Solubility of Platinum in Pyrite and Pyrrhotite

A temperature range of processes leading to the concentration of Pt in the crust widely varies from high-temperature orthomagmatic to low-temperature hydrothermal and biogenic. Pyrite FeS2 and pyrrhotite Fe1–xS are important components of sulfide ores, which contain platinum-group elements. Fe sulfides typically host from a few hundreds to a few tens ppm of dispersed (invisible) Pt. In this work, we summarized the available data on the solubility of Pt in pyrite and pyrrhotite, supplement them with the results of synthesis of these minerals in the presence of Pt phases, and present a model that can describe the solubility of Pt in a broad range of temperature and S2 fugacity. The resulting equations allow the calculation of the solubility of Pt (ppm) in a temperature range of 300 < t < 1100°C and S2 fugacity up to the equilibrium with Sl. Tables with the solubility of Pt in pyrite and pyrrhotite depending on temperature and S2 fugacity are presented. Isopleths of the solubility of Pt in Fe sulfides are plotted on a log f(S2)–1000/T diagram. The analysis of the position of the main field of ore formation on this diagram showed that pyrite and pyrrhotite dissolve up to a few and a few hundreds of ppm Pt, respectively, upon conditions typical of ore formation: t < 700°C and log f(S2) < –4. These estimations coincide with maximum Pt contents determined in minerals of natural sulfide ores.

A review and analysis of literature on the solubility of Pt in pyrite and pyrrhotite are provided by Filimonova et al. (2019Filimonova et al. ( , 2021. The solubility of Pt is determined experimentally in a temperature range of 470-650°С for pyrite (Makovicky et al., 1992;Cafagna and Jugo, 2016;Tauson et al., 2017;Filimonova et al., 2019) and 450-1100°С for pyrrhotite (Makovicky et al., 1988(Makovicky et al., , 1990(Makovicky et al., , 1992Ballhaus and Ulmer, 1995;Majzlan et al., 2002;Filimonova et al., 2021). The maximum content of the dispersed Pt is determined in The aim of our study is the creation of a model that can quantitatively describe the solubility of Pt in Fe sulfides in a broad range of temperature and S 2 fugacity on the basis of the synthesis and study of minerals coexisting with PtS 2(c) (pyrite) and PtS (c) (pyrite, pyrrhotite). Our data were processed together with literature data (Makovicky et al., 1988;Majzlan et al., 2002;Filimonova et al., 2019Filimonova et al., , 2021 taking into account the deportment of Pt in pyrite and pyrrhotite, which is identified by X-ray absorption spectroscopy (XAS). The solubility of Pt in Fe sulfides is calculated using modeled equations depending on the magmatic to hydrothermal parameters of ore formation.

DEPORTMENT OF Pt IN Fe SULFIDES
The modes of occurrence of Pt in Fe sulfides are based on the XAS study of synthetic minerals (Filimonova et al., 2019. Filimonova et al. (2019) provided results on pyrite synthesized at 580-590°С from melts of alkali metal chlorides; the Pt activity was given by the presence of Pt sulfides in the system. The synthesis resulted in the formation of pyrite crystals with up to 4 wt % Pt. Their study with scanning electron microscopy (SEM) and electron microprobe analysis (EMPA) showed that the Pt distribution along the pyrite grains is zonal and, within individual zones, homogeneous. According to the EMPA, there is a negative correlation between the Pt and Fe contents. A slope of the correlation line corresponds to the formation of a solid solution in the Pt-Fe-S system and/or the formation of PtS 2 . These data are in agreement with the results of the XAS study of synthesized grains, according to which there are two modes of occurrence of Pt in pyrite. The main mode is related to the Pt solid solution in a formal degree of oxidation of Table 1. Solubility of Pt in pyrite and pyrrhotite at 300-1100°С by experimental data and results of analysis of natural sulfides. Comparison of initial data with model calculation a Determined by diagram of (Toulmin and Barton, 1964), b are the are the mole amount of the end-member in the solid solution, c calculated according to Eqs. (11), (13), (15), and (16); and d coexists with Pt 0.92 Fe 0.08 S 2 (C Fe = 2.51 at %). x PtS x +4, which isomorphically substitutes for Fe and is octahedrally coordinated by S atoms (Fig. 1a). The Pt-S distance in pyrite is approximately 0.1 Å longer than the Fe-S distance in pure pyrite (R Pt-S = 2.35 Å, R Fe-S = 2.26 Å). The differences in the local atomic environment of Fe and Pt disappear at a distance of R > 2.5 Å from the cation. The second mode of occurrence of Pt was determined using high-resolution transmitting electron microscopy as nanosized PtS 2 inclusions. Heating leads to the partial decomposition (dissolution) of these inclusions and the formation of the (Fe 1-x Pt x )S 2 solid solution. Thus, the PtS 2 inclusions can be considered the quench products. Our data shows that both Pt solid solution and (at high Pt content) nanosized PtS 2 inclusions could exist in natural Pt-bearing pyrite.
It is interesting to compare the charges of Pt in pyrite and PtS 2 with the charge of Fe in pyrite. The quantum-chemical calculations of partial atomic charges of Pt by a DDEC-6 method yield the values of +0.43 e (Pt in pyrite) and +0.47 e (PtS 2 ) (Evstigneeva et al., 2021); i.e., the formation of the solid solution leads to a small (0.04 e) decrease in the Pt charge in comparison with related sulfide PtS 2 . At the same time, the Pt charge is significantly higher than that of Fe in pure pyrite and in the second coordination shell of Pt in solid solution (Fe,Pt)S (+0.16 and +0.18 е, respectively). Thus, the difference in the cation charges upon the replacement for pyrite (a mineral with a significant amount of covalent chemical bond) is compensated by the redistribution of the electron density. The stoichiometry of the related FeS 2 and PtS 2 remains the same during the formation of the solid solution and the Fe → Pt substitution occurs without vacancies in spite of the different formal cation charge (2+ for Fe and 4+ for Pt). This leads to an important conclusion: the composition of the solid solutions in the area of joint stability of FeS 2 and PtS 2 depends only on temperature rather than on the S 2 fugacity.
The state of Pt in pyrrhotite was determined from the study of crystals synthesized in a similar mode with pyrite . The analysis of their chemical composition showed that the increase in temperature and S 2 fugacity leads to the increase in the Pt content of pyrrhotite, which is 0.6 wt % at t = 720°C and log f(S 2 ) = -0.1 in the presence of PtS (c) . According to X-ray absorption near-edge structure (XANES) analysis of Pt L 3 -edge spectra, Pt in pyrrhotite occurs in formal degrees of oxidation of +4 and +2. Theoretical XANES modeling and interpretation of extended X-ray absorption fine structure (EXAFS) spectra showed that Pt 4+ substitutes for Fe in a crystalline lattice of pyrrhotite, whereas Pt 2+ forms PtS-like clusters. The structure of pyrrhotite can be presented as the intercalation of layers with full positions of cation sublattice, which are alternated with a vacancy layer (Fig. 1b). Atoms of isomorphic Pt 4+ are surrounded by S atoms at a distance of 2.39 ± 0.02 Å (the Fe-S distance in pyrrhotite is 2.44 Å). According to theoretical modeling of XANES spectra, the second coordination shell of isomorphic Pt hosts one vacancy in cation sublattice inside the same Fe layer containing the Pt atom. The scheme of isomorphic substitution in pyrrhotite can be described as 2Fe 2+ → Pt 4+ + Fe 2+ . In contrast to pyrite, the compensation of the charge upon the formation of pyrrhotite solid solution corresponds to a scheme based on the formal charges. We can expect the correlation of the composition of the solid solution between both the temperature and S 2 fugacity, the increase in which leads to an increase in the amount of vacancies in the cation sublattice and, thus, an increase in the solubility of Pt.
Note the similar interatomic Pt-S distances in pyrite and pyrrhotite (2.35 and 2.39 Å, respectively). This is probably related to the octahedral symmetry of the first coordination sphere of Pt in both minerals. Thus, the Fe → Pt replacement leads to expansion and compression of the first coordination sphere of cation in pyrite and pyrrhotite, respectively, which can be related to the different ionic radii of Fe. Being in a lowspin state, Fe in pyrite has a significantly lower radius that the high-spin Fe in pyrrhotite.
Similarly to pyrite, the Pt 2+ S clusters in pyrrhotite can be considered quench products. For pyrrhotite (as well as for pyrite), the high S 2 fugacity stabilizes the Pt solid solution and prevents the formation of clusters upon cooling.
Thus, the results of the study of Pt-bearing pyrite and pyrrhotite crystals indicate the formation of isomorphic solid solutions in the Pt-Fe-S system. In both minerals, Pt substitutes for Fe without the change in the type of coordination polyhedra and, in pyrrhotite, this replacement is accompanied by the formation of one vacancy in the cation sublattice. These data will be the basis for the description of the solubility of Pt in pyrite and pyrrhotite depending on temperature and S 2 fugacity.

ANALYTICAL METHODS
Synthesis was conducted using melts of alkali metal halogenides at a stationary temperature gradient. The phase composition of samples was determined using X-ray diffractometry (XRD). The Pt concentration and distribution in crystals were studied using EMPA, SEM, and laser-ablation inductively coupled mass spectrometry (LA ICP MS). The full data on the synthesis and analytical methods of study of synthesized crystals is given in Supplementary Materials (Appendix 1).

SOLUBILITY OF Pt IN PYRITE
AND PYRRHOTITE Figure 2 presents the log f(S 2 )-(1000/T, K) diagram of the Pt-Fe-S system, which shows the parameters of our experiments on synthesized pyrite and pyrrhotite, as well as the literature data. The synthesized samples correspond to a wide range of temperature (300-1100°С) and S 2 fugacity (from equilibrium with liquid sulphur to coexisting pyrrhotite, Pt, and PtS). This area overlaps the field of ore formation at most hydrothermal and orthomagmatic PGE deposits. According to the LA ICP MS and SEM/EDS analyses, the Pt distribution within the synthesized crystals of both minerals is homogeneous (Appendix 1, Fig. A1). On the basis of published (Makovicky et al., 1992;Majzlan et al., 2002;Large et al., 2007;Mironov et al., 2008;Filimonova et al., 2021Filimonova et al., , 2019 and original results, we can state that the solubility of Pt in pyrite and pyrrhotite depends on two main factors: (i) the temperature of synthesis (or ore-forming process) and (ii) S 2 fugacity f(S 2 ). These factors also affect which Pt-bearing phase (PtS 2(cr) , PtS (cr) or Pt (cr) /Pt 3 Fe (cr) ) is present in assemblage with pyrite and pyrrhotite. The data on the solubility of Pt depending on temperature and f(S 2 ) in natural and synthetic pyrite and pyrrhotite are given in Table 1. The log f(S 2 ) values are estimated by the composition of pyrrhotite on the basis of an equation from (Toulmin and Barton, 1964) (the log f(S 2 ) values are given in Table 1).
The Pt content of pyrite and pyrrhotite correlated from the inverse temperature is shown in Fig. 2 on the basis of original and published data. According to the figure, -the solubility of Pt in pyrite and pyrrhotite strongly increases with increasing temperature; and -the solubility of Pt in pyrite and pyrrhotite is variously correlated with temperature: the Pt content of pyrite increases faster with increasing temperature than of pyrrhotite; for example, pyrrhotite synthesized at 540-650°С contains 0.002 and up to 0.1 at % Pt in assemblage with pyrite containing up to 0.0008 and 0.6 at % Pt, respectively; and -the solubility of Pt in pyrite and pyrrhotite depends on S 2 fugacity; the peculiarities of this correlation will be discussed below; in general, the increasing S 2 fugacity, which is expressed in the increasing S content in a Pt-PtS-PtS 2 range, leads to the enhanced temperature correlation of the solubility of Pt both for pyrite and pyrrhotite.
In the area of the Fe 1-x S-PtS coexistence, the solubility of Pt in pyrrhotite weakly increases on an isotherm with increasing S 2 fugacity (Fig. 4). In the log C(Pt)-log f(S 2 ) coordination, a tangent of a slope angle of lines through experimental points is close to 0.3 (the solubility of Pt changes twice upon changing the S 2 fugacity by an order of magnitude).  (Toulmin and Barton, 1964). The N FeS values (the mole amount of FeS in pyrrhotite, N FeS = = 2 , where n is the amount of mole of chemical elements) correspond to isopleths of the composition of pyrrhotite. The following thermodynamic data are used: Fe 1-x S (Toulmin and Barton, 1964), FeS 2 , Pt, and PtS (Naumov et al., 1971), and PtS 2 (Mills, 1974 (Table 1, point 3). Thus, an approach that describes the solubility of Pt in pyrite and Fe in PtS 2 is reasonable for this system. This approach includes a model of asymmetric solid solution.
Considering the solid solutions in the PtS 2 -FeS 2 system, the mole free energy of the solution ( ) of two end-members with Gibbs energies and can be presented as follows: (1) where and are the mole amounts of endmembers . Mole free energy of mixing solution G min is a sum of ideal G id and excessive G ex energies: (2) Ideal free energy of the mixing solution G id is as follows: (3) In this work, we used the asymmetric solid solution model for the thermodynamic description of the solid solutions. Within this model, excessive mixing energy G ex is presented as one-parameter van-Laar equation proposed by Aranovich and Newton (1999): where are the mole volumes of end-members and W is the energetic mixing parameters. The expressions for the coefficients of activity of PtS 2 and FeS 2 in the solid solution are following (Aranovich and Newton, 1999):   Table 1 are shown by symbols, and the correlation between solubility and temperature is shown according to . The symbol size does not exceed the errors of the measured values of the Pt content. Numbers of points correspond to Table 1 Under thermodynamic equilibrium, the activity of end-members in coexisting solid solutions (PtS 2 in pyrite FeS 2 and FeS 2 in PtS 2 ) should be the same. Figure 5a illustrates a case of strong immiscibility with coexisting two solid solutions in the system: PtS 2 in pyrite FeS 2 (Fig. 5b) and FeS 2 in PtS 2 (Fig. 5c). Considering the solution of PtS 2 in pyrite (Fig. 5a) and suggesting that the PtS 2 activity in pyrite is close to 1, we obtain the equation (6) which, after logarithmation, yields (7) Because the Pt concentration of pyrite is low, it can be accepted that 0 and is close to 1. Thus, the W/RT molecular parameter can be estimated from Eq. (5a): where is the experimental mole amount of the Pt end-member in pyrite. Thus, the value of the W/RT parameter allows calculation of the coefficient of activity of the Fe end-member of the solid solution (Eq. 5b). The results of the calculation of the energetic mixing parameter and the solubility of the adjacent end-members are presented in Table 2.
This estimation of the energetic parameter yields satisfactory results for low temperatures (t < 500°C). For higher temperatures, when the coexisting solid solutions cannot be considered close to end-members because of the increasing solubility, the W/RT parameter was found using a graphical method of the total tangential curve of the correlation between and the composition (Eq. (1)): the W/RT values are selected to correspond to experimental values of the Pt concentrations. This method is shown in Figs. 5a-5c, and an example of the determination of activity of end-members depending on the energetic mixing parameter by graphical method is presented in Supplementary Materials 2.

RESULTS OF PROCESSING OF DATA ON Pt SOLUBILITY IN Fe SUFLIDES
Joint Pyrite-PtS 2(c) Stability Field The solubility of Pt in pyrite in the stability field of PtS 2(c) (S 2 fugacity varies from equilibrium with liquid sulphur to equilibrium of PtS 2 -PtS, Fig. 2) depends on the reaction (9) Thus, the Pt concentration of pyrite in the stability field of PtS 2(c) depends only on the temperature rather than on f(S 2 ). For calculation of the W/RT parameter by Eq. (8), we used points 1-3 from Table 1: . ,   (Naumov et al., 1971;Mills, 1974), and c values calculated by the total tangential method (see text for explanation) are shown in italics. The results of the calculation of the W/RT parameter and the solubility of joint end-members depending on temperature are shown in Table 2. As follows from data of Fig. 5b, the W/RT values describe with high precision both the solubility of PtS 2 in pyrite and FeS 2 solubility in PtS 2 .

Joint Pyrite-Cooperite PtS (c) Stability Field
The formation of the Pt-bearing pyrite in the stability field of PtS (c) can be described by the reaction (12) Thus, the Pt content of pyrite in the area of the diagram depends on both the temperature and f(S 2 ). In this case, the application of a regular solution model is difficult, because the energetic mixing parameter depends only on temperature and ignores the effect of S 2 fugacity. Thus, the correlation of the solubility of Pt in pyrite with S 2 fugacity and temperature below the PtS 2 -PtS equilibrium was described by the simple empirical equation . For this, the solubility of Pt (in form of PtS 2 ) in pyrite was calculated by Eq. (11) in a temperature range 300-500°С, which corresponds to experimental data (points 1-3 in Table 1).
These solubility values correspond to S 2 fugacity in the upper boundary of the stability field of PtS (c) on equilibrium line of PtS 2 -PtS (Fig. 2). For S 2 fugacity below this equilibrium in the stability field of PtS (c) , Table 1 contains only data concerning S 2 fugacity, which is equilibrated with a pyrite-pyrrhotite couple (points 4-6). These two data sets (calculation for PtS 2 -PtS equilibrium and experiment for pyrite-pyrrhotite equilibrium) were approximated by the equation Note that, according to Eq. (12), the solubility of Pt (in form of PtS 2 ) in pyrite increases proportionally to 0.5logf(S 2 ). According to the available experimental data, however, the correlation with S 2 fugacity is sig- , , . , 6. Isopleths of Pt contents of pyrite and pyrrhotite on the log f(S 2 ) -1000/T diagram (Toulmin and Barton, 1964). The sources of thermodynamic data coincide with Fig. 2. Numerical data on the solubility of Pt in Fe sulfides are presented in Supplementary Materials 3, Table A5 (log х of end member) and  (Mills, 1974)-PtS PtS (Naumov et al., 1971)-Pt "Main" field of ore formation (Barton, 1970)  nificantly stronger: the averaged coefficient in 2.7 (Eq. (13)). Thus, the measured solubility of Pt in pyrite at decreasing S 2 fugacity decreases much faster in comparison with theoretical correlation. In order that the calculated values of the solubility of Pt match the experimental ones and to avoid the calculation of the higher Pt concentration of pyrite, we decided to ignore the theoretical correlation and rely only on experimental results.

Pyrrhotite Joint pyrrhotite-cooperite PtS (c) stability field
It is known that the solubility of Pt (as PtS) in pyrrhotite depends on temperature and S 2 fugacity (e.g., Filimonova et al., 2019). The positive Pt-S correlation corresponds to the reaction (14) According to reaction (14), the increase in S 2 fugacity leads to a weak increase in the solubility of Pt in pyrrhotite. To describe the solubility of Pt (as PtS) in pyrrhotite, we used the data from Table 1, which belong to the stability field of PtS (c) (points 7-15). The following equation is a result of the calculation: (15) Joint pyrrhotite-Pt (c) stability field The experimental data for this area are absent. Because the composition of pyrrhotite in the Pt stability field weakly changes (Fig. 2), it can roughly be suggested that the solubility of Pt (as PtS) in pyrrhotite at a given temperature depends only on S 2 fugacity and can be presented by the reaction (16) Thus, for the calculation of the solubility of Pt in this area, the data on the Pt concentration in pyrrhotite, which correspond to S 2 fugacity on a PtS-Pt equilibrium line, could be extrapolated down S 2 fugacity using stoichiometry reaction (16): (∂logx(PtS)/∂logf(S 2 )) T = 0.5 (the Pt concentration changes by 0.5 log units at changing S 2 fugacity by an order of magnitude).

CONCLUSIONS
The results of the calculation of the solubility of Pt in pyrite and pyrrhotite by equations presented in a previous section (Eqs. (11), (13), (15), and (16)) are given in Appendix 3, Table A5 (logx of end-member), and Table A6 (ppm Pt). Our original and published data (Makovicky et al., 1992;Majzlan et al., 2002; (  Large et al., 2007;Mironov et al., 2008;Filimonova et al., 2019Filimonova et al., , 2021 allowed us to provide a model that describes the solubility of Pt in Fe sulfides in a broad range of temperature and S 2 fugacity. This model became possible due to the XAS determination of the mode of occurrence of Pt in Fe sulfides (Filimonova et al., 2019. The XAS data revealed the chemical composition of the solid solution end-members in the Pt-Fe-S system and described the correlation between the composition of the solid solution and physicochemical parameters (t, f(S 2 )). Figure 6 shows the contours of the solubility of Pt in pyrite and pyrrhotite calculated on the basis of current results, as well as the "main field of ore formation" according to (Barton, 1970). This field is not overlapped by the fields of high Pt contents in pyrite and pyrrhotite. Analysis of the diagram allows the following conclusions: -in most cases, pyrite will contain <1 ppm Pt; thus, pyrite with higher Pt concentrations forms under specific conditions, which correspond to high temperature and S 2 fugacity f(S 2 ) out of the "main field of ore formation"; and -in comparison with hydrothermal pyrite, pyrrhotite can dissolve the higher Pt concentration up tõ 100 ppm Pt at the upper boundary of the "main field of ore formation," which is related to the effect of temperature on the solubility of Pt: pyrrhotite in the "main field of ore formation" forms at higher temperatures relatively to the hydrothermal pyrite.

ACKNOWLEDGMENTS
We are grateful to A.V. Zotov and M.S. Nikolsky for fruitful discussion of the manuscript, L.Ya. Aranovich for consultations on the Van Laar model, and N.N. Eremin for valuable comments on the manuscript. The analytical chemical works were conducted in the Center for Collective Use "IGEM-analitika." FUNDING This work was supported by a grant of the President of the Russian Federation for State Support of Leading Scientific Schools of the Russian Federation no. NSh-2394.2022.1.5 (synthesis and study of crystals) and Russian Science Foundation no. 20-17-00184 (thermodynamic calculations, creation of the model of the solubility of Pt in sulfides).

CONFLICT OF INTEREST
The author declares that he has no conflict of interest.

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SUPPLEMENTARY INFORMATION
The online version contains supplementary material available at https://doi.org/10.1134/S1075701522060046.