The structure and stability of Fe4+xS3 and its potential to form a Martian inner core

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Due to the similarity between estimates of the core’s sulfur content and the iron - iron sulfide eutectic composition at core conditions, it has been concluded that temperatures are too high for Mars to have an inner core. Recent low density estimates for the core, however, appear consistent with sulfur contents that are higher than the eutectic composition, leading to the possibility that an inner core could form from a high-pressure iron sulfide phase. Here we report the crystal structure of a phase with the formula Fe 4 + x S 3 , the iron content of which increases with temperature, approaching the stoichiometry Fe 5 S 3 under Martian inner core conditions. We show that Fe 4 + x S 3 has a higher density than the liquid Martian core and that a Fe 4 + x S 3 inner core would crystalize if temperatures fall below 1960 (± 105) K at the center of Mars. Earth and environmental sciences/Planetary science/Core processes Earth and environmental sciences/Solid Earth sciences/Mineralogy Earth and environmental sciences/Planetary science/Inner planets Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Observations from NASA's InSight mission have revealed that the core of Mars is enriched in light elements, as its density appears to be substantially lower than that of Fe-Ni alloy 1 – 4 . Based on seismic wave reflections at the apparent core-mantle boundary of Mars, models considering either the existence 3 – 4 or absence 1 – 3 of a basal silicate magma layer indicate that the Martian core contains 9 to 20 wt.% or 20 to 25 wt.% of light elements, respectively. In either case, the abundance of light elements in the Martian core is significantly higher than in Earth's core (5 to 10 wt.%) 5 , implying considerable differences in accretion and differentiation processes during the early stages of planetary formation 6 . From cosmochemical perspectives and geochemical considerations, candidate light elements in the Martian core include S, O, C, and H 7 – 10 . Sulfur, in particular, is often highlighted as a likely major light element in the Martian core, primarily due to it being the most prevalent moderately volatile element in the solar nebula 11 , its siderophile ("iron-loving") behavior during core-mantle differentiation 12 , and the fact that core formation on Mars was likely not a sufficiently reducing or high-temperature process for Si or O to be major light elements 13 . Assessments based on similarly volatile lithophile elements argue for < 7 wt % S in the Martian core 10 but this would most likely require significant proportions of C and H to explain the core’s density deficit, which should, by the same arguments, be even more depleted in Mars than S. If similarly volatile elements are used to predict the S contents of ordinary and enstatite chondrites, the resulting concentrations for most of these meteorite sub-types are underestimated, raising the possibility that S contents of planetary bodies might vary independently of elements with similar condensation temperatures. Seismic and lander radio science data from the InSight mission have confirmed that Mars has a liquid core 1 – 4 , 14 , but the presence of a solid inner core cannot be currently excluded on geophysical grounds 1 – 2 . If further geophysical observations were to verify the existence, size, and density of a Martian inner core, then combined with the appropriate mineral physical interpretation, this would provide essential constraints on the composition and temperature of the interior, as well as the possible mechanisms that initiated and terminated the magnetic field in early Mars 15 – 16 . In the scenario of a S-rich Martian core, the cooling and solidification processes of an initially fully molten Martian core are primarily governed by the melting phase relations of the Fe-FeS system under the high-pressure and high-temperature (HP-HT) conditions relevant to the Martian core. The eutectic composition in the Fe-FeS system shifts in the direction of the Fe-rich side with increasing pressure, from approximately 15.5 wt.% S at 21 GPa 17 , i.e. the pressure at the top of the Martian core, to approximately 12 wt.% S at 40 GPa 18 – 21 , the pressure at the center of Mars. Within the possible compositional range of Mars’ core, either Fe or Fe sulfides could be liquidus phases that might crystalize as an inner core 16 , 18 . Understanding the crystal structures and densities of these liquidus phases is, therefore, critical for determining their behavior during cooling of the Martian core. In addition to the endmembers Fe and FeS, the solid phases reported under Martian core conditions in the Fe-FeS system include Fe 2 S, Fe 3 S, and Fe 3 + x S 2 17–18 . Fe 2 S is identified as a subsolidus phase in the Fe-FeS system at 21 GPa but is replaced by Fe 3 S or Fe 3 + x S 2 when the temperature increases above the solidus temperature on the FeS-rich side of the eutectic 17 . Whether Fe 2 S becomes a liquidus phase under higher pressures, corresponding to deeper Martian core conditions, remains unknown. Fe 3 S adopts a Fe 3 P-type structure and has a S content (16 wt.%) close to the eutectic composition of the Fe-FeS system at Martian core pressures 17 . During the cooling of the Martian core, if the sulfur concentration in the liquid core is above but close to the eutectic composition, Fe 3 S is expected to crystallize. Fe 3 S would be gravitationally stable at the center of the Martian core, as its density would be higher than that of the residual liquid 18 . However, if the bulk composition is more sulfur-enriched, for example, greater than 16 wt.% S at 21 GPa 17 , the phase described as Fe 3 + x S 2 would be the liquidus phase 16 . Fe 3 + x S 2 decomposes during decompression and cannot be recovered to ambient pressure 22 , 23 . Its crystal structure can, therefore, only be investigated in-situ , under high pressure conditions. The crystal system of Fe 3 + x S 2 has been determined to be orthorhombic using powder X-ray diffraction 23 , but its structure remains undetermined. Consequently, the density and elastic properties of Fe 3 + x S 2 remain largely unknown. In order to determine the crystal structure and density relations of the elusive Fe 3 + x S 2 phase, we conducted a series of HP-HT experiments within the Fe-FeS system, employing multiple in-situ and ex-situ characterization techniques. However, instead of Fe 3 + x S 2 , we obtained a crystal structure for an iron sulfide phase that is more accurately described, on the basis of its crystallography, as Fe 4 + x S 3 . This phase was synthesized within the P-T and compositional range where Fe 3 + x S 2 has been previously reported, which almost certainly has the same structure. We have further investigated the composition, density and potential role of Fe 4 + x S 3 in forming a Martian inner core. Results Structural refinement of Fe 4 + x S 3 As the target Fe 3 + x S 2 phase is known to decompose to nano-crystallites of a few different phases during decompression 22 , we performed high-pressure single crystal structure analyses in the diamond anvil cell (DAC) following in situ syntheses through laser heating (LH) at pressures of approximately 15 GPa and 21 GPa. The starting material for the LH-DAC experiments comprised degraded “Fe 3 + x S 2 ” crystals, which were initially synthesized at pressures ranging from 14 to 16 GPa in a multi-anvil (MA) press. Although these starting materials maintained a homogeneous composition on a scale of less than 100 nm, their crystal structure experienced degradation during the decompression process in the MA press, and therefore, cannot be directly used for structure determination. After syntheses in the LH-DAC, single crystal X-ray diffraction (SC-XRD) data were collected at room temperature and high pressures on the newly grown crystals in the reacted LH area. Using a micro-focused synchrotron X-ray beam (~ 1 µm * 1 µm) it was possible to index reflections from numerous sub-µm sized grains with different orientations in each sample. Structural solution of several of these grains led to the identification of a previously unknown structure exhibiting orthorhombic symmetry in the reacted areas of two experiments conducted at 15 GPa and 1150(± 200) K (run LJFeS01) and 21 GPa and 1400(± 200) K (run LD101). The reflections measured for all grains indicate clearly that the space group of this phase is Pnma . Structural refinement of two single crystals exhibiting the best discrepancy factors in each experiment (see more details in Supplementary Methods) indicates that the phase is characterized by five non-equivalent crystallographic sites for Fe and three non-equivalent sites for S. As shown in Fig. 1 , there are four Fe sites that are five-fold coordinated, forming four edge-sharing Fe-S square pyramids; whereas the remaining iron site is four-fold coordinated, creating a Fe-S tetrahedron. The fundamental building blocks of the structure of Fe 4 + x S 3 are consistent with the high pressure Fe 12 S 7 phase 24 , stable above 100 GPa and the Fe 2 S phase stable above 21 GPa 24 – 25 . The tetrahedral site can be considered as an interstitial site between neighboring Fe-S square pyramids. If all the Fe and S sites are fully occupied, this would lead to a stoichiometry corresponding to Fe 5 S 3 . However, refinements of the SC-XRD data indicate that the Fe tetrahedral site is not fully occupied, leading to a chemical formula Fe 4 + x S 3 (Supplementary Table 1 and Table 1 ), where x is the Fe occupancy at the tetrahedral site. In experimental run LD101, the occupancy of the tetrahedral site in the Fe 4 + x S 3 phase was found to be 0.77 (± 0.01), which can be described with the more appropriate stoichiometry Fe 4.77 S 3 , or following the formula of Fei et al. 17 , Fe 3.18 S 2 . In another experimental run, LJFeS01, conducted under lower pressure-temperature (P-T) conditions than LD101, the tetrahedral site occupancy was refined to 0.11 (± 0.01) Fe atoms. This results in the composition Fe 4.11 S 3 , or Fe 2.74 S 2 when expressed in the Fe 3 + x S 2 formula. Moreover, the unit cell volume of the Fe 4 + x S 3 phase at 21 GPa and 300 K synthesized in run LD101 (331.2 Å 3 ) is notably larger than that at 15 GPa and 300 K synthesized in run LJFeS01 (324.0 Å 3 ). This is clearly due to the increased Fe occupancy of the tetrahedral site, which causes an increase in tetrahedral volume and, therefore, an increase in unit-cell volume (see Supplementary Discussion and Supplementary Fig. 1). The details of the crystallographic parameters are presented in Table 1 and Supplementary Table 2. The Fe 4.11 S 3 crystal in run LJFeS01 was then further compressed up to 22.5 GPa at room temperature to examine its density and compressibility (Supplementary Table 3). The compression curve of Fe 4.11 S 3 at room temperature was then fitted using a second-order Birch-Murnaghan equation of state 26 , resulting in V 0 = 364.8(5) Å 3 and K 0 = 97(2) GPa. After normalizing to the same pressure, for example, 21 GPa, the densities of Fe 4.11 S 3 and Fe 4.77 S 3 samples are 23.7% and 20.2% lower than hcp Fe 27 , respectively. The non-stoichiometry, therefore, also affects the density, which increases with Fe content, in spite of the increase in the unit cell volume. Table 1 Atomic coordinates and equivalent isotropic displacement parameters for Fe 4 + x S 3 x y z Occ. U iso Fe 4.11 S 3 , 14.9(1) GPa, V = 324.0(6) Å 3 a = 10.897(5) Å, b = 3.125(1) Å, c = 9.515(18) Å Fe1 0.5697 (2) 0.25 0.5826 (3) 1 0.029 (1) Fe2 0.2731 (2) 0.25 0.0687 (3) 1 0.026 (2) Fe3 0.2850 (2) 0.25 0.7915 (4) 1 0.027 (2) Fe4 0.0246 (2) 0.25 0.6208 (4) 1 0.035 (1) Fe5 0.0587 (14) 0.25 0.215 (3) 0.11(1) 0.029 (5) S1 0.3728 (3) 0.25 0.5858 (5) 1 0.031 (2) S2 0.3758 (2) 0.25 0.2651 (6) 1 0.030 (2) S3 0.1275 (3) 0.25 0.4203 (5) 1 0.032 (2) Fe 4.77 S 3 , 21.1(5) GPa, V = 332.4 (2) Å 3 a = 11.073(3) Å, b = 3.182(1) Å, c = 9.435(4) Å Fe1 0.5724 (2) 0.25 0.5745 (3) 1 0.018 (1) Fe2 0.2779 (2) 0.25 0.0617 (3) 1 0.019 (1) Fe3 0.2723 (2) 0.25 0.7840 (3) 1 0.021 (1) Fe4 0.0285 (2) 0.25 0.6084 (4) 1 0.028 (1) Fe5 0.0640 (3) 0.25 0.2102 (4) 0.77 (1) 0.016 (1) S1 0.3688 (4) 0.25 0.5784 (4) 1 0.016 (1) S2 0.3740 (4) 0.25 0.2628 (5) 1 0.016 (1) S3 0.1340 (4) 0.25 0.4178 (5) 1 0.019 (1) The space group of Fe 4 + x S 3 is Pnma. All the data was collected at room temperature. To ascertain whether the Fe 4 + x S 3 phase we identified at high pressure and room temperature is thermodynamically stable at the HP-HT conditions of synthesis, and to determine if a phase transition occurs during temperature quenching, we conducted in situ HP-HT XRD measurements using an Fe plus 15 wt. % S composition, in a multi-anvil press (MA) at the beamline PSICHE, SOLEIL (Supplementary Table 4). A representative result (run MA233), as presented in Fig. 2 , reveals a series of peaks emerging in the energy-dispersive (ED) XRD pattern when the temperature reached 800 K at a pressure of approximately 14 GPa. These peaks, which cannot be indexed as polymorphs of Fe and FeS 28 , can all be indexed to the Pnma Fe 4 + x S 3 phase identified in our study. This finding supports the conclusion that the Pnma Fe 4 + x S 3 phase is indeed the thermodynamically stable phase under these HP-HT conditions. The unit cell expanded by around 6% as the temperature increased from 800 K to 1100 K. This degree of expansion is too large to be solely attributed to thermal expansion. This abnormal volume expansion confirms the results of our LH-DAC experiments that the Fe 4 + x S 3 phase tends to incorporate more iron and becomes progressively denser with increasing temperature. The Fe 4 + x S 3 phase discovered in this study is stable within the same P-T range reported for the Fe 3 + x S 2 and Fe 3 S 2 phases in the literature 17,22–23,29−31 . The composition range and temperature-composition relations of Fe 4 + x S 3 are consistent with that reported for both Fe 3 + x S 2 and Fe 3 S 2 (see Fig. 3 a). Therefore, the Fe 3 + x S 2 or Fe 3 S 2 phase, whose crystal structure was previously unknown, is certain to be the same as the Fe 4 + x S 3 phase identified in this study P-V-T-x relations of FeS Chemical composition analyses of the quenched products from our in-house MA experiments further demonstrate the nonstoichiometric nature of the Fe 4 + x S 3 phase, as well as its relationship with P, T, and sulfur activity. These experiments were carried out within the Fe-FeS system under a range of conditions: pressures from 14 to 27 GPa, temperatures from 918 to 1640 K, and varying bulk sulfur concentrations (Supplementary Table 5). Representative images illustrating the phase assemblages and textures of the recovered samples can be found in the Supplementary Fig. 2. Figure 3 a illustrates that the Fe/(Fe + S) ratio, and consequently the value of x in Fe 4 + x S 3 , increases notably with increasing temperature. A large range of variation in the value of x in Fe 4 + x S 3 , from 0.09 to 0.80, was observed in this study that approaches the theoretical limits permissible within the crystallographic framework (i.e. 0 to 1). However, x also varies depending on the nature of the coexisting phase, i.e. the Fe activity, being approximately 0.2 higher when coexisting with metallic iron compared to FeS at 16 GPa, based on the results in this study. Although we cannot quantify the effect of pressure on the variation of x from the current dataset, x may increase with pressure at a given temperature. This possibility is implied by the deviation observed in the previous study by Fei et al. 17 , conducted at 21 GPa, where x values are higher and deviate from the trend observed at 16 GPa in this study. With the established relationship between temperature and composition for Fe 4 + x S 3 , we can evaluate its P-V-T-x relations using the HP-HT data from this study and from the literature 23 . The experiments from Zhao et al. 23 were conducted at pressures between 13 and 16 GPa, and contain metallic iron. Therefore, we can fit the temperature-composition relationship from our in-house multi-anvil (MA) experiments and literature 28 , 30 with Fe 4 + x S 3 coexisting with metallic iron at approximately 16 GPa to constrain the compositional effects (i.e. influence of the x parameter) on volume. A linear fit of \(\:x=a\times\:\left(T-b\right)\) yields the result \(\:a=9.5\pm\:0.6\times\:{10}^{-4}\) \(\:{K}^{-1}\) and \(\:b\:=\:750\pm\:50\:K\) , where \(\:T\) is in K. The composition-volume relation can be determined using the single crystal refinements collected in this study, from the volume difference between the Fe 4.11 S 3 and Fe 4.77 S 3 samples, after normalization to the same pressure. After correcting the effects of composition and compressibility on the volume of Fe 4+x S 3 , we can estimate its thermal expansion. We assume that the thermal expansion coefficient of Fe 4+x S 3 does not vary significantly with x, and fit the P-V-T data of Fe 4+x S 3 from this study and the literature 23 using the thermal expansion expression: \(\:\alpha\:=1/V{\left(\partial\:V/\partial\:T\right)}_{P}\) , assuming \(\:\alpha\:\) remains constant over the limited pressure (13 to 16 GPa) and temperature range (800 to 1100 K). The resulting thermal expansion coefficient is 5.3±2.0 × 10 −5 K − 1 , which is comparable to that of the Fe 3 S phase (~ 3.6 × 10 −5 K − 1 at 1000 K and 15 GPa 32 ), but significantly smaller than that previously estimated for the “Fe 3 S 2 ” phase (~ 26.58 × 10 −5 K − 1 ) in the same pressure and temperature range 23 . The significant overestimation of 𝛼 in the previous study by Zhao et al. 23 is due to the fact that the volume expansion resulting from compositional variation with temperature was not accounted for separately in the evaluation of thermal expansion. The P-V-T-x relations of Fe 4+x S 3 are shown in Fig. 3 . These relations accurately describe the large volume changes observed in the experimental data, which are caused by both thermal expansion and compositional variation. Discussion Although there is currently no direct geophysical evidence confirming the existence of a Martian inner core, recent seismic and geodetic observations have provided important constraints on the state of the core as a whole 1 – 4 , 14 . Seismic measurements have detected the apparent core-mantle boundary of Mars, supplied decisive evidence that at least the upper region of Mars' core is in a liquid state and provided estimates for the core’s average density 1 – 4 that range from 5.7 to 6.65 g/cm³. The substantial variation in these density estimates stems from whether a basal magma layer is considered to exit, which in turn implies different thermal regimes for Mars’ interior. While the innermost state of Mars' core has not yet been revealed by seismic observations, the detected liquid region of the core sets an upper limit to a potential inner core radius of < 750 km 2 . Models based on geodesy also support the existence of a liquid core, though these observations are generally insensitive to an inner core unless it is sufficiently big 33 . Based on the assumption that the sulfur content of Mars' core may be quite close to the Fe-FeS eutectic, previous models have proposed that temperatures are likely too high for an inner core to form 18 , 34 . However, the relatively low densities recently proposed for the core 1 – 3 raises the possibility that the composition may lie to the S-rich side of the eutectic at conditions approaching the center of Mars. To examine this possibility, we first determine whether an Fe 4 + x S 3 inner core would be gravitationally stable and the temperature required for it to crystallize, then compare this with proposed Martian areotherms to assess the likely core crystallization regime. If we extrapolate the obtained P-V-T-x relations for Fe 4 + x S 3 to inner core conditions, the density will increase both due to compression and because x will approach 1, reaching a value of 7.5(± 0.3) g/cm 3 at the center of Mars (40 GPa and 2000K). This is larger than the range estimated using recent seismic observations for the density at the center of a liquid Martian core 1 – 4 (Supplementary Fig. 3), implying that an Fe 4 + x S 3 inner core would be gravitationally stable in a bottom-up crystallization regime. It is worth noting that in estimating the density of Fe 4 + x S 3 , the thermal expansion coefficient was assumed to be constant, which likely results in a slight underestimate of the inner core density. Even though this assumption does affect the conclusion of gravitational stability, further in situ HP-HT experiments would be required to establish a full thermodynamic model describing the P-V-T-x relations of Fe 4 + x S 3 , considering both the P-T effect on the variation of x and the effect of x on the thermoelastic properties of Fe 4 + x S 3 . Constraints on the temperature for inner core crystallization can be obtained by examining the thermal stability of Fe 4 + x S 3 , which increases quite significantly with pressure, from less than 1200 K at 14 GPa 17 to ~ 1500 K at 21 GPa 22 . At higher temperatures, Fe 4 + x S 3 will melt incongruently to form solid FeS and Fe-S liquid: \(\:{Fe}_{4+x}{S}_{3}\left(solid\right)=2FeS\left(solid\right)+{Fe}_{2+x}S\:\left(liquid\right)\) . The Fe 4 + x S 3 synthesized in this study coexists with Fe-S liquid at 1640 K and 27 GPa, indicating a melting temperature higher than this. An extrapolation of the melting curve to the pressure at the center of the Martian core (~ 40 GPa), indicates that Fe 4+x S 3 is stable up to approximately 1970(± 105) K (Supplementary Fig. 4). This relatively refractory behavior of Fe 4 + x S 3 underlines the potential for it to form planetary inner cores. The solidification regime of the Martian core will depend on the core’s composition and temperature. We have parameterized the melting phase relations in the Fe-FeS system up to 40 GPa considering the liquidus phases Fe, Fe 3 S, Fe 4 + x S 3 , and FeS and using our results and those from the literature (Supplementary Fig. 5). Since there is no experimental evidence to support the stability of Fe 12 S 7 and Fe 2 S 17 , 24 as liquidus phases under Martian core conditions, these phases were not considered in our model. Figure 4 shows Fe-S liquidus curves for different amounts of S, compared with Martian areotherms, from which the core solidification regime can be inferred by considering potential points of intersection. As illustrated in Fig. 5 ., during the cooling of Mars, if the core contains ~ 7–12 wt.% S, Fe-metal snow will form at the top of the Martian core, as proposed previously 18 . The crystalized Fe will sink but will be dissolved again in the deeper core region where the liquidus temperature is then lower than the areotherm (see curve 10 wt.% S in Fig. 4 ). If the Martian core contains ~ 13–16 wt.% S, the liquidus curve will first decrease with pressure (see curve 14 wt.% S in Fig. 4 ), where Fe-metal is the liquidus phase. However, as the S content of the eutectic melt decreases with increasing pressure, Fe 3 S will replace Fe as the liquidus phase at higher pressures (21 to 32 GPa, depending on the exact S content), which will cause the liquidus temperature to increase with pressure. In this case, the areotherm could intersect the liquidus curve at both the top and bottom of the Martian core, which means that both iron snow and bottom-up growth of Fe 3 S could occur simultaneously. However, if the Martian core contains 17–25 wt.% S, which would be quite consistent with recent density estimates 1 – 3 , Fe 4 + x S 3 will be the liquidus phase over the entire pressure range of the Martian core, with a liquidus temperature that increases continuously with pressure (see curves 18 and 22 wt.% S in Fig. 4 ). This means that an Fe 4 + x S 3 inner core will start to crystalize if the center of such a S-rich Martian core cools below approximately 1960 K. Mars has no active global magnetic field, implying that there is no dynamo operating in the Martian core. Crystallization of Fe in the form of iron snow would cause chemical convection below the snow zone, although whether this convection would provide enough energy to run a dynamo is debated 15–16,35−37 , as it is dependent on the generation of a positive net buoyancy flux 38 . In contrast, the crystallization of a sulfide inner core is consistent with the absence of an active dynamo, as the residual liquid would be richer in Fe and would, therefore, remain at the base of the outer core, inhibiting chemical convection 15 . The presence of an inner core composed of Fe 4 + x S 3 would likely have a negligible impact on interpretations of geodetic observations. For instance, with a small inner core allowed by current seismic constraints (e.g., a radius of < 600 km), the mass of an Fe₄₊ₓS₃ inner core would constitute less than 5% of the total core mass, altering the moment of inertia by only ~ 0.1%. Additionally, according to numerical calculations, the nutation effects of an inner core with a radius of 600 km are expected to be insignificant 33 . Thus, geodesy alone may be insufficient to constrain the existence of a relatively small inner core, and further seismic observations from future space missions, as well as additional analyses of InSight seismic data, are needed to provide more definitive evidence regarding the presence or absence of a Martian inner core. Further experimental measurements to enable seismic velocities of Fe 4 + x S 3 to be determined would be also important for the interpretation of potential inner core-related seismic signals. The temperature at the center of the Martian core would need to be lower than 1800 K to allow Fe 3 S to crystallize or for an 'iron snow' zone to reach the Martian center and form an inner core of Fe (Fig. 4 ). This corresponds to a temperature of approximately 1500–1600 K at the core-mantle boundary (CMB), which is lower than all current thermal models for Mars 34 , 39 – 43 . Therefore, crystallization of an Fe 3 S or Fe inner core are likely to be only future scenarios, possible only after Mars has cooled further 18 . On the other hand, the crystallization temperature of Fe 4 + x S 3 in a core containing, for example, 22 wt.% S—an amount that could satisfy the Martian core's density deficit (e.g., the core density model from Irving et al. 3 )—would be approximately 1960 (± 105) K. This approaches the lower limit of the estimated temperature of the Martian core in some thermal models 39 – 41 . The detection of a Martian inner core through further geophysical observations, along with an estimate of its density, would provide critical constraints on the chemical composition and temperature of the Martian core. Moreover, the existence of a Martian inner core would imply a relatively cool Martian interior, which would be incompatible with the presence of a basal magma layer on top of the CMB. Conversely, if an inner core is confirmed to be absent, the Fe 4 + x S 3 melting temperature, i.e., 1960 (± 105) K, would provide a lower limit for the temperature at the center of Mars. It is worth noting that the addition of other light elements, such as O, C, and H, may impact the crystallization phase relations of the Fe-FeS system, though the effects remain largely unknown due to a lack of experimental studies in more complex systems. On the one hand, the addition of multiple light elements could further lower the eutectic temperature of the system making an inner core less likely. On the other hand, it is possible that elements such as H, that can be incorporated in high pressure sulfides in stoichiometric proportions 44 , might partition sub-equally between liquid and melt phases and have little effect on crystallization temperatures. While this study provides a preliminary estimation of the likelihood of Fe 4 + x S 3 crystallization in the Martian core, further experiments involving relevant more complex chemical compositions are needed to test the hypotheses proposed here. Methods Starting material. The initial mixtures were composed of metallic iron powder (99.9%, 10 µm particle size) and high-purity elemental sulfur (99.999%). The bulk compositions of the mixtures are listed in Supplementary Table 5. The elements were mixed in an agate mortar under ethanol for about 45 minutes, followed by drying overnight in an oven at 340 K. For the in-house multi-anvil experiments, the mixed powder was directly used as the starting material, without any pre-treatment. For the synchrotron multi-anvil experiments, the powder mixtures underwent a pre-sintering process. This involved compressing the powders in a piston-cylinder press at 0.5 GPa and 1000 K for over 6 hours. Following sintering, the materials were machined into regular cylinders, each measuring approximately 1 mm in diameter and 0.6 mm in height. The sintered cylinders contained a mixture of metallic Fe and troilite (FeS). For the LH-DAC experiments, a pre-synthesized Fe 4 + x S 3 crystal separated from a prior multi-anvil experiment was utilized. The degraded crystal was pre-compressed into a thin pallet, roughly 10 µm thick, to serve as the starting material. In-house multi-anvil experiments. 10 mm and 7 mm edge length octahedral assemblies were compressed using tungsten carbide cubic anvils with 5 mm and 3 mm truncation edge lengths (TEL), respectively. The 10/5 assembly was used for experiments targeting pressures between 14 to 16 GPa. The 7/3 assembly was utilized for the experiments at 27 GPa 45 – 46 . In these in-house multi-anvil experiments, the pressure uncertainties at high temperatures are estimated to be ± 2 GPa. The starting materials were loaded into a gold capsule for run S7995, while MgO capsules were used in all other runs. After reaching the target loads, the samples were heated to high temperatures using LaCrO 3 heaters. Temperatures were monitored using a type D W-Re thermocouple, except for run S7995 and I1691a, where the temperature was estimated based on the power-temperature relation from previous experiments. The pressure effects on the electromotive force (EMF) of the thermocouple were corrected 47 . These temperatures were maintained for durations ranging from 1 to 10 hours, followed by rapid quenching to room temperature by shutting down the power source. Synchrotron multi-anvil experiments. The experiments were conducted at the beamline PSICHE at the SOLEIL synchrotron 48 . This assembly was equipped with a boron-doped diamond (BDD) heater, synthesized through the chemical vapor deposition (CVD) method 49 – 50 . The CVD-BDD heaters are notable for providing stable heating conditions and high X-ray transparency, which assists the collection of high quality XRD data. The assemblies were compressed to high pressures using tungsten carbide anvils with 5 mm TEL. The samples, which were placed in a corundum (Al 2 O 3 ) capsule, were illuminated by the white X-ray beams, and the energy-dispersive XRD patterns of the samples were collected in-situ at high pressures and high temperatures. The unit cell parameters of the phases present in the samples were determined through Rietveld Le Bail fitting, using the GSAS-II software package 51 . Temperatures were measured using a type D thermocouple, with corrections also applied for pressure effects on the EMF 49 . Pressures were evaluated using the equation of state of corundum 52 . The differences in pressure are less than 0.2 GPa when applying an alternative pressure standard for corundum 53 . Single crystal syntheses in LH-DAC and high-pressure SC-XRD. We employed a BX90-type diamond anvil cell 54 , equipped with a pair of diamond anvils each having a culet diameter of 250 µm for the high-pressure single crystal synthesis and measurements. Pre-indented rhenium gaskets were employed. A thin platelet of Fe 4 + x S 3 sample was sandwiched between two KCl layers and compressed to approximately 15 GPa in run LJFeS01. KCl provided both thermal insulation and the pressure marker 55 in the experiment. The sample was then heated from both sides using near-infrared lasers to a temperature of 1150 (200) K, employing a modified version of the portable double-sided laser of the ID14 beamline at ESRF 56 – 57 . The temperature for LJFeS01 was estimated based on the melting phase relations in the high-pressure Fe-FeS system 22 , as the Fe 4 + x S 3 phase coexisted with Fe-S liquid (Supplementary Fig. 6). For run LD101, helium was loaded at 1.2 kbar and served both as a pressure-transmitting medium and thermal insulator for laser heating. The sample was compressed to approximately 20 GPa and then heated to 1300 (200) K, employing the in-house laser-heating system at the Bayerisches Geoinstitut 58 , with temperatures estimated by fitting the radiation of the sample using a grey body approximation. The pressure of run LD101 was estimated based on a pressure calibration of the Raman shift of the diamond anvils 59 . For both runs, the samples were subjected to heating for durations ranging from 5 to 10 seconds before being rapidly quenched to room temperature. High-pressure XRD measurements were conducted at the high-pressure diffraction beamline ID15B at the ESRF in Grenoble. We utilized a focused X-ray beam with a wavelength of 0.4100 Å, and a beam size of approximately 1 µm × 1 µm. Initially, a 2D-scan XRD map with a step size of 2 µm was constructed by scanning the sample stage 60 . This process was aimed at locating phases of interest within the samples, as illustrated in Supplementary Fig. 6. Upon locating these phases, SC-XRD data collection was conducted over a range of -30 degrees to + 30 degrees for LJFeS01, and − 34 degrees to + 34 degrees for LD101, with an increment step of 0.5 degrees. The Domain Auto Finder program (DAFi) 61 was employed for the rapid identification of domains of Fe 4 + x S 3 microcrystals within the complete SC-XRD dataset collected from the multiphase samples. Domains of Fe 4 + x S 3 were primarily located in the region adjacent to the melt within the laser-heated spots. In the colder areas of the laser-heated spot, FeS III and several unidentified phases were indexed from the SC-XRD dataset. As this paper concentrates on the stability of liquidus phases, some further reflections for the unidentified subsolidus sulfide structures identified within the samples are outside of the scope of this discussion. Data reductions were performed using the CrysAlis Pro software package. The crystal structures of Fe 4 + x S 3 from each run were subsequently solved and refined using the Olex2 software package 62 . Further details regarding the structure solution and refinement can be found in Supplementary Methods. Sample Recovery and Chemical Analysis. After the completion of the in-house multi-anvil experiments, the run products were carefully recovered to ambient conditions, mounted in epoxy resin and subsequently polished for chemical analyses. The samples were analyzed using a JEOL JXA-8200 electron probe microanalyzer (EPMA), which was operated at 15 kV and 15 nA. Calibration standards of metallic iron, pyrite, and periclase were employed for Fe, S, and O, respectively. The solid phases of the samples were analyzed with a focused beam, approximately 1 µm in diameter. The compositions of the quenched liquids were measured using a defocused beam with a diameter ranging from 10 to 30 µm, depending on the size of the quenched texture. Parameterization of liquidus temperature. The pressure and composition dependencies of the liquidus temperature are parameterized following a similar approach to previous models 16 , 63 , incorporating more experimental constraints from this study. The melting phase diagram at a given pressure is constructed using the melting temperatures of the liquidus phases (Fe, Fe 3 S, Fe 4 + x S 3 , and FeS) and the eutectic temperature and composition as anchor points. It is assumed that the liquidus temperature has a linear dependence on sulfur concentration when Fe or FeS is the liquidus phase, and a parabolic dependence on sulfur concentration when Fe 4 + x S 3 or Fe 3 S are the liquidus phases. Fe, Fe 4 + x S 3 , and FeS are liquidus phases at pressures from 14 to 21 GPa, while Fe, Fe 3 S, Fe 4 + x S 3 , and FeS are liquidus phases at pressures above 21 GPa. We use the melting curves of Fe 64 and FeS 65 from the literature and evaluate the eutectic compositions and temperatures at high pressures (Supplementary Fig. 7), as well as the melting curves of Fe 3 S and Fe 4 + x S 3 (Supplementary Fig. 4), using data from this study and the literature 17 , 22 , 66 . The change in the peritectic composition from Fe 4 + x S 3 plus liquid to FeS plus liquid as a function of pressure was estimated based on data from this study and the literature 17 , 22 . The sulfur content is parameterized to increase with pressure until it reaches the composition of Fe 5 S 3 . Meanwhile, the peritectic composition at the point where Fe 3 S plus liquid reacts to Fe 4 + x S 3 plus liquid is assumed to be the composition of Fe 3 S (16.1 wt.% S). The parameters describing the model are listed in Supplementary Table 6. The melting phase relations at 15 GPa, 21 GPa, 27 GPa, and 40 GPa, generated using this model, are plotted in Supplementary Fig. 5 and compared with literature data to demonstrate consistency. Declarations Competing Interests The authors declare no competing interests. Author Contributions L.M. conceived and designed this project. L.M., X.L., T.B.B., L.D., W.Z., J.C., A.N., I.K., G.A., A.K., M.H., N.G., L.H., and D.J.F. performed the experiments. W.Z., T.B.B., L.D., X.L., and L.M. analyzed the single-crystal X-ray diffraction data. L.M., D.J.F., X.L., A.N., O.N., I.K., and L.D. contributed to the interpretation of the results. L.M. and D.J.F. wrote the paper with contributions from all the authors. Acknowledgments The authors thank L. Yuan, R. Pierru, and E. Kubik for insightful discussions. We appreciate assistance from D. Krauße, A. Potzel, and D. Wiesner in chemical characterization using electron microscopy. R. Njul, A. Rother, H. Fischer, and S. Übelhack are acknowledged for their help with sample preparation and the maintenance of the large volume presses at BGI. This research was supported by DFG grant FR1555/11. We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of experiment time at the ID15 beamline and offline laser-heating facilities of the ID14 beamline. IK acknowledges funding provided by the European Union (ERC, LECOR, project number 101042572). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Data Availability The data supporting the main findings of this work are available in the main text and the supplementary materials. Additional data can be available from the corresponding author upon request. References Stähler SC, Khan A, Banerdt WB, Lognonné P, Giardini D, Ceylan S, Drilleau M, Duran AC, Garcia RF, Huang Q, Kim D (2021) Seismic detection of the martian core. Science 373:443–448 Irving JC, Lekić V, Durán C, Drilleau M, Kim D, Rivoldini A, Khan A, Samuel H, Antonangeli D, Banerdt WB, Beghein C (2023) First observations of core-transiting seismic phases on Mars. Proc. Natl. Acad. Sci. U.S.A. 120, e2217090120 Samuel H, Drilleau M, Rivoldini A, Xu Z, Huang Q, Garcia RF, Lekić V, Irving JC, Badro J, Lognonné PH, Connolly JA (2023) Geophysical evidence for an enriched molten silicate layer above Mars’s core. Nature 622:712–717 Khan A, Huang D, Durán C, Sossi PA, Giardini D, Murakami M (2023) Evidence for a liquid silicate layer atop the Martian core. Nature 622:718–723 Hirose K, Labrosse S, Hernlund J (2013) Composition and state of the core. Annu Rev Earth Planet Sci 41:657–691 Chambers JE, Wetherill GW (2001) Planets in the asteroid belt. Meteorit Planet Sci 36:381–399 Wänke H, Dreibus G (1994) Chemistry and accretion history of Mars. Philos Trans R Soc A: Phys Eng Sci 349:285–293 Lodders K, Fegley B Jr (1997) An oxygen isotope model for the composition of Mars. Icarus 126:373–394 Sanloup C, Jambon A, Gillet P (1999) A simple chondritic model of Mars. Phys Earth Planet Inter 112:43–54 Yoshizaki T, McDonough WF (2020) The composition of Mars. Geochim Cosmochim Acta 273:137–162 Palme H, Lodders K, Jones A (2014) Solar system abundances of the elements in Treatise on Geochemistry, K. K. Turekian, H. D. Holland, EdsElsevier, ed. 2 Rose-Weston L, Brenan JM, Fei Y, Secco RA, Frost DJ (2009) Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation. Geochim Cosmochim Acta 73:4598–4615 Rubie DC, Jacobson SA, Morbidelli A, O’Brien DP, Young ED, de Vries J, Nimmo F, Palme H, Frost DJ (2015) Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed Solar System bodies and accretion of water. Icarus 248:89–108 Le Maistre S, Rivoldini A, Caldiero A, Yseboodt M, Baland RM, Beuthe M, Van Hoolst T, Dehant V, Folkner WM, Buccino D, Kahan D (2023) Spin state and deep interior structure of Mars from InSight radio tracking. Nature 619:733–737 Breuer D, Rueckriemen T, Spohn T (2015) Iron snow, crystal floats, and inner-core growth: modes of core solidification and implications for dynamos in terrestrial planets and moons. Prog Earth Planet Sci 2:1–26 Helffrich G (2017) Mars core structure—concise review and anticipated insights from InSight. Prog Earth Planet Sci 4:1–14 Fei Y, Li J, Bertka CM, Prewitt CT (2000) Structure type and bulk modulus of Fe 3 S, a new iron-sulfur compound. Am Min 85:1830–1833 Stewart AJ, Schmidt MW, Van Westrenen W, Liebske C (2007) Mars: A new core-crystallization regime. Science 316:1323–1325 Mori Y, Ozawa H, Hirose K, Sinmyo R, Tateno S, Morard G, Ohishi Y (2017) Melting experiments on Fe–Fe 3 S system to 254 GPa. Earth Planet Sci Lett 464:135–141 Morard G, Andrault D, Guignot N, Sanloup C, Mezouar M, Petitgirard S, Fiquet G (2008) In situ determination of Fe–Fe 3 S phase diagram and liquid structural properties up to 65 GPa. Earth Planet Sci Lett 272:620–626 Chudinovskikh L, Boehler R (2007) Eutectic melting in the system Fe–S to 44 GPa. Earth Planet Sci Lett 257:97–103 Fei Y, Bertka CM, Finger LW (1997) High-pressure iron-sulfur compound, Fe 3 S 2 , and melting relations in the Fe-FeS system. Science 275:1621–1623 Zhao B, Morard G, Boccato S, Mezouar M, Antonangeli D (2024) Phase diagram and thermo-elastic properties of Fe-S compounds up to 15 GPa: Thermodynamic constraints on the core of medium-sized telluric planets. Earth Planet Sci Lett 634:118676 Zurkowski CC, Lavina B, Chariton S, Prakapenka V, Campbell AJ (2022) Stability of Fe 2 S and Fe 12 S 7 to 125 GPa; implications for S-rich planetary cores. Geochem Perspect Lett 21 Oka K, Tateno S, Kuwayama Y, Hirose K, Nakajima Y, Umemoto K, Tsujino N, Kawaguchi S (2022) I. A cotunnite-type new high-pressure phase of Fe 2 S. Am Mineral 107:1249–1253 Birch F (1947) Finite elastic strain of cubic crystals. Phys Rev 71:809 Fei Y, Murphy C, Shibazaki Y, Shahar A, Huang H (2016) Thermal equation of state of hcp-iron: Constraint on the density deficit of Earth's solid inner core. Geophys Res Lett 43:6837–6843 Urakawa S, Someya K, Terasaki H, Katsura T, Yokoshi S, Funakoshi KI, Utsumi W, Katayama Y, Sueda YI, Irifune T (2004) Phase relationships and equations of state for FeS at high pressures and temperatures and implications for the internal structure of Mars. Phys Earth Planet Inter 143:469–479 Zhang L, Fei Y (2008) Effect of Ni on Fe–FeS phase relations at high pressure and high temperature. Earth Planet Sci Lett 268:212–218 Tsuno K, Ohtani E (2009) Eutectic temperatures and melting relations in the Fe–O–S system at high pressures and temperatures. Phys Chem Min 36:9–17 Urakawa S, Kamuro R, Suzuki A, Kikegawa T (2018) Phase relationships of the system Fe-Ni-S and structure of the high-pressure phase of (Fe 1 – x Ni x ) 3 S 2 . Phys Earth Planet Inter 277:30–37 Chen B, Gao L, Funakoshi KI, Li J (2007) Thermal expansion of iron-rich alloys and implications for the Earth's core. Proc. Natl. Acad. Sci. U.S.A. 104, 9162–9167 Defraigne P, Rivoldini A, Van Hoolst T, Dehant V (2003) Mars nutation resonance due to free inner core nutation. J Geophys Res : Planet 108:E12 Fei Y, Bertka C (2005) The interior of Mars. Science 308:1120–1121 Hauck SA, Aurnou JM, Dombard AJ (2006) Sulfur's impact on core evolution and magnetic field generation on Ganymede. J Geophys Res : Planet 111:E9 Bland MT, Showman AP, Tobie G (2008) The production of Ganymede's magnetic field. Icarus 198:384–399 Rückriemen T, Breuer D, Spohn T (2015) The Fe snow regime in Ganymede's core: A deep-seated dynamo below a stable snow zone. J Geophys Res : Planet 120:1095–1118 Hemingway DJ, Driscoll PE (2021) History and future of the Martian dynamo and implications of a hypothetical solid inner core. J Geophys Res : Planet 126, e2020JE006663 Hauck SA, Phillips RJ (2002) Thermal and crustal evolution of Mars. J Geophys Res : Planet 107, 6-1-6-19 Williams JP, Nimmo F (2004) Thermal evolution of the Martian core: Implications for an early dynamo. Geology 32:97–100 Plesa AC, Tosi N, Grott M, Breuer D (2015) Thermal evolution and Urey ratio of Mars. J Geophys Res : Planet 120:995–1010 Samuel H, Ballmer MD, Padovan S, Tosi N, Rivoldini A, Plesa AC (2021) The thermo-chemical evolution of Mars with a strongly stratified mantle. J Geophys Res : Planet 126, e2020JE006613 Huang Q, Schmerr NC, King SD, Kim D, Rivoldini A, Plesa AC, Samuel H, Maguire RR, Karakostas F, Lekić V, Charalambous C (2022) Seismic detection of a deep mantle discontinuity within Mars by InSight. Proc. Natl. Acad. Sci. U.S.A. 119, e2204474119 Abeykoon S, Howard C, Dominijanni S, Eberhard L, Kurnosov A, Frost DJ, Ballaran B, Terasaki T, Sakamaki H, Suzuki T, A., Ohtani E (2023) Deuterium content and site occupancy in iron sulfide at high pressure and temperature determined using in situ neutron diffraction measurements. J Geophys Res : Solid Earth, 128, e2023JB026710 Ishii T, Shi L, Huang R, Tsujino N, Druzhbin D, Myhill R, Li Y, Wang L, Yamamoto T, Miyajima N, Kawazoe T (2016) Generation of pressures over 40 GPa using Kawai-type multi-anvil press with tungsten carbide anvils. Rev Sci Instrum 87:024501 Liu Z, Nishi M, Ishii T, Fei H, Miyajima N, Ballaran B, Ohfuji T, Sakai H, Wang T, Shcheka L, S., Arimoto T (2017) Phase relations in the system MgSiO 3 -Al 2 O 3 up to 2300 K at lower mantle pressures. J Geophys Res : Solid Earth 122:7775–7788 Nishihara Y, Doi S, Kakizawa S, Higo Y, Tange Y (2020) Effect of pressure on temperature measurements using WRe thermocouple and its geophysical impact. Phys Earth Planet Inter 298:106348 King A, Guignot N, Henry L, Morard G, Clark A, Le Godec Y, Itié JP (2022) Combined angular and energy dispersive diffraction: optimized data acquisition, normalization and reduction. J Appl Crystallogr 55:218–227 Nishida K, Xie L, Kim EJ, Katsura T (2020) A strip-type boron-doped diamond heater synthesized by chemical vapor deposition for large-volume presses. Rev Sci Instrum 91:095108 Xie L, Yoneda A, Liu Z, Nishida K, Katsura T (2020) Boron-doped diamond synthesized by chemical vapor deposition as a heating element in a multi-anvil apparatus. High Press Res 40:369–378 Toby BH, Von Dreele RB (2013) GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J Appl Crystallogr 46:544–549 Shi W, Wei W, Sun N, Mao Z, Prakapenka VB (2022) Thermal Equations of State of Corundum and Rh 2 O 3 (II)-Type Al 2 O 3 up to 153 GPa and 3400 K. J Geophys Res : Solid Earth 127:023805 e2021JB Néri A, Man L, Chantel J, Farla R, Bauer G, Linhardt S, Boffa Ballaran T, Frost DJ (2024) The development of internal pressure standards for in-house elastic wave velocity measurements in multi-anvil presses. Rev Sci Instrum 95:013902 Kantor I, Prakapenka V, Kantor A, Dera P, Kurnosov A, Sinogeikin S, Dubrovinskaia N, Dubrovinsky L (2012) BX90: A new diamond anvil cell design for X-ray diffraction and optical measurements. Rev Sci Instrum 83:125102 Dewaele A, Belonoshko AB, Garbarino G, Occelli F, Bouvier P, Hanfland M, Mezouar M (2012) High-pressure–high-temperature equation of state of KCl and KBr. Phys Rev B 85:214105 Kupenko I, Dubrovinsky L, Dubrovinskaia N, McCammon C, Glazyrin K, Bykova E, Ballaran TB, Sinmyo R, Chumakov AI, Potapkin V, Kantor A (2012) Portable double-sided laser-heating system for Mössbauer spectroscopy and X-ray diffraction experiments at synchrotron facilities with diamond anvil cells. Rev Sci Instrum 83:124501 Aprilis G, Strohm C, Kupenko I, Linhardt S, Laskin A, Vasiukov DM, Cerantola V, Koemets EG, McCammon C, Kurnosov A (2017) Chumakov, A. I. Portable double-sided pulsed laser heating system for time-resolved geoscience and materials science applications. Rev Sci Instrum 88:084501 Fedotenko T, Dubrovinsky L, Aprilis G, Koemets E, Snigirev A, Snigireva I, Barannikov A, Ershov P, Cova F, Hanfland M, Dubrovinskaia N (2019) Laser heating setup for diamond anvil cells for in situ synchrotron and in house high and ultra-high pressure studies. Rev Sci Instrum 90:104501 Akahama Y, Kawamura H (2006) Pressure calibration of diamond anvil Raman gauge to 310 GPa. J Appl Phys 100:043516 Hrubiak R, Smith JS, Shen G (2019) Multimode scanning X-ray diffraction microscopy for diamond anvil cell experiments. Rev Sci Instrum 90:025109 Aslandukov A, Aslandukov M, Dubrovinskaia N, Dubrovinsky L (2022) Domain Auto Finder (DAFi) program: the analysis of single-crystal X-ray diffraction data from polycrystalline samples. J Appl Crystallogr 55:1383–1391 Dolomanov OV, Bourhis LJ, Gildea RJ, Howard JA, Puschmann H (2009) OLEX2: a complete structure solution, refinement and analysis program. J Appl Crystallogr 42:339–341 Rivoldini A, Van Hoolst T, Verhoeven O, Mocquet A, Dehant V (2011) Geodesy constraints on the interior structure and composition of Mars. Icarus 213:451–472 Dorogokupets PI, Dymshits AM, Litasov KD, Sokolova TS (2017) Thermodynamics and equations of state of iron to 350 GPa and 6000 K. Sci Rep 7:41863 Boehler R (1992) Melting of the Fe-FeO and the Fe-FeS systems at high pressure: Constraints on core temperatures. Earth Planet Sci Lett 111:217–227 Thompson S, Sugimura-Komabayashi E, Komabayashi T, McGuire C, Breton H, Suehiro S, Ohishi Y (2022) High-pressure melting experiments of Fe 3 S and a thermodynamic model of the Fe–S liquids for the Earth’s core. J Phys Condens Matter 34:394003 Momma K, Izumi F (2011) VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J Appl Crystallogr 44:1272–1276 Additional Declarations There is NO Competing Interest. Supplementary Files 20240521Fe4.11S3.cif Dataset 1 20240910Fe4.77S3.cif Dataset 2 Fe4xS3SIrevisionfinal.pdf Cite Share Download PDF Status: Published Journal Publication published 25 Feb, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5070782","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":389897362,"identity":"df2ed0a9-3a07-42fe-bef3-0337df3955cb","order_by":0,"name":"Lianjie Man","email":"data:image/png;base64,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","orcid":"","institution":"Bayerisches Geoinstitut, Universität Bayreuth","correspondingAuthor":true,"prefix":"","firstName":"Lianjie","middleName":"","lastName":"Man","suffix":""},{"id":389897363,"identity":"21ea34b0-9c4e-4fbd-b5fa-64b3357f88cb","order_by":1,"name":"Xiang Li","email":"","orcid":"https://orcid.org/0000-0003-3259-1784","institution":"University of Münster","correspondingAuthor":false,"prefix":"","firstName":"Xiang","middleName":"","lastName":"Li","suffix":""},{"id":389897364,"identity":"93d3ee74-e706-40df-a69e-8f463956d7e9","order_by":2,"name":"Tiziana Boffa-Ballaran","email":"","orcid":"","institution":"Bayerisches Geoinstitut","correspondingAuthor":false,"prefix":"","firstName":"Tiziana","middleName":"","lastName":"Boffa-Ballaran","suffix":""},{"id":389897365,"identity":"cf2141ae-646e-4346-9919-34635e6cf1ba","order_by":3,"name":"Wenju Zhou","email":"","orcid":"https://orcid.org/0000-0002-9556-1147","institution":"Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth","correspondingAuthor":false,"prefix":"","firstName":"Wenju","middleName":"","lastName":"Zhou","suffix":""},{"id":389897366,"identity":"939db92c-2491-4d77-8038-55af1ec49316","order_by":4,"name":"Julien Chantel","email":"","orcid":"https://orcid.org/0000-0002-8332-9033","institution":"Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations, F-59000 Lille, France","correspondingAuthor":false,"prefix":"","firstName":"Julien","middleName":"","lastName":"Chantel","suffix":""},{"id":389897367,"identity":"7c395df7-cf2a-4fcf-b8df-58af4d5e5002","order_by":5,"name":"Adrien Néri","email":"","orcid":"https://orcid.org/0000-0001-9703-8803","institution":"Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations","correspondingAuthor":false,"prefix":"","firstName":"Adrien","middleName":"","lastName":"Néri","suffix":""},{"id":389897368,"identity":"5d491e8b-56b3-41b2-b556-eb6f04cb427a","order_by":6,"name":"Ilya Kupenko","email":"","orcid":"https://orcid.org/0000-0003-3783-8360","institution":"University of Münster","correspondingAuthor":false,"prefix":"","firstName":"Ilya","middleName":"","lastName":"Kupenko","suffix":""},{"id":389897369,"identity":"dc77f2bd-b8fa-4483-aa2a-d326fb2e4325","order_by":7,"name":"Georgios Aprilis","email":"","orcid":"https://orcid.org/0000-0002-0020-9125","institution":"ESRF-The European Synchrotron, CS 40220, 38043, Grenoble, Cedex 9, France","correspondingAuthor":false,"prefix":"","firstName":"Georgios","middleName":"","lastName":"Aprilis","suffix":""},{"id":389897370,"identity":"2a1c9cf5-85c5-4628-92de-ae07f7862ba9","order_by":8,"name":"Alexander Kurnosov","email":"","orcid":"https://orcid.org/0000-0001-5049-4035","institution":"Bayerisches Geoinstitut, Universität Bayreuth","correspondingAuthor":false,"prefix":"","firstName":"Alexander","middleName":"","lastName":"Kurnosov","suffix":""},{"id":389897371,"identity":"f5b90a48-6e74-416c-8e0c-4b5815cbebd4","order_by":9,"name":"Olivier Namur","email":"","orcid":"","institution":"KU Leuven","correspondingAuthor":false,"prefix":"","firstName":"Olivier","middleName":"","lastName":"Namur","suffix":""},{"id":389897372,"identity":"e27a847c-25f0-4e2f-8462-f270c74ee1d6","order_by":10,"name":"Michael Hanfland","email":"","orcid":"","institution":"European Synchrotron Radiation Facility","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Hanfland","suffix":""},{"id":389897373,"identity":"542c242b-17d1-4664-964b-8ac49e13d015","order_by":11,"name":"Nicolas Guignot","email":"","orcid":"","institution":"Soleil Synchrotron","correspondingAuthor":false,"prefix":"","firstName":"Nicolas","middleName":"","lastName":"Guignot","suffix":""},{"id":389897374,"identity":"4471a63f-e3d5-45e3-a833-92a1e4814619","order_by":12,"name":"Laura Henry","email":"","orcid":"https://orcid.org/0000-0002-2531-620X","institution":"Soleil synchrotron","correspondingAuthor":false,"prefix":"","firstName":"Laura","middleName":"","lastName":"Henry","suffix":""},{"id":389897375,"identity":"23ab160d-31b9-48c8-8c7a-4a14a36a9121","order_by":13,"name":"Leonid Dubrovinsky","email":"","orcid":"https://orcid.org/0000-0002-3717-7585","institution":"Bayerisches Geoinstitut","correspondingAuthor":false,"prefix":"","firstName":"Leonid","middleName":"","lastName":"Dubrovinsky","suffix":""},{"id":389897376,"identity":"c02d5607-0b1b-4a89-85be-92ee04fae0b5","order_by":14,"name":"Daniel Frost","email":"","orcid":"https://orcid.org/0000-0002-4443-8149","institution":"Universität Bayreuth","correspondingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Frost","suffix":""}],"badges":[],"createdAt":"2024-09-11 11:33:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5070782/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5070782/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-56220-2","type":"published","date":"2025-02-25T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":71495651,"identity":"71ccd3a7-6e82-4463-bc05-1aee1d17ca8c","added_by":"auto","created_at":"2024-12-16 08:12:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":352589,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eIn situ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e single crystal structure determination of Fe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4+x\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3 \u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eunder high pressure.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e The diffraction mapping displays the reflections that satisfy the condition -h -1 l for Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e (space group: Pnma), which were collected at 14.9(1) GPa at room temperature following laser heating at 1150(±200) K (run LJFeS01). The data were acquired through a step-scan procedure spanning the range of ω from -30° to 30°. \u003cstrong\u003eb\u003c/strong\u003e The structural model of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e as determined by SC-XRD. \u003cstrong\u003ec\u003c/strong\u003e Depiction of the building blocks, including the Fe-S pyramid and semi-occupied Fe-S tetrahedron, that constitute Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. The crystal structure models were visualized using the software Vesta\u003ca href=\"#reference\"\u003e\u003csup\u003e67\u003c/sup\u003e\u003c/a\u003e.\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/6941356a20e31130f8a88c0e.png"},{"id":71495649,"identity":"aa17a270-5078-4d43-b4c5-55995593d9ab","added_by":"auto","created_at":"2024-12-16 08:12:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":46330,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eIn situ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e ED-XRD patterns collected in a synchrotron MA experiment using an Fe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e85\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e15 \u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003estarting material conducted at approximately 14 GPa and at the temperatures indicated.\u003c/strong\u003e The Ge detector was positioned at an angle of 8.02 degrees 2θ. The grey, dark yellow, black, violet, and red sticks indicate bcc Fe, hcp Fe, fcc Fe, FeS III, and Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e reflections, respectively. The minor peaks marked with black reversed triangles appear to be residual from FeS IV and those marked by diamonds are from FeO.\u0026nbsp;\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/d9c21194bb79250789d830df.png"},{"id":71495653,"identity":"0b8c2ec9-28a6-42c6-b260-d7cb88f63bea","added_by":"auto","created_at":"2024-12-16 08:12:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":38967,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eP-V-T-x relations of Fe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4+x\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eS\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e.\u003c/strong\u003e \u003cstrong\u003ea \u003c/strong\u003eCompositions of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e obtained from quenched MA experiments. In the present study, the Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e samples coexist with metallic Fe (red-filled circles, 16 GPa), solid FeS (black open inverted triangles, 14 GPa; black solid inverted triangles, 16 GPa), or Fe-S melt (blue solid diamonds, 16 GPa; blue open diamonds, 27 GPa). The grey symbols indicate results from the literature: open squares\u003ca href=\"#reference\"\u003e\u003csup\u003e30\u003c/sup\u003e\u003c/a\u003e, filled triangles\u003ca href=\"#reference\"\u003e\u003csup\u003e17\u003c/sup\u003e\u003c/a\u003e, open triangles\u003ca href=\"#reference\"\u003e\u003csup\u003e29\u003c/sup\u003e\u003c/a\u003e, and the filled star\u003ca href=\"#reference\"\u003e\u003csup\u003e28\u003c/sup\u003e\u003c/a\u003e. The red dashed line is a linear fit of the x-T relationship for samples coexisting with metallic iron at pressures of 15-16 GPa. \u003cstrong\u003eb\u003c/strong\u003e Compression curves of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3 \u003c/sub\u003efor various compositions and temperatures. The black dashed line, orange solid line, red solid line, and violet solid line show values generated from the P-V-T-x model at 300 K, 800 K, 950 K, and 1100 K. The x values in high temperature curves follow the x-T relations indicated by the red dashed line in Fig. 3a. The black diamonds and triangles are data collected in a DAC at 300 K in this study. The solid circles are the HP-HT data in this study and the open squares are the HP-HT data from the literature, which were interpreted as Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e\u003ca href=\"#reference\"\u003e\u003csup\u003e23\u003c/sup\u003e\u003c/a\u003e. The red dashed line indicates the EOS of “Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e” at 940 K, as reported by Zhao et al.\u003ca href=\"#reference\"\u003e\u003csup\u003e23\u003c/sup\u003e\u003c/a\u003e.\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/33a8d0fb73583612cc379d1f.png"},{"id":71497158,"identity":"8fb9365b-e19f-4bb7-a055-eb6aee9a52d7","added_by":"auto","created_at":"2024-12-16 08:28:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":17926,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFe-S system liquidus curves as a function of pressure.\u003c/strong\u003e Black dashed line: Fe-10 wt.% S liquid where Fe is the liquidus phase; blue dotted line: Fe-14 wt.% S where Fe\u003csub\u003e3\u003c/sub\u003eS is the liquidus phase; black dotted line: Fe-14 wt.% S where Fe is the liquidus phase \u0026lt; 25 GPa; red sold lines: Fe-18 wt.% S with Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e as the liquidus phase; red dash-dot line: Fe-22 wt.% S with Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e as the liquidus phase. The grey-shaded regions are estimated areotherm of the Martian core\u003csup\u003e16\u003c/sup\u003e with CMB temperatures at 1700 K and 1900 K.\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/3f2636e052f0ef66914d7889.png"},{"id":71495914,"identity":"7ec4a8a8-b936-41f5-823f-63696fb22189","added_by":"auto","created_at":"2024-12-16 08:20:10","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":12501,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSolidification regimes of the Martian core for different bulk core sulfur concentrations.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Iron snow. \u003cstrong\u003eb\u003c/strong\u003e Simultaneous iron snow and Fe\u003csub\u003e3\u003c/sub\u003eS crystalizing from the center. \u003cstrong\u003ec\u003c/strong\u003e Bottom-up crystallization of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/a82cd6bb861389fbfd26c811.png"},{"id":77204263,"identity":"bf66a196-f088-4a48-a50e-4c42a6afa93e","added_by":"auto","created_at":"2025-02-26 08:05:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1563749,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/69efa8d3-652a-4585-8d8c-93a2f13796eb.pdf"},{"id":71495912,"identity":"ea0f744a-5847-45c1-bec4-3b0b2cf35052","added_by":"auto","created_at":"2024-12-16 08:20:10","extension":"cif","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":48351,"visible":true,"origin":"","legend":"Dataset 1","description":"","filename":"20240521Fe4.11S3.cif","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/230f68072bb34f40407a0657.cif"},{"id":71495656,"identity":"c1f86322-bb2c-4e25-816d-25724c6ee8e5","added_by":"auto","created_at":"2024-12-16 08:12:10","extension":"cif","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":52802,"visible":true,"origin":"","legend":"Dataset 2","description":"","filename":"20240910Fe4.77S3.cif","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/d71158bee338fbcb0c89ec4e.cif"},{"id":71497573,"identity":"abf7d48b-32c6-4900-a6bc-3ad50cb346da","added_by":"auto","created_at":"2024-12-16 08:36:10","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":920418,"visible":true,"origin":"","legend":"","description":"","filename":"Fe4xS3SIrevisionfinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5070782/v1/541a38064f1e9b66ad2ec679.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"The structure and stability of Fe4+xS3 and its potential to form a Martian inner core","fulltext":[{"header":"Introduction","content":"\u003cp\u003eObservations from NASA's InSight mission have revealed that the core of Mars is enriched in light elements, as its density appears to be substantially lower than that of Fe-Ni alloy\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Based on seismic wave reflections at the apparent core-mantle boundary of Mars, models considering either the existence\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e or absence\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e of a basal silicate magma layer indicate that the Martian core contains 9 to 20 wt.% or 20 to 25 wt.% of light elements, respectively. In either case, the abundance of light elements in the Martian core is significantly higher than in Earth's core (5 to 10 wt.%)\u003csup\u003e5\u003c/sup\u003e, implying considerable differences in accretion and differentiation processes during the early stages of planetary formation\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. From cosmochemical perspectives and geochemical considerations, candidate light elements in the Martian core include S, O, C, and H\u003csup\u003e\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Sulfur, in particular, is often highlighted as a likely major light element in the Martian core, primarily due to it being the most prevalent moderately volatile element in the solar nebula\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, its siderophile (\"iron-loving\") behavior during core-mantle differentiation\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, and the fact that core formation on Mars was likely not a sufficiently reducing or high-temperature process for Si or O to be major light elements\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Assessments based on similarly volatile lithophile elements argue for \u0026lt;\u0026thinsp;7 wt % S in the Martian core\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e but this would most likely require significant proportions of C and H to explain the core\u0026rsquo;s density deficit, which should, by the same arguments, be even more depleted in Mars than S. If similarly volatile elements are used to predict the S contents of ordinary and enstatite chondrites, the resulting concentrations for most of these meteorite sub-types are underestimated, raising the possibility that S contents of planetary bodies might vary independently of elements with similar condensation temperatures.\u003c/p\u003e \u003cp\u003eSeismic and lander radio science data from the InSight mission have confirmed that Mars has a liquid core\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, but the presence of a solid inner core cannot be currently excluded on geophysical grounds\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. If further geophysical observations were to verify the existence, size, and density of a Martian inner core, then combined with the appropriate mineral physical interpretation, this would provide essential constraints on the composition and temperature of the interior, as well as the possible mechanisms that initiated and terminated the magnetic field in early Mars\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. In the scenario of a S-rich Martian core, the cooling and solidification processes of an initially fully molten Martian core are primarily governed by the melting phase relations of the Fe-FeS system under the high-pressure and high-temperature (HP-HT) conditions relevant to the Martian core. The eutectic composition in the Fe-FeS system shifts in the direction of the Fe-rich side with increasing pressure, from approximately 15.5 wt.% S at 21 GPa\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, i.e. the pressure at the top of the Martian core, to approximately 12 wt.% S at 40 GPa\u003csup\u003e\u003cspan additionalcitationids=\"CR19 CR20\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, the pressure at the center of Mars. Within the possible compositional range of Mars\u0026rsquo; core, either Fe or Fe sulfides could be liquidus phases that might crystalize as an inner core\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Understanding the crystal structures and densities of these liquidus phases is, therefore, critical for determining their behavior during cooling of the Martian core.\u003c/p\u003e \u003cp\u003eIn addition to the endmembers Fe and FeS, the solid phases reported under Martian core conditions in the Fe-FeS system include Fe\u003csub\u003e2\u003c/sub\u003eS, Fe\u003csub\u003e3\u003c/sub\u003eS, and Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e17\u0026ndash;18\u003c/sup\u003e. Fe\u003csub\u003e2\u003c/sub\u003eS is identified as a subsolidus phase in the Fe-FeS system at 21 GPa but is replaced by Fe\u003csub\u003e3\u003c/sub\u003eS or Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e when the temperature increases above the solidus temperature on the FeS-rich side of the eutectic\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Whether Fe\u003csub\u003e2\u003c/sub\u003eS becomes a liquidus phase under higher pressures, corresponding to deeper Martian core conditions, remains unknown. Fe\u003csub\u003e3\u003c/sub\u003eS adopts a Fe\u003csub\u003e3\u003c/sub\u003eP-type structure and has a S content (16 wt.%) close to the eutectic composition of the Fe-FeS system at Martian core pressures\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. During the cooling of the Martian core, if the sulfur concentration in the liquid core is above but close to the eutectic composition, Fe\u003csub\u003e3\u003c/sub\u003eS is expected to crystallize. Fe\u003csub\u003e3\u003c/sub\u003eS would be gravitationally stable at the center of the Martian core, as its density would be higher than that of the residual liquid\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. However, if the bulk composition is more sulfur-enriched, for example, greater than 16 wt.% S at 21 GPa\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, the phase described as Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e would be the liquidus phase\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e decomposes during decompression and cannot be recovered to ambient pressure\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Its crystal structure can, therefore, only be investigated \u003cem\u003ein-situ\u003c/em\u003e, under high pressure conditions. The crystal system of Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e has been determined to be orthorhombic using powder X-ray diffraction\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, but its structure remains undetermined. Consequently, the density and elastic properties of Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e remain largely unknown.\u003c/p\u003e \u003cp\u003eIn order to determine the crystal structure and density relations of the elusive Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e phase, we conducted a series of HP-HT experiments within the Fe-FeS system, employing multiple \u003cem\u003ein-situ\u003c/em\u003e and \u003cem\u003eex-situ\u003c/em\u003e characterization techniques. However, instead of Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e, we obtained a crystal structure for an iron sulfide phase that is more accurately described, on the basis of its crystallography, as Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. This phase was synthesized within the P-T and compositional range where Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e has been previously reported, which almost certainly has the same structure. We have further investigated the composition, density and potential role of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e in forming a Martian inner core.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStructural refinement of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e\u003c/h2\u003e \u003cp\u003eAs the target Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e phase is known to decompose to nano-crystallites of a few different phases during decompression\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, we performed high-pressure single crystal structure analyses in the diamond anvil cell (DAC) following \u003cem\u003ein situ\u003c/em\u003e syntheses through laser heating (LH) at pressures of approximately 15 GPa and 21 GPa. The starting material for the LH-DAC experiments comprised degraded \u0026ldquo;Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e\u0026rdquo; crystals, which were initially synthesized at pressures ranging from 14 to 16 GPa in a multi-anvil (MA) press. Although these starting materials maintained a homogeneous composition on a scale of less than 100 nm, their crystal structure experienced degradation during the decompression process in the MA press, and therefore, cannot be directly used for structure determination. After syntheses in the LH-DAC, single crystal X-ray diffraction (SC-XRD) data were collected at room temperature and high pressures on the newly grown crystals in the reacted LH area. Using a micro-focused synchrotron X-ray beam (~\u0026thinsp;1 \u0026micro;m * 1 \u0026micro;m) it was possible to index reflections from numerous sub-\u0026micro;m sized grains with different orientations in each sample. Structural solution of several of these grains led to the identification of a previously unknown structure exhibiting orthorhombic symmetry in the reacted areas of two experiments conducted at 15 GPa and 1150(\u0026plusmn;\u0026thinsp;200) K (run LJFeS01) and 21 GPa and 1400(\u0026plusmn;\u0026thinsp;200) K (run LD101). The reflections measured for all grains indicate clearly that the space group of this phase is \u003cem\u003ePnma\u003c/em\u003e. Structural refinement of two single crystals exhibiting the best discrepancy factors in each experiment (see more details in Supplementary Methods) indicates that the phase is characterized by five non-equivalent crystallographic sites for Fe and three non-equivalent sites for S.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, there are four Fe sites that are five-fold coordinated, forming four edge-sharing Fe-S square pyramids; whereas the remaining iron site is four-fold coordinated, creating a Fe-S tetrahedron. The fundamental building blocks of the structure of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e are consistent with the high pressure Fe\u003csub\u003e12\u003c/sub\u003eS\u003csub\u003e7\u003c/sub\u003e phase\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, stable above 100 GPa and the Fe\u003csub\u003e2\u003c/sub\u003eS phase stable above 21 GPa\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. The tetrahedral site can be considered as an interstitial site between neighboring Fe-S square pyramids. If all the Fe and S sites are fully occupied, this would lead to a stoichiometry corresponding to Fe\u003csub\u003e5\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. However, refinements of the SC-XRD data indicate that the Fe tetrahedral site is not fully occupied, leading to a chemical formula Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e (Supplementary Table\u0026nbsp;1 and Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), where x is the Fe occupancy at the tetrahedral site. In experimental run LD101, the occupancy of the tetrahedral site in the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase was found to be 0.77 (\u0026plusmn;\u0026thinsp;0.01), which can be described with the more appropriate stoichiometry Fe\u003csub\u003e4.77\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, or following the formula of Fei et al.\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, Fe\u003csub\u003e3.18\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e. In another experimental run, LJFeS01, conducted under lower pressure-temperature (P-T) conditions than LD101, the tetrahedral site occupancy was refined to 0.11 (\u0026plusmn;\u0026thinsp;0.01) Fe atoms. This results in the composition Fe\u003csub\u003e4.11\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, or Fe\u003csub\u003e2.74\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e when expressed in the Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e formula. Moreover, the unit cell volume of the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase at 21 GPa and 300 K synthesized in run LD101 (331.2 \u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e) is notably larger than that at 15 GPa and 300 K synthesized in run LJFeS01 (324.0 \u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e). This is clearly due to the increased Fe occupancy of the tetrahedral site, which causes an increase in tetrahedral volume and, therefore, an increase in unit-cell volume (see Supplementary Discussion and Supplementary Fig.\u0026nbsp;1). The details of the crystallographic parameters are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Supplementary Table\u0026nbsp;2. The Fe\u003csub\u003e4.11\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e crystal in run LJFeS01 was then further compressed up to 22.5 GPa at room temperature to examine its density and compressibility (Supplementary Table\u0026nbsp;3). The compression curve of Fe\u003csub\u003e4.11\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e at room temperature was then fitted using a second-order Birch-Murnaghan equation of state\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, resulting in V\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;364.8(5) \u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e and K\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;97(2) GPa. After normalizing to the same pressure, for example, 21 GPa, the densities of Fe\u003csub\u003e4.11\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and Fe\u003csub\u003e4.77\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e samples are 23.7% and 20.2% lower than hcp Fe\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e, respectively. The non-stoichiometry, therefore, also affects the density, which increases with Fe content, in spite of the increase in the unit cell volume.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAtomic coordinates and equivalent isotropic displacement parameters for Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ey\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ez\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eOcc.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eU\u003csub\u003eiso\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFe\u003c/b\u003e\u003csub\u003e\u003cb\u003e4.11\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eS\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, 14.9(1) GPa, \u003cem\u003eV\u0026thinsp;=\u003c/em\u003e\u0026thinsp;324.0(6) \u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003ea\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;10.897(5) \u0026Aring;, \u003cb\u003eb\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;3.125(1) \u0026Aring;, \u003cb\u003ec\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;9.515(18) \u0026Aring;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5697 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5826 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.029 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2731 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0687 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.026 (2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2850 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.7915 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.027 (2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0246 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.6208 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.035 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0587 (14)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.215 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.11(1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.029 (5)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3728 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5858 (5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.031 (2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3758 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2651 (6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.030 (2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1275 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4203 (5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.032 (2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFe\u003c/b\u003e\u003csub\u003e\u003cb\u003e4.77\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eS\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, 21.1(5) GPa, \u003cem\u003eV\u0026thinsp;=\u003c/em\u003e\u0026thinsp;332.4 (2) \u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003ea\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;11.073(3) \u0026Aring;, \u003cb\u003eb\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;3.182(1) \u0026Aring;, \u003cb\u003ec\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;9.435(4) \u0026Aring;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5724 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5745 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.018 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2779 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0617 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.019 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2723 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.7840 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.021 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0285 (2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.6084 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.028 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFe5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0640 (3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2102 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.77 (1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.016 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3688 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5784 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.016 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3740 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2628 (5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.016 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1340 (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4178 (5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.019 (1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eThe space group of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is Pnma. All the data was collected at room temperature.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo ascertain whether the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase we identified at high pressure and room temperature is thermodynamically stable at the HP-HT conditions of synthesis, and to determine if a phase transition occurs during temperature quenching, we conducted \u003cem\u003ein situ\u003c/em\u003e HP-HT XRD measurements using an Fe plus 15 wt. % S composition, in a multi-anvil press (MA) at the beamline PSICHE, SOLEIL (Supplementary Table\u0026nbsp;4). A representative result (run MA233), as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, reveals a series of peaks emerging in the energy-dispersive (ED) XRD pattern when the temperature reached 800 K at a pressure of approximately 14 GPa. These peaks, which cannot be indexed as polymorphs of Fe and FeS\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, can all be indexed to the Pnma Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase identified in our study. This finding supports the conclusion that the Pnma Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase is indeed the thermodynamically stable phase under these HP-HT conditions. The unit cell expanded by around 6% as the temperature increased from 800 K to 1100 K. This degree of expansion is too large to be solely attributed to thermal expansion. This abnormal volume expansion confirms the results of our LH-DAC experiments that the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase tends to incorporate more iron and becomes progressively denser with increasing temperature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase discovered in this study is stable within the same P-T range reported for the Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e and Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e phases in the literature\u003csup\u003e17,22\u0026ndash;23,29\u0026minus;31\u003c/sup\u003e. The composition range and temperature-composition relations of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e are consistent with that reported for both Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e and Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). Therefore, the Fe\u003csub\u003e3\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e or Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e phase, whose crystal structure was previously unknown, is certain to be the same as the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase identified in this study\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eP-V-T-x relations of FeS\u003c/h3\u003e\n\u003cp\u003eChemical composition analyses of the quenched products from our in-house MA experiments further demonstrate the nonstoichiometric nature of the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase, as well as its relationship with P, T, and sulfur activity. These experiments were carried out within the Fe-FeS system under a range of conditions: pressures from 14 to 27 GPa, temperatures from 918 to 1640 K, and varying bulk sulfur concentrations (Supplementary Table\u0026nbsp;5). Representative images illustrating the phase assemblages and textures of the recovered samples can be found in the Supplementary Fig.\u0026nbsp;2. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea illustrates that the Fe/(Fe\u0026thinsp;+\u0026thinsp;S) ratio, and consequently the value of x in Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, increases notably with increasing temperature. A large range of variation in the value of x in Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, from 0.09 to 0.80, was observed in this study that approaches the theoretical limits permissible within the crystallographic framework (i.e. 0 to 1). However, x also varies depending on the nature of the coexisting phase, i.e. the Fe activity, being approximately 0.2 higher when coexisting with metallic iron compared to FeS at 16 GPa, based on the results in this study. Although we cannot quantify the effect of pressure on the variation of x from the current dataset, x may increase with pressure at a given temperature. This possibility is implied by the deviation observed in the previous study by Fei et al.\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, conducted at 21 GPa, where x values are higher and deviate from the trend observed at 16 GPa in this study.\u003c/p\u003e \u003cp\u003eWith the established relationship between temperature and composition for Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, we can evaluate its P-V-T-x relations using the HP-HT data from this study and from the literature\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. The experiments from Zhao et al.\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e were conducted at pressures between 13 and 16 GPa, and contain metallic iron. Therefore, we can fit the temperature-composition relationship from our in-house multi-anvil (MA) experiments and literature\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e with Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e coexisting with metallic iron at approximately 16 GPa to constrain the compositional effects (i.e. influence of the x parameter) on volume. A linear fit of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x=a\\times\\:\\left(T-b\\right)\\)\u003c/span\u003e\u003c/span\u003e yields the result \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:a=9.5\\pm\\:0.6\\times\\:{10}^{-4}\\)\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}^{-1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:b\\:=\\:750\\pm\\:50\\:K\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e is in K. The composition-volume relation can be determined using the single crystal refinements collected in this study, from the volume difference between the Fe\u003csub\u003e4.11\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and Fe\u003csub\u003e4.77\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e samples, after normalization to the same pressure. After correcting the effects of composition and compressibility on the volume of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, we can estimate its thermal expansion. We assume that the thermal expansion coefficient of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e does not vary significantly with x, and fit the P-V-T data of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e from this study and the literature\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e using the thermal expansion expression: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:=1/V{\\left(\\partial\\:V/\\partial\\:T\\right)}_{P}\\)\u003c/span\u003e\u003c/span\u003e, assuming \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e remains constant over the limited pressure (13 to 16 GPa) and temperature range (800 to 1100 K). The resulting thermal expansion coefficient is 5.3\u0026plusmn;2.0 \u0026times; 10\u003csup\u003e\u0026minus;5\u003c/sup\u003e K\u003csup\u003e\u0026minus;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, which is comparable to that of the Fe\u003csub\u003e3\u003c/sub\u003eS phase (~\u0026thinsp;3.6 \u0026times; 10\u003csup\u003e\u0026minus;5\u003c/sup\u003e K\u003csup\u003e\u0026minus;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e at 1000 K and 15 GPa\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e), but significantly smaller than that previously estimated for the \u0026ldquo;Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e\u0026rdquo; phase (~\u0026thinsp;26.58 \u0026times; 10\u003csup\u003e\u0026minus;5\u003c/sup\u003e K\u003csup\u003e\u0026minus;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) in the same pressure and temperature range\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. The significant overestimation of \u0026#120572; in the previous study by Zhao et al.\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e is due to the fact that the volume expansion resulting from compositional variation with temperature was not accounted for separately in the evaluation of thermal expansion. The P-V-T-x relations of Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. These relations accurately describe the large volume changes observed in the experimental data, which are caused by both thermal expansion and compositional variation.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eAlthough there is currently no direct geophysical evidence confirming the existence of a Martian inner core, recent seismic and geodetic observations have provided important constraints on the state of the core as a whole\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Seismic measurements have detected the apparent core-mantle boundary of Mars, supplied decisive evidence that at least the upper region of Mars' core is in a liquid state and provided estimates for the core\u0026rsquo;s average density\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e that range from 5.7 to 6.65 g/cm\u0026sup3;. The substantial variation in these density estimates stems from whether a basal magma layer is considered to exit, which in turn implies different thermal regimes for Mars\u0026rsquo; interior. While the innermost state of Mars' core has not yet been revealed by seismic observations, the detected liquid region of the core sets an upper limit to a potential inner core radius of \u0026lt;\u0026thinsp;750 km\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Models based on geodesy also support the existence of a liquid core, though these observations are generally insensitive to an inner core unless it is sufficiently big\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Based on the assumption that the sulfur content of Mars' core may be quite close to the Fe-FeS eutectic, previous models have proposed that temperatures are likely too high for an inner core to form\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. However, the relatively low densities recently proposed for the core\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e raises the possibility that the composition may lie to the S-rich side of the eutectic at conditions approaching the center of Mars. To examine this possibility, we first determine whether an Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e inner core would be gravitationally stable and the temperature required for it to crystallize, then compare this with proposed Martian areotherms to assess the likely core crystallization regime.\u003c/p\u003e \u003cp\u003eIf we extrapolate the obtained P-V-T-x relations for Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e to inner core conditions, the density will increase both due to compression and because x will approach 1, reaching a value of 7.5(\u0026plusmn;\u0026thinsp;0.3) g/cm\u003csup\u003e3\u003c/sup\u003e at the center of Mars (40 GPa and 2000K). This is larger than the range estimated using recent seismic observations for the density at the center of a liquid Martian core\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;3), implying that an Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e inner core would be gravitationally stable in a bottom-up crystallization regime. It is worth noting that in estimating the density of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, the thermal expansion coefficient was assumed to be constant, which likely results in a slight underestimate of the inner core density. Even though this assumption does affect the conclusion of gravitational stability, further in situ HP-HT experiments would be required to establish a full thermodynamic model describing the P-V-T-x relations of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, considering both the P-T effect on the variation of x and the effect of x on the thermoelastic properties of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eConstraints on the temperature for inner core crystallization can be obtained by examining the thermal stability of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, which increases quite significantly with pressure, from less than 1200 K at 14 GPa\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e to ~\u0026thinsp;1500 K at 21 GPa\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. At higher temperatures, Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e will melt incongruently to form solid FeS and Fe-S liquid: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Fe}_{4+x}{S}_{3}\\left(solid\\right)=2FeS\\left(solid\\right)+{Fe}_{2+x}S\\:\\left(liquid\\right)\\)\u003c/span\u003e\u003c/span\u003e. The Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e synthesized in this study coexists with Fe-S liquid at 1640 K and 27 GPa, indicating a melting temperature higher than this. An extrapolation of the melting curve to the pressure at the center of the Martian core (~\u0026thinsp;40 GPa), indicates that Fe\u003csub\u003e4+x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is stable up to approximately 1970(\u0026plusmn;\u0026thinsp;105) K (Supplementary Fig.\u0026nbsp;4). This relatively refractory behavior of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e underlines the potential for it to form planetary inner cores.\u003c/p\u003e \u003cp\u003eThe solidification regime of the Martian core will depend on the core\u0026rsquo;s composition and temperature. We have parameterized the melting phase relations in the Fe-FeS system up to 40 GPa considering the liquidus phases Fe, Fe\u003csub\u003e3\u003c/sub\u003eS, Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, and FeS and using our results and those from the literature (Supplementary Fig.\u0026nbsp;5). Since there is no experimental evidence to support the stability of Fe\u003csub\u003e12\u003c/sub\u003eS\u003csub\u003e7\u003c/sub\u003e and Fe\u003csub\u003e2\u003c/sub\u003eS\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e as liquidus phases under Martian core conditions, these phases were not considered in our model. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows Fe-S liquidus curves for different amounts of S, compared with Martian areotherms, from which the core solidification regime can be inferred by considering potential points of intersection. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e., during the cooling of Mars, if the core contains\u0026thinsp;~\u0026thinsp;7\u0026ndash;12 wt.% S, Fe-metal snow will form at the top of the Martian core, as proposed previously\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. The crystalized Fe will sink but will be dissolved again in the deeper core region where the liquidus temperature is then lower than the areotherm (see curve 10 wt.% S in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). If the Martian core contains\u0026thinsp;~\u0026thinsp;13\u0026ndash;16 wt.% S, the liquidus curve will first decrease with pressure (see curve 14 wt.% S in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), where Fe-metal is the liquidus phase. However, as the S content of the eutectic melt decreases with increasing pressure, Fe\u003csub\u003e3\u003c/sub\u003eS will replace Fe as the liquidus phase at higher pressures (21 to 32 GPa, depending on the exact S content), which will cause the liquidus temperature to increase with pressure. In this case, the areotherm could intersect the liquidus curve at both the top and bottom of the Martian core, which means that both iron snow and bottom-up growth of Fe\u003csub\u003e3\u003c/sub\u003eS could occur simultaneously. However, if the Martian core contains 17\u0026ndash;25 wt.% S, which would be quite consistent with recent density estimates\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e will be the liquidus phase over the entire pressure range of the Martian core, with a liquidus temperature that increases continuously with pressure (see curves 18 and 22 wt.% S in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). This means that an Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e inner core will start to crystalize if the center of such a S-rich Martian core cools below approximately 1960 K.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMars has no active global magnetic field, implying that there is no dynamo operating in the Martian core. Crystallization of Fe in the form of iron snow would cause chemical convection below the snow zone, although whether this convection would provide enough energy to run a dynamo is debated\u003csup\u003e15\u0026ndash;16,35\u0026minus;37\u003c/sup\u003e, as it is dependent on the generation of a positive net buoyancy flux\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. In contrast, the crystallization of a sulfide inner core is consistent with the absence of an active dynamo, as the residual liquid would be richer in Fe and would, therefore, remain at the base of the outer core, inhibiting chemical convection\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe presence of an inner core composed of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e would likely have a negligible impact on interpretations of geodetic observations. For instance, with a small inner core allowed by current seismic constraints (e.g., a radius of \u0026lt;\u0026thinsp;600 km), the mass of an Fe₄₊ₓS₃ inner core would constitute less than 5% of the total core mass, altering the moment of inertia by only\u0026thinsp;~\u0026thinsp;0.1%. Additionally, according to numerical calculations, the nutation effects of an inner core with a radius of 600 km are expected to be insignificant\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Thus, geodesy alone may be insufficient to constrain the existence of a relatively small inner core, and further seismic observations from future space missions, as well as additional analyses of InSight seismic data, are needed to provide more definitive evidence regarding the presence or absence of a Martian inner core. Further experimental measurements to enable seismic velocities of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e to be determined would be also important for the interpretation of potential inner core-related seismic signals.\u003c/p\u003e \u003cp\u003eThe temperature at the center of the Martian core would need to be lower than 1800 K to allow Fe\u003csub\u003e3\u003c/sub\u003eS to crystallize or for an 'iron snow' zone to reach the Martian center and form an inner core of Fe (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). This corresponds to a temperature of approximately 1500\u0026ndash;1600 K at the core-mantle boundary (CMB), which is lower than all current thermal models for Mars\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan additionalcitationids=\"CR40 CR41 CR42\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. Therefore, crystallization of an Fe\u003csub\u003e3\u003c/sub\u003eS or Fe inner core are likely to be only future scenarios, possible only after Mars has cooled further\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. On the other hand, the crystallization temperature of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e in a core containing, for example, 22 wt.% S\u0026mdash;an amount that could satisfy the Martian core's density deficit (e.g., the core density model from Irving et al.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e)\u0026mdash;would be approximately 1960 (\u0026plusmn;\u0026thinsp;105) K. This approaches the lower limit of the estimated temperature of the Martian core in some thermal models\u003csup\u003e\u003cspan additionalcitationids=\"CR40\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The detection of a Martian inner core through further geophysical observations, along with an estimate of its density, would provide critical constraints on the chemical composition and temperature of the Martian core. Moreover, the existence of a Martian inner core would imply a relatively cool Martian interior, which would be incompatible with the presence of a basal magma layer on top of the CMB. Conversely, if an inner core is confirmed to be absent, the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e melting temperature, i.e., 1960 (\u0026plusmn;\u0026thinsp;105) K, would provide a lower limit for the temperature at the center of Mars.\u003c/p\u003e \u003cp\u003eIt is worth noting that the addition of other light elements, such as O, C, and H, may impact the crystallization phase relations of the Fe-FeS system, though the effects remain largely unknown due to a lack of experimental studies in more complex systems. On the one hand, the addition of multiple light elements could further lower the eutectic temperature of the system making an inner core less likely. On the other hand, it is possible that elements such as H, that can be incorporated in high pressure sulfides in stoichiometric proportions\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, might partition sub-equally between liquid and melt phases and have little effect on crystallization temperatures. While this study provides a preliminary estimation of the likelihood of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e crystallization in the Martian core, further experiments involving relevant more complex chemical compositions are needed to test the hypotheses proposed here.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e \u003cb\u003eStarting material.\u003c/b\u003e The initial mixtures were composed of metallic iron powder (99.9%, 10 \u0026micro;m particle size) and high-purity elemental sulfur (99.999%). The bulk compositions of the mixtures are listed in Supplementary Table\u0026nbsp;5. The elements were mixed in an agate mortar under ethanol for about 45 minutes, followed by drying overnight in an oven at 340 K. For the in-house multi-anvil experiments, the mixed powder was directly used as the starting material, without any pre-treatment. For the synchrotron multi-anvil experiments, the powder mixtures underwent a pre-sintering process. This involved compressing the powders in a piston-cylinder press at 0.5 GPa and 1000 K for over 6 hours. Following sintering, the materials were machined into regular cylinders, each measuring approximately 1 mm in diameter and 0.6 mm in height. The sintered cylinders contained a mixture of metallic Fe and troilite (FeS). For the LH-DAC experiments, a pre-synthesized Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e crystal separated from a prior multi-anvil experiment was utilized. The degraded crystal was pre-compressed into a thin pallet, roughly 10 \u0026micro;m thick, to serve as the starting material.\u003c/p\u003e \u003cp\u003e \u003cb\u003eIn-house multi-anvil experiments.\u003c/b\u003e 10 mm and 7 mm edge length octahedral assemblies were compressed using tungsten carbide cubic anvils with 5 mm and 3 mm truncation edge lengths (TEL), respectively. The 10/5 assembly was used for experiments targeting pressures between 14 to 16 GPa. The 7/3 assembly was utilized for the experiments at 27 GPa\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. In these in-house multi-anvil experiments, the pressure uncertainties at high temperatures are estimated to be \u0026plusmn;\u0026thinsp;2 GPa. The starting materials were loaded into a gold capsule for run S7995, while MgO capsules were used in all other runs. After reaching the target loads, the samples were heated to high temperatures using LaCrO\u003csub\u003e3\u003c/sub\u003e heaters. Temperatures were monitored using a type D W-Re thermocouple, except for run S7995 and I1691a, where the temperature was estimated based on the power-temperature relation from previous experiments. The pressure effects on the electromotive force (EMF) of the thermocouple were corrected\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. These temperatures were maintained for durations ranging from 1 to 10 hours, followed by rapid quenching to room temperature by shutting down the power source.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSynchrotron multi-anvil experiments.\u003c/b\u003e The experiments were conducted at the beamline PSICHE at the SOLEIL synchrotron\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. This assembly was equipped with a boron-doped diamond (BDD) heater, synthesized through the chemical vapor deposition (CVD) method\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. The CVD-BDD heaters are notable for providing stable heating conditions and high X-ray transparency, which assists the collection of high quality XRD data. The assemblies were compressed to high pressures using tungsten carbide anvils with 5 mm TEL. The samples, which were placed in a corundum (Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e) capsule, were illuminated by the white X-ray beams, and the energy-dispersive XRD patterns of the samples were collected \u003cem\u003ein-situ\u003c/em\u003e at high pressures and high temperatures. The unit cell parameters of the phases present in the samples were determined through Rietveld Le Bail fitting, using the GSAS-II software package\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. Temperatures were measured using a type D thermocouple, with corrections also applied for pressure effects on the EMF\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. Pressures were evaluated using the equation of state of corundum\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. The differences in pressure are less than 0.2 GPa when applying an alternative pressure standard for corundum\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSingle crystal syntheses in LH-DAC and high-pressure SC-XRD.\u003c/b\u003e We employed a BX90-type diamond anvil cell\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e, equipped with a pair of diamond anvils each having a culet diameter of 250 \u0026micro;m for the high-pressure single crystal synthesis and measurements. Pre-indented rhenium gaskets were employed. A thin platelet of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e sample was sandwiched between two KCl layers and compressed to approximately 15 GPa in run LJFeS01. KCl provided both thermal insulation and the pressure marker\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e in the experiment. The sample was then heated from both sides using near-infrared lasers to a temperature of 1150 (200) K, employing a modified version of the portable double-sided laser of the ID14 beamline at ESRF\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. The temperature for LJFeS01 was estimated based on the melting phase relations in the high-pressure Fe-FeS system\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, as the Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e phase coexisted with Fe-S liquid (Supplementary Fig.\u0026nbsp;6). For run LD101, helium was loaded at 1.2 kbar and served both as a pressure-transmitting medium and thermal insulator for laser heating. The sample was compressed to approximately 20 GPa and then heated to 1300 (200) K, employing the in-house laser-heating system at the Bayerisches Geoinstitut\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e, with temperatures estimated by fitting the radiation of the sample using a grey body approximation. The pressure of run LD101 was estimated based on a pressure calibration of the Raman shift of the diamond anvils\u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e. For both runs, the samples were subjected to heating for durations ranging from 5 to 10 seconds before being rapidly quenched to room temperature.\u003c/p\u003e \u003cp\u003eHigh-pressure XRD measurements were conducted at the high-pressure diffraction beamline ID15B at the ESRF in Grenoble. We utilized a focused X-ray beam with a wavelength of 0.4100 \u0026Aring;, and a beam size of approximately 1 \u0026micro;m \u0026times; 1 \u0026micro;m. Initially, a 2D-scan XRD map with a step size of 2 \u0026micro;m was constructed by scanning the sample stage\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e. This process was aimed at locating phases of interest within the samples, as illustrated in Supplementary Fig.\u0026nbsp;6. Upon locating these phases, SC-XRD data collection was conducted over a range of -30 degrees to +\u0026thinsp;30 degrees for LJFeS01, and \u0026minus;\u0026thinsp;34 degrees to +\u0026thinsp;34 degrees for LD101, with an increment step of 0.5 degrees. The Domain Auto Finder program (DAFi)\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e was employed for the rapid identification of domains of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e microcrystals within the complete SC-XRD dataset collected from the multiphase samples. Domains of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e were primarily located in the region adjacent to the melt within the laser-heated spots. In the colder areas of the laser-heated spot, FeS III and several unidentified phases were indexed from the SC-XRD dataset. As this paper concentrates on the stability of liquidus phases, some further reflections for the unidentified subsolidus sulfide structures identified within the samples are outside of the scope of this discussion. Data reductions were performed using the CrysAlis Pro software package. The crystal structures of Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e from each run were subsequently solved and refined using the Olex2 software package\u003csup\u003e\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e. Further details regarding the structure solution and refinement can be found in Supplementary Methods.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSample Recovery and Chemical Analysis.\u003c/b\u003e After the completion of the in-house multi-anvil experiments, the run products were carefully recovered to ambient conditions, mounted in epoxy resin and subsequently polished for chemical analyses. The samples were analyzed using a JEOL JXA-8200 electron probe microanalyzer (EPMA), which was operated at 15 kV and 15 nA. Calibration standards of metallic iron, pyrite, and periclase were employed for Fe, S, and O, respectively. The solid phases of the samples were analyzed with a focused beam, approximately 1 \u0026micro;m in diameter. The compositions of the quenched liquids were measured using a defocused beam with a diameter ranging from 10 to 30 \u0026micro;m, depending on the size of the quenched texture.\u003c/p\u003e \u003cp\u003e \u003cb\u003eParameterization of liquidus temperature.\u003c/b\u003e The pressure and composition dependencies of the liquidus temperature are parameterized following a similar approach to previous models\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e, incorporating more experimental constraints from this study. The melting phase diagram at a given pressure is constructed using the melting temperatures of the liquidus phases (Fe, Fe\u003csub\u003e3\u003c/sub\u003eS, Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, and FeS) and the eutectic temperature and composition as anchor points. It is assumed that the liquidus temperature has a linear dependence on sulfur concentration when Fe or FeS is the liquidus phase, and a parabolic dependence on sulfur concentration when Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e or Fe\u003csub\u003e3\u003c/sub\u003eS are the liquidus phases. Fe, Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, and FeS are liquidus phases at pressures from 14 to 21 GPa, while Fe, Fe\u003csub\u003e3\u003c/sub\u003eS, Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, and FeS are liquidus phases at pressures above 21 GPa. We use the melting curves of Fe\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e and FeS\u003csup\u003e\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e\u003c/sup\u003e from the literature and evaluate the eutectic compositions and temperatures at high pressures (Supplementary Fig.\u0026nbsp;7), as well as the melting curves of Fe\u003csub\u003e3\u003c/sub\u003eS and Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e (Supplementary Fig.\u0026nbsp;4), using data from this study and the literature\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e\u003c/sup\u003e. The change in the peritectic composition from Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e plus liquid to FeS plus liquid as a function of pressure was estimated based on data from this study and the literature\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. The sulfur content is parameterized to increase with pressure until it reaches the composition of Fe\u003csub\u003e5\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. Meanwhile, the peritectic composition at the point where Fe\u003csub\u003e3\u003c/sub\u003eS plus liquid reacts to Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e plus liquid is assumed to be the composition of Fe\u003csub\u003e3\u003c/sub\u003eS (16.1 wt.% S). The parameters describing the model are listed in Supplementary Table\u0026nbsp;6. The melting phase relations at 15 GPa, 21 GPa, 27 GPa, and 40 GPa, generated using this model, are plotted in Supplementary Fig.\u0026nbsp;5 and compared with literature data to demonstrate consistency.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eL.M. conceived and designed this project. L.M., X.L., T.B.B., L.D., W.Z., J.C., A.N., I.K., G.A., A.K., M.H., N.G., L.H., and D.J.F. performed the experiments. W.Z., T.B.B., L.D., X.L., and L.M. analyzed the single-crystal X-ray diffraction data. L.M., D.J.F., X.L., A.N., O.N., I.K., and L.D. contributed to the interpretation of the results. L.M. and D.J.F. wrote the paper with contributions from all the authors.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe authors thank L. Yuan, R. Pierru, and E. Kubik for insightful discussions. We appreciate assistance from D. Krau\u0026szlig;e, A. Potzel, and D. Wiesner in chemical characterization using electron microscopy. R. Njul, A. Rother, H. Fischer, and S. \u0026Uuml;belhack are acknowledged for their help with sample preparation and the maintenance of the large volume presses at BGI. This research was supported by DFG grant FR1555/11. We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of experiment time at the ID15 beamline and offline laser-heating facilities of the ID14 beamline. IK acknowledges funding provided by the European Union (ERC, LECOR, project number 101042572). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.\u003c/p\u003e\n\u003ch3\u003eData Availability\u003c/h3\u003e\n\u003cp\u003eThe data supporting the main findings of this work are available in the main text and the supplementary materials. Additional data can be available from the corresponding author upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSt\u0026auml;hler SC, Khan A, Banerdt WB, Lognonn\u0026eacute; P, Giardini D, Ceylan S, Drilleau M, Duran AC, Garcia RF, Huang Q, Kim D (2021) Seismic detection of the martian core. Science 373:443\u0026ndash;448\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIrving JC, Lekić V, Dur\u0026aacute;n C, Drilleau M, Kim D, Rivoldini A, Khan A, Samuel H, Antonangeli D, Banerdt WB, Beghein C (2023) First observations of core-transiting seismic phases on Mars. Proc. Natl. Acad. Sci. U.S.A. 120, e2217090120\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSamuel H, Drilleau M, Rivoldini A, Xu Z, Huang Q, Garcia RF, Lekić V, Irving JC, Badro J, Lognonn\u0026eacute; PH, Connolly JA (2023) Geophysical evidence for an enriched molten silicate layer above Mars\u0026rsquo;s core. Nature 622:712\u0026ndash;717\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhan A, Huang D, Dur\u0026aacute;n C, Sossi PA, Giardini D, Murakami M (2023) Evidence for a liquid silicate layer atop the Martian core. Nature 622:718\u0026ndash;723\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHirose K, Labrosse S, Hernlund J (2013) Composition and state of the core. Annu Rev Earth Planet Sci 41:657\u0026ndash;691\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChambers JE, Wetherill GW (2001) Planets in the asteroid belt. Meteorit Planet Sci 36:381\u0026ndash;399\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eW\u0026auml;nke H, Dreibus G (1994) Chemistry and accretion history of Mars. Philos Trans R Soc A: Phys Eng Sci 349:285\u0026ndash;293\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLodders K, Fegley B Jr (1997) An oxygen isotope model for the composition of Mars. Icarus 126:373\u0026ndash;394\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSanloup C, Jambon A, Gillet P (1999) A simple chondritic model of Mars. Phys Earth Planet Inter 112:43\u0026ndash;54\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYoshizaki T, McDonough WF (2020) The composition of Mars. Geochim Cosmochim Acta 273:137\u0026ndash;162\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePalme H, Lodders K, Jones A (2014) Solar system abundances of the elements in Treatise on Geochemistry, K. K. Turekian, H. D. Holland, EdsElsevier, ed. 2\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRose-Weston L, Brenan JM, Fei Y, Secco RA, Frost DJ (2009) Effect of pressure, temperature, and oxygen fugacity on the metal-silicate partitioning of Te, Se, and S: Implications for earth differentiation. Geochim Cosmochim Acta 73:4598\u0026ndash;4615\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRubie DC, Jacobson SA, Morbidelli A, O\u0026rsquo;Brien DP, Young ED, de Vries J, Nimmo F, Palme H, Frost DJ (2015) Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed Solar System bodies and accretion of water. Icarus 248:89\u0026ndash;108\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLe Maistre S, Rivoldini A, Caldiero A, Yseboodt M, Baland RM, Beuthe M, Van Hoolst T, Dehant V, Folkner WM, Buccino D, Kahan D (2023) Spin state and deep interior structure of Mars from InSight radio tracking. Nature 619:733\u0026ndash;737\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBreuer D, Rueckriemen T, Spohn T (2015) Iron snow, crystal floats, and inner-core growth: modes of core solidification and implications for dynamos in terrestrial planets and moons. Prog Earth Planet Sci 2:1\u0026ndash;26\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHelffrich G (2017) Mars core structure\u0026mdash;concise review and anticipated insights from InSight. Prog Earth Planet Sci 4:1\u0026ndash;14\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFei Y, Li J, Bertka CM, Prewitt CT (2000) Structure type and bulk modulus of Fe\u003csub\u003e3\u003c/sub\u003eS, a new iron-sulfur compound. Am Min 85:1830\u0026ndash;1833\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStewart AJ, Schmidt MW, Van Westrenen W, Liebske C (2007) Mars: A new core-crystallization regime. Science 316:1323\u0026ndash;1325\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMori Y, Ozawa H, Hirose K, Sinmyo R, Tateno S, Morard G, Ohishi Y (2017) Melting experiments on Fe\u0026ndash;Fe\u003csub\u003e3\u003c/sub\u003eS system to 254 GPa. Earth Planet Sci Lett 464:135\u0026ndash;141\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMorard G, Andrault D, Guignot N, Sanloup C, Mezouar M, Petitgirard S, Fiquet G (2008) In situ determination of Fe\u0026ndash;Fe\u003csub\u003e3\u003c/sub\u003eS phase diagram and liquid structural properties up to 65 GPa. Earth Planet Sci Lett 272:620\u0026ndash;626\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChudinovskikh L, Boehler R (2007) Eutectic melting in the system Fe\u0026ndash;S to 44 GPa. Earth Planet Sci Lett 257:97\u0026ndash;103\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFei Y, Bertka CM, Finger LW (1997) High-pressure iron-sulfur compound, Fe\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e, and melting relations in the Fe-FeS system. Science 275:1621\u0026ndash;1623\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao B, Morard G, Boccato S, Mezouar M, Antonangeli D (2024) Phase diagram and thermo-elastic properties of Fe-S compounds up to 15 GPa: Thermodynamic constraints on the core of medium-sized telluric planets. Earth Planet Sci Lett 634:118676\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZurkowski CC, Lavina B, Chariton S, Prakapenka V, Campbell AJ (2022) Stability of Fe\u003csub\u003e2\u003c/sub\u003eS and Fe\u003csub\u003e12\u003c/sub\u003eS\u003csub\u003e7\u003c/sub\u003e to 125 GPa; implications for S-rich planetary cores. Geochem Perspect Lett 21\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOka K, Tateno S, Kuwayama Y, Hirose K, Nakajima Y, Umemoto K, Tsujino N, Kawaguchi S (2022) I. A cotunnite-type new high-pressure phase of Fe\u003csub\u003e2\u003c/sub\u003eS. Am Mineral 107:1249\u0026ndash;1253\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBirch F (1947) Finite elastic strain of cubic crystals. Phys Rev 71:809\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFei Y, Murphy C, Shibazaki Y, Shahar A, Huang H (2016) Thermal equation of state of hcp-iron: Constraint on the density deficit of Earth's solid inner core. Geophys Res Lett 43:6837\u0026ndash;6843\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUrakawa S, Someya K, Terasaki H, Katsura T, Yokoshi S, Funakoshi KI, Utsumi W, Katayama Y, Sueda YI, Irifune T (2004) Phase relationships and equations of state for FeS at high pressures and temperatures and implications for the internal structure of Mars. Phys Earth Planet Inter 143:469\u0026ndash;479\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang L, Fei Y (2008) Effect of Ni on Fe\u0026ndash;FeS phase relations at high pressure and high temperature. Earth Planet Sci Lett 268:212\u0026ndash;218\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTsuno K, Ohtani E (2009) Eutectic temperatures and melting relations in the Fe\u0026ndash;O\u0026ndash;S system at high pressures and temperatures. Phys Chem Min 36:9\u0026ndash;17\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUrakawa S, Kamuro R, Suzuki A, Kikegawa T (2018) Phase relationships of the system Fe-Ni-S and structure of the high-pressure phase of (Fe\u003csub\u003e1\u0026thinsp;\u0026ndash;\u0026thinsp;x\u003c/sub\u003eNi\u003csub\u003ex\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e. Phys Earth Planet Inter 277:30\u0026ndash;37\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen B, Gao L, Funakoshi KI, Li J (2007) Thermal expansion of iron-rich alloys and implications for the Earth's core. Proc. Natl. Acad. Sci. U.S.A. 104, 9162\u0026ndash;9167\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDefraigne P, Rivoldini A, Van Hoolst T, Dehant V (2003) Mars nutation resonance due to free inner core nutation. J Geophys Res : Planet 108:E12\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFei Y, Bertka C (2005) The interior of Mars. Science 308:1120\u0026ndash;1121\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHauck SA, Aurnou JM, Dombard AJ (2006) Sulfur's impact on core evolution and magnetic field generation on Ganymede. J Geophys Res : Planet 111:E9\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBland MT, Showman AP, Tobie G (2008) The production of Ganymede's magnetic field. Icarus 198:384\u0026ndash;399\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR\u0026uuml;ckriemen T, Breuer D, Spohn T (2015) The Fe snow regime in Ganymede's core: A deep-seated dynamo below a stable snow zone. J Geophys Res : Planet 120:1095\u0026ndash;1118\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHemingway DJ, Driscoll PE (2021) History and future of the Martian dynamo and implications of a hypothetical solid inner core. J Geophys Res : Planet 126, e2020JE006663\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHauck SA, Phillips RJ (2002) Thermal and crustal evolution of Mars. J Geophys Res : Planet 107, 6-1-6-19\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWilliams JP, Nimmo F (2004) Thermal evolution of the Martian core: Implications for an early dynamo. Geology 32:97\u0026ndash;100\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePlesa AC, Tosi N, Grott M, Breuer D (2015) Thermal evolution and Urey ratio of Mars. J Geophys Res : Planet 120:995\u0026ndash;1010\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSamuel H, Ballmer MD, Padovan S, Tosi N, Rivoldini A, Plesa AC (2021) The thermo-chemical evolution of Mars with a strongly stratified mantle. J Geophys Res : Planet 126, e2020JE006613\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang Q, Schmerr NC, King SD, Kim D, Rivoldini A, Plesa AC, Samuel H, Maguire RR, Karakostas F, Lekić V, Charalambous C (2022) Seismic detection of a deep mantle discontinuity within Mars by InSight. Proc. Natl. Acad. Sci. U.S.A. 119, e2204474119\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbeykoon S, Howard C, Dominijanni S, Eberhard L, Kurnosov A, Frost DJ, Ballaran B, Terasaki T, Sakamaki H, Suzuki T, A., Ohtani E (2023) Deuterium content and site occupancy in iron sulfide at high pressure and temperature determined using in situ neutron diffraction measurements. J Geophys Res : Solid Earth, 128, e2023JB026710\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIshii T, Shi L, Huang R, Tsujino N, Druzhbin D, Myhill R, Li Y, Wang L, Yamamoto T, Miyajima N, Kawazoe T (2016) Generation of pressures over 40 GPa using Kawai-type multi-anvil press with tungsten carbide anvils. Rev Sci Instrum 87:024501\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu Z, Nishi M, Ishii T, Fei H, Miyajima N, Ballaran B, Ohfuji T, Sakai H, Wang T, Shcheka L, S., Arimoto T (2017) Phase relations in the system MgSiO\u003csub\u003e3\u003c/sub\u003e-Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e up to 2300 K at lower mantle pressures. J Geophys Res : Solid Earth 122:7775\u0026ndash;7788\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNishihara Y, Doi S, Kakizawa S, Higo Y, Tange Y (2020) Effect of pressure on temperature measurements using WRe thermocouple and its geophysical impact. Phys Earth Planet Inter 298:106348\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKing A, Guignot N, Henry L, Morard G, Clark A, Le Godec Y, Iti\u0026eacute; JP (2022) Combined angular and energy dispersive diffraction: optimized data acquisition, normalization and reduction. J Appl Crystallogr 55:218\u0026ndash;227\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNishida K, Xie L, Kim EJ, Katsura T (2020) A strip-type boron-doped diamond heater synthesized by chemical vapor deposition for large-volume presses. Rev Sci Instrum 91:095108\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXie L, Yoneda A, Liu Z, Nishida K, Katsura T (2020) Boron-doped diamond synthesized by chemical vapor deposition as a heating element in a multi-anvil apparatus. High Press Res 40:369\u0026ndash;378\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eToby BH, Von Dreele RB (2013) GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J Appl Crystallogr 46:544\u0026ndash;549\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi W, Wei W, Sun N, Mao Z, Prakapenka VB (2022) Thermal Equations of State of Corundum and Rh\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e (II)-Type Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e up to 153 GPa and 3400 K. J Geophys Res : Solid Earth 127:023805 e2021JB\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eN\u0026eacute;ri A, Man L, Chantel J, Farla R, Bauer G, Linhardt S, Boffa Ballaran T, Frost DJ (2024) The development of internal pressure standards for in-house elastic wave velocity measurements in multi-anvil presses. Rev Sci Instrum 95:013902\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKantor I, Prakapenka V, Kantor A, Dera P, Kurnosov A, Sinogeikin S, Dubrovinskaia N, Dubrovinsky L (2012) BX90: A new diamond anvil cell design for X-ray diffraction and optical measurements. Rev Sci Instrum 83:125102\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDewaele A, Belonoshko AB, Garbarino G, Occelli F, Bouvier P, Hanfland M, Mezouar M (2012) High-pressure\u0026ndash;high-temperature equation of state of KCl and KBr. Phys Rev B 85:214105\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKupenko I, Dubrovinsky L, Dubrovinskaia N, McCammon C, Glazyrin K, Bykova E, Ballaran TB, Sinmyo R, Chumakov AI, Potapkin V, Kantor A (2012) Portable double-sided laser-heating system for M\u0026ouml;ssbauer spectroscopy and X-ray diffraction experiments at synchrotron facilities with diamond anvil cells. Rev Sci Instrum 83:124501\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAprilis G, Strohm C, Kupenko I, Linhardt S, Laskin A, Vasiukov DM, Cerantola V, Koemets EG, McCammon C, Kurnosov A (2017) Chumakov, A. I. Portable double-sided pulsed laser heating system for time-resolved geoscience and materials science applications. Rev Sci Instrum 88:084501\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFedotenko T, Dubrovinsky L, Aprilis G, Koemets E, Snigirev A, Snigireva I, Barannikov A, Ershov P, Cova F, Hanfland M, Dubrovinskaia N (2019) Laser heating setup for diamond anvil cells for in situ synchrotron and in house high and ultra-high pressure studies. Rev Sci Instrum 90:104501\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAkahama Y, Kawamura H (2006) Pressure calibration of diamond anvil Raman gauge to 310 GPa. J Appl Phys 100:043516\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHrubiak R, Smith JS, Shen G (2019) Multimode scanning X-ray diffraction microscopy for diamond anvil cell experiments. Rev Sci Instrum 90:025109\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAslandukov A, Aslandukov M, Dubrovinskaia N, Dubrovinsky L (2022) Domain Auto Finder (DAFi) program: the analysis of single-crystal X-ray diffraction data from polycrystalline samples. J Appl Crystallogr 55:1383\u0026ndash;1391\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDolomanov OV, Bourhis LJ, Gildea RJ, Howard JA, Puschmann H (2009) OLEX2: a complete structure solution, refinement and analysis program. J Appl Crystallogr 42:339\u0026ndash;341\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRivoldini A, Van Hoolst T, Verhoeven O, Mocquet A, Dehant V (2011) Geodesy constraints on the interior structure and composition of Mars. Icarus 213:451\u0026ndash;472\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDorogokupets PI, Dymshits AM, Litasov KD, Sokolova TS (2017) Thermodynamics and equations of state of iron to 350 GPa and 6000 K. Sci Rep 7:41863\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBoehler R (1992) Melting of the Fe-FeO and the Fe-FeS systems at high pressure: Constraints on core temperatures. Earth Planet Sci Lett 111:217\u0026ndash;227\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThompson S, Sugimura-Komabayashi E, Komabayashi T, McGuire C, Breton H, Suehiro S, Ohishi Y (2022) High-pressure melting experiments of Fe\u003csub\u003e3\u003c/sub\u003eS and a thermodynamic model of the Fe\u0026ndash;S liquids for the Earth\u0026rsquo;s core. J Phys Condens Matter 34:394003\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMomma K, Izumi F (2011) VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J Appl Crystallogr 44:1272\u0026ndash;1276\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5070782/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5070782/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSeismic, geodetic and cosmochemical evidence point to Mars having a sulfur-rich liquid core. Due to the similarity between estimates of the core\u0026rsquo;s sulfur content and the iron - iron sulfide eutectic composition at core conditions, it has been concluded that temperatures are too high for Mars to have an inner core. Recent low density estimates for the core, however, appear consistent with sulfur contents that are higher than the eutectic composition, leading to the possibility that an inner core could form from a high-pressure iron sulfide phase. Here we report the crystal structure of a phase with the formula Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, the iron content of which increases with temperature, approaching the stoichiometry Fe\u003csub\u003e5\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e under Martian inner core conditions. We show that Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e has a higher density than the liquid Martian core and that a Fe\u003csub\u003e4\u0026thinsp;+\u0026thinsp;x\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e inner core would crystalize if temperatures fall below 1960 (\u0026plusmn;\u0026thinsp;105) K at the center of Mars.\u003c/p\u003e","manuscriptTitle":"The structure and stability of Fe4+xS3 and its potential to form a Martian inner core","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-16 08:12:05","doi":"10.21203/rs.3.rs-5070782/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"22fd396b-7750-436f-8cce-1c4b7886aecc","owner":[],"postedDate":"December 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":41558141,"name":"Earth and environmental sciences/Planetary science/Core processes"},{"id":41558142,"name":"Earth and environmental sciences/Solid Earth sciences/Mineralogy"},{"id":41558143,"name":"Earth and environmental sciences/Planetary science/Inner planets"}],"tags":[],"updatedAt":"2025-02-26T08:05:54+00:00","versionOfRecord":{"articleIdentity":"rs-5070782","link":"https://doi.org/10.1038/s41467-025-56220-2","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-02-25 05:00:00","publishedOnDateReadable":"February 25th, 2025"},"versionCreatedAt":"2024-12-16 08:12:05","video":"","vorDoi":"10.1038/s41467-025-56220-2","vorDoiUrl":"https://doi.org/10.1038/s41467-025-56220-2","workflowStages":[]},"version":"v1","identity":"rs-5070782","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5070782","identity":"rs-5070782","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}