# Isotopic fractionation of copper during silicate melt evaporation: effects of sulfur, fO2, and temperature

Guillaume Florin, Paul Pangritz, Christian J Renggli, Philipp Gleißner, Jasper Berndt, Arno Rohrbach, Harry Becker, Stephan Klemme

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Guillaume Florin, Paul Pangritz, Christian J Renggli, Philipp Gleißner, Jasper Berndt, et al. Isotopic fractionation of copper during silicate melt evaporation: effects of sulfur, fO2, and temperature. Geochimica et Cosmochimica Acta, 2025, 409, pp.131-146. 10.1016/j.gca.2025.09.015. hal-05446685

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# Isotopic fractionation of copper during silicate melt evaporation: effects of sulfur, fO₂, and temperature

Guillaume Florin<sup>a,d,∗</sup>, Paul Pangritz<sup>b,†</sup>, Christian J. Renggli<sup>b,c</sup>, Philipp Gleißner<sup>a,‡</sup>, Jasper Berndt<sup>b</sup>, Arno Rohrbach<sup>b</sup>, Harry Becker<sup>a</sup>, Stephan Klemme<sup>b,‡</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

Associate editor: James M.D. Day

**Keywords:**

Experiment

Degassing

Evaporation

Cu isotope

Non-traditional isotopes

Moderately volatile trace elements

## ABSTRACT

Moderately volatile trace elements (MVE) such as Cu are emitted in large quantities from volcanoes on Earth and are tracers and are important for volatility related processes on other planetary bodies such as the Moon. The evaporation of MVE from silicate melts is complex, as evaporation rates change with temperature, oxygen fugacity, and may also be influenced by the presence of ligand-forming elements such as S. While on Earth, MVE evaporation and their ligands can be evaluated by *in situ* sampling at volcanic vents and fumaroles, this is not possible on the Moon. Isotopic investigations of Apollo lunar picritic glasses provide evidence for evaporation and condensation processes on the lunar surface. Unlike Earth's oxidized volcanic activity, evidence suggests that ancient lunar volcanism was more reduced.

To study the effect of temperature, oxygen fugacity, and the influence of S on the degassing of Cu from silicate melts, we conducted experiments at 1150–1500 °C and different oxygen fugacities (logfO₂) ranging from strongly oxidizing conditions (i.e., in air) to reducing conditions that correspond to a fO₂ that is 6 log units lower than the Fayalite-Magnetite-Quartz buffer (FMQ). Experimental results show an increase of Cu volatility associated with strong isotopic fractionation with increasing temperature, and with increasingly reducing conditions for all starting materials. We also observe that the temperature and redox conditions have a competing effect on Cu evaporation and isotopic fractionation. In S-bearing systems, Cu content decreases together with increasing isotopic composition as the conditions become more reducing. The isotopic fractionation becomes less pronounced as the temperature increases from 1200 to 1500 °C while the Cu content continues to drastically decrease. As such, we observe a lower depletion in Cu content but a stronger enrichment of ⁶⁵Cu in the residue at 1200 and 1300 °C compared to 1400 and 1500 °C, and a negative correlation between Cu content and δ⁶⁵Cu under the most reducing conditions. We relate this to the behavior of Cu isotopes that are more fractionated in presence of S in the melt, and to Cu being more volatile than S under reducing conditions. We report α fractionation factors in the CuS system increasing from 0.9973 in oxidizing conditions to 0.9997 at high temperatures and reducing conditions (1400–1500 °C, ΔFMQ −2 to −6).

These results suggest that the presence of the ligand-forming element S strongly influences Cu degassing at low temperatures and under oxidizing environments, such as terrestrial fumaroles. Its influence is more limited during degassing of hot magmas and under more reducing conditions, such as on the Moon. In agreement with these observations, we report lower Gibbs-free energies of formation for CuO compared to CuS, implying that less energy is required for Cu evaporation in the presence of S. Therefore, Cu evaporation and related isotopic fractionation under isothermal conditions is expected to be higher in S-dominated systems compared to S free experimental systems. This conclusion is in contrast with Heck et al. (2025) and highlights the significant role of Fe in stabilizing FeS molecules in the silicate melt.

<footnote><sup>a</sup> Freie Universität Berlin, Institut für Geologische Wissenschaften, Malteserstrasse 74-100, 12249 Berlin, Germany</footnote>

<footnote><sup>b</sup> Universität Münster, Institut für Mineralogie, Corrensstrasse 24, 48149 Münster, Germany</footnote>

<footnote><sup>c</sup> Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 4, 37077 Göttingen, Germany</footnote>

<footnote><sup>d</sup> Laboratoire Magmas et Volcans, Université Clermont Auvergne, CNRS, IRD, OPGC, F-63000 Clermont-Ferrand, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: guillaume.florin@uca.fr (G. Florin).</footnote>
# 1. Introduction

Evaporation is a key process in natural systems that sparked scientific curiosity for centuries (Brutsaert, 1982). Originally, it was formalized, among others, by the pioneering work of Dalton (1802), Rayleigh (1902), and Hertz, Knudsen and Langmuir (e.g. Knudsen, 1909; Langmuir, 1916). Nowadays evaporation is recognized as a ubiquitous phenomenon which plays a key role at every stage of Solar System evolution, from flash heating of chondrules in the protoplanetary disk (e.g. Connolly et al., 2006; Rubin, 2000; Jones et al., 2000; Jones et al., 2018), and large-scale impacts such as the Moon forming event (e.g. Canup, 2014; Dauphas et al., 2022; Paniello et al., 2012), to evaporation from magma oceans and degassing during volcanism on Earth and other terrestrial planets (e.g. Day and Moynier, 2014; Boyce et al., 2015; Mather, 2015; Day et al., 2017; Paquet et al., 2025). During these events, multiple geochemical processes can occur simultaneously potentially hiding the evaporative signature. Therefore, distinguishing whether a specific chemical element was affected by vaporization requires both detailed knowledge and accurate quantification of the chemical and physical factors controlling its evaporation.

Multiple physical and chemical parameters influence the dynamics and extent of evaporation, with the temperature and pressure being the most important (Davis et al., 1990; Hirth and Pound, 1963; Mendybaev et al., 2021; Richter et al., 2002; Richter et al., 2007; Wang et al., 2001). Additionally, under reduced conditions, mono-atomic evaporation is more likely, whereas oxidizing conditions tend to trigger ligand forming elements, such as S, Cl, or O, to bind to the element of interest, modifying its diffusivity in the melt and hence its volatility (e.g. Renggli et al., 2017; Renggli and Klemme, 2020, 2021; Sossi et al., 2019; Sossi et al., 2020; Steenstra et al., 2024). Variations of these parameters determine whether evaporation occurs in equilibrium (Knudsen evaporation; Knudsen, 1909) or under disequilibrium (Langmuir evaporation; Langmuir, 1916), which each produce specific elemental and isotopic signatures. Quantifying the distinctive signatures of each parameter is needed in order to reconstruct the type of evaporation during geological processes.

The high-temperature fractionation of two isotopes (i, j) of a specific element, between a liquid and a vapor phase is governed by the isotopic fractionation factor which can be predicted as the inverse square root of their molar masses:

$$ \alpha_{\text{vap-liq}} = \left(\frac{M_i}{M_j}\right)^{0.5} \qquad (1) $$

In a pure Langmuir evaporation, this kinetic isotope fractionation factor will reflect the naturally occurring isotope ratio, whereas under pure Knudsen evaporation, it will be 1. Therefore, large isotopic fractionations between phases are expected in a Langmuir model, often resulting from gas-liquid (or solid) isolation, while in a Knudsen model, the residue and the gas should have very similar isotopic compositions due to gas-solid equilibration. This makes the kinetic isotope fractionation factor a particularly useful tool to characterize evaporation. However, as stated above, it is strongly sensitive to temperature, oxygen fugacity, and pressure, and to the abundance of ligand-forming elements like S, or O in the condensed phase. Then the complexity of natural cosmochemical and geochemical processes implies that a system either evolves under pure Langmuir or in an intermediate state between disequilibrium and equilibrium but rarely exist under pure Knudsen conditions.

Previous experiments on the evaporation of Cu from silicate melts demonstrated that the theoretical approach based on Hertz-Knudsen-Langmuir accurately describes the effect of temperature and oxygen fugacity on element loss and isotopic fractionation (e.g. Sossi et al., 2019). They also demonstrate that both the extent of Cu loss and the isotopic fractionation of the residual melt are strongly dependent on the oxygen fugacity ($fO_2$). In addition, decreasing the $fO_2$, while it increases

the volatility of Cu, counter-intuitively leads to lower isotope fractionation, i.e., fractionation factors that approach unity (Neuman et al., 2022; Ni et al., 2021; Norris and Wood, 2017; Sossi et al., 2019; Sossi et al., 2020). These experimental studies have in common that they investigated the Cu evaporation reaction:

$$ CuO_{0.5}(l) = Cu(g) + \frac{1}{4}O_2 \qquad (2) $$

Depending on the melt compositions, its S content, and the thermodynamic conditions, CuS$_{0.5}$ species may also form in the melt (Henley and Seward, 2018; Renggli et al., 2017; Symonds et al., 1990; Symonds et al., 1987; Zelenski et al., 2021). As such, S-gas species can be abundant and possible Cu-gas species can include Cu$_2$S(g). Thus, a variety of evaporation reactions must be considered to describe the net evaporation of Cu from silicate melts containing sulfur.

$$ CuO_{0.5}(l) + 0.5S^{2-}(l) = Cu(g) + \frac{1}{4}S_2 + \frac{1}{4}O_2 \qquad (3) $$

$$ CuO_{0.5}(l) + 0.5S^{2-}(l) = CuS_{0.5}(g) + \frac{1}{4}O_2 \qquad (4) $$

$$ CuS_{0.5}(l) = Cu(g) + \frac{1}{4}S_2 \qquad (5) $$

$$ CuS_{0.5}(l) = CuS_{0.5}(g) \qquad (6) $$

Because of their diverse chemical behavior, experimental evaporation of moderately volatile elements (MVE) from silicate melts are ideally suited to explore the variety and complexity of isotope fractionation in controlled environments (Klemme et al., 2022; Neuman et al., 2022; Ni et al., 2021; Sossi et al., 2019; Sossi et al., 2020). Indeed, MVE are usually well studied but their isotope fractionation factors are often not well constrained. For instance, lunar mare basalts suggest that the silicate Moon has a heavy Cu isotopic composition compared to the silicate Earth, (≈0.5 ‰ to > 3 ‰, Day et al., 2019; Florin et al., 2025; Moynier et al., 2006; Paquet et al., 2025). However, despite a significant Cu deficit of the silicate Moon compared to the silicate Earth (≈95.5 ‰, Herzog et al., 2009), the average Cu isotopic composition of mare basalts, is only moderately different from the silicate Earth value (≈ +0.63 ‰ Florin et al., 2025, Paquet et al., 2025). This is particularly noteworthy, as kinetic evaporation and isotope fractionation observed during evaporation of CuO from silicate glass ($a = 0.9972–0.9979$, Neuman et al., 2022; Sossi et al., 2020) is much larger than the extent of the proposed Cu isotopic fractionation in mare basalts ($a = 0.99945$, Paquet et al., 2025). These discrepancies raise questions about the applicability of CuO-based fractionation factors to the lunar environment and the magnitude of contribution of Cu evaporation to the Cu isotopic composition of mare basalts.

Hence, to better constrain the evaporation behavior of Cu as a function of temperature, $fO_2$, and to evaluate the effect of S on Cu evaporation and stable Cu isotope fractionation, we conducted an experimental study at temperatures between 1150 and 1500 °C, and at a broad range of oxygen fugacities ($\log fO_2$) relative to the Fayalite-Magnetite-Quartz buffer (FMQ) ranging from $\Delta$FMQ – 6 to ~ $\Delta$FMQ + 2 and under Earth atmospheric conditions. These experimental data are then used to discuss the elemental and isotopic behavior of Cu during evaporation from silicate melt in a S-bearing system in general and, as an example, applied to lunar mare basalt volcanism.

# 2. Methods

## 2.1. Experimental procedures

Experimental studies on evaporation of a variety of MVE from silicate melts, and using a variety of techniques, have been conducted by several research groups in recent years (Hashimoto, 1983; Klemme et al., 2022; Liu et al., 2022; Neuman et al., 2022; Ni et al., 2021; Norris
and Wood, 2017; Renggli et al., 2022; Richter et al., 2007; Richter et al., 2011; Richter et al., 2009; Sossi et al., 2019; Sossi et al., 2020; Wim-penny et al., 2022; Wimpenny et al., 2019). Pangritz et al. (2022) sug-gested that the commonly employed starting materials (e.g. Norris and Wood, 2017; Sossi et al., 2019) that consist of oxide mixtures to which trace element solutions were added, are not well suited for the study of volatile elements as it cannot be excluded that some elements begin to evaporate within the first seconds of the experiment, before the silicate melt formed.

The starting materials of our study consisted, therefore, of volatile element-rich silicate glasses in the system CaO-MgO-SiO₂-Al₂O₃-B₂O₃, with the silicate component at the anorthite (CaAl₂Si₂O₈)-diopside (CaMg₂Si₂O₆) eutectic at An₃₆Di₆₄, together with either only Cu or Cu + S (Cu/S = 2.39). The starting material compositions contain significant amounts of B (Table 1) and have, consequently, a low liquidus tem-perature (<1200 °C). This is sufficiently low to prevent the loss of vol-atile compounds from degassing during the vitrification (Pangritz et al., 2022). The starting material glasses were synthesized from chemical grade oxides Al₂O₃ (Sigma Aldrich), MgO (Sigma Aldrich), and SiO₂ (Sigma Aldrich), Ca-carbonate (Alfa Aesar), and crystalline boric acid (ABCR GmbH & Co.KG) following Pangritz et al. (2022). All mixtures were first decarbonated at 1000 °C for 3 h, then pulverized, fused for 30 min at 1200 °C in a Pt-Au crucible, and finally quenched in cold water. The volatile-free glass was pulverized a second time and mixed with the respective volatile compound in an agate mortar for at least 60 min with ethanol. For this study we used either Cu₂O for study of the CuO-system or CaSO₄ for S-bearing starting compositions (Alfa Aesar, Germany). Volatile doped glass-powders were then fused for 7 min at 1200 °C which is sufficiently low to completely melt the starting composition without evaporating the volatiles (see Table 1 for all starting material compositions). A detailed description of the synthesis of similar starting materials is given by Pangritz et al. (2022).

For each experiment, a small chip of synthesized volatile bearing glass (ca. 25–100 mg) was mounted on a 0.01 mm diameter Pt-wire loop and attached to an alumina rod. All samples were first stored in the upper “cold zone” (<200 °C) of a 70 cm long vertical alumina tube gas-mixing furnace (GERO GmbH, Germany) operated at one-atmosphere. Oxygen fugacity was controlled by a continuous flow of a CO-CO₂ gas mixture at a flow rate of 100 cm³ per minute (regulated by a Tylan mass flow controller). The most oxidizing experiments labeled “air,” were conducted under a flow of ambient air, resulting in a slight decrease in oxygen fugacity with increasing temperature. To limit contamination by recondensation onto the molten silicate glass, the gas mixture was introduced from the top of the furnace with gas flow downward, effec-tively transporting vaporized species away from the sample and toward the exhaust. To ensure full redox equilibrium, we flushed the furnace with the sample inside for 2 min before the experiment began. After 2 min, the sample was placed into the hot zone of the furnace for 15 min. At the end of the experiment, the sample was kept in the gas stream and moved upward from the hot middle zone to the cold upper end of the furnace. This ensures that the sample never reached the lower part of the tube, which might be contaminated by recondensing gas. Then the

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

EPMA analyses of vitrified starting materials [wt%]. av = average of EPMA measurements, σ = 2 times standard deviation error.

<table><thead><tr><th rowspan="2"></th><th colspan="2">Cu (n = 40)</th><th colspan="2">Cu-S (n = 37)</th></tr><tr><th>av.</th><th>σ</th><th>av.</th><th>σ</th></tr></thead><tbody><tr><td>SiO<sub>2</sub></td><td>43.8</td><td>0.3</td><td>45.3</td><td>0.3</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>13.51</td><td>0.09</td><td>14.07</td><td>0.06</td></tr><tr><td>MgO</td><td>9.49</td><td>0.06</td><td>7.4</td><td>0.04</td></tr><tr><td>CaO</td><td>20.58</td><td>0.08</td><td>20.77</td><td>0.08</td></tr><tr><td>B<sub>2</sub>O<sub>3</sub></td><td>9.6</td><td>0.3</td><td>10.5</td><td>0.3</td></tr><tr><td>CuO (µg/g)</td><td>21,740</td><td>0.1</td><td>9221</td><td>0.03</td></tr><tr><td>S (µg/g)</td><td>—</td><td>—</td><td>4890</td><td>0.02</td></tr><tr><td>Sum</td><td>99.41</td><td></td><td>99.26</td><td></td></tr></tbody></table>

sample was quenched in water. During the experiments, the temperature was monitored and controlled by a Type B thermocouple connected to a Eurotherm 2416 controller (Schneider Electric Systems, Germany). Throughout the run, temperature variations were less than ± 1 °C. A correction had to be applied to some of the reported initial run tem-teratures as initial experiments suffered from a faulty thermocouple.

All quenched samples were small glass spheres of 2–4 mm diameter. (Fig. 1). Two sets of samples have been produced, the elemental series, and the isotopic series (Table 3). Samples from the elemental series were dedicated to *in situ* elemental analysis. They were mounted in epoxy resin, polished down to the center of the spheres, and carbon-coated (20 nm thickness) for scanning electron microscope (SEM) and electron probe microanalyser (EPMA) analysis. The run products that were dedicated to isotopic analysis, the isotopic series, were separated from the Pt wire, weighed (samples mass range from 1.8 mg to 14.74 mg, Table 3), crushed entirely using an agate mortar, and placed in PFA vials in preparation for digestion and Cu purification.

## 2.2. Analytical procedure

### 2.2.1. Imaging and electron microprobe measurements

Major elements of the elemental series (Table 3) were determined *in situ* with a 5-spectrometer JEOL JXA 8530F electron probe micro-analyzer (EPMA) at the Institut für Mineralogie, Universität Münster. All measurements were done with a 15 kV acceleration voltage, a beam current of 60nA, and a 10 µm beam size. Counting times for B, S, Cu were 120 s and 60 s of on peak zero background, while other elements were measured with 20 s on the peak and 10 s of on peak zero background. Standardization was done using a suite of well-characterized synthetic and natural reference materials (Table 2). To monitor precision and accuracy of the EPMA method, we measured secondary standards as unknowns. Sulfur-containing experiments were standardized separately at every oxygen fugacity because the S-peak position varies for different S-species in the glass (Carroll and Rutherford, 1988). The matrix cor-rections were made according to the φ(ρz) procedure (Armstrong, 1991). Since both the starting material compositions and the run prod-ucts were measured using the same analytical conditions degassing due to the electron beam damage can be ignored.

Most experiments resulted in homogenous-looking glass spheres without any impurities (Fig. 1). Low-temperature experiments (e.g., <1300 °C) contained some air bubbles, that were found in the centers of the spheres. The bubbles likely originate from air trapped in the starting material during the synthesis. Indeed, at temperatures < 1300 °C and 15-minute experimental runtime, leftover air within the starting glasses was not able to fully migrate through the entire sphere because of higher melt viscosities and short run durations. Bubble formation did not affect the homogeneity of the elemental composition of the glass (Pangritz et al., 2022).

Bulk concentrations of the residual glasses (only for experiments without diffusion profiles, see “results” below for detailed discussions) and the un-degassed starting material compositions, obtained via mass balance calculation, were used to calculate the material loss in the glass after the experiment. The evaporation of Cu and S is shown by the mass fraction of each element over the starting material $X_i^{sample(t=15)} / X_i^{initial(t=0)}$ where X is the concentration of the respective element i. Initial con-centrations are given in Table 1. Data points with Cu contents lower than the EPMA detection limit of i.e., 130 µg/g, as well as measurements outside the 2σ standard deviations of the mean, were not considered.

In all experiments, Pt-metal loops were used to attach the sample to the alumina rod in the furnace. Partitioning of Cu in Pt-metal loops could have influenced the actual evaporation process. However, while most chalcophile and siderophile elements form alloys with Pt-metal, ther-modynamic calculations show low diffusion rates of Cu into Pt at our run temperatures (Liu et al., 2022), and recent similar study show extremely low Cu content in the Pt-loop (Heck et al., 2025). Therefore, the loss of
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** A): scanning electron microscope backscattered electron (sem-bse) image of the experiment cu_only_1432_b. red dotted line: location of the line profile measured by epma. bright white areas show parts of the pt-wire loop. b): epma profiles of the same experiment indicate no significant variation of all major elements and cu from the center to the rim of the glass. more sem-bse images are reported in fig. s1.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Table 2**

Standards use to create the starting material.</figcaption></figure>

<table><thead><tr><th>Element</th><th>Diff. Crystal</th><th>Std. name</th><th>Ref. material</th></tr></thead><tbody><tr><td>B</td><td>LDE2</td><td>Astimex_BN</td><td>boron nitride</td></tr><tr><td>Al</td><td>TAP</td><td>H_DistheneR8</td><td>kyanite</td></tr><tr><td>Mg</td><td>TAP</td><td>USNM_OlivineSanCarlos</td><td>olivine</td></tr><tr><td>Si</td><td>PETJ</td><td>USNM_Hypersthene</td><td>hypersthene</td></tr><tr><td>Ca</td><td>PETJ</td><td>H_DiopsideST48</td><td>diopside</td></tr><tr><td>Cu</td><td>LIFH</td><td>H_Kupferkies</td><td>chalcopyrite</td></tr><tr><td>S</td><td>PETL</td><td>Astimex_Pyrite</td><td>pyrite</td></tr></tbody></table>

Cu to the wire should have no significant effect on the experimental evaporation data (Sossi et al., 2019). Nonetheless, Cu in the Pt wire was measured with SEM EDX but no Cu could be detected (Fig. S2). Furthermore, B evaporation is minor and thus is unlikely to influence the kinetics of Cu evaporation in a significant manner (Flemetakis et al., 2024).

### 2.2.2. Purification of Cu and mass spectrometry

The isotope measurements and the entire chemical digestion, separation and purification process of the isotopic series (Table 3) was done in the geochemistry laboratories at Freie Universität Berlin, Germany. The step-by-step sample digestion and chemical procedure is described in detail by Florin et al. (2025). The run products were first digested in a 3:1 mixture of concentrated HF/HNO₃ at 130 °C on hot plate for several days, then fluorides were removed by fluxing the sample with 6 M HCl at 130 °C until the solution was free of precipitates. After conversion to 1 ml of 8 M HCl, the sample was loaded on a triple stack column procedure combining methods from Freymuth et al. (2020); Rosca et al. (2021); and Sossi et al. (2015). From the top to the bottom, the three columns are filled with: (1) 4 ml of TRU-Spec (100–200 mesh) in 10 ml Triskem™ columns, (2) 0.3 ml of prefilter resin in Micro Bio-SpinTM columns, (3) 2 ml of AG1x8 (200–400 mesh) in homemade PTFE columns (7 cm – Ø6mm). TRU-Spec resin is pre-cleaned with 1 M HNO₃, H₂O, 0.005 M HCl – 1 M HF, 0.5 M HCl, H₂O, and the anionic resin successively with 6 M HCl, H₂O, repeated three times. After sample loading, we first eluted the matrix with 10 ml 8 M HCl + 0.001 % H₂O₂, then the TRU-Spec upper rack is removed, and Cu is eluted from the AG1x8 with 4 ml 0.5 M HNO₃. Following evaporation of the purified Cu fraction, organics were removed by adding 0.2 ml 14 M HNO₃ + 0.2 ml 30 % H₂O₂. Removal of organics was verified by visually checking shininess of solutions and its stickiness onto the inside of beakers. Finally, samples

were converted to 0.28 M HNO₃ for analysis. Total analytical blanks throughout this study were < 0.1 ng and insignificant considering the 0.1 µg (Experiments label Cu14.5, Cu14.6, Cu15.5, and Cu15.6) to 1 µg Cu loaded on each column.

Elemental composition of Cu and S were determined from 1 % aliquots of the digestion solutions before Cu purification. Copper compositions were obtained by isotope dilution and for S by internal In doping and external standardization. Both elements were measured with a Thermo Scientific™ ElementXR™ SF-ICP-MS at medium resolution (Δm/m ≈ 4500). Uncertainties including measurement, pipetting, and weighing for both elements are 5 %.

The stable isotopic composition of Cu was analyzed at medium resolution (m/Δm ≈ 7500) with a Thermo Scientific™ Neoma™ MC-ICP-MS with an Aridus II (Cetalc) introduction system. We used a 60 µl/min PFA nebulizer and measured 30 ng/g Cu solutions, yielding 2–2.5 V on ⁶³Cu. In order to accurately correct for instrumental mass fractionation similar intensity is needed for ⁶³Cu and ⁶⁰Ni. Then solutions doped with 60 ng/g NIST-SRM 986 Ni standard were analyzed in sample standard bracketing mode and evaluated using a power law (Maréchal et al., 1999). Ratios were collected by 60 static scans with 8 s integration time per scan, resulting in an internal precision of 10–12 ppm (2SE) on the ⁶⁵Cu/⁶³Cu ratio for a single analysis. The copper isotopic compositions are given as per mil deviation (‰) from the ERM®-AE633 (Moeller et al., 2012) according to equation (7)

$$ \delta^{65}\text{Cu}/^{63}\text{Cu} \equiv \delta^{65}\text{Cu} = \left( \frac{^{65}\text{Cu}/^{63}\text{Cu}_{\text{Sample}}}{^{65}\text{Cu}/^{63}\text{Cu}_{\text{ERM-AE633}}} - 1 \right) \times 10^3 \quad (7) $$

In-house standard solutions, Cu-AA-FUB-H (δ⁶⁵CuERM-633 = +1.07 ± 0.02 ‰, n = 15, 2SE) and Cu-AA-FUB-L (δ⁶⁵CuERM-633 = -0.21 ± 0.02 ‰, n = 31, 2SE), show a good long-term reproducibility with previously reported data (Florin et al., 2025). Reference materials BCR-2 and AGV-1 processed through the chemistry yield elemental and isotopic compositions in good agreement with literature data (Freymuth et al., 2020; Jochum et al., 2005; Moeller et al., 2012), [Cu] = 15 µg/g and 57.9 µg/g, δ⁶⁵CuERM-633 = +0.22 ± 0.03 ‰ and +0.09 ± 0.05 ‰, respectively.

### 2.3. Data treatment

To analyze the effect of ligands forming elements on evaporative loss (f, equation 9) and on thermodynamic quantities, introduced by Sossi et al. (2019), we calculated modified equilibrium constants (K*) as well as Gibbs-free energies (ΔG*) for different evaporation reactions
<caption>**Table 3**</caption>

Experimental results and run conditions. $f_{Cu}$ and $f_{S}$ refer to the calculated fraction of the respective element relative to the starting composition. ΔFMQ values were corrected based on secondary temperature calibration. Runtime for each experiment is 15 min ± 10 s., b.d.l. = below detection limit, n: number of analyses. $\delta^{65}\text{Cu}_{\text{ERM633}}$ are reported in ‰ variations according to the ERM633 Cu standard. Runs labelled with an asterisk (*) are chemically zoned in Cu or S, they are included in the figures but excluded from thermodynamic modelling. Labels a to f refer to run of similar ΔFMQ or $f_{\text{O}_2}$.

<table><thead><tr><th>Starting material</th><th>Temperature (°C)</th><th>Sample (mg)</th><th>label</th><th>log (fO<sub>2</sub>)</th><th>ΔFMQ</th><th>Cu µg/g</th><th>S µg/g</th><th>f<sub>Cu</sub></th><th>± 2 s.d.</th><th>f<sub>S</sub></th><th>± 2 s.d.</th><th>ln(f<sub>Cu</sub>)</th><th>ln(f<sub>S</sub>)</th><th>δ<sup>65</sup>Cu<sub>ERM633</sub> (‰)</th><th>Δ<sup>65</sup>Cu<sub>SC</sub> (‰)</th><th>±2s.d.</th><th>n</th></tr></thead><tbody><tr><td rowspan="20">Cu</td><td>1125*</td><td></td><td>a</td><td>-0.68</td><td>8.7</td><td>20,653</td><td></td><td>0.95</td><td>0.18</td><td>-</td><td></td><td>-0.05</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1125</td><td></td><td>b</td><td>-6.91</td><td>2.3</td><td>21,957</td><td></td><td>1.01</td><td>0.13</td><td>-</td><td></td><td>0.01</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1125*</td><td></td><td>c</td><td>-8.41</td><td>0.9</td><td>19,783</td><td></td><td>0.91</td><td>0.11</td><td>-</td><td></td><td>-0.09</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1125*</td><td></td><td>d</td><td>-8.41</td><td>-1.1</td><td>20,653</td><td></td><td>0.95</td><td>0.11</td><td>-</td><td></td><td>-0.05</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1125*</td><td></td><td>e</td><td>-12.41</td><td>-3.1</td><td>6957</td><td></td><td>0.32</td><td>0.37</td><td>-</td><td></td><td>-1.14</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1125*</td><td></td><td>f</td><td>-14.41</td><td>-5.1</td><td>18,914</td><td></td><td>0.87</td><td>0.53</td><td>-</td><td></td><td>-0.14</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1209</td><td></td><td>b</td><td>-6.3</td><td>2</td><td>18,479</td><td></td><td>0.85</td><td>0.09</td><td>-</td><td></td><td>-0.16</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1209</td><td></td><td>e</td><td>-6.3</td><td>-3.5</td><td>2609</td><td></td><td>0.12</td><td>0.20</td><td>-</td><td></td><td>-2.12</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1255</td><td></td><td>a</td><td>-0.68</td><td>7.1</td><td>21,088</td><td></td><td>0.97</td><td>0.09</td><td>-</td><td></td><td>-0.03</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1255</td><td></td><td>b</td><td>-5.8</td><td>2</td><td>18,914</td><td></td><td>0.87</td><td>0.09</td><td>-</td><td></td><td>-0.14</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1255</td><td></td><td>c</td><td>-7.3</td><td>0.5</td><td>19,131</td><td></td><td>0.88</td><td>0.08</td><td>-</td><td></td><td>-0.13</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1255</td><td></td><td>d</td><td>-9.3</td><td>-1.5</td><td>5218</td><td></td><td>0.24</td><td>0.07</td><td>-</td><td></td><td>-1.43</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1255</td><td></td><td>e</td><td>-11.3</td><td>-3.5</td><td>2609</td><td></td><td>0.12</td><td>0.03</td><td>-</td><td></td><td>-2.12</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1255</td><td></td><td>f</td><td>-13.3</td><td>-5.5</td><td>2826</td><td></td><td>0.13</td><td>0.02</td><td>-</td><td></td><td>-2.04</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1314</td><td></td><td>b</td><td>-5.29</td><td>1.9</td><td>16,957</td><td></td><td>0.78</td><td>0.07</td><td>-</td><td></td><td>-0.25</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1314</td><td></td><td>e</td><td>-10.79</td><td>-3.6</td><td>1087</td><td></td><td>0.05</td><td>0.01</td><td>-</td><td></td><td>-3.00</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1370</td><td></td><td>a</td><td>-0.68</td><td>5.9</td><td>20,436</td><td></td><td>0.94</td><td>0.09</td><td>-</td><td></td><td>-0.06</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1370</td><td></td><td>b</td><td>-4.8</td><td>1.8</td><td>16,522</td><td></td><td>0.76</td><td>0.07</td><td>-</td><td></td><td>-0.27</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1370</td><td></td><td>c</td><td>-6.3</td><td>0.3</td><td>16,522</td><td></td><td>0.76</td><td>0.07</td><td>-</td><td></td><td>-0.27</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1370</td><td></td><td>d</td><td>-8.3</td><td>-1.7</td><td>3261</td><td></td><td>0.15</td><td>0.02</td><td>-</td><td></td><td>-1.90</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1370</td><td></td><td>e</td><td>-10.3</td><td>-3.7</td><td>870</td><td></td><td>0.04</td><td>0.01</td><td>-</td><td></td><td>-3.22</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1370</td><td></td><td>f</td><td>-12.3</td><td>-5.7</td><td>217</td><td></td><td>0.01</td><td>0.01</td><td>-</td><td></td><td>-4.61</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1432</td><td></td><td>b</td><td>-4.34</td><td>1.7</td><td>17,392</td><td></td><td>0.80</td><td>0.07</td><td>-</td><td></td><td>-0.22</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td>1432</td><td></td><td>e</td><td>-9.84</td><td>-3.8</td><td>435</td><td></td><td>0.02</td><td>0.01</td><td>-</td><td></td><td>-3.91</td><td>-</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="20">Cu-S</td><td>1178</td><td></td><td>a</td><td>-0.68</td><td>8</td><td>8207</td><td>3619</td><td>0.89</td><td>0.12</td><td>0.74</td><td>0.14</td><td>-0.12</td><td>-0.30</td><td></td><td></td><td></td><td></td></tr><tr><td>1178</td><td></td><td>b</td><td>-6.91</td><td>1.8</td><td>8576</td><td>3276</td><td>0.93</td><td>0.12</td><td>0.67</td><td>0.20</td><td>-0.07</td><td>-0.40</td><td></td><td></td><td></td><td></td></tr><tr><td>1178</td><td></td><td>bII</td><td>-6.91</td><td>1.8</td><td>8483</td><td>3570</td><td>0.92</td><td>0.07</td><td>0.73</td><td>0.30</td><td>-0.08</td><td>-0.31</td><td></td><td></td><td></td><td></td></tr><tr><td>1178</td><td></td><td>c</td><td>-8.41</td><td>0.3</td><td>8207</td><td>3032</td><td>0.89</td><td>0.13</td><td>0.62</td><td>0.20</td><td>-0.12</td><td>-0.48</td><td></td><td></td><td></td><td></td></tr><tr><td>1178*</td><td></td><td>d</td><td>-10.41</td><td>-1.7</td><td>3320</td><td>293</td><td>0.36</td><td>0.31</td><td>0.06</td><td>0.09</td><td>-1.02</td><td>-2.81</td><td></td><td></td><td></td><td></td></tr><tr><td>1178</td><td></td><td>e</td><td>-12.41</td><td>-3.7</td><td>1199</td><td>538</td><td>0.13</td><td>0.03</td><td>0.11</td><td>0.12</td><td>-2.04</td><td>-2.21</td><td></td><td></td><td></td><td></td></tr><tr><td>1178</td><td></td><td>f</td><td>-14.41</td><td>-5.7</td><td>553</td><td>1027</td><td>0.06</td><td>0.03</td><td>0.21</td><td>0.15</td><td>-2.81</td><td>-1.56</td><td></td><td></td><td></td><td></td></tr><tr><td>1225</td><td></td><td>b</td><td>-6.3</td><td>1.8</td><td>8944</td><td>2592</td><td>0.97</td><td>0.07</td><td>0.53</td><td>0.13</td><td>-0.03</td><td>-0.63</td><td></td><td></td><td></td><td></td></tr><tr><td>1225</td><td></td><td>e</td><td>-6.3</td><td>-3.7</td><td>1107</td><td>196</td><td>0.12</td><td>0.02</td><td>0.04</td><td>0.02</td><td>-2.12</td><td>-3.22</td><td></td><td></td><td></td><td></td></tr><tr><td>1283</td><td></td><td>a</td><td>-0.68</td><td>6.8</td><td>8391</td><td>538</td><td>0.91</td><td>0.07</td><td>0.11</td><td>0.03</td><td>-0.09</td><td>-2.21</td><td></td><td></td><td></td><td></td></tr><tr><td>1283</td><td></td><td>b</td><td>-5.8</td><td>1.7</td><td>4979</td><td>b,d,l</td><td>0.54</td><td>0.06</td><td>b.d.l.</td><td></td><td>-0.62</td><td>-4.72</td><td></td><td></td><td></td><td></td></tr><tr><td>1283*</td><td></td><td>c</td><td>-7.3</td><td>0.2</td><td>5440</td><td>98</td><td>0.59</td><td>0.17</td><td>0.02</td><td>0.02</td><td>-0.53</td><td>-3.91</td><td></td><td></td><td></td><td></td></tr><tr><td>1283</td><td></td><td>c_2</td><td>-7.3</td><td>0.2</td><td>2951</td><td>98</td><td>0.32</td><td>0.27</td><td>0.02</td><td>0.01</td><td>-1.14</td><td>-3.91</td><td></td><td></td><td></td><td></td></tr><tr><td>1283</td><td></td><td>d</td><td>-9.3</td><td>-1.8</td><td>277</td><td>b,d,l</td><td>0.03</td><td>0.01</td><td>b.d.l.</td><td></td><td>-3.51</td><td>-5.05</td><td></td><td></td><td></td><td></td></tr><tr><td>1283</td><td></td><td>f</td><td>-13.3</td><td>-5.8</td><td>461</td><td>b,d,l</td><td>0.05</td><td>0.05</td><td>b.d.l.</td><td></td><td>-3.00</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1326</td><td></td><td>b</td><td>-5.29</td><td>1.7</td><td>2674</td><td>b,d,l</td><td>0.29</td><td>0.05</td><td>b.d.l.</td><td></td><td>-1.24</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1326</td><td></td><td>e</td><td>-10.79</td><td>-4.8</td><td>277</td><td>b,d,l</td><td>0.03</td><td>0.01</td><td>b.d.l.</td><td></td><td>-3.51</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1375</td><td></td><td>a</td><td>-0.68</td><td>5.9</td><td>7653</td><td>b,d,l</td><td>0.83</td><td>0.06</td><td>b.d.l.</td><td></td><td>-0.19</td><td>-4.88</td><td></td><td></td><td></td><td></td></tr><tr><td>1375</td><td></td><td>b</td><td>-0.68</td><td>1.7</td><td>1475</td><td>b,d,l</td><td>0.16</td><td>0.02</td><td>b.d.l.</td><td></td><td>-1.83</td><td>-5.25</td><td></td><td></td><td></td><td></td></tr><tr><td>1375</td><td></td><td>c</td><td>-6.3</td><td>0.2</td><td>2029</td><td>b,d,l</td><td>0.22</td><td>0.02</td><td>b.d.l.</td><td></td><td>-1.51</td><td>-5.72</td><td></td><td></td><td></td><td></td></tr><tr><td>1375</td><td></td><td>d</td><td>-8.3</td><td>-1.8</td><td>461</td><td>b,d,l</td><td>0.05</td><td>0.01</td><td>b.d.l.</td><td></td><td>-3.00</td><td>-5.82</td><td></td><td></td><td></td><td></td></tr><tr><td>1375</td><td></td><td>e</td><td>-10.3</td><td>-3.8</td><td>277</td><td>b,d,l</td><td>0.03</td><td>0.01</td><td>b.d.l.</td><td></td><td>-3.51</td><td>-5.72</td><td></td><td></td><td></td><td></td></tr><tr><td>1432</td><td></td><td>b</td><td>-4.34</td><td>1.7</td><td>1107</td><td>b,d,l</td><td>0.12</td><td>0.02</td><td>b.d.l.</td><td></td><td>-2.12</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1432</td><td></td><td>e</td><td>-9.84</td><td>3.8</td><td>184</td><td>b,d,l</td><td>0.02</td><td>0.01</td><td>b.d.l.</td><td></td><td>-3.91</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1484</td><td></td><td>b</td><td>-3.9</td><td>1.6</td><td>738</td><td>b,d,l</td><td>0.08</td><td>0.02</td><td>b.d.l.</td><td></td><td>-2.53</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1484</td><td></td><td>eII</td><td>-9.4</td><td>-3.9</td><td>369</td><td>b,d,l</td><td>0.04</td><td>0.03</td><td>b.d.l.</td><td></td><td>-3.22</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

(continued on next page)
<table><caption>Table 3 (continued)</caption><thead><tr><th>Starting material</th><th>Temperature (°C)</th><th>Sample (mg)</th><th>label</th><th>log (fO<sub>2</sub>)</th><th>ΔFMQ</th><th>Cu µg/g</th><th>S µg/g</th><th>f<sub>cu</sub></th><th>± 2 s.d.</th><th>f<sub>s</sub></th><th>± 2 s.d.</th><th>ln(f<sub>cu</sub>)</th><th>ln(f<sub>s</sub>)</th><th>ln(f<sub>E</sub>)</th><th>δ<sup>65</sup>Cu<sub>RM633</sub> (%)</th><th>Δ<sup>65</sup>Cu<sub>SC</sub> (%)</th><th>±2s.d.</th><th>n</th></tr></thead><tbody><tr><td rowspan="12">Start. comp.</td><td>1200</td><td>12.00</td><td>Cu12.1</td><td>-0.68</td><td>7.7</td><td>7705</td><td>2686</td><td>0.836</td><td>0.017</td><td>0.549</td><td>0.011</td><td>-0.18</td><td>-0.60</td><td>0.16</td><td>0.39</td><td>0.23</td><td>0.03</td><td>4</td></tr><tr><td>1200</td><td>7.52</td><td>Cu12.2</td><td>-6.91</td><td>1.5</td><td>7821</td><td>2282</td><td>0.848</td><td>0.017</td><td>0.467</td><td>0.009</td><td>-0.16</td><td>-0.76</td><td>0.60</td><td>0.44</td><td>0.08</td><td>6</td></tr><tr><td>1200</td><td>14.40</td><td>Cu12.3</td><td>-8.41</td><td>0</td><td>5617</td><td>2213</td><td>0.609</td><td>0.012</td><td>0.453</td><td>0.009</td><td>-0.50</td><td>-0.79</td><td>0.79</td><td>0.63</td><td>0.09</td><td>4</td></tr><tr><td>1200</td><td>6.19</td><td>Cu12.4</td><td>-10.41</td><td>-2</td><td>2462</td><td>1937</td><td>0.267</td><td>0.005</td><td>0.396</td><td>0.008</td><td>-1.32</td><td>-0.93</td><td>3.33</td><td>3.17</td><td>0.13</td><td>6</td></tr><tr><td>1200</td><td>13.43</td><td>Cu12.5</td><td>-12.41</td><td>-4</td><td>2978</td><td>674</td><td>0.323</td><td>0.006</td><td>0.138</td><td>0.003</td><td>-1.13</td><td>-1.98</td><td>2.53</td><td>2.37</td><td>0.06</td><td>4</td></tr><tr><td>1200</td><td>8.60</td><td>Cu12.6</td><td>-14.41</td><td>-6</td><td>395</td><td>542</td><td>0.043</td><td>0.001</td><td>0.111</td><td>0.002</td><td>-3.15</td><td>-2.20</td><td>4.73</td><td>4.57</td><td>0.08</td><td>6</td></tr><tr><td>1300</td><td>6.50</td><td>Cu13.1</td><td>-0.68</td><td>6.6</td><td>5953</td><td>1422</td><td>0.646</td><td>0.013</td><td>0.291</td><td>0.006</td><td>-0.44</td><td>-1.24</td><td>0.32</td><td>0.16</td><td>0.06</td><td>5</td></tr><tr><td>1300</td><td>14.31</td><td>Cu13.2</td><td>-5.8</td><td>1.5</td><td>2887</td><td>369</td><td>0.313</td><td>0.006</td><td>0.076</td><td>0.002</td><td>-1.16</td><td>-2.58</td><td>2.30</td><td>2.14</td><td>0.06</td><td>4</td></tr><tr><td>1300</td><td>10.60</td><td>Cu13.3</td><td>-7.3</td><td>0</td><td>1063</td><td>451</td><td>0.115</td><td>0.002</td><td>0.092</td><td>0.002</td><td>-2.16</td><td>-2.38</td><td>2.79</td><td>2.63</td><td>0.04</td><td>5</td></tr><tr><td>1300</td><td>14.74</td><td>Cu13.4</td><td>-9.3</td><td>-2</td><td>669</td><td>229</td><td>0.073</td><td>0.001</td><td>0.047</td><td>0.001</td><td>-2.62</td><td>-3.06</td><td>4.97</td><td>4.81</td><td>0.12</td><td>4</td></tr><tr><td>1300</td><td>17.24</td><td>Cu13.5</td><td>-11.3</td><td>-4</td><td>652</td><td>207</td><td>0.071</td><td>0.001</td><td>0.042</td><td>0.001</td><td>-2.65</td><td>-3.16</td><td>7.10</td><td>6.94</td><td>0.05</td><td>5</td></tr><tr><td>1300</td><td>13.40</td><td>Cu13.6</td><td>-13.3</td><td>-6</td><td>27</td><td>210</td><td>0.003</td><td>0.001</td><td>0.043</td><td>0.001</td><td>-5.83</td><td>-3.15</td><td>3.57</td><td>3.41</td><td>0.05</td><td>4</td></tr><tr><td rowspan="12">Cu-S Isotopy</td><td>1300</td><td>13.90</td><td>Cu14.1</td><td>-0.68</td><td>5.6</td><td>5066</td><td>857</td><td>0.549</td><td>0.011</td><td>0.175</td><td>0.004</td><td>-0.60</td><td>-1.74</td><td>1.03</td><td>0.87</td><td>0.04</td><td>5</td></tr><tr><td>1400</td><td>6.80</td><td>Cu14.2</td><td>-4.8</td><td>1.5</td><td>3155</td><td>392</td><td>0.342</td><td>0.007</td><td>0.080</td><td>0.002</td><td>-1.07</td><td>-2.52</td><td>1.76</td><td>1.60</td><td>0.07</td><td>2</td></tr><tr><td>1400</td><td>11.00</td><td>Cu14.3</td><td>-6.3</td><td>0</td><td>760</td><td>21</td><td>0.082</td><td>0.021</td><td>0.004</td><td>0.001</td><td>-2.50</td><td>-5.47</td><td>3.01</td><td>2.85</td><td>0.07</td><td>6</td></tr><tr><td>1400</td><td>12.20</td><td>Cu14.4</td><td>-8.3</td><td>-2</td><td>203</td><td>6</td><td>0.022</td><td>0.006</td><td>0.001</td><td>0.000</td><td>-3.82</td><td>-6.70</td><td>0.47</td><td>0.31</td><td>0.09</td><td>2</td></tr><tr><td>1400</td><td>1.80</td><td>Cu14.5</td><td>-10.3</td><td>-4</td><td>62</td><td>15</td><td>0.006</td><td>0.001</td><td>0.003</td><td>0.001</td><td>-5.07</td><td>-5.79</td><td>1.28</td><td>1.12</td><td>0.02</td><td>2</td></tr><tr><td>1400</td><td>7.50</td><td>Cu14.6</td><td>-12.3</td><td>-6</td><td>14</td><td>107</td><td>0.001</td><td>0.000</td><td>0.022</td><td>0.005</td><td>-6.50</td><td>-3.83</td><td>2.40</td><td>2.24</td><td>0.04</td><td>5</td></tr><tr><td>1500</td><td>4.70</td><td>Cu15.1</td><td>-0.68</td><td>4.7</td><td>2092</td><td>28</td><td>0.227</td><td>0.011</td><td>0.006</td><td>0.001</td><td>-1.48</td><td>-5.15</td><td>1.83</td><td>1.67</td><td>0.02</td><td>5</td></tr><tr><td>1500</td><td>16.08</td><td>Cu15.2</td><td>-3.9</td><td>1.5</td><td>1141</td><td>10</td><td>0.124</td><td>0.031</td><td>0.002</td><td>0.000</td><td>-2.09</td><td>-6.22</td><td>3.15</td><td>2.99</td><td>0.15</td><td>4</td></tr><tr><td>1500</td><td>9.80</td><td>Cu15.3</td><td>-5.4</td><td>0</td><td>246</td><td>26</td><td>0.027</td><td>0.007</td><td>0.005</td><td>0.001</td><td>-3.62</td><td>-5.24</td><td>3.22</td><td>3.06</td><td>0.12</td><td>4</td></tr><tr><td>1500</td><td>13.02</td><td>Cu15.4</td><td>-7.4</td><td>-2</td><td>102</td><td>15</td><td>0.011</td><td>0.003</td><td>0.003</td><td>0.001</td><td>-4.50</td><td>-5.78</td><td>2.80</td><td>2.64</td><td>0.09</td><td>4</td></tr><tr><td>1500</td><td>9.56</td><td>Cu15.5</td><td>-9.4</td><td>-4</td><td>29</td><td>120</td><td>0.003</td><td>0.001</td><td>0.025</td><td>0.006</td><td>-5.78</td><td>-3.71</td><td>2.27</td><td>2.11</td><td>0.08</td><td>4</td></tr><tr><td>1500</td><td>4.90</td><td>Cu15.6</td><td>-11.4</td><td>-6</td><td>21</td><td>18</td><td>0.002</td><td>0.001</td><td>0.004</td><td>0.001</td><td>-6.11</td><td>-5.59</td><td>1.42</td><td>1.26</td><td>0.20</td><td>1</td></tr></tbody></table>

(equations 2–6). ΔG* was calculated from K* from the equation 8 (Sossi et al., 2019):

$$ \ln(f_E) = \frac{K^*}{fO_2^{n/4}} \frac{3M}{r\rho} \sqrt{\frac{1}{2\pi M_i RT}} (t - t_0) \quad (8) $$

where E is the element of interest and ln(f<sub>E</sub>) the evaporative loss, defined as the ratio of the mass fraction X<sub>E</sub> in the residual glass relative to the starting composition X<sub>E</sub><sup>0</sup>, as:

$$ \ln(f_E) = \ln\left(\frac{X_E}{X_E^0}\right) \quad (9) $$

K* is the equilibrium constant, fO<sub>2</sub> is the oxygen fugacity; n is the number of transferred electrons, M is the molar mass (g/mol) of the evaporated species; r is the radius of the silicate sphere (~0.001 m for Cu-S experiments); ρ is the density of the melt and was calculated from estimated oxide densities and melt composition (2750 kg/m<sup>3</sup>); M<sub>i</sub> is the molar mass of the melt, in g/mol, calculated from EPMA measurements on the starting material; R is the universal gas constant (J × K<sup>-1</sup> × mol<sup>-1</sup>); T is the temperature in Kelvin; t is the runtime of the experiment in seconds and t<sub>0</sub> accounts for the lag-time, the time at which the element begins evaporating, in our case we set t<sub>0</sub> = 0 s. The equations for electron transfer were modelled based on the HCS Chemistry (2018) software (note gas speciation shown in section 4.2 only consider gas species and their evolution according to oxygen fugacity) using Gibbs free energy minimization (Roine, 2018). For experiments without S, we assume Cu evaporates as Cu atoms, i.e., Cu is present in the melt as Cu<sub>2</sub>O and occurs as Cu atoms in the gas phase (equation 2). Therefore, the electron transfer is n = 1. For S-bearing experiments, we calculated both n = 1 and n = 0 since the S speciation may change through the fO<sub>2</sub> series. Using calculated K* and ΔG* (J/mol) values, we can quantify entropy (ΔS*, J × mol<sup>-1</sup> × K<sup>-1</sup>) and enthalpy (ΔH*, J/mol) for a given temperature following the Gibbs-Helmholtz equation:

$$ \Delta G^* = \Delta H^* - T \Delta S^* \quad (10) $$

Detailed description of the thermodynamic modeling and calculations are given in previous studies (Renggli et al., 2017; Sossi and Fegley, 2018; Sossi et al., 2019; Sossi et al., 2020; Symonds et al., 1987). All calculated thermodynamic values are given in Table 4 and in Table S2.

## 2.4. Cu speciation in the gas

We calculated the mole fractions of the different Cu gas species using the HCS Chemistry (2018) software package (Roine, 2018) that uses Gibbs-free energy minimization (Fig. 2). Note that in these calculations we only consider speciation in the gas phase and do not model gas-melt vaporization reactions. The relevant gaseous species in these models are given in the caption of Fig. 2. In the S-free experimental system, the calculated Cu-species in the gas are exclusively Cu and Cu<sub>2</sub> at all fO<sub>2</sub> (Figs. 2a, c, e). In the S-bearing system (Figs. 2b, d, f) the speciation of Cu changes as a function of fO<sub>2</sub>, and to a less extent also of temperature. At oxidizing conditions, the dominant gas species are SO<sub>2</sub>, Cu, and Cu<sub>2</sub>. Between ΔFMQ + 1.5 and ΔFMQ-2, CuS and Cu<sub>2</sub>S in the gas increase while SO<sub>2</sub> and both, Cu and Cu<sub>2</sub> decrease. At oxidation states lower than ΔFMQ-2, Cu-species remain constant while SO<sub>2</sub> decreases with a simultaneous increase of S and S<sub>2</sub>. This change in speciation towards Cu-S species at reducing conditions is also reflected by the experimental data, as S-bearing experiments show an increase in volatility relative to S-free starting compositions at ΔFMQ + 1.5. In addition, at 1200 °C and under reducing conditions (ΔFMQ-2 to ΔFMQ-6) the main Cu gas species are decreasing in the order of Cu<sub>2</sub>S-Cu-Cu<sub>2</sub>-CuS, ≈70%–25%–3%–2%, respectively (percentages are calculated according to the molar fraction of Cu gas species obtained from the HCS calculation). This repartitioning evolves with increasing temperature to ≈50.5%–43.5%–3%–3% at 1300 °C, and ≈30%–63%–3%–4% at 1400 °C (Fig. 2). No calculations have been done for Cu speciation at 1500 °C, yet it is
<table><caption>**Table 4**

Calculated thermodynamic properties of the varying starting material including Sossi et al. (2019) and Heck et al. (2025) data for their 15-minute experiments in a basaltic melt. The number of exchanged electrons in the Cu evaporation reaction is given as n.</caption><thead><tr><th></th><th></th><th>CuO</th><th>CuO (Sossi et al., 2019)</th><th>CuO (Heck et al., 2025)</th><th>CuS</th><th>CuS (Heck et al., 2025)</th><th>CuS</th></tr></thead><tbody><tr><td rowspan="3">logK*</td><td>Temp (°C)</td><td>1125*</td><td>1255</td><td>1370</td><td>1300</td><td>1400</td><td>1283</td></tr><tr><td>Temp (K)</td><td>1398</td><td>1528</td><td>1643</td><td>1573</td><td>1673</td><td>1451</td></tr><tr><td>n = 1</td><td>-4.76</td><td>-3.93</td><td>-3.45</td><td>-4.09</td><td>-3.7</td><td>-3.23</td></tr><tr><td rowspan="3">ΔG* (kJ·mol<sup>-1</sup>)</td><td>n = 1</td><td>127</td><td>115</td><td>108</td><td>123</td><td>-3.13</td><td>-1.71</td></tr><tr><td>n = 0</td><td></td><td></td><td></td><td></td><td>-2.9</td><td>-2.02</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>106</td><td>102</td></tr><tr><td rowspan="3">-ΔS* (kJ·mol<sup>-1</sup>·K<sup>-1</sup>)</td><td>n = 1</td><td></td><td>0.154</td><td>0.085</td><td>0.135</td><td>0.114</td><td>0.117</td></tr><tr><td>n = 0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">ΔH* (kJ·mol<sup>-1</sup>) at 1666.7 K</td><td>n = 1</td><td></td><td>393.29</td><td>264.25</td><td>356</td><td>308.3</td><td>275.5</td></tr><tr><td>n = 0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

expected that the increase of Cuₓ at the expense of CuₓS in the gas will continue. Particularly, if the gas becomes enriched in S as it evaporates in the early stages of the experiments, which is suggested by its strong depletion in experiments at 1400 °C and 1500 °C. These calculations confirm that S affects Cu evaporation, that Cu speciation in the gas phase changes as a function of fO₂, and that the difference in Cu loss is most likely caused by the higher volatility of Cu-S species compared to Cu⁰ (Fig. 2).

### 3. Results

#### 3.1. Experimental results and Cu concentrations in residual glasses

Copper and S mass fractions and experimental run conditions are listed in Table 3. While most glass samples are chemically homogenous (within the uncertainties of the EPMA), some run products at T < 1300 °C are chemically zoned in Cu or S, but they are homogenous for the other non-volatile elements. In the CuO system, elementals zonations were observed in all experiments at 1125 °C (except at ΔFMQ + 2.3, labeled b in Table 3). For the CuS-system, experiments at 1178 °C and ΔFMQ-1.7 (d), and at 1283 °C and ΔFMQ + 0.2 (c) are also significantly zoned. At reducing conditions Cu zonations in the glasses are observed and interpreted as the result of slow Cu diffusion rates, but increasing Cu volatility, causing the rate of evaporation to exceed the rate of diffusion (Sossi et al., 2019). These samples cannot be used to infer thermodynamic data, and they cannot be used in conjunction with the runs that have not been compromised by diffusion-limited experiments. The diffusion-limited experiments were included in the figures but were excluded from the thermodynamic modelling.

For all experiments, the proportions of Cu and S loss during an experiment are expressed as the evaporative loss ln(f<sub>Cu</sub>) and ln(f<sub>S</sub>) (equation 9; Table 3). In the S-free system, f<sub>Cu</sub> shows insignificant variation as a function of temperature at conditions above the FMQ buffer. This is not the result of a decoupling with temperature, but rather because of the relatively low volatility of Cu under oxidizing conditions, and the short experimental runtime combined with high Cu content. For similar temperatures, evaporation increases as conditions become more reducing (<ΔFMQ-3). Despite no change in vaporization reaction stoichiometry (equation 2; Fig. 3a) we explain this behavior by the lower fO₂ that favors the stability of Cu⁰ in the gas, which moves the equilibrium of the vaporization reaction towards the gas phase, in agreement with the observations by Sossi et al. (2019).

In contrast copper is more depleted in S-bearing experiments (Figs. 3b, c). Under all redox conditions, evaporative losses f<sub>Cu</sub> and f<sub>S</sub> increase with increasing temperature (Fig. 4), implying that both elements become more volatile with increasing temperature. Additionally, sulfur contents are weakly affected by a change in oxidation state, while Cu depletion is more pronounced under reducing condition (ΔFMQ-3.1 to ΔFMQ-4.8) than under oxidizing condition (ΔFMQ + 1.5 to ΔFMQ + 2.3). This difference compared to Cu-only experiments strongly suggests that the presence of S significantly influences Cu evaporation.

#### 3.2. Cu isotope compositions of the experimental run products

Copper isotopic compositions are reported relative to the starting material composition (SC: δ⁶⁵Cu<sub>ERM-633</sub> = +0.16 ‰) and expressed as Δ⁶⁵Cu<sub>SC</sub> = δ⁶⁵Cu<sub>ERM-633</sub>(sample) - 0.16 ‰ (Table 3; Fig. 5). According to our measurements, Δ⁶⁵Cu<sub>SC</sub> is influenced by temperature, oxygen fugacity, and S content. In detail, at constant ΔFMQ of air, 1.5 or 0, increasing the temperature from 1200 °C to 1500 °C increases the isotopic compositions of the silicate melt up to 1.67 ‰, 2.99 ‰, and 3.06 ‰ (Fig. 5, light grey arrows), respectively. Conversely, under the most reducing conditions (ΔFMQ = -6) the isotopic composition is decreasing with increasing temperature (dark grey arrow). Meanwhile, under intermediate fO₂ conditions (ΔFMQ = -2, -4) a transition is observed with Δ⁶⁵Cu<sub>SC</sub> increasing between 1200-1300 °C and 1400-1500 °C, but

<footnote>*includes experiments that were influenced by diffusion and native Cu-precipitations, see table 3.ª: Value without experiments that were influenced by diffusion and native Cu-precipitations.</footnote>
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Copper gas speciation in the two different systems calculated by HCS Chemistry (2018) software (Roine, 2018) at 1300 °C, 1200 °C, and 1400 °C and at-mospheric pressure. Calculations include Cu-C-O (A, C, E) Cu-C-O-S (B, D, F). The y-axis shows the log mole fraction of the gas species as a function of log fO₂. ΔFMQ refers to values relative to the FMQ buffer. In S-free systems (A, C, E), Cu and Cu₂ are the dominant Cu- species, not influenced by oxygen fugacity. Minor fractions of CuO are present at oxidizing conditions dropping rapidly towards more reducing conditions in all systems. In the S-bearing system (B, D, F) at oxidizing conditions, Cu and Cu₂ are the most dominant Cu species with SO₂ as the dominant S species. Towards lower log fO₂, Cu₂S and CuS mol fractions increase at concurrent decrease of SO₂ (and SO₃). At 1300 °C (D) and ΔFMQ-4, Cu₂S and Cu show the same abundance while Cu₂S is the dominant species at 1200 °C (C) and Cu the main one at 1400 °C (E). Calculations only consider gas speciation, gaseous species included in the calculations Cu + S system are: O₂, CO, CO₂, O₃, S, SO₂, SO₃, S₂, S₃, S₄, S₅, S₆, S₇, S₈, S₂O, COS, CS, CS₂, Cu, Cu₂, CuO, CuS, Cu₂S; and in the Cu-only system: O₂, CO, CO₂, O₃, Cu, Cu₂, CuO.</figcaption></figure>

suddenly decreasing between 1300 and 1400 °C.

At 1200 °C and 1300 °C a shift towards reducing conditions increases the $\Delta^{65}\text{CuSC}$ from + 0.23 ‰ to up to + 6.94 ‰ (Fig. 6 light grey arrow) which is more pronounced at 1300 °C than at 1200 °C. Then, at these temperatures $\Delta^{65}\text{CuSC}$ is inversely correlated with the loss of Cu and S ($\ln(f_{\text{Cu}})$, $\ln(f_{\text{S}})$) (Figs. 5 and 6). Contrary to 1200 °C, at 1300 °C the heaviest $\Delta^{65}\text{CuSC}$ is observed at $\Delta\text{FMQ}$-4, and not at $\Delta\text{FMQ}$-6. At 1400 °C, a similar enrichment in heavy Cu isotopes occurs between $\Delta\text{FMQ}$ air and 0, and between $\Delta\text{FMQ}$-2 and -6 (Fig. 6a, dark grey arrow). At $\Delta\text{FMQ}$-2 the Cu isotopic composition is reset to a $\Delta^{65}\text{CuSC}$ close to the one of $\Delta\text{FMQ}$ air, before increasing again and reaching values comparable to $\Delta\text{FMQ}$ 0 but at $\Delta\text{FMQ}$-6 (Fig. 6a, dark grey arrow). Interestingly, for both 1400 °C trends the $\Delta^{65}\text{CuSC}$ and the loss of Cu jointly increase, ruling out contamination (see 4.1). However, $\Delta^{65}\text{CuSC}$ variations with the loss of S are more complex since $\Delta^{65}\text{CuSC}$ increases with the loss of S under oxidizing conditions, but decreases with increasing

loss of S under reducing conditions (Fig. 6b, dark grey arrows). In addition, at 1400 °C the maximum extent of isotopic fractionation (+2.95 ‰ and + 2.24 ‰) is significantly smaller than at lower temperature. Finally, at 1500 °C, $\Delta^{65}\text{CuSC}$ slightly increases under the most oxidizing conditions, before decreasing from + 3.06 ‰ to + 1.26 ‰ from $\Delta\text{FMQ}$-2 to $\Delta\text{FMQ}$-6. Under these conditions, $\Delta^{65}\text{CuSC}$ does not correlate with $\ln(f_{\text{S}})$ and decreases with decreasing $\ln(f_{\text{Cu}})$, which might be related to the strong loss of S at 1500 °C and its diminishing influence on the $\Delta^{65}\text{CuSC}$. Overall, two distinct regimes of evaporation are observed. At 1200–1300 °C, increasingly reducing conditions enhance the isotopic composition of the silicate melt. In contrast, at 1400–1500 °C we observe a change in Cu behavior during evaporation that ultimately leads to a decrease of the copper isotopic composition of silicate melt when fO₂ become lower than $\Delta\text{FMQ}$-2.

The proportion of S available in the system seems to directly influence Cu evaporation (Fig. 6b). At low temperature (1200–1300 °C),
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Experimental determined evaporative loss ln(f) of copper (a and b) and sulfur (c) for oxidizing and reducing conditions as a function of temperature. Isotopic series refers to samples used for isotopic analyses. At low Cu content, discrepancies between elemental and isotopic series are related to uncertainties associated with EMPA analysis (30 to 75 %) compared to ICP-MS (2 to 10 %). Uncertainties are not displayed, but are given in Table 3. d.l.: detection limit for elemental series (EMPA).</figcaption></figure>

$\Delta^{65}\text{Cu}_{\text{SC}}$ is strongly correlated with $\ln(f_{\text{S}})$ and significantly increases until $\ln(f_{\text{S}}) \approx -3$, from 0.23 ‰ to 4.57 ‰ (1200 °C) and 0.16 ‰ to 6.94 ‰ (1300 °C) (Fig. 6b, light grey arrow). At 1400 °C and $\Delta\text{FMQ}$ air to $\Delta\text{FMQ}$ 0 the correlation is less robust (from 0.87 ‰ to 2.85 ‰), becomes opposite at $\Delta\text{FMQ} \le -2$, and disappears at 1500 °C (Fig. 6b, dark grey arrow). Oxygen fugacity series show a similar evolution. Under oxidizing conditions ($\Delta\text{FMQ}$ air to 0), $\Delta^{65}\text{Cu}_{\text{SC}}$ overall increases with decreasing $\ln(f_{\text{S}})$ from 1200 °C to 1500 °C. Under moderately reducing conditions ($\Delta\text{FMQ}$-2 to $\Delta\text{FMQ}$-4), $\Delta\Delta^{65}\text{Cu}_{\text{SC}}$ increases at 1200–1300 °C but decreases at 1400–1500 °C. In contrast, under highly reducing conditions ($\Delta\text{FMQ}$-6), $\Delta^{65}\text{Cu}_{\text{SC}}$ decreases steadily with increasing temperature, from 1200 °C to 1500 °C, and is strongly correlated with $\ln(f_{\text{S}})$ (Fig. 6b).

### 3.3. Experimental conditions

Samples with low Cu and S contents might be prone to contamination by residual Cu and S that accumulate in the furnace over multiple experiments and are subsequently released during new runs. Sossi et al. (2019) report high contamination of Na and K for similar furnaces, sometimes higher than the starting composition, which they attribute to the history of the furnace or to the alumina muffle tube. By comparison, they report limited contamination, < 3 µg/g, for other elements with various volatilities, including Cu, Zn, Ga, Ge, Pb, Cd, Zr, and a starting material containing 1000 µg/g of each element. Unlike Na and K in the Sossi et al. (2019) experiments, we do not observe Cu concentrations in silicate glasses higher than the initial Cu content. Furthermore, Sossi et al. (2019) reported a maximum Cu blank of 1.6 µg/g, which is insignificant compared to Cu concentrations of our experiments, except

for the most depleted samples for which it would contribute up to 10 % (14 µg/g, Table 3).

Our experiments contained up to 21740 µg/g Cu in Cu-only experiments, and 9221 µg/g Cu in S-bearing experiments which is more than 10 times higher than experimental charges in Sossi., et al (2019) and hence, contamination could be higher. Therefore, even if the experimental setup is designed to prevent contamination (see section 2.1), some residual glasses with light $\Delta\Delta^{65}\text{Cu}_{\text{SC}}$ at low Cu content (i.e. at 1300 °C, 1400 °C and 1500 °C) could still be contaminated by recondensation of light isotopes from previous experiments. Yet, several observations suggest that contamination can be ruled out. The data point at 1300 °C and $\Delta\text{FMQ}$-6 have a light $\Delta^{65}\text{Cu}_{\text{SC}}$ and is more depleted in Cu than samples at $\Delta\text{FMQ}$-4, but its $\Delta^{65}\text{Cu}_{\text{SC}}$ is consistent with $\ln(f_{\text{S}})$ and isotopic variation from 1200 °C to 1500 °C (Figs. 5, 6b). The reset of the isotopic composition at 1400 °C and $\Delta\text{FMQ}$-2 is balanced by an increasing isotopic composition from $\Delta\text{FMQ}$-2 to -6, while the Cu content decreases from 203 µg/g to 14 µg/g. This trend is inconsistent with the idea that low Cu samples are more contaminated than high-Cu ones. At 1500 °C, contamination cannot be totally excluded, as $\Delta^{65}\text{Cu}_{\text{SC}}$ decreases with decreasing Cu content. However, the consistency of the thermodynamic data (Tables 4 and S2) along with the lack of $\Delta^{65}\text{Cu}_{\text{SC}}-\ln(f_{\text{S}})$ correlation argues against it. The coherence of thermodynamic calculations, either with previous studies (CuO) and between the S-bearing datasets of this study, would not be expected if samples were significantly contaminated.
<figure><img src="image_8.png" /></figure>

**Fig. 4.** Evaporative loss of Cu and S as a function of temperature (color) and redox state (symbols). The dashed lines are linear regressions through each redox series and the numbers at the lower end of the lines refer to the redox state according to ΔFMQ. The solid line corresponds to equal loss of S and Cu. Overall, the data shows that S is more volatile than Cu at oxidizing conditions, i. e. above the ΔFMQ-2 where S evaporates as SO₂ (that also defines the maximum S volatility), and that S is less volatile than Cu below ΔFMQ-2. Displayed are results of the isotopic series only, because the ICP-MS allows quantification of lower S content compared to EMPA (uncertainties are smaller than symbol size).

<figure><img src="image_9.png" /></figure>

**Fig. 5.** Copper isotopic composition of the residual melts relative to the starting material (Δ⁶⁵Cu₅₀) plotted against redox state of the experiment (ΔFMQ). The he arrows show the directions of Δ⁶⁵Cu evolution at constant ΔFMQ, see text for details. Uncertainties are smaller than symbol size.

# 4. Discussion

## 4.1. Thermodynamic models for Cu evaporation

Results of this study indicate that Cu evaporation is influenced by several parameters, namely temperature, fO₂, and the presence of ligand volatiles such as S. To quantify their influences on Cu evaporation a thermodynamic model was constructed using equations 8 and 9 (Fig. 7). Except for 1125 °C in Cu-only experiments, copper contents in residual glasses decrease with decreasing oxygen fugacity at all temperatures. In

all datasets, both model curves, as well as the experimental results, show steeper trends (i.e., higher volatility) with increasing temperatures and reducing conditions (Fig. 7), indicating higher evaporative loss. For S evaporation (Figs. 7c, e), we observe a dependence on the fO₂, that is a maximum at ΔFMQ-2 (1400 °C) and FMQ (1500 °C). Note that all the melts at T > 1400 °C are heavily depleted in S apart for the run at T = 1500 °C and ΔFMQ-6 (Figs. 3 and 7e).

When compared to fCu (Fig. 3), S appears to be much more volatile than Cu under oxidizing conditions (fO₂ > ΔFMQ-2), while S becomes less volatile than Cu under the most reducing conditions (fO₂ < ΔFMQ-2). This observation can be related to the change of S speciation in the melt from SO₂ to S₂ at ΔFMQ-2 (see section 2.4) and highlights the higher volatility of S dissolved as sulfate compared to sulfide. This key observation aligns with the fact that the dominant Cu-gas species in an oxidized S-bearing system is Cu(g), and not a S-bearing Cu-species (see section 2.4), thus under these conditions only equation 5 apply.

To quantify the influence of ligand-forming elements on the thermodynamic properties of Cu evaporation, we calculated modified equilibrium constants (K*) (Sossi et al., 2019), Gibbs-free-energy (ΔG*), entropy (ΔS), and enthalpy (ΔH) for both compositions. Calculated K* (Fig. 8a) follows the trend towards higher values with increasing temperature where higher K* corresponds to higher evaporation following equation 8. Compared to Cu, Cu-S data points K* and ΔG* are more variable at low temperatures compared to higher temperatures (Fig. 8, Table 4). This may be due to the faster evaporation of S compared to Cu at higher temperatures (Figs. 2 and 3 show extremely low S in experiments at T > 1300 °C). Once S is entirely lost from the melt, Cu continues to degas in the same way as in the S-free system. This observation aligns with the change of isotopic fractionation above 1300 °C (Fig. 6). Therefore, at T < 1300 °C the S- species are involved in Cu-evaporation over the full 15-minute experimental runtime, whereas at T > 1300 °C, Cu evaporation as a S-species likely occurs only shortly in the first minutes of the experiments.

We calculate calculated ΔH* and -ΔS* values of 393 kJ·mol⁻¹ and 0.154 kJ·mol⁻¹·K⁻¹ for the S-free experiments, our values are reasonably similar to Heck et al. (2025) values of 356 kJ·mol⁻¹ and 0.135 kJ·mol⁻¹·K⁻¹ but significantly different from values of 264 kJ·mol⁻¹ and 0.085 kJ·mol⁻¹·K⁻¹ reported by Sossi et al. (2019). Comparing our K* and ΔG* values for S-free composition with literature data (Sossi et al., 2019; Heck et al., 2025), we observe significantly different results (Fig. 8). Since the offsets between the datasets are systematic, we assume that the different starting materials are the reason for these deviations. We used less viscous and more homogeneous B-bearing and Fe-free starting materials (Pangritz et al., 2022), while Sossi et al. (2019) and Heck et al. (2025) used Fe-bearing melts and Fe + S bearing melts, respectively. The ΔG* decreases with increasing temperature and plots on a straight line for the three independent set of experiments Cu-only and Cu-S (elemental and isotopic set), indicating equilibrium partial pressure as the major controlling factor on Cu loss (Sossi et al., 2019). Considering the general trend towards lower ΔG* from the Cu-only system to Cu-S (Table 4), we can confirm that Cu evaporation is influenced by the ligand-forming element S as a result of complexation in the gas phase. A change in ΔG* of + 21 % for S-bearing starting mixtures suggest large differences in the required energies for Cu evaporation at the same temperature, consistent with faster evaporation of Cu in the presence of S. In addition, the comparison of our ΔG* with Sossi et al. (2019) and Heck et al. (2025) indicates that the volatility of Cu decreases with the adjunction of Fe and decreases drastically with Fe + S. This could mean that in natural systems Fe plays a significant role in stabilizing FeS molecules in the silicate melt and thus has an impact on both S and Cu volatility.

## 4.2. Cu isotopic fractionation during evaporation from S-bearing experiments

In our experiments, the Cu isotopic composition varies strongly as a
<figure><img src="image_10.png" /><figcaption>Fig. 6. $\Delta^{65}\text{CuSC}$ reported against A) $\ln(\text{fCu})$ B) and $\ln(fS)$. The arrows indicate the evolution of $\Delta^{65}\text{Cu}$ in temperature series and Cu and S loss. Light grey arrows represent the evolution of $\Delta^{65}\text{Cu}$ at 1200 °C and 1300 °C, while dark grey arrows the evolution of $\Delta^{65}\text{Cu}$ at 1400 °C. For clarity of the figure, arrows are omitted for the evolution of $\Delta^{65}\text{Cu}$ at 1500 °C. Uncertainties are displayed when larger than symbol size.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 7. Experimental evaporative loss ($\ln(f)$) of Cu (a, b, d) and S (c, e) as a function of experimental redox conditions ($\Delta\text{FMQ}$). The datapoints are the measured values and solid and dashed lines represent the model fits calculated from our data after Sossi et al. (2019) following equation (5).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Calculated Gibbs free energy for different evaporation reactions as a function of temperature, based on thermodynamic data reported in this study. For S-free (black/red circles) runs, we included the diffusion-influenced dataset at 1150 °C (see also Table 4).</figcaption></figure>

function of the temperature, the oxygen fugacity, and notably the S content in the melt. Compared to previous studies of Cu evaporation in S-free systems (Neuman et al., 2022; Ni et al., 2021; Sossi et al., 2019; Sossi et al., 2020), the isotopic compositions in S-bearing melts are more variable (Figs. 5 and 6). We attribute this difference to the more complex speciation of Cu in the S-bearing system compared to the S-free system (Fig. 7). In a S-free Cu–O system the only change in Cu speciation occurs at $logfO_2 = -8$ with a transition from CuO to metallic Cu, which could explain the increase of the fractionation factor (i.e. $\alpha = (m_{63}/m_{65})^{0.5}$, where $m_{63}$ and $m_{65}$ are Cu masses) observed by Sossi et al. (2020). On the contrary, multiple species exist or coexist in the CuS system (Fig. 2), depending strongly on the redox conditions. Under oxidizing conditions Cu dominates in the gas phase, while at reducing conditions and T < 1300 °C, Cu₂S becomes the most abundant, and at T > 1300 °C, Cu becomes the most abundant species (Fig. 2).

This change of Cu speciation in gas in the S-bearing system is believed to directly influence the isotopic composition of the silicate melt. At oxidizing conditions (ΔFMQ air, 1.5, and 0) and 1200–1300–1400 °C, we do not observe fundamental changes in Cu speciation, Cu and Cu₂ dominate in the gas (Fig. 2c). Therefore, no variation of the Cu fractionation factor is expected, as for the S-free system (Sossi et al., 2020). This results in the clustering of $\Delta^{65}\text{CuSC}$ at 1200 °C, and in a linear increase of the $\Delta^{65}\text{CuSC}$ at 1300 °C–1400 °C, correlated with $\ln(f_{\text{Cu}})$ and $\ln(f_{\text{S}})$ as a function of decreasing oxidation state (Fig. 6). By comparison, from ΔFMQ-2 to ΔFMQ-6, Cu₂S and Cu become the most abundant species in the gas. The predicted change in speciation between ΔFMQ 0 and ΔFMQ-2 corresponds to a observed strong increase of $\Delta^{65}\text{CuSC}$ by + 2.5 ‰ and + 2.1 ‰ in the melt at 1200 °C and 1300 °C, respectively. Two processes can explain the latter observation. First, Cu₂S is more volatile than Cu (this study and Barin and Platzki, 1995). Secondly, sulfides are preferentially enriched in $^{63}\text{Cu}$ compared to silicate and metal (Savage et al., 2015; Williams and Archer, 2011; Xia et al., 2019). The combination of higher volatility and lighter isotopic composition of Cu₂S compared to Cu implies a greater loss of $^{63}\text{Cu}$ as soon as Cu₂S formed in the gas.

This strong increase of $\Delta^{65}\text{CuSC}$ is not observed under reducing conditions at 1400 °C, nor at any $fO_2$ at 1500 °C. Under these conditions S is lost almost completely during the first minutes of the experiments (Fig. 4). At $\Delta\text{FMQ} < 0$ and 1400 °C, we observe a negative correlation between $\Delta^{65}\text{CuSC}$ and $\ln(f_{\text{S}})$ whereas no clear correlation is observed at 1500 °C (Fig. 6). This indicates that the Cu₂S and CuS species are not forming abundantly in the gas. However, the $\Delta^{65}\text{CuSC} - \ln(f_{\text{S}})$ covariation still implies that $\Delta^{65}\text{CuSC}$ is influenced by a small amount of Cu₂S formation and evaporation. We suggest that the turning point of the isotopic composition between FMQ and ΔFMQ-2 at 1400 °C correspond to a change from Cu plus minor CuO evaporation to Cu plus minor Cu₂S evaporation.

At 1500 °C the most oxidized experiments (ΔFMQ-air, +1.5) follow the main $\Delta^{65}\text{CuSC} - \ln(f_{\text{Cu}})$ correlation (Fig. 6a light grey arrow), which suggests a combination of Cu and very minor CuO evaporation. On the contrary, the reduced experiments do not follow this correlation and might represent Cu evaporation with minimal contribution from Cu₂S, as for the 1400 °C and ΔFMQ-2 to ΔFMQ-6 experiments. As the $\Delta^{65}\text{CuSC}$ reaches its maximum at ΔFMQ 0 (lowest sulfur solubility) before decreasing, it is tempting to attribute $\Delta^{65}\text{CuSC}$ variations to Cu speciation. Nevertheless, the 1500 °C series does not show a similar turning point as 1400 °C experiments, neither an increase of $\Delta^{65}\text{CuSC}$ with $\ln(f_{\text{Cu}})$, nor a correlation with $\ln(f_{\text{S}})$. Therefore, the increasingly lighter $\Delta^{65}\text{CuSC}$ is unlikely to directly result from changes of Cu speciation related to S solubility, but we surmise that another process is involved. If Cu⁰ primarily occurs in the gas, given the small mass difference between $^{63}\text{Cu}$ or $^{65}\text{Cu}$ (3.1 ‰) and the high diffusivity of Cu under reduced conditions (> 400 µm/s; Ni and Zhang, 2016), it is possible that at 1500 °C, and after 15 min, the difference in diffusion speed between $^{63}\text{Cu}$ and $^{65}\text{Cu}$ decreases as the environment becomes more reducing. Finally, even though S seems to have little influence at 1500 °C, the ΔFMQ-6 series from 1200 °C to 1500 °C shows a strong decrease of $\Delta^{65}\text{CuSC}$ with decreasing $\ln(f_{\text{S}})$ and increasing temperature. This confirms that higher mass fractions of S in the glass enhance the extent of isotopic fractionation, and that even a small fraction of S influences $\Delta^{65}\text{CuSC}$.

To characterize the effects of Cu speciation on the isotopic composition in the Cu-S system, we report the isotopic composition as 1000 × $\ln(R_{\text{Cu}}/R_{\text{CuO}})$ as a function of evaporative loss (i.e. $\ln(f_{\text{Cu}})$), with $R_{\text{Cu}}$ and $R_{\text{CuO}}$ the isotopic ratios of the sample and of the starting composition (Fig. 9). The fractionation factor $\alpha$ is calculated from $m = 1000 \times (1 - \alpha)$, where m is the slope of the linear regressions (Neuman et al., 2022). This resulted in $\alpha = 0.99738$ under oxidizing conditions and 1200 °C to 1300 °C, which is close to the fractionation factor in the S-free Cu–O system ($\alpha = 0.9972$; Sossi et al., 2020; and $\alpha = 0.9961–0.9960$; Neuman et al., 2022; Ni et al., 2021). The fractionation factor approaches unity as the system becomes more reducing, reaching $\alpha = 0.99860$ at 1200 °C and ΔFMQ-6. This interval of $\alpha = 0.99738$ to 0.99860 encompasses most of the experiments that exhibit minimal S loss from the melt ($\ln(f_{\text{S}}) > -2$). However, the experiments done at 1400 °C and under reducing conditions (ΔFMQ < air), or at 1500 °C and ΔFMQ < +1.5, range from 0.99860 (1200 °C; ΔFMQ-6) to 0.99977 (1500 °C; ΔFMQ-6). This range of fractionation factors also corresponds to the variations of the ΔFMQ-6 series which shows a positive correlation between $\Delta^{65}\text{CuSC}$ and $\ln(f_{\text{S}})$ (Fig. 6b).

We suggest that the difference in Cu isotopic fractionation at 1200–1300 °C and under oxidizing conditions does not change when the S-bearing system is compared to S-free system, in line with the absence of CuₓS in the gas phase at oxidizing conditions. On the contrary, at high temperatures (1400–1500 °C) or under highly reducing conditions
<figure><img src="image_13.png" /><figcaption>Fig. 9. Copper isotopic composition expressed as 1000 × ln(R<sub>Cu</sub>/R<sub>Cu0</sub>), with R<sub>Cu</sub> and R<sub>Cu0</sub> the isotopic ratios of the sample and of the starting material reported against ln([Cu]/[Cu]<sub>0</sub>), i.e., ln(fCu). In this diagram the isotopic fractionation factor α is equivalent to the slope m of linear regressions with m = 1000 × (1 − α). Under oxidizing conditions and temperatures of 1200 °C and 1300 °C α = 0.99738, similar to previous estimations of 0.9972–0.9979 highlighted by the grey area (Neuman et al., 2022; Sossi et al., 2020). As the experimental conditions become more reducing and hotter, the fractionation factor decreases to a minimum value of 0.99977.</figcaption></figure>

(ΔFMQ-6), the progressive removal of reduced sulfur produces a shift of α closer to unity which is significantly different from values reported by Sossi et al (2019, 2020) for S-free melts. The absence of S is expected to result in the evaporation of Cu as monoatomic, or diatomic species. As such, isotopic fractionation based on bond stiffness (i.e., the preferential incorporation of ⁶³Cu over ⁶⁵Cu in Cu-S) and occurring within the melt prior to evaporation would be inhibited. Under these conditions the isotopic fractionation will be controlled by Cu self-diffusion (by contrast to CuS or CuO) in the silicate melt, which itself is function of 1/T²:

$$ \alpha = 1 + \frac{A}{T^2} \qquad (9) $$

where α is the fractionation factor, T the temperature in Kelvin, and a constant A function of the mass difference between isotopes and the activation energy (Criss, 1991, 1999). Therefore, the small mass difference between ⁶³Cu or ⁶⁵Cu (3.1 %), the high diffusivity of Cu in reduced conditions (> 400 µm/s; Ni and Zhang, 2016), and the high temperature could explain the α values being closer to unity with increasing temperature.

### 4.3. Implications for copper isotopic composition of lunar mare basalts

Lunar mare basalts are volcanic deposits that originate from lunar mantle sources formed during the solidification of the lunar magma ocean (LMO). They are good candidates to compare with our experimental data because their compositions suggests that the lunar interior is reduced (IW-1; ≈ΔFMQ-4.4; Fogel and Rutherford, 1995; Nicholis and Rutherford, 2009) and significantly depleted in Cu and S compared to the bulk silicate Earth (Gleißner et al., 2022, and references therein). Mare basalt crystallized over a large range of temperatures similar to earth, between 1050 °C and 1300 °C (Bombardieri et al., 2005; Longhi, 1992; O’Hara and Biggar, 1975). Also, they have isotopic compositions that are on average heavier than the Earth by ≈+0.5 to + 1 ‰ (Florin et al., 2025; Herzog et al., 2009; Moynier et al., 2006; Paquet et al., 2025). The isotopic compositions are interpreted as reflecting near-equilibrium isotopic fractionation during the proposed lunar devolatilization processes (Dauphas et al., 2022; Paquet et al., 2025) and are best modeled by volatile loss with Rayleigh fractionation for α = 0.99945 (Paquet et al. 2025). However, the timing of evaporation remains

ambiguous, and Cu loss could be interpreted either as evidence for volatile loss during mare basalt emplacement or with a major vapor extraction event, such that Moon forming impact or the lunar magma ocean.

In order to test the possibility that some δ⁶⁵Cu of mare basalts reflect evaporation, we modeled isotope fractionation with our new fractionation factors using all the δ⁶⁵Cu mare basalts data available (Florin et al., 2025; Herzog et al., 2009; Moynier et al., 2006; Paquet et al., 2025). We assume two starting compositions, a volatile depleted silicate Moon like composition ([Cu] = 16 µg/g and δ⁶⁵Cu = +0.57 ‰; Paquet et al., 2025) and for comparison a BSE-like composition ([Cu] = 30 µg/g and δ⁶⁵Cu = +0.07 ‰ Savage et al. (2015); Wang and Becker (2015), Fig. 10). We calculate the ln(fCu) = ln([Cu]/[Cu]<sub>0</sub>) accordingly ([Cu]<sub>0</sub> = 16 or 30 µg/g). The value of 16 µg/g Cu is an estimate based on the mare basalt with the highest Cu content, implicitly suggesting that all mare basalt magmas had similar Cu contents before evaporation. This assumption contradicts previous studies that shown that each parental melt and associated mantle sources were characterized by different mass fractions of MVE (Florin et al., 2025; Gleißner et al., 2022). Given that Cu is a moderately incompatible element during mantle melting, these ln(fCu) values cannot be used as proxies to estimate degassing from the LMO or during the Moon forming impact. In any scenario, Cu contents of lunar mantle sources must be significantly lower than in mare basalts, and only the residual liquid of the lunar magma ocean solidification could be enriched in incompatible MVE (e.g. Barnes et al., 2019; Tian et al., 2020). Therefore, such high Cu contents are only meaningful in the context of studying Cu degassing at the very end of LMO crystallization or during mare basalt emplacement.

Assuming that evaporation is the sole process responsible for Cu isotope differences between mare basalts, this process would require α ranging from 0.99934 to 0.99945 (Fig. 10), corresponding to experimental conditions of 1400–1500 °C, a fO₂between FMQ to ΔFMQ-2, and low S contents (Figs. 6 and 9). These conditions required to reproduce δ⁶⁵Cu are more oxidizing (Delano, 1980; Fogel and Rutherford, 1995; Nicholis and Rutherford, 2009) and reflect higher temperature (e.g. 1165 °C O’Hara and Biggar, 1975; 1215 °C for olivine in quartz-normative samples, and 1177 °C for olivine in olivine-normative samples, Bell et al., 2023) than the conditions proposed for mare basalts emplacement, therefore questioning these results. One possibility is that the volatility of Cu is overestimated due to the lack of Fe in our experiments (Heck et al. 2025). However, the relation between loss of Cu and isotopic fractionation cannot be inferred without measuring Fe bearing experimental material or without ab initio calculation leaving this question open.

If the lighter δ⁶⁵Cu values of high-Ti mare basalts are also linked to kinetic evaporation, only the heaviest samples can be modelled with an α value closer to unity (i.e., 0.99977) and a BSE-like starting composition. Otherwise only 3 out of 19 high-Ti mare basalts fit such an evaporation model. We have shown that α approaches unity because the S content of experimental silicate melts drastically decreases during evaporation, Consequently, an α value of 0.99977 implies very low S-content and Cu evaporation likely as Cu, without bonding to any ligand element. By comparison, S content increases from low-Ti (≈760 µg/g) to high-Ti (≈1525 µg/g) mare basalts (Florin et al., 2025; Gleißner and Becker, 2024; Kallnik et al., 2024). Thus, the decrease of δ⁶⁵Cu from low-Ti to high-Ti mare basalts does not agree with the behavior expected from experimental evaporation. Hence, we argue that the δ⁶⁵Cu difference between low- and high-Ti mare basalts cannot be explained by progressive evaporation of Cu from an initially S-bearing silicate melt that would end S-depleted. It is possible that a CuCl system provides α values that better fit, however Paquet et al. (2025) concluded that no correlation exists between δ⁶⁵Cu and δ³⁷Cl, most likely ruling out this possibility. Another possibility is that the mismatch between the Rayleigh model and high-Ti basalts reflects the role of Fe, and possibly Ti, in stabilizing Cu in mare basalt melts, or the influence of boron occurring in our experiments. In summary, some mare basalt Cu isotope data align
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Copper isotopic composition of mare basalts against ln(f<sub>Cu</sub>). Model starting composition according to A) BSE like Cu elemental and isotopic composition (Wang and Becker, 2015; Savage et al., 2015); B) Estimation of volatile depleted silicate Moon like Cu elemental and isotopic composition (Paquet et al., 2025). Lines show the evolution of the remaining silicate melt during evaporation following Rayleigh fractionation models. The red one is a pure Rayleigh model (α = 0.98449), the black ones are calculated using the isotopic fractionation factors defined in this study from left to right (0.99734, 0.99860, 0.99977). The long-dashed line uses an alpha value of 0.99934 defined to fit mare basalt data and the green double dashed dotted line has an alpha value of 0.99945 defined by Sossi et al. (2020) and used in Paquet et al. (2025) to model mare basalt compositions. Mare basalt Cu concentration data are from (Gleißner and Becker, 2024; Gleißner et al., 2022; Kallnik et al., 2024; Paquet et al., 2025) and isotope data are from Florin et al. (2025) (Circles), Paquet et al. (2025) (Diamonds), and Herzog et al. (2009); Moynier et al. (2006) (Triangles).</figcaption></figure>

with a Rayleigh distillation model with an α of 0.99935–0.99945. For most other mare basalts, δ⁶⁵Cu data cannot be explained by evaporation. Thus, we suggest that they are more likely representative of differences in their source compositions caused by isotopic fractionation between metallic alloys and silicate in the LMO as recently demonstrated by Florin et al., (2025).

**5. Conclusions**

We conducted copper evaporation experiments from iron-free silicate melts doped with CuO and CuS over a temperature range from 1150 °C to 1500 °C and at oxygen fugacities (logfO₂ relative to the fayalite-magnetite-quartz buffer) from ΔFMQ-6 to atmospheric conditions, and run durations of 15 min each.

* We report an increasing volatility of Cu associated with significant isotopic fractionation with increasing temperature and decreasing oxygen fugacity, consistent with previous studies.

* A thermodynamic analysis of the experimental data shows that, in Fe-free silicate melt, ΔG* of the evaporation reactions decreases from the S-free system to the S-bearing system, indicating that Cu becomes more volatile in the presence of S, particularly at reduced conditions. In addition, the effect of S on Cu evaporation is more pronounced at lower temperatures (below 1350 °C) than at higher temperatures. We conclude that S strongly influences Cu evaporation as a result of the formation of Cu-S compounds in the gas phase. Yet, at temperatures above 1350 °C, ligand forming sulfur is largely lost from the melt before Cu is evaporated.

* In the S-bearing system, we observed two distinct behaviors in Cu isotopic composition. First, at 1200 °C and 1300 °C, we report a strong enrichment of the residual melt in heavy Cu isotopes with increasingly reducing conditions. This enrichment correlates with ln(f<sub>Cu</sub>) and ln(f<sub>S</sub>) and is the largest under the most reduced conditions (i.e., δ⁶⁵Cu = +4.73 ‰ at 1200 °C and ΔFMQ -6; δ⁶⁵Cu = +7.10 ‰ at 1300 °C and ΔFMQ -4). Secondly, at 1400 °C, the isotopic fractionation is smaller than at lower temperatures, with δ⁶⁵Cu decreasing at ΔFMQ -2 while CuS is the predominant species. At

1500 °C, the δ⁶⁵Cu decreases with increasingly reducing conditions. This decrease with increasing temperature under highly reducing conditions is confirmed by the series at ΔFMQ-6, in which δ⁶⁵Cu dropped from + 4.73 ‰ at 1200 °C to + 1.42 ‰ at 1500 °C.

* We suggest that this evolution at ΔFMQ-6 results from the combination of: (1) S depletion, which reduces the number of available S atoms that can be bound to Cu, thereby favoring a progressive equal evaporation of ⁶³Cu and ⁶⁵Cu as temperature increases; and (2) higher Cu diffusion rates in the melt at higher temperatures.

* We report fractionation factors of 0.99738 < α < 0.99860 at 1200 °C-1300 °C to 0.99977 under the most reducing and highest temperature conditions.

* According to this new set of experiments, we suggest that the δ⁶⁵Cu composition of most lunar mare basalts cannot be explained by evaporative loss of Cu during mare basalt emplacement.

**Data availability**

All data are available through Mendeley Data at: https://doi.org/10.17632/wxctx5b5dk.1.

**CRediT authorship contribution statement**

**Guillaume Florin:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization.
**Paul Pangritz:** Writing – review & editing, Writing – original draft, Validation, Investigation, Formal analysis.
**Christian J. Renggli:** Writing – review & editing, Supervision, Methodology, Formal analysis, Conceptualization.
**Philipp Gleißner:** Writing – review & editing, Writing – original draft, Validation, Investigation.
**Jasper Berndt:** Formal analysis, Data curation.
**Arno Rohrbach:** Writing – review & editing, Project administration, Investigation, Funding acquisition, Formal analysis, Conceptualization.
**Harry Becker:** Writing – review & editing, Writing – original draft, Supervision, Resources, Project administration, Funding acquisition.
**Stephan Klemme:** Writing – review & editing, Writing – original draft, Resources, Project administration, Methodology, Investigation, Funding acquisition,
Conceptualization.

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.

Acknowledgments

Our thanks go to Beate Schmitt for her superb support in the analytical labs, Maik Trogisch for his expert sample preparation, and to all other members of the workhops at Uni Münster (Lars Peuker, Peter Weitkamp, Christopher Fritzsche, Samuel Flunkert, Andrew Hardes) for keeping the experimental labs at the Institute for Mineralogy in good running order. We warmly thank J. M. D. Day for his careful and efficient editorial handling, and the three anonymous reviewers for their constructive and thoughtful feedback, that greatly helped to improve this manuscript.

This research was partially supported by DFG Project 263649064 - SFB TRR170. This is TRR170 publication #230.

CJR was partially funded by DFG Project 442083018

Appendix A. Supplementary material

Table S1: Elemental content for each run and model calculation. Table S2: Thermodynamic calculations. Figure S1: SEM images of experimental runs. Figure S2: SEM analysis in Pt wires. Supplementary material to this article can be found online at https://doi.org/10.1016/j.gca.2025.09.015.

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