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Wolframite solubility and precipitation in hydrothermal fluids: insight fromthermodynamic modeling

Xiangchong Liu, Changhao Xiao

PII: S0169-1368(19)30735-8DOI: https://doi.org/10.1016/j.oregeorev.2019.103289Reference: OREGEO 103289

To appear in: Ore Geology Reviews

Received Date: 6 August 2019Revised Date: 26 November 2019Accepted Date: 14 December 2019

Please cite this article as: X. Liu, C. Xiao, Wolframite solubility and precipitation in hydrothermal fluids: insightfrom thermodynamic modeling, Ore Geology Reviews (2019), doi: https://doi.org/10.1016/j.oregeorev.2019.103289

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1

Wolframite solubility and precipitation in hydrothermal fluids: insight from

thermodynamic modelingXiangchong Liua,b,c, Changhao Xiaoa,b,c

a. Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China,

b. The Laboratory of Dynamic Diagenesis and Metallogenesis, Institute of Geomechanics, CAGS, China

c. Key Laboratory of Paleomagnetism and Tectonic Reconstruction, Ministry of Natural Resources, Beijing 100081, China

Abstract: Wolframite, a solid-solution series between hübnerite (MnWO4) and ferberite

(FeWO4), is the main tungsten-bearing ore mineral in vein-type tungsten deposits. Much

progress has been made on characterizing the mineralizing fluids precipitating wolframite,

but it remains poorly understood what are the mechanisms depositing wolframite effectively

and the variables controlling Mn/Fe ratios in wolframite. This study examines chemical

controls on wolframite solubility in hydrothermal fluids and Mn/Fe ratios in wolframite using

thermodynamic models for fluids in the systems of W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H.

The fluid-buffered models are established based on the characteristics of vein-type tungsten

deposits. The modeling results indicate that solubilities of hübnerite and ferberite in

hydrothermal fluids at typical W-mineralizing conditions (300-400 oC, 500-1500 bars, 5-15

wt. % NaCl equivalent, pH=4-6) reach up to hundreds of ppm. The predominant tungsten,

manganese, and iron species in fluids are , and , respectively. An HWO ―4 MnCl0

2 FeCl2 ―4

increase in pH and a decrease in fluid temperature and salinity are efficient mechanisms

precipitating hübnerite and ferberite from acidic hydrothermal fluids. Hübnerite and ferberite

are also significantly dissolved in alkaline hydrothermal fluids, but their solubilities in alkaline

fluids are insensitive to fluid temperature and salinity. This may affect W mineralization at

stages with different pH levels (e.g. the greisen stage and the alkaline stage). The Mn/Fe

2

ratio of mineralizing fluids is the principal variable controlling Mn/Fe ratios in wolframite.

More supply of Fe than Mn from the fertile magma tends to produce Fe-rich mineralizing

fluids. This may be one of reasons why ferberite is more common than hübnerite in tungsten

deposits and why hübnerite is more likely to precipitate at an early stage.

Keywords: tungsten deposits; wolframite; ferberite; hübnerite; thermodynamic model

1. Introduction

Tungsten mineralization is genetically related to highly fractionated granites and

dominated by greisen, quartz-vein, skarn, and porphyry types (Černý et al., 2005; Huang

and Jiang, 2014; Mao et al., 2013; Zhao et al., 2017). The main ore minerals in tungsten

deposits are scheelite and wolframite (e.g. Brown and Pitfield, 2013; Gong, 2015; Harlaux et

al., 2018; Lu et al., 2003; Rasmussen et al., 2011), the latter of which often occurs in

vein-type tungsten deposits. Vein-type tungsten deposits account for approximately 44 % of

known tungsten economic resources next to skarn tungsten deposits (48%) (Werner et al.,

2014). Southern China hosts the most abundant vein-type tungsten deposits in the world

(Liu and Ma, 1993; Zhao et al., 2017). Large-scale or clustered vein-type tungsten deposits

were also exploited around the Mole Granite, Australia (Audétat et al., 2000b), in

Panasqueira, Portugal (Foxford et al., 2000; Launay et al., 2018), in southwest England

(Sanderson et al., 2008), in the Erzgebirge, Germany and the Czech Republic (Breiter et al.,

1999; Štemprok et al., 1994), in the Variscan French Massif Central (Harlaux et al., 2017,

2018) , and in the Iberian Massif, Spain (Garate-Olave et al., 2017; Llorens and Moro, 2012).

3

Wolframite, (Mn,Fe)WO4, is a solid-solution series between hübnerite (MnWO4) and

ferberite (FeWO4) (e.g. Harlaux et al., 2018; Pačevski et al., 2007; Sakamoto, 1985; Tindle

and Webb, 1989; Xie et al., 2017; Zhang et al., 2018b). Much progress has been made on

characterizing the mineralizing fluids precipitating wolframite (e.g. Breiter et al., 2017;

Campbell and Panter, 1990; Chen et al., 2018; Korges et al., 2017; Legros, 2018; Li et al.,

2018b; Ni et al., 2015), but it is still poorly understood how much tungsten can dissolve in

mineralizing fluids. The thermodynamic model developed by Wood and Samson (2000) put

a quantitative constraint on ferberite solubility in hydrothermal fluids, but solubility of the

other end-member hübnerite remains poorly constrained. Therefore, it is necessary to

develop thermodynamic models that incorporate Mn species and reactions in NaCl aqueous

solutions.

Wolframite shows variable Mn/Fe ratios either in a single crystal or at different depths of

a tungsten deposit (e.g. Harlaux et al., 2018; Pačevski et al., 2007; Xie et al., 2017). The

reasons for this phenomenon have been debated for many years (e.g. Amosse, 1981;

Campbell, 1988; Hollister, 1970; Pačevski et al., 2007; Taylor and Hosking, 1970; Tindle and

Webb, 1989). Some studies find correlation between the Mn/Fe ratios in wolframite and

some variables (e.g. temperature, pH, and Mn/Fe ratio of mineralizing fluids) (Amossé,

1978; Hollister, 1970; Horner, 1979), while others do not support it (Buhl and Willgallis,

1984; Buhl and Willgallis, 1985; Moore and Howie, 1978; Nakashima et al., 1986). Ferberite

is identified in many tungsten deposits of southern China (e.g. Xie et al., 2017; Zhang, 1981;

Zhang et al., 2018a), at the Panasqueira deposit, Portugal (Lecumberri-Sanchez et al.,

2017), in most tungsten deposits of the Variscan French Massif Central (Harlaux et al.,

4

2018), in some tungsten deposits of the Iberian Massif, Spain (Llorens and Moro, 2012), and

in the tungsten deposits of central Rwanda (Goldmann et al., 2013). Hübnerite is rarer than

ferberite (King, 2005), but it is reported to be the dominant tungsten-bearing mineral in some

vein-type tungsten deposits (e.g. Casadevall and Rye, 1980; Frolova et al., 2014; Harlaux et

al., 2018; Neiva, 2008; Tindle and Webb, 1989; Wu et al., 2017). Until now, it remains poorly

understood what controls the wolframite solid-solution composition.

Chemical mass transfer modeling is a powerful tool for understanding the transport and

deposition of metals in ore-forming hydrothermal systems (e.g. Gibert et al., 1992; Heinrich,

2005; Heinrich et al., 1996; Hofstra et al., 1991; Liu et al., 2018; Migdisov et al., 2019;

Phillips and Evans, 2004; Sushchevskaya and Bychkov, 2010; Wood and Samson, 2000). In

this study, thermodynamic models in the system of W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H

were established to quantify wolframite solubility in NaCl solutions and identify the variables

that may control Mn/Fe ratios in wolframite.

2. Geochemical characteristics of W-mineralizing fluids

Wood and Samson (2000) and Naumov et al. (2011) have summarized the

geochemical parameters (e.g. temperature, pressure, and salinity) of W-mineralizing fluids,

and most of those parameters are determined from opaque minerals (e.g. quartz, topaz, and

cassiterite). The W-mineralizing fluids have homogenization temperatures from 200 to 400

oC (Naumov et al., 2011). Recent infrared microthermometric studies of fluid inclusions in

wolframite suggest that the mineralization temperatures of tungsten deposits range from 300

to 400 oC (e.g. Chen et al., 2018; Li et al., 2018b; Ni et al., 2015; Pan et al., 2019). The

5

mineralization pressures fall in the range of 500-1500 bars and the fluid salinities are

typically less than 10 wt. % NaCl equivalent (Naumov et al., 2011; Wood and Samson,

2000). Based on muscovite-K-feldspar equilibria, pH of mineralizing fluids is estimated to be

at neutral to moderately acid levels (pH=4-6) (Polya, 1989; Seal et al., 1987; So et al., 1991;

So and Yun, 1994). Recent laboratory experiments suggest that significant tungsten could

also dissolve in alkaline aqueous fluids at 300-400 oC (Li et al., 2018a). The fluids’ oxygen

fugacity commonly falls between quartz-fayalite-magnetite and hematite-magnetite buffers

(e.g. Han et al., 2016; Jiang et al., 2004; Wood and Samson, 2000). CO2-bearing fluid

inclusions are recently found in wolframite of a few tungsten deposits (e.g. Chen et al., 2018;

Pan et al., 2019), but the CO2 contents in those mineralizing fluids have not been precisely

determined yet. Compiled data in Wood and Samson (2000) suggest that the mole fraction

of CO2 in fluid inclusions is typically between 0 and 0.1.

Recently reported in-situ compositions of fluid inclusions in tungsten deposits were

compiled here to examine the relationship between W and other ore elements (e.g. Fe and

Mn) and put a better constraint on thermodynamic modeling. The data sources include the

Sn-W deposits around the Mole Granite, Australia (Audétat et al., 2000a), the Panasqueira

tungsten deposit, Portugal (Lecumberri-Sanchez et al., 2017), the tungsten deposits in the

Erzgebirge, Germany and the Czech Republic (Korges et al., 2017), and the Piaotang and

Maoping tungsten deposits, China (Legros et al., 2019). Note that wolframite is the main ore

mineral of those tungsten deposits.

Most W concentrations in fluid inclusions of those tungsten deposits have a range of a

few to hundreds of ppm (Fig. 1a). The two tungsten deposits in China have the largest

6

average tungsten concentration (Fig. 1b). Both Fe and Mn are identified from fluid inclusions

in the Sn-W deposits around the Mole Granite and the tungsten deposits in the Erzgebirge,

while only Fe or Mn are found in the other tungsten deposits. The molality ratios of W against

Fe and Mn range mainly from 10-4 to 10-1, and the W/Fe ratios are slightly lower than the

W/Mn ratios on average (Fig. 2a). The W/(Fe+Mn) ratios fall into a wider range of 10-5 to 1

and peaks at 10-3 and 10-1 (Fig. 2b).

Wood and Samson (2000) employed stoichiometric dissolution of ferberite and

scheelite ( ) as one of mass balance equations in their models. However, W ∑W = ∑Fe + ∑Ca

concentrations in mineralizing fluids are generally a few orders of magnitude lower than Fe

and Mn concentrations (Fig. 2). Constrained by the W/Fe ratios and W/Mn ratios of fluid

inclusions above, the following two equations were used to replace stoichiometric dissolution

of ferberite and hübnerite:

∑W = ∑Mn/λ (1)

∑W = ∑Fe/λ (2)

in which ranges from 10 to 1000.λ

3. Species and reactions in fluid-buffered thermodynamic models

Two limiting cases of fluid-rock interactions in natural hydrothermal systems are

fluid-buffered and rock-buffered (Heinrich, 1990). In the fluid-buffered case, chemical

reactions are controlled entirely by equilibria among fluid species, while fluids are in

equilibrium contact with excess rock in the rock-buffered case. Rock-buffered

thermodynamic models are more applicable to skarn-type and greisens-type tungsten

7

deposits, which cannot be created without metasomatism (e.g. Gibert et al., 1992; Halter et

al., 1998). The thermodynamic models for vein-type tungsten deposits in this study are

fluid-buffered because high-efficiency tungsten mineralization in those deposits requires

large fluid focusing and incomplete buffering of mineralizing fluids by granitic rocks

(Heinrich, 1990; Lecumberri-Sanchez et al., 2017; Liu et al., 2014, 2015; Polya, 1988).

The tungsten species in NaCl aqueous solutions included in the model are , H2WO04

, and (Redkin, 2010; Wang et al., 2019a; 2019b; Wood and Samson, 2000). HWO ―4 WO2 ―

4

Wood and Samson (2000) postulated the existence of alkaline tungstate ion pairs such as

and in their model, but their postulation is supported neither by molecular NaHWO04 NaWO ―

4

dynamic simulations conducted by Mei et al. (2019) nor by solubility experiments conducted

by Wang et al. (2019b). Therefore, neither nor are incorporated in the NaHWO04 NaWO ―

4

present models.

The valence states of iron (Fe) and manganese (Mn) ions are sensitive to oxygen

fugacity. Hydrothermal fluids in the crust generally have a low oxidation potential, and

dissolved Fe is predominantly in the +2 oxidation state (Heinrich and Seward, 1990;

Testemale et al., 2009). Under the reduced conditions of W-mineralizing fluids, the amount

of Fe3+ in hydrothermal fluids is negligible compared to that of Fe2+ (cf. Wood and Samson,

2000). Mn occurs in the valence states of +2, +3, and +4 in natural environments (Wolfram

and Krupp, 1996). However, transport of Mn in hydrothermal fluids is widely accepted to be

in the +2 oxidation state (cf. Gammons and Seward, 1996; Tian et al., 2014). Thus, the effect

of oxygen fugacity was implicitly considered and Fe2+, Mn2+, and their reactions with Cl- and

OH- were incorporated in the models.

8

The solubility product of FeWO4 was modeled by Wood and Samson (2000) using the

thermodynamic data in SUPCRT (Shock et al., 1992) and the temperature-dependent heat

capacity of ferberite proposed by Polya (1990). Wood and Samson (2000)’s method was

used to reproduce the solubility product of FeWO4. However, the solubility product of

MnWO4 and the equilibrium constant of formation cannot be calculated using current MnCl02

thermodynamic database (e.g. SUPCRT updated by 2017, see http://geopig.asu.edu/).

Empirical formulas were developed to fill this gap. Molality (mol/kg) was used for the

concentrations of the species in this study.

3.1 The solubility product of MnWO4

The dissolution reaction of MnWO4 in aqueous solutions is as follows:

(3)MnWO4(s)⇌Mn2 + (aq) + WO42 ― (aq)

The solubility product was calculated by the following equation:𝐾𝑠𝑝

(4)𝑙𝑜𝑔𝐾𝑠𝑝 =― ∆𝑟𝐺0

𝑃𝑇

log (10)𝑅𝑇

in which is the common logarithm, R is the universal gas constant (8.31446 J K-1mol-1), 𝑙𝑜𝑔

and T is the temperature in K. The standard reaction Gibbs energy for the reaction (1) ∆𝑟𝐺0𝑃𝑇

is:

(5)∆𝑟𝐺0𝑃𝑇 = ∆𝑓𝐺0

𝑃𝑇(Mn2 + ) + ∆𝑓𝐺0𝑃𝑇(WO4

2 ― ) ― ∆𝑓𝐺0𝑃𝑇(MnWO4)

The of a solid species (e.g. and ) is a function of T, P as follows:∆𝑓𝐺0𝑃𝑇 MnWO4 FeWO4

∆𝑓𝐺0𝑃𝑇

= ∆𝑓𝐺0298.15𝐾,1𝑏𝑎𝑟 ― 𝑆0

298.15(𝑇 ― 298.15) + ∫𝑇

298.15𝐶0

𝑃𝑑𝑇 ― 𝑇∫𝑇

298.15

𝐶0𝑃

𝑇 𝑑𝑇 + 𝑉0298.15(𝑃 ― 1)

(6)

where is the standard molar Gibbs energy at 298.15 K and 1 bar; is the ∆𝑓𝐺0298.15𝐾,1𝑏𝑎𝑟 𝑆0

298

standard molar entropy; is the isobaric heat capacity; is the molar volume; P is the 𝐶0𝑃 𝑉0

298

9

pressure in bar. Except the heat capacity of , all the other thermodynamic MnWO4

parameters of , , and can be accessed from the package SUPCRT WO42 ― Mn2 + MnWO4

(Johnson et al., 1992) and the data compiled by Robie and Hemingway (1995).

Yakovleva and Rezukhina (1960) fitted a heat capacity function of from their MnWO4

experimental data at the temperature range of 293-1074 K (see Fig. 3). However, there is a

large gap between their function and the heat capacity of at lower temperatures MnWO4

obtained by Landee and Westrum (1976). To fill this gap, the experimental data of

Yakovleva and Rezukhina (1960) and Landee and Westrum (1976) were used to fit the

Hass-Fisher heat capacity function against temperature (Haas and Fisher, 1976):

(7)𝐶0𝑃 = 𝐴0 + 𝐴1𝑇 + 𝐴2𝑇2 + 𝐴3𝑇 ―0.5 + 𝐴4𝑇 -2

The fitted coefficients are shown in Table 1, and Supplementary data 1 lists the 𝐴0 ― 𝐴4

experimental data used for fitting. Compared to the function of Yakovleva and Rezukhina

(1960), the heat capacity function fitted here joins smoothly with the low-temperature data,

and asymptotically approaches a limit at high temperature as required by theory (cf. 𝐶0𝑃

Kieffer, 1985). The heat capacity of from 298 to 900 K is 3-6% lower than that of MnWO4 Fe

(Fig. 4a). WO4

The of was derived by substituting the fitted heat capacity function and ∆𝑓𝐺0𝑃𝑇 MnWO4

other thermodynamic data of in Table 1 into the equation (6) (see Supplementary MnWO4

data 2). The of from 200 to 400 oC is 8-9 % higher than that of (Fig. ∆𝑓𝐺0𝑃𝑇 MnWO4 FeWO4

4b). The of , , and were calculated from the thermodynamic data ∆𝑓𝐺0𝑃𝑇 Mn2 + Fe2 + WO4

2 ―

in SUPCRT (see Fig. 5). Thus, the solubility product of was reproduced by the 𝐾𝑠𝑝 MnWO4

equation (4). Horner (1979) also reproduced the of using the empirical formula 𝐾𝑠𝑝 MnWO4

proposed by Chernysh and Ivanova (1969), but his differs from that of this study by 𝐾𝑠𝑝

three orders of magnitude maximum (Fig. 6). of reproduced by this study 𝐾𝑠𝑝 MnWO4

10

seems more reasonable because the thermodynamic data required for calculating the

standard reaction Gibbs energy of dissolution differ from those of within MnWO4 FeWO4

one order of magnitude (Table 1 and Fig. 3-5). Thus, the solubility product of fitted MnWO4

by this study was used in the model.

3.2 The formation constant of 𝐌𝐧𝐂𝐥𝟎𝟐

Mn is transported mainly in the form of and chloride complexes like and Mn2 + MnCl02

in hydrothermal fluids (Boctor, 1985; Gammons and Seward, 1996; Suleimenov and MnCl +

Seward, 2000). Several laboratory experiments have been conducted to determine

equilibrium constants of at high temperatures. Gammons and Mn2 + + 2Cl ― = MnCl02

Seward (1996) measured the formation constants of at temperatures up to 300 oC MnCl02

using solubility measurements, and Suleimenov and Seward (2000) using ultraviolet

spectra. Tian et al. (2014) also measured formation constants of at MnCl2(H2O)2

temperatures up to 550 oC using in situ X-ray absorption spectroscopy. The three sources of

experimental data were used to fit the density model of Anderson et al. (1991), respectively:

(8)𝑙𝑛𝐾 = 𝑝1 + 𝑝2/𝑇 + 𝑝3𝑙𝑛𝜌/𝑇

, in which is the natural logarithm of the equilibrium constant K, , , are 𝑙𝑛𝐾 𝑝1 𝑝2 𝑝3

empirical parameters, and is water density. The IAPWS-95 formulation was used to 𝜌

reproduce water density (Wagner and Pruss, 2002). The three empirical equations have a

high fitting degree (Table 2 and Fig. 7a-7c).

The three empirical equations were used to reproduce formation constants of at MnCl02

the same temperature and pressure conditions (Fig. 7d). The values of Gammons and

Seward (1996) and Tian et al., (2014) are higher than those of Suleimenov and Seward

11

(2000) at 300-400 oC. Both (a tetrahedral complex) and (a MnCl2(H2O)2 MnCl2(H2O)4

octahedral complex) exist in hydrothermal fluids at temperatures over 200 oC, and the

former exceeds the latter over 300 oC (Tian et al., 2014). This suggests that formation

constants of at temperatures over 200 oC should be higher than those of MnCl02 MnCl2

; therefore, the experimental data of Suleimenov and Seward (2000) may (H2O)2

underestimate the formation constants of at temperatures 300 oC. The formation MnCl02 ≥

constants of fitted from Tian et al., (2014) are 0.44-0.72 log units lower than MnCl2(H2O)2

those of fitted from Gammons and Seward (1996). A reasonable explaination for this MnCl02

difference is that the formation constants of from Gammons and Seward (1996) MnCl02

probably includes constributions from both the and identified by MnCl2(H2O)2 MnCl2(H2O)4

Tian et al., (2014). Therefore, the empirical equation fitted from Gammons and Seward

(1996) was used in the models.

3.3 High-order Fe (II) and Mn (II) chloride complexes

High-order chloride complex of Fe (II) and Mn (II) were found using X-ray absorption

spectroscopy measurements (e.g. Testemale et al., 2009; Tian et al., 2014). , a FeCl2 ―4

higher order chloride complex of Fe (II) is stable at high temperature (>300 oC) and high

chloride molality (>2 mol/kg) (Testemale et al., 2009). , a higher order chloride MnCl ―3

complex of Mn (II), was found to be the dominant species in high-salinity (>3 mol/kg

chloride) and high-temperature ( 400 oC) solutions. The conditions of the dominance of ≥

these two high-order chloride complexes overlap the mineralizing conditions of tungsten

deposits in the world. Thus, and were considered in the models presented FeCl2 ―4 MnCl ―

3

here.

12

The formation constants of from Testemale et al., (2009) and the formation FeCl2 ―4

constants of from Tian et al., (2014) were employed to fit the density model MnCl ―3

(equation 8), respectively. The empirical functions fit those experimental data well (see

Table 2), and formation constants of both and increase with temperature FeCl2 ―4 MnCl ―

3

but decrease with pressure (Fig. 8).

4. Thermodynamic modeling for fluids in the W-Mn-Cl-Na-O-H and

W-Fe-Cl-Na-O-H systems

Wolframite solubility in hydrothermal fluids was constraint by thermodynamic models in

the W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H systems, respectively. For the W-Mn-Cl-Na-O-H

system, was assumed to be saturated in hydrothermal fluids. Seventeen equations MnWO4

were incorporated in the models to solve the concentrations of the seventeen species (Table

3). Among those equations, thirteen non-linear equations were established from the thirteen

reactions. For example, the non-linear equation for the association of Na+ and Cl- into NaClo

(the fifth reaction in Table 3) is:

𝑙𝑜𝑔𝐾 =𝛾𝑁𝑎𝐶𝑙𝑜[𝑁𝑎𝐶𝑙𝑜]

𝛾𝑁𝑎 + [𝑁𝑎 + ]𝛾𝐶𝑙 ― [𝐶𝑙 ― ] (8)

in which is the equilibrium constant; and are the concentration and the 𝑙𝑜𝑔𝐾 [𝑁𝑎𝐶𝑙𝑜] 𝛾𝑁𝑎𝐶𝑙𝑜

activity coefficient of in aqueous solutions. The other four equations were obtained 𝑁𝑎𝐶𝑙𝑜

from the charge and mass balance relations shown in Table 3.

Similarly, was assumed to be saturated in hydrothermal fluids in the FeWO4

thermodynamic model for the W-Fe-Cl-Na-O-H system. Another seventeen equations were

established from thirteen reactions and four charge and mass balance relations shown in

13

Table 4.

The activity of a species in electrolyte solutions is its effective concentration and equals

its concentration multiplied by its activity coefficient. The activity coefficients of electrically

charged species in the models were calculated by an extended Debye-Hückel equation as

parameterized by Helgeson et al. (1981) for NaCl-dominated solutions to high pressure and

temperature :

𝑙𝑜𝑔𝛾𝑖 =―𝐴𝑧2

𝑖 𝐼

1 + 𝑎𝐵 𝐼+ 𝑏𝐼 (9)

𝐼 =12

𝑛

∑𝑖 = 1

𝑐𝑖𝑧2𝑖 (10)

in which is the activity coefficient， is the charge number, A and B are two parameters 𝛾𝑖 𝑧𝑖

related to the dielectric constant and density of water, and are temperature-dependent 𝑎 𝑏

constants, is the ionic strength in mol/kg, and is the molar concentration. The activity 𝐼 𝑐𝑖

coefficients of the neutral species (e.g. HCl, NaCl) and the activity of H2O in our models

were assumed to unity.

Activity coefficients of charged species and the equilibrium constants of the reactions

were calculated using the R package CHNOSZ developed by Dick (2019). CHNOSZ is an

open-source R language package that uses the revised Helgeson-Kirkham-Flowers

electrostatic equations of state (Helgeson et al., 1981) and the thermodynamic properties of

minerals and aqueous species in SUPCRT (Johnson et al., 1992). The extended term

parameter (‘B-dot’) of the extended Debye-Hückel equation in CHNOSZ is derived from the

data of Helgeson (1969) and Helgeson et al., (1981) and explorations of Manning et al.

(2013) who predicts values of B-dot up to 1000 oC and 30 kbars using the empirical

14

correlations with the density of water. The nonlinear equations were solved using another R

language package rootSolve (cf. Soetaert and Herman, 2008), and the solving process is

shown in Appendix 1.

The temperature, pressure, salinity, and pH levels used in the models are 300-400 oC,

500-1500 bars, 5-15 wt. % NaCl equivalent, and pH=3-9, respectively (see section 2).The

model of (equations 1 and 2) was first calculated and compared to the results of λ = 10

and . The output of all the calculations is listed in Supplementary data 3.λ = 100 λ = 1000

5. Results

5.1 W-Mn-Cl-Na-O-H system

It was assumed that was fixed in the model. The dominant tungsten species at λ = 10

300-400 oC changes from , , to as pH increases from 3 to 9 (Fig. 9a H2WO04 HWO ―

4 WO2 ―4

and 9c). Manganese species at 400 oC is dominated by independent on pH. The MnCl02

dominant manganese species at 300 oC changes to MnO0 as pH moves to alkaline levels.

A few to thousands of ppm tungsten can be dissolved in hydrothermal fluids.

Hübnerite solubility is positively correlated to fluid temperature and salinity (Fig. 10). Note

that hübnerite solubility at alkaline conditions is less sensitive to temperature than that at

acidic conditions. More tungsten would dissolve as pH moves towards more acidic and more

alkaline conditions. Hübnerite solubility decreases with increasing fluid pressure at pH<8.5

(Fig. 11). Typical W-mineralizing fluids with a pH=4-6 can dissolve a few to hundreds of ppm

tungsten, while alkaline hydrothermal fluids dissolve tens of ppm at most.

Hübnerite solubility decreases by approximately one order of magnitude as increases λ

15

from 10 to 1000 (Fig. 12). A few to hundreds ppm of tungsten can be dissolved in

hydrothermal fluids with a pH=4-6.

5.2 W-Fe-Cl-Na-O-H system

was first used in the model of W-Fe-Cl-Na-O-H. Iron species is dominated by λ = 10

at pH<7 and by HFeO2- at pH>8 (Fig. 13). The curve of ferberite solubility against pH FeCl2 ―

4

is an upward-opening parabola. Acidic hydrothermal fluids dissolve approximately 1000 ppm

tungsten at most, while alkaline hydrothermal fluids can contain hundreds of ppm tungsten

(Fig. 14). Ferberite solubility increases with fluid temperature and salinity at acidic conditions

but it becomes insensitive to fluid temperature and salinity at alkaline conditions (Fig. 14).

The influence of fluid pressure on ferberite solubility depends on pH (Fig. 15). A few to

hundreds of ppm tungsten can be dissolved in hydrothermal fluids with pH=4-6. Fig. 16

shows that an increase of from 10 to 1000 causes a decrease of ferberite solubility by λ

1-1.5 orders of magnitude.

5.3 difference between Mn and Fe molalities at a fixed W concentration

To examine the difference between Mn and Fe in hydrothermal fluids, the concentration

of total tungsten species in hydrothermal fluids was fixed to replace the mass constraints

expressed by equation (1) and (2) for the models of W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H,

respectively. Tungsten concentrations of 50 ppm and 200 ppm were used in the models (see

Fig. 1), and other charge and mass constraints remained unchanged. Thus, the molalities of

Mn and Fe in the two models were calculated, respectively. In hydrothermal fluids with 50

ppm W, 1.4-5.4 times more Mn is needed than Fe at acidic conditions, while 2-3 orders of

magnitude more Fe is needed than Mn at alkaline conditions (Fig. 17). Increasing the fixed

16

tungsten concentration to 200 ppm does not alter the trend of more Mn in acidic

hydrothermal fluids and more Fe at alkaline conditions (Fig. 18).

6. Discussion

6.1 Comparisons to other thermodynamic modeling and experimental

resultsThe thermodynamic predictions in Wood and Samson (1998) show that the

predominant tungsten species changes from and to as pH H2WO04 HWO ―

4 WO2 ―4

increases from acidic to alkaline conditions (see their Fig. 4). This is in accord with the

dominant W species shown in Fig. 9a and 9c.

Tian and his co-authors (2014) also calculated the Mn(II) species percentages with HCl

concentrations from 0.0003 to 0.0043 mol/kg from 200 to 450 oC. From their Fig. 9,

concentrations of (the sum of and ) exceed those of MnCl02 MnCl2(H2O)2 MnCl2(H2O)4

under conditions of 300-400 oC and 10 wt. % NaCl equivalent. This is consistent with MnCl ―3

the results of this study at acidic conditions (Fig. 9b and 9d).

is the dominant iron(II) species at acidic conditions in the model of FeCl2 ―4

W-Fe-Cl-Na-O-H (Fig. 13). This is consistent with the calculations of Testemale et al.,

(2009). At alkaline conditions, the dominant iron(II) species changes to be HFeO2- (Fig. 13),

which is also consistent with the results in Wood and Samson (2000).

Recent crystallization experiments of hübnerite suggest that hübnerite is significantly

dissolved in strongly alkaline fluids at 300-400 oC (Li et al., 2018a). This is accord with the

high hübnerite solubility in alkaline fluids found from this study (see Fig.10 and 11).

6.2 Wolframite solubility and precipitation mechanisms

Thermodynamic models in the W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H systems put two

17

end-member constraints on wolframite solubility and precipitation mechanisms in

hydrothermal fluids. Both hübnerite and ferberite solubility in hydrothermal fluids reach a few

to hundreds of ppm (Fig. 10, 11, 12, 14, 15, and 16). This is consistent with the W

concentrations of fluid inclusions from tungsten deposits in the world (Fig. 1). At pH=4-6,

hübnerite solubility is slightly higher than ferberite solubility, while the latter is significantly

higher than the former at alkaline conditions (Fig. 10 and 14).

Both hübnerite and ferberite solubilities in hydrothermal fluids decrease as pH moves to

neutral levels (Fig. 10 and 14). Therefore, neutralization by fluid mixing or fluid-rock

interaction would cause precipitation of hübnerite and ferberite. A decrease in temperature

also precipitates hübnerite and ferberite from acidic fluids, but simple cooling becomes less

efficient in precipitating ferberite and hübnerite at alkaline conditions (Fig. 10 and 14). This

may explain why alkali metasomatism (e.g. albitization) causes little W mineralization in

tungsten deposits (e.g. He, 1987; Hu et al., 2004; Liu and Ma, 1993; Pirajno and SchlogI,

1987; Zhang et al., 2018b). A decrease in fluid salinity could also precipitate hübnerite and

ferberite from acidic fluids, but ferberite solubility in alkaline fluids is less sensitive to fluid

salinity than in acidic fluids. The insensitivity of wolframite solubility to temperature and

salinity may prevent precipitation of wolframite from alkaline fluids and allow significant

tungsten mineralization at later stages. This may explain why the main mineralization stage

of giant tungsten deposits occurred at greisen stages rather than at alkaline stages (e.g. the

Dahutang tungsten deposit in Zhang et al., 2018b).

It is found from this study that a decrease in fluid pressure increases solubilities of both

hübnerite and ferberite solubility in acidic hydrothermal fluids (Fig. 11 and 15); therefore,

18

fluid pressure drop cannot cause wolframite precipitation. This is in contrast with Liu et al.

(2018) where CO2 loss accompanying a drop in fluid pressure is found to be effective

mechanisms for ferberite precipitation. This gap can be reconciled by that the influence of

fluid pressure on wolframite solubility depends on the existence of CO2 in mineralizing fluids.

6.3 Mn/Fe ratios in wolframite

The thermodynamic models presented here provide an insight into the factors

controlling Mn/Fe ratios in wolframite. The availability of Fe and Mn is essentially important

to precipitate wolframite from the mineralizing fluids (e.g. Jiang et al., 2018;

Lecumberri-Sanchez et al., 2017; Yang et al., 2019; Zhang et al., 2018b). The results of this

study suggest that more Mn than Fe is needed to produce mineralizing fluids with the same

W concentration at acidic conditions (see the dashed box in Fig. 17 and 18), especially at

higher temperatures. This indicates that hübnerite precipitation requires Mn-rich mineralizing

fluids, and the Mn/Fe ratio of mineralizing fluids controls the wolframite composition. This is

also found by Amossé (1978) using thermo-chemical study of the system MnWO4-FeWO4.

At least two factors affect the Mn/Fe ratio of mineralizing fluids. The one factor is the

Mn/Fe ratio of the granite magma genetically related to tungsten deposits. Tungsten

mineralization is genetically related to the peraluminous S- and I-type granites derived from

partial melting of crustal rocks (e.g. Černý et al., 2005; Harlaux et al., 2017; Zhao et al.,

2017), which contains more Fe than Mn on average (Rudnick and Gao, 2013). The Fe (II)

concentrations in the W-related granites are at least 1-2 orders of magnitude higher than

those of Mn (II) (e.g. Bussink, 1984; Hall, 1971; Ramı́rez and Grundvig, 2000; René, 2018;

19

Stussi, 1989; Wang et al., 2017). The other factor is the partition coefficients of Mn and Fe

between melt and fluid. Zajacz et al. (2008)’s laboratory experiments on coexisting silicate

melts and fluid inclusions from the Ehrenfriedersdorf pegmatite in the Erzgebirge suggest

that Mn and Fe have similar fluid/melt coefficients. Therefore, W-related magmas tend to

release Fe-rich mineralizing fluids rather than Mn-rich ones. This may explain why hübnerite

is less common than ferberite in most tungsten deposits. For the case when Mn-rich

mineralizing fluids are released from the parental magma or buffered by Mn-rich wallrocks,

hübnerite is more likely to precipitate at an early stage. As Mn is consumed, the wolframite

precipitated at later stages tends to be relatively Fe-rich. This prediction is consistent with a

common phenomenon among vein-type tungsten deposits that wolframite crystallized from

early to late shows a decrease in Mn/Fe ratios (Michaud and Pichavant, 2019).

7. Conclusions

Fluid-buffered thermodynamic models of the W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H

systems were established to examine chemical controls on wolframite solubility in

hydrothermal fluids and Mn/Fe ratios in wolframite. Most thermodynamic data used in the

model were accessed from SUPCRT updated until 2017, and the heat capacity of MnWO4,

the formation constant of , , and were fitted from experimental data in MnCl02 MnCl ―

3 FeCl2 ―4

the literature. The thermodynamic models provide the following implications:

(1) The predominant tungsten, manganese, and iron species in hydrothermal fluids at

typical W-mineralizing conditions are , and , respectively.HWO ―4 MnCl0

2 FeCl2 ―4

(2) Both hübnerite solubility and ferberite solubility in acidic hydrothermal fluids reach up

20

to hundreds of ppm. Hübnerite and ferberite deposition could be triggered by an increase in

pH and a decrease in fluid temperature and salinity. A drop in fluid pressure cannot

precipitate hübnerite and ferberite.

(3) Hübnerite and ferberite have a solubility of tens to hundreds of ppm in alkaline

hydrothermal fluids, but their solubilities are insensitive to fluid temperature and salinity. This

may explain why alkaline metasomatism seldom causes significant W mineralization. The

insensitivity of ferberite and hübnerite solubility to fluid temperature and salinity may also

prevent W from precipitating from alkaline fluids at an early stage and allow significant W

mineralization in later greisens.

(4) The Mn/Fe ratio of mineralizing fluids is the principal variable controlling Mn/Fe

ratios in wolframite. More Mn than Fe is needed to maintain hydrothermal fluids with the

same W concentration, but more supply of Fe than Mn from the fertile magma tends to

produce Fe-rich mineralizing fluids. This may one of reasons why ferberite is more common

than hübnerite in tungsten deposits and why hübnerite is more likely to precipitate at an early

stage.

Acknowledgements

The work was financially funded by the National Natural Science Foundation of China

(41602088, 41702095), a China Geological Survey project (DD20190161), and a Basic

Research Fund for Central Research Institutes (JYYWF20180602). X.C. Liu appreciates

Zhang Dehui for discussion on high-order Fe (II) and Mn (II) chloride complexes and thanks

Han Shuqin for her help in translating a Russian paper, experimental data of which were

21

used in this study. Tian Yuan’ and Mei Yuan’s explanations also helped X.C. Liu understand

different Mn(II) chloride complexes in thei paper. The author appreciates Weihua Liu,

another anonymous reviewer, and the editor for their comments and advices on the original

manuscript.

Appendix 1

Nonlinear equations driven by reaction and balance constraints shown in Table 3 and

Table 4 were solved by the the R package rootSolve. Good initial values of the variables are

a prerequisite for deriving the optimal roots (Crerar, 1975). The procedure of solving the

nonlinear equations in the models is as follows:

(1) The initial ionic strength is set to be half of the morlality of NaCl in solutions, and the 𝐼0

initial activities of both Na+ and Cl- equal . 𝐼0

(2) Calculate the activity coefficients of all ionic speices using the equation (9) with the initial

ionic strength . Note that the only species-specific parameter required in equation (9) is 𝐼0

the electrical charge, meaning that the activity coefficient of Na+ equals that of H+ and the

activity coefficient of Fe2+ equals that of WO42-.

(3) Calculate the concentration of H+ using its activity coefficient and a given pH. According

the non-linear equations like equation (8), calculate all other species’ initial activities one

by one using using the initial activities of H+, Na+, and Cl-. These initial activities of ionic

speices will be used as initial values for solving the nonlinear equations.

(4) Solve the nonlinear equations simultaneously using the R package rootSolve. Then,

update the ionic strength and the activity coefficients of ionic speices and take the roots as

the initial values for the next solving.

(5) Repeat step (4) until the absolute error of the ionic strength is less than a threshond. A

threshold of 0.01 was used in the models, and 3-5 iterations were often needed before

22

terminating iterations.

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Table 1 The thermodynamic data of and FeWO4 MnWO4

∆𝑓𝐺0298 (𝑘𝐽/𝑚𝑜𝑙) 𝑆0

298(𝐽𝐾 ―1𝑚𝑜𝑙 ―1) 𝐶𝑝(𝐽𝐾 ―1𝑚𝑜𝑙 ―1) 𝑉0298,1𝑏𝑎𝑟(𝐽𝑏𝑎𝑟 ―1𝑚𝑜𝑙 ―1)

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FeWO4 1085.155 131.8 68.87 + 1.88 × 10 ―4T ― 9.08 × 10 ―5T2 4.038

MnWO4 1235.4 132.5155.68 + 9.15 × 10 ―2T ― 5.31 × 10 ―5T2

―1.17 × 103T ―0.5 + 5.30 × 104T ―24.189

The and of are from Polya (1990), and the of was fitted in this study. The ∆𝑓𝐺0298 𝐶𝑝 FeWO4 𝐶𝑝 MnWO4

other parameters are from Robie and Hemingway (1995).

Table 2 the fitted coefficients for the formation constants of , , , and MnCl02 MnCl2(H2O)2 FeCl2 +

4 MnCl ―3

Reactions p1 p2 (K) p3 (K m3/kg) Data sources

Mn2+ + 2Cl- = MnCl20 12.82 143203.80 -21707.02 1

Mn(H2O)62+ + 2Cl- =

MnCl2(H2O)2(aq) + 4H2O

23.00 38543.20 -6947.83 2

Mn2+ + 2Cl- = MnCl20 17.99 116125.25 -18171.62 3

Fe2+ + 4Cl- = FeCl42- -7.35 -15516.49 23144.03 4

Mn2+ + 3Cl- = MnCl3- 20.18 106765.42 -16943.63 3

1, Gammons and Seward (1996); 2, Suleimenov and Seward (2000); 3, Tian et al., (2014); 4, Testemale

et al., (2009).

Table 3 Chemical reactions and mass and charge balance constraints for the model of W-Mn-Cl-Na-O-H system

Number Reaction and balance constraints1 H2O = H+ + OH-

36

2 H+ + Cl- = HCl0

3 H++ WO42- = HWO4

-

4 H+ + HWO4- = H2WO4

0

5 Na+ + Cl- = NaCl0

6 Na+ + H2O = NaOH0 + H+

7 MnWO4(s) = Mn2++ WO42-

8 Mn2++Cl- = MnCl+

9 Mn2+ + 2Cl- = MnCl20

10 Mn2+ + 3Cl- = MnCl3-

11 Mn2+ + H2O = MnOH+ + H+

12 Mn2+ + H2O = MnO0 + 2H+

13 Mn2+ + 2H2O = HMnO2- + 3H+

14. Charge balance [H+]+[Na+]+2[Mn2+]+[MnCl+]+[MnOH+]= [OH-] +[Cl-]+ [HWO4

-]+2[WO42-]+[MnCl3-]+[HMnO2

-]15. Cl mass balance ΣCl=[Cl-]+[HCl0]+[NaCl0]+[MnCl+]+2[MnCl20]+3[MnCl3-]

16. ΣW =ΣMn/λ ([H2WO40]+[HWO4

-]+[WO42-]) =λ

[Mn2+]+[MnCl+]+[MnCl20]+[MnCl3-]+[MnOH+]+[MnO0]+[HMnO2-]

17. A given pH from 3 to 9

[H+]=10 ―pH/γH +

represents the species’ molality in solutions. is a constant ranging from 10 to 103.[ ∙ ] λ

Table 4 Chemical reactions and mass and charge balance constraints for the model of W-Fe-Cl-Na-O-H system

Number Reaction and balance constraints

37

1 H2O = H+ + OH-

2 H+ + Cl- = HCl0

3 H++ WO42- = HWO4

-

4 H+ + HWO4- = H2WO4

0

5 Na+ + Cl- = NaCl0

6 Na+ + H2O = NaOH0 + H+

7 FeWO4(s) = Fe2++ WO42-

8 Fe2++Cl- = FeCl+

9 Fe2+ + 2Cl- = FeCl20

10 Fe2+ + 4Cl- = FeCl42-

11 Fe2+ + H2O = FeOH+ + H+

12 Fe2+ + H2O = FeO0 + 2H+

13 Fe2+ + 2H2O = HFeO2- + 3H+

14. Charge balance [H+]+[Na+]+2[Fe2+]+[FeCl+]+[FeOH+]= [OH-] +[Cl-]+ [HWO4

-]+2[WO42-]+[HFeO2

-]+2[FeCl42-]15. Cl mass balance ΣCl=[Cl-]+[HCl0]+[NaCl0]+[FeCl+]+2[FeCl20]+4[FeCl42-]

16. ΣW =ΣFe/λ ([H2WO40]+[HWO4

-]+[WO42-]) =λ

[Fe2+]+[FeCl+]+[FeCl20]+[FeOH+]+[FeO0]+[HFeO2-]+[FeCl42-]

17. A given pH from 3 to 9

[H+]=10 ―pH/γH +

represents the species’ molality in solutions. is a constant ranging from 10 to 103.[ ∙ ] λ

Fig. 1 The heat capacity of MnWO4 fitted from experimental data of Yakovleva and Rezukhina (1960) and

Landee and Westrum (1976)

The squares and dots represent experimental data of Yakovleva and Rezukhina (1960) and Landee and

38

Westrum (1976), respectively. The red curve is reproduced from the empirical function fitted in this study

and the fitting degree R2=99.53 %. The blue curve is reproduced from the function of Yakovleva and

Rezukhina (1960).

Fig. 2 Comparisons on the heat capacity (a) and the Gibbs free energy (b) of FeWO4 and MnWO4

(a) The heat capacity of FeWO4 was calculated from the empirical equation proposed by Polya (1990),

while the heat capacity of MnWO4 was reproduced from the empirical equation fitted in this study. (b) The

Gibbs free energy of FeWO4 and MnWO4 were reproduced by the equation (4) at 1000 bars.

Fig. 3 The Gibbs free energy of and at 1000 bars reproduced from SUPCRTMn2 + Fe2 +

Fig. 4 The isobaric solubility product of and FeWO4 MnWO4

Fig. 5 The formation constants of fitted from experimental data in the literatureMnCl02

(a) The fitted data are from Gammons and Seward (1996) who conducted solubility experiments at

saturated vapour pressures. The fitting degree R2=99.99%. (b) The experimental data of Suleimenov and

Seward (2000) were used. The data were measured at saturated vapour pressures. The fitting degree

R2=99.87%. (c) The formation constants of in Tian et al., (2014) were used to fit the density MnCl2(H2O)2

model. The fitting degree R2=99.98%. (d) It compares the formation constants of at 500 bars MnCl02

reproduced from the three empirical equations.

Fig. 6 The formation constant (log K) of (a) and (b)MnCl ―3 FeCl2 +

4

(a) The lines are reproduced by fitting the experimental data (the dots) from Testemale et al., (2009). The

fitting degree R2=99.99%. (b) The lines are reproduced by fitting the experimental data (the dots) from

Tian et al., (2014). The fitting degree R2=99.40%.

Fig. 7 Frequency distribution of tungsten concentrations of fluid inclusions in tungsten deposits

39

The tungsten concentrations (unit in ppm) have been logarithmically transformed with respect to base 10.

Fig. 8 The molality ratios of W/Fe (Fig. 8a, upper), W/Mn (Fig. 8b, lower), and W/(Fe+Mn) (Fig. 8b) of fluid

inclusions in tungsten deposits

Fig. 9 The dominant tungsten (Fig. 9a and 9c) and manganese (Fig. 9b and 9d) species at 500 bars and

10 wt.% NaCl equivalent

The W (Mn) species percentage in Y-axis is calculated by the morlality ratio of a W (Mn) species against

the totall W (Mn).

Fig. 10 Influences of fluid temperature (a) and salinity (b) on hübnerite solubility

The dashed box represents the typical pH of W-mineralizing fluids.

Fig. 11 Influences of fluid pressure on hübnerite solubility

The dashed box represents the typical pH of W-mineralizing fluids.

Fig. 12 Influences of Mn/W ratios (see in equation (7)) on hübnerite solubilityλ

The dashed box represents the typical pH of W-mineralizing fluids.

Fig. 13 The dominant iron at 400 oC (a) and 300 oC (b) and 10 wt.% NaCl equivalent

The species percentage in Y-axis is calculated by the morlality ratio of a Fe species against the totall Fe.

Fig. 14 Influences of fluid temperature (a) and salinity (b) on ferberite solubility

The dashed box represents the typical pH of W-mineralizing fluids.

Fig. 15 Influences of fluid pressure on ferberite solubility

The dashed box represents the typical pH of W-mineralizing fluids.

Fig. 16 Influences of Fe/W ratios (see in equation (8)) on ferberite solubilityλ

The dashed box represents the typical pH of W-mineralizing fluids.

40

Fig. 17 The Mn/Fe molality ratios at a fixed 50 ppm (a) and 200 ppm (b) W concentration

For the case of W=50 ppm, the molalities of Mn and Fe were calculated from the models of

W-Mn-Cl-Na-O-H and W-Fe-Cl-Na-O-H, respectively. The dashed box represents the typical pH of

W-mineralizing fluids. More Mn than Fe is needed to form mineralizing fluids with the same W

concentration.

1. Fluid-buffered thermodynamic models were built for vein-type tungsten deposits.2. Tungsten solubility in acidic fluids is sensitive to temperature, pH, and salinity.3. MnWO4 and FeWO4 can be significantly dissolved in alkaline hydrothermal fluids.4. Tungsten solubility in alkaline fluids is insensitive to temperature and salinity.5. The Mn/Fe ratio of mineralizing fluids controls Mn/Fe ratios in wolframite.