Analytical protocol for measuring micro-molar quantities of sulfur volatile species in experimental high pressure and temperature fluids

Three syntheses of redox-buffered SOH fluids were conducted at 3 GPa and 700 °C (Table 1) using the double capsule technique (Fig. 1). To validate our methodology, we employed iron–wüstite (IW) and fayalite–magnetite–quartz (FMQ) redox buffers (Fig. 2a, b) to explore a range of potential fluid compositions under relatively reducing and oxidizing conditions. According to thermodynamic models, the IW-buffered experiment is predicted to produce a fluid with low H₂S content along with the pyrrothite formation at the expense of pyrite, as highlighted by Eq. (1):

The relevant fH₂-buffering reactions are shown together with the equilibria that involve the SOH fluid in the inner capsule.

Buffer assemblages: a iron–wüstite (i.e., Iron–Wü) in SOH-IW2 and b ferrosilite–magnetite–quartz (i.e., Fs–Mag–Q) in SOH–FMQ1. Run products: c newly formed pyrrhotite (Po) derived from pyrite (Pyr) reaction in experiment SOH-IW2; d pyrite (Pyr) crystals in experiment SOH-FMQ1.

In contrast, the FMQ-buffered run should result in a H₂S-free fluid composed entirely of H₂O, thus serving as our blank control. For this experiment, as H₂S formation—and therefore pyrrhotite generation—is not predicted, the initial pyrite/pyrrhotite ratio is expected to remain unchanged.

For our experiments, a runtime of 5-h was set for SOH-IW2 and SOH-FMQ1 runs, while a 6-h runtime was chosen for run SOH-IW1 (Table 1). This duration was based on previous experimental works conducted on magmatic systems¹⁴. Since these studies were performed at higher temperatures (T = 1300 °C) compared to our experiments, we initially set longer runtimes ranging from 1 week to 8 to 10 h. Additional details, including a complete list of the experiments conducted, are reported in Supplementary Tables 1 and 2. However, in all the IW-buffered experiments exceeding 6 h, the inner capsule was invariably found devoid of fluids (Supplementary Table 1), suggesting that runtimes beyond 5 h may trigger capsule weakening due to the produced H₂S, resulting in fluid loss during quenching.

In all the experiments conducted under reducing conditions, i.e., SOH-IW1 and SOH-IW2, microtextures revealed the consumption of pyrite to form pyrrhotite as the solid run product (Fig. 2c), in agreement with thermodynamic predictions. In contrast, in the FMQ-buffered experiment (SOH-FMQ1), the initial pyrite/pyrrhotite ratio appears to be preserved (Fig. 2d).

Image analysis performed on X-ray compositional maps (Fig. 3, Supplementary Fig. 1) clearly illustrates the growth of pyrrhotite at the expense of pyrite (Fig. 3a–c) especially towards the inner-capsule walls (Supplementary Table 3). Remarkably, no reaction between the produced sulfur-bearing volatile species and either the inner or outer capsule was evidenced (Fig. 3b). This suggests that fluid loss did not occur during the experiment, confirming that Au is a suitable material for this type of synthesis.

Solid run products (i.e pyrrhotite = Po and pyrite = Pyr) of the different runs are reported as follows: a SOH-IW2; d SOH-IW1; g SOH-FMQ1. Compositional X-ray maps of sulfur for the performed experiments are illustrated in b SOH-IW2; e SOH-IW1; h SOH-FMQ1. Compositional X-ray maps of iron are shown in c SOH-IW2; f SOH-IW1; i SOH-FMQ1. Compositional X-ray maps scale is expressed in count per second for both sulfur and iron. Image analysis was performed through a specifically designed Wolfram Mathematica® routine.

X-ray compositional maps also indicate that the width of the pyrrhotite-rich layer is more pronounced in the 6-h run (SOH-IW1, Fig. 3d–f and Supplementary Table 3) compared to the 5-h run (SOH-IW2, see Fig. 3a–c). This observation provides compelling evidence that the pyrrhotite-forming reaction reported in Eq. (1) has occurred, driven by H₂ diffusion from the outer Au capsule, progressing from the edge of the inner capsule toward its central part.

In contrast, the FMQ-buffered experiment SOH-FMQ1 confirms that the initial pyrite/pyrrhotite ratio was preserved, with no precipitation of newly formed pyrrothite (Fig. 3g–i and Supplementary Table 3).

Our results underscore the critical importance of runtime in determining capsule resistance and the successful outcome of the experiment. This is evident from runs SOH-IW1 and SOH-IW2, conducted under identical P, T, and redox conditions but with slightly different runtimes (6 and 5 h, respectively; see Table 1). The fluid synthesized in the experiment SOH-IW1 (Table 1) generated a ΔP of 39 mbar in the piercing chamber, which, according to the volume and the temperature of the chamber itself, corresponds to 36.05 μmol of total volatiles. The fluid primarily consisted of H₂O (97.1 mol%), with minor amounts of H₂S (2.9 mol%, Supplementary Fig. 2). In contrast, the fluid released from the experiment SOH-IW2 generated a ΔP of 128 mbar, corresponding to 106.72 μmol of volatiles. The analyzed fluid (Fig. 4a–e) is composed of H₂O (73.6 mol%), H₂S (13.2 mol%), H₂ (9.0 mol%) and SO₂ (4.36 mol%). This measured bulk fluid composition is nearly identical to that predicted by thermodynamic models for chemical equilibrium (Fig. 4a). However, the chemical speciation of the analyzed fluid deviates from thermodynamic predictions (Table 1), showing higher H₂ and lower H₂O contents, even with some oxidized sulfur (SO₂) despite of the highly reducing conditions. This apparent discrepancy may be explained by a back-reaction likely occurring in the fluid during the temperature drop imposed at the end of the experiment, which changed the pristine speciation of the fluid at high P-T conditions. Hydrogen and SO₂ could have formed from water and H₂S, a reaction that is known to occur spontaneously at hydrothermal conditions¹⁵, as described by Eq. (2):

Run SOH-IW2: a bulk fluid composition measured by the capsule-piercing QMS (red dot) compared to fluid composition predicted by the thermodynamic model using Eos¹⁸ (black dot). The size of the red dot includes the analytical uncertainty. Signal integration (peak area) expressed as m/z for the different channels (i.e., measured volatile components) measured as partial pressures over time: b channel 2: H₂; c channel 18: H₂O; d channel 34: H₂S; e channel 64: SO₂. The red line represents the background signal. Run SOH-FMQ1: f bulk measured fluid composition (red dot) compared to the predicted composition (black dot). The size of the red dot includes the analytical uncertainty. Signal integration (peak area) expressed as m/z for the different investigated channels: g channel 2: H₂; h channel 18: H₂O; i channel 34: H₂S; l channel 64: SO₂. For both experiments quantitative analysis was performed by integration of the peak area through a specifically designed Wolfram Mathematica® routine.

The preservation of the bulk fluid composition in experiment SOH-IW2 strongly suggests that these changes in fluid speciation are merely the result of a partial late-stage chemical re-equilibration during quenching to room conditions. These results align with previous findings on COH systems, which have demonstrated that ex-situ techniques effectively preserve the bulk fluid composition^8,9 but not necessarily the fluid speciation^7,8, which is highly sensitive to pressure and temperature conditions and may be altered during quenching. In this framework, the development of rapid quenching techniques will be of crucial importance for the investigation of natural systems and, in particular, of geological fluids. While still in the early stages of implementation¹⁶, these methods utilize faster cooling rates compared to those routinely employed in experimental petrology laboratories. This advancement holds the potential to provide more accurate representations of fluid speciation under HP–HT conditions, thereby enhancing our understanding of fluid behavior in geological processes.

The results obtained from experiment SOH-IW2 confirm that chemical equilibrium between the solid and fluid phases is achieved within five hours. The lower H₂S content in experiment SOH-IW1, which ran for six hours, compared to experiment SOH-IW2, appears counterintuitive to chemical kinetics principles. This behavior is due to H₂S loss due to diffusion, as evidenced by a strong “rotten egg” smell when the outer capsule was peeled off. As previously stated, no reaction with the inner or outer capsule was observed during microprobe analysis (Fig. 3b, e), indicating that fluid loss occurred at the end of the experiment, i.e., during quenching. Nevertheless, experiment SOH-IW1 is crucial for developing our protocol for several reasons. First, the extremely low H₂S contents (1.03 μmol ± 0.072, see Table 1 and Supplementary Fig. 2) obtained in experiment SOH-IW1 provide an excellent opportunity to rigorously test the analytical sensitivity of the QMS measurements. Our data unequivocally show that, despite the low amount of produced H₂S, the proposed protocol ensures high-precision measurements of sulfur volatiles. This is evidenced by the extremely low standard deviation values (7 mol%) on H₂S measurements.

Second, this experiment demonstrates that once chemical equilibrium is achieved, the produced H₂S begins to weaken the inner capsule, leading to fluid diffusion during quenching. Therefore, experiments should not exceed 5 h, i.e., the time required to reach chemical equilibrium.

A series of additional experiments (Supplementary Results), conducted under different pressure and temperature conditions (Supplementary Table 2, Supplementary Figs. 3 and 4), shows that temperature is a key factor in governing the kinetics of the H₂S-forming reaction, while pressure has minimal impact. These preliminary findings suggest that our protocol, although optimized for 3 GPa and 700 °C, can be effectively adapted across a broader range of pressure and temperature conditions.

Based on the results obtained from experiment SOH-IW2, we ran our blank control, experiment SOH-FMQ1, for five hours. The produced fluid (Table 1 and Fig. 4f) consists of pure H₂O (100 mol%, Fig. 4g–l) and is generated at ΔP of 38 mbar. As for experiment SOH-IW2, the fluid bulk composition overlaps with that predicted by thermodynamic models (Fig. 4f).

The consistency between the experimental data and thermodynamic models suggests that the bulk composition in the fluid was preserved throughout quenching and fluid measurement. The proposed protocol thus represents a robust and reliable methodology, optimized for specific pressure and temperature conditions for quantitative analysis of ultra-low amounts of sulfur-bearing fluid.