Thermodynamics of schafarzikite (FeSb₂O$_4$) and tripuhyite (FeSbO$_4$)

Abstract

In this work, we investigated the thermodynamic properties of synthetic schafarzikite (FeSb₂O$_4$) and tripuhyite (FeSbO$_4$). Low-temperature heat capacity ($C_p$) was determined by relaxation calorimetry. From these data, third-law entropy was calculated as $110.7\pm 1.3$ J mol$^{-1}$K$^{-1}$ for tripuhyite and $187.1\pm 2.2$ J mol$^{-1}$ K$^{-1}$ for schafarzikite. Using previously published $\Delta _fG^o$ values for both phases, we calculated their $\Delta _fH^o$ as $-947.8\pm 2.2$ for tripuhyite and $-1061.2\pm 4.4$ for schafarzikite. The accuracy of the data sets was tested by entropy estimates and calculation of $\Delta _fH^o$ from estimated lattice energies (via Kapustinskii equation). Measurements of $C_p$ above $T = 300$ K were augmented by extrapolation to $T = 700$ K with the frequencies of acoustic and optic modes, using the Kieffer $C_p$ model. A set of equilibrium constants ($\log K$) for tripuhyite, schafarzikite, and several related phases was calculated and presented in a format that can be employed in commonly used geochemical codes. Calculations suggest that tripuhyite has a stability field that extends over a wide range of pH-p$\epsilon$ conditions at $T = 298.15$ K. Schafarzikite and hydrothermal oxides of antimony (valentinite, kermesite, and senarmontite) can form by oxidative dissolution and remobilization of pre-existing stibnite ores.

Introduction

Antimony occurs in natural systems mostly in the oxidation states +3 and +5. Lower oxidation states, such as in native antimony (Sb$^0$) or antimonide minerals (Sb$^-$, e.g., in gudmundite, FeSbS) are less common and restricted to strongly reducing environments (e.g., Normand et al. 1996). In hydrothermal fluids, antimony [as Sb(III)] is mostly transported as hydroxocomplexes [Sb(OH)$_3^0$] or thiocomplexes (HSb₂S$_4^-$) (Krupp 1988; Spycher and Reed 1989; Shikina and Zotov 1991). Phase relations and the transport of antimony in sulfur-rich hydrothermal fluids (HS$^-$ molalities of >0.01 m) are known (Williams-Jones and Normand 1997) and the by far most common product is stibnite (Sb₂S$_3$). Other primary minerals of Sb(III) are less common to rare, including sulfides (e.g., tetrahedrite, (Cu,Ag)$_{10}$ (Fe,Zn)₂Sb$_4$S$_{13}$, or berthierite, FeSb₂S$_4$) or oxides (kermesite, Sb₂S₂O, valentinite, Sb₂O$_3$) (Majzlan 2021). A rare Sb(III) oxide is schafarzikite (FeSb₂O$_4$), either as a primary mineral (Sejkora et al. 2007) or a product of weathering (Krenner 1921; Leverett et al. 2012). Minerals of pentavalent antimony are usually late products of weathering (Majzlan et al. 2011; Radková Borčinová et al. 2020), the early and intermediate ones still containing Sb³⁺ (e.g., secondary kermesite, cervantite, stibiconite, Majzlan 2021). There are exceptions, though, such as the description of rutile-tripuhyite (TiO₂-FeSbO$_4$) solid solution in epigenetic quartz veins, presumably related to “residual pegmatitic solutions” (Cabella et al. 2003). Among the secondary Sb(V) minerals, tripuhyite appears to be particularly abundant (Leverett et al. 2012) because of its low solubility and abundance of Fe at most sites where Sb minerals weather. The mineral was reported from mining sites (also under the names jujuyite and squawcreekite, Hussak and Prior 1897; Ahlfeld 1948, and others).

In this work, we have investigated the thermodynamic properties of schafarzikite and tripuhyite. Relaxation calorimetry and differential scanning calorimetry were used to measure heat capacity of both phases and to calculate their third-law entropies. Selection of Gibbs free energies of formation from the literature generated a full data set of thermodynamic functions at $T = 298.15$ K. High-temperature properties were derived by extrapolation of the experimental heat capacity data to 700 K, using the Kieffer model. The accuracy of the resulting data was tested by construction of appropriate phase diagrams. Furthermore, the solubility of schafarzikite and the associated minerals (kermesite, valentinite, senarmontite) was calculated and used to elucidate the formation of natural assemblages of these minerals.

Materials and methods

Tripuhyite was synthesized by mixing Fe₂O$_3$ (319.38 mg) and Sb₂O$_3$ (582.99 mg) powders and heating them at 1250 K for 24 h in a corundum boat in air (Martinelli et al. 2002; Leverett et al. 2012). The oxides were mixed in a stoichiometric (1:1 molar) ratio thoroughly by grinding the mixture in an agate mortar. The difficulty related to this synthesis is the volatility of Sb₂O$_3$ at high temperatures, evidenced by yellow dusting on the corundum boat. The amount of Sb₂O$_3$ that will be lost during the high-temperature treatment cannot be predicted. Therefore, despite numerous attempts, the product was never phase-pure tripuhyite, although tripuhyite was always the dominant phase. All samples contained minor amount of either hematite or senarmontite. Very low solubility of tripuhyite allowed for an additional treatment in 5 M HCl of the tripuhyite-senarmontite mixtures. Repeated soaking for 6 h at room temperature, filtering, and drying led eventually to a pure sample and removed senarmontite completely. This sample was used for the further experiments, including calorimetry.

Schafarzikite was synthesized from a mixture of Fe₂O$_3$ (14.650 mg), Sb₂O$_3$ (80.226 mg), and metallic Fe (5.123 mg) (Chater et al. 1985; Leverett et al. 2012). The initial chemicals were mixed as thoroughly as possible and sealed in evacuated silica tubes. The silica tubes were heated in an oven at 770 K for 10 days. Many runs were carried out, without successful synthesis of pure schafarzikite. Even though fine, powdery metallic iron was used, this chemical was found not to react to completion. Its presence was easily checked in the sealed tubes by a magnet. Removing the iron and senarmontite impurities by an acid treatment turned out to be not feasible because schafarzikite dissolved fairly quickly. At the end of this treatment, not only the impurities but also schafarzikite itself were gone. Eventually, one of the runs produced pure schafarzikite, although there was no difference between this run and the other ones, either in the chemical composition of the starting mixture or the physical conditions (temperature, duration of heating).

Powder X-ray diffraction (pXRD) data of the solid samples were collected with a Bruker D8 ADVANCE with DAVINCI design, and with Cu K$\alpha$ radiation, Ni filter, and additionally with a Lynxeye 1D detector. A step size of 0.02° 2$\Theta$ and a 0.25 s time per step were used. Lattice parameters were refined using the JANA2006 program (Petříček et al. 2014).

Heat capacity ($C_p$) was measured by relaxation calorimetry using a commercial Physical Properties Measurement System (PPMS, from Quantum Design, San Diego, California). With due care, the accuracy can be within 1% from 5 to 300 K, and 5% from 0.7 to 5 K (Kennedy et al. 2007). Powdered samples were wrapped in a thin Al foil and compressed to produce a $\approx$ 0.5 mm thick pellet which was then placed onto the sample platform of the calorimeter for measurement. The heat capacity was measured in the PPMS in a 2–300 K temperature interval. The heat capacities at T > 280 K were measured by differential scanning calorimetry (DSC), up to 570 K for tripuhyite and up to 670 K for schafarzikite, using a Perkin Elmer Diamond DSC. Details of the method are described in Benisek et al. (2012).

Results

Both samples used in this work were phase-pure, with sharp powder X-ray diffraction peaks. Full-profile refinements gave the lattice parameters listed in Table 1. The data are shown in Figs. S1 and S2. The heat capacity of both samples as function of temperature is shown in Figs. 1 and 2. The $C_p$ data for both phases are listed in Tables S1 and S2.

Table 1 Lattice parameters of the studied samples

There is excellent agreement of the data for schafarzikite between this work and the earlier measurements of Chater et al. (1986). The agreement relates to both the magnitude of the heat capacity and also the position of the magnetic anomaly in the $C_p$ data. They also measured $C_p$ of the isostructural NiSb₂O$_4$ and the data are shown for comparison in Fig. 1. The difference in the third-law entropy calculated from our data and from those of Chater et al. (1986) for FeSb₂O$_4$ is only 0.1% (Table 2). The third-law entropy for NiSb₂O$_4$, calculated from the data in Chater et al. (1986), is also given in Table 2. Thermodynamic functions of tripuhyite and schafarzikite, calculated at regularly spaced temperature intervals, are listed in Tables S3 and S4.

Fig. 1

a Heat capacity of schafarzikite, measured by relaxation calorimetry, differential scanning calorimetry, and approximated by the Kieffer (1985) model, compared with previously published data for FeSb₂O$_4$ and NiSb$_2$O$_4$ (Chater et al. 1986). b The low-temperature region with the magnetic anomaly. The symbols used are the same as in a)

Fig. 2

Heat capacity of tripuhyite, measured by relaxation calorimetry, differential scanning calorimetry, and approximated by the Kieffer (1985) model

In the low-temperature data sets, there is a conspicuous lambda-type anomaly for schafarzikite, with a $C_p$ maximum at $T = 41.9$ K. This anomaly is undoubtedly related to a magnetic phase transition in this phase. The absence of a similar feature in the data for tripuhyite (Fig. 2) is surprising but the pXRD data (Fig. S1) showed that the sample consisted of pure and highly crystalline tripuhyite.

In the region of overlap, there is a good agreement between the relaxation-calorimetry and DSC data around room temperature. The difference is $+0.4$% for tripuhyite and $-0.8$% for schafarzikite. For fitting purposes, the DSC data were adjusted to match the relaxation-calorimetry data in the region of overlap.

The high-temperature data of tripuhyite are smooth up to the highest temperature of measurement. For schafarzikite, though, this is not the case. Above $\approx$ 470 K, the data show a broad and weak exothermic anomaly, interpreted as partial oxidation of the sample. For this reason, the data for schafarzikite above 470 K were excluded from fitting.

The low-temperature $C_p$ data were described by a series of polynomials and the $C_p/T$ function was integrated up to $T = 298.15$ K to obtain standard entropies for both phases. The results of the integration listed in regular temperature intervals are summarized in Tables S1 and S2.

Discussion

Check of the third-law entropies with the Neumann–Kopp rule

As the simplest approximation, the third-law entropies can be estimated as a sum of the entropies of the components. For example, for schafarzikite, S$^o$(FeSb$_2$O$_4$) $\approx$ S$^o$(FeO) + S$^o$(Sb$_2$O$_3$). Such a simple test may be performed as a rough accuracy check of the experimental values. The third-law entropies of the oxide components and the estimates for schafarzikite and tripuhyite are listed in Table 2. The estimates can be compared to the experimentally determined values in this study and calculated from C$_{p}$ data in Chater et al. (1986) (Table 2). The match for schafarzikite is excellent, with a difference of 1.9 %. For tripuhyite, the different is larger, 4.0 %, likely attributed to a less certain value of S$^o$(Sb$_2$O$_5$). This compound is hygroscopic and sensitive to oxygen pressure, therefore difficult to handle and measure.

Table 2 Third-law entropies of oxide components and entropy estimates for schafarzikite and tripuhyite

Selection of $\Delta _fG^o$ in this work

In this work, we relied on the $\Delta _fG^o$ from Leverett et al. (2012), based on their solubility experiments. There is an alternative set of $\Delta _fG^o$ values from the work of Swaminathan and Sreedharan (2003). They performed EMF measurements at high temperatures (between 750 and 1000 K) and extrapolated the results down to T = 298.15 K. The agreement of the $\Delta _fG^o$ values for schafarzikite is excellent, with $-959.4\pm 4.3$ kJ mol$^{-1}$ from Leverett et al. (2012) and $-962.5\pm 3.5$ kJ mol$^{-1}$ from Swaminathan and Sreedharan (2003). For tripuhyite, though, agreement is much worse, with $-836.8\pm 2.2$ kJ mol$^{-1}$ from Leverett et al. (2012) but $-878.8\pm 5.5$ kJ mol$^{-1}$ from Swaminathan and Sreedharan (2003). Even though Leverett et al. (2012) found the match ‘perfectly reasonable’, the difference of $\approx$40 kJ mol$^{-1}$ is too large. Given that the results of Swaminathan and Sreedharan (2003) are based on an extrapolation over $\approx$ 470 K, preference is given in this work to the solubility data of Leverett et al. (2012). Another argument in favor of the data set from Leverett et al. (2012), put forward by themselves, is the resulting solubility of tripuhyite. Leverett et al. (2012) considered the chemical reaction $\alpha -$FeOOH + Sb(OH)$^0_5 \rightarrow$ FeSbO$_4$ + 3 H$_2$O. If the $\Delta _fG^o$ from Swaminathan and Sreedharan (2003) would be accepted, then goethite ($\alpha -$FeOOH) would be predicted to react to tripuhyite at $\log a$(Sb(OH)$^0_5$) = $-18$. This conclusion speaks clearly against observations in nature. In our database of mine drainage waters (>1100 analyses) and unpolluted surface streams (>9000 analyses), $\log m$(Sb(V)) is equal to or higher than $-9$. If we accepted the $\Delta _fG^o$ datum from Swaminathan and Sreedharan (2003), it would mean that Sb in all these environments should be bound in tripuhyite. That, to our best knowledge, is not the case. Furthermore, the calculations of Burton et al. (2020) show that the aqueous molalities of Sb(V) would need to be as high as $10^{-3}$ to reach saturation with respect to tripuhyite. These are strong hints, albeit not a proof, that $\Delta _fG^o$ for tripuhyite from Swaminathan and Sreedharan (2003) is too exothermic and likely inaccurate.

Table 3 Thermodynamic data for tripuhyite and schafarzikite, used to derive the equilibrium constants for the dissolution reactions (5) and (6)

Check of the enthalpies of formation ($\Delta _fH^o$)

The enthalpies of formation, presented in Table 3, were calculated from the experimentally measured S$^o$, selected $\Delta _fG^o$, and entropies for pure elements from Robie and Hemingway (1995). The $\Delta _fH^o$ values can be tested against prediction by the Born-Haber cycle, assuming that the lattice energy (U$_L$) of the phases of interest is known. Using such a test, the enthalpies calculated in this work or the tabulated enthalpies of formation of gaseous ions can be tested for their accuracy. The determination of the latter enthalpies is beyond the scope of this work but the discrepancies detected here could be an impuls for re-evaluation of the enthalpy data.

Yoder and Flora (2005) suggested that the lattice energies of complex compounds can be approximated as a sum of the lattice energies of their components. For example, U$_L$(FeSb$_2$O$_4$) $\approx$ U$_L$(FeO) + U$_L$(Sb$_2$O$_3$). Yoder and Flora (2005) provided lattice energies for a number of components but not for oxides of antimony. Lattice energies (U$_L$) can be calculated with the Kapustinskii equation

$$\begin{aligned} U_L = \frac{1213.8 \nu \mid z^+ z^- \mid }{r^+ + r^-} \left( 1 - \frac{0.345}{r^+ + r^-} \right) \end{aligned}$$

(1)

where $r^+$ and $r^-$ are the crystal radii of the cation and anion, respectively; $z^+$ and $z^-$ are the nominal charges of the cation and anion, respectively; and $\nu$ is the number of atoms in the formula unit. The radii of elements were taken from Shannon (1976). The calculated lattice energies are listed in Table 4 and compare very well to those proposed by Yoder and Flora (2005).

Table 4 Lattice energies of oxide components, ionization energies of elements, and predicted enthalpies of formation of several binary antimony compounds

The differences between the $\Delta _fH^o$ predicted from the Born–Haber cycle and experiment are large. They are much larger than the differences reported for many other phases by Yoder and Flora (2005). The predicted values are systematically much more exothermic than the experimental values. The explanation for this discrepancy could be (i) inaccuracy of the experimental $\Delta _fH^o$ values, (ii) inaccuracy of the ionization enthalpies for Sb³⁺(g) and Sb$^{5+}$(g) (Wagman et al. 1982; Table 4), or (iii) failure of the assumption applied by Yoder and Flora (2005). They assumed that the lattice energies for a binary compound can be calculated by summing the lattice energies of the constituent simple salts.

Admittedly, the $\Delta _fH^o$ values presented in this work need not represent the ‘absolute truth’, but systematic errors of the magnitude of hundreds of kJ mol$^{-1}$ are difficult to imagine. We see such discrepancies as impossible either in our work (for MgSb$_2$O$_6$, Majzlan et al. 2021) or in the solubility studies on schafarzikite and tripuhyite (Leverett et al. 2012). We note, though, that a discrepancy of similar sign and magnitude exists also for FeAsO$_{4}$ (data not shown here), suggesting that there is a certain problem with the ions of the metalloids Sb and As. This problem could be perhaps related to the ionization enthalpies but it is beyond the scope of this contribution.

Stability relations at $T = 298.15$ K and $P = 10^5$ Pa

The data in Table 3, combined with the equilibrium constants for aqueous species (Filella and May 2003), can be used to produce phase diagrams such as the one in Fig. 3. The complete thermodynamic data sets at $T = 298.15$ K for schafarzikite and tripuhyite are listed in Table 3. The total aqueous molalities in Fig. 3 were chosen from an analysis of contaminated water from Desbarats et al. (2010, 2011) to reflect conditions that may be encountered in field settings. Most of the area between the stability boundaries of water is covered by the stability field of tripuhyite. Schafarzikite is stable only in a narrow range of redox conditions under moderately to strongly basic conditions. Hence, tripuhyite is indeed the ‘ultimate sink’ of antimony in oxidation zones (Leverett et al. 2012) but schafarzikite is not.

Fig. 3

pH-p$\epsilon$ diagram of the system Fe-Sb-S-O-H at T = 298.15 K. The activities were set to $\log a(\Sigma$Sb) = $-7.5$, $\log a(\Sigma$S) = $-3.1$, $\log a(\Sigma$Fe) = $-6.2$, after an aqueous solution contaminated in the field by Sb and reported by Desbarats et al. (2010, 2011)

Thermodynamic data at elevated temperatures

In addition to the data for $T = 298.15$ K, heat capacity at elevated temperatures is needed for the modeling of hydrothermal systems. The DSC data do not reach the temperatures required for this work. Therefore, the $C_p$ data sets were extrapolated to $T = 700$ K with a Kieffer model (Kieffer 1985). The isochoric heat capacities were calculated (Kieffer 1985, her equation 60) as

$$\begin{aligned} C_v \propto S(x_i) + K(x_l,x_u) + E(x_E) \end{aligned}$$

(2)

where $S(x_i)$ is the heat capacity function of a monatomic solid with a sine dispersion function, $K(x_l,x_u)$ refers to heat capacity of an optic continuum between frequencies $x_l$ and $x_u$, and $E(x_E)$ is the heat capacity function of an Einstein oscillator. These functions and their prefactors are in detail defined by the equations 57–60 in Kieffer (1985) and will not be repeated here.

The frequencies $x_i$, $x_l$, $x_u$, and $x_E$ can be found in the literature, determined either experimentally or by ab initio computations. For tripuhyite, the frequencies were taken from Parlinski and Kawazoe (2000) who calculated the phonon dispersion for the rutile-type SnO$_2$ structure. Since tripuhyite also adopts the rutile structure (Berlepsch et al. 2003), the frequencies were tested and found to produce a satisfactory fit. For schafarzikite, no publication presented the phonon frequencies for this or structurally related phases. We estimated the frequencies for the optic modes from the Raman spectrum of schafarzikite (https://rruff.info/Schafarzikite, accessed on July 24, 2022; Lafuente et al. 2015).

The isochoric heat capacity $C_v$ can be used to calculate the isobaric heat capacity $C_p$ as

$$\begin{aligned} C_p = C_v + VT \alpha ^2 B \kappa \end{aligned}$$

(3)

where V is the molar volume, T is the thermodynamic temperature, $\alpha$ is thermal expansion coefficient, and B is the bulk modulus. The calculated $C_p$ is usually slightly lower than the experimental $C_p$ data. Such difference can be corrected by $\kappa$ that can be regarded as an adjustable parameter in the Eq. (3). We stress that the parameter $\kappa$ is the only adjustable value in the entire calculations; the frequencies used to calculate $C_v$ are based on earlier published data for both phases. The parameters used to calculate $C_v$ and $C_p$ from the model of Kieffer (1985) are listed in Table S5.

The fits are compared to the experimental data and the extrapolations are shown in Figs. 1 and 2. The results in the range of 280–700 K were re-fitted with polynomials accepted by the program SUPCRTBL (Johnson et al. 1992; Zimmer et al. 2016):

$$\begin{aligned} C_p = a + bT + cT^{-2} + dT^{-0.5}. \end{aligned}$$

(4)

The coefficients a–d are listed in Table 3 in the format required by SUPCRTBL. Note that the values for the coefficients a, c, and d are to be used in SUPCRTBL as listed; the value of b should be multiplied by 10$^{-5}$ before inserting into the Eq. (4). The resulting $C_p$ is in kJ mol$^{-1}$K$^{-1}$. The entire thermodynamic data sets, formatted for the program SUPCRTBL, can be found in Table S6. From this table, they can be directly copied into SUPCRTBL and used to calculate $\log K$ values.

Validity of the $C_p$ data sets

Apart from the match of the DSC data and the $C_p$ polynomials derived from the Kieffer fits (Figs. 1, 2), there is another way to test the accuracy of the $C_p$ data (Table 3). Swaminathan and Sreedharan (2003) reported (in their Table 5) linear fits to $RT \ln P_{O_2}$ functions for various reactions that involve schafarzikite or tripuhyite as reactants or products. From the data in Table 3, $\log P_{O_2}$ (or $\log f_{O_2}$) can be calculated for the same reactions, using SUPCRTBL. The results of this exercise are shown in Fig. 4.

For a reaction that involves only schafarzikite from the two title phases in this study (Fig. 4a), the agreement is excellent. For the reactions that involve also tripuhyite (Fig. 4b), there is no agreement. This discrepancy, however, can be traced back to the difference in the $\Delta _fG^o$ values between (Leverett et al. 2012) and the work of Swaminathan and Sreedharan (2003).

The ability of our data set to reproduce the high-temperature equilibria investigated by Swaminathan and Sreedharan (2003) gives us additional confidence that the Kieffer-based $C_p$ data are accurate, at least for schafarzikite. There is no reason to assume that the Kieffer-based $C_p$ data for tripuhyite are inaccurate but a proof thereof is missing.

Fig. 4

Values of $\log P_{O_2}$ as a function of temperature for selected chemical reactions, calculated from the data presented in this work (Table 3) and the program SUPCRTBL (symbols), compared with the data presented by Swaminathan and Sreedharan (2003) (curves)

Equilibrium constants for dissolution reactions

Using the data sets presented in Table 3 and the program SUPCRTBL, equilibrium constants ($\log K$) were calculated for these two dissolution reactions

$$\begin{aligned}{} & {} \textrm{FeSbO}_4 + 3\textrm{H}^+ \rightarrow \textrm{Fe}^{3+} + \mathrm{Sb(OH)}_{3}^0 + 0.5\textrm{O}_2\mathrm{(aq)} \end{aligned}$$

(5)

$$\begin{aligned}{} & {} \textrm{FeSb}_2\textrm{O}_4 + 2\textrm{H}^+ + 2\textrm{H}_2\textrm{O} \rightarrow \textrm{Fe}^{2+} + 2\mathrm{Sb(OH)}_3^0. \end{aligned}$$

(6)

The dissolution reaction for tripuhyite was defined as a redox reaction because no thermodynamic data are available for aqueous Sb(V) species at elevated temperatures. The calculated $\log K$ values are listed in Table 5.

Table 5 Equilibrium constants ($\log K$) for the dissolution reactions of tripuhyite (reaction 5) and schafarzikite (reaction 6) as a function of temperature (T) in Kelvin

Some geochemical software accepts a function that expresses $\log K$ in terms of absolute temperature T in Kelvin instead of $\log K$ values at a pre-selected temperature grid. GWB expresses the temperature dependence of $\log K$ as

$$\begin{aligned} \log K = a + b(T-T_r) + c(T^2-T_r^2) + d(1/T-1/T_r) + e(1/T^2-1/T_r^2) + f ln(T/T_r) \end{aligned}$$

(7)

where T is the absolute temperature in Kelvin and $T_r = 298.15$ K. PHREEQC, for example, uses the function in its -analytic option

$$\begin{aligned} \log K = A_1 + A_2T + A_3/T + A_4 \log T + A_5/T^2. \end{aligned}$$

(8)

The fit parameters for these two functions are listed in Table 6.

Table 6 Fit parameters for equations that fit $\log K$ values at elevated temperature for the programs Geochemists Workbench (Eq. 7) and PHREEQC (Eq. 8) for dissolution reactions of tripuhyite (reaction 5) and schafarzikite (reaction 6)

Additionally, data for kermesite were added according to Williams-Jones and Normand (1997) (their Eq. 7), noting that their expression for $\log K$ is based on somewhat uncertain experimental results of Babčan (1976). Data for stibnite, valentinite, senarmontite, and native antimony were compiled by Bessinger and Apps (2005) who relied on earlier work of Akinfiev et al. (1994) and Zotov et al. (2003). Data blocks that can be copied and pasted into the input sources for SUPCRTBL and GWB are listed in the electronic supplementary information to this publication (Tables S6 and S7, respectively).

The effort to use all these data for geochemical modeling at elevated temperatures is hampered by the lack of $\log K$ values for any redox equilibrium between Sb(III) and Sb(V) aqueous species. Another problem is the lack of data for high-temperature (i.e., above room temperature) equilibria between the Sb$_2$O$_3$ polymorphs (senarmontite and valentinite) and Sb$_2$O$_4$ or Sb$_2$O$_5$. The equilibria among the Sb(III) species at elevated temperatures were critically summarized by Bessinger and Apps (2005). The dissociation constant for antimonic acid was measured and extrapolated to high temperature by Accornero et al. (2008). Still, in the absence of reliable data for the Sb(III)–Sb(V) equilibria, modeling at moderately or highly oxidizing conditions is impossible. Only a few remarks can be made for environments which are reducing.

An attempt to construct such a diagram is presented in Fig. 5 for $T = 398.15$ K. The activity of Fe(II) (10$^{-7}$) was selected to represent the concentrations expected at this temperature, either by dissolution of pyrite (S and O controlled by the pyrite-hematite-magnetite buffer) (Fontboté et al. 2017) or by dissolution of magnetite alone (Holser and Schneer 1961). The diagram shows that under reducing conditions, schafarzikite will progressively displace the stability field of kermesite with increasing pH. We note that the neutral pH at this temperature is 5.95, around the value at which schafarzikite will first precipitate from the solution.

Fig. 5

An activity-activity phase diagram for the system Fe-Sb-S-O-H at $T = 398.15$ K and saturated vapor pressure, constructed from constant-pH sections calculated by Geochemists Workbench Diagram (Bethke and Yeakel 2016). In this diagram, the $\log a(Fe(II)) = -7$. Under these conditions, the FMQ buffer is located at $\log fO_{2,\textrm{aq}} = -59.8$ and the MH buffer at $\log fO_{2,\textrm{aq}} = -54.1$. Point of neutral pH is located at pH 5.95

Paragenesis of schafarzikite and its formation

The paragenetic sequence that includes schafarzikite was described from the type locality Pernek (Slovakia) by Krenner (1921) and Sejkora et al. (2007). Their and our observations are summarized graphically in Fig. 6. A similar assemblage of minerals, with spectacular specimens of primary kermesite and valentinite but without schafarzikite, occurs also in Pezinok, about 6 km from the deposits in Pernek. The mineralization in Pezinok was investigated by Bukovina (2006) who performed a microthermometric study on fluid inclusions in stibnite. He determined homogenization temperatures of 130–170 °C and salinities usually between 2 and 6 wt.% NaCl eq.

Fig. 6

Precipitation sequence of minerals that associate with schafarzikite in Pernek, Slovakia. Compiled from the descriptions in Krenner (1921); Sejkora et al. (2007), and our observations. The horizontal lines show the relative precipitation timing of the minerals included in the figure

Textural evidence suggests that the assemblage of Sb oxides formed by remobilization of the older stibnite ores in Pezinok and Pernek. The same conclusion was generalized by Normand et al. (1996) and Williams-Jones and Normand (1997) who wrote that ‘where kermesite, senarmontite, and valentinite have been shown to be of hypogene origin, they are interpreted to represent reworking of earlier sulfide mineralization by later, more oxidizing solutions’. The question not addressed in those studies is what kind of processes lead to such remobilization. The problem lies in strikingly different solubilities of these minerals.

Bukovina (2006) suggested that the Sb oxides at Pezinok precipitated from fluids with slightly lower temperature than those recorded for stibnite (130–170 °C). The oxidizing solutions that caused the reworking of the earlier mineralization could have been of meteoric or marine origin and their salinity is not known. For a general model, presented below, we assume a temperature of 125 °C and salinities between 2 and 6 wt.% NaCl. Under all relevant pH conditions (up to pH > 10), Sb(OH)$_3^0$ is the predominant Sb(III) species. No other Sb(III) species will be considered.

The solubility of senarmontite (Sb$_2$O$_3$) is pH-independent, according to the reaction

$$\begin{aligned} \textrm{Sb}_2\textrm{O}_3 + 3\textrm{H}_2\textrm{O} \rightarrow 2\mathrm{Sb(OH)}_3^0. \end{aligned}$$

(9)

At T = 125 °C, the solubility calculated for the reaction (9) is 88 ppm Sb. For valentinite, the solubility is even higher because valentinite is metastable with respect to senarmontite (Golunski et al. 1981). For stibnite, similarly high solubility is reached at $\approx$ 300 °C and drops rapidly upon temperature decrease, to well <1 ppm at 125 °C.

The solubility of kermesite is also pH-independent, according to the reaction

$$\begin{aligned}{} & {} \textrm{Sb}_2\textrm{S}_2\textrm{O} + 5\textrm{H}_2\textrm{O} \rightarrow 2\mathrm{Sb(OH)}_3^0 + 2\textrm{H}_2\textrm{S}^0 \end{aligned}$$

(10)

$$\begin{aligned}{} & {} \log K_{10, 125 ^\circ C} = -21.767 = 2 \log a(\mathrm{Sb(OH})_3^0) + 2 \log a(\textrm{H}_2\textrm{S}^0) \end{aligned}$$

(11)

At assumed $\log a(\textrm{H}_2\textrm{S}^0) = -2$, the solubility is 0.16 ppb Sb. If $\log a(H_2S^0) = -4$, the solubility increases to 16 ppb Sb. Similar values of $\log a$(H$_2$S$^0$) were selected as representative for a hydrothermal ore fluid by Barnes (1979).

The solubility of schafarzikite can be described by reaction (6). Under pH conditions relevant for dilute natural fluids, the predominant Fe(II) species is Fe$^{2+}$. The corresponding equilibrium constant is

$$\begin{aligned} \log K_{6,125 ^\circ C}= & {} -7.375 = \log a(\textrm{Fe}^{2+})\nonumber \\{} & {} + 2 \log a(\mathrm{Sb(OH)}_3^0) + 2\textrm{pH} \end{aligned}$$

(12)

$$\begin{aligned} \log a(\mathrm{Sb(OH)}_3^0)= & {} -0.5 (7.375 + \log a(\textrm{Fe}^{2+})) - \textrm{pH} \end{aligned}$$

(13)

At neutral pH at this temperature (pH 5.95), the predicted Sb solubility is 98 ppb Sb, three orders of magnitude lower than that of senarmontite or valentinite. Solubility increases toward lower pH values (Fig. 7a).

Fig. 7

a Solubility of schafarzikite according to the reaction (6), compared to the solubility of senarmontite (reaction 9). The black curves show the equilibrium concentration of antimony in a hydrothermal fluid, the numbers on the curves are the assumed $\log a$(Fe$^{2+}$) values. b Solubility of schafarzikite according to the reaction (14), in the presence of chloride in the hydrothermal fluid. The curves from a are retained as gray curves for comparison. For comparison, the curves from a are retained and shown in gray in this panel. The black curves show the equilibrium concentration at $\log a$(FeCl$^+$) = $-7$ and the numbers on the curves are the salinities in weight% NaCl. All $\log K$ values necessary for the construction of these diagrams were calculated with SUPCRTBL (Zimmer et al. 2016)

In saline hydrothermal fluids, the species FeCl$^+$ is predicted to predominate over Fe$^{2+}$ at moderate salinities. The solubility reaction of schafarzikite is then

$$\begin{aligned}{} & {} \textrm{FeSb}_2\textrm{O}_4 + 2\textrm{H}_2\textrm{O} + 2\textrm{H}^+ + \textrm{Cl}^- \rightarrow \textrm{FeCl}^+ + 2\mathrm{Sb(OH)}_3^0 \end{aligned}$$

(14)

$$\begin{aligned}{} & {} \log K_{14, 125 ^\circ C} = -6.981 \nonumber = \log a(\textrm{FeCl}^+) + 2 \log a(\mathrm{Sb(OH)}_3^0) \\ {} & {} \quad\quad\quad\quad\quad\quad + 2\textrm{pH} - \log a(\textrm{Cl}^-) \end{aligned}$$

(15)

$$\begin{aligned}{} & {} \log a(\mathrm{Sb(OH)}_3^0) = -0.5 (\log a(\textrm{FeCl}^+) + 6.981 + 2pH - \log a(\textrm{Cl}^-)) \end{aligned}$$

(16)

The addition of chloride into the fluid increases the schafarzikite solubility markedly. For $\log a(FeCl^+) = -7$, the Sb solubility is predicted to increase by a factor of $\approx$ 3 between 0 and 6 wt.% NaCl (Fig. 7b).

The solubility curves of senarmontite and schafarzikite intersect in the acidic region (Fig. 7). The acidic nature of the fluids, however, is not compatible with the fact that Fe-dolomite is a major gangue mineral in these deposits (Chovan etal. 1994; Sejkora et al. 2007), the host rocks underwent extensive carbonatization (Moravanský and Lipka 2004), and the late-hydrothermal assemblage concluded with precipitation of calcite and aragonite (Krenner 1921). In addition, the supposition of the acidic nature of the fluids does not explain the occurrence of kermesite in this assemblage. We recall that the solubility of kermesite under the conditions considered is very low, around 0.1–10 ppb Sb, depending on the activity of H$_2$S in the fluid.

How can then a hydrothermal fluid at 125 °C acquire concentrations of almost 100 ppm Sb from the sparingly soluble stibnite? Such concentrations are needed to precipitate senarmontite and valentinite. The dissolution of stibnite must be oxidative, leading to the release of Sb(III) into the solution and the shift in the predominance field of SO$_4^{2-}$ (Fig. 8). Only in this way, the solution can harbor sufficient Sb to precipitate senarmontite or valentinite. Small fluctuations in the redox state of the fluid will allow the deposition of kermesite and valentinite/senarmontite, without massive and rapid supersaturation with respect to kermesite. In this way, the precipitation sequence in Fig. 6 can be rationalized.

Iron can be sourced into the fluid from pyrite or berthierite during the oxidative dissolution of the sulfides. Since schafarzikite has higher solubility than kermesite (in terms of Sb), sufficient Fe must be brought into the fluid to force the precipitation of schafarzikite. At the deposits studied (Pezinok and Pernek), schafarzikite occurs only at Pernek. At the same time, this deposit contains primary ores with stibnite and abundant pyrite. At Pezinok, pyrite that accompanies stibnite is less common.

Fig. 8

Phase diagram for the system Sb-O-S as a function of fugacities of gaseous O$_2$ and S$_2$. A small portion of a similar diagram for the system Fe-O-S is also shown. The dashed vertical lines show the predominance boundary between H$_2$S$^0$ and SO$_4^{2-}$. All $\log K$ values necessary for the construction of this diagram were calculated with SUPCRTBL (Zimmer et al. 2016)

Conclusions

Schafarzikite and hydrothermal oxides of antimony (valentinite, kermesite, senarmontite) can form by oxidative remobilization of stibnite ores. During this process, the predominant species of sulfur will be sulfate and the fluid is able to build up high concentrations of Sb necessary to precipitate Sb$_2$O$_3$. Fluctuations in the redox potential and the Fe content of the fluid may cause precipitation of kermesite or schafarzikite, respectively. Under near-surface strongly oxidizing conditions, these minerals may be transient sinks of antimony during weathering. Fast oxidation of Sb(III) to Sb(V) (Leuz and Johnson 2005) will cause their dissolution and conversion to fully oxidized weathering products, such as tripuhyite.

Tripuhyite has an extensive stability field at $T = 298.15$ K. Under oxidizing conditions in mining waste, it is certainly the principal sink of antimony. Calculation of equilibria above room temperature is hampered by the lack of data for Sb(V) aqueous species.