; Schoonen and Barnes 1991; Graham and Ohmoto 1994). At moderate temperature conditions
(<100 °C), the formation of pyrite has commonly been regarded to occur via two possible mechanisms, by reaction of soluble FeS precursors either with H₂S or with polysulfide dianions, Sₙ²⁻ (Rickard and Luther 2007 for details). However, few constraints on the mechanisms of pyrite formation are available at hydrothermal temperatures, since very few data exist on Fe-S aqueous speciation at such conditions. By analogy with other metals overviewed above, monomeric Fe(HS)ₙ²⁻ complexes would be expected to predominate at elevated temperatures both because of the increasing thermal disorder destabilizing polymeric species more common at ambient conditions, and very low equilibrium concentrations of polysulfide dianions themselves (e.g., Fig. 4.29). Equilibrium constants for FeHS⁺ have only been reported at ambient conditions in seawater (as compiled in Rickard and Luther 2006, 2007) with values of logK ≈ 4–6 of the reaction

$$Fe^{2+} + HS^{-} = FeHS^{+} \qquad (4.85)$$

These values compare favorably with those of the analogous CoHS⁺ species deduced from CoS(s) solubility experiments by Migdisov et al. (2011), with logK ≈ 5.8–6.5 in the temperature range 25–300 °C for the reaction analogous to (4.85). Higher-order Fe-HS species, such as Fe(HS)₂₀ and Fe(HS)₃⁻, were invoked in some low-temperature studies, but their stoichiometry remains tentative. Recently, Laskar (2022) conducted exploratory pyrite solubility experiments in NaHS-HCl-NaOH solutions (0.6 m S) at 300 °C and 500 bar and found that Fe(HS)₂₀, with a logK value of 11±1 for the reaction

$$Fe^{2+} + 2 HS^{-} = Fe(HS)_{2}^{0} \qquad (4.86)$$

would account for the measured FeS₂(s) solubility in a wide pH range (4–8), with Fe concentrations (10⁻⁵ to 10⁻⁴ m) being 2 to 6 orders of magnitude higher at the experimental solution compositions than those of the known Fe chloride and hydroxide complexes discussed above. Reaction (4.86) constant, combined with the thermodynamic data of FeCl₂⁰ from Sverjensky et al. (1997), translates to logK of ~7.5 for the HS⁻ vs Cl⁻ ligand exchange reaction

$$FeCl_{2}^{0} + 2 HS^{-} = Fe(HS)_{2}^{0} + 2 Cl^{-} \qquad (4.87)$$

This value is comparable with those for analogous exchange reactions (4.68) and (4.69) for Zn and Pb (logKZn,Pb ≈ 6–8 at 300 °C). Therefore the Fe hydrosulfide complexes may be comparable in abundance with Fe chlorides in moderate-temperature and moderate-salinity hydrothermal fluids with Cl/S ratios of 1000.

Experiments of Laskar (2022) in sulfide-sulfate solutions revealed further enhancement of pyrite solubility (up to 10⁻³–10⁻² m Fe) compared to sulfide solutions of similar S concentration and pH. This solubility increase was tentatively interpreted by a complex with the S₃⁺ ion, Fe(HS)S₃⁰, with a logK value of ~2.7 at 300 °C and 500 bar for the ligand exchange reaction:

$$Fe(HS)_{2}^{0} + S_{3}^{\cdot -} = Fe(HS)_{2}^{0} + HS^{-} \qquad (4.88)$$
These, yet exploratory, data indicate that the affinity of Fe<sup>II</sup> for S<sub>3</sub><sup>•−</sup> may be greater than for HS<sup>−</sup>, in line with the other transition metals such as Pt and Pd as was discussed above.

This first experimental evidence for [Fe-HS-S<sub>3</sub>] complexes implies that such species may play a role in pyrite formation mechanisms and control Fe isotope exchange kinetics between pyrite and hydrothermal fluid. Pokrovski et al. (2021c) performed in situ pyrite precipitation experiments at 400–450 °C in saline hydrothermal fluids, along with analyses of Fe isotopes in both fluid and mineral combined with DFT quantum-chemistry calculations of electronic and molecular structures of [Fe-HS-S<sub>3</sub>]-type complexes of different stoichiometry and their corresponding β-factors (see Eldridge et al. 2025 for isotopic definitions). Such transient complexes (e.g., Fe(HS)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub><sup>0</sup>, Fe(HS)<sub>2</sub>(S<sub>3</sub>)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub><sup>2−</sup>) may account for the observed kinetic isotope fractionation experiments between the fluid and precipitating pyrite. Using their data along with those from recent Fe isotope fractionation studies during pyrite precipitation at lower temperatures (300–350 °C, Syverson et al. 2013, 2015), Pokrovski et al. (2021c) developed a two-stage kinetic model (Fig. 4.33) accounting for non-equilibrium Fe isotope signatures commonly observed in pyrite vs fluid from submarine hydrothermal vents. The model may further enable estimating, using Fe isotope signatures, the dynamic of relatively short (<year-scale) mineralizing events in ancient hydrothermal metal sulfide deposits that cannot be assessed using more traditional dating approaches. Thus, (poly)sulfide complexes may open new doors to our quantitative understanding of both transfer and precipitation of a number of metals in hydrothermal fluids.

Finally, another interesting facet of the Fe-S relationships recently emerged for magmatic conditions (they are covered in detail by Simon and Wilke 2025). In addition to chemical transport of sulfur and metals as dissolved complexes, recent experimental and modeling work showed that iron sulfide melt micro particles (FeS), which are primary hosts of chalcophile metals (Cu, Au, Mo, PGE) in arc magmas, may physically be transported by magmas. This transport may be possible particularly for small particles whose sinking velocity (governed by Stokes’ law) is slower than the magma ascent rate (Heinrich and Connolly 2022). Vapor nucleation in magmas at shallow depth may further promote sulfide upward transport and concentration, by flotation of sulfide melt on vapor bubbles (Mungall et al. 2020; Iacomo-Marziano et al. 2022). This mechanism provides additional potential for metal mobilization and concentration prior or during fluid degassing and subsequent metal transport as chemically dissolved complexes to magmatic-hydrothermal ore deposits.

### 4.4.7 Arsenic
Arsenic is distinguished from the base and noble metals discussed above by i) a much larger range of oxidation states under natural conditions, spanning from arsenide (–III to 0) to arsenite (III) and arsenate (V) in the solid phase, and ii) distinct aqueous speciation largely dominated by As<sup>III</sup> and As<sup>V</sup> oxyhydroxide species.

For As<sup>III</sup>, arsenious acid, As(OH)<sub>3</sub><sup>0</sup>, and its first deprotonated counterpart (AsO(OH)<sub>2</sub><sup>-</sup>, at pH >8–9) are the major forms in aqueous solution, but oxy-hydrosulfide and other thionate species may also be abundant at certain conditions (see below). In its species, As<sup>III</sup> is almost exclusively tri-pyramidal coordinated with O(H) or S(H) ligands, with a non-bonding lone electron pair (4s<sup>2</sup>) occupying a fourth summit of the distorted tetrahedron, as imposed by 4s<sup>2</sup>4p<sup>3</sup> hybridization of outer electron orbitals. There is an apparent ambiguity in some thermodynamic databases, by expressing the stoichiometry of As<sup>III</sup> oxyhydroxide species as HAsO<sub>2</sub><sup>0</sup> and AsO<sub>2</sub><sup>-</sup> (e.g., Shock et al. 1997) vs As(OH)<sub>4</sub><sup>-</sup> (Baes and Mesmer 1976). They differ from the more structurally correct formula above by one H<sub>2</sub>O molecule and are based on the convention that the thermodynamic properties of hydration reaction such as HAsO<sub>2</sub><sup>0</sup> + H<sub>2</sub>O = As(OH)<sub>3</sub><sup>0</sup>, are equal to zero at any temperature and pressure. Therefore, this choice has no impact on the complexation or solubility constants involving such species in water-dominated fluids in which H<sub>2</sub>O activity is close to 1. These stoichiometry differences might, however, become meaningful in fluids of water activity distinctly less than 1 (e.g., in carbonic fluids) or in low-density water vapors. However, a number of Raman and X-ray absorption spectroscopy and solubility studies has convincingly shown that As<sup>III</sup> keeps a As(OH)<sub>3</sub><sup>0</sup> stoichiometry across a very wide range of water activity and fluid density (e.g., Pokrovski et al. 1999, 2002a, 2013a). Neither cationic As<sup>III</sup> hydroxide species, nor As<sup>III</sup> chloride complexes are known in aqueous solution of pH>0 (Baes and Mesmer 1976; Nordstrom et al. 2014). The dissociation constant of As(OH)<sub>3</sub><sup>0</sup> to AsO(OH)<sub>2</sub><sup>-</sup> is well constrained at <100 °C. In contrast, at higher temperatures, unexplained discrepancies yet persist between, from one hand, potentiometric measurements (Pokrovski, 1996) supported by independent theoretical predictions (Shock et al. 1997; Smith et al. 1998), and, from the other hand, UV-spectroscopy measurements (Zakaznova-Herzog et al. 2006a). The differences attain 1.5–2.0 log units at 300 °C, meaning that the arsenite anion would be dominant at pH>7 according to the latter work, instead of pH>8–9 as per the earlier studies.

Pentavalent As<sup>V</sup>, stable in surficial oxygenated environments, displays a stronger affinity to oxygen or hydroxyl ligands than As<sup>III</sup>, with a series of tetrahedrally coordinated oxyhydroxide species of arsenic acid, AsO(OH)<sub>3</sub><sup>0</sup>, AsO<sub>2</sub>(OH)<sub>2</sub><sup>-</sup>, AsO<sub>3</sub>(OH)<sub>2</sub><sup>-</sup>, and AsO<sub>4</sub><sup>3-</sup>, subsequently dominating from pH<2 to pH>11 at ambient conditions – a dissociation pattern very similar to that of phosphoric acid (H<sub>3</sub>PO<sub>4</sub>=(HO)<sub>3</sub>PO). Their dissociation constants were measured only up to 95
°C (Zhu et al. 2016 and references therein). These data may be extrapolated with reasonable confidence to temperatures of ~300 °C using the HKF model (Shock and Helgeson 1988 as revised by Shock et al. 1997) that proved itself to be robust for dissociation constants (see section 4.3.3).

Further extension of the HKF model prediction reliability for both As<sup>III</sup> and As<sup>V</sup> species has been enabled by direct in situ measurements of heat capacity and volume of arsenic and arsenious acids to 350 °C and 300 bar (Perfetti et al. 2008). These data provided further constraints on the HKF-model coefficients for both As(OH)<sub>3</sub><sup>0</sup> and AsO(OH)<sub>3</sub><sup>0</sup>. Coupled with solubility measurements of arsenopyrite to 450 °C (Pokrovski et al. 2002b) and available calorimetric data for iron sulfarsenide phases, Perfetti et al. (2008) generated a consistent set of thermodynamic properties in the system FeAs<sub>(s)</sub>-FeAs<sub>2(s)</sub>-FeAsS<sub>(s)</sub>-As(OH)<sub>3</sub><sup>0</sup><sub>(aq)</sub>. These properties were used by Xing et al. (2019) to propose a first quantitative thermodynamic model of arsenic solid solution in arsenian pyrite, Fe(As,S)<sub>2</sub>, which is a common host of arsenic in sediment-hosted, epithermal, and orogenic gold deposits. These data allow predictions of arsenic transport in high-temperature hydrothermal fluids (300–500 °C) that is mainly controlled by arsenian pyrite and arsenopyrite. The predicted As(OH)<sub>3</sub><sup>0</sup> concentrations (10–100 ppm As) are in good agreement with analyses of natural fluid inclusions from Cu-W-Sn-As magmatic-hydrothermal deposits (Pokrovski et al. 2002b). In lower temperature epithermal environments (<200 °C), arsenic sulfides, such as orpiment (As<sub>2</sub>S<sub>3</sub>) and realgar (AsS), become the As solubility controlling phases (Pokrovski et al. 1996). Less certainty as to the exact As speciation and redox exists at present for higher T-P fluids (>500 °C and 2 kbar). Extrapolations of the As<sup>V</sup> oxyhydroxide species thermodynamic data to magmatic and deep-metamorphic conditions indicate that As<sup>V</sup> oxyhydroxide complexes might over compete As<sup>III</sup> complexes only in extremely oxidizing fluids of f<sub>O2</sub>~QFM+10. Such fluids may be released during out-of-equilibrium serpentinite breakdown in deep subduction-zone settings (Pokrovski et al. 2022a; references therein).

The major role of sulfur in arsenic fate in high-temperature hydrothermal fluids is thus mostly to control the solubility of arsenic sulfide and iron sulfarsenide minerals rather than to directly complex arsenic, which stays as As(OH)<sub>3</sub><sup>0</sup> both in the fluid and vapor phases and hydrous silicate melts (Pokrovski et al. 2005b, 2008a; Borisova et al. 2010). In contrast, at lower temperatures (<200–300 °C), sulfide complexation becomes increasingly important. There exists a plethora of experimental solubility, potentiometric and spectroscopic studies at temperatures <150 °C, thoroughly reviewed by Wood and Samson (1998) and Rickard and Luther (2006). These data show extremely variable [As<sup>III</sup>-S]-type complexes stoichiometries, spanning from trimeric species with As-S-As bonds (e.g., H<sub>2</sub>As<sub>3</sub>S<sub>6</sub><sup>-</sup> or more structurally correct As<sub>3</sub>S<sub>4</sub>(SH)<sub>2</sub><sup>-</sup>, e.g., Spycher and Reed 1989; Helz et al. 1995) to a series of monomeric complexes (e.g., As(SH)<sub>3</sub><sup>0</sup>, AsS(SH)<sub>2</sub><sup>-</sup>,
$AsS_2(SH)^{2-}$ and $AsS_3^{3-}$, see Zakaznova-Herzog and Seward 2012 for a recent compilation of available references), along with mixed [As-(O(H),S)$_3$]-type species (e.g., $As(OH)_2(SH)^0$, $As(OH)S_2^-$, e.g., Wilkin et al. 2003; Bostick et al. 2005; Beak et al. 2008), depending on As concentration, As/S ratio, pH, and saturation degree with As sulfide phases ($As_2S_3$). These experimental findings have inspired both static DFT and MD computational studies of structures and energetics of selected As-S species (e.g., Tossell and Zimmermann 2008; He et al. 2017). However, until now, no consensus has been reached on the species nature and stability and there is no reliable estimation of their stability constants at hydrothermal conditions. Recent analyses of thioarsenates and thioarsenites in natural geothermal waters (see section 4.4.12) point to transient out-of-equilibrium nature of such species. They may play a role of precursors during the formation of arsenic sulfide minerals, as well as of potential ligands for selectively complexing some chalcophile metals (e.g., Au, Ag, Cu) — the hypotheses that still require experimental and spectroscopic confirmation for hydrothermal fluid conditions.

### 4.4.8 Antimony

Antimony is quite similar to arsenic, both in redox and speciation, with a range of antimonide, sulfide and oxide minerals with Sb nominal oxidation states from –III to V, and major aqueous species as $Sb^{III}$ and $Sb^V$ oxyhydroxides in dilute aqueous solution. However, the major differences with As are i) generally lower solubility of the analogous Sb solid phases in aqueous solution, ii) different coordination and electronic structure of $Sb^{III}$ and $Sb^V$ species, and iii) greater affinity of $Sb^{III}$ to chloride.

Pentavalent $Sb^V$ is stable in oxygenated near-surface waters as octahedrally-coordinated species $Sb(H_2O)(OH)_5^{0-}$ dominant at acidic pH and deprotonating to $Sb(OH)_6^{2-}$ at pH>3 (Tella and Pokrovski 2012 and references therein). The octahedral coordination, enabled by the empty 4d shell of Sb, is sterically favorable for the formation of chelate complexes of 5- and 6-membered rings with oxygen-bearing organic ligands such as fulvic and humic acids in surficial environments. This specific coordination control makes $Sb^V$ different from $As^V$ whose tetrahedral $[AsO_4]^{2-}$ coordination does not allow formation of stable complexes with di-functional organic ligands (Pokrovski and Schott 1998; Tella and Pokrovski 2012). Similarly to $As^{III}$, trivalent $Sb^{III}$, which is stable at hydrothermal conditions, forms oxyhydroxide complexes, with trigonal-pyramidal $Sb(OH)_3^{0-}$ (sometimes expressed as $HSbO_2^{0-}$) being dominant in the pH range from ~2 to ~12 at ambient temperatures (Baes and Mesmer 1976; Zakaznova-Herzog and Seward 2006b). In more acidic and more alkaline solutions, respectively, cationic ($Sb(OH)_2^{+}$ or $H_4SbO_3^{+}$) and anionic counterparts, with variable expressions of their stoichiometry by addition or subtraction of water molecules
(Sb(OH)₄⁻, H₂SbO₃⁻ or SbO₂⁻), become dominant; however, more recent in situ XAS measurements demonstrated that the true SbIII coordinations in solution are distorted fourfold configuration with O(H) ligands, Sb(OH)₂(H₂O)₂⁺ and Sb(OH)₄⁻, respectively (Tella and Pokrovski 2009). In contrast with AsIII, which always remains trifold, such fourfold coordinations have much less steric constraints for the formation of organic chelate species in natural waters (Tella and Pokrovski 2009). At near-ambient conditions, SbIII is known to form complexes with chloride in strongly acidic and with (hydro)sulfide in neutral-to-alkaline solutions, but no consensus about the dominant stoichiometry and stability constant values has ever been reached, as reviewed in detail by Filella and May (2003) and Rickard and Luther (2006).

Under hydrothermal conditions, SbIII appears to be more speciation-versatile than AsIII, by forming oxyhydroxide, sulfide and chloride complexes. Trihydroxide, Sb(OH)₃⁰, stands out as the major species at elevated temperatures. Paradoxically, its domain of predominance in pH space narrows down with increasing temperature according to rare available data (e.g., 2<pH<12 at 25 °C vs 3<pH<9 at 300 °C; Zakaznova-Herzog and Seward 2006b). This behavior is, however, in apparent disagreement with the general tendency of strengthening hydrolysis and favoring the stability of uncharged species; it was not supported by other earlier data, showing Sb(OH)₂⁺ predominance field to be retracted towards more acidic pH with increasing temperature (Popova et al. 1975). More in situ data are required to resolve these discrepancies. It may not be excluded that changes in the SbIII coordination in acidic and alkaline solutions with temperature might partly be responsible for such hydrolysis pattern.

The thermodynamic properties of Sb(OH)₃⁰, dominant within the typical hydrothermal fluid pH range, have thoroughly been constrained by extensive Sb₂O₃(s), Sb(s) and Sb₂S₃(s) solubility works to supercritical conditions (450 °C, 1 kbar) by Zotov et al. (2003). The HKF-model dataset derived using their own data and those from some previous studies (see Wood and Samson 1998), is recommended for modeling antimony solubility and transport at elevated temperatures, which is mainly controlled by the reaction

$$0.5 \text{ Sb}_2\text{S}_3\text{(s)} + 3 \text{H}_2\text{O} = \text{Sb(OH)}_3^0 + 1.5 \text{H}_2\text{S}_{\text{(aq)}} \quad (4.89)$$

The HKF model predictions of Zotov et al. (2003) were further supported by recent solubility studies of Sb₂S₃(s) in sulfide-bearing solutions that reported similar K₈₉ values between 200 and 350 °C (within <0.5 log units; Olsen et al. 2018, 2019). By contrast, the old HKF values of HSbO₂⁰ (Shock et al. 1997) based on low-temperature data underestimate Sb₂S₃(s) solubilities up to 4 orders of magnitude above 300 °C (Fig. 4.34); they thus require to be updated in commonly used databases (e.g., SUPCRTBL).
Unlike arsenic, Sb<sup>III</sup>, having a more metallic character, forms different chloride and oxychloride complexes in acidic saline solutions both at ambient (e.g., Filella and May 2003 for a review) and hydrothermal conditions. The latter have been explored by solubility, XAS and Raman spectroscopy studies (e.g., Oelkers et al. 1998; Ovchinnikov et al. 1982; Pokrovski et al. 2006; Persaud 2022). They reveal SbCl<sub>3</sub><sup>0</sup>, SbCl<sub>4</sub><sup>-</sup>, and SbCl<sub>6</sub><sup>3-</sup> in concentrated HCl solutions (>1 m HCl), and Sb(OH)<sub>2</sub>Cl<sup>0</sup> and Sb(OH)<sub>3</sub>Cl<sup>-</sup> in less acidic, and thus more geologically relevant, fluids (pH>2). The formation constants of those species were reported within rather narrow T ranges or were limited in some studies to exchange reactions between different Sb-Cl complexes with no systematic referencing to the key species Sb(OH)<sub>3</sub><sup>0</sup> or Sb solid phases to be applicable to natural fluids (e.g., Persaud 2022). The rare geologically relevant available data indicate that Sb(OH)<sub>3</sub>Cl<sup>-</sup> may compete with Sb(OH)<sub>3</sub><sup>0</sup> in saline near-neutral pH solutions above 300 °C and 5-10 wt% NaCl (Pokrovski et al. 2006), but more data over larger T and salinity ranges are required. The uncharged oxychloride Sb(OH)<sub>2</sub>Cl<sup>0</sup> and trichloride SbCl<sub>3</sub><sup>0</sup> have been shown to be more volatile than the other Sb<sup>III</sup> species discussed above, and therefore responsible for enhanced Sb partitioning into the vapor phase in acidic vapor-brine systems (Pokrovski et al. 2008b), in contrast to As<sup>III</sup> partitioning, which is unaffected by the presence of HCl (Pokrovski et al. 2005b). This contrasting vapor-liquid fractionation pattern between As<sup>III</sup> and Sb<sup>III</sup> may help tracing the acidity conditions operating in magmatic-hydrothermal systems using the As/Sb ratios in coexisting vapor and brine fluid inclusions.

Like for arsenic, the role of sulfur in Sb behavior in geological fluids remains the least constrained, mainly due to the notorious difficulties of experimenting and measuring in sulfur-bearing aqueous systems in general, along with the low solubility of the thermodynamically stable Sb<sub>2</sub>S<sub>3</sub>(s) solid thereby posing analytical challenges. A plethora of different Sb-S-OH complexes, both monomeric and dimeric having Sb-S-Sb bonds, has tentatively been proposed at low temperatures, with caution that more polymerized species may equally exist due to a strong tendency of Sb<sup>III</sup>, similar to As<sup>III</sup>, of forming colloidal solutions in sulfide systems (Krupp 1988; Rickard and Luther 2006). At hydrothermal conditions, only a few theoretical and experimental studies are available that reported both stoichiometry and stability constants (see Wood and Samson 1998 and Olsen et al. 2019 for more detailed comparisons). A theoretical attempt has been made by Spycher and Reed (1989) who critically re-evaluated available experimental data on Sb and As sulfide systems and suggested a first systematic set of solubility constants of Sb<sub>2</sub>S<sub>3</sub>(s) to 300 °C, with the dominant formation of H<sub>2</sub>Sb<sub>2</sub>S<sub>4</sub><sup>0</sup>, HSb<sub>2</sub>S<sub>4</sub><sup>-</sup> and Sb<sub>2</sub>S<sub>4</sub><sup>2-</sup> complexes in acidic (pH<3), near-neutral (4<pH<8) and alkaline (pH>9) solutions, respectively

$$Sb_2S_{3(s)} + HS^- + n-1 H^+ = H_nSb_2S_4^{n-2}, n = 0, 1, \text{ and } 2 \quad (4.90)$$
An analogous pH-dependent scheme with three trimeric complexes was suggested for As<sup>III</sup> (section 4.4.7). The Spycher and Reed (1989) evaluation of existing experimental studies was, however, criticized by Krupp concerning different aspects in the tough business of extracting species stoichiometries and equilibrium constants. Such a debate that has seen two comments-replies (Krupp 1990a,b; Spycher and Reed 1990a,b) remains a rare example in sulfur hydrothermal research. Krupp (1988) Sb<sub>2</sub>S<sub>3</sub>(s) solubility measurements from 25 to 350 °C represent a remarkable experimental study of the last century in the metal-sulfur speciation topic. His work reported the same three dimeric sulfide species as above, but with stability constants of reaction (4.90) being lower as much as 2 log units for the most geologically relevant HSb<sub>2</sub>S<sub>4</sub><sup>-</sup> complex. In addition to those sulfide complexes, Krupp (1988) suggested the formation of a hydroxysulfide species, Sb<sub>2</sub>S<sub>2</sub>(OH)<sub>2</sub><sup>0</sup>, that became increasingly dominant over the sulfide species in acidic-to-neutral pH above 200 °C. More discrepancy has been added by another theoretical evaluation of some selected available studies by Russian teams (Akinfiev et al. 1993, as cited in Zotov et al. 1995) that reported a set of HKF coefficients for the three Sb sulfide complexes above. Their study ignores, however, Krupp's mixed species and yields K<sub>90</sub> values for HSb<sub>2</sub>S<sub>4</sub><sup>-</sup> of 1 to 3 log units lower than those of Krupp (1988). The issue of Sb-S complexation in hydrothermal fluids has remained without any advance for more than 25 years, until recent solubility works of a New Zealand team (Olsen et al. 2018, 2019). They conducted systematic Sb<sub>2</sub>S<sub>3</sub>(s) solubility measurements in NaOH-H<sub>2</sub>S solutions over the 30-400 °C range from P<sub>sat</sub> to 300 bar using a flow-through reactor along with Sb K-edge XAS measurements at 30 °C. Their proposed speciation scheme at 30 °C remains quite complex, with at least 5 species, H<sub>3</sub>SbS<sub>2</sub>O<sup>0</sup>, HSb<sub>2</sub>S<sub>4</sub><sup>-</sup>, H<sub>2</sub>Sb<sub>2</sub>S<sub>5</sub><sup>2-</sup>, Sb(OH)<sub>3</sub><sup>0</sup> and Sb<sub>2</sub>S<sub>4</sub><sup>2-</sup>, from pH 2 to 12 in the order of their respective maximum abundance. This speciation scheme significantly simplifies at hydrothermal conditions, with HSb<sub>2</sub>S<sub>4</sub><sup>-</sup> and Sb<sub>2</sub>S<sub>4</sub><sup>2-</sup> being predominant below 150-200 °C and with Sb(OH)<sub>3</sub><sup>0</sup> at higher temperatures. Their reaction (4.89) and (4.90) constants are within 0.5 log units of those of Zotov et al. (2003) and Krupp (1988), respectively. The Olsen et al. (2019) dataset for HSb<sub>2</sub>S<sub>4</sub><sup>-</sup> and Sb<sub>2</sub>S<sub>4</sub><sup>2-</sup> is recommended in Sb speciation modeling. According to these and most previous studies, Sb(OH)<sub>3</sub><sup>0</sup> is responsible for Sb transport in most hydrothermal fluids above 300 °C. These fluids are often undersaturated with stibnite because of increasingly high Sb<sub>2</sub>S<sub>3</sub>(s) solubility with the temperature rise (>100s to 1000s ppm Sb at H<sub>2</sub>S concentrations 0.001-0.01 m at 300-400 °C) compared to natural Sb fluid concentrations (typically <1-10 ppm, Kouzmanov and Pokrovski 2012). Sulfide complexes may only be important for Sb transport in geothermal waters and epithermal fluids at temperatures below 150-200 °C as well as in sulfide-rich sedimentary fluids, if mineral-fluid equilibrium is reached; however, out-of-equilibrium Sb (and As) transport as
colloidal sulfide particles and/or dissolved thionate species was also evidenced in rapidly cooling
and decompressing geothermal waters (see section 4.4.12).

4.4.9 Bismuth

Bismuth pursues the As<sup>III</sup>-Sb<sup>III</sup> trend in aqueous speciation, with its major oxidation state of Bi<sup>III</sup> in most chemical compounds, with more metallic character, and growing affinity to chloride and sulfide both in solid phase and aqueous solution. At ambient conditions, the Bi<sup>3+</sup> cation is only stable in very acidic solutions (pH<1); with increasing pH, even in very dilute solutions (<10<sup>-5</sup> m Bi), it hydrolyses to a variety of polynuclear hydroxide cations (e.g., Bi<sub>6</sub>(OH)<sub>12</sub><sup>6+</sup>, Bi<sub>9</sub>(OH)<sub>22</sub><sup>5+</sup>) that are converted at pH>8 to Bi(OH)<sub>3</sub><sup>0</sup> and possibly to Bi(OH)<sub>4</sub><sup>-</sup> at pH>13, similar to Sb<sup>III</sup> (Baes and Mesmer 1976). Bismuth trioxide, Bi<sub>2</sub>O<sub>3</sub>(s), is about 1 order of magnitude less soluble in water than Sb<sub>2</sub>O<sub>3</sub>(s), with solubility increasing from 10<sup>-5</sup> to 0.01 m between 25 and 300 °C. With increasing temperature, the pH space of the stability domain of Bi(OH)<sub>3</sub><sup>0</sup> further widens similar to that of Sb<sup>III</sup>. Its stoichiometry in hydrothermal solutions was confirmed by in situ XAS (Tooth et al. 2013), and its thermodynamic properties were derived from solubility measurements to 600 °C and 800 bar (Kolonin and Laptev 1982; Tooth et al. 2013). The HKF model parameters of Bi(OH)<sub>3</sub><sup>0</sup> reported by Tooth et al. (2013) are recommended for thermodynamic modeling, whereas an older HKF data set for dehydrated BiO<sub>2</sub><sup>0</sup> of Shock et al. (1997) based on lower-temperature data underestimates Bi<sub>2</sub>O<sub>3</sub>(s) solubility by >2 orders of magnitude above 300 °C. Bismuthinite, Bi<sub>2</sub>S<sub>3</sub>(s), a typical hydrothermal Bi-bearing mineral, is much less soluble as Bi(OH)<sub>3</sub><sup>0</sup> than stibnite or orpiment (Fig. 4.34), with equilibrium Bi concentrations less than ppb at H<sub>2</sub>S concentrations of 0.001–0.01 m, typical of moderate-temperature hydrothermal fluids. These solubility predictions largely underestimate Bi concentrations, of 10s to 100s ppm, measured by LA-ICPMS in some natural fluid inclusions (e.g., Kouzmanov and Pokrovski 2012 and references therein; Schirra et al. 2022; Galdos et al. 2024), thereby calling for complexes other than with hydroxide.

Indeed, being more metallic than As and Sb, Bi<sup>III</sup> has a much greater affinity for the Cl<sup>-</sup> ligand. Chloride complexes, BiCl<sub>n</sub><sup>3-n</sup> with n from 1 to 6, have been widely recognized at ambient conditions in saline acidic solutions. However, more discrepancy persists at elevated temperatures between two major sources of data. Kolonin and Laptev (1982) suggested BiCl<sub>6</sub><sup>3-</sup> as the major complex based on solubility and UV-Vis measurements to 300 °C at P<sub>sat</sub>. In contrast, Etschmann et al. (2016) employed in situ XAS methods to show that BiCl<sub>3</sub><sup>0</sup> largely dominates over BiCl<sub>6</sub><sup>3-</sup> at typical pH and salinities of hydrothermal fluids. Etschmann et al. (2016) derived the stability constants of Bi chloride complexes based on the variation of the number of Cl atoms in the Bi first
coordination shell from EXAFS and using the RB model. Their thermodynamic constants for the reaction

$$ \mathrm{BiCl}_{3}^{0}+3 \mathrm{H}_{2} \mathrm{O}=\mathrm{Bi}(\mathrm{OH})_{3}^{0}+3 \mathrm{Cl}^{-}+3 \mathrm{H}^{+} \qquad (4.91) $$

imply that in moderately saline hydrothermal fluids ($a_{Cl}^{-} = 1$), the chloride complex would dominate over the hydroxide at pH<5 at 350 °C and $P_{sat}$, which may explain the elevated Bi concentrations analyzed in saline fluid inclusions.

The major unknown in Bi hydrothermal chemistry is the effect of sulfur. Complexes with thiol-organic ligands (e.g., thiocarbamide and its derivatives) may stabilize dissolved Bi<sup>III</sup> in solution in the absence of sulfide. Reduced sulfur (H<sub>2</sub>S) would play a negative effect on Bi sulfide minerals solubilities if Bi formed dominantly hydroxide or chloride species in the fluid (see section 4.4.1 and Fig. 4.25; e.g., like Mo or Zn, Fe, Cu). The low Bi<sub>2</sub>S<sub>3</sub>(s) solubility compared to analogous Sb and As sulfides (Fig. 4.34) makes the measurements of sulfide complexes analytically challenging and/or requires quite elevated temperatures to increase solubility (>400 °C). The only information, we are aware of, about such complexes under hydrothermal conditions are theoretical estimations of Skirrow and Walshe (2002). These authors adopted an analogy with sulfide complexes of arsenic and antimony and tentatively assumed Bi<sup>III</sup> complex stoichiometry similar to that of Sb<sup>III</sup> (Bi<sub>2</sub>S<sub>4</sub><sup>2-</sup>, HBi<sub>2</sub>S<sub>4</sub><sup>-</sup> and Bi<sub>2</sub>S<sub>2</sub>(OH)<sub>2</sub><sup>0</sup>). However, given the large differences in the affinity of these elements to the different ligands (see above), such estimations should be regarded with caution, thus awaiting experimental evidence. Similarly, the role of polysulfide anions and radical ions cannot be excluded. Interestingly, the only structurally characterized metal complex of a polysulfide radical ion is that of S<sub>4</sub><sup>-</sup> with Bi<sup>III</sup> in metalorganic compounds (Schwamm et al. 2017). Thus, given the elevated Bi affinity to reduced sulfur, S<sub>3</sub><sup>-</sup> might be a potentially important ligand for Bi<sup>III</sup> in S-rich fluids, and in lesser extend for As<sup>III</sup> and Sb<sup>III</sup>.

In contrast, in sulfur-poor, reducing (pyrrhotite stable), high-temperature (>400 °C) environments, bismuth metal melts may be stable at the expense of Bi sulfides or sulfosalts and coexist with a hydrothermal fluid, as found in skarn, intrusion-related, orogenic and volcanogenic massive sulfide gold deposits. Such melts have been suggested to be very efficient scavengers of gold from the hydrothermal fluid, thereby providing an additional mechanism of concentrating the metal (e.g., Tooth et al. 2008, 2011; Du et al. 2023 and references therein). The presence of reduced As<sup>-1</sup> in arsenian pyrite, arsenopyrite and löllingite stable in some of such S-poor reducing systems will be an additional competing mechanism of Au concentration, via coupled redox reactions between Au<sup>1</sup> and As<sup>III</sup> in hydrothermal fluid leading to the formation of [Au<sup>II</sup>As<sub>n</sub>S<sub>6-n</sub>] complexes in the Fe<sup>II</sup> crystallographic sites of the sulfoarsenide mineral structure (Pokrovski et al. 2021a).
### 4.4.10 Molybdenum

Among metals and metalloids forming sulfide ore in the Earth's crust, molybdenum is the most chemically variable one, exhibiting redox states from -II to VI and coordinations from 4 to 9, in compounds with different O, Cl and S ligands known in chemistry and material sciences. However, at naturally relevant conditions, the most common redox states are IV and VI in which Mo can be both tetrahedrally and octahedrally coordinated with O²⁻/OH⁻, Cl⁻ and S²⁻ ligands. The most common stable solid phase in hydrothermal-magmatic systems is molybdenite, MoIVS₂(s), whereas oxides, MoVI O₃(s) and MoIV O₂(s), and molybdates (e.g., CaMoVI O₄(s)), being far more soluble, occur only occasionally. In contrast with the solid state, Mo aqueous speciation is more variable and remains very poorly quantified at hydrothermal conditions. Most available work currently converges to the conclusion that hexavalent MoVI is the major redox state in aqueous solution over a wide T-P-fO₂ range (Wood and Samson 1998; Zotov et al. 1995; references therein). Even though the MoVI primary ligand is oxygen or hydroxyl in molybdate species, this extremely versatile element is equally capable of forming a plethora of oxy-chloride-sulfide complexes.

**Oxyhydroxide complexes.** MoVI is a hard cation strongly hydrolyzed in dilute aqueous solution (<10⁻⁴ m Mo) at ambient conditions, by forming at pH<4 molybdic acid conventionally expressed as H₂MoO₄ and, at higher pH, its dissociation products, the tetrahedral (hydro)molybdate ions, HMoO₄⁻ and MoO₄²⁻:

$$H_2MoO_4 = HMoO_4^{-} + H^+ \qquad (4.92)$$

$$HMoO_4^{-} = MoO_4^{2-} + H^+ \qquad (4.93)$$

In contrast to its deprotonated counterparts, molybdic acid likely has a structural formula of MoO₂(OH)₂(H₂O)₂ in which Mo is in a distorted octahedral coordination made up by O, OH and OH₂ ligands, rather than Mo(OH)₆, MoO₃(H₂O)₃ or H₂MoO₄ formulations commonly encountered in the literature (Liu et al. 2013b; Zhang et al. 2019; references therein). Cationic monomer species, such as MoO(OH)₂⁺ and MoO₂²⁺, with MoVI in octahedral coordination complemented by water molecules, have also been invoked at very low Mo concentrations in strongly acid (pH<1) aqueous solutions (Gruywagen 1999; Zhang et al. 2019). However, they are unlikely to be significant for natural fluids and were not considered in hydrothermal research. A remarkable feature of MoVI (and its chemical congener, tungsten, WVI) aqueous chemistry, often ignored by geoscientists, is a very strong tendency to form polymeric anions at acidic pH at concentrations as low as 10⁻³ m (~100 ppm Mo). Such anions are composed of clusters with 7 or more Mo(O,OH)₆ octahedra linked by their edges, such as Mo₇O₂₄⁶⁻ and Mo₈O₂₆⁴⁻ and their partly protonated counterparts. Their formation constants from MoO₄²⁻ have been determined at ambient conditions (e.g., Baes and Mesmer 1976; Gruywagen 1999). In addition, there is a plethora of heteropoly molybdate anions in
which the central cavity of the cluster is occupied by a different element in tetrahedral XO₄ coordination (where X = Si, Ge, P, As). Among them is the famous [Xⁿ⁺Mo₁₂O₄₀ⁿ⁻⁸] often called the Keggin ion after its discoverer (see Cotton et al. 1999). These remarkable configurations can undergo reduction to blue mixed-valence species (MoIV,V,VI) without loss of structure. The blue color of such partly reduced Mo species is used since a long time in quantitative colorimetry of monomeric silica in aqueous solution. Silicic acid is trapped as SiO₄ in the Mo Keggin structure, which is then partly reduced using oxalic acid thereby developing a stable blue color (e.g., Charlot 1966). Interestingly, a blue color due to reduced Mo species has been observed in the sampled or quenched fluids from Mo hydrothermal solubility experiments (e.g., Kudrin 1989; Kokh et al. 2016), indicating that reduced Mo forms might also be present in hydrothermal fluids. Polymeric molybdates have commonly been ignored in the interpretation of hydrothermal experiments even at elevated Mo concentrations (>0.01 m), arguing that growing thermal disorder would be unfavorable for their stability (Ivanova et al. 1975; Dadze et al. 2017a). Interestingly, WVI has recently been demonstrated by in situ Raman spectroscopy to form stable polymeric oxy-hydroxides at hydrothermal conditions (Carocci et al. 2022). By analogy, a similar behavior might be expected for MoVI, awaiting direct spectroscopic evidence. Monomeric molybdic acid dissociation reaction constants to HMoO₄⁻ (K₉₂) and MoO₄²⁻ (K₉₃) have currently been constrained to 350 °C by recent UV-Vis spectroscopy and MoO₃(s) and CaWO₄(s) solubility measurements (Minubaeva and Seward 2010; Dadze et al. 2018a). These K values are in good mutual agreement (within 1 log unit), but differ, especially for K₉₂, from those reported in older solubility studies of MoO₂(s) (e.g., Kudrin 1989). In the absence of direct evidence for Mo polymeric species at elevated temperatures, we recommend using the Dadze et al. (2018a) set of K₉₂ and K₉₃ values in hydrothermal fluid modeling to at least 350 °C and <1 kbar. The K₉₂ value shows a particular temperature behavior of increasing dissociation in contrast to analogous acids of similar strength (H₃PO₄, H₂SO₄, H₃AsO₄). Such a difference is likely due to Mo coordination change from 6 to 4 upon molybdic acid dissociation (reaction 4.92) and may therefore be explained by the entropy principle postulating that more compact species of lower coordination are generally favored at elevated temperatures. In this regard, MoVI contrasts with PVI, SVI and AsV that always keep their tetrahedral coordination with oxygen.

*Alkali ion pairs.* In saline (NaCl and KCl) solutions, a moderate increase of MoO₂(s) solubility at temperatures 300–450 °C has originally been interpreted by the formation of the NaHMoO₄⁰ and KHMoO₄⁰ ion pairs (Kudrin 1989) such as:

$$Na⁺ + HMoO₄⁻ = NaHMoO₄⁰(aq) \qquad (4.94)$$

The same Na ion pair was recently suggested as the dominant species in MoO₃(s) solubility measurements in NaCl and NaCF₃SO₃ (triflate) solutions at 250, 300 and 350 °C (Shang et al. 2020).
These data show a moderate increase in MoO₃(s) solubility (<1.5 log unit) in the presence of high
sodium contents (>1 m Na) as opposed to more dilute solutions (<0.1 m Na). However, their data
were criticized by Plyasunov (2020) demonstrating that Shang et al.'s (2020) MoO₃(s) solubilities in
Na-poor solutions appear to be systematically lower, by a similar magnitude, than most existing
data (Ivanova et al. 1975; Dadze et al. 2017a,b). Dadze et al. (2017b) interpreted a similar increase
in MoO₃(s) solubility in NaClO₄ solutions (up to 2.2 m Na) at 300 °C by an activity coefficient effect
rather than ion pairing. In light of the relatively high MoO₃(s) solubility in water at elevated
temperatures (~0.01m at 300 °C), along with the potential tendency to form Mo VI polymeric
oxyhydroxide species (see above), the addition of an electrolyte in such systems might favor
disruption of the polymeric structures thereby increasing solubility. Dadze et al. (2018a) interpreted
their CaMoO₄(s) solubility measurements (<5×10⁻⁴ m Mo) in highly saline solutions (up to 3.8 m
NaCl) at 300 °C as monomeric molybdic acid and molybdate ions, with no evidence for statistically
significant contributions from ion pairs or chloride complexes. Kokh et al. (2017) tentatively
suggested the KHMoO₄⁰复杂来 describe the solubility of MoS₂(s) in supercritical H₂O-CO₂
fluids of low salinity (450 °C, ~700 bar, <0.1 m KCl) in the presence of the pyrite-magnetite-
pyrrhotite and potassic feldspar-quartz-muscovite assemblages, but other alternative Cl⁻ and HS⁻
/S²⁻ complexes could not be tested. More recently, Guan et al. (2023) added further confusion to the
debate about the Na ion pairs, by publishing a set of HKF coefficients for NaHMoO₄⁰ derived from
the three temperature datapoints, 250, 300 and 350 °C, of Shang et al. (2020). The reported
thermodynamic functions predict an unrealistically strong stability for NaHMoO₄⁰ at temperatures
<300 °C, with an ion pair formation constant value of reaction (4.94) at 25 °C of 8 log units higher
than any known-so-far ion pair between Na⁺ or K⁺ and –1 and –2 charged anions (e.g., Cl⁻, HSO₄⁻,
SO₄²⁻, B(OH)₄⁻, HCO₃⁻ and MoO₄²⁻; see Pokrovski et al. 2024). In addition, some of the reported
HKF parameters, such as the Born parameter value (ω) of NaHMoO₄⁰ is several times more negative
that those of notoriously gas-like aqueous species (e.g., dissolved noble gases). Such values are
unphysical for hydrated ion pairs and neutral complexes that are known to have positive ω (e.g.,
Plyasunov and Shock 2001; Perfetti et al. 2008; Pokrovski et al. 2024). Both stability constants and
HKF parameters of sodium hydromolybdate ion pair are, therefore, artifacts of the HKF parameter
derivation procedures used in Guan et al. (2023) and should be rejected. Thus, the effect of salt in
general, and of alkalis in particular, on Mo aqueous speciation in hydrothermal fluids awaits more
constrained studies before it could be considered in quantitative speciation models and used as the
basis for interpreting the effect of chloride and sulfur discussed below.

*The effect of chloride.* Oxychloride complexes, of general stoichiometry MoVI O₂Clₙ(H₂O)₄-
n²⁻, with growing number of Cl ligands when increasing temperature from 25 to 340 °C, have been
reported using in situ X-ray absorption spectroscopy only in strongly acid solutions (2–6 m HCl) (Borg et al. 2012). In contrast, only the spectral signal from molybdate anions was observed in the same study for highly saline (to 6 m NaCl) near-neutral pH solutions in the same *T* range. At higher temperatures, in a synthetic fluid inclusion study by Ulrich and Mavrogenes (2008), Mo aqueous concentrations in the system Mo<sub>(s)</sub>-H<sub>2</sub>O-KCl at 500–800 °C to 3 kbar were tentatively interpreted by potassium ion pairs or oxychloride species. However, Ulrich and Mavrogenes’s interpretation of in situ XANES spectra acquired from a few individual fluid inclusions was later criticized by Borg et al. (2012) showing that these spectra closely resembled that of molybdenum oxide solid (MoO<sub>2(s)</sub>) rather than of an aqueous species. Kudrin (1989) tentatively interpreted his MoO<sub>2(s)</sub> solubility data (see above) in terms of KHMoO<sub>4</sub><sup>0</sup> rather than chloride complexes. We note that the effect of alkalis vs chloride is virtually impossible to separate in NaCl or KCl solutions (Wood and Samson 1998). A potentially pertinent Cl species, MoO<sub>2</sub>(OH)<sub>2</sub>Cl<sup>-</sup>, has recently been proposed based on MoO<sub>3(s)</sub> solubility measurements in moderately saline fluids at 300 °C (Dadze et al. 2018b). This complex was, however, ignored by the same authors in an accompanying study of CaMoO<sub>4(s)</sub> solubility at 300 °C and 100 bar in more concentrated NaCl solutions (to 3.5 m NaCl, Dadze et al. 2018a), pointing to a lack of sufficient resolution in detecting such weak complexes by the solubility method at moderate temperatures. Similarly, at much higher *T* (600–800 °C) and *P* (26 kbar), a synthetic fluid inclusion study of Bali et al. (2012) reported only a fairly moderate increase in MoO<sub>2(s)</sub> solubility, by a factor of 5 with a 40-fold increase in salinity, pointing either to potential weak chloride and/or alkali complexes or an activity coefficient effect. Thus, the effect of chloride on Mo mobility in hydrothermal fluids yet remains both inconsistent and controversial. Its quantification would require more concerted studies using combined approaches.

*The effect of sulfur.* In ambient aqueous solution, hexavalent Mo<sup>VI</sup> has been known since a long time to form a series of colored monomeric oxysulfide complexes with increasing sulfide concentration, by stepwise replacement of the O<sup>2</sup><sup>-</sup> by S<sup>2</sup><sup>-</sup> ligand in the molybdate ion: MoO<sub>4</sub><sup>2</sup><sup>-</sup>, MoO<sub>3</sub>S<sup>2</sup><sup>-</sup>, MoO<sub>2</sub>S<sup>2</sup><sup>-</sup>, MoOS<sub>3</sub><sup>2</sup><sup>-</sup>, and MoS<sub>4</sub><sup>2</sup><sup>-</sup>, with the color changing from transparent to yellow, orange, orange-red, and red, respectively. Both thermodynamics and kinetics of these complexes formation have been thoroughly studied using UV-Vis spectroscopy (Erickson and Heltz 2000; Rickard and Luther 2006; references therein). The oxysulfide species, among which tetrasulfide is major (Fig. 4.35a), dominate the Mo<sup>VI</sup> speciation in sulfidic pore waters and euxinic marine and lake water columns at near-neutral pH and sulfide concentrations above 0.01 millimol (Helz 2021; references therein). A paradoxical feature of these complexes is the association of Mo in its highest oxidation state (VI) with S in its lowest oxidation state (–II), which is likely due to electron delocalization via π-bonding. The remarkably strong bonding affinity between molybdenum and
sulfur in contrasting oxidation states suggests that even greater Mo-S affinities might be expected for lower-valence Mo states (e.g., IV) and with intermediate-valence S species such as polysulfides in hydrothermal fluids – an hypothesis requiring thorough investigation.

The effect of sulfur on Mo transport in sulfur-bearing hydrothermal systems, where molybdenite is the stable phase remains extremely poorly documented. The few early MoS₂(s) solubility studies in H₂S-bearing fluids, overviewed by Wood and Samson (1998) and Zotov et al. (1995), showed a negative effect of H₂S on the solubility, likely consistent with molybdate-type dominant species (e.g., reactions 4.92 and 4.93). In contrast, Kokh et al. (2016) observed an increase in both MoS₂(s) liquid-phase solubility and Mo vapor-liquid partition coefficient with increasing H₂S concentration at 350 °C in a multicomponent minerals-aqueous solution-vapor system (FeS₂-MoS₂-CuFeS₂-SnO₂-PtS₂-Au-KCl-HCl-K₂S₂O₃-CO₂-H₂O), pointing to the formation of Mo-S type of complexes both in liquid and vapor phases. Zhang et al. (2012) measured, using the synthetic fluid inclusion method, MoS₂(s) solubility in saline fluids with fS₂ and fO₂ buffered by the pyrite(py)-pyrrhotite(pyh)-magnetite(mag), py-pyh-Ni-NiO, pyh-QFM, and py-pyh-Co-CoO assemblages at 600–800 °C and 2 kbar. Their Mo concentration trends were formally consistent with a tentative complex stoichiometry of NaHMoO₂S₂⁰. No thermodynamic constant has been proposed by the authors who fitted their solubility trends by an empirical equation as a function of temperature, salinity, and sulfur and oxygen fugacity, therefore restricted within the parameters ranges of their experiments. More recently, in an analogous synthetic fluid inclusions study (at 600 °C, 2 kbar), Li et al. (2021) obtained similar MoS₂(s) solubilities (10s ppm Mo) in H₂O-CO₂ fluids in the presence of the py-pyh-mag assemblage, but the species identity could not be constrained. Liu et al. (2020) applied the XAS method to alkaline NaHS solutions to 340 °C coupled with MD calculations of species structures and their XANES spectra. Their spectroscopic data are consistent with formation of mixed-ligand complexes, MoO₄·S₄·2⁻ (n = 0 to 4). The sulfide ligand number of the dominant complex decreased both with increasing temperature for a given solution composition and with decreasing NaHS concentration at a given temperature. Alternatively, their data were equally consistent with a mixture of the endmember complexes, MoO₄²⁻ and MoS₄²⁻, with a decrease in the sulfide complex fraction with temperature and NaHS concentration. Based on the only available 25 °C data of Erickson and Helz (2000) and using an isocoulombic extrapolation (equation 4.10), Liu et al. (2020) further estimated the stability constants of the following exchange reaction to 300 °C

$$ \mathrm{MoO_4^{2-} + n H_2S_{(aq)} = MoO_{4-n}S_n^{2-} + n H_2O_{(liq)}; n = 1 \text{ to } 4} \quad (4.95) $$

The predicted reaction (4.95) constant values systematically decrease with increasing temperature for all sulfide species. For example, the logK₉₅ value for the major MoS₄²⁻ complex ranges from 19.9 at 25 °C to 10.3 at 300 °C. These values mean that MoS₄²⁻ will over compete MoO₄²⁻ at >10⁻
⁵ and >0.003 m H₂S in the fluid, respectively at 25 °C and 300 °C. The other intermediate Mo-O-S complexes show up at hydrothermal conditions only at rather alkaline pH (Fig. 4.35b). The theoretical predictions of the MoS₄²⁻ stability were confirmed by Laskar (2022) and Kokh et al. (2024) by direct MoS₂(s) solubility measurements coupled with in-situ XAS at 300 °C in NaHS-HCl solutions of near-neutral and alkaline pH (pH>6–7). In more acidic fluids (pH<5–6) and in the presence of both sulfide and sulfate, MoS₂(s) solubility values were too high to be explained by MoS₄²⁻ alone, thereby implying additional complexes, likely with the trisulfur radical ion. These data were interpreted by a mixed sulfide-trusulfur complex, MoS₃(S₃)⁻, according to the reaction

$$ \mathrm{MoS}_{2}(\mathrm{s}) + \mathrm{H}_{2}\mathrm{S}_{(\mathrm{aq})} + \mathrm{S}_{3}^{\cdot -} + 0.5 \mathrm{O}_{2}(\mathrm{aq}) = \mathrm{MoS}_{3}(\mathrm{S}_{3})^{-} + \mathrm{H}_{2}\mathrm{O}_{(\mathrm{liq})} \quad (4.96) $$

with an equilibrium logK₉₆ value of 14.3±0.3 at 300°C and 500 bar. These first results point to polysulfide ions as potentially important carriers of Mo in porphyry-type hydrothermal fluids (Kokh et al. 2024).

As a conclusion, at present, only oxyhydroxide (Dadze et al. 2018a) and oxysulfide (Liu et al. 2020; Kokh et al. 2024) complexes of Mo may be modeled with a good accuracy in moderate-temperature hydrothermal fluids (<350 °C), but they await to be placed in a more widely used thermodynamic framework (e.g., HKF model). More systematic solubility, spectroscopy and modeling work is needed to quantify the effect of chloride, alkalis and different sulfur ligands, including sulfur radical ions, on Mo speciation at hydrothermal-magmatic conditions.

### 4.4.11 Sulfate complexes of metals

In light of the overwhelming abundance of chloride in most hydrothermal environments along with their generally reducing conditions favoring sulfide and polysulfide ligands, sulfate complexes of metals in hydrothermal fluids have received rather modest attention. Because the SO₄²⁻ ion is rather rigid and its charge is high, monodentate coordination is generally most common and the order of the complexes is typically limited to 1:1 and 1:2, at least at near-ambient conditions. However, examples of bidentate coordination and metal complexes with three sulfate ligands exist in the literature. Sulfate is a chemically hard anion. Therefore, the stability of its metal complexes generally increases from soft to intermediate and to hard cations, as shown in Fig. 4.36. This figure compiles available formation constants for the 1:1 metal sulfate complexes, which represent the largest set amongst the known stoichiometries, plotted versus their corresponding first hydrolysis constants at 25 °C and 1 bar for the three groups of cations – hard, intermediate and soft. Sulfate ion pairs with alkali and alkali-earth metals and the solubility of their sulfate minerals were discussed in more detail in section 4.3.4; here we focus on other metals.
**Soft metals** (shown in red in Fig. 4.36) generally form the weakest complexes with sulfate. As a result, few data are available at ambient conditions, and virtually no data exist at hydrothermal temperatures. High-temperature thermodynamic properties of 1:1, 1:2, and 1:3 sulfate complexes of PtII, PdII, RhII,III, and RuII,III have been theoretically estimated by Sassani and Shock (1998) using HKF model correlations on the basis of meagre data at ambient conditions. Such complexes have negligibly low abundances in virtually any natural hydrothermal environments thereby being unable to compete with the Cl⁻, HS⁻ and S₃²⁻ ligands (e.g., Pokrovski et al., 2021b; Laskar et al. 2022).

**Intermediate or borderline cations** (shown in blue in Fig. 4.36) form stronger sulfate complexes whose stability is linearly correlated with their hydroxide counterparts. This group of cations, as well as the soft group above, generally has four-fold (tetrahedral or square-planar) and six-fold (octahedral) coordinations in solution forming single-bond linkages with sulfate via an oxygen atom, [M-O-SO₃]. Such coordinations are poorly compatible with a bidentate linkage with a sulfate anion via two oxygen atoms due to steric strain. Bidentate (i.e. edge-sharing MOₙ and SO₄ polyhedra) are equally uncommon in these metal sulfate solid structures (Pan and Mi 2025). A very limited amount of experimental work exists on sulfate complexes of base metals (Fe, Mn, Zn, Pb, Cu, Ni) in aqueous solution at elevated temperatures. Most stability constants are theoretical estimations based on near ambient-temperature data. For example, FeII and FeIII sulfate complexes such as FeHSO₄⁺, FeSO₄⁰, FeSO₄⁺, and Fe(SO₄)₂²⁻ have been considered in the chemical literature, among which FeSO₄⁰ appears to be the best constrained one. Their stability constants and basic thermodynamic functions (ΔH⁰, S⁰) at 25 °C were thoroughly revised by Lemire et al. (2013). On the basis of this and earlier compilations, van't Hoff-type isocoulombic extrapolations to 200–300 °C of the formation constants of these and some other metal sulfate complexes (e.g., ZnSO₄⁰, NiSO₄⁰) can be found in the LLNL or Thermoddem databases. We are unaware of any set of HKF-model parameters for base-metal sulfate complexes (except MnSO₄⁰, Sverjensky et al. 1997) that would allow reliable extrapolations to supercritical temperatures. Many sulfate minerals, including alkali, alkali-earth and base metals, have a retrograde solubility in dilute aqueous solution with temperature, at least at pressures close to Psat. Those of heavy metals are weakly soluble in water even at ambient conditions (e.g., congruent solubility, in molality units, of BaSO₄ ≈ 10⁻⁵, PbSO₄ ≈ 10⁻⁴, CdSO₄ and SrSO₄ ≈ 10⁻³, and Ag₂SO₄ ≈ 10⁻² m), rendering it difficult measurements of aqueous sulfate complexation with such metals. Because complexes with hard ligands generally become stronger with increasing temperature, sulfate might compete with chloride complexes of FeII and ZnII in oxidized and salt-poor fluids from subduction zones. For example, formation of sulfate complexes was hypothesized to account for relatively “light” δ⁵⁶Fe and δ⁶⁶Zn signatures inferred for oxidized fluids released by prograde metamorphism of the subduction slab (Debret et
al. 2016, 2020; references therein). Thermodynamic data on sulfate complex stability at such conditions are required to allow quantitative interpretations of metal isotope signatures in subduction zones.

*Hard cations*, such as alkali-earth and rare earth metals, Al³⁺, and actinides are prone to forming much stronger complexes with the hard SO₄²⁻ ligand than those of soft and borderline metals mentioned above, as can be seen in Fig. 4.36 (shown in green). However, all these metals are also strongly hydrolyzed in aqueous solution at elevated temperatures, so that there is competition between the SO₄²⁻ (and HSO₄⁻) and the OH⁻ ligands for these metal cations in aqueous solution. In contrast to the soft and borderline groups of cations, there is much more scatter from the average linear trend of SO₄²⁻ vs OH⁻ complex stability for the hard group. This scatter is due to *i*) larger uncertainties related to the determination of sulfate and hydroxide complex stability for strongly hydrolyzed and poorly soluble cations of this group, and *ii*) larger variety and versatility of the metal coordination for which large and distorted MOₙ polyhedral are typical, with *n* from 7 to 9. The latter property allows for easier formation of bidentate sulfate complexes with less steric strain compared to lower-coordination cations of the intermediate and soft groups. For example, bidentate YOₙ-SO₄ linkages in hydrothermal fluids were inferred from spectroscopic and molecular simulation approaches (e.g., Guan et al. 2020, 2022). The potential tendency to form stronger bidentate complexes for this group of metals in aqueous solution is in line with the numerous examples of such cation-sulfate geometries, which are commonly present along with monodentate in alkaline earth and rare earth sulfate solids (Pan and Mi 2025).

Because of the competition with hydrolysis, sulfate complexes (and eventually hydrosulfate, HSO₄⁻, which is a weaker ligand) are expected to be more significant at mildly acidic conditions (typically 2<pH<4) at which the metal cation is not yet fully hydrolyzed and the sulfate anion is yet not fully protonated (e.g., Fig. 4.16b). For example, Tagirov and Schott (2001) generated an HKF-coefficients dataset for AlSO₄⁺, which eventually may be dominant in acidic, sulfate-rich, but fluoride- and salt-poor fluids. Whereas a substantial dataset exists at near-ambient conditions on the uranyl ion (U VI O₂²⁺) sulfate complexes (see the review of Grente et al. 2020), it is only recently that the stability constants of UO₂SO₄⁰ and UO₂(SO₄)₂²⁻ were measured to 200 °C using UV-Vis spectroscopy by Kalintsev et al. (2019), and RB-model equations of logK generated by the authors may reliably be used to ~300 °C. Their results suggest that sulfate may be the dominant carrier of U VI in oxidized fluids of acidic pH (<4) with sulfate concentrations above ~1000 ppm S. In the recent years, there has been a surge of interest for REE sulfate complexes in deep fluids given the multiple instances of REE economic concentration in carbonatites and similar rocks whose mineralogy and fluid/melt inclusions provide clear evidence for the presence of alkali metal sulfate-
carbonate-chloride brines (e.g., Walter et al. 2020a,b, 2021; references therein). These findings motivated recent experimental studies of REE complexes with sulfate as well as the solubility of sulfate minerals of REE and major alkali and alkali earth metals. A significant quantitative advance, compared has been made by Migdisov's team through systematic generation of key experimental data for different REE complexes ($Cl^-$, $OH^-$, $F^-$, $PO_4^{3-}$) including those with sulfate at hydrothermal temperatures (see the review of Migdisov et al. 2016), thereby bringing reliable constraints to previous theoretical predictions almost exclusively based on low-temperature data (Wood et al. 1990; Haas et al. 1995). More specifically, based on their own experimental data, Migdisov et al. (2016) have generated a set of RB-model parameters for the 1:1 and 1:2 sulfate complexes of the 14 rare earth elements. Their data suggest that sulfate complexes may efficiently over compete $Cl^-$ and $F^-$ in sulfur-rich (1-2 wt% sulfate) acidic (2<pH<5) fluids at 200-400 °C and relatively elevated pressures (>1 kbar) at which the solubility of Na and K sulfates becomes prograde (e.g., Wan et al. 2023; references therein). Thus, drop in pressure and the resulting precipitation of sulfate minerals as well as unmixing to sulfate-rich brine and vapor may be the major controls on REE distribution and precipitation (e.g., Wan et al. 2021; Guan et al. 2022).

### 4.4.12 Speciation of thioanions in natural hydrothermal waters

In addition to our ability to thermodynamically predict metals speciation and the effect of sulfur of their solubility in hydrothermal fluids as overviewed above, recent progress in analytical techniques has also allowed some metal and metalloids speciation to be directly measured in modern geothermal fluids. Many natural hydrothermal waters contain substantial concentrations of dissolved sulfide (see Table 4.1) and are enriched in various elements having high affinity for reduced sulfur; for example, arsenic, antimony, molybdenum, and tungsten (W) (e.g., Xu et al. 1998; McCleskey et al. 2010; Kaasalainen and Stefánsson 2011a,b, 2012). These trace elements are known to form oxyanions as well as thioanions in aqueous solution (see above).

Aqueous As, Sb, Mo and W thioanions have been encountered in hot spring waters by in situ analyses involving chromatographic separation followed by inductively coupled plasma mass spectrometry (IC-ICPMS and IPC-ICPMS) or hydride generation and atomic fluorescence spectrometry (IC-HG-FAA) (Vassileva et al. 2001; Keller et al. 2014a,b; Lohmayer et al. 2015; Planer-Friedrich and Scheinost 2011; Planer-Friedrich et al. 2020). The results reveal arsenite ($H_nAs^{III}O_4^{n-3}$), arsenate ($H_nAs^V O_4^{n-3}$), thioarsenite ($H_nAs^{III}S_3^{n-3}$) and thioarsenate ($H_nAs^V S_x O_{4-x}^{n-3}$, with $x≤4$) to coexist in natural thermal waters (Planer-Friedrich et al. 2007; Keller et al. 2014a). Similar species distribution is observed for aqueous Sb, Mo and W, with coexisting antimonite ($H_nSb^{III}O_3^{n-3}$) and antimonate ($H_nSb^V O_4^{n-3}$) together with tri- and tetra-thioantimonate ($H_nSb^V S_3 O^{n-6}$).
$^3$ and $H_nSb^VS_4O^{n-3}$), as well as molybdates ($H_nMo^{VI}O_4^{n-2}$) and thiomolybdates ($H_nMo^{VI}S_xO_{4-x}^{n-2}$) and tungstate ($H_nW^{VI}O_4^{n-2}$) and thiotungstates ($H_nW^{VI}S_xO_{4-x}^{n-2}$) (e.g., Planer-Friedrich and Scheinost 2011; Ullrich et al. 2013; Planer-Friedrich et al. 2020). At low sulfide-to-metal ratios, the aqueous oxyanions predominate, whereas with increasing sulfur concentrations, the thioanions become more important accounting, for example, for up to 90, 80, 75 and 50% of the total dissolved As, Mo, W and Sb, respectively, in thermal waters with of 0.005 to 0.5 mmol/kg of $H_2S$, pH > 8 and temperatures of 50-100°C (Planer-Friedrich et al. 2020).

The thioanions form by nucleophilic attachment of $HS^-$ to the metal(loid)-oxygen bond (Erickson and Helz 2000). Such reactions are favored by the increased abundance of the $HS^-$ ion upon pH increase and high sulfide to metal(loid) ratios. At acidic pH, formation of thioanions is limited due to precipitation of sulfides whereas at alkaline pH, excess of $OH^-$ over $HS^-$ favors oxyanion formation. Moreover, thermodynamic species distribution is not attained (e.g., Keller et al. 2014a), indicating that the formation and relative abundance of thioanions are kinetically controlled, which is clearly seen by the fact that oxy- and thioanions with As and Sb of variable oxidation state (III vs V) coexist in the same water samples.
**4.5 Sulfur concentration, speciation and reactions in geological fluids**

Hydrothermal fluids in general may be subdivided into modern and ancient systems. The former can be observed in situ and directly sampled and analyzed. The latter are not accessible for direct observation, and the only straightforward information on their composition stems from fluid inclusions. Using these two major sources of information, coupled with mineral paragenesis compositions and physical-chemical modeling for both types of fluids, we outline the key controls on sulfur behavior in modern geothermal systems and in three major types of paleo ore-forming environments controlled by magmatic-hydrothermal, metamorphic, and sedimentary-basin fluids.

**4.5.1 Active geothermal on-land and deep-sea sources**

Geothermal systems are typically classified into volcanic and non-volcanic systems (Goff and Janik 2000). Volcanic geothermal systems occur in areas of active volcanism where permeability and geothermal gradient are high. Hydrothermal fluid temperatures of such systems are usually between 200 and 350°C but may be as high as 450°C. Non-volcanic geothermal systems are commonly observed within permeable rock formations or within tectonically active areas with hydrothermal fluid temperatures ranging from above ambient to ~150°C. The hydrothermal fluids are sourced from meteoric water or seawater or a mixture thereof. Components of connate, magmatic and metamorphic fluids may also be present in hydrothermal fluids (Chambefort and Stefánsson 2020).

Hydrothermal fluids have been divided into reservoir (i.e. so called primary) fluids and surface (i.e. secondary) fluids. Reservoir fluids are those observed at depth within geothermal systems. The main types of reservoir hydrothermal fluids are NaCl waters, acid-sulfate waters and high-salinity brines. Surface hydrothermal fluids have chemically evolved upon ascent to surface through processes such as i) boiling to form liquid water and vapor, ii) phase separation of saline fluids into a hypersaline brine and a more dilute vapor, iii) vapor condensation in shallow ground water or surface water to produce steam-heated waters, and iv) mixing of hydrothermal fluids with shallower non-thermal ground and surface water (Arnórsson et al. 2007).

The composition of reservoir hydrothermal fluids is typically obtained by combining liquid and vapor phase well discharge concentrations (m) with the vapor fraction (x), i.e. $m = x^{vap} \times m^{vap} + (1-x^{vap}) \times m^{liq}$. The concentrations of sulfate and $H_2S$ for the reservoir fluid are variable, typically ranging from a few ppm up to 100s ppm in some cases (Table 4.1). Other intermediate-valence sulfur species in reservoir hydrothermal fluids are considered to be insignificant and usually