# Incorporation of palladium into pyrite: Insights from X-ray absorption spectroscopy analysis and modelling

Olga N. Filimonova, Irina I. Snigireva, Paul Thompson, Didier Wermeille

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Olga N. Filimonova, Irina I. Snigireva, Paul Thompson, Didier Wermeille. Incorporation of palladium into pyrite: Insights from X-ray absorption spectroscopy analysis and modelling. Science of the Total Environment, 2024, 920, pp.170927. 10.1016/j.scitotenv.2024.170927. hal-05097687

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# Incorporation of palladium into pyrite: Insights from X-ray absorption spectroscopy analysis and modelling

Olga N. Filimonova<sup>a, b, *</sup>, Irina I. Snigireva<sup>c</sup>, Paul Thompson<sup>a, b</sup>, Didier Wermeille<sup>a, b</sup>

## HIGHLIGHTS

* pyrite formed at high sulphur fugacity in the Pd-saturated system can contain up to a few wt% of Pd

* Pd replaces Fe in the cationic subshell of pyrite

* the oxidation state of isomorphous Pd in $Fe^{+2}S_{2}(\text{cub})$ is close to +2

* the values of covalent radii of Pt and Pd control their incorporation into pyrite structure

* Pd can be recovered from pyrite-bearing ores as a by-product

## GRAPHICAL ABSTRACT

<figure><img src="image_4.png" /></figure>

## ARTICLE INFO

Editor: Daniel Alessi

**Keywords:**

Platinum-group elements

Solid solution

Formal oxidation state

Local atomic environment

X-ray absorption spectroscopy

## ABSTRACT

Pyrite ($FeS_2$) often accommodates elevated concentrations of platinum-group elements in ores of magmatic and hydrothermal origin. In order to elucidate the role of pyrite in concentrating Pd, Pd-doped synthetic crystals were studied via X-ray absorption spectroscopy (XAS). Crystals were obtained by salt-flux method in the system saturated with respect to Pd at the temperature of 580 °C and sulphur fugacity of $log f(S_2) = -0.4$. Scanning electron microscopy, electron probe microanalysis, and laser ablation inductively coupled plasma mass spectrometry studies demonstrated a uniform distribution of Pd within the pyrite crystals. The median and average values of Pd content of ~0.7 ± 0.1 wt% were measured. Comparison of the Pd K-edge X-ray absorption near edge structure (XANES) spectra with the spectra of standards revealed that the formal oxidation state of Pd was close to +2. Fitting of the extended X-ray absorption fine structure (EXAFS) and Finite Difference Method for Near-Edge Structure (FDMNES) theoretical simulations of XANES spectra showed that Pd substituted for Fe in the crystal structure of pyrite. The isomorphous Pd in pyrite was octahedrally coordinated by S atoms at ~2.385 Å. The Pd—S interatomic distance was 5.6 % larger than that of Fe—S due to the difference in their covalent radii of ~5.3 %. The expansion caused by the incorporation of Pd into the pyrite structure disappeared at the distance of $R > 3$ Å. The information on the state of Pd in pyrite, including the local atomic environment and formal oxidation state, is essential for scientific and industrial purposes, e.g. physical-chemical modelling and improvement of leaching and extraction processing respectively.

<footnote><sup>a</sup> The XMaS Beamline CRG c/o European Synchrotron Radiation Facility (ESRF), 71 avenue des Martyrs, 38000 Grenoble, France</footnote>

<footnote><sup>b</sup> Department of Physics, University of Liverpool, Oliver Lodge Laboratory, Liverpool L69 7ZE, UK</footnote>

<footnote><sup>c</sup> ESRF, 71 avenue des Martyrs, 38000 Grenoble, France</footnote>

<footnote>* Corresponding author at: The XMaS Beamline CRG c/o European Synchrotron Radiation Facility (ESRF), 71 avenue des Martyrs, 38000 Grenoble, France. E-mail address: olga.filimonova@esrf.fr (O.N. Filimonova).</footnote>
# 1. Introduction

The typical base metal sulphides (BMS) such as pyrrhotite (po, Fe₁ₓS), pentlandite (pn, (FeNi)₉S₈), chalcopyrite (ccp, CuFeS₂), and pyrite (py, FeS₂cubic) form the large ore deposits of various origin. These sulphides often host platinum-group elements (PGEs) and other chalcolphile elements such as Ag, As, Au, Cu, Ni, Sb, Se, and Te. The data on the solubility of Pd in FeS₂ from the deposits of different genesis are given in Table 1 (hereinafter formula FeS₂ stands for the cubic structure). For example, Pd-bearing pyrite occurs in the magmatic Cu-Ni-PGE sulphide deposits, including orthomagmatic high-temperature (Brzozowski et al., 2023; McFall et al., 2019; Graham et al., 2017; Knight et al., 2017; Piña et al., 2016; Smith et al., 2014; Cabri et al., 2008; Poltavets et al., 2006), post-magmatic intermediate to high-temperature (Boucher et al., 2023; Li et al., 2023; Robb et al., 2023; Duran et al., 2015; Piña et al., 2012; Gervilla and Kojonen, 2002), post-magmatic intermediate-temperature (Vikentyev et al., 2021; Kudrin et al., 2021; Kravtsova et al., 2020), and hydrogenous-diagenetic low-temperature deposits (Pašava et al., 2013; Orberger et al., 2007). In particular, the concentration of Pd in pyrite from high-temperature orthomagmatic ores of Bushveld (South Africa)

reaches 60–460 ppm of Pd (Piña et al., 2016; Smith et al., 2014; Cabri et al., 2008), in pyrite from post-magmatic Lac des Îles deposits located in Western Ontario (Canada) – 130 ppm (Duran et al., 2015), in pyrite from New Afton group of deposits (Canada) – up to 70 ppm (Boucher et al., 2023). The pyrite of post-magmatic origin can contain up to 6 ppm of Pd (Natalka, Russia, Kravtsova et al., 2020). Pyrites from hydrogenous-diagenetic type of deposits host up to a few hundred ppm of Pd (Huangjiawan, China, Pašava et al., 2013).

The investigations of the ternary Pd-Fe-S and quaternary Pd-Ni-Fe-S pure synthetic systems have shown that at the po-py equilibrium, pyrite dissolves up to 3.6 wt% of Pd at 725 °C (Makovicky and Karup-Møller, 1995), n × 100 ppm (n < 8) at 500–550 °C (Makovicky and Karup-Møller, 2016; Makovicky et al., 1988, 1990), and 1.6 ppm at 400 °C (Lipko et al., 2022). These data are also given in Table 1. The experiments on the determination of Pd content in pyrite synthesized in equilibrium with liquid sulphur (S₁) presented in our research have never been carried out.

Despite the large accumulated knowledge on Pd contents in natural and synthetic samples, the mechanism of Pd incorporation into pyrite is still unknown. The sharp increase in Pd content observed in synthetic

<caption>**Table 1**</caption>

Origin of Pd-bearing pyrites, their approximate formation temperatures, types of ore deposits, and the concentration of Pd in pyrites together with the solubility of Pd in pyrite in the temperature range of 725–400°C obtained in experiments.

<table><caption>Natural systems Pd – Fe – S</caption><thead><tr><th>Pyrite-generation process</th><th>Deposit type</th><th>Max. C<sub>Pd</sub> in pyrite, ppm</th><th>Deposit</th><th>Reference</th></tr><tr><th>Genetic type (temperature level)</th><th>Subtype</th><th></th><th></th><th></th></tr></thead><tbody><tr><td rowspan="5">Orthomagmatic (high)</td><td>Direct crystallization from alkaline magma</td><td>Cu-Ni-PGE-Au magmatic</td><td>28.4</td><td>Sron Garbh, Scotland</td><td>Graham et al., 2017</td></tr><tr><td rowspan="2">Exsolution from S-rich mss</td><td rowspan="2">Cu-Ni-PGE magmatic</td><td>465.7</td><td>Merensky Reef, South Africa</td><td>Cabri et al., 2008</td></tr><tr><td>71.2</td><td>Thunder Bay, Canada</td><td>Brzozowski et al., 2023</td></tr><tr><td rowspan="2">Direct crystallization from basaltic magma</td><td rowspan="2">Cu-Fe-Ti-V-Au-PGE late magmatic</td><td>60.0</td><td>Bushveld, South Africa</td><td>Smith et al., 2014</td></tr><tr><td>22.4</td><td>McFall et al., 2019</td><td>Knight et al., 2017</td></tr><tr><td rowspan="5">Post-magmatic (intermediate to high)</td><td rowspan="2">Direct crystallization from komatiitic magma</td><td rowspan="2">PGE late magmatic</td><td>1.5</td><td>Fazenda Mirabela, Brazil</td><td>Poltavets et al., 2006</td></tr><tr><td>0.6</td><td>Volkovsky Pluton, Russia</td><td>Poltavets et al., 2006</td></tr><tr><td rowspan="2">Crystallization via replacement or sulfidation</td><td rowspan="2">Cu-Fe-Ti-V-Au-PGE late magmatic</td><td>60.4</td><td>Great Dyke, South Africa</td><td>Piña et al., 2016</td></tr><tr><td>2.3</td><td>Fedorov-Pansky, Russia</td><td>Cabri et al., 2010</td></tr><tr><td rowspan="3">Fluid/brine-related crystallization</td><td rowspan="2">Cu-Ni-PGE</td><td>131.0</td><td>Lac-des-Îles, Canada</td><td>Duran et al., 2015</td></tr><tr><td>30.0</td><td>Kevitsa, Finland</td><td>Gervilla and Kojonen, 2002</td></tr><tr><td>Alkaline Cu–Au porphyry</td><td>Alkaline Cu–Au porphyry</td><td>&lt;0.1</td><td>Aguablanca, Spain</td><td>Piña et al., 2012</td></tr><tr><td rowspan="3">Fluid-related crystallization</td><td rowspan="2">Intrusion-related/orogenic Au quartz-sulfide</td><td>71.0</td><td>New Afton, Canada</td><td>Boucher et al., 2023</td></tr><tr><td>33.6</td><td>Robb et al., 2023</td><td>Kudrin et al., 2021</td></tr><tr><td>Cu-Au porphyry</td><td>0.5</td><td>Jiguanzui-Taohuazui, China</td><td>Li et al., 2023</td></tr><tr><td rowspan="3">Post-magmatic (intermediate)</td><td rowspan="3">Fluid-related crystallization</td><td>VMS</td><td>0.2</td><td>Uchaly, Russia</td><td>Vikentyev et al., 2021</td></tr><tr><td>Intrusion-related/orogenic Au quartz-sulfide</td><td>5.8</td><td>Natalka, Russia</td><td>Kravtsova et al., 2020</td></tr><tr><td>Mo-Ni-(+Pt)-rich black shales</td><td>&lt;0.1</td><td>Svetlinsk, Russia</td><td>Kudrin et al., 2021</td></tr><tr><td rowspan="2">Hydrogenous-diagenetic (low)</td><td rowspan="2">Diagenesis/catagenesis</td><td>390.0</td><td>Huangjiawan, China</td><td>Vikentyev et al., 2021</td></tr><tr><td>66.0</td><td></td><td>Pašava et al., 2013</td></tr></tbody></table>

<table><caption>Synthetic systems Pd – Fe – S</caption><thead><tr><th>Model of genetic type</th><th>Temperature of synthesis, °C</th><th>Synthetic assemblage</th><th>Max. C<sub>Pd</sub> in pyrite, ppm</th><th>System</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="2">Orthomagmatic (high)</td><td>725</td><td>py - po - PdS</td><td>36,000</td><td>Dry condensed phase system Pd-(Ni)-Fe-S</td><td>Makovicky and Karup-Møller, 1995</td></tr><tr><td>580</td><td>py - S<sub>1</sub></td><td>7000</td><td></td><td>This study</td></tr><tr><td rowspan="2">Post-magmatic (intermediate to high)</td><td>550</td><td>py - PdS -NiS<sub>2</sub></td><td>530</td><td></td><td>Makovicky and Karup-Møller, 2016</td></tr><tr><td>500</td><td>py - po - PdS</td><td>800<sup>a</sup></td><td></td><td>Makovicky et al., 1988</td></tr><tr><td>Post-magmatic (intermediate)</td><td>400</td><td>po - py</td><td>1.6</td><td>Ag-Pd-Cd-Mn-Fe-S</td><td>Lipko et al., 2022</td></tr></tbody></table>

<footnote>a At the resolution threshold of microprobe measurements of 1000 ppm.</footnote>
pyrites (Table 1) indicates the uniformity of the Pd distribution. Nevertheless, the incorporation may occur through one or a few mechanisms. On the one hand, isomorphic Pd can be accommodated by a pyrite matrix. On the other hand, the exceptional Pd enrichment of pyrite could happen due to the formation of uniformly distributed nano-sized minerals inside of the mineral host matrix (e.g. PdS, Pd<sub>2.2</sub>S, PdS<sub>2</sub>). Thus, the state of Pd in pyrite can be reliably determined only by spectroscopic methods, e.g. X-ray photoelectron spectroscopy (XPS) or X-ray absorption spectroscopy (XAS). XAS analysis applied in this study has had a tremendous impact in the fields of geochemistry and mineral physics over the past 30 years (Farges and Wilke, 2016, and references therein). The method is based on the acquisition of absorption spectra of excited elastic photons as the incident X-rays eject electrons from the tightly bound core valence to the continuum. The XAS spectrum is divided into lower and higher energy regions: X-ray absorption near edge structure (XANES, up to 50 eV above the absorption edge) and extended X-ray absorption fine structure (EXAFS, up to 1000 eV above the absorption edge). This method allows to identify the formal oxidation state and band occupancy of the absorbing atom and enables determination of types of the neighbouring atoms at R < 10 Å, coordination numbers, and the interatomic distances around the absorbing atom (Iglesias-Juez et al., 2022; Galoisy, 2004; Mottana, 2004).

In this study, we employed one of the most extensively used simulation software, the self-consistent ab initio FDMNES (Finite Difference Method for Near-Edge Structure, Guda et al., 2015; Joly, 2001) code to model XANES spectra. The comparison of FDMNES-simulated XANES with the recorded experimental spectra provides such information as shape and symmetry of the first coordination polyhedron(s) of the absorbing atom, ordering/distortion of the first coordination shell polyhedron, the type of nearest-neighbour atoms, and the interatomic distances (at R < 3 Å).

The goal of the present study was to determine the state of Pd in pyrite (including the position in the mineral host, formal oxidation state, local atomic environment) by means of XAS analysis combined with the ab initio FDMNES theoretical modelling. The Pd-doped crystals were obtained at the temperature of 580 °C and sulphur fugacity log f (S<sub>2</sub>) = -0.4 via conventional salt flux technique. The use of synthetic Pd-enriched crystals enabled the recording of good quality XANES and state-of-the-art EXAFS spectra, in order to investigate the formal oxidation state and local atomic environment of Pd in FeS<sub>2</sub> crystal structure. Our experimental data showed that Pd formed an isomorphous solid solution in pyrite. The factors promoting the formation of Pd-bearing pyrites were analysed, and, then, employed to interpret the state of Pd in natural FeS<sub>2</sub>.

## 2. Materials and methods

### 2.1. Synthesis of pyrite in the Pd-Fe-S system

Pd-doped pyrite crystals were obtained via salt flux technique at a steady-state temperature gradient (Chareev, 2016; Chareev et al., 2016). The charge composition was: crystalline S and metallic Fe (99.5 % purity, Labteh), and Pd wire of 0.5 mm diameter about 50 mm long. The initial reagents were loaded inside the silica glass ampoule (8 mm ID, 11 mm OD, ~100 mm length) together with a RbCl/NaBr/KI salt mixture, which volume never exceeded 80 % of the ampoule. The silica glass ampoule was evacuated, sealed using an oxygen torch gas burner, placed into a horizontal tube furnace, and heated up to the synthesis temperature of 640 °C at the hot end of the ampoule. The temperature of 580 °C registered at the cold end of the ampoule corresponded to the temperature of Pd-bearing pyrites formation. The initial charge migrated from the hot end to the cold end of the ampoule. The duration of the experiment was one month. Then, the ampoule was extracted from the furnace and quenched in cold water. The cold end of the ampoule containing the doped grains was cut off. Approximately 0.5 g of the obtained crystals and crystal aggregates were rinsed in distilled water

and acetone, and dried in the muffle furnace at a temperature of 70 °C to prevent oxidation.

### 2.2. Analytical methods

#### 2.2.1. XRD, SEM/EDS, and EPMA

The X-Ray diffraction (XRD) data were collected at ID28 diffractometer (CrysAlisPRO, Rigaku Oxford Diffraction) at the wavelength λ = 0.697 Å with a typical beam size of about 40 µm (FWHM). The data were recorded from an irregular-shaped grain by a single-photon-counting PILATUS3 1 M detector, positioned at 244 mm away from the sample, in shutter-free mode with 0.25° angular step. The experimental geometry and the orientation matrix were refined using the CrysAlisPro software (Girard et al., 2019). A locally developed software was used for high-resolution reconstructions.

Three crystals of Pd-doped pyrite (py-I, py-II, and py-III) were potted in epoxy, polished, and studied via a scanning electron microscope equipped with an energy dispersive spectrometer (SEM/EDS) and electron probe microanalyser (EPMA). The details of analyses are given in Tables A1 and A2 in Supplementary material. SEM/EDS analysis was performed using a Zeiss LEO 1530 microscope equipped with a secondary electron (SE) gun and backscattered detectors for imaging (BSE), and EDS. The EDS limit of detection for Pd was 0.1 wt%. EPMA analysis was performed using a JEOL JXA-8200 WDS/EDS combined electron probe microanalyser equipped with five wavelength dispersive X-ray spectrometers. The EPMA limit of detection for Pd was 0.03 wt%.

#### 2.2.2. LA-ICP-MS

The concentration of Pd (isotope ¹⁰⁵Pd) was measured via laser ablation inductively coupled plasma spectrometry (LA-ICP-MS) method (Thermo X Series2 quadrupole ICP-MS coupled with New Wave 213 laser). The in-house pyrrhotite Fe<sub>0.9</sub>S and sulphide reference material MASS-1 (Wilson et al., 2002) were used as reference materials. The details of the preparation and calibration of the in-house reference material are given in Tagirov et al. (2016).

#### 2.2.3. XAS

The recording of TFY-XAS (total fluorescence yield mode) spectra was performed at the XMaS beamline BM28 at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The storage-ring operating conditions were 6.0 GeV and 40 mA (4-bunch filling). The photon energy was scanned using the Si(111) monochromator. The Pt-coated toroidal mirror was focusing the x-rays onto the sample. Rejection of higher energy harmonics was achieved by the double reflection of two Pt-coated flat mirrors. A silicon drift diode detector (SDD, Ketek GmbH) was used to record the experimental spectra. The size of the beam was ~80 × 80 µm². The energy calibration was performed using a Pd foil (maximum of the first derivative at 24350 eV).

The spectra of reference materials of Pd<sup>0</sup>, PdS, and K<sub>2</sub>PdCl<sub>6</sub> were measured in transmission mode. Standards of PdS and K<sub>2</sub>PdCl<sub>6</sub> were spread on adhesive Kapton tape. All energy scans were recorded from 24,100 to 25,350 eV. From 2 to 8 scans were averaged for each experimental spectrum of standards and samples respectively.

Data reduction and fitting of Pd K-edge absorption spectra were performed using the Athena (preliminary data processing, analysis of XANES spectra) and Artemis (EXAFS spectra fitting) programs of the software package IFEFFIT (Ravel and Newville, 2005) using theory from the version of FEFF6 (Zabinsky et al., 1995).

## 3. Experimental results

### 3.1. XRD, SEM/EDS, EPMA, and LA-ICP-MS analyses

Pd-doped crystals of 0.5 to 3 mm size were synthesized at the py-S<sub>1</sub> equilibrium at 580 °C in the Pd-saturated system. XRD analysis
unambiguously identified pyrite structure (space group *P* $\bar{a}$3, e.g., Brostigen et al., 1969; Fig. A1). Based on the optical microscopy observations, no Pd-rich phases (e.g. Pd, PdS, PdS₂) were observed on the surfaces of three studied crystals. Backscattered electron images (BSE) demonstrate the uniform distribution of Pd in the matrix of pyrite (Fig. 1). Average chemical compositions of the grains are given in Table 2. Full chemical compositions are presented in Supplementary material (Tables A3 and A4). The values obtained by SEM/EDS analysis exhibit a large systematic error in Fe and S contents in comparison with EPMA data.

According to EPMA and EDS analyses, the content of Pd in all the grains varied from 0.3 to 1.4 wt%. The median value between all the data was approximately 0.7 wt%. In order to define the average concentration of Pd in the pyrite matrix LA-ICP-MS analysis was performed. Time-resolved LA-ICP-MS signals are shown in Supplementary Fig. A2. The smooth shape of the signals within the crystal zones demonstrate the homogeneous character of Pd distribution in pyrite. The maximum content of homogeneously distributed Pd determined by LA-ICP-MS is 0.70 ± 0.07 wt% (±2σ). This value represents the capacity of pyrite to incorporate Pd at the given temperature and sulphur fugacity.

The homogeneous distribution of Pd on the level of tens of microns determined by BSE-imaging and LA-ICP-MS cannot rule out the formation of nano-sized inclusions of Pd-bearing phase(s) in the pyrite matrix. Therefore, we performed the “model lines” analyses (e.g. Kovalchuk et al., 2019; Fleet and Mumin, 1997). The binary plot given in Fig. 2 shows a negative dependence between the concentration of Fe (major element) and Pd (trace element) determined by EPMA together with the three model lines ‘py + Pd⁰’, ‘py + PdS’, ‘py + PdS₂/(Pd,Fe)S₂’. The experimental data can only be described by the latter model, which corresponds to the formation of a solid solution (Pd,Fe)S₂ or/and presence of a mixture of PdS₂ and FeS₂. To discriminate between these two models and determine the mechanism of Pd incorporation into the pyrite structure, a XAS experiment was conducted.

## 3.2. XANES spectra analysis

The Pd K-edge normalised XANES spectra and their derivatives for Pd-doped pyrites (py-I and py-III) are shown in Fig. 3A and B, along with spectra of reference materials: Pd⁰, Pd²⁺S, Pd⁴⁺K₂Cl₆. Positions of the absorption edges (e.j.), white lines (WL), and the differences between edge jump of samples/standards and e.j. of Pd⁰ (e.j. sample/standard – e.

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Selected backscattered electron (BSE) images of synthetic Pd-bearing pyrites demonstrating a uniform Z-contrast distribution of Pd in sulphide. A, B: py-II; C, D: py-III.</figcaption></figure>

<table><caption>**Table 2**
The content of Pd in synthetic pyrites.</caption><thead><tr><th>Method</th><th>Minimum, maximum, average contents in wt% ± 2σ</th><th>py-I</th><th>py-II</th><th>py-III</th></tr></thead><tbody><tr><td rowspan="4">EDS<sup>a</sup></td><td>Min</td><td>0.5 ±<br>0.1</td><td>0.7 ±<br>0.1</td><td>Below<br>detection limit</td></tr><tr><td>Max</td><td>1.9 ±<br>0.1</td><td>1.3 ±<br>0.1</td><td>1.4 ± 0.1</td></tr><tr><td>Average</td><td>1.2 ±<br>0.4</td><td>1.0 ±<br>0.2</td><td>0.8 ± 0.3</td></tr><tr><td>Min</td><td>0.3 ±<br>0.02</td><td></td><td></td></tr><tr><td rowspan="4">EPMA<sup>b</sup></td><td>Max</td><td>1.3 ±<br>0.02</td><td></td><td></td></tr><tr><td>Average</td><td>0.8 ±<br>0.1</td><td></td><td></td></tr><tr><td>Min</td><td>0.5 ±<br>0.1<sup>d</sup></td><td>–</td><td>0.02 ± 0.01</td></tr><tr><td>Max</td><td>0.70 ±<br>0.07</td><td>–</td><td>0.2 ± 0.1</td></tr><tr><td rowspan="2">LA-ICP-MS<sup>c</sup></td><td>Min</td><td>0.6 ±<br>0.1</td><td>–</td><td>0.1 ± 0.1</td></tr><tr><td>Average</td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Concentration of Pd as a function of concentration of Fe. Results of EPMA are shown by squares. Model lines were calculated theoretically. Thick grey lines correspond to three equivalent models: Pd substitutes for Fe in FeS₂ or Fe substitutes for Pd in PdS₂ – (Pd,Fe)S₂, or the mixture PtS₂ + FeS₂. Alternative models of Pd in pyrite (PdS + FeS₂, Pd⁰ + FeS₂) are shown by dashed and dotted lines.</figcaption></figure>

j. Pd⁰) are given in Table 3 and shown in Fig. 3C.

To facilitate the discussion of XAS data, the local atomic coordination of the cations in the structures of Pd⁰, PdS, PdS₂, K₂PdCl₆, and FeS₂ are given in Table 4, and the cations (Fe/Pd) polyhedra are shown in Fig. 4. Throughout this text, we are going to use the term “formal” oxidation state, which implies that the oxidation state is calculated based on the principle of charge balance. The real charges, for example, Bader charges, can be substantially different from the formal ones (e.g. Evstigneeva et al., 2021).

<footnote><sup>a</sup> EDS detection limit = 0.1 wt%.</footnote>

<footnote><sup>b</sup> EPMA detection limit = 0.03 wt%.</footnote>

<footnote><sup>c</sup> LA-ICP-MS detection limit = 0.05 ppm, the values determined by Iolite software (Paton et al., 2011).</footnote>

<footnote><sup>d</sup> LA-ICP-MS line analysis (Ø 60 × length 200 µm), other analyses – spots (Ø 60 µm).</footnote>
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** A: Normalised XANES spectra of standards (Pd<sup>0</sup>, Pd<sup>2+</sup>S, Pd<sup>4+</sup>K<sub>2</sub>Cl<sub>6</sub>) and Pd-bearing pyrite; B: derivatives of XANES spectra. Vertical dotted lines denote positions of the edge jumps of references spectra and samples; C: formal oxidation states of Pd as a function of [e.j. sample/standard – e.j. Pd<sup>0</sup>] position.</figcaption></figure>

<caption>**Table 3**</caption>

Positions of the main spectra features: absorption edge (edge jump, e.j.) and first intensive peak (white line, WL) of Pd K-edge normalised spectra of standards and synthetic Pd-doped pyrites as determined by the Athena program (Ravel and Newville, 2005). The uncertainty of the energy values is ±0.5 eV.

<table><thead><tr><th rowspan="2">Standard or sample</th><th colspan="3">Feature position (eV)</th></tr><tr><th>e.j., eV</th><th>WL, eV</th><th>e.j. sample/standard – e.j. Pd<sup>0</sup></th></tr></thead><tbody><tr><td>Pd<sup>0</sup> foil</td><td>24,350.0</td><td>24,369.0</td><td>0</td></tr><tr><td>Pd<sup>2+</sup>S</td><td>24,353.0</td><td>24,360.5</td><td>3</td></tr><tr><td>Pd<sup>4+</sup>K<sub>2</sub>Cl<sub>6</sub></td><td>24,358.0</td><td>24,366.0</td><td>8</td></tr><tr><td>py-I</td><td>24,354.0</td><td>24,361.5</td><td>4</td></tr><tr><td>py-III</td><td>24,354.0</td><td>24,361.5</td><td>4</td></tr></tbody></table>

### 3.2.1. Standards

In metallic Pd<sup>0</sup>, Pd is surrounded by 12 Pd atoms (cuboctahedron) at the distance of 2.75 Å. In PdS, Pd atoms are surrounded by 4 S atoms at R<sub>Pd-S</sub> ~ 2.30 Å (distorted square). The formal oxidation states of Pd in PdS is considered to be close to +2. The formula can be written as Pd<sup>2+</sup>S<sup>2-</sup>. In K<sub>2</sub>PdCl<sub>6</sub> structure, Pd<sup>4+</sup> is surrounded by 6 Cl atoms (octahedron) at 1.94 Å. The positions of the e.j. of Pd<sup>0</sup>, Pd<sup>2+</sup>S, and K<sub>2</sub>Pd<sup>4+</sup>Cl<sub>6</sub> spectra are 24,350, 24,353, and 24,358 eV, respectively. The positions of e.j. of standards are directly correlated with the formal oxidation state of Pd in these compounds: the increase of the oxidation state leads to the rightward shift of the e.j. position, i.e. to higher (binding) energies. This dependence is shown in Fig. 3C at the graph which was obtained in order to estimate the formal oxidation state of Pd

in pyrite.

### 3.2.2. Pyrite

The shape and main spectral features of Pd-doped pyrites spectra of py-I and py-III are different from those of Pd<sup>0</sup> and K<sub>2</sub>Pd<sup>4+</sup>Cl<sub>6</sub>. The e.j. positions of spectra of samples are shifted towards higher energies in comparison with that of spectrum of Pd (24,350 eV), and towards lower energies in comparison with that of spectrum of K<sub>2</sub>PdCl<sub>6</sub> (24,358 eV). The value of the e.j. position of samples (24,354 eV) is close to Pd<sup>2+</sup>S (24,353 eV). According to the calibration curve in Fig. 3C, the formal oxidation state of Pd in pyrites is close to +2.2. This value slightly exceeds the formal oxidation state of Fe of +2 in the pure pyrite and the formal oxidation state of Pd of +2 in PdS. In other words, the electron density is slightly shifted from the absorbing atom towards the matrix. Unfortunately, high-energy Pd K-edge spectra do not show the extensive shape difference between Pd in octahedral and tetrahedral coordination (as would the L<sub>3</sub>-edge spectra, e.g. Brovchenko et al., 2023).

### 3.3. EXAFS spectra analysis

The Pd K-edge EXAFS spectra together with their Fourier transforms are shown in Fig. 5A and B for py-I and py-III, respectively. Results of the EXAFS spectra fittings are given in Table 5. Fitting of the spectra suggests that Pd incorporates in the cationic site of the pyrite structure. The interatomic distance Pd—S of 2.385 Å is increased in comparison with the Fe—S distance of 2.26 Å. Pd—S distance increases by almost 5.6 % compared to Fe—S distance in the pure pyrite. In the second and further

<caption>**Table 4**</caption>

Composition of the local atomic environment of Pd (or Fe) in Pd, PdS, PdS2, K<sub>2</sub>PdCl<sub>6</sub>, and FeS<sub>2</sub>.

<table><thead><tr><th>Name of mineral</th><th>Pd in Pd<sup>0</sup></th><th>Pd in PdS<sup>0</sup></th><th>Pd in PdS<sub>2</sub></th><th>Pd in K<sub>2</sub>PdCl<sub>6</sub></th><th>Fe in FeS<sub>2</sub></th><th>Pd in py-I and III<sup>b</sup></th></tr></thead><tbody><tr><td rowspan="3">Local atomic environment up to 5 Å</td><td>12 Pd at 2.75 Å (cuboctahedron)</td><td>4 S at ~2.34 Å (distorted square)</td><td>4 S at ~2.30 Å (distorted square)</td><td>6 Cl at 1.94 Å (octahedron)</td><td>6 S at 2.26 Å (octahedron)</td><td>6 S at 2.385 Å (octahedron)</td></tr><tr><td>6 Pd at 3.89 Å</td><td>4 Pd at 3.66 Å</td><td>6 S at 3.31–3.49</td><td>8 K at 3.53 Å</td><td>6 S at 3.45 Å</td><td>6 S at 3.45 Å</td></tr><tr><td>24 Pd at 4.76 Å</td><td>12–14 S 3.72 Å<br>16–24 S at 5.55 Å</td><td>4 Pd at 3.89 Å<br>4 S at 4.41 Å<br>8 Pd at 4.66 Å</td><td>24 Cl at 4.60 Å</td><td>2 S at 3.60 Å<br>12 Fe at 3.83 Å<br>6 S at 4.45 Å</td><td>2 S at 3.60 Å<br>12 Fe at 3.86 Å<br>6 S at 4.46 Å</td></tr><tr><td>Reference</td><td>Wyckoff (1963)</td><td>Grønvold and Røst (1956)</td><td>Grønvold and Røst (1957), Selb et al. (2017)</td><td>Takazawa et al. (1988)</td><td>Brostigen et al. (1969)</td><td>Initial data from Brostigen et al. (1969)</td></tr></tbody></table>

<footnote><sup>a</sup> Averaged from 3 Wyckoff positions: 4j, 2e, 2c.</footnote>

<footnote><sup>b</sup> Merged from the spectra of py-I and py-III.</footnote>
<figure><img src="image_8.png" /><figcaption>Fig. 4. The nearest coordination shells of cation (Fe/Pd) in the structures of (A) FeS₂, (B) PdS₂, and (C) PdS.</figcaption></figure>

coordination shells, no expansion was observed: Pd—S and Pd—Fe dis-
tances are close to Fe—S and Fe—Fe in the pure pyrite structure (Bros-
tigen et al., 1969). The attempts to introduce heavy Pd atom in the local
atomic environment of Pd at the distances typical of Pd⁰, PdS, and PdS₂
failed (structures adapted from Wyckoff (1963), Grønvold and Røst
(1956), and Grønvold and Røst (1957), respectively). Thus, the results of
the EXAFS fitting suggest that isomorphic Pd incorporates in the pyrite
structure without formation of the nano-sized minerals and Pd—Pd
clustering.

4. Theoretical results

4.1. FDMNES modelling of XANES spectra

The goal of the XANES spectra simulations was to verify the model of
Pd incorporation into the pyrite structure proposed from the fitting of
the EXAFS spectra. Modelling of Pd *K*-edge XANES spectra was per-
formed using the ab initio finite difference method for near-edge
structure (FDMNES) code (Joly, 2001; Guda et al., 2015). Relativistic
calculations were performed with a 5 Å cluster radius and a 3 × 3 × 3
supercell structure. The spectra were calculated in the energy range
between –45 and 100 eV around the Pd absorption *K*-edge, and then
convoluted with a Lorentzian function to take into account the core-hole
lifetime.

4.1.1. Standards

Cubic K₂PdCl₆ (space group F m ¯3m, lattice parameter *a* = 9.6374 Å, Takazawa et al., 1988) and tetragonal PdS crystal structures (space group P 4₂/m, lattice parameter *a* = *b* = 6.4287, *c* = 6.6082 Å, Grønvold and Røst, 1956) were used as initial structures to simulate the spectra of the reference materials. The calculated (red dotted line) and experimental spectra of Pd in K₂PdCl₆ are shown in Fig. 6 A. For PdS, the initial structure contains three fully occupied Wyckoff positions of Pd. Therefore, three separate spectra were simulated for each of the positions, and then averaged. Individual contributions and the average spectrum are shown in Fig. A3. In Fig. 6 B the experimental spectrum of Pd in PdS is compared to the averaged simulated spectrum. For Pd in both reference materials, K₂PdCl₆ and PdS, the simulated and experimental XANES spectra exhibit similar main features and shapes, respectively. The parameters of simulation and convolution (Gamma_hole = 6 eV, E<sub>Fermi</sub> = 0 eV; Gamma_max = 12 eV) validated for K₂PdCl₆ and PdS were used to simulate and convolute the XANES spectra of Pd-bearing pyrite.

4.1.2. Pyrite

The refinement of the local atomic environment of Pd in py-I and py-
III performed by EXAFS spectra fitting demonstrated that (i) Pd²⁺ atoms
in pyrites were surrounded by 6 S atoms (octahedron) at 2.385 Å, (ii) the
expansion resulting from the incorporation of Pd atoms in the FeS₂
structure disappeared in the second coordination shell, where

<figure><img src="image_9.png" /><figcaption>Fig. 5. The *k*²-weighted background-subtracted EXAFS spectra (insert) together with their Fourier transforms (not corrected for phase shift, black lines – experiment, dotted red lines – simulation).</figcaption></figure>
<caption>**Table 5**</caption>

Parameters of Pd local atomic structure in pyrites determined by fitting of Pd K-edge EXAFS spectra determined by the Artemis program (Ravel and Newville, 2005).

<table><caption>**Table 5 (continued)**</caption><thead><tr><th rowspan="2">Atom</th><th colspan="5">Experimental data<sup>a</sup></th><th rowspan="2">Theoretical data<sup>b</sup></th></tr><tr><th>N</th><th>R, Å</th><th>σ<sup>2</sup>, Å<sup>2</sup></th><th>E<sup>0</sup>, eV</th><th>Fit quality</th><th>R, Å (N)</th></tr></thead><tbody><tr><td>py-I (R-range: 1.3-7.7, k-range: 3-10.5)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>S</td><td>6</td><td>2.39<br>±<br>0.01</td><td>0.005<br>±<br>0.001</td><td>3.9<br>±<br>1.5</td><td>12.4</td><td>0.022</td><td>2.26 (6)</td></tr><tr><td>S</td><td>6</td><td>3.46<br>±<br>0.02<sup>c</sup></td><td>0.005<br>±<br>0.003<sup>c</sup></td><td></td><td></td><td></td><td>3.45 (6)</td></tr><tr><td>S</td><td>2</td><td>3.61<sup>c</sup></td><td>0.005<sup>c</sup></td><td></td><td></td><td></td><td>3.60 (2)</td></tr><tr><td>Fe</td><td>12</td><td>3.87<br>±<br>0.02</td><td>0.005<br>±<br>0.003</td><td></td><td></td><td></td><td>3.83 (12)</td></tr><tr><td>MS<sup>d</sup></td><td>24</td><td>4.24<br>±<br>0.09</td><td>0.003<br>±<br>0.013</td><td></td><td></td><td></td><td>4.18 (24)</td></tr><tr><td>S</td><td>6</td><td>4.47<br>±<br>0.04</td><td>0.004<br>±<br>0.001</td><td></td><td></td><td></td><td>4.45 (6)</td></tr><tr><td>S</td><td>18</td><td>5.00<br>±<br>0.12</td><td>0.025<br>±<br>0.020</td><td></td><td></td><td></td><td>5.16 (6),<br>5.26 (12)</td></tr><tr><td>Fe</td><td>6</td><td>5.47<br>±<br>0.05</td><td>0.001<br>±<br>0.004</td><td></td><td></td><td></td><td>5.42 (6)</td></tr><tr><td>S</td><td>12</td><td>5.88<br>±<br>0.06</td><td>0.003<br>±<br>0.006</td><td></td><td></td><td></td><td>5.87 (12)</td></tr><tr><td>S</td><td>12</td><td>6.46<br>±<br>0.05</td><td>0.002<br>±<br>0.006</td><td></td><td></td><td></td><td>6.43 (12)</td></tr><tr><td>MS<sup>e</sup></td><td>24</td><td>7.72<br>±<br>0.04</td><td>0.005<br>±<br>0.003</td><td></td><td></td><td></td><td>7.66 (24)</td></tr><tr><td>py-III (R-range: 1.3-7.7, k-range: 3-10.5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>S</td><td>6</td><td>2.38<br>±<br>0.01</td><td>0.005<br>±<br>0.001</td><td>1.2<br>±<br>1.0</td><td>12.9</td><td>0.012</td><td>2.26 (6)</td></tr><tr><td>S</td><td>6</td><td>3.44<br>±<br>0.02<sup>c</sup></td><td>0.008<br>±<br>0.002<sup>c</sup></td><td></td><td></td><td></td><td>3.45 (6)</td></tr><tr><td>S</td><td>2</td><td>3.59<sup>c</sup></td><td>0.008<sup>c</sup></td><td></td><td></td><td></td><td>3.60 (2)</td></tr><tr><td>Fe</td><td>12</td><td>3.84<br>±<br>0.02</td><td>0.006<br>±<br>0.001</td><td></td><td></td><td></td><td>3.83 (12)</td></tr><tr><td>MS<sup>d</sup></td><td>24</td><td>4.23<br>±<br>0.04</td><td>0.003<br>±<br>0.007</td><td></td><td></td><td></td><td>4.18 (24)</td></tr><tr><td>S</td><td>6</td><td>4.45<br>±<br>0.03</td><td>0.003<br>±<br>0.004</td><td></td><td></td><td></td><td>4.45 (6)</td></tr><tr><td>S</td><td>18</td><td>4.94<br>±<br>0.04</td><td>0.016<br>±<br>0.005</td><td></td><td></td><td></td><td>5.16 (6),<br>5.26 (12)</td></tr><tr><td>Fe</td><td>6</td><td>5.42<br>±<br>0.02</td><td>0.001<br>±<br>0.002</td><td></td><td></td><td></td><td>5.42 (6)</td></tr><tr><td>S</td><td>12</td><td>5.87<br>±<br>0.03</td><td>0.003<br>±<br>0.003</td><td></td><td></td><td></td><td>5.87 (12)</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Atom</th><th colspan="5">Experimental data<sup>a</sup></th><th rowspan="2">Theoretical data<sup>b</sup></th></tr><tr><th>N</th><th>R, Å</th><th>σ<sup>2</sup>, Å<sup>2</sup></th><th>E<sup>0</sup>, eV</th><th>Fit quality</th><th>R, Å (N)</th></tr></thead><tbody><tr><td>S</td><td>12</td><td>6.45<br>±<br>0.06</td><td>0.007<br>±<br>0.007</td><td></td><td></td><td></td><td>6.43 (12)</td></tr><tr><td>MS<sup>d</sup></td><td>24</td><td>7.70<br>±<br>0.02</td><td>0.006<br>±<br>0.002</td><td></td><td></td><td></td><td>7.66 (24)</td></tr></tbody></table>

<sup>a</sup> Amplitude reduction factor $S_0^2 = 0.90$; the number of variables in the fit ($N_{var} = 21$) was lower than the number of independent points ($N_{ind} = 30$).

<sup>b</sup> $FeS_{2cubic}$ - Brostigen et al. (1969).

<sup>c</sup> After preliminary fitting, the parameters used for Path 3 (2 S atoms at ~3.6 Å) were determined to be equal to those of Path 2 (6 S atoms at ~3.45 Å).

<sup>d</sup> $MS = Pd - Fe - S - Pd$.

<sup>e</sup> $MS = Pd - Fe - Fe - Pd$.

interatomic distances were close to the distances typical of the Fe local atomic environment in pure $FeS_2$. For simulations, a cubic $FeS_2$ crystal structure (space group $P \bar{a}3$, lattice parameter $a = 5.4179 \AA$, Brostigen et al., 1969) was modified, respectively. Pd atom was introduced in the cationic site, the Me-S interatomic distance in the first coordination shell was increased from $2.26 \AA$ (Fe-S distance in pure pyrite) to ~2.36-2.42 Å (representing Pd-S distance in the doped pyrite). We simulated three spectra of Pd in $(Pd,Fe)S_2$ for various Pd-S interatomic distances: 2.36, 2.39, and 2.42 Å. The results of the simulations are shown in Fig. 6C and D for py-I and py-III respectively. The shapes of all the simulated spectra are close to that of experimental ones. The increase in Pd-S interatomic distance resulted in both an increase in intensity and a significant shift of the position of peak B (the second peak) towards lower energies. To numerically evaluate the quality of the simulations, we found the energy difference ($\Delta E$) between the positions of the WL and peak B (Table 6). The energy difference ($\Delta E$) increases with a decrease of the interatomic distance Pd-S in the following sequence: $\Delta E(2.42 \AA) < \Delta E(2.39 \AA) < \Delta E(2.36 \AA)$. The values of $\Delta E$ in the experimental spectra are close to those in the first simulation ($R_{Pd-S} = 2.36 \AA$, Fig. 6E). The difference of $0.025 \AA$ between the values of $R_{Pd-S}$ determined by FDMNES simulations (2.36 Å) and EXAFS spectra fitting (2.385 ± 0.015 Å) can be accounted for by the uncertainty of the FDMNES method (Andreeva et al., 2019) which slightly exceeds the uncertainty of the EXAFS spectra fitting (±0.02 Å for the 1st coordination sphere, Table 4).

# 5. Discussion

## 5.1. Solubility

The concentration of Pd in all the crystals synthesized at 580 °C varied between 0.3 and 1.4 wt%. The average Pd content obtained via LA-ICP-MS method and the median value obtained by EPMA were ~ 0.7 wt% (Tables 1, A3, A4). This result together with the literature data on Pd concentrations in natural and synthetic pyrites obtained at 400-725 °C is given in Table 1 and plotted in Fig. 7.

There are two major factors controlling the solubility of Pd in pyrite ($log C_{Pd}^{SS}$, ppm): temperature (1000/T, 1/K) and sulphur fugacity ($log f_{S_2}$, bar). At the same time, the stability field of pyrite on the diagram 1000/T - log $f_{S_2}$ (Toulmin and Barton, 1964) can be nominally divided into the two fields: 'py + $PdS_2$' and 'py + $PdS$' (Fig. A4 in Supplementary material). The formation of Pd solid solution in the field 'py + $PdS_2$' can be described by the reaction which does not involve sulphur, in other words, in this field, the content of Pd depends only on temperature:

$$ \mathrm{PdS}_{2\mathrm{cr}} = \mathrm{PdS}_{2\mathrm{ss}}, \log C_{\mathrm{Pd}}^{\mathrm{SS}} = f\left(\frac{1000}{T}\right). \quad (1) $$
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** A, B: Experimental Pd K-edge XANES spectra of standards of Pd<sup>0</sup> and PdK<sub>2</sub>Cl<sub>6</sub> (solid black lines) plotted together with the spectra calculated by FDMNES code (dotted red lines). The energy origin is defined relative to the theoretical Fermi level; C, D: experimental Pd K-edge XANES spectra of samples py-I and py-III (black solid lines) shown together with the spectra of models with various Pd—S interatomic distances calculated by FDMNES code: A – R<sub>Pd-S</sub> = 2.36 Å (dotted red lines), B – R<sub>Pd-S</sub> = 2.39 Å (dotted violet lines), and C – R<sub>Pd-S</sub> = 2.42 Å (dotted purple lines); D: the difference between peak B and WL (eV) as a function of the interatomic distance R<sub>Pd-S</sub> (Å). Squares – values obtained from calculated spectra. Red dashed line – regression through the values. Horizontal blue rectangular area indicates the value derived from the experimental spectra of py-I and py-III. The best value describing the experimental one is obtained for the model where Pd cation is surrounded by 6 S atoms at 2.36 Å in structure of pyrite.</figcaption></figure>
<table><caption>**Table 6**
The best model of Pd local atomic environment in pyrite obtained experimentally (sample) and determined by means of the FDMNES simulations of Pd K-edge XANES spectra.</caption><thead><tr><th>Simulation or sample No.</th><th><i>R</i><sub>Pd-S</sub><br>Å</th><th>Δ(WL position - peak B position), eV</th><th>Reference</th></tr></thead><tbody><tr><td>Samples: py-I and py-III</td><td>2.385</td><td>66.0</td><td>EXAFS, this study</td></tr><tr><td>A</td><td>2.36</td><td>66.5</td><td>Brostigen et al., 1969</td></tr><tr><td>B</td><td>2.39</td><td>62.5</td><td>Brostigen et al., 1969</td></tr><tr><td>C</td><td>2.42</td><td>59.5</td><td>Brostigen et al., 1969</td></tr></tbody></table>

A trend of Pd solubility in pyrite synthesized in the equilibrium with palladium disulphide is shown in grey dashed line in Fig. 7.

At lower sulphur fugacity in the stability field of PdS<sub>(cr)</sub>, the concentration of Pd solid solution in pyrite depends on temperature, and also changes proportionally to the square root of sulphur fugacity, because the formation of the solid solution occurs according to the reaction involving sulphur:

$$ \mathrm{PdS_{cr} + S_{2g} = PdS_{2ss}, \log C_{\mathrm{Pd}}^{\mathrm{SS}} = f(\frac{1000}{T}; \log f_{S_2}).} \quad (2) $$

At py-po equilibrium the value of sulphur fugacity depends on the temperature. That means that the equilibrium can be considered

univariant. Based on the reaction (2) we plotted a regression line corresponding to the Pd solubility limit in pyrite formed in equilibrium with pyrrhotite, this trend is shown in black dotted line in Fig. 7. Our results combined with a new data set on the Pd solubility in pyrite can be used to build an accurate thermodynamic model similar to the one proposed for Pt-bearing pyrite in Filimonova et al. (2022).

According to the literature data on natural pyrites (Table 1), Pd concentration increases with higher pyrite formation and/or enrichment temperature but never exceeds experimentally determined solubility limits proposed in our study. For example, at the temperatures of 300–500 °C, the content of Pd in synthetic and natural pyrites are of the same order of magnitude (~30 ppm) indicating the saturation of pyrite with respect to Pd. However, at t > 500 °C, the content of Pd in the natural pyrites is clearly below the solubility limit. At t > 690 °C, the difference between natural and experimental data is even more pronounced: the Pd content C<sub>Pd</sub> in synthetic samples varies between 2 and 4 wt%, while in the natural samples formed at the same temperatures, the Pd content does not exceed 500 ppm (Cabri et al., 2008). This fact can be accounted for by the appearance of *hpn* (high pentlandite) at t > 500 °C (Kitakaze and Komatsu, 2020), which contains extremely high Pd concentration of a few wt% (Brovchenko et al., 2023 and references therein; Kalugin et al., 2021).

The only exception is pyrite formed in deposits of hydrogenous-diagenetic origin. The high amount of Pd of 390 ppm observed in low-temperature pyrite (see Table 1, Pašava et al., 2013; Orberger et al., 2007) is likely to happen due to biogenic-related origin, thus the state of

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** The concentration of Pd in pyrite as a function of the synthesis/origin reciprocal temperature. Sketch diagram is built based on the data from Table 1. The dashed and dotted lines indicate the solubility limit of Pd in pyrite formed at the equilibrium py-S<sub>l</sub> and py-po respectively.</figcaption></figure>
Pd may be different from the one determined in this study, e.g. Pd⁰.

## 5.2. Incorporation mechanism

As determined by Pd K-edge EXAFS spectra fitting, the isomorphous Pd in doped pyrites is octahedrally coordinated by 6 S atoms at a distance of ~2.385 Å. The Me-S distance in the first coordination shell increased from $R_{Fe-S}$ = 2.26 Å to $R_{Pd-S}$ = 2.385 Å. In the distant coordination shells of Pd the interatomic distances Pd—S and Pd—Fe are close to those in the local atomic environment of Fe in the pure pyrite structure up to 8 Å. Thus, the expansion of the cationic polyhedron disappears at $R > 3$ Å. Based on the literature data apart from solid solution Au- and Pt-rich pyrites can contain Au/Pt-rich nano-sized inclusions or clusters (Au₂S clusters, PtS₂ nano-sized inclusions/clusters, Filimonova et al., 2019, 2021). However, in case of Pd-rich pyrite, no additional contributions from the heavy Pd atom were observed in the local atomic environment of Pd within the experimental limit of ~5 %. That means that the possible contribution of PdS, Pd₂.₃S, or PdS₂ nano-minerals is absent or negligible.

Analysis of Pd K-edge XANES spectra revealed that the absorption edges of the experimental spectra of Pd in pyrites were slightly rightward shifted compared to PdS. Pd oxidation state was close to +2.2 in both samples of pyrite, slightly exceeding the formal oxidation state in Pd²⁺S (standard) and Fe²⁺S₂ (host mineral). However, Guda et al. (2021) demonstrated that the increase in the coordination number of the absorbing atom can also lead to the rightward energy shift of the main features of the spectra. Thus, the slight rightward shift of the spectra of Pd in pyrite compared to PdS can be accounted for by the difference in the coordination numbers of Pd: $N_S = 4$ in PdS and $N_S = 6$ in FeS₂.

The shape of the experimental spectra was more pronounced, also indicating the higher charge (the electron density is moved towards the matrix), and larger and more symmetrical local atomic geometry than in that of Pd in PdS. We also note that based on the data obtained for Pt in (Pt,Fe)S₂ (Evdstigneeva et al., 2021), the real DDEC charges can substantially differ from the formal ones: formal oxidation states (Fe²⁺, Pt⁴⁺)S₂ vs. real charges (Fe⁰.¹⁸⁺, Pt⁰.⁴⁴⁺)S₂⁰.¹. The modelling of the XANES spectra of Pd in pyrite showed that Pd²⁺ incorporates in the pyrite structure, expanding the first coordination shell, the distant coordination shells are located at distances typical of pure pyrite. Thus, based on the XAS spectra analyses and FDMNES simulations, the formula of Pd-rich synthetic pyrite can be written as $[Pd,Fe]²⁺[S₂]²⁻$.

## 5.3. Crystallographic considerations

Based on the classical approach proposed by Pauling (1940), Hannay and Smyth (1946) suggested to evaluate the percentage of ionic

character (Ionic %) of bonding in the compounds according to the formula:

$$ \text{Ionic\%} = 0.16 \times (\chi_{\text{anion}} - \chi_{\text{cation}}) + 0.035 \times (\chi_{\text{anion}} - \chi_{\text{cation}})^2. \quad (3) $$

Pauling electronegativities were revisited by Allred (1961) with the precision of ±0.1 electronegativity units (el.u.). The values of average electronegativities (χ) for S, Fe, Pd, and Pt are 2.58, 1.83, 2.20, and 2.28 el.u. respectively. Thus, using Eq. (3), we can define the percentage of ionic character for the Fe—S, Pd—S, and Pt—S bonds: IonicFe-S = 14 %, IonicPd-S = 7 %, IonicPt-S = 5 % (for example, the same calculation for the strongly ionic bonding Cs—F shows the amount of the ionic bonding of 87 %). This observation suggests that the character of Me-S bonding (Me = Fe, Pd, and Pt) is mostly covalent and the use of the values of ionic radii (Shannon, 1976) can be misleading. Thus, in case of the incorporation of Group 10 elements into the pyrite structure, we have to compare the covalent radii rather than the ionic radii.

In this study, we used the revisited covalent radii obtained by Cornero et al. (2008). Comparison of the covalent radii of Fe (1.32 Å) vs. Pd (1.39 Å) and Fe vs. Pt (1.36 Å) suggests that in case of the isomorphic substitution Fe → Pd and Fe → Pt the increase in the interatomic distances $R_{Pd-S}$ and $R_{Pt-S}$ of 5.3 and 3 % should be observed. Comparison of the Pd—S and Pt—S distances of 2.385 and 2.35 Å, determined experimentally by EXAFS method in this study and in Filimonova et al. (2019), shows that the interatomic distance Pd—S increases by 5.6 % compared to Fe—S, and the interatomic distance Pt—S—by 4 % compared to Fe—S. The increase of interatomic distance calculated from the covalent radii and according to experimental data is similar. In Fig. 8 three graphs are presented: Me-S interatomic distances vs. covalent and ionic radii (8 Å) and Me-S interatomic distances vs. χS – χMe (8B). The only significant correlation is observed for the dependence Me-S interatomic distances vs. covalent radii. These facts suggest that the values of covalent radii are more likely to control the incorporation of Pt and Pd into Fe position of pyrite structure rather than electronegativities of the metals, or the values of ionic radii.

# 6. Implications and conclusions

In the modern metal mining, a minor percentage of the extracted materials are the valuable target elements (e.g. PGEs, Au, and Ag: a few ppm to hundreds of ppm, Bourgeois et al., 2020, Sefako et al., 2019). Both fresh mines and old deposits tailings containing useful elements can produce economically valuable mineral concentrates (Dold, 2020, and references therein). Unfortunately, the vast majority of the micro-admixtures remain in the wastes. Pyrite itself can serve as a sorbent for the carrier of nuclear waste (U and Se, Tc, Am, Mingliang et al., 2014;

<figure><img src="image_12.png" /><figcaption>Fig. 8. A: Me-S interatomic distances vs. covalent and ionic radii; B: Me-S interatomic distances vs. χS – χMe.</figcaption></figure>
Bruggeman et al., 2007; Das et al., 2011) while pyrite matrix is an exceptional source of Fe, S, H₂SO₄, Pd (Table 1), Au (Pokrovski et al., 2021; Deditius et al., 2014), Pt (Filimonova et al., 2019; Smith et al., 2014; Cabri et al., 2008; Gervilla and Kojonen, 2002) etc. The noble and critical metals can be obtained as a by-product of mining and beneficiation of pyrite-bearing ores. Understanding the state of elements like Au and PGE in pyrite and other sulphide mineral containers is also fundamental for developing physical-chemical models of their geochemical transport and precipitation. Thus, the understanding of PGE speciation and their substitution mechanisms in pyrite are of both high economic interest and scientific significance.

The description of the substitution Fe²⁺ → Pd²⁺ in the pyrite structure is the most important new insight from this study. Our results elucidate the significant role of pyrite as a host mineral of Pd in the deposits of different origin from high-temperature orthomagmatic to low-temperature hydrothermal. The presence of any additional nano-sized Pd minerals in the matrix of pyrite was ruled out based on XAS analyses. The content of Pd in natural pyrite formed below 500 °C can reach the solubility limit of 30 ppm. However, at the temperatures above 500 °C, pyrites are not saturated with respect to Pd (for example, at *t* ~ 690–720 °C, C~Pd~ in synthetic samples – 2-4 wt%, C~Pd~ in natural samples – 500 ppm, Cabri et al., 2008). This fact can be accounted for by the appearance of *hpn* (high pentlandite) extremely enriched with Pd (at *t* > 500 °C, Kitakaze and Komatsu, 2020). Further experiments are needed to determine the effect of geologically important toxic and useful admixtures (for example, Ag, As, Bi, Sb, Se, Pb, Pt, and Tl) on the concentration and state of Pd in pyrite. The results of this paper combined with the new data on the Pd solubility will be used to build an accurate thermodynamic model of Pd-bearing pyrites.

## CRediT authorship contribution statement

**Olga N. Filimonova:** Writing – original draft, Visualization, Software, Investigation, Formal analysis, Conceptualization. **Irina I. Snigireva:** Investigation, Paul Thompson: Investigation, Data curation. **Didier Wermeille:** Writing – review & editing, Supervision.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

https://data.mendeley.com/preview/f88ctjpscs?b1a9365a-bc8c-468c-9299-f78c032cd4cc

## Acknowledgments

We acknowledge the XMaS/BM28 beamline (a UK EPSRC funded National Research Facility) at the European Synchrotron Radiation Facility for beam time allocation (experiment No. IH-ES-120). We thank Dr. habil. Boris Tagirov (https://orcid.org/0000-0002-7038-2337), Dr. habil. Dmitriy Chareev (https://orcid.org/0000-0002-9380-2680), Elena Kovalchuk, and Vera Abramova (https://orcid.org/0000-0002-7021-5272) for their inestimable help in organizing and performing the synthesis experiments and EPMA analyses of the Pd-doped crystals carried out in 2017. We thank PhD, Dr. habil. Alexei Bosak for performing the XRD analysis at the ID28 beamline at the ESRF. We are grateful to two anonymous reviewers and Associate Editor, Professor, Ph.D., Daniel S Alessi for constructive comments that helped to improve the manuscript.

# Appendix A. Supplementary data

The Supplementary material file contains additional information on XRD, EPMA, LA-ICP-MS, phase relations, and XAS analyses (Tables A1–A4 and Figs. A1–A4). Supplementary data to this article can be found online at https://doi.org/10.1016/j.scitotenv.2024.170927.

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