The Hydrothermal Minerals

Abstract

Over 2200 chemical analyses of hydrothermal minerals collected at depth in different active geothermal systems were compiled and processed in this work. In agreement with the outcomes of previous studies, it turned out that hydrothermal quartz, calcite, adularia, albite, anorthite, and laumontite are virtually pure solid phases. Therefore, their activities can be assumed to be equal to one. In contrast, the other hydrothermal minerals of interest, i.e., white mica, chlorite, epidote, prehnite, wairakite, and garnet, are solid solutions of variable composition. Therefore, the activities of pertinent endmembers (i.e., muscovite, 7Å-clinochlore, clinozoisite, prehnite, wairakite, and grossular) were computed, under the assumption of random mixing of atoms on energetically equivalent sites. Then, following the approach delineated in Sect. 2.2.1, the Gibbs free energy and the thermodynamic equilibrium constant of the dissolution reaction of the solid solutions with average activity of these pertinent endmembers were computed. These log K values are points of reference more representative than the log K of the dissolution reactions of the corresponding pure minerals.

4.1 The Hydrothermal Alteration Suites and Their Zones

A general relationship between the occurrence of hydrothermal alteration minerals and temperature was recognized long ago, although the formation of these secondary solid phases is controlled also by fluid chemistry, permeability, and duration of hydrothermal activity (e.g., Browne and Ellis 1970; Kristmannsdóttir 1979; Browne 1978; Bird et al. 1984). As pointed out by Reyes (1990), two distinct hydrothermal alteration suites occur in the high-temperature geothermal systems of the Philippines, namely (a) the neutral-pH suite, associated with the neutral-pH, alkali chloride liquids and (b) the acidic alteration suite, related with sulfur-rich aqueous solutions of low pH.

Based on the key phyllosilicate minerals, the neutral-pH suite is divided in the following four zones:

• (1) Smectite zone, extending up to temperatures of 180 °C. Smectite is accompanied by chlorite, above 120 °C, and low-temperature zeolites, such as heulandite, stilbite, and ptilolite, although laumontite occurs above 120 °C.

• (2) Transition zone, corresponding to temperatures of 180–220 °C. It is characterized by the increase in chlorite, the appearance of illite-smectite, and the persistence of laumontite, which is the typical Ca–Al-silicate of this zone. Albite, adularia, and sphene appear in this zone.

• (3) Illite zone, corresponding to temperatures of 220 to 270–280 °C, although illite is stable at higher temperatures as well. Wairakite, epidote, and prehnite are the representative Ca–Al-silicates of this zone. They are accompanied by chlorite, adularia, albite, sphene, and sulfide minerals.

• (4) Biotite zone, extending at temperatures higher than 270–280 °C. It is characterized by the appearance of high-temperature minerals, such as garnet (e.g., andradite and grossular), amphibole (e.g., actinolite and tremolite), and pyroxene (e.g., diopside), as well as by the persistence of illite, chlorite, albite, adularia, wairakite, epidote, sphene, and sulfide minerals.

Some minerals, such as quartz, calcite, and pyrite, occur at any temperature.

Based on the key hydroxy silicate of aluminum, the acidic alteration suite is divided in the following four zones: (i) The kaolinite zone, extending up to temperatures of 120 °C. (ii) The dickite ± kaolinite zone, corresponding to temperatures of 120–200 °C. (iii) The dickite ± phyrophyllite zone, corresponding to temperatures of 200–260 °C. (iv) The phyrophyllite ± illite zone, corresponding to temperatures of 230–320 °C. These hydroxy silicates of aluminum are typically accompanied by sulfur, alunite, anhydrite, diaspore, and pyrite as well as by other less common solid phases.

The same hydrothermal alteration zones present in active geothermal systems are also recognizable in hydrothermal ore deposits, which are fossil geothermal systems (Pirajino 2009). This homogeneity in the sequence of alteration minerals is not surprising considering that rocks act as suppliers of chemical elements during water-rock interaction and there are relatively limited differences in the concentrations of major (rock-forming) elements in different lithotypes (e.g., Turekian and Wedepohl 1961), apart from the extreme case of monomineralic rocks such as limestones, dolomites, and quartzites.

As pointed out by Giggenbach (1980, 1984, 1988), the non-conservative elements transferred to the aqueous solution by CO₂-driven rock dissolution remain in part in the fluid and are partly incorporated in hydrothermal alteration minerals. Under favorable conditions (e.g., constant temperature, low fluid/rock ratio), the aqueous solution is expected to approach and possibly attain the condition of chemical equilibrium with the hydrothermal alteration minerals, after a lapse of time largely depending on the kinetics of relevant dissolution-precipitation reactions.

Focusing on the felsic rocks prevailing in the continental crust, the thermodynamically stable hydrothermal paragenesis is expected to comprise quartz, muscovite (or illite), albite, adularia, clinochlore (or chlorite), and either a Ca–Al-silicate, if CO₂ fugacity is relatively low, or calcite, if CO₂ fugacity is comparatively high, in accordance with mineralogical evidence (e.g., Ellis 1970; Ellis and Mahon 1977; Giggenbach 1984, 1988; Arnórsson et al. 1983a, b; Arnórsson and Gunnlaugsson 1985). If so, the activities of undissociated SiO₂ and Al³⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ ions are fixed. In addition to the solid phases listed above, anhydrite, fluorite, and calcite may also be part of the hydrothermal mineral assemblage, thus fixing the activities of SO₄²⁻, F⁻, and HCO₃⁻ ions, respectively (Guidi et al. 1990; Chiodini et al. 1991 and references therein).

Therefore, the activity of all these compatible¹ aqueous species can be involved in geothermometers and $f_{{{\text{CO}}_{2} }}$-indicators, referring to suitable mineral-solution reactions. For performing correctly this task, it is necessary to know the main characteristics of these minerals and if they occur in active geothermal systems either as pure (or nearly pure) solid phases or as components of solid solutions. In fact, in the first case their activity can be assumed to be equal to one (based on the standard state convention for solids, see Sect. 2.1.2), whereas in the second case their activity must be properly calculated and involved in some way in geothermometers and $f_{{{\text{CO}}_{2} }}$-indicators (see Sect. 2.2.1). Therefore, the next sections of this chapter are devoted to summarize the main characteristics of relevant hydrothermal alteration minerals, especially their chemical composition, which is used to compute the activity of solid solution components of interest.

4.2 Feldspars

4.2.1 Main Characteristics of Feldspars

There is a number of books completely dedicated to feldspar minerals, such as Ribbe (1983), Smith and Brown (1988), and Deer et al. (2001).

Feldspars have either monoclinic or triclinic symmetry. The crystal structure of feldspars consists of a three dimensional framework of (Si, Al)–O or T–O tetrahedra, with each oxygen atom constituting the vertex of two adjacent tetrahedra. Each Si atom balances half charges of the four oxygen atoms in its Si–O tetrahedron, but one negative charge is unbalanced in each Al–O tetrahedron. Therefore, large monovalent and bivalent cations (collectively denoted M) occupy the interstices to maintain the charge balance. Because there is one interstice for every four tetrahedra and the interstices are completely filled up, the general crystallochemical formula of feldspars is MT₄O₈, where M is commonly Na⁺, K⁺ or Ca²⁺ and T is usually Al³⁺ or Si⁴⁺, with 1 ≤ Al ≤ 2 and 2 ≤ Si ≤ 3.

Most feldspars are ternary solid solutions of albite [Ab, NaAlSi₃O₈], orthoclase [Or, KAlSi₃O₈], and anorthite [An, CaAl₂Si₂O₈]. The solid solutions predominantly composed of albite and orthoclase form the alkali feldspar series, whereas the solid solutions primarily made up of albite and anorthite form the plagioclase series.

At high temperatures (>1000 °C), feldspars exhibit remarkable solid solution. Accordingly, the plagioclase series comprises high-anorthite, with An > 90%; high-bytownite, with 70 < An < 90%; high-labradorite, with 50 < An < 70%; high-andesine with 30 < An < 50%; high-oligoclase, with 10 < An < 30%; and high-albite, with An < 10%. According to Parsons (2010), the alkali feldspar series comprises K-sanidine, with Or >80%; sanidine, with 50 < Or < 80%; Na-sanidine with 35 < Or < 50%; and anorthoclase, with Or < 35%, although different nomenclatures are adopted by other authors. High-albite and anorthoclase are triclinic at room temperature but they assume monoclinic symmetry when observed at elevated temperatures due to shearing transformation. Sanidine has monoclinic symmetry at all temperatures.

At low temperatures (<300 °C) feldspars exhibit very limited solid solution and the stable phases are triclinic low-microcline, low-albite and anorthite, all with nearly stoichiometric composition. In fact, low-temperature natural feldspars are frequently made up of intergrowths of two or more phases. Ideally, low-microcline, low-albite and anorthite are expected to exhibit Al–Si order. Nevertheless, disordered structures are frequent because of metastable crystallization.

There are two mechanisms for the transition from monoclinic to triclinic symmetry. In alkali feldspars with Ab > 60% it occurs by a quick shearing phase transformation brought about by twisting of (Si, Al)–O tetrahedra. In contrast, a slow ‘diffusive’ order-disorder transformation occurs in the Or-rich alkali feldspars, in which the Al ions, distributed randomly between four equivalent sites at high temperatures, become ordered on one of these sites during cooling.

For what concerns the substitutions, the M-site can be occupied by Rb⁺, Tl⁺, and NH₄⁺ and in part by Li⁺ and Cs⁺ in alkali feldspars and by Sr²⁺, Ba²⁺, Pb²⁺, and Eu²⁺, as well as by (La³⁺, Na⁺) in alkali-earth feldspars. The ammonium alkali feldspar is buddingtonite, NH₄AlSi₃O₈ · ½ H₂O, whereas the barium plagioclase is celsian, Cls, BaAl₂Si₂O₈. The main substitutions in T-sites of natural feldspars are B and Fe. The boron analog of albite is reedmergnerite, NaBSi₃O₈.

4.2.2 The Chemistry of Hydrothermal Feldspars

Both adularia (i.e., hydrothermal orthoclase) and hydrothermal albite are widespread in active geothermal systems where they usually occur at temperatures higher than 120–150 °C, in spite of some notable exceptions (e.g., Browne 1970, 1978; Reyes 1990). For instance, only adularia occurs in the Cerro Prieto geothermal field, whereas hydrothermal albite is absent although primary plagioclase usually represents up to 10% of the sandstone mineral constituents at all depths (Bird et al. 1984; Schiffman et al. 1985). Conversely, hydrothermal albite replaces primary plagioclase at temperatures higher than 120 °C in the geothermal system of Onikobe, whereas adularia is absent (Seki et al. 1983). Hydrothermal anorthite and plagioclases of intermediate composition are uncommon.

In this work, several chemical analyses of hydrothermal feldspars obtained from deep boreholes drilled in active geothermal systems were compiled. 480 chemical analyses were considered of acceptable quality, having sum of oxides from 98 to 102 wt%, and processed to compute the percentages of albite, orthoclase, and anorthite.

The Ab–Or–An triangular plot of Fig. 4.1 displays the composition of 119 hydrothermal feldspars from the geothermal fields of Roosevelt Hot Springs, Utah (Ballantyne 1978), Salton Sea, California (Shearer et al. 1988), Heber, California (Browne 1977), Cerro Prieto, Mexico (Schiffman et al. 1985), Miravalles, Costa Rica (Milodowski et al. 1989), Berlin, El Salvador (Ruggieri et al. 2006), Kilauea, Hawaii (Bargar et al. 1996), Onikobe, Japan (Seki et al. 1983), Broadlands-Ohaaki, New Zealand (Lonker et al. 1990), Waiotapu, New Zealand (Hedenquist and Browne 1989) Milos, Greece (Liakopoulos 1987), as well as Latera (Cavarretta et al. 1985), Larderello (Cavarretta et al. 1982), and Pantelleria (Fulignati et al. 1997), Italy. Among these 119 hydrothermal feldspars, there are 60 adularias with Ab < 15 mol%, 54 albites, and 5 anomalous samples, namely 1 probable mixture (intergrowth) of adularia and albite (with ~25 mol% Ab), 3 plagioclases of variable composition (1 oligoclase, 1 andesine, and 1 bytownite), and 1 celsian-rich adularia from Berlin, formally constituted by 74.7 mol% Or, 19.1 mol% Cls, 3.6 mol% Ab, and 2.6 mol% An.

Fig. 4.1

Ab-Or-An triangular plot showing the composition of 119 hydrothermal feldspars from different active geothermal fields, including Roosevelt Hot Springs (Ballantyne 1978), Salton Sea (Shearer et al. 1988), Heber (Browne 1977), Cerro Prieto (Schiffman et al. 1985), Miravalles (Milodowski et al. 1989), Berlin (Ruggieri et al. 2006), Kilauea (Bargar et al. 1996), Onikobe (Seki et al. 1983), Broadlands-Ohaaki (Lonker et al. 1990), Waiotapu (Hedenquist and Browne 1989), Milos (Liakopoulos 1987), Latera (Cavarretta et al. 1985), Larderello (Cavarretta et al. 1982), and Pantelleria (Fulignati et al. 1997)

Neglecting the 5 anomalous samples, the composition of adularias and hydrothermal albites from these different geothermal systems is described by the following statistical parameters:

• (i) X_Or in adularia (N = 60): Min = 0.864, Max = 1.000, Mean = 0.946, Median = 0.951, Std. Dev. = 0.030.

• (ii) X_Ab in albite (N = 54): Min = 0.889, Max = 1.000, Mean = 0.981, Median = 0.989, Std. Dev. = 0.022.

The composition of adularia shows limited variations in well State 2-14 at Salton Sea, with X_Or from 0.90 to 0.98 (Shearer et al. 1988). The composition of hydrothermal plagioclase is close to end-member albite at depths <1828.8 m, whereas the hydrothermal plagioclase is richer in An at depths >1828.8 m. Three hydrothermal feldspars coexists in samples below 3017.5 m depth, K-feldspar with X_Or ~ 0.91, albite-oligoclase with X_Ab 0.95–0.86, and oligoclase-andesine with X_Ab 0.75–0.63.

Both hydrothermal albite and oligoclase, with X_Ab from 0.883 to 0.850, occur in an altered diabase dike or sill at Heber (Browne 1977). Textural relations suggest that oligoclase is an early mineral, probably not in equilibrium with present-day geothermal fluids.

At Cerro Prieto, adularia has X_Or varying from 0.91 to 0.97, with a mean close to 0.95, whereas hydrothermal albite is absent (Schiffman et al. 1985), as already mentioned above.

In most of the Miravalles reservoir, hydrothermal plagioclase is almost pure albite (Milodowski et al. 1989). Uncommon hydrothermal oligoclase (with X_Ab close to 0.85) might be explained by the presence of primary plagioclase relicts in albite. Rare hydrothermal bytownite (with X_An of 0.77) occurs at 1453 m depth in association with grandite garnet (60–65 mol% andradite) and magnetite. Adularia shows small concentrations of Na and variable concentrations of Ba, which are higher in the cores of crystals.

At Berlin, hydrothermal albite has X_Ab from 0.90 to 0.98, whereas a Ba-bearing feldspar with X_Cls up to 0.191 occurs in well TR-2 at about 1500 m depth (Ruggieri et al. 2006).

At Onikobe (Seki et al. 1983), the replacement of primary plagioclase by hydrothermal albite (with X_Ab > 0.95) begins at 120–180 °C and the process comes to completion at temperatures higher than 230–240 °C. Adularia is absent as already mentioned above.

Adularia and hydrothermal albite span small compositional intervals at Broadlands-Ohaaki, with X_Or in adularia from 0.94 to 0.995 and X_Ab in hydrothermal albite from 0.96 to 0.99, irrespective of primary plagioclase composition (Lonker et al. 1990). The intermediate compositions of adularia in well BR8 at 774–781 m depth cannot be explained involving primary sanidine because it is absent at Broadlands-Ohaaki (Browne and Ellis 1970). They are likely due to fine intergrowths of hydrothermal albite with adularia (Lonker et al. 1990).

At Waiotapu, hydrothermal albite and adularia are common as alteration products of primary andesine at temperatures higher than ~180 °C (Hedenquist and Browne 1989). Adularia is later than albite as indicated by textural evidence. Most hydrothermal plagioclase has X_Ab from 0.90 to 0.99, but some samples range from albite to andesine. The X_Or in adularia varies from 0.94 to 0.995.

At Milos, albite is practically pure, with X_Ab ranging from from 0.999 to 1.000, whereas X_Or in adularia varies from 0.926 to 0.974 (Liakopoulos 1987).

At Larderello, adularia has X_Or ranging from 0.950 to 0.959 in the Sasso-22 well at depths of 1600–2263 m based on microprobe analyses, whereas plagioclase compositions (as X_Ab) determined by optical microscopy are: (i) from 0.97 to 0.95 in the San Ippolito 122 well at 783 m depth; (ii) from 0.87 to 0.86 in the Sasso 22 well at 2770 m depth; (iii) from 0.66 to 0.60 in the Anqua well at 2635 m depth (Cavarretta et al. 1982).

At Pantelleria, hydrothermal albite has X_Ab varying from 0.982 to 0.992 and adularia has X_Or ranging from 0.946 to 1.000 (Fulignati et al. 1997).

As shown in the Ab–Or–An triangular plot of Fig. 4.2, the 361 hydrothermal feldspars from Reykjanes, Iceland (mostly from Libbey and Williams-Jones 2016 and subordinately from Marks et al. 2010; Fowler et al. 2015) comprise 150 adularias with Or >85 mol%, 182 albite-oligoclase samples, and 18 anorthites as well as 14 anomalous samples which are probable mixtures (i.e., intergrowths of two or more phases, possibly including relicts of primary phases), 8 rich in adularia and 6 rich in oligoclase.

Fig. 4.2

Ab-Or-An triangular plot showing the composition of 361 hydrothermal feldspars from the Reykjanes geothermal field (data mainly from Libbey and Williams-Jones 2016 and subordinately from Marks et al. 2010 and Fowler et al. 2015)

Neglecting these 14 anomalous samples, the composition of the hydrothermal feldspars from Reykjanes is defined by the following statistical parameters:

• (i) X_Or in adularia (N = 150): Min = 0.870, Max = 0.992, Mean = 0.954, Median = 0.963, Std. Dev. = 0.025.

• (ii) X_Ab in albite-oligoclase (N = 179): Min = 0.697, Max = 0.977, Mean = 0.889, Median = 0.910, Std. Dev. = 0.060.

• (iii) X_An in anorthite (N = 18): Min = 0.900, Max = 0.991, Mean = 0.955, Median = 0.963, Std. Dev. = 0.030.

Reykjanes is unique among the considered geothermal systems for the presence of hydrothermal anorthite, which occurs only in the deepest parts of the geothermal system, where temperature is >300 °C. Hydrothermal anorthite is distinguishable from its igneous counterpart being more An-rich and having much lower concentrations of K and Mg (Libbey and Williams-Jones 2016).

In contrast, hydrothermal albite and oligoclase are abundant throughout the Reykjanes geothermal system, where they mainly occur as replacement of primary plagioclase, although they are also present as subhedral crystals in veins and vugs (Libbey and Williams-Jones 2016). Therefore, most oligoclase might actually represent the product of incomplete replacement of a more calcic primary plagioclase, which could be still present as relict. If so, oligoclase would be less frequent then evaluated above for Reykjanes, consistent with what is generally observed in active geothermal fields (Browne 1977).

Summing up, accepting that oligoclase compositions are due to the possible presence of relicts of primary plagioclase in hydrothermal albite and that mixed compositions are due to intergrowths of different endmember feldspars, it can be concluded that both adularia and albite are the most abundant hydrothermal feldspars in active geothermal systems, where they occur as pure or nearly pure solid phases. Based on this evidence, the activities of Or in adularia and Ab in albite can be reasonably assumed equal to one.

4.2.3 The Structural State and Degree of Ordering of Hydrothermal Alkali Feldspars

Only few investigations were performed so far to characterize the structural state and Al–Si order-disorder on the tetrahedral sites of authigenic K- and Na-feldspars from active geothermal systems.

The occurrence of almost pure adularia as hydrothermal mineral at temperature ≤265 °C in the Wairakei geothermal system was shown long ago by Steiner and coworkers (Steiner 1970 and references therein). Optical data indicate that hydrothermal K-feldspar is partly monoclinic and partly triclinic although X-ray diffractograms indicate only monoclinic lattice. According to Steiner (1970) either monoclinic and triclinic adularia are precipitated almost concomitantly, or triclinic K-feldspar alone is formed and the associated monoclinic structure is only apparent, being simulated by very fine twinning that is optically not detectable. If so, hydrothermal, pure potassium feldspar may have any degree of Si–Al ordering on crystallization.

McDowell (1986) investigated the structural state and Al–Si order on the tetrahedral sites of the authigenic and re-equilibrated detrital K- and Na-feldspars coexisting at temperatures of 250–360 °C in the Salton Sea geothermal reservoir and recovered from the Elmore 1 borehole. The ordering parameter Z (as defined by Thompson 1969) is 0.79 ± 0.09 at ~335 °C and 0.70 ± 0.07 at ~360 °C for albite (N = 6), whereas Z is 0.81 at ~335 °C for K-feldspar (N = 1).

Shearer et al. (1988) noted a systematic increase with depth of Al–Si disorder in K-feldspar from Salton Sea, but this information refers to allogenic-authigenic mixtures of this mineral because the XRD analyses do not distinguish allogenic and authigenic solid phases. Therefore, Shearer et al. (1988) concluded that the systematic increase in Al–Si disorder with depth probably suggests the presence of higher fractions of disordered authigenic (sanidine-like) K-feldspar in the hydrothermal assemblage.

Hedenquist and Browne (1989) studied the hydrothermal minerals at Waiotapu, concluding that (i) the albite structure is partially ordered, based on the position of the d₂₀₄ reflection whereas (ii) adularia is almost completely ordered (maximum microcline) as indicated by the position of d₀₆₀ and d₂₀₄ reflections.

Adularias from low-temperature hydrothermal veins are remarkable for the extensive differences in structural state, from totally disordered monoclinic sanidine (or the highly disordered triclinic form) to highly ordered microcline, chiefly depending on nucleation and crystallization rates and temperature (Černý and Chapman 1986). To be noted that hydrothermal alkali feldspars probably formed under supersaturation conditions rather than at equilibrium. Consequently, their degree of ordering is expected to be a function of the extent of supersaturation, with the Al–Si distribution on the tetrahedral sites becoming more and more disordered with increasing supersaturation. In fact, at conditions of sufficient supersaturation, the disordered phase is kinetically favored over its ordered equivalent, irrespective of their relative thermodynamic stabilities (Carpenter and Putnis 1985).

The post-crystallization thermal regime can also affect the Al–Si distribution on the tetrahedral sites of alkali feldspar. For instance, initially disordered phases kept at high temperature could re-organize their lattice acquiring a more ordered Al–Si distribution. Owing to these potential thermal effects on the hydrothermal feldspars, it is advisable to take into consideration the authigenic alkali feldspars present in sedimentary rocks, which formed at low temperatures and were certainly not affected by annealing and, therefore, are expected to give reliable indications on the degree of ordering of adularia and albite.

According to Morad (1978), diagenetic K-feldspar crystals are monoclinic and, less commonly, triclinic with various degrees of Al–Si ordering, whereas diagenetic albite is well-ordered, triclinic. Kastner and Siever (1979) recognized that authigenic feldspars may have almost any state of Al–Si ordering, from completely ordered, triclinic microclines and albites to highly disordered monoclinic sanidines. Albites tend to be ordered (e.g., Kastner and Waldbaum 1968; Fishman et al. 1995) whereas the structural state of K-feldspar depends on rock type, probably due to kinetic factors. K-feldspars are fully ordered in carbonate rocks, are highly disordered in ash beds, whereas a wide range of ordering degree is found in sandstones and shales.

Further indications are given by the experiments performed by Flehmig (1977), who synthesized highly pure K-feldspar and albite crystals by means of hydroxide gels, mainly at 20 °C apart from a few runs at 3 and 60 °C. Strictly speaking, the factors controlling crystal growth in gels are the free solute concentrations and pH in the gel pores. However, since these parameters cannot be measured, the corresponding parameters in the supernatant solution were reported and discussed by Flehmig (1977). He found that the structural state and the degree of ordering of the synthesized feldspars depends on pH and Na and K concentrations. The growth of K-feldspar crystals took place in the pH range 5–10, with more ordered triclinic K-feldspar (microcline) at higher pH and alkali concentrations and less ordered monoclinic K-feldspar at lower pH and alkali concentrations. Albite crystals were obtained only at pH ≥8 and high Na concentrations and showed high degrees of ordering. Similar influences of pH and alkali concentration on the formation of low albite had previously been recognized by Martin (1969).

On the basis of the evidence summarized above, the hydrothermal alkali feldspars occurring in active geothermal systems are expected to be triclinic, fully ordered, albite and variably ordered adularia, from fully ordered microcline to completely disordered sanidine, with either triclinic or monoclinic symmetry.

These expectations are at variance with the findings of Stefánsson and Arnórsson (2000), who underscored that primary disordered plagioclases and alkali-feldspars of compositions typically found in volcanic rocks tend to dissolve in geothermal waters with simultaneous precipitation of ordered alkali-feldspars with near pure endmember compositions. However, Stefánsson and Arnórsson (2000) used the solubility constants of feldspars of Arnórsson and Stefánsson (1999) whose reliability is questionable, at least as far as the alkali feldspars are concerned, as shown in the next section.

4.2.4 The Thermodynamic Properties of Endmember Alkali Feldspars

As already underscored in Sect. 2.2, in the geochemical literature there is a lack of consensus on the thermodynamic data of several minerals, including the alkali feldspars. The reproduction of the monoclinic/triclinic transition temperature of alkali feldspars, which is close to 500 °C in K-feldspar and close to 660 °C in Na-feldspar at low pressures (Deer et al. 2001), represents a good way to prove the reliability of the thermodynamic data of alkali feldspars, because of the simplicity of the solid-solid reactions of interest (see below).

First, the thermodynamic data of high-albite, low-albite, sanidine, and microcline from Holland and Powell (1998) and Arnórsson and Stefánsson (1999), see Table 4.1, were inserted into SUPCRT92.

Table 4.1 Standard state molal thermodynamic properties, at 25 °C, 1 bar, of maximum-microcline, high-sanidine, low-albite, and high-albite from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and AS99 = Arnórsson and Stefánsson (1999)^a

The heat capacity coefficients of Holland and Powell (1998) refer to the polynomial equation:

$${\text{C}}_{\text{P}}^{{\circ }} = {\text{a}} + {\text{b}} \cdot {\text{T}} + {\text{c}} \cdot {\text{T}}^{ - 2} + {\text{d}} \cdot {\text{T}}^{ - 1/2} ,$$

(4.1)

whereas the heat capacity coefficients of Arnórsson and Stefánsson (1999) are consistent with the polynomial relation:

$${\text{C}}_{\text{P}}^{{\circ }} = {\text{a}} + 2{\text{b}} \cdot {\text{T}} + {\text{c}} \cdot {\text{T}}^{ - 2} + {\text{f}} \cdot {\text{T}}^{2} + {\text{g}} \cdot {\text{T}}^{ - 1/2} .$$

(4.2)

Therefore, heat capacity coefficients were recalculated to make them consistent with the Maier-Kelley relation, Eq. (2.17). The thermodynamic data of Holland and Powell (2011) were not considered because these authors give the same entropy (214.3 J K⁻¹ mol⁻¹) for sanidine and microcline probably due to a typo. In fact, Holland and Powell (1998) give different entropies for sanidine (230 J mol⁻¹ K⁻¹) and microcline (216 J mol⁻¹ K⁻¹), as expected from configurational entropy considerations (Openshaw et al. 1976).

Second, the standard Gibbs free energy, ΔG°_r, of the solid-solid reaction;

$${\text{Microcline}} = {\text{Sanidine}}$$

(4.3)

was calculated by means of SUPCRT92 as a function of temperature, at both 1 bar and 1 kbar, considering alternatively the thermodynamic data of Helgeson et al. (1978), Holland and Powell (1998), and Arnórsson and Stefánsson (1999).

Results are displayed in the diagram of ΔG°_r versus temperature (Fig. 4.3) which shows that:

Fig. 4.3

Diagram of the standard Gibbs free energy of sanidine/microcline transition as a function of temperature, at a pressure of 1 bar and 1 kbar, based on the thermodynamic data of Helgeson et al. (1978), Holland and Powell (1998), and Arnórsson and Stefánsson (1999)

• (a) the thermodynamic data of Helgeson et al. (1978) are consistent with a sanidine/microcline transition temperature close to 500 °C, in agreement with the available experimental evidence (see above),

• (b) as explicitly stated in the paper of Holland and Powell (1998), their thermodynamic data are consistent with a sanidine/microcline transition temperature of 452°C, which is ~50 °C lower than the experimental datum;

• (c) the thermodynamic data of Arnórsson and Stefánsson (1999) are consistent with a sanidine/microcline transition temperature of 210 °C, which is ~290 °C lower than the experimental value.

Third, the ΔG°_r of the solid-solid reaction;

$${\text{High-albite}} = {\text{Low-albite}}$$

(4.4)

was computed as a function of temperature, at both 1 bar and 1 kbar, taking into account alternatively the thermodynamic data of Helgeson et al. (1978), Holland and Powell (1998), and Arnórsson and Stefánsson (1999).

Results are presented in the plot of ΔG°_r versus temperature (Fig. 4.4) which shows that:

Fig. 4.4

Diagram of the standard Gibbs free energy of high-albite/low-albite transition as a function of temperature, at a pressure of 1 bar and 1 kbar, based on the thermodynamic data of Helgeson et al. (1978), Holland and Powell (1998), and Arnórsson and Stefánsson (1999)

• (a) the thermodynamic data of Helgeson et al. (1978) are consistent with a high-albite/low-albite transition temperature close to 660 °C, in accordance with the available experimental evidence (see above),

• (b) the thermodynamic data of Holland and Powell (1998) are consistent with a high-albite/low-albite transition temperature of 460–465 °C, which is ~200 °C lower than the experimental datum;

• (c) the thermodynamic data of Arnórsson and Stefánsson (1999) are consistent with a high-albite/low-albite transition temperature of 515 °C, which is ~145 °C lower than the experimental value.

Summing up, only the thermodynamic data of Helgeson et al. (1978) are consistent with the monoclinic/triclinic transition temperatures of alkali feldspars whereas the thermodynamic data of Holland and Powell (1998) and Arnórsson and Stefánsson (1999) are not. Consequently, the thermodynamic data of Helgeson et al. (1978) can be used to compute the log K values of the exchange reactions involving alkali feldspars and other Al-bearing minerals of interest for geothermometry and $f_{{{\text{CO}}_{2} }}$ evaluation, as discussed in Chaps. 6–9, whereas the thermodynamic data of Holland and Powell (1998) and Arnórsson and Stefánsson (1999) cannot be used to this aim. In addition to these general implications, the monoclinic/triclinic transition temperatures of alkali feldspars have other specific implications on Na–K geothermometry, whose discussion is postponed to Sect. 6.1.

4.2.5 The Thermodynamic Properties of Variably Ordered Alkali Feldspars

Since the conversion between the monoclinic and triclinic crystal structures in K-feldspar has little or no effect on its thermodynamic behavior, the different thermodynamic properties of ordered microcline and disordered sanidine are entirely due to substitutional Al–Si order-disorder or nearly so (Helgeson et al. 1978). In contrast, the displacive transformation in albite from monoclinic to triclinic symmetry is accompanied by a relatively large heat of transition and, therefore, albite experiences two superimposed lambda transitions with increasing temperature, one caused by exchange of Al and Si atoms on its tetrahedral sites, and the other produced by displacive changes in its symmetry (Helgeson et al. 1978).

Accepting that variably ordered adularia occurs in active geothermal systems (see Sect. 4.2.3), the thermodynamic properties of adularia with ordering parameter Z varying from 0.9 to 0.1, at steps of 0.1 units, were calculated in this work and added to the SUPCRT92 thermodynamic database. In these calculations, maximum-microcline and high-sanidine were assumed to be representative of adularia with ordering parameter Z of 1 and 0, respectively. Following Helgeson et al. (1978), the standard molal enthalpy and the standard molal entropy of substitutional disorder for variably ordered adularia, ΔH°_ds,Adl (in cal mol⁻¹) and ΔS°_ds,Adl (in cal K⁻¹ mol⁻¹), respectively, at 25 °C, 1 bar, were computed using the simple relations:

$$\Delta {\text{H}}_{{{\text{ds}},{\text{Adl}}}}^{{\circ }} = 2650 \cdot (1 - {\text{Z}})$$

(4.5)

$$\Delta {\text{S}}_{{{\text{ds}},{\text{Ad}}1}}^{\circ } = 3.4 \cdot (1 - {\text{Z}}).$$

(4.6)

The standard molal Gibbs free energy of substitutional disorder for variably ordered adularia, ΔG°_ds,Adl (in cal mol⁻¹), at 25 °C, 1 bar, was then obtained by means of the fundamental Eq. (2.1), rewritten as:

$$\Delta {\text{G}}_{{{\text{ds}},{\text{Adl}}}}^{\circ } = \Delta {\text{H}}_{{{\text{ds}},{\text{Adl}}}}^{\circ } - {\text{T}} \cdot \Delta {\text{S}}_{{{\text{ds}},{\text{Adl}}}}^{\circ } .$$

(4.7)

Helgeson et al. (1978) assumed the same heat capacity power function coefficients for high-sanidine and maximum-microcline, because the difference in the heat capacity of the two K-feldspars, at 25 °C and 1 bar, is only 0.07 cal K⁻¹ mol⁻¹ (Openshaw et al. 1976). Here, this hypothesis was adopted for adularia, irrespective of its ordering parameter Z.

Accepting that hydrothermal albite occurring in active geothermal systems is fully ordered (see Sect. 4.2.3), there is no need to calculate the thermodynamic properties of variably ordered albite. Nevertheless, the thermodynamic properties of albite with ordering parameter Z varying from 0.9 to 0.1, at steps of 0.1 units, were also computed in this work and added to the SUPCRT92 thermodynamic database. In these calculations, low-albite and high-albite were assumed to be representative of albite with ordering parameter Z of 1 and 0, respectively. Following Helgeson et al. (1978), the standard molal enthalpy and the standard molal entropy of substitutional disorder for variably ordered albite, $\Delta {\text{H}}_{{{\text{ds}},{\text{Ab}}}}^{{\circ }}$ (in cal mol⁻¹) and $\Delta {\text{S}}_{{{\text{ds}},{\text{Ab}}}}^{{\circ }}$ (in cal K⁻¹ mol⁻¹), respectively, at 25 °C, 1 bar, were calculated utilizing the equations:

$$\Delta {\text{H}}_{{{\text{ds}},{\text{Ab}}}}^{\circ } = 2630 \cdot (1 - {\text{Z}}).$$

(4.8)

$$\Delta {\text{S}}_{{{\text{ds}},{\text{Ab}}}}^{\circ } = 2.79 \cdot (1 - {\text{Z}}).$$

(4.9)

The standard molal Gibbs free energy of substitutional disorder for variably ordered albite, $\Delta {\text{G}}_{{{\text{ds}},{\text{Ab}}}}^{{\circ }}$ (in cal mol⁻¹), at 25 °C, 1 bar, was then be computed by means of the fundamental relation (2.1) rewritten as:

$$\Delta {\text{G}}_{{{\text{ds}},{\text{Ab}}}}^{\circ } = \Delta {\text{H}}_{{{\text{ds}},{\text{Ab}}}}^{\circ } - {\text{T}} \cdot \Delta {\text{S}}_{{{\text{ds}},{\text{Ab}}}}^{\circ }.$$

(4.10)

The same heat capacity power function coefficients were adopted for any variably ordered albite because those of high-albite are equal to those of low-albite, at least below 350 °C (Helgeson et al. 1978).

The molar volumes of variably ordered adularia were computed through linear interpolation of the values of maximum-microcline and high-sanidine reported by Helgeson et al. (1978). Similarly, the molar volumes of variably ordered albite were calculated through linear interpolation of the values of low-albite and high-albite given by Helgeson et al. (1978). The standard state molal thermodynamic properties, at 25 °C, 1 bar, of variably ordered adularia and albite are listed in Table 4.2 together with those of maximum-microcline, high-sanidine, low-albite, and high-albite reported by Helgeson et al. (1978).

Table 4.2 Standard state molal thermodynamic properties, at 25 °C, 1 bar, of maximum-microcline, high-sanidine, low-albite, and high-albite (from Helgeson et al. 1978) as well as of variably ordered adularia and albite (this work)

4.3 White Micas

4.3.1 Main Characteristics of White Micas

The three rock-forming white micas are muscovite [KAl ^VI₂ (AlSi₃)^IVO₁₀(OH)₂], paragonite [NaAl ^VI₂ (AlSi₃)^IVO₁₀(OH)₂], and margarite [CaAl ^VI₂ (AlSi₂)^IVO₁₀(OH)₂]. As pointed out by Guidotti and Sassi (2002): (i) muscovite may contain up to 38 mol% of paragonite in solution, (ii) paragonite may contain up to 15 mol% of muscovite in solution, and (iii) practically no solution occurs between muscovite and margarite.

In spite of these possible mixing relations, muscovite prevails by far over paragonite and margarite in white micas (or sericites) from active geothermal systems, including phengites and illites. Phengites may be described as binary solid solutions of muscovite and celadonites [K(M³⁺)^VI(M²⁺)^VISi ^IV₄ O₁₀(OH)₂] (Ernst 1963; Velde 1977). In the chemical formula of celadonite, M³⁺ generally represents Al³⁺ or Fe³⁺, whereas M²⁺ usually stands for Fe²⁺ or Mg²⁺, thus leading to four limiting compositions called celadonite [K(Fe³⁺)^VI(Mg²⁺)^VISi ^IV₄ O₁₀(OH)₂], Fe-celadonite [K(Fe³⁺)^VI(Fe²⁺)^VISi ^IV₄ O₁₀(OH)₂], Fe–Al-celadonite [KAl^VI(Fe²⁺)^VISi ^IV₄ O₁₀(OH)₂] and Mg–Al-celadonite [KAl^VI(Mg²⁺)^VISi ^IV₄ O₁₀(OH)₂] (Li et al. 1997). Illites are solid solutions of muscovite, celadonites and pyrophyllite [Al₂Si₄O₁₀(OH)₂] (Weaver and Pollard 1973).

Following Brigatti and Guggenheim (2002) and references therein, we recall that the 2:1 mica structure is constituted by two opposing tetrahedral (T) sheets with an octahedral (M) sheet between them to produce a TMT layer. The general chemical formula of micas is:

$${\text{A}}^{\rm{XII}} {\text{M}}_{2 - 3}^{\rm{VI}} \;\square \;_{1 - 0}^{\rm{VI}} {\text{T}}_{4}^{\rm{IV}} {\text{O}}_{10} ({\text{X}})_{2} ,$$

in which:

• A^XII refers to the twelve-coordinated interlayer sites, which are generally occupied by K, Na, Ca, Ba, and rarely by Rb, Cs, Sr, NH₄, and H₃O;

• M^VI indicates the six-coordinated octahedral sites, which are usually occupied by Mg, Fe²⁺, Al, and Fe³⁺, although Li, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn may also be present in peculiar micas;

• □^VI indicates a vacant six-coordinated octahedral site;

• T^IV denotes the four-coordinated tetrahedral sites, which are generally occupied by Si, Al and Fe³⁺ and infrequently by B and Be;

• X refers to (OH), F, Cl, O, S.

The smallest structural unit of micas contains three octahedral sites. All the three octahedral sites are occupied in the so-called trioctahedral micas, such as biotite and phlogopite, whereas only two octahedral sites [usually M(2)] are occupied and one is vacant [generally M(1)], in the micas known as dioctahedral, such as muscovite, paragonite, margarite, celadonite, and illite, which are those of interest to us.

4.3.2 The Activities of Muscovite, Celadonites, and Pyrophyllite in Hydrothermal White Micas

Following Helgeson et al. (1978), Aagaard and Helgeson (1983), Helgeson and Aagaard (1985), and Aagaard and Jahren (1992), the activities of muscovite, a_Ms, pyrophyllite, a_Prl, celadonite, a_Cel, Fe-celadonite, a_Fe–Cel, Fe–Al-celadonite, a_{Fe–Al–Cel}, and Mg–Al-celadonite, a_{Mg–Al–Cel}, in white micas are computed using the following equations:

$$a_{\text{Ms}} = {\text{k}}_{\text{Ms}} \cdot {\text{X}}_{\text{K,A}} \cdot {\text{X}}_{{{\text{Al,M}}\left( 2\right)}}^{2} \cdot {\text{X}}_{\text{Al,T}} \cdot {\text{X}}_{\text{Si,T}}^{3}$$

(4.11)

$$a_{\text{Prl}} = {\text{k}}_{\text{Prl}} \cdot {\text{X}}_{{{\square } , {\text{A}}}} \cdot {\text{X}}_{{{\text{Al,M}}\left( 2\right)}}^{2} \cdot {\text{X}}_{\text{Si,T}}^{4}$$

(4.12)

$$a_{\text{Cel}} = {\text{k}}_{\text{Cel}} \cdot {\text{X}}_{\text{K,A}} \cdot {\text{X}}_{{{\text{Mg,M}}(2)}} \cdot {\text{X}}_{{{\text{Fe}}^{3 + } ,{\text{M}}(2)}} \cdot {\text{X}}_{\text{Si,T}}^{4}$$

(4.13)

$$a_{{{\text{Fe}} - {\text{Cel}}}} = {\text{k}}_{{{\text{Fe}} - {\text{Cel}}}} \cdot {\text{X}}_{{{\text{K}},{\text{A}}}} \cdot {\text{X}}_{{{\text{Fe}}^{2 + } ,{\text{M}}(2)}} \cdot {\text{X}}_{{{\text{Fe}}^{3 + } ,{\text{M}}(2)}} \cdot {\text{X}}_{\text{Si,T}}^{4}$$

(4.14)

$$a_{{{\text{Fe}} - {\text{Al}} - {\text{Cel}}}} = {\text{k}}_{{{\text{Fe}} - {\text{Al}} - {\text{Cel}}}} \cdot {\text{X}}_{{{\text{K}},{\text{A}}}} \cdot {\text{X}}_{{{\text{Fe}}^{2 + } ,{\text{M}}(2)}} \cdot {\text{X}}_{{{\text{Al}},{\text{M}}(2)}} \cdot {\text{X}}_{\text{Si,T}}^{4}$$

(4.15)

$$a_{\text{Mg - Al - Cel}} = {\text{k}}_{\text{Mg - Al - Cel}} \cdot {\text{X}}_{\text{K,A}} \cdot {\text{X}}_{{{\text{Mg,M}}(2)}} \cdot {\text{X}}_{{{\text{Al,M}}(2)}} \cdot {\text{X}}_{\text{Si,T}}^{4}$$

(4.16)

which are based on the assumption of random mixing of atoms on energetically equivalent sites. In Eqs. (4.11)–(4.16):

k_Ms = 9.4815, k_Prl = 1, k_Cel = k_Fe–Cel = k_{Fe–Al–Cel} = k_{Mg–Al–Cel} = 4 are constants relating the inter- and intra-crystalline standard states;

X_K,A and X_□,A are the mole fractions of potassium and vacancies on the interlayer A site;

X_Al,M(2), ${\text{X}}_{{{\text{Fe}}^{3 + } ,{\text{M}}(2)}}$, X_Mg,M(2), ${\text{X}}_{{{\text{Fe}}^{2 + } ,{\text{M}}(2)}}$ are the mole fractions of aluminum, trivalent iron, magnesium, and divalent iron on the M(2) octahedral sites;

X_Al,T and X_Si,T are the mole fractions of aluminum and silicon on the T tetrahedral sites.

Chemical analyses of white micas are available for several active geothermal systems, including Salton Sea, California, for the temperature range 190–322 °C McDowell and Elders (1980, 1983); Coso, California, for the temperature interval 190–250 °C (Bishop and Bird 1987); Roosevelt Hot Springs, Utah, for temperatures varying from 212 to 255 °C (Ballantyne 1978; Capuano and Cole 1982); Los Azufres, Mexico, for temperatures ranging from 190 to 270 °C (Cathelineau 1988; Cathelineau and Izquierdo 1988); Bouillante, Guadeloupe, for the temperature range 204–260 °C (Mas et al. 2006); Larderello, Italy, for the temperature interval 248–315 °C (Boyce et al. 2003); Pantelleria, Italy, at temperatures of 170 and 275 °C (Fulignati et al. 1997); Aluto-Langano, Ethiopia, for the temperature range 215–300 °C (Teklemariam et al. 1996); Waiotapu, New Zealand, for the temperature interval 170–282 °C (Hedenquist and Browne 1989); Broadlands-Ohaaki, New Zealand, for temperatures varying from 222 to 300 °C (Lonker and Gerald 1990; Lonker et al. 1990); Kakkonda, Japan, at temperatures of 205 and 300 °C (Inoue et al. 2004).

These 94 chemical analyses of white mica samples were compiled. Since the FeO and Fe₂O₃ contents are not reported and only the total Fe content is available, it is necessary to adopt some hypotheses concerning the redox state of iron to compute, first, site occupancies and, second, the activities of muscovite, pyrophyllite, and celadonite components using Eqs. (4.11)–(4.16). The adopted hypotheses are that 86.5% of total Fe is present as Fe³⁺, which is the average value for illites according to Weaver and Pollard (1973), and that Fe³⁺ is present only in the octahedral sites. The exclusive occurrence of Fe³⁺ in the octahedral sites is a reasonable assumption considering both that Fe³⁺ occupies the octahedral sites in the ferric endmembers of celadonite (e.g., Li et al. 1997), pyrophyllite (e.g., Badaut et al. 1992 and references therein), and muscovite (e.g., Guidotti and Sassi 2002), and that Fe³⁺ tetrahedral substitution does not take place in dioctahedral micas, whereas it occurs in trioctahedral micas, such as tetra-ferriphlogopite, tetra-ferri-annite and anandite (Brigatti and Guggenheim 2002). To be noted that the alternative assumption of Fe completely present as Fe²⁺ (which was adopted by Cathelineau and Izquierdo (1988) determines changes (i) in the mole fractions of Fe²⁺ and Fe³⁺ on the M(2) octahedral sites, whereas other mole fractions are unaffected by the hypotheses on the Fe redox state and (ii) in the activities of celadonite, Fe-celadonite, and Fe–Al-celadonite, whereas the activities of Mg–Al-celadonite, muscovite, and pyrophyllite are not influenced by the assumptions on the Fe redox state.

The correlation plot of the activity of muscovite in the white mica samples versus the mole fraction of Al on the tetrahedral site (Fig. 4.5), is a good starting point to analyze the data of geothermal white micas. Since illites and white micas in general are solid solutions of muscovite, celadonites and pyrophyllite (see above), they are expected to be found along the tie line joining the muscovite point and the point representative of both celadonites and pyrophyllite or at least close to this Ms − (Prl + Cel) tie line. Allowing for a maximum deviation of ±0.12 a_Ms units, 75 chemical analyses were considered representative of white micas, whereas the remaining 19 were rejected. All these rejected samples show negative deviations from the Ms − (Prl + Cel) tie line, possibly because they are white micas mixed with other clay minerals or other phyllosilicates. Alternatively, assuming that all Fe is present as Fe³⁺ and occupies the tetrahedral sites, 11 samples would deviate from the Ms − (Prl + Cel) tie line by more than 0.12 a_Ms units, although the other 8 would exhibit smaller deviations.

Fig. 4.5

Diagram of the activity of muscovite versus the mole fraction of Al on the T tetrahedral sites for the 94 white mica samples from different geothermal fields (see legend), also showing the idealized stoichiometry of the components of white micas, that is muscovite, pyrophyllite and celadonites

Aagaard and Helgeson (1983) underscored that the distribution of Al³⁺ ion among the tetrahedral and octahedral sites of clay minerals allows one to distinguish illites from montmorillonites and mixed-layer clays. In fact, these minerals occupy different fields in the plot of Fig. 4.6, which was slightly modified adding the idealized stoichiometry of the components of white micas, that is muscovite, pyrophyllite and celadonites.

Fig. 4.6

Diagram of the mole fraction of Al on the M(2) octahedral sites versus the mole fraction of Al on the T tetrahedral sites for the 94 white mica samples from different geothermal fields (see legend). The grey fields of illites, mixed-layer clays, and montmorillonites (smectites) are from Aagaard and Helgeson (1983). The idealized stoichiometry of the components of white micas, that is muscovite, pyrophyllite and celadonites, are also shown

As expected: (i) the 75 accepted samples of geothermal white micas are situated inside the compositional space delimited by these three endmembers, and most of these samples are found in the field of illites or close to it, whereas (ii) the 19 rejected samples are positioned to the right of the Ms–Prl–Cel triangle. However, assuming that all Fe is present as Fe³⁺ and occupies the tetrahedral sites, also the 19 rejected samples would be found inside the Ms–Prl–Cel triangle or close to it. Since the ambiguity concerning these 19 rejected samples cannot be resolved, it is advisable to rely only on the other 75 samples.

The activity of the muscovite endmember in the considered 75 white mica samples varies between 0.007 and 0.875, with an average of 0.654, a median of 0.688 and a standard deviation of 0.156. The sum of the activities of the celadonite components ranges from 0.033 to 0.677, with an average of 0.228, a median of 0.202 and a standard deviation of 0.130. The activity of the pyrophyllite component spans the range 0.000 to 0.156, with an average of 0.060, a median of 0.056 and a standard deviation of 0.035.

The muscovite endmember prevails in 70 of the 75 white mica samples, the celadonite components dominates the remaining 5 samples, whereas the pyrophyllite endmember is always subordinate, as shown by the triangular diagram of Fig. 4.7.

Fig. 4.7

Triangular diagram comparing the activities of muscovite, celadonites and pyrophyllite for the 75 accepted white mica samples from different geothermal fields (see legend)

The two diagrams of Fig. 4.8 show that:

Fig. 4.8

Diagrams of the activity of the muscovite component versus a the sum of the activities of the celadonite components and b the activity of the pyrophyllite component for the 75 accepted white mica samples from different geothermal fields (symbols as in Figs. 4.5, 4.6 and 4.7). The idealized stoichiometry of muscovite, pyrophyllite and celadonites are also shown

• (i) the activities of the muscovite and pyrophyllite endmembers in the white mica samples of interest are not correlated, as also indicated by the very low value of the squared linear regression coefficient, R² = 0.027, whereas

• (ii) there is a significant negative correlation between the activity of the muscovite component and the sum of the activities of the celadonite components, as also pointed out by the squared linear regression coefficient, R² = 0.748.

The activity of the muscovite endmember, the sum of the activities of the celadonite components and the activity of the pyrophyllite endmember have no significant relation with temperature for the 75 accepted white mica samples as pointed out by the very small R² values of 0.0004, 0.0191, and 0.174, respectively. In contrast, a_Ms, a_ΣCel, and a_Prl exhibit a meaningful temperature dependence for the 19 rejected samples, with R² values of 0.686, 0.705, and 0.266, respectively. Again, this evidence suggests that white micas are mixed with other clay minerals or other phyllosilicates in these 19 rejected samples.

4.3.3 The Thermodynamic Properties of Muscovite

The values of the ΔG°_f and ΔH°_f of muscovite at 25 °C, 1 bar given in the first row of Table 4.3 were calculated by Helgeson et al. (1978) from the equilibrium constants derived from high pressure, high temperature experimental data for the following equilibria:

Table 4.3 Standard state molal thermodynamic properties, at 25 °C, 1 bar, of muscovite [KAl₂(AlSi₃)O₁₀(OH)₂] from H78 = Helgeson et al. (1978), S91 = Sverjensky et al. (1991), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011) as well as of pyrophyllite [Al₂Si₄O₁₀(OH)₂] from H78 = Helgeson et al. (1978)

$$2\;{\text{muscovite}} + 6\;{\text{quartz}} + 2\;{\text{H}}^{ + } = 3\;{\text{pyrophyllite}} + 2\;{\text{K}}^{ + }$$

(4.17)

$${\text{muscovite}} + {\text{quartz}} = {\text{K-feldspar}} + {\text{andalusite}} + {\text{H}}_{2} {\text{O}} .$$

(4.18)

Sverjensky et al. (1991) adopted a similar approach and considered the following equilibria:

$$1.5\;{\text{K-feldspar}} + {\text{H}}^{ + } = 0.5\;{\text{muscovite}} + 3\;{\text{quartz}} + {\text{K}}^{ + }$$

(4.19)

$${\text{muscovite}} + {\text{H}}^{ + } + 1.5\;{\text{H}}_{2} {\text{O}} = 1.5\;{\text{kaolinite}} + {\text{K}}^{ + }$$

(4.20)

$${\text{muscovite}} + {\text{H}}^{ + } + 3\;{\text{quartz}} = 1.5\;{\text{pyrophyllite}} + {\text{K}}^{ + }$$

(4.21)

$${\text{muscovite}} + {\text{H}}^{ + } = 1.5\;{\text{andalusite}} + 1.5\;{\text{quartz}} + 1.5\;{\text{H}}_{2} {\text{O}} + {\text{K}}^{ + } .$$

(4.22)

However, Sverjensky et al. (1991) used more recent thermodynamic data for the relevant aqueous species, obtaining the ΔG°_f, ΔH°_f, and S° values at 25 °C, 1 bar listed in the second row of Table 4.3. These ΔG°_f, ΔH°_f, and S° values differ from those of Helgeson et al. (1978) by 634 cal mol⁻¹, 992 cal mol⁻¹, and 1.20 cal K⁻¹ mol⁻¹, respectively. Sverjensky et al. (1991) proposed also to adjust the free energies and enthalpies at 25 °C, 1 bar of all the K-bearing silicates by adding −236 cal mol⁻¹ to preserve the consistency with phase equilibria at high pressures and temperatures. In principle, the thermodynamic data of muscovite of Sverjensky et al. (1991) are probably more representative than those of Helgeson et al. (1978), but their adoption and the addition of −236 cal mol⁻¹ to the free energies and enthalpies at 25 °C, 1 bar of all the K-bearing silicates are not sufficient for maintaining the internal consistency of the thermodynamic database of Helgeson and coworkers unless a thorough revision is performed.

The suggestion of Sverjensky et al. (1991) was questioned by Holland and Powell (1998), who proposed the ΔG°_f, ΔH°_f, and S° values at 25 °C, 1 bar given in the third row of Table 4.3 which differ from those of Helgeson et al. (1978) by 3018 cal mol⁻¹, 2813 cal mol⁻¹, and 1 cal K⁻¹ mol⁻¹, respectively. Holland and Powell (2011) suggested the ΔG°_f and ΔH°_f at 25 °C, 1 bar listed in the fourth row of Table 4.3. These ΔG°_f and ΔH°_f are more similar to those of Helgeson et al. (1978) than the free energy and enthalpy proposed Holland and Powell (1998), with deviations of 1211 cal mol⁻¹ and 1024 cal mol⁻¹, respectively. Because of the remarkable differences in the thermodynamic data stored for muscovite in these different thermodynamic databases, it is meaningless to pick up the data from distinct databases because it would be like mixing apples and oranges.

As shown in Sect. 4.3.2, muscovite is the main component of white mica solid solutions, whereas pyrophyllite and celadonites play a subordinate role. Among the different components of white mica solid solutions, Helgeson et al. (1978) report the thermodynamic properties of muscovite and pyrophyllite (seventh row of Table 4.3) but not of celadonites.

Following the approach delineated in Sect. 2.2.1, it is advantageous to consider the white mica solid solution with average activity of muscovite, a_Ms = 0.654, and to compute the Gibbs free energy and the thermodynamic equilibrium constant of its dissolution reaction. The results obtained taking into account the muscovite thermodynamic data of Helgeson et al. (1978) are listed in Table 4.4 as a function of temperature together with the standard molal Gibbs free energies and the natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reaction of pure muscovite:

Table 4.4 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure muscovite and the white mica solid solution with average activity of muscovite as a function of temperature

$${\text{KAl}}_{3} {\text{Si}}_{3} {\text{O}}_{10} ({\text{OH}})_{2} + 10\;{\text{H}}^{ + } = {\text{K}}^{ + } + 3\;{\text{Al}}^{3 + } + 3\;{\text{SiO}}_{{2({\text{aq}})}} + 6\;{\text{H}}_{2} {\text{O}} .$$

(4.23)

4.4 Chlorites

4.4.1 Main Characteristics of Chlorites

The structure of chlorites consists in the regularly alternating (i) octahedral, brucite-like layers, also known as the hydroxide or O sheets, and (ii) tetrahedral-octahedral-tetrahedral, talc-like layers, also known as T–O–T or 2:1 sheets (e.g., Bailey 1988). Chlorites are, therefore, defined as T–O–T + O or 2:1 + 1 phyllosilicates.

Wiewiora and Weiss (1990) proposed a crystallochemical classification involving six octahedral positions and four tetrahedral positions, corresponding to half unit cell. The six octahedral sites are occupied by both (i) trivalent (and tetravalent) cations, such as Al³⁺, Fe³⁺, Cr³⁺, (and Ti⁴⁺), whose sum is indicated by R³⁺ and (ii) divalent cations, such as Mg²⁺, Fe²⁺, Mn²⁺, and Ni²⁺, whose sum is represented by R²⁺. Vacancies are indicated by the symbol □. The four tetrahedral sites are occupied by Si and Al. Therefore, the chemistry of chlorites is described by the general crystallochemical formula (from Wiewiora and Weiss 1990, modified by De Caritat et al. 1993):

$$({\text{R}}_{u}^{2 + } {\text{R}}_{y}^{3 + } {\square }_{\text{z}} )^{\text{VI}} ({\text{Si}}_{(4 - x)} {\text{Al}}_{x} )^{\text{IV}} {\text{O}}_{10 + w} ({\text{OH}})_{8 - w}$$

where u + y + z = 6, z = (y – x − w)/2, and w is usually zero or a small number. Octahedral occupancy is the sum of all cations in the octahedral sites and is given by Σ^VI = u + y. Based on the general crystallochemical formula of chlorites, the charge balance is expressed by the following relation:

$$2u + 3y - x - w - 12 = 0.$$

(4.24)

Foster (1962) compiled 150 chemical analyses of chlorites and found that: (i) Si^IV values range between 2.34 and 3.45 and 99% of these values are in the 2.40–3.40 interval, corresponding to 0.60 < x < 1.60; (ii) octahedral vacancies range from −0.05 to +0.55 but are usually in the 0.0 to +0.3 interval; (iii) all the data have charge balance within the range −0.05 to +0.05, with 94% of those data falling within the smaller interval −0.03 to +0.03. The last point implies that the charge balance assumption is reasonable for the chlorite structure.

4.4.2 Crystal Chemistry of Hydrothermal and Diagenetic Chlorites

Referring to the general crystallochemical formula of chlorites, the chemical composition of chlorites with Mg or Fe²⁺, Al, and □ in the octahedral positions is limited by the following four nodes:

• (1) u = 6, y = 0, z = 0, x = 0, corresponding to the stoichiometry of either serpentine, Mg₆Si₄O₁₀(OH)₈, or greenalite, ${\text{Fe}}_{6}^{2 + } {\text{Si}}_{4} {\text{O}}_{10} ({\text{OH}})_{8}$;

• (2) u = 4, y = 2, z = 0, x = 2, which is consistent with the formulae of either amesite, (Mg₄Al₂)(Si₂Al₂)O₁₀(OH)₈, or Fe²⁺-amesite, $\left( {{\text{Fe}}_{4}^{2 + } {\text{Al}}_{2} } \right)\left( {{\text{Si}}_{2} {\text{Al}}_{2} } \right){\text{O}}_{10} ({\text{OH}})_{8}$;

• (3) u = 0, y = 4.67, z = 1.33, x = 2 or (Al_4.67□_1.33)(Si₂Al₂)O₁₀(OH)₈; this composition exceptionally rich in Al has no equivalent among the chlorites found in nature.

• (4) u = 0, y = 4, z = 2, x = 0 or (Al₄□₂)Si₄O₁₀(OH)₈; this chemical composition is relatively similar to that of some natural dioctahedral chlorites.

These four nodes and some intermediate compositions are shown in the chlorite classification diagram of Wiewiora and Weiss (1990) of Fig. 4.9, in which octahedral R²⁺ and tetrahedral Si are reported on the abscissa and ordinate axes, respectively, whereas octahedral Al and vacancies are represented in the grid. Both 181 chemical analyses of hydrothermal chlorites from different active geothermal systems and 54 chemical analyses of diagenetic chlorites are shown in this plot.

Fig. 4.9

Projection of chlorite structural formulae in the plot of tetrahedral Si versus the sum of octahedral divalent cations, R²⁺, both expressed in atoms per half unit cell (from Wiewióra and Weiss 1990). Names of Mg-bearing chlorites are in blue whereas names of Fe²⁺-bearing chlorites are in red. Structural formulae refer to 181 hydrothermal chlorites from different geothermal systems (see legend) and 54 diagenetic chlorites occurring in deeply buried sandstones from the Gulf Coast and the Norwegian Continental Shelf (see legend)

Chlorites, especially those from low-temperature environments, are often interstratified with smectite, vermiculite, saponite, and/or illite. Since the resolution of the scanning electron microscope is insufficient to establish the possible presence of these minerals in the analyzed chlorites, the chemical analyses with (CaO + Na₂O + K₂O) > 0.5 wt% were rejected. This procedure was adopted by previous authors (e.g., Foster 1962), based on the assumption that these elements are not hosted in the chlorite lattice.

The considered diagenetic chlorites were obtained from deeply buried sandstones of both (i) the Gulf Coast area, Texas, where pressure is in the 300–1200 bar interval and temperature is in the 102–232 °C range (Bourdelle et al. 2013) and (ii) the Norwegian Continental Shelf at depths of 2393–4967 m, where temperature varies from 90 to 180 °C (Jahren and Aagaard 1992).

The considered hydrothermal chlorites were sampled from the following active geothermal systems: Newberry Caldera, Oregon, at 287 °C (Keith and Bargar 1988); Roosevelt Hot Springs, Utah, in the temperature range 228–253 °C (Ballantyne 1978; Capuano and Cole 1982); Salton Sea, California, in the temperature interval 190–322 °C (McDowell and Elders 1980, 1983); Los Azufres, Mexico, for temperatures ranging from 210 to 310 °C (Cathelineau and Nieva 1985; Cathelineau 1988); Los Humeros, Mexico, for temperatures varying from 145 to 315 °C (Martinez-Serrano and Dubois 1998; Martinez-Serrano 2002); Bouillante, Guadeloupe, in the temperature range 182–260 °C (Mas et al. 2006); Reykjanes, Iceland, in the temperature interval 170–331 °C (Libbey and Williams-Jones 2016); Aluto-Langano, Ethiopia, for temperatures ranging from 180 to 300 °C (Teklemariam et al. 1996); Tendaho, Ethiopia, for temperatures varying from 165 to 270 °C (Gianelli et al. 1998); Larderello, Italy, in the temperature range 248–315 °C (Boyce et al. 2003); Pantelleria, Italy, at 256 °C (Fulignati et al. 1997); Broadlands-Ohaaki, New Zealand, in the temperature interval 267–300 °C (Lonker et al. 1990); Waiotapu, New Zealand, at temperatures of 285–290 °C (Hedenquist and Browne 1989); Toyoha, Japan, for temperatures varying from 209 to 298 °C (Inoue et al. 2010).

All these literature data were compiled and their structural formulae were calculated on the basis of 10 oxygen atoms and 8 hydroxyl groups for a total of 28 negative charge units. Iron was distributed between Fe²⁺ and Fe³⁺ assuming that negative charges are balanced by the same number of positive charges, which is a reasonable hypothesis (see above). In this way, Fe²⁺ resulted to range between 1.08 and 4.33 atoms per half unit cell, whereas Fe³⁺ turned out to be strongly subordinated, with a maximum value of 0.39.

The diagram of Fig. 4.9 shows that:

• (a) 90% of the hydrothermal chlorites have tetrahedral Si values ranging from 2.7 and 3.2, R²⁺ varying between 4.4 and 4.9, octahedral Al oscillating from 1.0 to 1.6, and octahedral occupancy of 5.8–6.0;

• (b) the diagenetic chlorites have Si^IV values generally varying from 2.7 and 3.2, which compares with the range of the hydrothermal chlorites, but other parameters are different, with R²⁺ usually oscillating between 3.8 and 4.4, octahedral Al generally ranging from 1.5 to 1.8 and octahedral occupancy of 5.5–5.8.

These differences between the diagenetic and hydrothermal chlorites considered here (apart from the similarity in tetrahedral Si values) were already underscored by previous authors (e.g., De Caritat et al. 1993 and references therein).

In the diagram of Fig. 4.9, the Mg-bearing chlorites (whose names are in blue) cannot be distinguished from the Fe²⁺-bearing chlorites (whose names are in red) having the same R²⁺ value. This distinction is conveniently performed by means of the plot of Fig. 4.10, in which the Fe²⁺/(Fe²⁺ + Mg) ratio is contrasted with the octahedral Al value.

Fig. 4.10

Diagram of the Fe²⁺/(Fe²⁺ + Mg) atomic ratio versus the octahedral Al value, in atoms per half unit cell for 181 hydrothermal chlorites from different geothermal systems (see legend) and 54 diagenetic chlorites occurring in deeply buried sandstones from the Gulf Coast and the Norwegian Continental Shelf (see legend). Names of Mg-bearing chlorites are in blue whereas names of Fe²⁺-bearing chlorites are in red

This diagram highlights that:

• (i) The diagenetic chlorites are richer in ferrous iron, with the Fe²⁺/(Fe²⁺ + Mg) ratio ranging from 0.47 to 0.91 and can be considered mixtures of Fe²⁺-amesite, amesite, and sheridanite, with the ferrous endmember generally prevailing over the magnesian components.

• (ii) The hydrothermal chlorites have highly variable Fe²⁺/(Fe²⁺ + Mg) ratio, from 0.23 to 0.94, that is from Fe²⁺-rich compositions, close to ripidolite, to Mg-rich compositions, relatively similar to clinochlore or sheridanite.

Considering separately each geothermal system which is represented by at least 4 chlorite samples (N ≥ 4), usually the Fe²⁺/(Fe²⁺ + Mg) ratio distributes in a relatively small range, in the order of 0.21–0.30 units, as is the case of Tendaho (range = 0.21, N = 6), Roosevelt (range = 0.22, N = 29), Reykjanes (range = 0.23, N = 61), Larderello (range = 0.26, N = 15), Los Humeros (range = 0.29, N = 11), and Salton Sea (range = 0.30, N = 12). The 9 chlorite samples from Los Azufres span an even smaller Fe²⁺/(Fe²⁺ + Mg) range, of 0.09 units only, whereas a relatively large Fe²⁺/(Fe²⁺ + Mg) range characterizes the chlorites from Broadlands (range = 0.47, N = 9), Bouillante (range = 0.49, N = 15), Aluto-Langano (range = 0.56, N = 6), and Toyoha (range = 0.60, N = 4).

The relatively small Fe²⁺/(Fe²⁺ + Mg) range of most geothermal systems suggests that they are hosted in rocks of relatively uniform mineralogical and chemical composition. In particular, the hydrothermal chlorites from geothermal systems hosted in silica-rich rocks, such as granite at Larderello (Boyce et al. 2003), have Fe²⁺-rich compositions, whereas the hydrothermal chlorites from geothermal systems associated to silica-poor rocks, such as basalt at Reykjanes (Libbey and Williams-Jones 2016) have Mg-rich compositions.

In contrast, the relatively large Fe²⁺/(Fe²⁺ + Mg) range of Broadlands, Bouillante, Aluto-Langano, and Toyoha calls for either (i) the occurrence of rocks of different mineralogical and chemical composition, for instance basalts and silicic ignimbrites at Aluto-Langano (Teklemariam et al. 1996) or (ii) the local presence of mineralized zones bearing sulfide minerals, as is the case of Broadlands (Weissberg et al. 1979) and Toyoha (Inoue et al. 2010), or (iii) the occurrence of successive alteration stages during the thermal history of the geothermal system, as is the case of Bouillante (Mas et al. 2006).

These findings agree with what was recognized long ago by Albee (1962), who pointed out that chlorite chemistry depends upon the composition of both the rock and the minerals associated with it. This matter was thoroughly discussed by De Caritat et al. (1993).

Also fluids can control to some extents the composition of chlorites. For instance, the Mg-rich chlorites of Reykjanes and Bouillante might be due to the inflow of Mg-rich seawater into these geothermal systems, as suggested by Arnórsson for Reykjanes and Sanjuan et al. (2001) for Bouillante.

4.4.3 The Activities of Clinochlore and Chamosite in Hydrothermal and Diagenetic Chlorites

Following Helgeson et al. (1978), Aagaard and Helgeson (1983), Helgeson and Aagaard (1985), and Aagaard and Jahren (1992), the activity of clinochlore, a_Clc, and the activity of chamosite, a_Chm, in the chlorite solid solutions of interest were calculated by means of the following relations:

$$a_{\text{Clc}} = {\text{k}}_{\text{Clc}} \cdot {\text{X}}_{\text{Mg,O}}^{5} \cdot {\text{X}}{}_{\text{Al,O}} \cdot {\text{X}}_{\text{Al,T}} \cdot {\text{X}}_{\text{Si,T}}^{3}$$

(4.25)

$$a_{\text{Chm}} = {\text{k}}_{\text{Chm}} \cdot {\text{X}}_{{{\text{Fe}}^{2 + } ,{\text{O}}}}^{5} \cdot {\text{X}}{}_{\text{Al,O}} \cdot {\text{X}}_{\text{Al,T}} \cdot {\text{X}}_{\text{Si,T}}^{3}$$

(4.26)

which are based on the hypothesis of random mixing of atoms on energetically equivalent sites. In Eqs. (4.25) and (4.26):

k_Clc = k_Chm = 141.55776 are constants relating the inter- and intra-crystalline standard states;

${\text{X}}_{\text{Mg,O}}$, ${\text{X}}_{{{\text{Fe}}^{2 + } , {\text{O}}}}$, and ${\text{X}}_{{{\text{Al}},{\text{O}}}}$ are the mole fractions of magnesium, divalent iron, and aluminum, on the octahedral sites;

X_Al,T and X_Si,T are the mole fractions of aluminum and silicon on the tetrahedral sites.

The selected 181 hydrothermal chlorites have:

• (i) activity of the clinochlore endmember varying from 4.39 × 10⁻⁷ to 0.250, with an average of 0.0553, a median of 0.0451 and a standard deviation of 0.0484, and

• (ii) activity of the chamosite endmember ranging from 6.77 × 10⁻⁴ to 0.589, with an average of 0.0480, a median of 0.0173 and a standard deviation of 0.0794.

The 54 diagenetic chlorites considered in this work have:

• (i) activity of the clinochlore endmember ranging from 4.04 × 10⁻⁶ to 0.0333, with an average of 0.00513, a median of 0.00216 and a standard deviation of 0.00832, and

• (ii) activity of the chamosite endmember varying from 0.0194 to 0.539, with an average of 0.135, a median of 0.0875 and a standard deviation of 0.110.

As shown in the diagram of Fig. 4.11a, the activities of both endmembers in the considered chlorite solid solutions are linked by a hyperbolic relationship, which reflects the tight inverse correlation between ${\text{X}}_{{{\text{Mg}},{\text{O}}}}$ and ${\text{X}}_{{{\text{Fe}}^{2 + } ,{\text{O}}}}$ (Fig. 4.11b; R-squared = 0.891, N = 235).

Fig. 4.11

Plots of a the activity of clinochlore, a_Clc, versus the activity of chamosite, a_Chm, and b the mole fraction of octahedral Fe²⁺ versus the mole fraction of octahedral Mg for 181 hydrothermal chlorites from different geothermal systems (see legend) and 54 diagenetic chlorites occurring in deeply buried sandstones from the Gulf Coast and the Norwegian Continental Shelf (see legend)

The activities of both clinochlore and chamosite are poorly correlated with the temperature measured at the depth of provenance of the chlorite samples, as shown by the squared linear regression coefficients of the pairs a_Clc–temperature and a_Chm–temperature for the entire dataset as well as for each geothermal system which is represented by at least 4 chlorite samples (Table 4.5). The only exception is the Toyoha geothermal field, but the relatively high R² values are probably fortuitous, also taking into account the low number of available samples.

Table 4.5 Squared linear regression coefficients of the pairs a_Clc–temperature and a_Chm–temperature for the entire chlorite dataset as well as for each geothermal system which is represented by at least 4 chlorite samples

The lack of correlation between temperature and the activities of both clinochlore and chamosite in the chlorite solid solution is not surprising considering that, according to De Caritat et al. (1993) and other authors, there is a lack of confidence in applying the chlorite geothermometers which have been designed by several workers to obtain indications of palaeo-temperature from chlorite composition and structure.

4.4.4 The Thermodynamic Properties of Chlorites

The only minerals of the chlorite group considered by Helgeson et al. (1978) are 7Å-clinochlore and 14Å-clinochlore, both of stoichiometry Mg₅Al₂Si₃O₁₀(OH)₈. The clinochlore with 7Å basal spacing is metastable with respect to its 14Å counterpart at all temperatures and pressure. According to Helgeson et al. (1978), the reason for this is probably the relatively high activation energy required for the conversion of 7Å-clinochlore to the 14Å variety. This hypothesis could explain the persistence of 7Å-clinochlore in weathering profiles, sedimentary environments, hydrothermal alteration zones, and laboratory experiments at temperatures lower than 400–500 °C. Accepting this explanation, 7Å-clinochlore is the clinochlore variety of interest for this work.

As shown by Table 4.6, the thermodynamic data of seven chlorite minerals are listed by both Holland and Powell (1998) and Holland and Powell (2011), namely Ordered Clinochlore [Mg₅Al₂Si₃O₁₀(OH)₈], Al-free chlorite [Mg₆Si₄O₁₀(OH)₈], 14Å-Amesite [Mg₄Al₄Si₂O₁₀(OH)₈], Daphnite [Fe₅Al₂Si₃O₁₀(OH)₈], Mn-chlorite [Mn₅Al₂Si₃O₁₀(OH)₈], Sudoite [Mg₂Al₄Si₃O₁₀(OH)₈], and Fe-Sudoite [Fe₂Al₄Si₃O₁₀(OH)₈]. Incidentally, the term chamosite should be used instead of daphnite, for consistency with the chlorite classification of Wiewiora and Weiss (1990).

Table 4.6 Standard state molal thermodynamic properties, at 25 °C, 1 bar, of different chlorite minerals from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011)

Since the 14Å basal spacing is specified only for amesite, we assume that all the other compositions have 7Å basal spacing. If so, the ΔG°_f and ΔH°_f values reported by Holland and Powell (1998) for clinochlore differ from those of Helgeson et al. (1978) by 17887 cal mol⁻¹ and 21091 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f values given by Holland and Powell (2011) deviate from those of Helgeson et al. (1978) by 14845 cal mol⁻¹ and 16160 cal mol⁻¹, respectively. Moreover, for the same mineral, there are differences from 1404 to 6298 cal mol⁻¹ in ΔG°_f and from 1781 to 8910 cal mol⁻¹ in ΔH°_f between the database of Holland and Powell (1998) and that of Holland and Powell (2011). Again, due to these considerable differences in the thermodynamic data stored for clinochlore in the different thermodynamic databases, it is not possible to put together the data from distinct databases because it would be equivalent to mix apples and oranges.

Following the approach outlined in Sect. 2.2.1, it is advisable to consider the chlorite solid solution with average activity of clinochlore, a_Clc = 0.0553, and to compute the Gibbs free energy and the thermodynamic equilibrium constant of its dissolution reaction. The results obtained considering the 7Å-clinochlore thermodynamic data of Helgeson et al. (1978) are listed in Table 4.7 as a function of temperature together with the standard molal Gibbs free energies and the natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reaction of pure 7Å-clinochlore:

Table 4.7 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure 7Å-clinochlore and the chlorite solid solution with average activity of clinochlore as a function of temperature

$${\text{Mg}}_{5} {\text{Al}}_{2} {\text{Si}}_{3} {\text{O}}_{10} ({\text{OH}})_{8} + 16\;{\text{H}}^{ + } = 5\;{\text{Mg}}^{2 + } + 2\;{\text{Al}}^{3 + } + 3\;{\text{SiO}}_{{2({\text{aq}})}} + 12\;{\text{H}}_{2} {\text{O}}$$

(4.27)

4.5 Epidotes

4.5.1 Main Characteristics and Nomenclature of the Minerals of the Epidote Group

The following notes on the nomenclature and main features of the minerals of the epidote group are largely based on the review paper of Franz and Liebscher (2004). The minerals of the epidote group are monoclinic sorosilicates with the general formula A₂M₃[Si₂O₇][SiO₄]O(OH) indicating the presence of both SiO₄ tetrahedra and Si₂O₇ groups, as well as the M cations in six-fold octahedral coordination and the A cations in eight-fold coordination (further details in the next section). Orthorhombic zoisite is a polymorph of clinozoisite and is structurally very similar to the monoclinic minerals of the epidote group.

According to the Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association (IMA) on the nomenclature of epidote minerals:

• (i) The term epidote refers to the mineral, the whole mineral group and the composition Ca₂(Al₂Fe³⁺)[Si₂O₇][SiO₄]O(OH). To avoid confusion, the terms epidote and epidote component (or endmember) are used in this book to indicate the mineral/mineral group and the solid solution component (endmember), respectively.

• (ii) The name clinozoisite identifies the stoichiometry Ca₂Al₃[Si₂O₇][SiO₄]O(OH).

• (iii) The term piemontite refers to the composition Ca₂(Al₂Mn³⁺)[Si₂O₇][SiO₄]O(OH).

• (iv) The name mukhinite identifies the stoichiometry Ca₂(Al₂V³⁺)[Si₂O₇][SiO₄]O(OH).

• (v) The terms allanite-Ce, allanite-La, allanite-Nd, and allanite-Y refer to the composition [Ca(REE)](Al₂Fe²⁺)[Si₂O₇][SiO₄]O(OH), in which REE = Ce, La, Nd, and Y, respectively.

The name tawmawite was used for the Cr³⁺ endmember, Ca₂(Al₂Cr³⁺)[Si₂O₇][SiO₄]O(OH), but is not approved by IMA. Also the term pistacite, which was utilized to describe either Fe³⁺-rich epidotes of stoichiometry close to Ca₂(Al₂Fe³⁺)[Si₂O₇][SiO₄]O(OH) or the hypothetical endmember ${\text{Ca}}_{2} {\text{Fe}}_{3}^{3 + } \left[ {{\text{Si}}_{2} {\text{O}}_{7} } \right]\left[ {{\text{SiO}}_{4} } \right]{\text{O}}({\text{OH}})$ should generally be avoided.

Most monoclinic epidote minerals occurring in geological systems belong to the clinozoisite-epidote solid solution series with epidote mole fractions, X_Ep, usually lower than 0.4, whereas compositions with X_Ep as high as 0.4–0.5 were rarely found. Natural binary solid solutions along the clinozoisite-piemontite join are uncommon because most samples also contain Fe³⁺. In addition, the octahedral M sites can be rarely occupied by Cr³⁺ and V³⁺, whereas the concentration of the divalent cations Fe²⁺, Mn²⁺, and Mg²⁺ on these sites is usually very low. The A sites generally house Ca²⁺, which can be substituted by Sr²⁺, Ba²⁺, Pb²⁺, and REE³⁺. Allanite minerals exhibit larger and more complex compositional variations, according to the formula [(Ca,Ce,La,Y)₂(Al,Fe³⁺,Fe²⁺,Mn²⁺)₃[Si₂O₇][SiO₄]O(OH)].

Orthorhombic zoisite exhibits composition closer to the endmember stoichiometry Ca₂Al₃Si₃O₁₂(OH) than the monoclinic minerals of the epidote group. Similar to what occurs in monoclinic epidotes, Fe³⁺, Mn³⁺, Cr³⁺, and V³⁺ substitute for Al³⁺ in the octahedral M sites (although the mole fraction of Fe³⁺ is usually ≤0.15), whereas Sr²⁺ and Pb²⁺ substitute for Ca²⁺ in the A sites of zoisite.

Usually, hydrothermal epidote from active geothermal systems shows a wide interval in octahedral substitution of Al³⁺ for Fe³⁺, with important oscillatory or irregular compositional zoning. These variable characteristics of hydrothermal epidote are due to the variations, in time and space, of temperature, permeability, and fluid parameters such as flux, pH, CO₂ partial pressure, redox potential, and the aqueous speciation of Al and Fe (Bird and Spieler 2004).

4.5.2 The Crystal Chemistry of Epidote Solid Solutions

This section is mainly focused on the equilibrium mixing model of Bird and Helgeson (1980) and, therefore, it is largely derived from their article. Epidote solid solutions can be represented by the following crystallochemical formula:

$${\text{A}}_{2}^{\rm{VIII}} {\text{M}}(1)^{\rm{VI}} \;{\text{M}}(2)^{\rm{VI}} \;{\text{M}}(3)^{\rm{VI}} {\text{T}}_{3}^{\rm{IV}} {\text{O}}_{12} ({\text{OH}}),$$

in which:

• A^VIII refers to the two large eight-fold coordinated sites, which are predominantly occupied by Ca²⁺ ions;

• ${\text{M}}(1)^{\text{VI}} ,\;{\text{M}}(2)^{\text{VI}} ,\;{\text{and}}\;{\text{M}}(3)^{\text{VI}}$ indicate the three six-fold coordinated octahedral sites, which are energetically different and are occupied by Al³⁺ and Fe³⁺ ions;

• T stands for the three tetrahedral sites, which are almost completely occupied by Si⁴⁺ ions.

Crystal structure site refinements and Mössbauer spectral data indicate that the Fe³⁺ ions are mainly housed by the largest and most distorted ${\text{M}}(3)^{\text{VI}}$ octahedral sites, although minor quantities of Fe³⁺ occur also in the ${\text{M}}(1)^{\text{VI}}$ sites. In contrast, the ${\text{M}}(2)^{\text{VI}}$ sites contain only Al³⁺ ions. According to Bird and Helgeson (1980), Fe³⁺ ions are only present in the M(3) octahedral sites if epidote is completely ordered, whereas octahedral disordering of epidote can be represented by the following reaction:

$$\begin{aligned} {\text{Ca}}_{2} {\text{Al}}_{{{\rm{M}}(1)}} {\text{Al}}_{\rm{M(2)}} {\text{Fe}}_{\rm{M(3)}} {\text{Si}}_{3} {\text{O}}_{12} ({\text{OH}}) & \to {\text{Ca}}_{2} ({\text{Al}}{}_{{1 - {\text{x}}}}{\text{Fe}}_{\rm{x}} )_{{{\rm{M}}(1)}} {\text{Al}}_{\rm{M(2)}} ({\text{Al}}{}_{\rm{x}}{\text{Fe}}_{{1 - {\text{x}}}} )_{{{\rm{M}}(3)}} \\ & \quad \quad \quad {\text{Si}}_{3} {\text{O}}_{12} ({\text{OH}}) \end{aligned}$$

where x represents the mole fraction of Fe³⁺ ion on the M(1) sites. Bird and Helgeson (1980) defined an ordering parameter for epidote, σ = 1 − 2x, which assumes the value 1 if the mineral is fully ordered and becomes equal to 0 if it is entirely disordered. The intracrystalline exchange reaction of Al³⁺ and Fe³⁺ ions among the M(1) and M(3) sites:

$${\text{Fe}}_{{{\text{M}}(3)}}^{3 + } + {\text{Al}}_{{{\text{M}}(1)}}^{3 + } \leftrightarrow {\text{Fe}}_{{{\text{M}}(1)}}^{3 + } + {\text{Al}}_{{{\text{M}}(3)}}^{3 + }$$

(4.28)

is regulated by the intracrystalline standard state equilibrium constant:

$$\text{K} = \frac{{a_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} \cdot a_{{{\text{Al}}_{{{\text{M}}(3)}}^{3 + } }} }}{{a_{{{\text{Fe}}_{{{\text{M}}(3)}}^{3 + } }} \cdot a_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }} }},$$

(4.29)

which is a temperature function as expressed by the relation:

$$\log \;{\text{K}} = - 1523.4 \cdot \left( {\frac{1}{\text{T}} - \frac{1}{\text{Tr}}} \right) - 5.0,$$

(4.30)

with Tr = 298.15. Assuming that the ratios between the activity coefficients of Al³⁺ and Fe³⁺ ions on the M(1) and M(3) sites are equal to 1, it follows that the ordering parameter σ is related to K by the relation:

$$\text{arctanh} \;\upsigma = - (\ln \;{\text{K}})/4.$$

(4.31)

Therefore, it is possible to compute σ, knowing or assuming a suitable temperature value. Following Bird and Helgeson (1980), the next step is the calculation of the mole fraction of Fe³⁺ ions on the M(3) sites using the relation:

$$\begin{aligned} {\text{X}}_{{{\text{Fe}}_{{{\text{M}}(3)}}^{3 + } }} & = - \left[ {\frac{{{\text{X}}_{\text{Ep}} }}{{{\text{K}} - 1}} + \left( {\frac{{{\text{K}} \cdot (1 - {\text{X}}_{\text{Ep}} ) + {\text{X}}_{\text{Ep}} + 1}}{{2 \cdot ({\text{K}} - 1)}}} \right)^{2} } \right]^{0.5} \\ & \quad - \frac{{{\text{K}} \cdot (1 - {\text{X}}_{\text{Ep}} ) + {\text{X}}_{\text{Ep}} + 1}}{{2 \cdot ({\text{K}} - 1)}} \end{aligned}$$

(4.32)

which is written in a simplified form, that is assuming absence of ions other than Al³⁺ and Fe³⁺ on the M(3) sites. Then, the mole fractions of Fe³⁺ and Al³⁺ ions on the M(1) sites and the mole fraction of Al³⁺ ions on the M(3) sites are computed by means of the equations:

$${\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} = {\text{X}}_{\text{Ep}} - {\text{X}}_{{{\text{Fe}}_{{{\text{M}}(3)}}^{3 + } }}$$

(4.33)

$${\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }} = 1 - {\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }}$$

(4.34)

$${\text{X}}_{{{\text{Al}}_{{{\text{M}}(3)}}^{3 + } }} = 2 - {\text{X}}_{\text{Ep}} - {\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }}.$$

(4.35)

The mole fractions computed by means of Eqs. (4.32) through (4.35) are then used to calculate the activities of the clinozoisite and epidote endmembers based on the hypothesis of random mixing of atoms on energetically equivalent sites (Helgeson et al. 1978; Bird and Helgeson 1980; Bird and Norton 1981; Helgeson and Aagaard 1985):

$$a_{\text{Czo}} = {\text{X}}_{{{\text{Ca}}_{\text{A}}^{2 + } }}^{2} \cdot {\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }} \cdot {\text{X}}_{{{\text{Al}}_{{{\text{M}}(3)}}^{3 + } }} \cdot {\text{X}}_{{{\text{Si}}_{\text{T}}^{4 + } }}^{3}$$

(4.36)

$$a_{\text{Ep}} = {\text{k}}_{\text{Ep}} \cdot {\text{X}}_{{{\text{Ca}}_{\text{A}}^{2 + } }}^{2} \cdot \left( {{\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }} \cdot {\text{X}}_{{{\text{Fe}}_{{{\text{M(}}3)}}^{3 + } }} } \right)^{{\frac{{1 +\upsigma}}{2}}} \cdot \left( {{\text{X}}_{{{\text{Al}}_{{{\text{M(}}3)}}^{3 + } }} \cdot {\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} } \right)^{{\frac{{1 -\upsigma}}{2}}} \cdot {\text{X}}_{{{\text{Si}}_{\text{T}}^{4 + } }}^{3}$$

(4.37)

where k_Ep is the constant relating the inter- and intra-crystalline standard states, which is given by:

$${\text{k}}_{\text{Ep}} = \left( {\frac{{1 +\upsigma}}{2}} \right)^{{ - (1 +\upsigma)}} \cdot \left( {\frac{{1 -\upsigma}}{2}} \right)^{{ - (1 -\upsigma)}} .$$

(4.38)

The equilibrium model of Bird and Helgeson (1980) for partitioning of Al³⁺ and Fe³⁺ ions among the M(1) and M(3) sites in epidote was based on the data available at that time. In subsequent researches, the order-disorder degree was found either higher than theoretically predicted by the equilibrium model or in good agreement with model’s predictions or lower than theoretically predicted by the model (Franz and Liebscher 2004). In spite of possible limitations, the model of Bird and Helgeson (1980) is used in the next section, first, to calculate the equilibrium distribution of Al³⁺ and Fe³⁺ ions among the M(1) and M(3) sites in epidote solid solutions coming from active geothermal systems, starting from the analytical data, and second, to compute the activities of the epidote and clinozoisite components of the epidote solid solutions of interest.

4.5.3 The Activities of Clinozoisite and Epidote Endmembers in Hydrothermal Epidote Solid Solutions

A total of 436 chemical analyses of epidote solid solutions collected in deep geothermal wells at variable depths and temperatures were compiled. Most samples, for a total of 259, come from the geothermal system of Reykjanes, Iceland, at temperatures of 176–345 °C (mainly from Libbey and William-Jones 2016 and subordinately from Fowler et al. 2015 and Ottolini et al. 2012). Of the remaining 177 chemical analyses, 57 are from Larderello, Italy, at temperatures of 250–368 °C (Cavarretta et al. 1980, 1982), 40 are from Milos, Greece, at temperatures of 305–323 °C (Liakopoulos 1987), 23 are from Salton Sea, California, at temperatures of 250–353 °C (Keith et al. 1968; Bird et al. 1988; Cho et al. 1988; Shearer et al. 1988), 14 are from Los Humeros, Mexico, at temperatures of 235–350 °C (Martinez-Serrano 2002), 9 are from Waiotapu, New Zealand, at temperatures of 220–285 °C (Hedenquist and Browne 1989), 8 are from Cerro Prieto, Mexico, at temperatures of 325–350 °C (Schiffman et al. 1985), 8 are from Kakkonda, Japan, at temperatures of 225–285 °C (Muramatsu and Doi 2000; Sawaki et al. 2001), 8 are from Onikobe, Japan, at temperatures of 125–173 °C (Seki et al. 1983), 4 are from Broadlands, New Zealand, at temperatures of 260–300 °C (Lonker et al. 1990), 2 are from Hachimantai, Japan, at temperatures of 200–230 °C (Shimazu and Yajima 1973), 2 are from Newberry Caldera, Oregon, at temperature of 260 °C (Keith and Bargar 1988), and 2 are from Miravalles, Costa Rica, at temperature of 240 °C (Milodowski et al. 1989).

Clinozoisite is the main component of these hydrothermal epidote solid solutions, with mole fraction varying between 0.527 and 0.893, both average and median equal to 0.728, and standard deviation of 0.061. Being the complement to 1 of the clinozoisite mole fraction, the epidote component mole fraction ranges from 0.107 to 0.463, both average and median are equal to 0.272, and standard deviation is the same of clinozoisite, 0.061. Consequently, available data are positioned along a line of slope-1 in the correlation plot of the clinozoisite mole fraction versus the epidote component mole fraction (Fig. 4.12a). The composition of the considered hydrothermal epidote solid solutions compares with that of most monoclinic epidote minerals occurring in different geological systems.

Fig. 4.12

Plots of a the clinozoisite mole fraction versus the epidote component mole fraction and b the activity of clinozoisite versus the activity of the epidote component for 436 hydrothermal epidote solid solutions from different geothermal systems (see legend)

The activity of clinozoisite varies between 0.523 and 0.888, with a mean of 0.703, a median of 0.706, and a standard deviation of 0.057, whereas the activity of the epidote component ranges from 0.115 to 0.495, with an average of 0.288, a median of 0.287 and a standard deviation of 0.066. Also in the correlation diagram of the activity of clinozoisite versus the activity of the epidote component (Fig. 4.12b), sample points are distributed along a line of slope-1, because activities of both clinozoisite and epidote endmembers are not very different from the corresponding mole fractions. Nevertheless, in Fig. 4.12b there is a considerable scatter, which is evidently due to varying deviations from ideality.

Such deviations are described by the activity coefficients of both clinozoisite and epidote endmembers which were computed by means of Eq. (2.3) solved with respect to λ. Interestingly, the activity coefficient of clinozoisite is usually <1, with minimum of 0.763 and maximum of 1.001, whereas the activity coefficient of epidote is generally >1, up to a maximum of 1.129, even though its minimum value is 0.839 (Fig. 4.13a). However, average and median are close to unity, being 0.966 and 0.973, respectively, for clinozoisite and 1.060 and 1.066, respectively, for the epidote component. The standard deviation is small in both case, with 0.028 for clinozoisite and 0.035 for the epidote component.

Fig. 4.13

Plots of a the activity coefficient of clinozoisite versus the activity coefficient of the epidote component and b the ordering parameter σ versus the measured temperature, for 436 hydrothermal epidote solid solutions from different geothermal systems (see legend)

These deviations from ideality are ascribable to the varying degree of substitutional order/disorder which is a temperature function, as defined by Eq. (4.30) and shown in Fig. 4.13b, according to the equilibrium model of Bird and Helgeson (1980).

The temperature measured at the depth of collection of hydrothermal epidote was considered in calculations, although observed mineral alteration may have formed under thermal conditions different from contemporary temperatures. In addition, Arnórsson (1995) noted that the number of hydrothermal minerals reported in a single drill hole sample is commonly greater than permitted by consideration of the phase rule, indicating that secondary mineral assemblages may form over a range of temperatures and fluid compositions, and that metastable phase relations are not uncommon.

The hydrothermal epidote samples appear to be relatively ordered, as indicated by the range of the ordering parameter σ, from 0.863 to 0.973, with a mean of 0.905, a median of 0.904, and a standard deviation of 0.018. However, deviations from the equilibrium distribution predicted by the model of Bird and Helgeson (1980) are possible, due to occurrence of metastable states of substitutional order/disorder on the octahedral sites. For instance, this condition was ascertained by means of ⁵⁷Fe Mössbauer spectroscopy for four epidote samples from the State 2–14 drill hole, Salton Sea (Bird et al. 1988) and for the epidotes from the fossil geothermal system of Saint Martin (Patrier et al. 1991), see also Liebscher (2004).

4.5.4 The Thermodynamic Properties of Epidotes

The thermodynamic properties of four minerals of the epidote group are reported by Helgeson et al. (1978), namely clinozoisite and zoisite, both of chemical formula Ca₂Al₃Si₃O₁₂(OH), as well as epidote (which refers to the stable state of substitutional order/disorder at any pressure and temperature) and ordered epidote, both of stoichiometry Ca₂FeAl₂Si₃O₁₂(OH). Holland and Powell (1998) estimated the thermodynamic properties of four minerals of the epidote group, again clinozoisite and zoisite, both of chemical formula Ca₂Al₃Si₃O₁₂(OH), and ordered epidote of stoichiometry Ca₂FeAl₂Si₃O₁₂(OH), as well as a solid phase richer in Fe³⁺, called Fe-epidote, of chemical composition Ca₂Fe₂AlSi₃O₁₂(OH). Monoclinic epidote minerals were treated as regular solid solutions of clinozoisite, ordered epidote, and Fe-epidote extending the model of Bird and Helgeson (1980) through incorporation of non-ideal mixing. Holland and Powell (2011) revised the thermodynamic properties of the four minerals of the epidote group considered by Holland and Powell (1998) and estimated also the thermodynamic properties of ordered piemontite, of chemical formula Ca₂MnAl₂Si₃O₁₂(OH). All these data are reported in Table 4.8.

Table 4.8 Standard state molal thermodynamic properties, at 25 °C, 1 bar, of different epidote minerals from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011)

The ΔG°_f and ΔH°_f reported by Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 4570 and 4467 cal mol⁻¹ for clinozoisite, 951 and 286 cal mol⁻¹ for ordered epidote, and 4456 and 4667 cal mol⁻¹ for zoisite. The ΔG°_f and ΔH°_f listed by Holland and Powell (2011) differ from those of Helgeson et al. (1978) by 3927 and 3824 cal mol⁻¹ for clinozoisite, 2582 and 2843 cal mol⁻¹ for ordered epidote, and 3963 and 4103 cal mol⁻¹ for zoisite. Besides, for the same mineral, there are differences from 493 to 4071 cal mol⁻¹ in ΔG°_f and from 564 to 6066 cal mol⁻¹ in ΔH°_f between the database of Holland and Powell (1998) and that of Holland and Powell (2011).

A very detailed analysis of the thermodynamic properties of zoisite, orthoepidote, clinozoisite, and epidote was performed by Gottschalk (2004), who examined inter alias the experimental measurements carried out by several authors, as well as the values reported in internally consistent datasets, underscoring the discrepancies between different sources and the missing pieces of information.

Finally, the recommended values of the thermodynamic parameters are listed by Gottschalk (2004), but no supporting motivation is given. The concluding statement of Gottschalk (2004) “However, the specific choice of a value might be somewhat subjective and reflects the opinion of the author” might seem disappointing at the end of such a thorough review. However, it is a further example of the impossibility to select reliable values of thermodynamic properties by focusing the attention on a single group of minerals only. A much wider analysis is needed to establish the internal consistency of the whole thermodynamic database.

Adopting the approach described in Sect. 2.2.1, it is advisable to consider the epidote solid solution with average activity of clinozoisite, a_Czo = 0.703, and to compute the Gibbs free energy and the thermodynamic equilibrium constant of its dissolution reaction. The results obtained taking into account the clinozoisite thermodynamic data of Helgeson et al. (1978) are listed in Table 4.9 as a function of temperature together with the standard molal Gibbs free energies and the natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reaction of pure clinozoisite:

Table 4.9 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure clinozoisite and the epidote solid solution with average activity of clinozoisite as a function of temperature

$${\text{Ca}}_{2} {\text{Al}}_{3} {\text{Si}}_{3} {\text{O}}_{12} ({\text{OH}}) + 13\;{\text{H}}^{ + } = 2\;{\text{Ca}}^{2 + } + 3\;{\text{Al}}^{3 + } + 3\;{\text{SiO}}_{{2({\text{aq}})}} + 7\;{\text{H}}_{2} {\text{O}} .$$

(4.39)

4.6 Prehnite

As indicated by several authors (e.g., Papike and Zoltai 1967; Baur et al. 1990), there are two prehnite polymorphs, namely monoclinic clinoprehnite and orthorhombic orthoprehnite, which in turn have two distinct structures according to Akizuki (1987). The two prehnite polymorphs have very similar unit cell volumes, 469.5(1) and 468.7(2) ų, respectively, and supposedly a tiny energetic difference, as also suggested by their close association in nature (Baur et al. 1990). Therefore, the two polymorphs of prehnite are not distinguished in the following discussion.

4.6.1 The Crystal Chemistry of Prehnite/Ferri-Prehnite Solid Solutions

Single crystal structure analyses (e.g., Preisinger 1965; Papike and Zoltai 1967; Zunić et al. 1990; Baur et al. 1990; Artioli et al. 1995; Akasaka et al. 2003) indicate that prehnite solid solutions have seven-coordinated sites A filled by Ca²⁺, octahedral sites M(1) containing both Al³⁺ and Fe³⁺, and two different types of tetrahedral sites T1 and T2. The T1 sites are entirely occupied by Si⁴⁺ or nearly so, whereas the T2 sites house Al³⁺ and Si⁴⁺ in variable degrees of order-disorder. The structural formula of prehnite solid solutions can thus be written as (Bird and Helgeson 1980, modified):

$${\text{Ca}}_{2} \left[ {{\text{Al}}_{{(1 - {\text{y}})}} {\text{Fe}}_{\text{y}} } \right]^{{{\text{M}}(1)}} ({\text{Si}})_{2}^{{{\text{T}}1}} \left( {{\text{Al}}_{{(1 - {\text{x}})}} {\text{Si}}_{\text{x}} } \right)^{{{\text{T}}2}} {\text{O}}_{10} ({\text{OH}})_{2}$$

where y is the mole fraction of Fe³⁺ on the octahedral sites M(1) and x is the mole fraction of Si⁴⁺ on the tetrahedral sites T2.

Prehnite solid solutions from natural systems show considerable octahedral substitution of Fe³⁺ for Al³⁺, which may be as high as 60 mol percent based on the chemical analyses of this mineral from different metamorphic environments (Bird and Helgeson 1980, and references therein), whereas other compositional variations are very limited. In fact, sodium, potassium, magnesium, ferrous iron and manganese substitution for calcium on the seven-coordinated sites, as well as the substitution of Fe³⁺ or Al³⁺ for Si⁴⁺ on the tetrahedral sites are usually lower than 0.1 atoms per formula unit.

Under the hypotheses of random intrasite mixing and equal interaction of Al³⁺ and Fe³⁺ on the octahedral sites M(1) and Al³⁺ and Si⁴⁺ on the tetrahedral sites T2, the activity of the prehnite endmember [Ca₂Al(AlSi₃)O₁₀(OH)₂] and the ferri-prehnite component [Ca₂Fe(AlSi₃)O₁₀(OH)₂] in prehnite solid solutions are calculated by means of the relations (Helgeson et al. 1978; Helgeson and Aagaard 1985):

$$a_{\text{Prh}} = {\text{k}}_{\text{Prh}} \cdot {\text{X}}_{{{\text{Ca}}_{\text{A}}^{2 + } }}^{2} \cdot {\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }} \cdot ({\text{X}}_{{{\text{Al}}_{{{\text{T}}2}}^{3 + } }} \cdot {\text{X}}_{{{\text{Si}}_{{{\text{T}}2}}^{4 + } }} )$$

(4.40)

$$a_{{{\text{Fe}} - {\text{Prh}}}} = {\text{k}}_{{{\text{Fe}} - {\text{Prh}}}} \cdot {\text{X}}_{{{\text{Ca}}_{\text{A}}^{2 + } }}^{2} \cdot {\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} \cdot ({\text{X}}_{{{\text{Al}}_{{{\text{T}}2}}^{3 + } }} \cdot {\text{X}}_{{{\text{Si}}_{{{\text{T}}2}}^{4 + } }} )$$

(4.41)

where k_Prh = k_Fe-Prh = 4 are the constants relating the inter- and intra-crystalline standard states.

4.6.2 The Endmember Activities in Hydrothermal Prehnite/Ferri-Prehnite Solid Solutions

In this work, a total of 127 chemical analyses of prehnite solid solutions obtained from deep geothermal wells at different temperatures and depths were compiled. Most of these chemical analyses, namely 96, comes from the two geothermal systems of Darajat, Indonesia (N = 61, temperatures 225–350 °C; Herdianita 2012) and Reykjanes, Iceland (N = 35; temperatures 170–342 °C; Libbey and Williams-Jones 2016). Of the other 31 chemical analyses, 14 are from Onikobe, Japan (temperatures 112–173 °C; Seki et al. 1983), 7 are from Cerro Prieto, Mexico (temperatures 325–350 °C; Schiffman et al. 1985), 4 are from Heber (temperature 175 °C; Wheeler et al. 2001), 3 are from Kakkonda, Japan (temperature 225 °C; Muramatsu and Doi 2000), 1 is from Larderello, Italy (temperature 290 °C; Cavarretta et al. 1982), 1 is from Miravalles (temperature 240 °C; Milodowski et al. 1989), and 1 is from Krafla (temperature not specified; Kristmannsdóttir 1979).

The plots of Fig. 4.14a, b are very similar because the activities of the prehnite and ferri-prehnite endmembers computed by means of Eqs. (4.40) and (4.41) are nearly equal to the mole fractions of Al³⁺ and Fe³⁺ on the octahedral sites M(1), respectively. Since ${\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }} + {\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} \cong 1$ and $a_{\text{Prh}} + a_{{{\text{Fe}} - {\text{Prh}}}} \, { \cong } \, 1$, most prehnite solid solutions are situated close to the line of equation ${\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} = 1 - {\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }}$ in Fig. 4.14a and to the line of equation a_Fe-Prh = 1 − a_Prh in Fig. 4.14b.

Fig. 4.14

Plots of a the mole fraction of Al³⁺ on the octahedral sites M(1) versus the mole fraction of Fe³⁺ on the octahedral sites M(1) and b the activity of prehnite versus the activity of ferri-prehnite for 127 prehnite solid solutions from different active geothermal systems (see legend). The dashed line corresponds to the equations ${\text{X}}_{{{\text{Fe}}_{{{\text{M}}(1)}}^{3 + } }} = 1 - {\text{X}}_{{{\text{Al}}_{{{\text{M}}(1)}}^{3 + } }}$ in a an a_Fe-Prh = 1 − a_Prh in b

Prehnite is the main component of most hydrothermal prehnite solid solutions, with activities ranging between 0.373 and 0.998, average of 0.763, median of 0.779, and standard deviation of 0.154. The activity of ferri-prehnite varies from 0.000 to 0.564, with average of 0.210, median of 0.190, and standard deviation of 0.148.

Interestingly, the prehnite solid solutions from the geothermal systems hosted in basaltic rocks, such as Reykjanes and Onikobe, are generally richer in ferri-prehnite than the prehnite samples from the geothermal systems housed in granites or clastic sedimentary rocks, such as Larderello, Cerro Prieto, and especially Kakkonda, where prehnite is Fe-free. The hydrothermal prehnite samples of Darajat distribute over the whole compositional range, although the solid solutions rich in prehnite are more abundant than those rich in ferri-prehnite.

4.6.3 The Thermodynamic Properties of Prehnite

Helgeson et al. (1978), Holland and Powell (1998), and Holland and Powell (2011) report the thermodynamic properties of prehnite of stoichiometry Ca₂Al₂Si₃O₁₀(OH)₂, but Holland and Powell (2011) give also the thermodynamic parameters of ferri-prehnite of composition Ca₂FeAlSi₃O₁₀(OH)₂ and describe deviation from ideality of prehnite solid solutions in terms of a regular solution model. According to Helgeson et al. (1978), the standard state molal ΔG°_f, ΔH°_f, and S° at 25 °C, 1 bar of prehnite should be regarded as provisional approximations. All these thermodynamic data of prehnite and ferri-prehnite are reported in Table 4.10, showing that the ΔG°_f and ΔH°_f of Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 1702 and 502 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f of Holland and Powell (2011) differ from those of Helgeson et al. (1978) by 1449 and 248 cal mol⁻¹, respectively.

Table 4.10 Standard state molal thermodynamic properties, at 25 °C, 1 bar of prehnite and ferri-prehnite from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011)

Employing the approach described in Sect. 2.2.1, it is advisable to consider the prehnite/ferri-prehnite solid solution with average activity of prehnite, a_Prh = 0.763, and to compute the Gibbs free energy and the thermodynamic equilibrium constant of its dissolution reaction. The results obtained taking into account the prehnite thermodynamic data of Helgeson et al. (1978) are listed in Table 4.11 as a function of temperature together with the standard molal Gibbs free energies and the natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reaction of pure prehnite:

Table 4.11 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure prehnite and the prehnite/ferri-prehnite solid solution with average activity of prehnite as a function of temperature

$${\text{Ca}}_{2} {\text{Al}}_{2} {\text{Si}}_{3} {\text{O}}_{10} ({\text{OH}})_{2} + 10\;{\text{H}}^{ + } = 2\;{\text{Al}}^{3 + } + 2\;{\text{Ca}}^{2 + } + 3\;{\text{SiO}}_{{2({\text{aq}})}} + 6\;{\text{H}}_{2} {\text{O}} .$$

(4.42)

4.7 Laumontite and Wairakite

4.7.1 Main Characteristics of Ca-Zeolites

Laumontite and wairakite are the two most common zeolites in active geothermal systems (e.g., Browne 1978; Kristmannsdóttir and Tomasson 1976), together with heulandite [(Na,K,Ca_0.5)₁₀(A1₁₀Si₂₆O₇₂)·24H₂O] − clinoptilolite [(Na,K,Ca_0.5)_5.4 (A1_5.4Si_30.6O₇₂) · 20 H₂O], forming a continuous compositional series (Bish and Boak 2001). Less frequent zeolites comprise stilbite [NaCa₄(Al₉Si₂₇O₇₂) · 30 H₂O], chabazite [(Ca_0.5,Na,K)₄(A1₄Si₈O₂₄) · 12 H₂O], thomsonite [Ca₇Na₅(Al₁₉Si₂₁O₈₀) · 24 H₂O], scolecite [Ca₈(Al₁₆Si₂₄O₈₀) · 24 H₂O], mordenite [Na₃Ca₂K(Al₈Si₄₀O₉₆) · 28 H₂O], yugawaralite [Ca₂(Al₄Si₁₂O₃₂) · 8 H₂O], levyne [(Ca_0.5,Na)₆(A1₆Si₁₂O₃₆) · 18 H₂O], gismondine [Ca₄(Al₈Si₈O₃₂) · 16 H₂O], and gmelinite [(Na,K,Ca_0.5)₈(Al₈Si₁₆O₄₈) · 22 H₂O].

Only laumontite and wairakite are considered in this work, because all their thermodynamic properties (and those of analcime) were retrieved by Helgeson et al. (1978). In contrast, Helgeson et al. (1978) estimated only the standard molal entropy and heat capacity power function coefficients for and other zeolites, including chabazite [Ca(A1₂Si₄O₁₂) · 6 H₂O], epilstilbite [Ca(A1₂Si₆O₁₆) · 5 H₂O], heulandite [Ca(A1₂Si₇O₁₈) · 6 H₂O], natrolite [Na₂(A1₂Si₃O₁₀) · 2 H₂O], Na-phillipsite [Na₂(A1₂Si₅O₁₄) · 5 H₂O], K-phillipsite [K₂(A1₂Si₅O₁₄) · 5 H₂O], Ca-phillipsite [Ca(A1₂Si₅O₁₄) · 5 H₂O], and stilbite [NaCa₂(A1₅Si₁₃O₃₆) · 14 H₂O].

The activity of aqueous silica and relevant cations, such as H⁺, Na⁺, K⁺, Ca²⁺, and Al³⁺ are essential fluid parameters determining which zeolites will form or whether zeolites will form at all. Temperature plays an important role in controlling zeolite stability, partly because of the high water content of zeolites, whereas pressure is less important (Chipera and Apps 2001).

Zeolites usually occur in the shallower parts of active geothermal systems, at temperatures <200 °C, although wairakite forms at temperatures >200 °C and is often associated with epidote (Bird et al. 1984). A peculiarity of laumontite is its occurrence also as precipitate from hot spring waters, at atmospheric pressure and temperatures from 43 to 89 °C (McCulloh et al. 1981). In contrast, wairakite occurs almost exclusively in geothermal systems, both active and fossil. Indeed, the name wairakite is after Wairakei, New Zealand, where this zeolite was first found during the study of hydrothermal alteration minerals in cores recovered from local boreholes (Steiner 1955; Coombs 1955).

4.7.2 Crystal Chemistry of Wairakite and Analcime

The identification of several samples with chemistry and physical properties (e.g., refractive indices and density) intermediate between those of wairakite [CaAl₂Si₄O₁₂ · 2H₂O] and those of analcime [NaAlSi₂O₆ · H₂O] suggests the existence of a continuous isomorphous series between these two endmembers (Passaglia and Sheppard 2001 and references therein). These samples with intermediate properties are classified either as analcime if Na/(Na + Ca) > 0.5 or as wairakite if Na/(Na + Ca) < 0.5. The Si/(Si + Al + Be) ratio has average value of 0.67 in both analcime and wairakite and range 0.60 to 0.74 in analcime and 0.65 to 0.70 in wairakite. Subordinate extra-framework cations are Ca, K, Mg, and Cs in analcime and Na and Cs in wairakite.

Pure wairakite is monoclinic and has six tetrahedral sites, of which four are occupied by Si⁴⁺ and two by Al³⁺, as well as an octahedral site housing one Ca²⁺ ion (Armbruster and Gunter 2001). Ca is coordinated by two H₂O molecules and four oxygen atoms, belonging to two AlO₄ tetrahedra. Allowing for the substitutions of Na⁺ and K⁺ for Ca²⁺ on the octahedral M2 sites, of Fe³⁺ for Al³⁺ on the tetrahedral T2 sites, and of Ti⁴⁺ for Si⁴⁺ on the tetrahedral T1 sites, the structural formula of wairakite/analcime solid solutions can be written as:

$$\left[ {{\text{Ca}}_{{(1 - {\rm{x}} - {\text{y}})}} {\text{Na}}_{\rm{x}} {\text{K}}_{\rm{y}} } \right]\left[ {{\text{Al}}_{{(1 - {\text{m}})}} {\text{Fe}}_{\rm{m}}^{3 + } } \right]_{2} \left[ {{\text{Si}}_{{(1 - {\text{p}})}} {\text{Ti}}_{\rm{p}} } \right]_{4} {\text{O}}_{12} \cdot 2\;{\text{H}}_{2} {\text{O}}$$

where x and y are the mole fractions of Na⁺ and K⁺, respectively, on the octahedral M2 sites, m is the mole fraction of Fe³⁺ on the tetrahedral T2 sites, and p is the mole fraction of Ti⁴⁺ on the tetrahedral T1 sites. Under the hypothesis of random mixing of atoms on energetically equivalent sites, the activity of the wairakite endmember [Ca(Al₂Si₄)O₁₂ · 2H₂O] and the analcime component [Na(AlSi₂)O₆ · H₂O] in the wairakite/analcime solid solutions can be calculated by means of the relations (Helgeson et al. 1978; Helgeson and Aagaard 1985):

$$a_{\text{Wrk}} = {\text{k}}_{\text{Wrk}} \cdot {\text{X}}_{{{\text{Ca}}_{{{\text{M}}2}}^{2 + } }} \cdot {\text{X}}_{{{\text{Al}}_{{{\text{T}}2}}^{3 + } }}^{2} \cdot {\text{X}}_{{{\text{Si}}_{{{\text{T}}1}}^{4 + } }}^{4}$$

(4.43)

$$a_{\text{Anl}} = {\text{k}}_{\text{Anl}} \cdot {\text{X}}_{{{\text{Na}}_{{{\text{M}}2}}^{ + } }} \cdot {\text{X}}_{{{\text{Al}}_{{{\text{T}}2}}^{3 + } }} \cdot {\text{X}}_{{{\text{Si}}_{{{\text{T}}1}}^{4 + } }}^{2}$$

(4.44)

where k_Wrk = k_Anl = 1 are the constants relating the inter- and intra-crystalline standard states.

4.7.3 Crystal Chemistry of Laumontite

According to Armbruster and Gunter (2001) fully hydrated laumontite has stoichiometry CaAl₂Si₄O₁₂ · 4.5 H₂O, but previous studies, including Helgeson et al. (1978), assumed that it contains 4H₂O molecules. Upon exposure to low humidity at room temperature, laumontite experiences partial dehydration with production of leonhardite, of stoichiometry CaAl₂Si₄O₁₂ · 3.5 H₂O. The reaction is reversed by soaking leonhardite in H₂O at room temperature (Coombs 1952). The Si/(Si + Al + Be) ratio of laumontite has average value of 0.67 and range 0.65–0.69, similar to analcime and wairakite (see above). Subordinate extra-framework cations are Na and K (Passaglia and Sheppard 2001).

Similar to wairakite, the laumontite structure is monoclinic and has six tetrahedral sites, of which four house Si⁴⁺ and two house Al³⁺ ions, as well as an octahedral site occupied by a Ca²⁺ ion (Armbruster and Gunter 2001). Ca is coordinated by three H₂O molecules and four oxygen atoms, belonging to AlO₄ tetrahedra.

Again, as for wairakite/analcime solid solutions, permitting the vicariance of Na⁺ and K⁺ for Ca²⁺ on the octahedral M2 sites, of Fe³⁺ for Al³⁺ on the tetrahedral T2 sites, and of Ti⁴⁺ for Si⁴⁺ on the tetrahedral T1 sites, the structural formula of laumontite solid solutions can be written as:

$$\left[ {{\text{Ca}}_{{(1 - {\rm{x}} - {\text{y}})}} {\text{Na}}_{\rm{x}} {\text{K}}_{\rm{y}} } \right]\left[ {{\text{Al}}_{{(1 - {\text{m}})}} {\text{Fe}}_{\rm{m}}^{3 + } } \right]_{2} \left[ {{\text{Si}}_{{(1 - {\text{p}})}} {\text{Ti}}_{\rm{p}} } \right]_{4} {\text{O}}_{12} \cdot 4.5\;{\text{H}}_{2} {\text{O}}$$

where x and y are the mole fractions of Na⁺ and K⁺, respectively, on the octahedral M2 sites, m is the mole fraction of Fe³⁺ on the tetrahedral T2 sites, and p is the mole fraction of Ti⁴⁺ on the tetrahedral T1 sites. Hence, the structural formula of laumontite solid solutions is equal to that of wairakite/analcime solid solutions (see above), apart from the different number of water molecules.

Assuming random mixing of atoms on energetically equivalent sites, the activity of the laumontite endmember [Ca(Al₂Si₄)O₁₂ · 4.5 H₂O] and the related hypothetical alkali component [(Na,K)(Al₂Si₄)O₁₂ · 4.5 H₂O] in the laumontite solid solutions can be computed using the relations (Helgeson et al. 1978; Helgeson and Aagaard 1985):

$$a_{\text{Lmt}} = {\text{k}}_{\text{Lmt}} \cdot {\text{X}}_{{{\text{Ca}}_{{{\text{M}}2}}^{2 + } }} \cdot {\text{X}}_{{{\text{Al}}_{{{\text{T}}2}}^{3 + } }}^{2} \cdot {\text{X}}_{{{\text{Si}}_{{{\text{T}}1}}^{4 + } }}^{4}$$

(4.45)

$$a_{{{\text{Na,K}} - {\text{Lmt}}}} = {\text{k}}_{\text{Na,K-Lmt}} \cdot ({\text{X}}_{{{\text{Na}}_{{{\text{M}}2}}^{ + } }} + {\text{X}}_{{{\text{K}}_{{{\text{M}}2}}^{ + } }} ) \cdot {\text{X}}_{{{\text{Al}}_{{{\text{T}}2}}^{3 + } }}^{2} \cdot {\text{X}}_{{{\text{Si}}_{{{\text{T}}1}}^{4 + } }}^{4}$$

(4.46)

where k_Lmt = k_Na,K-Lmt = 1 are the constants relating the inter- and intra-crystalline standard states.

4.7.4 The Activity of Wairakite in Hydrothermal Wairakite/Analcime Solid Solutions

A total of 136 chemical analyses of wairakite/analcime solid solutions sampled in geothermal wells at different depths and temperatures were compiled in this work. Most of these chemical analyses, namely 119, come from the two geothermal systems of Onikobe, Japan (N = 60; temperature 110–240 °C; Seki et al. 1983) and Darajat, Indonesia (N = 59; temperature 220–267 °C; Herdianita 2012). The remaining 17 chemical analyses are from Hachimantai, Japan (N = 6; temperature 160–195 °C; Shimazu and Yajima 1973), Waiotapu, New Zealand (N = 3; temperature 220–285 °C; Hedenquist and Browne 1989), Cerro Prieto, Mexico (N = 2; temperature 320 °C; Schiffman et al. 1985), Krafla (N = 1, temperature not given; Kristmannsdottir, 1979), Reydarfjordur (N = 1; temperature not reported; Viereck et al. 1982), Yellowstone, Wyoming (N = 1; temperature 138 °C; Bargar and Beeson 1981), Kakkonda, Japan (N = 1; temperature not specified; Muramatsu and Doi 2000), Wairakei, New Zealand (N = 1; temperature not given; Steiner 1955), and Larderello, Italy (temperature 120 °C; Cavarretta et al. 1982).

The compiled wairakite/analcime solid solutions have wairakite activity ranging from 0.573 to 0.999, with average of 0.891, median of 0.920, and standard deviation of 0.090 and analcime activity varying from 0.000 to 0.427, with mean of 0.096, median of 0.068, and standard deviation of 0.091. As expected, in the diagram of Fig. 4.15a, most wairakite/analcime solid solutions are located close to the line of equation a_Anl = 1 − a_Wrk.

Fig. 4.15

Plots of a the activity of wairakite versus the activity of analcime for 136 wairakite/analcime solid solutions from different active geothermal systems (see legend) and b the activity of laumontite versus the activity of alkali-laumontite for 45 laumontite/alkali-laumontite solid solutions from various active geothermal systems (see legend). The dashed line corresponds to the equations a_Anl = 1 − a_Wrk in a an a_Na,K-Lmt = 1 − a_Lmt in b

The wairakite/analcime samples coming from the two most studied geothermal systems show different characteristics, with those from Onikobe spanning a compositional range much larger than those from Darajat. In fact, at Onikobe, wairakite activity varies from 0.648 to 0.977, with average of 0.844, median of 0.846, and standard deviation of 0.083, whereas, at Darajat, wairakite activity ranges from 0.857 to 0.999, with average of 0.942, median of 0.946, and standard deviation of 0.037. The different activities of wairakite and analcime at Onikobe and Darajat might be due to differences in temperatures and in the lithological framework between the two geothermal fields.

4.7.5 The Activity of Laumontite in Hydrothermal Laumontite/Alkali-Laumontite Solid Solutions

In this work, it was possible to compile only 45 chemical analyses of laumontite/alkali-laumontite solid solutions, all obtained from geothermal wells at varying depths and temperatures, apart from those of Sespe Hot Springs which were collected at the surface.

Most of these chemical analyses, namely 19, come from the geothermal system of Darajat, Indonesia (temperature 220–231 °C; Herdianita 2012). The other 26 laumontite data are from Reydarfjordur (N = 6; temperature not reported; Mehegan et al. 1982; Viereck et al. 1982; Exley 1982), Yellowstone, Wyoming (N = 5; temperature 120–140 °C; Bargar and Beeson 1985), Breitenbush-Austin, Oregon (N = 5; temperature 110–140 °C; Oscarson and Bargar 1996), Onikobe, Japan (N = 5; temperature 118–175 °C; Seki et al. 1969, 1983), Sespe Hot Springs (N = 3, temperature 89 °C; McCulloh et al 1981), Paratunka, Kamchatka (N = 1, temperature not given, Petrova 1970), and Krafla (N = 1, temperature not given; Kristmannsdóttir 1979).

The considered laumontite/alkali-laumontite solid solutions exhibit laumontite activity varying from 0.873 to 0.992, with mean of 0.946, median of 0.951, and standard deviation of 0.031 whereas the activity of the alkali-component ranges from 0.002 to 0.127, with average of 0.051, median of 0.048, and standard deviation of 0.032. Not surprisingly, in the diagram of Fig. 4.15b, most laumontite/alkali-laumontite solid solutions are situated near the line of equation a_Na,K-Lmt = 1 − a_Lmt.

4.7.6 The Thermodynamic Properties of Wairakite and Laumontite

The thermodynamic properties of wairakite of stoichiometry CaAl₂Si₄O₁₂ · 2 H₂O and laumontite of composition CaAl₂Si₄O₁₂ · 4 H₂O given by Helgeson et al. (1978), Holland and Powell (1998), and Holland and Powell (2011) are shown in Table 4.12.

Table 4.12 Standard state molal thermodynamic properties, at 25 °C, 1 bar of wairakite and laumontite from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), HP11 = Holland and Powell (2011), and Ki96 = Kiseleva et al. (1996)

Helgeson et al. (1978) derived the thermodynamic properties of wairakite and laumontite from the experimental data of Liou (1970, 1971a), considering the following equilibria:

$${\text{wairakite}} = {\text{anorthite}} + 2\;{\text{quartz}} + 2\;{\text{H}}_{2} {\text{O}}$$

(4.47)

$${\text{laumontite}} = {\text{wairakite}} + 2\;{\text{H}}_{2} {\text{O}} .$$

(4.48)

However, the thermodynamic properties of laumontite are inconsistent with the experimental data of Thompson (1970) for the equilibrium reaction:

$${\text{laumontite}} = {\text{anorthite}} + 2\;{\text{quartz}} + 4\;{\text{H}}_{2} {\text{O,}}$$

(4.49)

as pointed out by Helgeson et al. (1978).

Holland and Powell (1998) derived the enthalpy of both zeolites from the experimental results of Thompson (1970), Liou (1970, 1971a, b), and Cho et al. (1987) and estimated the entropy of laumontite and wairakite by means of the method of Holland (1989), considering an entropy contribution of zeolitic H₂O of 6.9 cal K⁻¹ mol⁻¹. The differences between the thermodynamic properties reported by Helgeson et al. (1978) and those of Holland and Powell (1998) and Holland and Powell (2011) are probably due to the use of different experimental data to retrieve these thermodynamic data. To be noted also that:

• (i) The ΔH°_f values of Helgeson et al. (1978), Holland and Powell (1998), and Holland and Powell (2011) differ from the calorimetric results of Kiseleva et al. (1996) by +4147, −4209, and −2782 cal mol⁻¹, respectively, for laumontite and by +9046, −4742, and −3752 cal mol⁻¹, respectively, for wairakite.

• (ii) The S° values of Helgeson et al. (1978), Holland and Powell (1998), and Holland and Powell (2011) deviate from the calorimetric outcomes of Kiseleva et al. (1996) by +0.1, −6.8, and −4.9 cal K⁻¹ mol⁻¹, respectively, for laumontite and by +9.3, −6.1, and −4.9 cal K⁻¹ mol⁻¹, respectively, for wairakite.

A thorough discussion on the thermodynamic properties of several zeolites, including laumontite and wairakite, is provided by Chipera and Apps (2001).

Adopting the approach delineated in Sect. 2.2.1, it is advisable to take into consideration the wairakite/analcime solid solution with average activity of wairakite, a_Wrk = 0.891, and the laumontite/alkali-laumontite solid solution with mean activity of laumontite, a_Lmt = 0.946, and to calculate the Gibbs free energy and the thermodynamic equilibrium constant of their dissolution reactions. The results calculated using the wairakite and laumontite thermodynamic data of Helgeson et al. (1978) are listed in Tables 4.13 and 4.14, respectively, as a function of temperature together with the standard molal Gibbs free energies and the natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of pure wairakite:

Table 4.13 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure wairakite and the wairakite/analcime solid solution with average activity of wairakite as a function of temperature

Table 4.14 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure laumontite and the laumontite/alkali−laumontite solid solution with average activity of laumontite as a function of temperature

$${\text{CaAl}}_{2} {\text{Si}}_{4} {\text{O}}_{12} \cdot 2\;{\text{H}}_{2} {\text{O}} + 8\;{\text{H}}^{ + } = {\text{Ca}}^{2 + } + 2\;{\text{Al}}^{3 + } + 4\;{\text{SiO}}_{{2({\text{aq}})}} + 6\;{\text{H}}_{2} {\text{O}}$$

(4.50)

and pure laumontite:

$${\text{CaAl}}_{2} {\text{Si}}_{4} {\text{O}}_{12} \cdot 4\;{\text{H}}_{2} {\text{O}} + 8\;{\text{H}}^{ + } = {\text{Ca}}^{2 + } + 2\;{\text{Al}}^{3 + } + 4\;{\text{SiO}}_{{2({\text{aq}})}} + 8\;{\text{H}}_{2} {\text{O}} .$$

(4.51)

For laumontite there is a difference of 0.024 units between the log K_Lmt and log K_Lmt,aa values, corresponding to differences of 30–63 cal mol⁻¹ in the Gibbs free energies of the dissolution reactions. Therefore, there is not much difference in using the thermodynamic data of pure laumontite or those of the laumontite/alkali-laumontite solid solution of average laumontite activity occurring in active geothermal systems.

4.8 Garnets

Winchell (1933) divided the silicate garnets in the following two series:

• the ugrandites, comprising the endmember garnets uvarovite [Ca₃Cr₂Si₃O₁₂], grossular [Ca₃Al₂Si₃O₁₂], and andradite [Ca₃(Fe³⁺,Ti⁴⁺)₂Si₃O₁₂], as well as intermediate compounds;

• the pyralspites, including the endmember garnets pyrope [Mg₃Al₂Si₃O₁₂], almandine $\left[ {{\text{Fe}}_{3}^{2 + } {\text{Al}}_{2} {\text{Si}}_{3} {\text{O}}_{12} } \right]$, and spessartine [Mn₃Al₂Si₃O₁₂], and also the intermediate compositions.

According to Deer et al. (1982), there is an almost complete and continuous variation in composition within each of these two series whereas the variation between ugrandites and pyralspites is less continuous.

4.8.1 Crystal Chemistry of Garnets

Garnet solid solutions are represented by the general crystallochemical formula (Novak and Gibbs 1971):

$${\text{X}}_{3}^{\rm{VIII}} {\text{Y}}_{2}^{\rm{VI}} {\text{Z}}_{3}^{\rm{IV}} {\text{O}}_{12} ,$$

in which, consistent with the endmembers recognized by Winchell (1933):

• X^VIII refers to the eight-fold dodecahedral coordinated sites, which are occupied by the divalent cations Ca²⁺, Mg²⁺, Mn²⁺, and Fe²⁺.

• ${\text{Y}}^{\text{VI}}$ indicates the six-fold octahedral coordinated sites, housing the trivalent cations Al³⁺, Fe³⁺, and Cr³⁺ as well as Ti⁴⁺.

• ${\text{Z}}^{\text{IV}}$ designates the four-fold tetrahedral coordinated sites that are mainly occupied by Si⁴⁺ ions and subordinately by Al³⁺.

According to Rickwood (1968), possible endmembers garnets could be of the following three types:

• Type 1: $\left\{ {{\text{R}}_{3}^{2 + } } \right\}\;[{\text{R}}_{2}^{3 + } ]({\text{R}}_{3}^{4 + } ){\text{O}}_{12}$

• Type 2: $\left\{ {{\text{R}}_{3}^{2 + } } \right\}\;[{\text{R}}^{3 + } {\text{R}}^{4 + } ]({\text{R}}^{3 + } {\text{R}}_{2}^{4 + } ){\text{O}}_{12}$

• Type 3: $\left\{ {{\text{R}}_{3}^{2 + } } \right\}\;[{\text{R}}_{2}^{4 + } ]({\text{R}}_{2}^{3 + } {\text{R}}^{4 + } ){\text{O}}_{12}$.

Accepting the presence of Fe³⁺ and Ti⁴⁺ in the tetrahedral sites in addition to Si⁴⁺ and Al³⁺, but disregarding the endmembers with more Ti⁴⁺ in tetrahedral sites than in octahedral sites and with more than one element of any valence state, it is possible to obtain 12 endmember garnets of type (1), none of type (2), and 8 of type (3). Rickwood (1968) proposed also a procedure to recast garnet analyses into the mole fractions of 19 endmember garnets, which were suitably chosen to accommodate also Y on the dodecahedral sites, V and Zr on the octahedral sites, and H on the tetrahedral sites.

More recently, Locock (2008) suggested an alternative method, designed to recalculate garnet analyses into the mole fractions of 29 endmember garnets, including 15 natural minerals species and 14 hypothetical components. The Locock’s method is consistent with the general crystallochemical formula given above, including 8 cations and 12 anions (O or F) with no vacancies in the dodecahedral and octahedral sites.

If ferric and ferrous iron are not measured separately, their proportions are computed from the total iron concentration given as FeO, using the relation of Droop (1987), which is based on the hypotheses that iron is the only multivalent element and that there are no vacant cation sites. Both assumptions are justified for most Al-silicate garnets. Based on their general crystallochemical formula (see above), the relation of Droop (1987) can be written as follows for garnets:

$${\text{N}}_{{{\text{Fe}}^{3 + } }} = 24 \cdot \left( {1 - 8/{\text{S}}} \right).$$

(4.52)

In Eq. (4.52), S is the total number of cations initially computed assuming all iron to be Fe²⁺. If S < 8, then all iron is actually present as Fe²⁺. Alternatively, if S > 8, Eq. (4.52) is used to calculate ${\text{N}}_{{{\text{Fe}}^{3 + } }}$. Then, the number of Fe²⁺ ions per formula unit, ${\text{N}}_{{{\text{Fe}}^{2 + } }}$, is computed by subtracting ${\text{N}}_{{{\text{Fe}}^{3 + } }}$ from the number of Fe²⁺ ions per formula unit previously computed assuming all iron to be Fe²⁺, ${\text{N}}_{{{\text{Fe}}^{2 + } ,{\text{in}}}}$:

$${\text{N}}_{{{\text{Fe}}^{2 + } }} = {\text{N}}_{{{\text{Fe}}^{2 + } ,{\text{in}}}} - {\text{N}}_{{{\text{Fe}}^{3 + } }} .$$

(4.53)

If Eq. (4.53) gives a negative result, ${\text{N}}_{{{\text{Fe}}^{2 + } }}$ is set equal to zero.

Mn³⁺ is calculated only for compositions that cannot charge balance with Fe³⁺ alone. Only fluorine and the following oxides (expressed in weight percent) are considered: SiO₂, TiO₂, ZrO₂, SnO₂, Y₂O₃, Al₂O₃, Sc₂O₃, Cr₂O₃, V₂O₃, FeO, MnO, MgO, CaO, Na₂O, H₂O. The following oxidation states are assumed: Ti⁴⁺, Sn⁴⁺, Cr³⁺, V³⁺. To be underscored that titanium occurs exclusively at the tetravalent oxidation state in garnet, as suggested by most experimental evidence (Locock 2008).

In the Locock’s method cation and anion assignments are as follows: Mn³⁺ is assigned to the octahedral site. H is assumed to occur as (H₄O₄)₃ in substitution for (SiO₄)₃. H₄ is treated as one cation. Si is assigned to the tetrahedral site, but Si in excess of 3 apfu is assigned to the octahedral site. The tetrahedral site is filled, first with Si and H₄ and afterwards with Al and Fe³⁺, if necessary and possible. F substitutes for O in a coupled substitution with vacancies on the tetrahedral site. Zr, Sn and Ti are assigned exclusively to the octahedral site. Any remaining Al and Fe³⁺ as well as Sc, V and Cr are assigned to the octahedral site. The remainder of the octahedral site is filled with Fe²⁺ and Mg, if necessary and possible. Ca, Mn²⁺, and Na are assigned to the dodecahedral site with the remaining Fe²⁺ and Mg, if any. Proportions are based on 8 cations, including F-related tetrahedral vacancies and H₄.

The proportions of the 29 endmembers are computed by the Locock’s procedure in the order given in Table 4.15.

Table 4.15 Endmembers considered in the procedure proposed by Locock (2008) to recalculate garnet analyses

In other terms, the proportions of the Mn³⁺ endmembers henritermierite and blythite are computed first and are followed by katoite, F-garnets, and yttrogarnet. The proportions of the remaining endmembers are calculated based on the octahedral cations, in the order: Zr, Sn, Ti, Si, Sc, V, Cr, Al, Fe³⁺. For a given octahedral cation, endmembers are usually considered in order of increasing rarity. The rigorous assignment of cations to particular sites may lead to non-ideal subtotals for that site, e.g., if (Ca + Na) > 3, or if (Ti + Zr) > 2, or if (Si + H₄) > 3. To be noted that the chemical formula of andradite reported in Table 4.15 does not comprise Ti, in contrast with the stoichiometry of andradite adopted by other authors (e.g., Deer et al. 1982 and references therein).

The Microsoft Excel spreadsheet provided by Locock (2008) was used in this work to compute the mole fractions of endmember garnets and the mole fractions of cations on the dodecahedral, octahedral, and tetrahedral sites. Cations mole fractions were then used to calculate the activities of andradite and grossular in garnet solid solutions by means of the following relations (Bird and Norton 1981):

$$a_{\text{Grs}} = {\text{k}}_{\text{Grs}} \cdot {\text{X}}_{{{\text{Ca}}_{\text{X}}^{2 + } }}^{3} \cdot {\text{X}}_{{{\text{Al}}_{\text{Y}}^{3 + } }}^{2} \cdot {\text{X}}_{{{\text{Si}}_{\text{Z}}^{4 + } }}^{3}$$

(4.54)

$$a_{\text{Adr}} = {\text{k}}_{\text{Adr}} \cdot {\text{X}}_{{{\text{Ca}}_{\text{X}}^{2 + } }}^{3} \cdot {\text{X}}_{{{\text{Fe}}_{\text{Y}}^{3 + } }}^{2} \cdot {\text{X}}_{{{\text{Si}}_{\text{Z}}^{4 + } }}^{3}$$

(4.55)

where k_Grs = k_Adr = 1 are the constants relating the inter- and intra-crystalline standard states. Equations (4.54) and (4.55) are based on the hypothesis of random mixing of atoms on energetically equivalent sites (Helgeson et al. 1978; Helgeson and Aagaard 1985).

4.8.2 The Composition of Hydrothermal Garnet Solid Solutions

A total of 201 chemical analyses of garnet solid solutions collected in deep geothermal wells at different depths and temperatures were compiled. The majority of these samples, for a total of 137, come from the geothermal systems of Darajat (N = 83; measured temperature 137–235 °C; Herdianita 2012) and Reykjanes, Iceland (N = 54; measured temperature 176–321 °C; Libbey and William-Jones 2016). Of the remaining 64 chemical analyses, 21 are from Latera, Italy (measured temperatures 220–343 °C; Cavarretta et al. 1985), 9 are from Larderello, Italy (present day temperatures 175–375 °C; Cavarretta et al. 1982; Gianelli and Ruggieri 2002), 9 are from Reydarfjordur, Iceland (inferred temperature of garnet formation 300–360 °C; Exley 1982; Mehegan et al. 1982), 8 are from Los Humeros, Mexico (measured temperatures of 300–325 °C; Martinez Serrano 2002), 6 are from Sabatini, Italy (measured temperatures 165–290 °C; Cavarretta and Tecce 1987), 5 are from Kilauea, Hawaii (present-day temperature 322 °C; Bargar et al. 1996), 4 are from Miravalles, Costa Rica, (measured temperature 255 °C; Milodowski et al. 1989), and 1 each are from Cerro Prieto, Mexico (present-day temperature 325 °C; Schiffman et al. 1985) and Mofete, Italy (measured temperature 324 °C; Balducci and Chelini 1992).

The sum of the mole fractions of endmember garnets calculated adopting the Locock’s method and using the Microsoft Excel spreadsheet provided by Locock (2008) is higher than 0.9 in 192 cases, between 0.87 and 0.90 in 5 cases (2 from Reydarfjordur and 1 each from Reykjanes, Los Humeros, and Darajat), close to 0.81 in 2 cases (1 from Reykjanes and 1 from Darajat) and 0.53–0.58 in 2 cases from Darajat. These few samples with values of the sum of the mole fractions of endmember garnets significantly lower than 1 and correspondingly very high remainders might be affected by analytical problems but were not rejected to avoid loss of information.

Andradite and grossular are the most frequent and important endmembers of the considered hydrothermal garnets, with 195 and 139 concentrations ≠ 0, varying from 0.02 to 99.39 mol% and from 0.07 to 81.59 mol%, respectively. Pyrope and spessartine are also common endmembers but less important, with 105 and 94 contents ≠ 0, ranging from 0.04 to 13.92 mol% and from 0.03 to 10.80 mol%, respectively. Almandine is not so common, with 37 concentrations ≠ 0, but varying from 0.01 to 84.69 mol%. The highest almandine concentrations (58.05–84.69 mol%) are found in eight garnets from Larderello rocks affected by contact metamorphism (Gianelli and Ruggieri 2002). Titanium is mainly accommodated in schorlomite-Al and morimotoite, with 77 and 49 contents ≠ 0, ranging from 0.01 to 7.76 mol% and from 0.02 to 9.98 mol%, respectively, and subordinately in morimotoite-Mg and Na–Ti garnet, with 28 and 24 contents ≠ 0, ranging from 0.06 to 5.00 mol% and from 0.02 to 1.83 mol%, respectively.

Moreover, the sum of the andradite and grossular mole fractions is relatively close to unity in most of the considered hydrothermal garnets. In fact, they are situated close to the dashed line corresponding to the equation X_Adr = 1 – X_Grs in the binary diagram of Fig. 4.16a. The only exceptions are the eight almandine-rich garnets from Larderello (see above), which are situated relatively close to the origin in the binary diagram of Fig. 4.16a, having small contents of grossular and especially andradite. Authors of previous studies (e.g., Cavarretta et al. 1982, 1985; Exley 1982; Mehegan et al. 1982; Bird et al. 1984; McDowell and Elders 1983; Schiffman et al. 1985; Cavarretta and Tecce 1987; Milodowski et al. 1989; Balducci and Chelini 1992; Gianelli et al. 1998; Martinez-Serrano 2002; Marks et al. 2010; Herdianita 2012; Libbey and Williams-Jones 2016) already recognized the prevalence of andradite and grossular in most hydrothermal garnets from active geothermal systems, which are therefore called grandites.

Fig. 4.16

Correlation diagrams between a the mole fractions of grossular and andradite and b the activities of grossular and andradite for the 173 garnet solid solutions coming from different geothermal systems (see legend). The dashed lines refer to the equations X_Adr = 1 − X_Grs in a and $a_{\text{Adr}} = 1 + a_{\text{Grs}} - 2 \cdot \sqrt {a_{\text{Grs}} }$ in b

Moreover, disregarding the eight almandine-rich garnets from Larderello, andradite prevails over grossular in 145 grandites, i.e., 75% of the 193 cases, whereas grossular dominates over andradite in the other 48 grandites, i.e., 25% of the 193 cases (Fig. 4.16a). Of these 48 grossular-rich garnets, 15 are from Latera, 13 are from Reykjanes, 8 are from Darajat, and 6 each are from Sabatini and Los Humeros. It should be noted that garnets are often zoned and exhibit wide intra-crystal compositional variations, with grossular-rich core and andradite-rich rim in some cases, and vice versa in other samples, that were attributed to changes in fluid chemistry in some previous studies. Contact metamorphism and metasomatic processes were also invoked to explain garnet compositions.

4.8.3 The Activity of Grossular and Andradite in the Hydrothermal Garnet Solid Solutions

Excluding the eight almandine-rich garnets from Larderello and the three samples from Darajat with very high remainders, the other 190 garnet solid solutions have andradite activity varying from 0.00539 to 0.972, with mean of 0.541, median of 0.625, and standard deviation of 0.340, whereas grossular activity ranges from <2.27 × 10⁻⁷ (in 22 cases) to 0.674, with average of 0.127, median of 0.0142, and standard deviation of 0.179.

The correlation plot of Fig. 4.16b shows that andradite and grossular activities of most garnets approximate the relation $a_{\text{Adr}} = 1 + a_{\text{Grs}} - 2 \cdot \sqrt {a_{\text{Grs}} }$ (dashed line), apart from the eight almandine-rich garnets from Larderello and the three samples from Darajat with very high remainders (see above).

This relationships is obtained considering that ${\text{X}}_{\text{Adr}} \approx {\text{X}}_{{{\text{Fe}}_{\text{Y}}^{3 + } }}$ and ${\text{X}}_{\text{Grs}} \approx {\text{X}}_{{{\text{Al}}_{\text{Y}}^{3 + } }}$, which are reasonable approximations in most cases, as indicated by Fig. 4.17a, b, respectively. Consequently, Eqs. (4.54) and (4.55) simplify to $a_{\text{Grs}} \approx {\text{X}}_{{{\text{Al}}_{\text{Y}}^{3 + } }}^{2} \approx {\text{X}}_{\text{Grs}}^{2}$ and $a_{\text{Adr}} \approx {\text{X}}_{{{\text{Fe}}_{\text{Y}}^{3 + } }}^{2} \approx {\text{X}}_{\text{Adr}}^{2}$, respectively. Considering that ${\text{X}}_{\text{Adr}} \approx 1 - {\text{X}}_{\text{Grs}}$ (see above), it is a simple matter to obtain, by substitution and rearrangement, the relation written above linking andradite and grossular activities.

Fig. 4.17

Correlation diagrams between a the mole fraction of andradite and the mole fraction of trivalent iron on the octahedral sites and b the mole fraction of grossular and the mole fraction of aluminum on the octahedral sites for the 173 garnet solid solutions coming from different geothermal systems (see legend). The dashed lines refer to the equations $\text{X}_{\text{Adr}} = {\text{X}}_{{{\text{Fe}}_{\text{Y}}^{3 + } }}$ in a and ${\text{X}}_{\text{Grs}} = {\text{X}}_{{{\text{Al}}_{\text{Y}}^{3 + } }}$ in b

4.8.4 The Thermodynamic Properties of Grossular and Andradite

Helgeson et al. (1978) report the thermodynamic properties of grossular and andradite only, whereas almandine, pyrope, and spessartine are also included in the dataset of Holland and Powell (1998), and almandine, knorringite, majorite, pyrope, and spessartine are also comprised in the database of Holland and Powell (2011). The standard state molal thermodynamic properties, at 25 °C, 1 bar of grossular [Ca₃Al₂Si₃O₁₂] and andradite $\left[ {{\text{Ca}}_{3} {\text{Fe}}_{2}^{3 + } {\text{Si}}_{3} {\text{O}}_{12} } \right]$ listed in these three compilations are shown in Table 4.16.

Table 4.16 Standard state molal thermodynamic properties, at 25 °C, 1 bar of grossular and andradite from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011)

For grossular, the ΔG°_f and ΔH°_f of Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 4214 and 4574 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f listed by Holland and Powell (2011) differ from those of Helgeson et al. (1978) by 3946 and 4306 cal mol⁻¹, respectively.

For andradite, the ΔG°_f and ΔH°_f of Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 1033 and 2398 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f listed by Holland and Powell (2011) differ from those of Helgeson et al. (1978) by 910 and 2162 cal mol⁻¹, respectively.

More recently, Dachs and Geiger (2019) investigated the thermodynamics of three grossular-rich natural solid solutions and three synthetic andradite-grossular solid solutions of composition ${\text{Ca}}_{3} \left( {{\text{Al}}_{0.5} {\text{Fe}}_{1.5}^{3 + } } \right){\text{Si}}_{3} {\text{O}}_{12} ,{\text{Ca}}_{3} \left( {{\text{AlFe}}^{3 + } } \right){\text{Si}}_{3} {\text{O}}_{12}$, and ${\text{Ca}}_{3} \left( {{\text{Al}}_{1.5} {\text{Fe}}_{0.5}^{3 + } } \right){\text{Si}}_{3} {\text{O}}_{12}$ . Using the S° calorimetric value of 325.0 ± 2.0 J K⁻¹ mol⁻¹ (corresponding to 77.68 ± 0.48 cal K⁻¹ mol⁻¹) for andradite (Geiger et al. 2018) and published phase-equilibrium results on three andradite-bearing reactions, they obtained the value of −5763.3 ± 1.5 kJ mol⁻¹ (corresponding to −1377.462 ± 0.359 kcal mol⁻¹) for the standard enthalpy of formation of andradite. This ΔH°_f value is lower than those of Helgeson et al. (1978), Holland and Powell (1998), and Holland and Powell (2011) by 3543, 1145, and 1381 cal mol⁻¹, respectively.

Following the approach outlined in Sect. 2.2.1, it is advisable to consider the grossular/andradite solid solution with average activity of grossular, a_Grs = 0.127, and to calculate the Gibbs free energy and the thermodynamic equilibrium constant of its dissolution reaction. The results obtained considering the grossular thermodynamic data of Helgeson et al. (1978) are listed in Table 4.17 as a function of temperature together with the standard molal Gibbs free energies and the natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reaction of pure grossular:

Table 4.17 Standard molal Gibbs free energies and natural and decimal logarithms of the thermodynamic equilibrium constant of the dissolution reactions of both pure grossular and the grossular/andradite solid solution with average activity of grossular as a function of temperature

$${\text{Ca}}_{3} {\text{Al}}_{2} {\text{Si}}_{3} {\text{O}}_{12} + 12\;{\text{H}}^{ + } = 2\;{\text{Al}}^{3 + } + 3\;{\text{Ca}}^{2 + } + 3\;{\text{SiO}}_{{2({\text{aq}})}} + 6\;{\text{H}}_{2} {\text{O}} .$$

(4.56)

4.9 Calcite

Anhydrous calcium carbonate occurs as three distinct polymorphs, i.e., calcite, aragonite, and vaterite, whose crystals have trigonal, orthorhombic, and hexagonal symmetry, respectively. Calcite is the thermodynamically stable polymorph at low pressures, aragonite is stable at high pressures (e.g., >3 kbar at 0 °C and >4.4 kbar at 100 °C; Crawford and Hoersch 1972 and references therein), whereas vaterite is unstable and is quickly converted into aragonite or calcite through dissolution and growth (Ogino et al. 1987).

Aragonite is a member of the isomorphous group of orthorhombic carbonates comprising strontianite [SrCO₃], witherite [BaCO₃], and cerussite [PbCO₃], in which Ca²⁺, Sr²⁺, Ba²⁺, and Pb²⁺ have nine-fold coordination. Orthorhombic BaCO₃ and SrCO₃ invert to the trigonal calcite-type structure at temperatures of 806 and 912 °C, respectively, which are much higher than the range of geothermal interest (Chang 1965).

Calcite belongs to the isomorphous group of trigonal carbonates including magnesite [MgCO₃], siderite [FeCO₃], rhodochrosite [MnCO₃], smithsonite [ZnCO₃], sphaerocobaltite [CoCO₃], gaspeite [NiCO₃], and otavite [CdCO₃]. As required by the electroneutrality condition, these trigonal carbonates host divalent cations, the largest of which is Ca²⁺, whose size represents the uppermost value for six-fold octahedral coordination (Reeder 1990). Complete miscibility occurs between calcite and otavite, whereas limited miscibility occurs between calcite and the trigonal carbonates of Mg, Fe, Mn, Co, and Ni. Nevertheless, significant amounts of Mg, Fe, Mn, Zn, Co, Ni, and Cd are likely to be scavenged from the aqueous solution by calcite precipitation (e.g., McIntire 1963; Marini et al. 2001). Similar considerations hold true for Sr, Ba, and Pb although their carbonates are expected to mix with aragonite instead of calcite.

4.9.1 The Composition of Calcite-Rich Trigonal Carbonates from Active Geothermal Systems

A total of 313 chemical analyses of solid solutions of calcite-rich trigonal carbonates sampled from deep geothermal wells at different depths and temperatures were compiled in this work. The weight percentages of relevant oxides (CaO, MgO, MnO, FeO, ZnO, SrO, BaO, and PbO) were converted into the corresponding moles and their sum was computed. A number of moles of CO₂ equal to the sum of the moles of the relevant oxides was assumed to be present in the mineral and the corresponding CO₂ weight percentage was computed accordingly. The chemical analyses with sum of weight percentages, including CO₂, between 92 and 104% were accepted, whereas the few analyses with sum of oxides <92 wt% were rejected.

Most of the accepted chemical analyses of calcite-rich trigonal carbonates, namely 251, are representative of the two geothermal systems of Darajat, Indonesia (N = 175, temperature 110–300 °C; Herdianita 2012) and Reykjanes, Iceland (N = 76; temperature 19–289 °C; Libbey and Williams-Jones 2016). Of the other 62 chemical analyses, 25 are from Milos, Greece (temperature 190 °C; Liakopoulos 1987), 16 are from Onikobe, Japan (temperature 110–225 °C; Seki et al. 1983), 10 are from Broadlands, New Zealand (temperature 230–290 °C; Lonker et al. 1990), 5 are from Cerro Prieto, Mexico (temperature 185–335 °C; Schiffman et al. 1985), 4 are from Pantelleria, Italy (temperature 85–120 °C; Fulignati et al. 1997), and 2 are from Newberry Caldera, Oregon (temperature 35–130 °C; Keith and Bargar 1988). The main statistical parameters for the mole fractions of calcite, magnesite, siderite, rhodochrosite, SrCO₃, BaCO₃, smithsonite, and PbCO₃ in the considered solid solutions of calcite-rich trigonal carbonates are listed in Table 4.18.

Table 4.18 Main statistical parameters for the mole fractions of calcite, magnesite, siderite, rhodochrosite, SrCO₃, BaCO₃, smithsonite, and PbCO₃ in the solid solutions of calcite−rich trigonal carbonates from different active geothermal systems

As expected, calcite is by far the main component of the solid solutions of interest, with mole fractions ranging between 0.705 and 1.000, average of 0.972, median of 0.988, and standard deviation of 0.043. Based on the average values, the second major component is rhodochrosite, with mole fractions ranging between 0.0000570 and 0.130, average of 0.0139, median of 0.00522, and standard deviation of 0.0214, and is followed by magnesite, siderite, SrCO₃, PbCO₃, smithsonite, and BaCO₃, in order of decreasing importance. To be noted that the number of available data, N, decreases in the following order: CaCO₃ > MgCO₃ > MnCO₃ > FeCO₃ > SrCO₃ > PbCO₃ > BaCO₃ > ZnCO₃.

4.9.2 The Carbonate Minerals Other Than Calcite from Active Geothermal Systems

Calcite is not the only carbonate mineral present in active geothermal systems. Although calcite is a common and important mineral at Ohaaki-Broadlands, occurring in all boreholes, siderite is also present (Browne and Ellis 1970). Siderite is uncommon, but it occurs in quantities of up to 10% in some Broadlands wells, at temperatures between 37 and 130 °C. At Salton Sea, siderite occurs at weakly higher temperatures, close to 135 °C, but it is absent at the depths/temperatures where base metal sulfides are found (Muffler and White 1969). At Wairakei, siderite is reported to be present at depth of only 27 m and low temperatures (Steiner 1953). At Newberry, siderite is abundant and is locally associated with magnesite and solid solutions of ankerite [CaFe(CO₃)₂] and dolomite [CaMg(CO₃)₂] at depths of 320 to 697 m, where measured temperature varies from 35 to 100 °C. It was probably precipitated after the emplacement of a sill, during a thermal event that caused alteration of Fe-sulfides (Keith and Bargar 1988). Both siderite and ankerite occur also at Darajat, where calcite is the most common hydrothermal mineral (Herdianita 2012).

4.9.3 The Thermodynamic Properties of Calcite

Helgeson et al. (1978), Holland and Powell (1998), and Holland and Powell (2011) report the thermodynamic properties of calcite and aragonite of chemical formula CaCO₃ (Table 4.19). For calcite, the ΔG°_f and ΔH°_f of Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 308 and 163 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f listed by Holland and Powell (2011) differ from those of Helgeson et al. (1978) by 227 and 82 cal mol⁻¹, respectively.

Table 4.19 Standard state molal thermodynamic properties, at 25°C, 1 bar of calcite and aragonite from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011)

For aragonite, the ΔG°_f and ΔH°_f of Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 269 and 88 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f listed by Holland and Powell (2011) differ from those of Helgeson et al. (1978) by 207 and 47 cal mol⁻¹, respectively.

These differences are much smaller than those generally observed for Al-silicates. Nevertheless, they determine some differences in the Gibbs free energy of calcite-aragonite conversion. For instance, this ΔG°_r value, at 25°C, 1 bar, is 225 cal mol⁻¹ based on the data of Helgeson et al. (1978), 186 cal mol⁻¹ according to Holland and Powell (1998), and 205 cal mol⁻¹ based on the data of Holland and Powell (2011).

Since calcite generally occurs as a virtually pure phase (see Sect. 4.9.1), its activity can be assumed to be equal to one. Therefore, there is no need to correct the Gibbs free energy and the thermodynamic equilibrium constant of its dissolution reaction.

4.10 Quartz and Other Silica Minerals

The main crystalline polymorphs of silica stable at low pressures are quartz, cristobalite, and tridymite. Quartz and chalcedony (i.e., microcrystalline quartz with sub-microscopic pores) are the most common hydrothermal minerals in most geothermal fields, if not all, and distribute in a wide temperature range, from 120 to 350 °C according to Henley and Ellis (1983). Above ~180 °C, aqueous solutions are saturated with respect to quartz, whereas at lower temperatures, silica activity is controlled by chalcedony solubility (e.g., Arnórsson et al. 1983a; Fournier 1991). Cristobalite and tridymite also occur as hydrothermal minerals, especially at relatively low temperatures, but are by far less common than quartz and chalcedony.

The crystal structure of all these silica polymorphs consists of a three-dimensional framework of SiO₄ tetraedra, which are linked together by sharing the corners with other tetraedra. In these lattices, therefore, each oxygen atom has two silicon atoms as nearest neighbors and each silicon atom is surrounded by four oxygen atoms (Deer et al. 2004). In spite of these similarities, each silica polymorph has its own crystal structure: α-quartz and β-quartz crystals have trigonal and hexagonal symmetry, respectively; α-cristobalite and β-cristobalite crystals have tetragonal and cubic symmetry, respectively, whereas tridymite occurs in seven distinct crystalline forms indicated by the symbols HP, LHP, OC, OS, OP, MC, and MX-1 (Pryde and Dove 1998).

4.10.1 The Activity of Endmember Quartz in Hydrothermal Quartz

A total of 209 chemical analyses of quartz were compiled in this work. All these analyses are representative of quartz samples collected in the deep wells of the Reykjanes geothermal field, Iceland at different depths, from 150 to 2846 m, and temperatures, from 19 to 342 °C (Libbey and Williams-Jones 2016).

As expected, SiO₂ is by far the main component of these quartz samples, with mole fractions varying between 0.967 and 0.999, average of 0.993, median of 0.994, and standard deviation of 0.005. These statistical parameters indicate that hydrothermal quartz is a pure phase and its activity can be assumed to be equal to one. Strictly speaking this finding concerns the Reykjanes geothermal system only, but it may be considered a general conclusion, in spite of the lack of data for hydrothermal quartz from other geothermal systems.

4.10.2 The Thermodynamic Properties of the Quartz/Chalcedony Mechanical Mixture

Helgeson et al. (1978) report the thermodynamic properties of α- and β-quartz, α- and β-cristobalite, chalcedony, amorphous silica, and coesite. The latter mineral is disregarded in Table 4.20 being stable at very high pressures, outside the range of interest of geothermal systems. Holland and Powell (1998) and Holland and Powell (2011) report instead the thermodynamic properties of quartz, cristobalite, and tridymite (Table 4.20).

Table 4.20 Standard state molal thermodynamic properties, at 25 °C, 1 bar of silica polymorphs from H78 = Helgeson et al. (1978), HP98 = Holland and Powell (1998), and HP11 = Holland and Powell (2011)

For quartz, the ΔG°_f and ΔH°_f of Holland and Powell (1998) differ from those of Helgeson et al. (1978) by 53 and 56 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f listed by Holland and Powell (2011) are closer to those of Helgeson et al. (1978), with differences of 5 and 13 cal mol⁻¹, respectively. The opposite is true for cristobalite. In fact, the ΔG°_f and ΔH°_f of Holland and Powell (1998) deviate from those of Helgeson et al. (1978) by 6 and 206 cal mol⁻¹, respectively, whereas the ΔG°_f and ΔH°_f reported by Holland and Powell (2011) exhibit larger deviations from those of Helgeson et al. (1978), 114 and 636 cal mol⁻¹, respectively.

The methodological approach of Helgeson et al. (1978) for treating quartz is different from that adopted by Holland and Powell (1998) and Holland and Powell (2011). In fact, Helgeson et al. (1978) report the thermodynamic properties of α-quartz at 25 °C, 1 bar, the enthalpy, entropy, and volume of the α-β quartz transition at 575 °C, 1 bar (which are listed in the column ΔH°_f, S°, and V° in Table 4.20 to avoid inserting three more columns), and the heat capacity coefficients of β-quartz. These are the data stored in SUPCRT92, which are used to compute the thermodynamic properties of quartz up to 2000 K. The same applies to other minerals that undergo phase transitions, such as high-albite, 7Å-clinochlore, and prehnite, among those of interest to us.

In contrast, quartz is treated adopting a pressure-dependent Landau tricritical model by Holland and Powell (1998) and Holland and Powell (2011). In this way, there is no need to give separate thermodynamic data for α- and β-quartz. However, it is necessary to consider the pressure-dependent critical temperature and the excess volume, entropies, and energies. The properties given in the Holland and Powell data sets are the Landau critical temperature at 1 bar, T_c° = 847 K (i.e., the α-β quartz transition within 1 K); the thermal expansion parameter a° = 0.65 K⁻¹ mol⁻¹; the bulk modulus at 298 K, κ₂₉₈ = 750 kbar mol⁻¹; the maximum entropy of disorder, S_max = 4.95 J K⁻¹ mol⁻¹ (=1.183 cal K⁻¹ mol⁻¹); and the maximum volume of disorder V_max = 0.1188 J bar⁻¹ mol⁻¹ (=1.188 cm³ mol⁻¹). The approach of Holland and Powell allows calculation of mineral-fluids equilibria up to a pressure of at least 100 kbar, a value exceeding the maximum pressures present in geothermal systems by about three orders of magnitude.

Unlike quartz, α- and β-cristobalite are treated by Helgeson et al. (1978) as two distinct minerals. This different approach was probably adopted because the transition temperature of cristobalite is poorly defined.

The thermodynamic data of chalcedony, cristobalite, and amorphous silica reported by Helgeson et al. (1978) are consistent with those of quartz and were retrieved from solubility measurements at high temperatures by Walther and Helgeson (1977) in their study on the thermodynamic properties of aqueous silica as a function of temperature and pressure.

As shown in Sect. 5.2.2, the solubilities of quartz and chalcedony, at saturation temperatures and pressures, computed using the thermodynamic data of quartz and chalcedony from Helgeson et al. (1978) and those of aqueous SiO₂ from Shock et al. (1989), bracket the functions describing quartz solubilities according to different studies. Therefore, a mechanical mixture constituted by 50% chalcedony and 50% quartz was added to the SUPCRT92 database. At 25 °C, 1 bar, α-quartz and chalcedony have the same entropy, volume, and heat capacity coefficients, whereas the ΔG°_f and ΔH°_f values differ by 370 and 368 cal mol⁻¹, respectively, due to the distinct grain size of these two silica minerals. Therefore, the quartz/chalcedony mechanical mixture has the same entropy, volume, and heat capacity coefficients of the two endmember minerals, whereas its Gibbs free energy and enthalpy are different, with ΔG°_f = −204,461 cal mol⁻¹ and ΔH°_f = −217,466 cal mol⁻¹.

Interpolation of the undissociated SiO₂ concentration data fixed by the quartz/chalcedony mechanical mixture leads to the following polynomial equation (${\text{c}}_{{{\text{SiO}}_{2} }}$ in mg/kg):

$$\begin{aligned} {\text{T}}\left( {^\circ {\text{C}}} \right) &= 2.7195{\text{E}} - 12 \cdot {\text{c}}_{{{\text{SiO}}_{2} }}^{5} - 6.6268{\text{E}} - 9 \cdot {\text{c}}_{{{\text{SiO}}_{2} }}^{4} + 6.4341{\text{E}} - 6 \cdot {\text{c}}_{{{\text{SiO}}_{2} }}^{3} \\&\quad - 3.2559{\text{E}} - 3 \cdot {\text{c}}_{{{\text{SiO}}_{2} }}^{2} + 1.1233 \cdot {\text{c}}_{{{\text{SiO}}_{2} }} + 39.790 \end{aligned}$$

(4.57)

which is valid from 100 to 350 °C, at water saturation pressures, and reproduces the equilibrium temperatures within 0.5 °C below 325 °C and within 5.5  °C above 325 °C.

4.11 Conclusive Considerations on Hydrothermal Minerals

Over 2200 chemical analyses of hydrothermal minerals collected at depth in different active geothermal systems were compiled, processed, and discussed in the previous sections of this chapter. In agreement with the outcomes of previous studies, it turned out that hydrothermal quartz, calcite, adularia, albite, anorthite, and laumontite are virtually pure solid phases and their activities can be assumed to be equal to one. In contrast, the other hydrothermal minerals of interest, i.e., white mica, chlorite, epidote, prehnite, wairakite, and garnet, are solid solutions of variable composition. Therefore, the activities of pertinent endmembers were computed, under the assumption of random mixing of atoms on energetically equivalent sites, obtaining the following results:

• (i) In the considered 75 hydrothermal white mica solid solutions, muscovite activity varies from 0.007 to 0.875, but it is higher than 0.40 in most cases. Accordingly, average muscovite activity is 0.654, the median value is 0.688 and the standard deviation is relatively small, 0.156.

• (ii) The selected 181 hydrothermal chlorites have highly different Fe²⁺/(Fe²⁺ + Mg) ratio, from 0.23 to 0.94, with compositions varying from Mg-rich values, relatively similar to clinochlore or sheridanite, to Fe²⁺-rich values, close to ripidolite. The activity of the clinochlore endmember spans a very wide interval, from 4.39 × 10⁻⁷ to 0.250, with an average of 0.0553, a median of 0.0451 and a relatively large standard deviation of 0.0484.

• (iii) Clinozoisite is the main component of the 436 hydrothermal epidote solid solutions of interest. Its activity varies from 0.523 to 0.888, with a mean of 0.703, a median of 0.706, and a small standard deviation of 0.057. According to the equilibrium model of Bird and Helgeson (1980), these hydrothermal epidote samples appear to be relatively ordered, but deviations from the equilibrium distribution are possible, due to occurrence of metastable states of substitutional order/disorder on the octahedral sites.

• (iv) Prehnite prevails in most of the 127 selected prehnite/ferri-prehnite solid solutions. Its activity ranges from 0.373 to 0.998, with average of 0.763, median of 0.779, and a relatively small standard deviation of 0.154.

• (v) Wairakite is the main endmember component of the 136 wairakite/analcime solid solutions under consideration. Its activity varies from 0.573 to 0.999, with mean of 0.891, median of 0.920, and a comparatively small standard deviation of 0.090.

• (vi) The sum of the andradite and grossular mole fractions is relatively close to unity in most of the considered 201 hydrothermal garnets, which can be classified as grandites, apart from eight almandine-rich garnets from Larderello. Grossular is the main component in 25% of the cases only. Its activity ranges from <2.27 × 10⁻⁷ (in 22 cases) to 0.674, with average of 0.127, median of 0.0142, and relatively large standard deviation of 0.179.

The solid solutions with average activity of muscovite, 7Å-clinochlore, clinozoisite, prehnite, wairakite, and grossular were considered as points of reference. The ΔG°_f and the log K of their dissolution reactions were computed and compared with the ΔG°_f and the log K of the dissolution reactions of the corresponding pure minerals.

The dilution of the endmember component of interest in a given solid phase increases its stability with respect to that of the pure mineral. An overall view of this effect is provided by the diagram of CO₂ fugacity versus temperature for the system SiO₂–Al₂O₃–CaO–H₂O–CO₂ (Fig. 4.18, modified from Giggenbach 1997), which was constructed assuming saturation with calcite and quartz/chalcedony at any $f_{{{\text{CO}}_{2} }}$ and temperature.

Fig. 4.18

Diagram of CO₂ fugacity versus temperature for the system SiO₂–Al₂O₃–CaO–H₂O–CO₂ (modified from Giggenbach 1997), prepared assuming saturation with quartz/chalcedony and calcite at any $f_{{{\text{CO}}_{2} }}$ and temperature

In this diagram, the red lines depict the stability fields of the pure hydrothermal minerals, but the blue lines describe the stability fields of the garnet, epidote, wairakite/analcime and prehnite/ferri-prehnite solid solutions with average activities of the relevant endmembers, that is grossular, clinozoisite, wairakite, and prehnite, respectively. Both grids were prepared assuming that laumontite, kaolinite and pyrophyllite are pure phases. The comparison of the two grids shows what follows:

• (i) The stability field of the garnet solid solution expands considerably with respect to that of pure grossular, at the expense of the stability field of prehnite. This significant effect is due to the substantial difference between the average activity of prehnite, 0.763, and the average activity of grossular, 0.127. To be noted that the following relation:

$$\log \;f_{{{\text{CO}}_{2} ,{\text{Prh}} - {\text{Grs}}}} = \log \;{\text{K}}_{\text{Cal}} + \log \;{\text{K}}_{\text{Prh}} - \log \;{\text{K}}_{\text{Grs}} ,$$

(4.58)

links the logarithm of CO₂ fugacity to the log K of the dissolution reactions of calcite, prehnite, and grossular, which are as follows:

$${\text{Cal}} + 2\;{\text{H}}^{ + } = {\text{Ca}}^{2 + } + {\text{CO}}_{{2({\text{g}})}} + {\text{H}}_{2} {\text{O}}$$

(4.59)

$$\text{Prh} + 3\;{\text{Qtz}}/{\text{Chc}} + 10\;{\text{H}}^{ + } = 2\;{\text{Ca}}^{2 + } + 2\;{\text{Al}}^{3 + } + 6\;{\text{H}}_{2} {\text{O}}$$

(4.60)

$${\text{Grs}} + 3\;{\text{Qtz}}/{\text{Chc}} + 12\;{\text{H}}^{ + } = 3\;{\text{Ca}}^{2 + } + 2\;{\text{Al}}^{3 + } + 6\;{\text{H}}_{2} {\text{O}}$$

(4.61)

• (ii) Also the stability field of the epidote solid solution exhibits a certain expansion in comparison to that of pure clinozoisite, especially to disadvantage of the stability field of wairakite and laumontite, whereas the clinozoisite-prehnite boundary experiences a small shift. This behavior is partly attributable to the fact that the average activity of clinozoisite, 0.703, is similar to that of prehnite, 0.763, but is significantly lower than those of wairakite, 0.891, and laumontite, which is assumed to be equal to 1. However, the differential expansion of the stability field of clinozoisite is also controlled, in part, by the stoichiometry of relevant reactions, as pointed out by the following relations:

$$\log \;f_{{{\text{CO}}_{2} ,{\text{Czo-Prh}}}} = \log \;{\text{K}}_{\text{Cal}} + \log \;{\text{K}}_{{{\text{Czo}}}} - 1.5 \cdot \log \;{\text{K}}_{\text{Prh}}$$

(4.62)

$$\log \;f_{{{\text{CO}}_{2} ,{\text{Wrk-Czo}}}} = \log \;{\text{K}}_{\text{Cal}} + 3 \cdot \log \;{\text{K}}_{{{\text{Wrk}}}} - 2 \cdot \log \;{\text{K}}_{{{\text{Czo}}}}$$

(4.63)

$$\log \;f_{{{\text{CO}}_{2} ,{\text{Lmt-Czo}}}} = \log \;{\text{K}}_{\text{Cal}} + 3 \cdot \log \;{\text{K}}_{\text{Lmt}} - 2 \cdot \log \;{\text{K}}_{{{\text{Czo}}}}$$

(4.64)

linking the logarithm of CO₂ fugacity to the log K of the dissolution reactions of clinozoisite, wairakite, and laumontite, which are as follows:

$${\text{Czo}} + 3\;{\text{Qtz}}/{\text{Chc}} + 13\;{\text{H}}^{ + } = 2\;{\text{Ca}}^{2 + } + 3\;{\text{Al}}^{3 + } + 7\;{\text{H}}_{2} {\text{O}}$$

(4.65)

$${\text{Wrk}} + 4\;{\text{Qtz}}/{\text{Chc}} + 8\;{\text{H}}^{ + } = {\text{Ca}}^{2 + } + 2\;{\text{Al}}^{3 + } + 6\;{\text{H}}_{2} {\text{O}}$$

(4.66)

$${\text{Lmt}} + 4\;{\text{Qtz}}/{\text{Chc}} + 8\;{\text{H}}^{ + } = {\text{Ca}}^{2 + } + 2\;{\text{Al}}^{3 + } + 8\;{\text{H}}_{2} {\text{O}} .$$

(4.67)

as well as by the log K of the dissolution reactions of calcite, Eq. (4.59), and prehnite, Eq. (4.60).

Since hydrothermal quartz, calcite, adularia, albite, anorthite, and laumontite occur as virtually pure solid phases, they can be involved without any particular worries and precautions in the theoretical, activity-based geothermometers and $f_{{{\text{CO}}_{2} }}$-indicators representing the aim of this work.

Also the use of white mica, epidote, prehnite, and wairakite for theoretical geothermometry and $f_{{{\text{CO}}_{2} }}$ evaluation does not pose particular problems because these minerals exhibit limited compositional variations and, consequently, minor deviations are generally expected from their average activities.

The involvement of chlorite and garnet in theoretical geothermometers and $f_{{{\text{CO}}_{2} }}$-indicators is instead a risky business because these minerals show considerable compositional variations and, therefore, large deviations may occur from their average activities.

Moreover, it must be recalled that (i) hydrothermal feldspars present in active geothermal systems are most likely triclinic, fully ordered, albite and variably ordered adularia, from fully ordered microcline to completely disordered sanidine, with either triclinic or monoclinic symmetry (see Sect. 4.2.3) and (ii) microcline and sanidine have different thermodynamic properties (see Sect. 4.2.5).

The thermodynamic data of Helgeson et al. (1978) are used in this book because they resulted to be consistent with the monoclinic/triclinic transition temperatures of alkali feldspars whereas the thermodynamic data of Holland and Powell (1998) and Arnórsson and Stefánsson (1999) did not, as discussed in Sect. 4.2.4. Unfortunately, as shown in previous sections, there are large differences between the thermodynamic data of Helgeson et al. (1978) and those of Holland and Powell (1998, 2011), for most relevant solid phases, although these three databases are internally consistent. Owing to these large differences, it is meaningless to select data from distinct databases because it would be like mixing apples and oranges, as already recalled above.

In principle, the preparation of a common thermodynamic database for the whole scientific community would be highly desirable. In practice, it is a prohibitive challenge that is probably doomed to remain a chimera for a certain lapse of time, hopefully not too long.