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Fluids and physicochemical properties and processes in the Earth


The Earth's fluid budget is dominated by species in the system C–O–H–N–S together with halogens such as F and Cl. H2O is by far the most abundant. Such fluids are one of the two main mass transport agents (fluid and magma) in the Earth. Among those, in particular aqueous fluids are efficient solvents of geochemically important components at high temperature and pressure. The solution capacity of aqueous fluids can be enhanced further by dissolved halogens and sulfur. CO2 or nitrogen species has the opposite effect.

Fluid-mediated transport in the Earth is by fluids passing through cracks at shallow depth and via percolation channels along grain boundaries at greater depth. Percolation velocity is linked to permeability, which, in turn is governed by rock porosity. Porosity is controlled by wetting angles, θ, at the interface between fluid and mineral surfaces. When θ < 60°, fluid will wet all grain boundaries of an isotropic crystalline material, whereas when greater than 60°, grain boundary wetting does not occur as readily, and fluid-mediated transport efficiency can be greatly reduced. The size of the wetting angle is negatively correlated with the solubility of silicate components in the fluids, which means that fluid composition, temperature, and pressure affect the wetting angles and, therefore, fluid-mediated mass transport efficiency in the interior of the Earth.

Geophysical and geochemical anomalies in the Earth's interior have been linked to the presence of fluids. Fluid infiltration in crustal and mantle rocks will enhance electrical conductivity and seismic wave attenuation. For example, 5–10% H2O-rich fluids in the mantle wedge above subducting plates have been suggested from enhanced electrical conductivity. Similar fluid fractions have been suggested to be consistent with seismic velocities in these regions. The geochemistry of the crust and the mantle can be affected by fluid-mediated transport of major, minor, and trace elements. When such altered materials serve as source rocks of partial melts, those geochemical alterations also lead to changes in partial melt compositions. As an example, the presence of such aqueous fluid in the mantle wedge above subducting and dehydrating subducting slabs is consistent with partial melting of an H2O-bearing mantle wedge above subducted oceanic crust.

1 Introduction

Fluids are one of the two main mass transport agents in the Earth. Magma is the other transport agent. Fluids can be comprised of oxidized species such as H2O, CO2, SO3, and N2 and reduced species such as H2, CH4, H2S, and NH3 depending on oxygen fugacity, fO2, conditions. H2O is by far the most abundant of these fluid species (Jambon 1994).

The two main fO2-dependent carbon species are CO2 or CH4 (Eggler and Baker 1982; Taylor and Green 1989). Redox-dependent sulfur and nitrogen species can be found under specific circumstances such as during subduction zone melting, for example (Busigny et al. 2011; Wallace and Edmonds 2011).

The impact of fluids as mass transport agents on properties and processes of rock-forming materials depends on temperature, pressure, composition of the fluid, bulk rock composition, and redox conditions. The composition of fluids, in turn, reflects the conditions of fluid of formation, including the composition of their source rock. Conditions of fluid formation in metamorphic processes depend primarily on stability and phase boundaries of volatile-bearing crystalline materials (e.g., Winkler 1965; Connolly 2005; Evans and Tomkins 2020). The conditions also can include those that govern solubility of volatiles in magma, and, therefore, the circumstances under which one or more fluid species may exsolve during cooling and crystallization of fluid-rich magma (Eggler and Kadik 1979; Aubaud et al. 2005; Papale et al. 2006; Moretti et al. 2018; Audetat and Edmonds 2020). Oxygen fugacity also can be important for the solubility in magma of elements that can exist in multiple oxidation states (Peiffert et al. 1996; Klein-BenDavid et al. 2011).

The properties and composition of the rock matrix through which fluid migration takes place also are important for penetration of fluids into rocks (see Holness 1997; for review). The stress field can also influence fluid migration (Riley and Kohlstedt 1991; Hustoft and Kohlstedt 2006). Fluid density and viscosity are additional variables that can influence fluid migration although in general the density and viscosity contrasts between fluids, regardless of their composition, and rock matrix are so great that these often can be ignored. An exception to this suggestion is that where the temperature/pressure/compositions are such that fluids are supercritical and cannot be distinguished from fluid-rich magma. Under such conditions, density and viscosity of fluid can resemble those of volatile-rich magmatic liquids. This situation is not uncommon for H2O-rich systems in the upper mantle, for example (Shen and Keppler 1995; Bureau and Keppler 1999; Kessel et al. 2005; Mibe et al. 2007).

Carbon in its oxidized form, CO2, is the second-most abundant fluid species in the Earth (Jambon 1994). In the modern Earth, which likely becomes increasingly reducing with depth (Frost and McCammon 2008), methane (CH4) may be the dominant C-species in the lower mantle. Methane may also have been the dominant C-species in the Early Earth (O'Neill 1991; O'Neill et al. 1998). Reduced carbon as CH4 also has been reported from portions of descending slabs in modern subduction zones, for example (Tao et al. 2018). Absent hydrogen, carbides are possible. Carbide minerals are found as inclusions of deep-seated diamonds, for example (Kaminsky and Wirth 2017).

H2O is the most important and abundant fluid component in the Earth (Jambon 1994). H2O also is the most effective solvent of major, minor, and trace elements at high temperature and pressure (Manning 1994; Zhang and Frantz 2000; Newton and Manning 2007, 2008). The transport properties of H2O-rich fluids and their role in mass transport processes are, therefore, a central theme of this review. The impact of other components such as CO2, halogen, and sulfur species, on mass transport and rock-forming processes, will be incorporated as appropriate.

2 Review

In order to characterize the behavior of fluids in the Earth's interior, we will first discuss fluid sources. This will be followed by fluid properties including solubility of geochemically important elements and partitioning of elements between fluid and magma. The presentation will conclude with a discussion of how fluids migrate through a crystalline matrix and consequences of fluid distribution for geochemical and geophysical properties of the Earth's interior.

2.1 Sources of fluid

Except for the Earth's primordial volatiles, fluids are recycled usually with sediments at the beginning of a cycle. These sediments typically were deposited on the ocean floor and are comprised of both inorganic and organic components. Early stages of fluid cycles also can include metamorphic rocks formed in the hydrothermal environment existing during cooling of mid-ocean ridge volcanics that interact with H2O and its dissolved salts (see, for example, Evans and Tomkins 2020; for recent review).

During metamorphism of sediments, fluid components become part of hydrous, carbonate, and sulfide minerals and, sometimes, halogens such as F and Cl. These fluids, in turn, for the most part are gradually released with increasing metamorphic grade such as seen with increasing depth in subduction zones, for example. Under some circumstances, fluids might be transported through the transition zone and into the lower mantle. The extent to which this may take place, depends on the bulk composition, redox conditions, and thermal environment of the descending slab (van Keken et al. 2011; Bebout et al. 2013; Ohtani 2019).

Fluids derived from dehydration reactions during metamorphism also can trigger partial melting followed by fluid incorporation in the magmatic liquids thus formed (Wyllie 1982; Ulmer 2001). During crystallization and decompression of such fluid-bearing magma, some or all of the fluid will be exsolved to form a separate fluid phase. The composition of those fluids will depend on the fluids in the source region of melting and temperature and pressure conditions during cooling and crystallization (Audetat and Edmonds 2020).

Under certain circumstances fluids in the crust and upper mantle can migrate toward the surface along grain boundaries (Mysen et al. 1978; Watson et al. 1993) or, under some circumstances, through cracks, such as may be found in shear zones below some island arcs (White et al. 2019), without causing partial melting. Such movement is likely for fluids with low solubility in magmatic liquids and has limited impact solidus temperatures of rocks.

2.1.1 Fluids and devolatilization during metamorphism

Fluids released in metamorphic processes by exceeding stability fields of minerals that contain volatiles, are dominated by H2O because most major volatile-bearing metamorphic minerals are H2O-bearing (clay minerals, serpentine, mica, and amphiboles). Their H2O contents typically are greater the lower their upper temperature stability (Evans and Tomkins 2020; see also Fig. 1A).

Fig. 1
figure 1

Modified from Evans and Tomkins (2020)

H2 and CO2 generation during metamorphic processes. A. Cumulative H2O loss as a function of increasing metamorphic grade. B. CO2 loss from decarbonation reactions at 0.5 GPa as a function of CO2–H2O fluid composition.

Carbon dioxide is the second-most important fluid component in metamorphic rocks such as in the subducting plates although under some circumstances, reduced carbon in the form of CH4 as well as more complex hydrocarbons may form (Chu and Ague 2013; Yardley and Bodnar 2014; see also Manning et al. 2013; for review). The CO2 is primarily found in carbonate minerals such as calcite, aragonite, dolomite, and magnesite, but can also occur in smaller concentrations as parts of solid solutions in apatite and scapolite (Moecher and Essene 1990; Harlov 2015). In metamorphic systems with mixed CO2–H2O fluid, the stability of the CO2 and H2O-bearing minerals depends not only on temperature, pressure, and bulk chemical composition, but also varies with the proportion of CO2 and H2O (Connolly 2005; Evans and Tomkins 2020; see also Fig. 1B). For example, during subduction, fluid is predominantly H2O + CO2 with its CO2/H2O ratio increasing with depth of fluid release (Poli and Schmidt 2002; Connolly 2005). This CO2/H2O increase is because carbonate minerals (calcite, aragonite etc.) generally are stable to higher pressure and temperatures (greater depth) than many of the OH-bearing minerals in metamorphosed subducting slabs. These stability features lead to increased proportion of CO2 (Connolly 2005) relative to that of H2O from hydrous minerals (Poli and Schmidt 2002), and, therefore, the increased CO2/H2O ratio of released fluid with increasing depth in subduction zones.

This released fluid provides a means of mass transfer to the overlying mantle wedge that ultimately undergoes partial melting. This changing CO2/H2O ratio depending on depth (pressure) affects the solubility of geochemically important elements, the migration behavior of the fluid through crystalline subduction zone rocks, and the bulk composition of partial melts from the metasomatically altered mantle wedge (see, for example, Mysen and Boettcher 1975; Watson 1990; Manning 2004; Manning and Frezzotti 2020).

Chlorides can be important fluid components in particular during release of volatiles in subduction zones (Scambelluri and Philippot 2001; Kawamoto et al. 2014). The origin of such salts typically is ocean water and/or hydrothermal fluids trapped in pore space during sedimentation, diagenesis, and hydrothermal action near active mid-ocean ridges. Halite (NaCl) sometimes could have formed and been transported into the mantle with other sediments during subduction (e.g., Yardley and Graham 2002). Chlorine also can form solid solutions in minerals such as biotite, amphibole, and scapolite in addition to its entrapment in fluid inclusions (Goldschmidt and Newton 1977; Pillippot et al. 1998; Chevychelov et al. 2008; Henry and Daigle 2018).

Sulfur is a minor component of metamorphic fluids in most settings. It can exist, however, as pyrite and as a minor component in scapolite solid solutions together with components such as CO32− and Cl (Orville 1975; Goldsmith and Newton 1977; Morrissey and Tomkins 2020). Nitrogen when in reduced form (e.g., NH+4) can be exchanged in K+ in feldspar, mica, and dense magnesian phases. Under such conditions, nitrogen can be transported deep into the mantle near subducting plates (Hallam and Eugster 1976; Plessen et al. 2010) because such phases are stable to pressures sometimes in excess of 20 GPa (Konzett and Fei 2000; Trønnes 2002).

2.1.2 Fluids exsolved from magma

The composition of fluids released from cooling magma depends on magma composition, and on its partial melting source. The composition of fluids exsolved from cooling magma also varies with the temperature and pressure at which the fluids are released. Such variables result in varying partition coefficients between fluid and magmatic liquid. Therefore, partition coefficients of fluid species between magma and a coexisting fluid phase govern the composition of the fluid. Partitioning of H2O between fluid and melt

The temperature–pressure coordinates of the H2O (fluid)/hydrous melt equilibria as well as the coordinates of the critical point, above which fluids and melts are completely miscible, are significantly dependent on silicate composition (e.g., Shen and Keppler 1997; Bureau and Keppler 1999; Kessel et al. 2005). The fluid/melt partition coefficient of H2O in silicate–H2O systems at temperatures above their liquidii also varies significantly with temperature and pressure at conditions less than those of the critical point of rock–H2O systems. The exact temperature–pressure trends of fluid/melt partition coefficient curve toward the critical endpoint in the example in Fig. 2 in differ ways because the composition of the two systems shown in that figure differs. The temperature and pressure ranges of the two experimental data sets also are significantly different. Such differences are even more obvious when comparing compositionally different hydrous magmatic systems because temperatures and pressures of the critical endpoints increase the more mafic the silicate composition. For example, the critical point of the system MgO–SiO2–H2O may be at pressures in excess of 10 GPa although this pressure is the subject of considerable discussion with suggested pressures for the critical point in peridotite–H2O varying between 3.4 and about 11–13.5 GPa (Stalder et al. 2001; Mibe et al. 2002, 2007; Melekhova et al. 2007). In basalt–H2O systems, the critical point has been suggested to be near 3.4–5 GPa (Kessel et al. 2005; Mibe et al. 2011), and in granite–H2O systems near 1 GPa (Shen and Keppler 1997; Sowerby and Keppler 1998).

Fig. 2
figure 2

H2O partitioning between fluid and melt in the Na2O–Al2O3–SiO2–H2O system. Data from Shen and Keppler (1997) and Mysen (2013)

In the case of multicomponent fluids, the fluid/melt partition coefficient of H2O becomes a function of fluid composition (Botcharnikov et al. 2015; Webster et al. 2009). For example, Webster et al. (2009) reported that the H2O content of fluid increases with increased salinity (NaCl and KCl). In melt-H2O–CO2 systems, the partition coefficient is particularly sensitive to pressure and melt composition because the much greater solubility of H2O in silicate melts compared with the solubility of CO2 (Eggler and Kadik 1979; Iacono-Marziano et al. 2012). Partitioning of carbon-bearing species between fluid and melt

Oxidized carbon in magmatic systems, absent other components such as H2O, exists as CO2 in a C–O fluid phase and as CO2 and CO32− complexes in silicate melts. In melt-C–O–H systems, additional speciation is possible. Here, oxidized carbon can occur as CO2, CO32−, and HCO3 in both melts and fluids (Mysen 2015a, 2018). Under reducing conditions, CH4 and CH3 groups can be stabilized in both silicate melts and silicate-bearing fluids (Mysen et al. 2009, 2011). The proportion of these species and their partitioning behavior between fluid and melt vary with fluid and silicate composition, temperature and, likely, with pressure.

The exchange equilibrium of carbon-bearing species between melt and fluid under oxidizing conditions is (Fig. 3A):

$${\text{CO}}_{{3}}^{{{2} - }} \left( {{\text{melt}}} \right) \, + {\text{ HCO}}_{{3}}^{ - } \left( {{\text{fluid}}} \right) \, = {\text{ CO}}_{{3}}^{{{2} - }} \left( {{\text{fluid}}} \right) \, + {\text{ HCO}}_{{3}}^{ - } \left( {{\text{melt}}} \right)$$

whereas reducing under conditions the exchange equilibrium is (Fig. 3B):

$${\text{CH}}_{{4}} \left( {{\text{melt}}} \right) \, + {\text{ CH}}_{{3}} \left( {{\text{fluid}}} \right) \, = {\text{ CH}}_{{4}} \left( {{\text{fluid}}} \right) \, + {\text{ CH}}_{{3}} \left( {{\text{melt}}} \right)$$
Fig. 3
figure 3

Exchange equilibrium coefficients of carbon species from Eqs. (1) and (2). A. From Eq. (1), which describes the equilibrium under oxidizing conditions. B. From Eq. (2), which describes the equilibrium under reducing conditions.

Under oxidizing conditions and with increasing temperature, the CO3/HCO3 abundance ratio in melts increases faster than in coexisting fluid. The enthalpy change, ∆H, for reaction (1) is − 44 ± 9 kJ/mol with the assumption of ideal mixing (Mysen 2015a). In comparison, under sufficiently reducing conditions, the temperature dependence of the CH4/CH3 abundance ratio in fluid is greater than in coexisting melt with a ∆H for reaction (2) of 34 ± 3 kJ/mol (Mysen 2015a). It must be kept in mind, however, that because the experiments used to extract the data in Fig. 3 were carried out in a fixed volume hydrothermal diamond anvil cell (Bassett et al. 1994), the pressure also increased when the temperature increased. It was assumed, therefore, that the ∆V of the exchange equilibria (1) and (2) is negligible and that pressure did not, therefore, impact on the calculated ∆H-values. Partitioning of halogens between fluid and melt

Chlorine has attracted the most attention among experimental studies of the partitioning of halogens between fluid and magma. This attention likely at least in part is because Cl-complexes are often considered responsible for enrichments of economically important metals such as, for example, Mo, Cu, and Au in fluids and melts (Frank et al. 2011; Zajacz et al. 2013).

At the pressures of the subcritical region in melt-H2O–Cl systems such as, for example, the phonolite magma + H2O + Cl (below about 180 MPa; see also Fig. 4A), the Cl concentration in melt changes little as a function of the Cl in the coexisting fluid phase. However, at higher pressures the concentrations in coexisting melts and fluids are correlated albeit in a nonlinear way (Fig. 4B). It is also notable that the Cl concentration in the melt decreases with increasing pressure because of the partial molar volume difference of NaCl in aqueous fluid and H2O-rich melt is negative (Shinohara et al. 1989; Signorelli and Carroll 2002). Under anhydrous conditions, on the other hand, the Cl solubility in silicate melts is a positive function of pressure (Webster et al. 1999; Dalou and Mysen 2015).

Fig. 4
figure 4

Modified from Signorelli and Carroll (2000)

Chlorine distribution between saline fluid and phonolitic magma, A. Fluid–melt equilibria with immiscibility gap as a function of NaCl concentration in H2O–NaCl fluid and pressure. B. Evolution of Cl concentration in coexisting melt and saline fluid as a function of chlorine concentration in fluid and melt at pressures indicated.

The chlorine partition coefficient between brine and hydrous magma, DClfluid/melt, decreases with increasing pressure and decreasing temperature (Kilinc and Burnham 1972; Shinohara et al. 1989; Signorelli and Carroll 2000; Webster 1992; Hsu et al. 2019). Moreover, the DClfluid/melt is a strong function of Cl concentration and also changes with SiO2 content of the magma (Webster et al. 2009; Beerman et al. 2015; see also Fig. 5A–C). The more silica-rich, and, therefore, more felsic, the greater the fluid/melt partition coefficient (Botcharnikov et al. 2015). This relationship would likely be even more pronounced if the NBO/T parameter of the melt was used in replacement of the SiO2 (Signorelli and Carroll 2002; Metrich and Rutherford 1992). The SiO2 of magmatic liquids typically is negatively correlated with the melt NBO/T so that the lower the SiO2 concentration, generally the greater is the NBO/T of the melt (Mysen and Richet 2019; Chapter 18). Other compositional variables affecting the fluid/melt partition coefficient of Cl include Al2O3/(CaO + Na2O + K2O) (Iveson et al. 2017; Signorelli and Carroll 2002).

Fig. 5
figure 5

Modified from Botcharnikov et al. (2015) and Beermann et al. (2015)

Fluid/melt partition coefficient of Cl A. as a function of pressure for two different magma compositions as indicated. B. As a function of Cl concentration in andesitic melt at two different temperatures as indicated, and C. as a function of SiO2 concentration in melt.

The chlorine concentration also affects DClfluid/melt (Beermann et al. 2015; Hsu et al. 2019). Increasing Cl concentration such as from NaCl dissolved in aqueous fluid, for example, results in increasing fluid/melt partition coefficient (Fig. 6A). Increasing CO2 concentration in an H2O–CO2–NaCl environment, on the other hand, results in decreasing DClfluid/melt (Hsu et al. 2019; See also Fig. 6B).

Fig. 6
figure 6

Fluid/melt partition coefficient of chlorine, \({D}_{\mathrm{Cl}}^{\mathrm{fluid}/\mathrm{melt}}\) A. as a function of mol fraction of NaCl in fluid at two different temperatures as indicated. B. \({D}_{\mathrm{Cl}}^{\mathrm{fluid}/\mathrm{melt}}\) as a function of mol fraction of CO2 in H2O–CO2 fluid with NaCl added. The melt composition is that of a composition along the join SiO2–NaAlO2 with a slight excess of Al2O3 (Composition (wt%) on an anhydrous basis, SiO2: 80., Al2O3: 12.6, Na2O: 7.3) Modified after Hsu et al. (2019)

Relatively few experiments have been carried out to determine fluid/melt partitioning of F (Xiong et al. 1998; Kravchuk et al. 2004; Chevychelov et al. 2008; Webster et al. 2009). For those for which experimentally determined partition coefficients, DFfluid/melt, exist, these partition coefficients typically are less than 1 (Fig. 7). The partitioning behavior of fluorine differs, therefore, from all other halogens for which the fluid/melt partition coefficients are greater than 1 (Dolejs and Zajacz 2018). This difference between F and Cl partition coefficients reflects the different solubility behavior of Cl and F in magmatic liquids (Dalou et al. 2015; Dalou and Mysen 2015). For example, whereas Cl solubility decreases as silicate melts become more aluminous, the opposite trend was observed for F (Dalou et al. 2015). The fluorine solubility in silicate melts also increases with increasing H2O content, a behavior that contrasts with that of Cl, the solubility of which decreases with increasing H2O content of silicate melts (Dalou and Mysen 2015).

Fig. 7
figure 7

Fluorine concentration in coexisting aqueous fluid and H2O-rich melt for various granitic melt compositions. Modified after Dolejs and Zajacs (2018)

Fluid/melt partition coefficients of F, Cl, Br, and I follow a simple relationship of the form (Bureau et al. 2000);

$$\ln D_{i}^{{\text{fluid/melt}}} = \, - 11.7 + 7.2r\left( {\text{\AA}} \right).$$

where r is the radius of the halogen (Fig. 8). This relationship likely is because the solubility of halogens in silicate melts is less the greater their ionic radius.

Fig. 8
figure 8

Fluid/melt partitioning at 200 MPa and 900° as a function of the ionic radius of the halogen. (The melt composition is (wt%): SiO2: 67.09, Al2O3: 18.08, Na2O: 11.06.) (Modified after Bureau et al. 2000) Partitioning of sulfur between fluid and melt

Sulfur is the third-most abundant volatile component in the Earth (Jambon 1994). It is of particular interest because S-rich fluids can be important transport media of metals to form economically viable ore deposits because transition metals such as, for example, Zn, Cu, Mo, Pb, and Ag can form sulfide complexes when dissolved in fluids and magma (Pokrovski et al. 2008; Botcharnikov et al. 2011). Oxidized sulfur, whether in fluid or magma, does not enhance the solubility of such elements significantly. Oxidized sulfur also can govern degassing processes of magma during their ascent and cooling (Oppenheimer 2003).

Oxygen fugacity, fO2, is an important variable governing the behavior of sulfur in fluids (and magmatic liquids) because the oxygen fugacity can govern the redox state of sulfur (e.g., Nagashima and Katsura 1973; O'Neill and Mavrogenes 2002; Jugo et al. 2010). It has proposed, for example, that fluid/melt partition coefficients can be described with an expression of the type (Gennaro et al. 2020):

$$\log \, D_{S}^{{\text{fluid/melt}}} = \, a/T \, + \, bP \, + \, c\Delta {\text{NNO }} + \, d.$$

In this equation, T is temperature (°C), P is pressure (MPa) and NNO is the oxygen fugacity difference from that of the nickel–nickel oxide (NNO) oxygen buffer (log units).

Under oxidizing conditions, where sulfur exists predominantly as S6+, its solution behavior in fluids appears to follow Henry's law (Fig. 9). However, the slope of the curves in Fig. 9, and, therefore, the Henry's Law constant, depends on the bulk composition of the system. It also depends on H2O content (Webster and Botcharnikov 2011), SiO2 content (Scaillet et al. 1998), the proportion of the sum of alkali metals and alkaline earths versus Si + Al + Fe3+ (Webster and Botcharnikov 2011) and, therefore, the NBO/T of the melt (Zajacz 2015). Increased peralkalinity also leads to increased DSfluid/melt. Finally, the fluid/melt partition coefficient of reduced sulfur decreases rapidly with increasing FeO concentration, which is not surprising given the particularly strong affinity of S2− for Fe2+ (Richardson and Fincham 1954; O'Neill and Mavrogenes 2002).

Fig. 9
figure 9

Sulfur content coexisting aqueous fluid and hydrous melt as a function of their sulfur content at 500 MPa and 1240 °C with the oxygen fugacity controlled 1.4 log units above that of the NNO buffer for systems as indicated on diagrams. (Modified after Zajacs 2015)

2.2 Solubility of major elements in fluids

Fluids in the Earth are important transport agents because of significant solubility in fluids of geochemically and geophysically important components. This solubility depends on the fluid composition, the element of interest, temperature, and pressure. For aliovalent elements, the oxygen fugacity also can be important.

2.2.1 SiO2 in aqueous fluid

The concentration of SiO2 in most terrestrial rocks exceeds 40 wt% (Allegre et al. 2001), which typically is more than twice the terrestrial abundance of any other major oxide component. Characterization of the interaction between H2O fluid and SiO2 to high temperatures and pressures is, therefore, fundamental to our understanding of the role of H2O as a transport agent of rock-forming components in the Earth.

Solubility determination of SiO2 in H2O fluid in the SiO2–H2O system at pressures and temperatures below the second critical end point (near 1 GPa and 1080 °C; see Kennedy et al. 1962) have, therefore, been the subject of extensive experimental work (Kennedy 1950; Morey and Hesselgesser 1951; Weill and Fyfe 1964; Anderson and Burnham 1965; Fournier and Potter 1982; Manning 1994; Newton and Manning 2000). The SiO2 solubility increases with both temperature and pressure (Fig. 10). It varies particularly rapidly with temperature near the critical temperature of H2O resulting in an inflection of the solubility curve (Fig. 10A). As the pressure is increased, the extent of the inflection of those solubility curves diminishes so that above about 100 MPa, the inflection point is barely discernible. Moreover, the pressure at which the inflection of the solubility curve occurs, shifts to high temperature higher the total pressure.

Fig. 10
figure 10

Solubility of SiO2 in aqueous fluid. A. As a function of temperature across the critical endpoint at pressures as indicated on individual curves. B. As a function of temperature at pressures from 100 to 700 MPa as indicated on individual curves. C. As a function of pressure at temperatures indicated. Data from Weill and Fyfe (1964) (A), Anderson and Burnham (1965) (B), and Manning (1994) (C)

Aqueous fluids are important in rock-forming processes to much greater depth than the approximately 5 km (equivalent to about 150 MPa) of the early experimental data from Kennedy (1950). Weill and Fyfe (1964) extended the pressure and temperature ranges to 400 MPa in the 400°-550 °C respectively (Fig. 10B). More recent experimental SiO2 solubility data have been dominated by the experiments of Craig Manning and coworkers. They have reported SiO2 solubility in aqueous fluids to pressures near 2 GPa (see, for example, Manning 1994; Newton and Manning 2000, 2008; Hunt and Manning 2012). They found that the rate of SiO2 solubility increases with pressure is greater the higher the temperature (Fig. 10C), an observation that also is similar to earlier experimental studies of SiO2 solubility in the SiO2–H2O system (Weill and Fyfe 1964; Anderson and Burnham 1965). Moreover, the isothermal SiO2 solubility becomes linear when expressed as a function of the log ρH2O (density of pure H2O). From regression analysis of their own data together with other published experimental data over a range of temperatures, Manning (1994) arrived at an empirical expression that may be used to calculate the solubility in SiO2 in H2O to perhaps 2 GPa total pressure;

$$\begin{gathered} \log m_{{{\text{SiO}}2}} = 4.262 - \frac{5764.2}{T} + \frac{{1.7513 \bullet 10^{6} }}{{T^{2} }} - \frac{{2.2869 \bullet 10^{8} }}{{T^{3} }} + \hfill \\ \left( { 2.8454 - \frac{1006.9}{T} + \frac{{3.5689 \bullet 10^{5} }}{{T^{2} }}} \right) \bullet \log \rho_{{{\text{H}}2{\text{O}}}} \hfill \\ \end{gathered}$$

where mSiO2 is molality of SiO2 in the aqueous solution (kg/mol), \({\rho }_{\mathrm{H}2\mathrm{O}}\) is density (g/cm3) of pure H2O and T is temperature (kelvin). In Eq. (5), pressure effects are built into the relationship between solubility and density of H2O. Of course, \({\rho }_{\mathrm{H}2\mathrm{O}}\) also depends on temperature even though in Eq. (5), temperature also is one of the explicit variables in the regression of SiO2 solubility.

Most of the proposed solution mechanisms for SiO2 in H2O fluid refer to OH-bearing silicate monomers and dimers and perhaps even trimers as the structural entities of dissolved silica (Wendlandt and Glemser 1964; Newton and Manning 2003; Zotov and Keppler 2002; Mysen 2010; Mysen et al. 2013). For example, Manning and coworkers (Newton and Manning 2003, 2008; Hunt and Manning 2012) modeled the SiO2 solubility mechanisms in aqueous fluids in terms of degree of polymerization of SiO2 species as a function of total SiO2 content of the fluid. As an example, near the second critical endpoint of the SiO2–H2O system (1080 °C and 1 GPa; see Kennedy et al. 1962), speciation in SiO2–H2O fluid as a function of SiO2 concentration such as illustrated in Fig. 11 was proposed (Newton and Manning 2008). In this model, the degree of polymerization of the silicate species in aqueous fluid is correlated positively with the total SiO2 concentration, a structural feature apparently originally proposed by Wendlandt and Glemser (1964) on the basis of their silicate solubility data.

Fig. 11
figure 11

Modified from Newton and Manning (2008)

Speciation of dissolved SiO2 in aqueous fluid as a function of SiO2 concentration in the fluid.

Direct experimental determination of the structure of SiO2–H2O fluids at high temperature and pressure initially was reported by Zotov and Keppler (2002) and subsequently expanded upon by Mysen (2010) and Mysen et al. (2013). At pressures and temperatures below 0.6 GPa and 500 °C, only monomers [Si(OH)4] were detected by Zotov and Keppler (2002). With an additional temperature and pressure increase, the latter authors also found silicate dimers in SiO2–H2O fluid and proposed a dimerization reaction such as

$$2{\text{H}}_{4} {\text{SiO}}_{4} = {\text{ H}}_{6} {\text{Si}}_{2} {\text{O}}_{7} + {\text{ H}}_{2} {\text{O}},$$

for which the equilibrium constant as a function of temperature and pressure was reported as;

$$\ln K\left( {P, T} \right) = \ln K\left( {P_{o} ,T} \right) - \frac{{\Delta V_{{{\text{eqn}}.\left( 6 \right)}} }}{{{\text{RT}}}}\left( {P - P_{o} } \right) - \frac{1}{{{\text{RT}}}}\mathop \smallint \limits_{Po}^{P} V_{{{\text{H}}2{\text{O}}}} dP,$$

where ∆Veqn.(6) denotes the volume change for reaction shown as Eq. (6), the VH2O is molar volume of pure H2O, P is pressure, and T is temperature (kelvin).

Zotov and Keppler (2002) reported an enthalpy for Eq. (6) of 12.6 ± 1.3 kJ/mol. This enthalpy value is considerably greater than that which Sverjensky et al. (2014) from thermodynamic modeling and Mysen (2010) from Raman spectroscopy reported for reaction (6). The difference between the results of Zotov and Keppler (2002) and Mysen (2010) reflects different structural assignments of the Raman intensities used to deduce silicate species abundance in SiO2–H2O fluids. The enthalpy values in those two studies are in accord, however, when using the same assignments of the Raman bands reported in those two experimental studies.

Q0, Q1, and Q2 speciesFootnote 1 of silica were detected in aqueous fluid from vibrational spectra of the SiO2–H2O system when temperatures and pressures were extended to 900 °C and 5.4 GPa, respectively (Mysen et al. 2013). Here, the abundance of the variously polymerized Qn-species (n > 0) is positively correlated with the concentration of SiO2 in the aqueous fluid, which, of course, is the same relationship as proposed from the SiO2 solubility in the SiO2–H2O system (Wendlandt and Glemser 1964; Newton and Manning 2008) and from the thermodynamic modeling of solubility in this system (Sverjensky et al. 2014).

For the mol fraction of Q0, Q1, and Q2 species, for example, the following relationship holds (Mysen et al. 2013);

$$\frac{{X_{Q1} + X_{Q2} }}{{X_{Q0} }} = 1.3 + 0.1 \bullet \left( {m_{{{\text{SiO}}2}} } \right)^{1.5} ,$$

where the X-values are mol fractions and mSiO2 is molality (Fig. 12). It is clear, therefore, the concentration of SiO2 is a critical factor in determining the degree of polymerization of dissolved SiO2. This relationship between polymerization of Qn-species and SiO2 concentration in fluids resembles qualitatively the relationship between SiO2 content and the degree of polymerization Qn-species of silicate melts (Mysen et al. 1982; McMillan 1984; Buckermann et al. 1992; Cody et al. 2005).

Fig. 12
figure 12

Modified from Mysen et al. (2013)

Silicate species (Q.n-species) in SiO2–H2O as a function of total SiO2 concentration at temperatures and pressures indicated.

2.2.2 SiO2 in saline fluids

Aqueous fluids, in particular in subduction zone settings, can be saline with NaCl the dominant salt (Keppler 1996; Scambelluri and Philippot 2001; Manning and Aranovich 2014; Kawamoto et al. 2013). There are, therefore, numerous reports on experimental determination of SiO2 solubility in H2O–NaCl fluids at high temperature and pressure (Anderson and Burnham 1967; Xie and Walther 1993; Newton and Manning 2000, 2006; Shmulovich et al. 2001; Cruz and Manning 2015; Scheuermann et al. 2018).

The SiO2 solubility in H2O–NaCl fluids decreases with increasing NaCl concentration at pressures at and above about 0.5 GPa. At such pressures, the log mSiO2 is a linear or near linear function of NaCl mol fraction in the fluid, XNaCl (Fig. 13). Notably, the slope of this relationship is nearly independent of temperature in the temperature range examined experimentally (500°–900 °C), while the solubility itself increases with increasing temperature (Fig. 13). However, at pressures below 0.5 GPa, in H2O–NaCl fluids, there is an initial SiO2 solubility increase with increased mol fraction of NaCl (XNaCl) equal to or less than about 0.1 before a further XNaCl increase results in lowered SiO2 solubility (Xie and Walther 1993; Newton and Manning 2000).

Fig. 13
figure 13

Modified from Newton and Manning (2000)

Solubility of SiO2 in H2O–NaCl fluid as a function of salinity at different temperatures as indicated and 0.5 GPa total pressure.

The reason for the changing SiO2 solubility dependence on NaCl concentration below and above about 0.5 GPa is not well known. One might surmise, however, that this solubility behavior is because two different solution mechanisms are active in the SiO2–H2O–NaCl system. One is dilution of H2O by NaCl in the fluid, which is likely to shift to the left a solubility reaction such as: Footnote 2

$${\text{SiO}}_{2} \left( {{\text{xtal}}} \right) \, + \, n{\text{H}}_{2} {\text{O }} = {\text{ SiO}}_{2} \bullet n{\text{H}}_{2} {\text{O}}\left( {{\text{fluid}}} \right)$$

This shift would decrease the silica solubility in the fluid. The extent to which this shift affects the SiO2 solubility depends on the fugacity of H2O, fH2O, which by itself decreases with decreasing pressure (Burnham et al. 1969). Therefore, one would expect the influence on SiO2 by the dilution of the fluid with NaCl, would be less the lower the pressure, the second mechanism involves chemical interaction between dissolved silica and Na+ from the NaCl. Such interaction results in formation of depolymerized Qn-species in the fluid where Na+ forms bonding with nonbridging oxygen in those Qn-species. Based on the analogy between structural behavior of Na2O–SiO2 melts as a function of their Na/Si ratio (e.g., Maekawa et al. 1991; Buckermann et al. 1992) and with H2O in solution (Cody et al. 2005), from steric considerations of the local charge environment surrounding nonbridging oxygens, Na–O bonding is favored over H–O bonding in these structures (Cody et al. 2005) because of the much smaller ionic radius of H+.Footnote 3 It is likely that the solution mechanism of silicate components in silicate-rich H2O–NaCl fluids resembles those documented for silicate melts and that this mechanism would enhance the solubility of SiO2 in saline fluids.

Whether the first or the second mechanism dominates would depend significantly on pressure, which, in turn, governs the fH2O. The lower the pressure, the smaller the effect of fH2O in reaction (9) and the more important is the second process. It is suggested that those relationships would explain the pressure-dependent effect of NaCl on the solubility of SiO2 in H2O–NaCl fluids. This explanation also implies that the pressure at which the solubility crossover takes place will depend on both temperature, which affects fH2O and the concentration of chloride in the H2O–NaCl fluid. It also means that different chlorides will have different effects on the solubility of SiO2 in the fluid.

A number of additional models for solution of SiO2 in H2O–NaCl fluids has been proposed (Franck 1973; Walther and Schott 1988; Newton and Manning 2000, 2016; Cruz and Manning 2015; Shi et al. 2019). Among those models, that of Shi et al. (2019) seems to reproduce the SiO2 solubility in H2O–NaCl fluids over the widest range of temperature, pressure and NaCl concentration.

Shi et al. (2019) considered the simple solubility reaction expressed with Eq. (9), with the equilibrium constant for this reaction

$$K = \frac{{a_{{{\text{SiO}}2}} }}{{a_{{{\text{SiO}}2\left( {{\text{xtal}}} \right)}} a_{{{\text{H}}2{\text{O}}}}^{n} }},$$


$$a_{{{\text{SiO}}2}} = m_{{{\text{SiO}}2}} \gamma_{{{\text{SiO}}2}} ,$$


$$a_{{{\text{H}}2{\text{O}}}} = d_{{{\text{H}}2{\text{O}}}} \lambda_{{{\text{H}}2{\text{O}}}}$$

In Eqns. (912), a is activity, γ is activity coefficient and dH2O is the concentration of H2O.

These equations can be combined to yield (Shi et al. 2019);

$$\log m_{{{\text{SiO}}2}} = \, \log \, K \, + \, n\log r_{{{\text{soln}}}} F \, + \, \log \left( {{{\gamma_{{{\text{H}}2{\text{O}}}} } \mathord{\left/ {\vphantom {{\gamma_{{{\text{H}}2{\text{O}}}} } {\gamma_{{{\text{SiO}}2}} }}} \right. \kern-\nulldelimiterspace} {\gamma_{{{\text{SiO}}2}} }}} \right)$$

where γSiO2 and γH2O are the activity coefficients of SiO2 and H2O in H2O–NaCl fluid, respectively. F is the mass fraction of H2O, and ρsoln is the density of the solution. This model describes the experimental data for SiO2–H2O systems quite accurately (Fig. 14).

Fig. 14
figure 14

Modified from Shi et al. (2019)

Solubility of SiO2 in H2O–NaCl fluid as a function of salinity at 700 °C and 1 GPa calculated with the model of Shi et al. (2019) and compared with experimental data from Newton and Manning (2000).

2.2.3 MgO-SiO2 in aqueous fluid

Characterization of SiO2-bearing aqueous solutions is a critical first step toward understanding the behavior of aqueous solutions in natural processes. However, determination of only SiO2 solubility and only in the SiO2–H2O system is an obvious oversimplification of conditions in nature.

As a next step toward characterization of the solution behavior of chemically more complex silicates in fluids in the Earth's mantle, the system SiO2–MgO–H2O often has been employed as model peridotite system because the abundance of SiO2 + MgO comprises 70–80% of mantle peridotite (McDonough et al. 1995; Nakamura and Kushiro 1974; Konzett and Ulmer 1999; Zhang and Frantz 2000; Newton and Manning 2002; Mibe et al. 2002; Stalder et al. 2001; Kawamoto et al. 2004).

In the MgO–SiO2–H2O system at pressures near 1.5 GPa, there is a continuous solubility from melt near the SiO2 corner to the H2O corner where aqueous fluid contains only SiO2 (Fig. 15A). In other words, at least at this pressure, the solute in aqueous fluids is essentially pure SiO2 in equilibrium with Mg-rich crystalline phases such as Mg2SiO4 (forsterite) or MgSiO3 (enstatite). This finding is in accord with more recent experimental data in the same system both near this as well as at higher pressure (Zhang and Frantz 2000; Stalder et al. 2001; Mibe et al. 2002; Newton and Manning 2002; Kawamoto et al. 2004). In fact, the Mg/Si ratio of the silicate solute is near 0 at pressures at or below about 2 GPa before this ratio begins to increase as pressure is increased beyond 2 GPa (Kawamoto et al. 2004; Mibe et al. 2002; Zhang and Frantz 2000; see also Fig. 15B).

Fig. 15
figure 15

Modified from Nakamura and Kushiro (1974) (A) and Mibe et al. (2002) (B)

A. Phase relations in the system Mg2SiO4–SiO2–H2O at 1280 °C and 1.5 GPa. B. Evolution of fluid composition in the system Mg2SiO4–SiO2–H2O as a function of pressure.

By extending the solubility data in the MgO–SiO2–H2O system from the 1.5 GPa in the Nakamura and Kushiro (1974) study to higher pressures, a second critical endpoint may be approached (Mibe et al. 2007; Melekhova et al. 2007). For example, at and above the 10 GPa pressure, Melekhova et al. (2007) reported that the MgO content of the fluid increased rapidly with increasing temperature, until near 13.5 GPa where the temperature effect on MgO solubility had disappeared. This evolution led Melekhova et al. (2007) to suggest that the critical endpoint in the MgO–SiO2–H2O system is somewhere between 11 and 13.5 GPa in the 1000–1350 °C temperature range of their study.

The estimated pressure–temperature coordinates of the proposed critical point from the Melekhova et al. (2007) study from the simple MgO–SiO2–H2O system (11–13.5 GPa/1000–1350 °C) differ significantly, however, from the pressure/temperature coordinates of a synthetic peridotite with typical peridotite composition (3.8 GPa/1000 °C) reported by Mibe et al. (2007). There are, of course, some important compositional differences that could affect the different critical point coordinates. The MgO–SiO2–H2O system examined by Melekhova et al. (2007) did not contain FeO, Al2O3, and alkali oxides, whereas the peridotite composition employed by Mibe et al. (2007) did. Addition of any and all of those latter components enhance the solubility in aqueous fluids as discussed in more detail later in this presentation. Enhanced solubility in aqueous fluid typically correlates with lowered pressure (and temperature) of the critical point. This latter observation is, therefore, consistent with expecting the pressure–temperature coordinates of critical point in a peridotite–H2O system (Mibe et al. 2007) to be lower than in the simpler MgO–SiO2–H2O system (Melekhova et al. 2007). However, existing information is insufficient to quantify those difference and, therefore, whether this explains the different pressures and temperatures reported on those two experimental studies.

There is, however, an additional difference between the two sets of experiments, a difference that also aid in explaining why the pressure/temperature coordinates of the critical points reported for the MgO–SiO2–H2O (Melekhova et al. 2007) and peridotite–H2O (Mibe et al. 2007) differ. In the MgO–SiO2–H2O system, the critical point was estimated from the discontinuous evolution of MgO concentration of quenched fluid (analyzed at ambient temperature and pressure after extraction of the sample) as a function of temperature at 11 and 13.5 GPa. This evolution led Melekhova et al. (2007) to bracket the critical point in the MgO–SiO2–H2O system between 11 and 13.5 GPa and between 1000 and 1350 °C. Notably, though, the temperature evolution of the SiO2 concentration in fluid did not show any discontinuity as a function of temperature in the same pressures and the same temperature ranges. It is not clear, therefore, how reliable the estimated pressure–temperature coordinates of the critical point determined solely from the discontinuous MgO concentration of fluid actually are.

The critical point reported for the peridotite–H2O system (Mibe et al. 2007) was determined by using X-ray imaging of the sample in situ, while it was at any pressure–temperature condition. A sample consisting of melt + fluid transformed to a single supercritical fluid phase going up temperature near 3.8 GPa and 1000 °C. There was exsolution of fluid from this fluid to form a melt + fluid during cooling. This method is closely similar to that used in the original studies of critical points in granite–H2O systems (Nowak and Behrens 1995; Shen and Keppler 1997; Bureau and Keppler 1999). In light of the discussion above, it is concluded that most likely, the pressure–temperature coordinates of the critical endpoint in the peridotite–H2O system from the Mibe et al. (2007) experiments should be considered more reliable and those from the Melekhova et al. (2007) study.

This conclusion also means that the reported pressure-temperature coordinations of the critical point of basalt–H2O and eclogite–H2O by Kessel et al. (2005), using the same method as that of Melekhova et al. (2007), probably also are not accurate.

The SiO2 concentration in aqueous fluids in equilibrium with enstatite in the MgO–SiO2–H2O system is less polymerized than the SiO2 solute in fluid in the SiO2–H2O system at the same temperature and pressure (Zhang and Frantz 2000; Mysen et al. 2013). This difference happens because the silica activity defined by crystalline phases coexisting with fluid (forsterite and enstatite) in MgO–SiO2–H2O system is lower than in the SiO2–H2O system where at silica saturation, quartz coexists with fluid. The lower SiO2 concentration in MgO–SiO2–H2O fluid leads to less polymerization of silicate species in aqueous solution. A comparison of the Qn-species evolution in fluids with temperature and pressure in SiO2–H2O and MgO–SiO2–H2O system illustrates this difference (Fig. 16).

Fig. 16
figure 16

Q.n speciation in SiO2–H2O and MgO–SiO2–H2O fluid as a function of temperature at the pressures indicated on individual curves. Modified after Mysen et al. 2013

The equilibrium among the Qn-species in the MgO–SiO2–H2O fluid at any pressure and temperature is, therefore, simpler than in the SiO2–H2O [Eqns. (6), (8), and (9)]:

$$Q^{1} = \, 2Q^{0} .$$

A striking difference between the results for MgO–SiO2–H2O fluids and those of SiO2–H2O fluids is that whereas the ∆H and ∆V for the polymerization reaction in SiO2–H2O fluids depend on pressure and temperature, there are no such effects for the structurally simpler equilibrium relations in MgO–SiO2–H2O fluids (Mysen et al. 2013). This difference may also reflect the lesser extent of silicate polymerization in the MgO–SiO2–H2O fluids. The less polymerized silicate species in the latter fluids might lead to lesser  excess volume of mixing in these latter MgO–SiO2–H2O fluids.

2.2.4 MgO–SiO2 in saline fluids

The solubility of Mg2SiO4 (forsterite) and MgSiO3 (enstatite) in H2O–NaCl fluid has been determined at 1 GPa (Macris et al. 2020) who reported incongruent solution of enstatite in H2O–NaCl fluids, whereas forsterite dissolved congruently. Both solubility and the Mg/Si ratio in the fluid increase with increasing NaCl concentration in the fluid (Fig. 17). This solubility behavior differs from that of SiO2 in H2O–NaCl fluids where the silicate solubility as a function of NaCl concentration varies with both NaCl concentration in fluid and with pressure (Xie and Walther 1993; Newton and Manning 2000; see also Sect. 2.2.2 and Fig. 13) This different solution behavior in fluids in the SiO2–H2O–NaCl and –NaCl systems probably results from additional solution mechanisms in MgO–SiO2–H2O–NaCl fluids. First, the decreasing SiO2 concentration (increasing Mg/Si ratio) with increasing NaCl of the fluid such as seen in the Mg2SiO4–H2O–NaCl system (Fig. 17B) in principle is the same trend as the solubility behavior of SiO2 in H2O–NaCl fluids, which also shows decreasing solubility with increasing NaCl (Fig. 17). Second, the solubility of the MgO component in saline fluids increases with increasing NaCl concentration probably (Macris et al. 2020) through formation of Mg–Cl type complexes in the fluid. In fact, Macris et al. (2020) proposed that mixed OH, Cl species (MgClOH) existed in such saline fluids. They suggested two possible, but in their words, nonunique solution mechanisms for forsterite (Mg2SiO4) in H2O + NaCl fluids to rationalize the reported solubility data at 1 GPa and 800° and 900 °C, respectively:

$${8}00^\circ {\text{C}}:{\text{ Mg}}_{{2}} {\text{SiO}}_{{4}} \left( {{\text{fo}}} \right) \, + {\text{ 3H}}_{{2}} {\text{O}}\left( {{\text{fluid}}} \right) \, + {\text{ NaCl}}\left( {{\text{fluid}}} \right) \, = {\text{ MgClOH}}\left( {{\text{fluid}}} \right) \, + {\text{ Mg}}\left( {{\text{OH}}} \right)_{{2}} \left( {{\text{fluid}}} \right) \, + {\text{ NaSiO}}\left( {{\text{OH}}} \right)_{{3}} \left( {{\text{fluid}}} \right),$$


$${9}00^\circ {\text{C}}:{\text{Mg}}_{{2}} {\text{SiO}}_{{4}} \left( {{\text{fo}}} \right) + {\text{2H}}_{{2}} {\text{O}}\left( {{\text{fluid}}} \right) + {\text{NaCl}}\left( {{\text{fluid}}} \right) = {\text{MgClOH}}\left( {{\text{fluid}}} \right) + {\text{Mg}}\left( {{\text{OH}}} \right)_{{2}} \left( {{\text{fluid}}} \right) + {\text{ NaSiO}}_{{2}} {\text{OH}}\left( {{\text{fluid}}} \right).$$
Fig. 17
figure 17

Modified from Macris et al. (2020)

A. Mg2SiO4 solubility in H2O–NaCl fluid as a function of mol fraction of NaCl at 1 GPa and at temperatures indicated. B. Mg/Si ratio of H2O–NaCl fluid in equilibrium with forsterite + enstatite at 1 GPa and 800° and 900 °C as a function of NaCl concentration of the fluid.

The speciation proposed in Eqn. (15a, b) has not been determined directly, and other reactions can also be written. However, they may serve to illustrate how Mg–Cl bonding in fluid complexes may account for the enhanced solubility of forsterite in NaCl-bearing fluids.

The concept illustrated for forsterite solubility in H2O–NaCl fluid should perhaps also apply to solution of MgSiO3 in such fluids. However, if so, as a portion of the Mg2+ in MgSiO3 would be tied up in the Mg-bearing fluid complexes, the Mg/Si ratio of the crystalline would, if anything, be expected to decrease from that of the MgSiO3 stoichiometry and perhaps lead to formation of SiO2 polymorphs. Such an evolution contrasts with the reported incongruent solution of MgSiO3 (enstatite) in H2O–NaCl fluids to produce Mg2SiO4 (forsterite) + fluid. The latter behavior would be analogous the solubility behavior of MgSiO3 (enstatite) in pure H2O at similar temperature are pressure conditions (Zhang and Frantz 2000). Clearly, these relationships require further confirmation by direct determination of the complexes formed in the H2O–NaCl fluids in these systems.

2.2.5 H2O–Al2O3(–NaCl–KOH–SiO2) in aqueous fluid

Given that Al2O3 typically is the second- or third-most abundant rock-forming oxide in most igneous and metamorphic rocks, characterization of its solubility behavior in fluids is important. Moreover, although it is commonly assumed that Al2O3 is the least soluble in pure H2O among the major rock-forming major oxides (e.g., Carmichael 1969), evidence from rocks indicates that Al2O3 can be quite mobile under some circumstances (e.g., Kerrick 1990; McLelland et al. 2002). Al2O3 solubility in aqueous fluid

Examination of Al2O3 solubility in aqueous fluids is constrained by the pressure–temperature stability field of corundum, which in the Al2O3–H2O system is limited at low temperature by transformation to diaspore and H2O, which takes place between ~ 500 and 600 °C in the 1–4 GPa pressure range, for example (Kennedy 1959). At higher temperature, the Al2O3 solubility in aqueous fluid in the Al2O3–H2O system, which is in the ppm range, is a positive and linear function of pressure (Becker et al. 1983; see Fig. 18);

$${\text{Al}}_{2} {\text{O}}_{3} \left( {{\text{fluid}}} \right) = - 12.37 + 0.724 \, P\left( {{\text{GPa}}} \right).$$

where Al2O3 (fluid) is in ppm.

Fig. 18
figure 18

Solubility of corundum (Al2O3) in aqueous fluid in the Al2O3–H2O system as a function of pressure at 670–700 °C. Modified after Becker et al. (1983)

A simple solution model for Al2O3 in aqueous solutions such as

$${\text{Al}}\left( {{\text{OH}}} \right)_{4}^{ - } + {\text{ H}}^{ + } = {\text{ Al}}\left( {{\text{OH}}} \right)_{3}^\circ \, + {\text{ H}}_{2} {\text{O}},$$

has been proposed (Pokrovski and Helgeson 1995). However, the equilibrium constant for this reaction in the 50–220 MPa pressure range reached a minimum between 250 and 300 °C before increasing as the temperature is increased further (Walther 1997).Footnote 4 This changing temperature-dependent solubility behavior may lead to the suggestion that more than one solution mechanism of Al2O3 in aqueous solution is possible such as, for example;

$${\text{Al}}\left( {{\text{OH}}} \right)_{3}^\circ \, + {\text{ H}}^{ + } = {\text{ Al}}\left( {{\text{OH}}} \right)_{2}^{ + } + {\text{ H}}_{2} {\text{O}},$$

in addition to equilibrium (17). Al2O3 solubility in aqueous fluid in more complex systems with and without halogens

In order to mimic better natural conditions, SiO2 and alkali metals need to be added to the Al2O3–H2O system (Currie 1968; Anderson and Burnham 1983; Manning 2007; Wohlers et al. 2011; Schmidt et al. 2014). The influence of SiO2 alone on Al2O3 solubility in aqueous fluid is between 3.3 and 4.8 times greater than the Al2O3 solubility in the Al2O3–H2O system without SiO2 (Becker et al. 1983; Manning 2007; Tropper and Manning 2007). It should be noted, however, that whereas the Si content of such fluid was 0.3 ± 0.1 molal, that of Al was 0.008 ± 0.007 molal. In other words, for all practical purposes, the solute in SiO2-bearing fluids in those experiments was essentially all silicate and did not indicate enhanced Al2O3 solubility in aqueous SiO2-bearing aqueous solution.

By adding KOH or NaCl to H2O fluid, the Al2O3 solubility increases by several orders of magnitude compared with the Al2O3 solubility in pure H2O (Pascal and Anderson 1989; Walther 1997, 2001; Wohlers and Manning 2009; Newton and Manning 2006; see also Fig. 19). This solubility is a positive function of the KOH and NaCl concentrations at given temperature and pressure (Pascal and Anderson 1989; Azaroual et al. 1996; Newton and Manning 2006).

Fig. 19
figure 19

Modified from Azaroual et al. (1996) (A) and Newton and Manning 2006 (B)

A. Aluminum solubility in alkaline fluid, mAl, as a function of KOH concentration in the Al2O3–H2O–KOH system at 50–200 MPa pressure and 400 °C. B. Aluminum solubility in H2O–NaCl fluid as a function of NaCl concentration in the system Al2O3–H2O–NaCl at 800 °C and 1 GPa.

Addition of NaCl to corundum + quartz increases the Al2O3 solubility further compared with Al2O3 solubility in the quartz-free system (Newton and Manning 2008; see also Fig. 20). Here, the molality, mAl2O3, is a complex and positive function of both the SiO2 and NaCl concentrations, which has been described with the empirical expression (Newton and Manning 2008):

$$X_{{{\text{NaCl}}}} \le 0.3:m_{{{\text{Al}}2{\text{O}}3}} = m_{{{\text{Al}}2{\text{O}}3}}^{0} + \left( {0.0025 - 0.048X_{{{\text{NaCl}}}} + 9.733X_{{{\text{NaCl}}}}^{2} } \right)m_{{{\text{SiO}}2}} + \left( {0.0012 - 0.21X_{{{\text{NaCl}}}} + 0.0757X_{{{\text{NaCl}}}}^{(1/2)} } \right)m_{{{\text{SiO}}2}}^{2} ,$$

where \({m}_{\mathrm{Al}2\mathrm{O}3}^{0}\) is the molality in NaCl-free fluid. A somewhat different expression was given for more NaCl-rich solutions.

Fig. 20
figure 20

Phase relations in the Al2O3–SiO2–H2O–NaCl in terms of Al2O3 and SiO2 solubility at 1 GPa and 800 °C. The lines denoted 0.03, 0.1 etc., are NaCl isopleths calculated from the expression with individual NaCl isopleths calculated from Eq. (18). Modified after Newton and Manning (2008)

The solubility of Al2O3 in fluids in the NaAlSi3O8–H2O system is another example of effects on solubility of added components at high temperature and pressure (Currie 1968; Anderson and Burnham 1983; Woodland and Walther 1987; Schmidt et al. 2014). The total aluminosilicate solubility in the NaAlSi3O8–H2O system is on the order of 1 wt%. However, the dissolution of NaAlSi3O8 in H2O fluid is slightly incongruent as first observed by Currie (1968), who reported that Na/Al in the aqueous solution is greater than 1 (Fig. 21). Incongruent dissolution of NaAlSi3O8 in a fluid with excess Na and Si over that of the NaAlSi3O8 stoichiometry, as also reported more recently by Mysen and Shang (2003) from experiments in closely related systems, implies that an Al-rich crystalline phase should be formed. In the system NaAlSi3O8–H2O, this phase could be corundum (Al2O3) or an Al-rich silicate phase such as sillimanite or kyanite (AlSi2O5), for example. However, neither Currie (1968) nor Anderson and Burnham (1965, 1983) reported any crystalline phase in their run product. This matter remains, therefore, unresolved.

Fig. 21
figure 21

Modified from Currie (1968)

Solubility in the system NaAlSi3O8–H2O A. Concentration of Al in fluid as a function of pressure at temperatures indicated. B. Concentration of Na in fluid as a function of pressure at temperatures indicated.

Addition of NaCl to the NaAlSi3O8–H2O system results in decreased solubility in the fluid (Fig. 22). Moreover, the solubility in aqueous solution approaches congruent as the pressure is increased (Shmulovich et al. 2001). In this regard the NaAlSi3O8 solubility behavior in saline solutions resembles the solubility in pure H2O. We note, however, that the results of Shmulovich et al. (2001) differ some from those reported by Tagirov et al. (2002) who reported decreased NaAlSi3O8 solubility with increased NaCl at low NaCl concentration in aqueous fluids and increased solubility at high concentration (Fig. 23). This behavior led Tagirov et al. (2002) to propose different Al-bearing species depending on the NaCl concentration (Fig. 23). In this model, at low NaCl concentration, the Al-species is \(\mathrm{Al}(\mathrm{OH}{)}_{4}^{-}\). With increasing NaCl concentration, the activity of NaCl is sufficient to stabilize and NaAl(OH)3Cl0 species in the fluid, which was proposed to explain the increased NaAlSi3O8 solubility at high NaCl concentrations.

Fig. 22
figure 22

Solubility of NaAlSi3O8 in H2O–NaCl fluid in the system NaAlSi3O8–H2O–NaCl as a function of NaCl concentrations at 0.9 GPa and temperatures shown on individual curves. Modified after Shmulovich et al. (2001)

Fig. 23
figure 23

Modified from Tagirov et al. (2002)

Al speciation in H2O–NaCl fluid n as a function of Al and Na concentration in the system albite–aragonite–quartz–H2O–NaCl at 400 °C and 50 MPa in slightly acidic solution with pH = 7.1–4.8.

2.3 Solubility of minor and trace elements in fluids

Transport of trace elements in fluids often is dominated by fluids rich in H2O and chloride. Such transport can be particularly important in subduction zone settings where magma can carry unique trace element signatures caused by their transport in aqueous fluids from a dehydrating subducting slab to the overlying mantle wedge where partial melting takes place (Mysen and Boettcher 1975; Wyllie 1982; Ayers and Watson 1993a; Elliott et al. 1997; Iizuka and Mysen 1998; Brenan et al. 1998; Baier et al. 2008; Till et al. 2012; D'Souza and Canil 2018). A number of relevant solubility data exist. Here, we will provide a few important examples.

2.3.1 Titanium solubility

Rutile is often employed to deduce petrogenetic history of igneous rocks (e. g., Foley et al. 2000). The Ti concentration in fluids at high temperature and pressure is critical for stabilization of rutile in source regions of magma. Such data are important because rutile governs the abundance of a number of geochemically important trace elements has been used to account for the low abundance of HFSE for example (Ayers and Watson 1993b; Brenan et al. 1994; Stalder et al. 1998; Keppler 2017). The Ti concentration in zircon also has been used as a geothermometer (Watson et al. 2006).

The solubility of TiO2 in pure H2O is quite low, perhaps around 10 ppm or so under conditions of the lower crust and upper mantle. The Ti solubility in the TiO2–H2O fluids increases slightly with increasing temperature and pressure, but remains in the tens of ppm range (Antignano and Manning 2008; Mysen 2012; see also Fig. 24). Raman spectra of the TiO2–H2O solutions at temperatures and pressures similar to those of the solubility experiments by Antignano and Manning (2008) indicate that TiO2 in pure H2O solutions exists in or near sixfold coordination with oxygen (Mysen 2012).

Fig. 24
figure 24

Titanium concentration in in aqueous fluid in equilibrium with rutile in the system TiO2–H2O A. as a function of temperature at 1 GPa pressure, and B. as a function of pressure at 800 °C Modified after Antignano and Manning (2008)

The TiO2 solubility in aqueous solution in the TiO2–SiO2–H2O system is not appreciably different from the solubility in Si-free TiO2–H2O system (Antignano and Manning 2008). However, by adding an Na-containing compound to such systems, the TiO2 solubility in aqueous fluids is greatly enhanced (Hayden and Manning 2011; Mysen 2012). For example, the Ti solubility in such fluids increased from a few tens of ppm in the TiO2–H2O system to 0.3–0.4 wt% when NaAlSi3O8 is added (Hayden and Manning 2011) and to about 0.6 wt% by adding NaCl to the TiO2–H2O system (Tanis et al. 2016). The Ti solubility in NaF–H2O fluids increases by an additional 50–100% compared with the Ti solubility in H2O–NaCl fluids (Tanis et al. 2016).

From the in situ Raman spectra of the fluids containing Na-silicate compounds, Ti4+ is in fourfold coordination with oxygen, which, of course, contrasts with the approximately sixfold coordination of Ti4+ in TiO2–H2O solution in similar temperature and pressure ranges (Mysen 2012). From the vibrational spectra of TiO2-saturated aqueous solutions with Na and Si added to the system, a solubility reaction such as (Mysen 2012);

$$4Q^{1}_{{{\text{Si}}}} \left( {{\text{Na}}} \right) \, + \, 4{\text{H}}_{2} {\text{O}} + {\text{ TiO}}_{2} = \, 4Q_{{{\text{Si}}}}^{o} \left( {{\text{HNa}}} \right) \, + Q_{{{\text{Ti}}}}^{0} \left( {{\text{Na}}} \right).$$

was found to describe the solubility behavior of Ti4+. The Ti4+ forms, therefore, an oxycomplex in the form of a Q0-like species in which Ti4+ is in fourfold coordination (equivalent to TiO44−). In Eq. (20), the QSio(HNa) formulation is meant to indicate that both H+ and Na+ form bonding with nonbridging oxygen in isolated SiO4 tetrahedra, whereas in the Q1Si(Na) complex, Na+ alone forms bonding with nonbridging oxygen in the slightly more polymerized dimers (Q1).

It is possible, but has not been documented as yet, that any alkali-bearing compound would cause TiO2 solution behavior analogous to that in Eq. (20). The solution mechanism in Eq. (19) is, therefore, greatly different from Ti4+ in solution in pure H2O where Ti4+ is in sixfold coordination with oxygen. From the temperature dependence of equilibrium (20), it is evident that the ∆H is lower by up to about 50% in the (Na + Al)-bearing systems compared with the ∆H from the simpler Na-silicate + TiO–H2O system (Mysen 2012).

The trace element signatures of magma formed by partial melting of the mantle wedge above subducting plates to a considerable extent reflect contributions to the peridotite geochemistry from fluids derived from the slab itself (e.g., Zheng 2019). The extensive depletion of high field strength elements (HFSE) in island arc magmas is particularly notable (Keppler 2017). Those geochemical features have been ascribed to the presence of rutile (TiO2) during partial melting of the peridotite wedge (Brenan et al. 1994; Foley et al. 2000). Given the generally low TiO2 concentration in typical mantle peridotite (e.g., Putirka et al. 2011) and the absence, therefore, of rutile in common peridotite, whether or not rutile is present during partial melting of a mantle wedge may depend on the extent to which its TiO2 content mantle wedge source region of partial melts may have been altered by ingress of fluid from a dehydrating subducting slab. This possibility, in turn, would depend on the availability of alkali metals in the fluid derived from the slab because alkali metals appear to be critical factors controlling the TiO2 solubility of the fluid as evidenced in the experimental data regarding greatly enhanced Ti solubility when forming oxytitanate complexes in aqueous fluid discussed above. The TiO2 concentration in such aqueous fluids can vary by nearly 3 orders of magnitude depending on such compositional factors (Mysen 2012)! Therefore, if the subducting slab were of felsic composition, the fluid derived from it would be alkali-rich and can contain significant proportions of TiO2, whereas were the fluid derived from dehydrating mafic and ultramafic rocks, the fluids would contain less alkalies and, therefore, will have less TiO2 in solution. One might propose, therefore, that the extent to which rutile exists in the mantle wedge undergoing partial melting to yield island arc magma with attendant HFSE depletion of the partial melt, depends on the geochemistry of the source of the fluids that contributed to the mantle wedge composition.

2.3.2 Other trace elements in fluids

The principles that govern the Ti solubility in simple aqueous solutions as well as compositionally more complex solution environment may also aid in our understanding of how other trace elements dissolve in aqueous solutions. These trace elements may include other HFSE such as Zr, Hf, Nb, and Ta, transition metals including Cr and Mo, and actinides such as U and Th. In other words, their solubility in aqueous solutions could be greatly enhanced by formation of oxycomplexes that are charge compensated by alkali metals or possibly alkaline earths (Keppler and Wyllie 1991; Peiffert et al. 1996; Ulrich and Mavrogenes 2008; Bali et al. 2011, 2012; Wilke et al. 2012; Watenphul et al. 2014; Mysen 2012; Keppler 2017). In addition, for some of these trace elements (e.g., uranium, thorium, molybdenum, niobium, and tantalum), redox conditions also can affect the solubility in important ways (e. g., Bailey and Ragnarsdottir 1994; Peiffert et al. 1996). Salinity also can be important (Rustioni et al. 2021). Zirconium Solubility

The solubility of ZrO2 in fluids in the ZrO2–H2O system at pressures and temperatures corresponding to the deep crust and upper mantle is at the ppm level (Wilke et al. 2012; Mysen 2015c). This solubility (Fig. 25) resembles that of TiO2 in the TiO2–H2O system under similar temperature and pressure conditions (Fig. 24) with a simple solution mechanism such as

$${\text{ZrO}}_{2} \left( {{\text{xtal}}} \right) = {\text{ZrO}}_{2} \left( {{\text{fluid}}} \right),$$

with the equilibrium constant;

$$K = m_{{{\text{ZrO}}2}} \left( {{\text{fluid}}} \right),$$

where m is molality. From linear relationship between ln K and 1/T (kelvin), the ∆H = 43 ± 16 kJ/mol for the solution reaction illustrated in Eq. (21). This enthalpy resembles the 50–60 kJ/mol value for Ti solution in the TiO2–H2O system (Mysen 2012).

Fig. 25
figure 25

Modified from Mysen (2015c)

Zirconium solubility in aqueous solutions as a function of temperature and pressure for the various systems indicated on individual dashed lines.

The Zr solubility, much as the Ti solubility, is quite sensitive to added components in the fluid. For example, addition of Na+ to aqueous solutions results in Zr solubility increases by approximately an order of magnitude (Fig. 25). The simplest way to describe the solution mechanism of ZrO2 under these conditions may be expressed as (Mysen 2015c):

$${\text{ZrO}}_{2} \left( {{\text{xtal}}} \right) \, + \, 4{\text{ NaOH }} = {\text{ Na}}_{4} {\text{ZrO}}_{4} \left( {{\text{fluid}}} \right) \, + {\text{ H}}_{2} {\text{O}}.$$

In this environment, Zr4+ is in fourfold coordination with oxygen as evidenced by the Raman spectra of such fluids recorded, while the fluid and coexisting Zr-bearing crystalline materials were at the high temperature and pressure of interest (Mysen 2015c). However, from existing X-ray and Raman spectroscopic data of such fluids (Wilke et al. 2012; Mysen 2015c), several more complex reactions involving zirconosilicate or separate silicate and zirconate complexes could be considered. Given the structural interpretation Raman spectra of the fluids in ZrO2–SiO2–NaOH–H2O, some Si–OH bonding in addition to Zr4+ in fourfold oxygen coordination is likely with one reaction that is consistent with all structural data is (Mysen 2015c):

$${\text{2ZrO}}_{{2}} + {\text{NaOH}} + {\text{2SiO}}_{{2}} = {\text{NaZr}}_{{2}} {\text{Si}}_{{2}} {\text{O}}_{{8}} \left( {{\text{OH}}} \right) + {\text{H}}_{{2}} {\text{O}},$$

This structural behavior of Zr4+ differs its solution mechanism in the simple ZrO2–H2O fluid system, where the vibrational spectra have been interpreted to indicate oxygen coordination numbers in excess of 6 (Mysen 2015c).

In summary, the key to enhanced solubility of HFSE in aqueous solutions is the stabilization of oxycomplexes associated with alkali metals or, perhaps alkaline earths. The exact form in which the metal cation is added to the solution may not be so important. It is likely, for example, that the more electropositive the metal cation is, the greater is its effect, and the greater is the solubility of the oxycomplex in aqueous fluids. One might speculate, therefore, that much as was discussed for Ti solubility above, fluid in equilibrium with felsic magma will be alkali metal rich and, therefore, form Zr-bearing oxycomplexes with greater solubility in aqueous solutions than fluids in equilibrium with mafic igneous rocks where the more electronegative alkaline earths are less likely to stability the oxycomplex. Molybdenum solubility

The solubility of molybdenum in aqueous, saline solutions is in the 100–10,000 ppm range (Ulrich and Mavrogenes 2008; Bali et al. 2012; Hurtig and Williams-Jones 2014). It is a strong function of both oxygen fugacity and solution salinity (Bali et al. 2012).

The Mo solubility increases by about 2 orders of magnitude when the fO2 increases by about 4 orders of magnitude. The solubility of oxidized Mo increases by about an order of magnitude when the NaCl concentration increases from 0 to about 15 wt% (Fig. 26).

$$\log \, m_{{{\text{Mo}}}} = 0.44\log f_{{{\text{O}}2}} + 0.42\log \, m_{{{\text{NaCl}}}} - 1.8 \bullet 1000/T\left( K \right) + 4.8.$$
Fig. 26
figure 26

Molybdenum solubility in H2O–NaCl solutions. A. As a function of oxygen fugacity in 5 wt% NaCl saline solution at 2.61 GPa and 700 °C. B. As a function of NaCl concentration at 2.61 GPa and 700 °C at the oxygen fugacity of the NNO buffer. Modified after Bali et al. (2012) Trace element solubility and sulfur in aqueous solution

Sulfur in aqueous solution can exist in multiple oxidation states, which can affect its influence on the solubility of trace elements in S-bearing fluids. The sulfur species are H2S, SO2, SO3, and HSO3 (Binder and Keppler 2011; Eldridge et al. 2018). An additional sulfur species, S3, originally proposed by Pokrovski and Dubrovinski (2011) has been suggested to be an important intermediate species stabilizing transition metals (Tossell 2012; Pokrovski et al. 2015). In the numerical simulations by Tossell (2012), the simple reaction:

$$S_{6}^{2 - } = \, 2S_{3}^{ - } ,$$

has a negative free energy change at high temperature (− 110 kJ/mol at 450 °C, for example), while at ambient temperature the ∆G of the reaction is positive (25 kJ/mol). From this information, it follows that the S3− would be stabilized with high temperature.

Reduced sulfur in aqueous solution can have particular influence on solubility of metals such as Au, Ag, Cu, Mo, and Zn (Gibert et al. 1998; Trigub et al. 2017; Pokrovski et al. 2008; Frank et al. 2011; Tagirov and Seward 2010; Zhang et al. 2012). The solution mechanisms of these elements in some ways resemble one another, and only the solution behavior of Au will be summarized here.

The solubility of Au with reduced sulfur in aqueous solution, is positively correlated with concentration of H2S (Fig. 27A; see also Trigub et al. 2017). The Au solubility also increases rapidly with increasing pH (Fig. 27B).

Fig. 27
figure 27

A. Solubility of Au in H–O–S solutions as a function of H2S content, mH2S, at 450 °C and 100 MPa and pH = 3 ± 0.2. B. Solubility of Au in H–O–S solutions as a function of pH at 450 °C and 100 MPa with molality of H2S, mH2S = 1, and hydrogen fugacity, fH2 = 0.1 MPa. C. Speciation of Au-sulfide complexes in H–O–S solutions as a function of pH and Au concentration. Modified after Pokrovski et al. (2008) and Trigub et al. (2017)

The Au solution mechanism has been described with an expression of the type (Pokrovski et al. 2008);

$${\text{Au}}\left( s \right) + 2{\text{H}}_{2} {\text{S}}\left( {{\text{aq}}} \right) \, = {\text{ Au}}\left( {{\text{HS}}} \right)_{2}^{ - } + {\text{H}}^{ + } + \, 0.5{\text{ H}}_{2} .$$

Pokrovski et al. (2008) concluded that AuHS° complexes dominated with pH < 5, whereas at higher pH conditions, the dominant Au species was Au(HS)2 (Fig. 27C). The existence of such sulfur species also has been inferred from Au L3-edge X-ray absorption (Trigub et al. 2017).

2.4 Structure and properties of fluids

Physical and chemical properties of fluids, including their solvent capacity, vary with fluid composition as well as type and proportion of oxide solutes. The properties, in turn, reflect the fluid structure and the solution mechanism(s) of the solute(s). It is necessary, therefore, to ascertain how fluid structure varies with composition of solvent and solute, temperature, and pressure. With this information, modeling transport properties and processes of fluids and fluid–rock interaction in the Earth's interior becomes a tractable problem.

2.4.1 Structure of H2O fluid

Under most conditions, H2O affects the physics and chemistry of rock-forming materials more than other fluid components and species in the C–O–H–N–S system (Kohlstedt et al. 2006; Kushiro 1972; Whittington et al. 2000; Bouhifd et al. 2006; Grove et al. 2012). These effects include interaction between H2O dissolved in magmatic liquids as well as in crystalline materials, and the extent and efficiency with which fluids migrate through rock matrices. These and other effects reflect the structure of H2O and the interaction between its structural elements and the materials with which H2O interacts.

The structure of H2O is comprised of monomers, dimers, and sometimes even more polymerized species under the temperature and pressure conditions of the Earth's interior (Gorbaty and Kalinichev 1995; Hoffmann and Conradi 1997; Katayama et al. 2010). In these structures, many of the individual H2O molecules are linked together with hydrogen bonding, the proportions of which vary with temperature and pressure (Schneider et al. 1958; Hoffmann and Conradi 1997; Sahle et al. 2013). The density of H2O fluid is also linked to the proportions of those structural entities, and, therefore, to temperature and pressure.

The latter structural features have been interpreted from the proton NMR spectra of H2O (Hoffmann and Conradi 1997), recorded spectra from ambient conditions to 40 MPa and 600 °C. In these spectra, the chemical shift of 1H is sensitive to both temperature and pressure (Fig. 28). The discontinuity on the curves in Fig. 28 reflects the crossing of the liquid–vapor curve of H2O.

Fig. 28
figure 28

Modified from Hoffman and Conradi (1997)

1H NMR chemical shift of O A. as a function of temperature, and. B. As a function of pressure. Translation to extent of hydrogen bonding is based on relationship between chemical shift and H2O fluid density.

The 1H chemical shift decreased with increasing temperature and increased with increasing pressure (Fig. 28). This spectral evolution reflects decreasing abundance of hydrogen bonded structure the higher the temperature and an increased abundance of hydrogen bonding with increasing pressure (Hoffmann and Conradi 1997; see also Fig. 29). For example, from 1H NMR spectra of pure H2O, Hoffmann and Conradi (1997) estimated the proportion of hydrogen bonding decreasing from about 80% of the H2O structure at ambient temperature and pressure to less than 10% of the H2O structure at 600 °C in in the 30–40 MPa pressure range as illustrated in Fig. 29. The influence of pressure under isothermal condition is a 10–30% hydrogen bond-fraction increase between ambient pressure and 30 GPa.

Fig. 29
figure 29

Schematic representation of the structure of H2O at low temperature with about 80% of the H2O molecules connected with hydrogen bonding (long arrow between H and O atoms) and high temperature with about 10% hydrogen bonding and the result of H2O molecules isolated from one another

This structural model developed from the NMR data is consistent with that of results from X-ray and neutron diffraction, which also have been interpreted to indicate that the extent of hydrogen bonding in H2O fluid increased with increasing pressure (Sahle et al. 2013; Soper and Ricci 2000). Similar conclusions were reached from high-temperature/high-pressure Raman spectra of fluid and supercritical H2O fluid (Walrafen et al. 1988; Frantz et al. 1993; Foustoukos and Mysen 2012).

Pressure and temperature not only affect hydrogen bonding in the H2O structure, Katayama et al. (2010) found increased coordination numbers for the H2O molecule so that at pressures near 4 GPa the number reached 9 (Fig. 30) based on X-ray diffraction data recorded along the pressure–temperature trajectory of the melting curve of H2O to 17 GPa and 850 K. This coordination number (9) means that each H2O molecule is surrounded by 9 other H2O molecules. Katayama et al. (2010) also commented that this coordination number is typical for simple liquids such as noble gases (8–9). At pressure above about 4 GPa, no further coordination changes were reported. Those higher-pressure X-ray data were interpreted to show a decreased nearest-neighbor distance at pressures above about 4 GPa.

Fig. 30
figure 30

Oxygen coordination number of H2O as a function of pressure. Modified rom Katayama et al. (2010)

2.4.2 Structure of H2O–NaCl fluid

Radial distribution functions derived from neutron diffraction using (H2O, D2O) + NaCl fluids show the nearest H2O molecules about 2 Å from the Cl anion (Botti et al. 2004). The oxygen in the H2O molecules was located about 3 Å from the Cl anion. The average solvation number for H2O from both the Cl–H and Cl–O distances is 5.8 (Heuft and Meijer 2003). The larger fraction of the H2O is in hydration shells surrounding Cl compared with the number of H2O molecules surrounding Na+.

2.4.3 Structure and thermodynamics of H2O–C–OH fluids

The two C-bearing species considered here are CO2 and CH4 as these are the two main C-bearing species relevant to rock-forming processes in the Earth. Carbon dioxide dominates under redox conditions above that defined by the magnetite–wüstite (MW) buffer, whereas under more reducing conditions, CH4 is the main species.

In the modern Earth, CO2 likely is the principal species in the upper mantle, whereas under deeper mantle conditions, the fO2 may be sufficiently low (and fH2 high) for CH4 to be the main species. During the first few tens of millions of years of the Earth's history, redox conditions were at and below the IW oxygen buffer (Righter and Drake 1997; Gessmann and Rubie 2000) such that CH4 was the principal C-bearing fluid species in the Earth. H2O–CO2

Fluids in the H2O–CO2 system comprise molecular CO2, CO32−, together with HCO3 groups at least to pressures below about 1.6 GPa (Frantz 1998; Schmidt 2014; Mysen 2015a). At higher pressure, Martinez et al. (2004) concluded that the bicarbonate, HCO3, was not stable in the fluid. At 200 MPa, molecular CO2 becomes increasingly important with increasing temperature as do the CO32− groups (Frantz 1998). From experiments in the H2O–CO2 fluid system at higher pressure (Schmidt 2014), the CO32− and CO2 abundance decreases with increasing pressure, whereas that of the HCO3 shows an increase. These pressure effects on C–O–H speciation in H2O–CO2 fluids diminish with decreasing temperature.

Property measurements of H2O–CO2 fluid have focused on thermodynamic properties such as activity-composition and volume relations. From volume data, activity and activity coefficients of the fluid species have been obtained (Frost and Wood 1997; Deering et al. 2016) because activity coefficient of component i, γi, is linked to its partial molar volume and the volume of pure i, \(\overline{V }\) i and Vi, respectively so that:

$$\ln \gamma_{i} = \frac{1}{{{\text{RT}}}}\mathop \smallint \limits_{1}^{P} \overline{{(V_{i} }} - V_{i} )dP.$$

In this equation, R is the gas constant, T is temperature, and P is pressure.

Activity-composition relations of H2O-CO2 fluids also have been obtained by combining decarbonation and dehydration reactions such as, for example (Aranovich and Newton 1999);

$${\text{CaCO}}_{3} + {\text{ SiO}}_{2} = {\text{ CaSiO}}_{3} + {\text{ CO}}_{2} ,$$
$${\text{MgCO}}_{3} + {\text{ MgSiO}}_{3} = {\text{ Mg}}_{2} {\text{SiO}}_{4} + {\text{ CO}}_{2} ,$$


$${\text{Mg}}_{3} {\text{Si}}_{4} {\text{O}}_{10} \left( {{\text{OH}}} \right)_{2} = \, 3{\text{MgSiO}}_{3} + {\text{ SiO}}_{2} + {\text{ H}}_{2} {\text{O}},$$

The results of Aranovich and Newton (1999), using this method (Fig. 31), were quite similar to those reported by Duan and Zhang (2006) from numerical simulation of the mixing behavior in H2O–CO2 fluids (solid lines in Fig. 31).

Fig. 31
figure 31

Experimentally determined activity-composition relations along the H2O–CO2 join at 800 °C and 1.4 GPa. Data points are from experimental results by Aranovich and Newton (1999) and calculated curves from Duan and Zhang (2006). Curves denoted γCO2 = 1 and γH2O = 1 indicate lines of ideal mixing H2O–CH4

From the experimental data available for silicate-saturated H2O-CH4 fluids in equilibrium with-saturated silicate melts, molecular CH4 coexist with CH3 groups. These latter groups substitute for oxygen in the silicate tetrahedra of silicate dissolved in the fluid (Mysen et al. 2011). An equilibrium reaction of the type;

$$Q^{n} + \, 2{\text{CH}}_{4} = \, 2{\text{CH}}_{3}^{ - } + {\text{ H}}_{2} {\text{O }} + \, Q^{n + 1} ,$$

where the superscript, n, denotes the number of bridging oxygen in the silicate species described with the Qn-notation.

Equilibrium (32) shifts to the right with increasing temperature, which results in ∆H = 16 ± 5 kJ/mol for the reaction. The ∆H-value of equilibrium (32) for the fluid is about 1/3 of that in coexisting melt (Mysen 2015b). This enthalpy difference likely reflects the greater deviations from ideal mixing in silicate melts compared with silicate-saturated H2O–CH4 fluid at high temperature and pressure.

Volume of mixing is among the few property measurements available for H2O–CH4 fluids (Fig. 32). There is a distinctly nonlinear volume evolution as a function of H2O–CH4 fluid composition (Shmonov et al. 1993). The results of the numerical simulation of H2O–CH4 fluid volumes by Zhang et al. (2007) (solid lines in Fig. 32) are in very good agreement with the experimental data of Shmonov et al. (1993).

Fig. 32
figure 32

Modified from Zhang et al. (2007)

Molar volumes of H2O–CH4 fluids as a function of H2O/CH4 ratio at 400 °C and pressures indicated on curves from experiments by Shmonov et al. (1993) and compared with calculated molar volumes by Zhang et al. (2007). Lines are results from Zhang et al. (2007), whereas data points from experiments by Shmonov et al. (1993).

2.4.4 Structure and thermodynamics of H2O–S–O–H fluid

Sulfur, the third-most important fluid species in many igneous processes (Symonds et al. 1994), can occur both in reduced, S2−, and oxidized, SO2 and SO3, forms depending on redox conditions during magmatic processes. Reduced sulfur species dominate with fO2 conditions more reducing than near that of the NNO buffer (O'Neill and Mavrogenes 2002). Oxidized sulfur is the main species under more oxidizing conditions (Scaillet et al. 1998).

This fO2-dependent redox ratio of sulfur means, for example, that igneous rocks more mafic than andesite will have essentially all sulfur in melts and exsolving gases in sulfide form (H2S) because the oxygen fugacity during their formation and evolution of such more mafic magma typically is less than that defined by the NNO oxygen buffer (Carmichael and Ghiorso 1990). On the other hand, more silica-rich igneous rocks such as andesite, dacite, and rhyolite, which typically are formed at greater oxygen fugacity conditions than that of the NNO oxygen buffer during their formation (Carmichael and Ghiorso 1990), have essentially all their sulfur in oxidized form, SO2 and SO3, or their hydrated form, sulfuric acid (Scaillet et al. 1998; Jugo 2009). These latter sulfur species can become important components of fluids formed by degassing of such felsic magma.

From the temperature dependence of the equilibrium constant for the reaction

$$2{\text{H}}_{2} {\text{S }} + \, 3{\text{O}}_{2} = \, 2{\text{SO}}_{2} + \, 2{\text{H}}_{2} {\text{O}},$$

the ∆H is 1442 ± 63 kJ/mol (Binder and Keppler 2011) with no discernible pressure dependence. In contrast, the reaction describing oxidation from SO2 to SO3

$${\text{SO}}_{2} + \, 0.5{\text{O}}_{2} = {\text{ SO}}_{3} ,$$

is both temperature and pressure dependent. From the temperature dependence, the ∆H decreases (becomes more negative) from − 160 ± 50 kJ/mol to − 308 ± 9 kJ/mol between 150 and 250 MPa, for example (Binder and Keppler 2011).

2.5 Fluid migration and mass transport; permeability and porosity

Transport of mass in the Earth for the most part takes place via movement of fluids and magma. In this section, we will discuss how some of the properties of fluids affect their migration through crystalline rocks and how fluid properties can affect rock-forming properties and processes. The extent and ease of fluid migration, in turn, depend on the rock porosity, which has been linked to permeability via Archie's Law (Archie 1942);

$$k = \frac{{d^{2} \phi^{n} }}{C},$$

In this equation, k is permeability, \(\phi\) is the fluid fraction (porosity), d is grain size, and C is a constant. The value of the superscript, n, commonly is reported to be between 1 and 3 (Dullien 1992), although for natural fluids and magma, values less than 1 are often reported for best fit to experimental data (Wark and Watson 1998; Price et al. 2006; Shimojuku et al. 2012).

Archie's Law [Eq. (35)] assumes that there is only one grain size, but in rocks, more often than not, this is not the case. For example, with two different grain sizes, 1 and 2, in the following relationships describes the relations between porosity and grain size (Wark and Watson 2000):

$$\frac{{\phi_{2} }}{{\phi_{1} }} = \left( {\frac{{d_{1} }}{{d_{2} }}} \right)^{n} .$$

Additional variables include different surface energies of different crystallographic surfaces.

Fluids in the Earth's interior often are dominated by H2O + CO2 and also can include chloride and sulfur compounds. The latter components can have substantial impact on the fluid transport capacity both in terms of their efficiency as solvents as well as the permeability of such fluids in a crystalline rock matrix (Watson et al. 1990; Holness 1992; Huang et al. 2020).

Migration of fluids through a rock matrix has been the subject of experimental study (Mysen et al. 1978; Cohen and Watson 1996; Wark and Watson 1998; Nakamura and Watson 2001). For example, in early experiments to determine the velocity of H2O passing through a crystalline peridotite under conditions relevant to fluid migration from a dehydrating subducting plate into the overlying peridotite mantle wedge, migration velocity of this aqueous fluid were reported to be on the order a few mm/hr (Mysen et al. 1978). This rate (mm/hr), from laboratory experiments conducted under hydrostatic or near hydrostatic conditions, differs significantly from that inferred from earthquake swarms in the Marianas and Izu-Bonin arcs, where White et al. (2019) interpreted seismic data to be consistent with fluid movement from a dehydrating slab into overlying mantle to be on the order of km/hr. These different migration rates may be because in the experiments by Mysen et al. (1978), aqueous fluid migrated along grain boundaries in a hydrostatic medium, whereas it is possible that the rate interpreted from the earthquake swarms exists in an environment under shear where fluid could migrate along in shear zones above subducting plate with much less resistance to fluid movements. Migration rate in such a setting would be much faster than grain boundary travel in a hydrostatic environment. This difference may account for the different fluid transport rate in experiments (Mysen et al. 1978) compared with rates under natural conditions (White et al. 2019).

To conduct experiments to determine fluid migration velocity under controlled conditions directly relevant to fluid flow in the Earth, grain size and grain size distribution, whether or not different minerals exist in the mineral assemblage, proportion and composition of fluid, porosity of the crystalline assemblage, and interfacial energies between solids and between solids and fluid must be controlled (Jurewicz and Watson 1985; Korenagi and Kelemen 1998; Wark and Watson 2000; Mu et al. 2016; Iwamori et al. 2007; Huang et al. 2020). Fluid migration in the Earth's interior often can take place in a stress field such as existing near the interface of subducting plates and the overlying mantle wedge (e. g., Hacker et al. 2003). The orientation of fluid and melt pockets in a stress field varies with the magnitude of the stress field so that increasing differential stress results in increasing deviation from the direction of the stress field (Daines and Kohlstedt 1997). Deformation of the fluid/rock system will be the result (Wanamaker and Kohlstedt 1991; Walte et al. 2011).

2.5.1 Fluid wetting angle

A major variable affecting fluid migration through a rock matrix is the wetting angle or dihedral angle. This angle, often represented by the symbol, θ, is the angle at the junction between two adjoining solid and liquid (fluid or melt) (Fig. 33).

Fig. 33
figure 33

Schematic illustration of dihedral angle, Θ, in an isotropic medium of solid and fluid

The key factor determining the wetting angle of liquids in a solid matrix and, therefore, permeability, porosity, and ultimately migration rate is the energy of the solid–solid and solid–liquid interfaces of the crystalline assemblage with which the liquid is in contact. With a fixed solid–solid interface energy, γss, the main factor governing the wetting angle becomes the energy of the solid–liquid interface, γsl, because:

$$\theta = 2\arccos \frac{{\gamma_{ss} }}{{2 \bullet \gamma_{sl} }}.$$

Under the simple conditions described with Eq. (37), for θ < 60°, the fluid will form an interconnected network, whereas with θ > 60° it will not.

The ratio of the two interfacial energies, \(\frac{{\gamma }_{\mathrm{ss}}}{{\gamma }_{\mathrm{sl}}}\), and, therefore, the dihedral or wetting angle, is linked to the solubility in the fluid phase of one or more of the components in the solid (Takei and Shimizu 2003). In the environment such as expressed with Eq. (37), the wetting angle is proportional to the solubility of the components of the solid materials in the fluid. For example, using experimental data on wetting angles and dissolved components in aqueous fluid in contact with olivine at mantle pressures and temperature, a tripling of the solute concentration in the aqueous solvent results in a 25% lowering of the wetting angle of this fluid as pressure, and, therefore, solute concentration, is increased from 1 to 8 GPa (Fig. 34).

Fig. 34
figure 34

Modified from Takei and Shimizu (2003)

A. Solubility in aqueous fluid in forsterite–H2O system and B. dihedral angle (expressed as the ratio, ρ = 1/(2cos(θ/2)) as a function of pressure.

The relationship between solubility and wetting angle such as in Fig. 34 exists because the concentration and speciation of components dissolved in aqueous fluids near the interface of fluid with a mineral such as olivine, for example, increasingly resemble each other as solute concentration increases with increasing pressure. In the case of forsterite + H2O, this evolution exists because the solubility of mantle components such as MgO and SiO2 in aqueous fluids increases with increasing pressure (Zhang and Frantz 2000; Newton and Manning 2002; Kawamoto et al. 2004). The local structure of the dissolved silicate components also becomes increasingly similar to that of the adjoining olivine crystals at the fluid/olivine interface (Mysen et al. 2013). This evolving structural similarity of aqueous fluid and forsterite results in lowering of γsl and, therefore, a decreased θ. Wetting angle and composition of fluid and crystalline matrix

Dihedral angle of aqueous fluid has been determined for crustal rock-forming minerals such as quartz, plagioclase, calcite, and dolomite (Watson and Brenan 1987; Hay and Evans 1988; Laporte and Watson 1991; Holness 1992, 1993, 1995; Nakamura and Watson 2001; Yoshino et al. 2002). Wetting behavior by H2O fluids in contact with mantle mineral assemblages has been determined for olivine, pyroxenes, and garnet and their high-pressure polymorphs (Watson et al. 1987, 1990; Mibe et al. 2003; Ono et al. 2002; Mibe et al. 1998; Yoshino et al. 2007; Matsukage et al. 2017; Liu et al. 2018).

In the quartz–H2O system, the dihedral angle, θ, is slightly above 60° at upper crustal pressures, but decreases rapidly with increasing pressure to those of the deep continental crust and uppermost mantle (Fig. 35; see also Watson et al. 1990; Holness 1992). The θ also decreases as a near linear function of temperature and at 1 GPa pressure where it crosses the 60° threshold at temperatures near 1100 °C (Fig. 35B). This temperature-dependent dihedral angle could be linked to the rapidly increasing quartz solubility in aqueous fluid as the temperature approaches supercriticality, which is just below 1100 °C at pressures near 1 GPa (see also Kennedy et al. 1962, for discussion of phase relations in the SiO2–H2O system).

Fig. 35
figure 35

Modified from Watson et al. (1990)

A. Dihedral angle in dunite–H2O at 1200 °C as a function of pressure. B. Dihedral angle in dunite–H2O as a function of temperature at 1 GPa.

By adding CO2 to H2O, the dihedral angle, θ, in the quartz-H2O–CO2 system, for example, this angle increases rapidly with increasing CO2/(CO2 + H2O) of the fluid at fixed temperature and pressure (Watson and Brenan 1987; Holness 1992; Holness and Graham 1995). The dihedral angle is near 100° for the SiO2–CO2 system (Fig. 36). This much larger dihedral angle for fluid in the SiO2–CO2 system compared with the SiO2–H2O system is consistent with the much lower solubility of SiO2 in CO2 fluid than in H2O fluid (Newton and Manning 2000).

Fig. 36
figure 36

Modified from Watson and Brenan (1987)

Dihedral angle in quartz-H2O–CO2 at 1 GPa and 950°-1150 °C as a function of fluid composition.

Fluid salinity also can affect the dihedral angle such as observed, for example, in the quartz-H2O–NaCl system (Watson and Brenan 1987; Laporte and Watson 1991; Holness 1992). The SiO2 solubility in H2O–NaCl fluids is, however, a complex function of pressure and NaCl concentration (Newton and Manning 2000). It is no surprise, therefore, that the dihedral angle in this system also is a complex function of salinity of the fluid (Fig. 37).

Fig. 37
figure 37

Evolution of dihedral angle in quartz + H2O + NaCl at 800 °C as a function of pressure. Modified after Holness (1992)

Plagioclase is a major part of mineral assemblages in most crustal rocks. That importance notwithstanding, experimental data on fluid wetting angles in plagioclase + fluid systems are not common. In one study with H2O fluid in contact with anorthite-rich plagioclase (Yoshino et al. 2002), the θ decreased with increasing anorthite component in the plagioclase. Within the pressure–temperature stability field of anorthite in the CaAl2Si2O8–H2O system (Boettcher 1970; see also Fig. 38), the pressure above which the θ < 60° decreases from about 1.2 GPa and 700 °C to about 0.8 GPa and 1200 °C. Above these temperature and pressure conditions, the θ = 60° isopleth intersects the incongruent melting curve of anorthite + H2O to yield corundum + melt (Boettcher 1970). It must be emphasized, however, that the experimental data in Fig. 38 extend from pure anorthite to only about 95% of the anorthite component in plagioclase. Extrapolation to lower An component concentration in plagioclase, therefore, is uncertain. It is, in fact, likely that the dihedral angle might decrease as the plagioclase becomes more albite-rich, because the solubility of NaAlSi3O8 in H2O fluid is likely greater than that of CaAl2Si2O8 in H2O (Anderson and Burnham 1983; Newton and Manning 2007). Such different solubilities, which depend on plagioclase composition, would mean that the increasing dihedral angle of in the plagioclase–H2O system in the initial high-An component composition range is likely to change to lowering of the angle between plagioclase and aqueous fluid as the plagioclase becomes more albitic.

Fig. 38
figure 38

Modified from Yoshino et al. (2002)

Pressure–temperature relations of dihedral angles as indicated for the system anorthite–H2O. Stability limit of the CaAl2Si2O8–H2O system is from Boettcher (1970).

Considerable experimental data exist for wetting behavior of aqueous fluid in contact with olivine. In the olivine–H2O system under crustal temperature and pressure conditions, the dihedral angle exceeds 60° (Mibe et al. 1998, 1999). However, this angle decreases relatively rapidly with increasing temperature. The angle decrease is particularly rapid at pressure and temperature conditions where the olivine–H2O system approach and perhaps exceed the supercritical temperature and pressure conditions (Mibe et al. 1998, 1999; Yoshino et al. 2007; Huang et al. 2020; see also Fig. 39).

Fig. 39
figure 39

Modified from Yoshino et al. (2007)

Dihedral angle of aqueous fluid in the olivine–H2O system as a function of pressure at temperatures indicated.

Addition of CO2 to aqueous fluid in equilibrium with olivine results in wetting angle changes that are qualitatively similar to adding CO2 to fluids in contact with other silicate minerals such as quartz, for example (Watson and Brenan 1987; Huang et al. 2020). In all cases, the dihedral angle increases as a systematic function of increasing CO2 concentration in the fluid (Huang et al. 2020). Most likely, decreasing Mg2SiO4 solubility in Mg2SiO4–H2O–CO2 fluids with increasing CO2/(CO2 + H2O) governs this dihedral angle evolution.

In the olivine–H2O–NaCl system, in contrast to the olivine–H2O–CO2 system, the dihedral angle decreases rapidly from above 70° in pure H2O at 1 GPa and 800 °C to less than 60° with 10 mol% NaCl and less in solution. However, little or no angle change was reported with 10–50% NaCl in the aqueous fluid (Liu et al. 2018). This dihedral angle trend with increasing salinity of aqueous fluid likely reflects complex solubility behavior of olivine in NaCl–H2O fluids perhaps involving a combination of chloride complexing together with formation of silicate complexes. A complex such as MgClOH suggested by Macris et al. (2020) for MgO dissolution in fluids in the MgO–H2O–NaCl system is one possibility because forsterite solubility in saline fluids increases with increasing chloride concentration (Macris et al. 2020). However, more complex species, perhaps including Si4+, could also exist in the H2O–NaCl fluids, but absent direct structural information, this (and perhaps other) possibilities cannot be evaluated with confidence.

The fluid wetting angles in pyroxene–H2O and garnet–H2O systems are significantly greater than those of aqueous fluid in contact with the main upper mantle mineral phase, olivine (Ono et al. 2002; Mibe et al. 2003; Liu et al. 2018). The angle in both systems remains at or above 60° at least to pressures near 5 GPa, but decreases rapidly as conditions approach those of the critical endpoint in the eclogite–H2O system.

The relationship between wetting angle, pressure, temperature, and solubility in H2O-rich fluid in a mantle environment would imply that the migration rate of aqueous fluid in a mantle wedge overlying a dehydrating subducting slab, will increase with increasing depth because the solubility of fluids in peridotite–H2O systems increases with increasing pressure such as discussed above (e g., Kawamoto et al. 2004; Melakhova et al. 2007). Furthermore, given that aqueous fluids in subduction zones commonly are saline and increasing salinity in model peridotite–H2O–chloride systems enhances the solubility in the fluid (Macris et al. 2020), this situation would further enhance the mobility of aqueous fluids in the mantle wedge above subducting plates. Fluid wetting angles and rock properties

The temperature and pressure effects on wetting angles and connectivity of aqueous fluids in contact with minerals in the Earth's interior can have profound effects on geochemical properties of fluid-bearing upper mantle materials and mineral assemblages (Watson 1991; Brenan 1993; Iizuka and Mysen 1998; Bebout et al. 1999; Kawamoto et al. 2014). Wetting angle and fluid connectivity also can affect geophysical properties of fluid-bearing rock systems (Wiens et al. 2006; Reynard et al. 2011; Yoshino and Katsura 2013; Ogawa et al. 2014). Moreover, as wetting angle governs connectivity and wetting angle varies with temperature, pressure, and fluid composition, geochemical and geophysical properties that may be linked to fluid in rocks would also depend on those variables.

Geochemical properties of materials that have experienced fluid infiltration include trace and major element diffusion and abundance as well as possible isotopic changes (Watson 1991; Brenan 1993; Iizuka and Mysen 1998; Brenan et al. 1998; Lupulescu and Watson 1999; Manning 2004; Foustoukos and Mysen 2012; Dalou et al. 2015; Labidi et al. 2016). For example, diffusivity depends on volume fraction and composition of permeating fluids. The diffusivity of halogens through a rock sample containing H2O, for example, can vary by orders of magnitude depending on the volume of H2O even at small fluid concentrations (Fig. 40; see also Brenan 1993). Similarly, Watson (1991) documented how the diffusion constant for Fe in H2O and (H2O + CO2)-bearing mineral systems depends on both the proportion of fluid and its H2O/CO2 ratio.

Fig. 40
figure 40

Modified from Brenan (1993)

Chlorine diffusion in quartz-H2O as a function of total fluid concentration.

The evolution of fluid-sensitive trace elements such as Be, B, and Li in subduction zone settings is another example of fluid infiltration causing geochemical changes. Here, Brenan et al. (1998) determined their abundance and abundance ratio in aqueous fluids that were derived from dehydration of hydrous minerals (lawsonite and amphibole) in the subducting plate. They commented that decreased B/Be abundance ratio in the fluid with depth in subduction zones reflects decreasing H2O concentration in the subducting slab with depth (Poli and Schmidt 2002). What most likely happens is decreasing H2O/CO2 ratio in the fluid with increasing depth. That decrease could result in decreasing B/Be ratio in the fluid because of different solubilities of B and Be as a function of the H2O/CO2 ratio of this fluid, which, in turn would change mineral/fluid partition coefficients.

Electrical conductivity and seismic velocity are two important geophysical properties often employed to estimate fluid (and melt) distribution in the Earth. Electrical conductivity as a function of fluid fraction, salinity, and fluid connectivity have been calibrated experimentally (Shimojuku et al. 2012; Guo et al. 2016; Sun et al. 2020; Huang et al. 2021). Seismic velocities in subduction zones also have been used to estimate total H2O content (Carlson and Miller 2003; Hacker and Abers 2004). Fluid connectivity may also help explain relationships between electrical conductivity and seismic properties such as observed in subduction zones, for example (Fig. 41; see also Pommier 2014).

Fig. 41
figure 41

Modified from Pommier (2014)

Relationship between electrical conductivity and P-wave attenuation from a variety of fore-arc and back-arc subduction zones as discussed in Pommier (2014).

There exist high-conductivity layers in the Earth's deep crust (Guo et al. 2018). Layers of high electrical conductivity also have been reported from subduction zones (Wanamaker et al. 2009; Guo and Keppler 2019). This high electrical conductivity could result from on the order of 1% aqueous fluid with significant salinity. From experimental data on electrical conductivity in forsterite + H2O mixtures without chloride, Huang et al. (2021) concluded that the high electrical conductivity often reported from the mantle wedge above subducting plates could be accommodated by 5–10 volume % aqueous fluid in the wedge (Fig. 42). Of course, were the fluid saline, as is often suggested (Kawamoto et al. 2014; Kumagai et al. 2014), the volume fraction of fluid could be smaller. A significantly smaller fraction of aqueous fluid (perhaps less than 1%) would be consistent with modeling results from Iwamori (2007), for example. Water concentrations in the 0.5–1 wt% range in the source regions of andesitic magma in this mantle wedge would also be consistent with results of melting experiments on hydrous peridotite mantle (Till et al. 2012).

Fig. 42
figure 42

Modified from Huang et al. (2021)

Electrical conductivity of forsterite + H2O as a function of fluid volume. Also shown is a range of conductivity anomalies in mantle wedges above subducting plates.

3 Concluding remarks

Fluids and magmatic liquids are the dominant transport media in the Earth. Complete miscibility between fluid and melt in silicate–H2O systems can be found at pressures and temperatures in excess of about 1 GPa and 800 °C for granite–H2O. These pressure and temperature coordinates increase as a system becomes more mafic and reaches conditions of the lowermost upper mantle for peridotite–H2O. Under such conditions, fluids and melts are indistinguishable.

Fluids in the Earth dominantly are compositions in the system C–O–H–N–S. Other volatiles that sometimes occur in significant proportions include halogens, and in particular F and Cl, and noble gases. Halogens can affect physical and chemical properties of both magma and crystalline materials, whereas noble gases likely do not affect most properties significantly.

Several of the C–O–H–N–S components can exist in different oxidation states within the redox range of the silicate Earth. Oxidized species in fluids are H2O, CO2, N2, SO2, and SO3. Anionic complexes such as OH, CO32−, HCO3, and SO42− groups often coexist with the molecular species in terrestrial fluids and dissolved in magmatic liquids. Reduced terrestrial fluid are CH3,NH2, NH3, S2−, and HS with those reduced anionic species often coexisting with the reduced molecular species, H2, CH4, NH3, and H2S. H2O dominates most environments whether under oxidizing or reducing conditions.

Among the typical fluid species, H2O tends to be the most efficient solvent of major, minor, and trace elements at high temperature and pressure. The solution capacity of aqueous fluids sometimes is enhanced further by dissolved halogens and sulfur. In contrast, addition of CO2 or nitrogen species to aqueous fluids has the opposite effect.

The solubility in aqueous solutions of minor and trace elements such as, for example, Ti, Zr, and Hf as well as other HFSE can be significantly affected by alkali metals by forming metal oxyanion complexes. Formation of aluminate complexes will enhance the solubility of Al2O3 in aqueous fluids in a similar manner. Such complexes can be 5–6 orders of magnitude more soluble in aqueous solutions compared with the solubility of the elements in their cation or simple oxide form. It is also likely that the solubility of such complexes increases the more electropositive the metal cation associated with the oxyanion complex(es).

Fluid-mediated transport is accomplished with fluid passing through cracks and through percolation channels along grain boundaries. Percolation velocity is linked to permeability, which, in turn, is governed by rock porosity. Finally, porosity is controlled by wetting angles, θ, at the interface between fluid and the mineral surfaces of surrounding rocks. This angle is negatively correlated with the solubility of silicate components in the fluids. When θ < 60°, the fluid will wet all grain boundaries of an isotropic crystalline material thus leading to enhanced mass transport ability, whereas when greater than 60°, grain boundary wetting does not occur and fluid-mediated transport is diminished. With anisotropic crystal structures, the wetting angles for individual crystal surfaces will vary depending on the properties of the specific surface.

For fluids, the compositions of which are dominated by H2O, CO2, and salts such as chlorides, the θ is the greatest for CO2 fluids and the smallest for brines (H2O + salt). Essentially all CO2 fluids in contact with silicate minerals exhibit θ > 60° and would not, therefore, result in wetting of grain boundaries. CO2-rich fluids are not, therefore, efficient mass transport media in the Earth. This could be the situation during granulite metamorphism, for example, because the principal fluid component in granulite facies rocks tends to be CO2-rich (e.g., Touret et al. 2011). In the continental upper mantle, CO2 also is major fluid component, so wetting by fluid in such tectonic settings is not likely. With H2O and H2O + chlorides, however, the θ < 60° so that complete wetting of grain boundaries is common. This situation exists under lower grade metamorphism and during fluid transport in of subduction zones (typically < 100 km depth).

Geophysical and geochemical anomalies in the Earth's interior can be linked to the presence of fluids and, in particular, the extent to which fluids wet grain boundaries. For example, the geochemistry of the mantle wedge above subduction zones can be affected in this manner. Similarly, fluid infiltration will lead to enhanced electrical conductivity and enhanced seismic wave attenuation such as often reported near convergent plate boundaries.

Availability of data and materials

Not applicable.


  1. In the Qn-notation, the superscript, n, denotes the number of bridging oxygen in the silicate species. This means that the equivalent species for Q0, Q1, and Q2 are SiO4, SiO3.5, and SiO3, respectively. It also means that the greater the value of n, the more polymerized is the silicate network of the Qn-species.

  2. Equation (9) does not consider the speciation of dissolved SiO2 in aqueous fluid, but whether this is done or not, any decrease in the fugacity of H2O, fH2O, would shift such a reaction to the left.

  3. This structural feature has been documented in silicate melts with the aid of MAS NMR spectroscopy of silicate melts, for example (Lee and Stebbins, 2003).

  4. The 250˚-300˚C for the proposed minimum solubility is at temperatures below the lower temperature limit of corundum in the Al2O3–H2O system (Kennedy, 1959). Walther (1997) reported, however, corundum with fluid to temperatures as low as 272˚C. The apparent conflict with the phase equilibrium data of Kennedy (1959) does not seem to be resolved.






θ :

Wetting angle

ϕ :


γ :

Surface energy

H :


D i fluid/melt :

Partition coefficient of i between fluid and melt

T :


P :



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