A diamond-bearing core-mantle boundary on Mercury

Domain: earth_science
Published: 2024-06-14
Editorial outcome: minor_revision

Abstract
Abundant carbon was identified on Mercury by MESSENGER, which is interpreted as the remnant of a primordial graphite flotation crust, suggesting that the magma ocean and core were saturated in carbon. We re-evaluate carbon speciation in Mercury’s interior in light of the high pressure-temperature experiments, thermodynamic models and the most recent geophysical models of the internal structure of the planet. Although a sulfur-free melt would have been in the stability field of graphite, sulfur dissolution in the melt under the unique reduced conditions depressed the sulfur-rich liquidus to temperatures spanning the graphite-diamond transition. Here we show it is possible, though statistically unlikely, that diamond was stable in the magma ocean. However, the formation of a solid inner core caused diamond to crystallize from the cooling molten core and formation of a diamond layer becoming thicker with time.

Introduction
Spectral data from the MESSENGER spacecraft revealed that the unusual darkness of Mercury’s surface is due to the widespread presence of graphite1. Measurements by neutron and gamma-ray spectroscopy quantified the abundance of carbon in the crust to ca. 2–4 wt%2,3, although a recent reinvestigation of the data suggests lower concentrations (<1 wt.%)4. The close association of graphite with crustal material observed in deep craters support an endogenous origin for graphite5,6 and rules out major exogeneous contributions by comets7.

Because of the highly reduced conditions that prevailed during Mercury’s differentiation (in the range IW−2.6 to IW−7.38,9, reported in log units relative to iron-wüstite thermodynamic equilibrium, IW), light elements in Mercury’s iron core are thought to be dominated by silicon, sulfur, and carbon10–13. Although carbon likely degassed from the magma ocean as CO2, CO, and CH4 species14–18 and was lost to space, the abundance of graphite in the Mercurian crust indicates that the planet remained saturated in a carbon phase during metal-silicate differentiation, core formation, and the entirety of magma ocean crystallization6. Additionally, because the solubility of carbon in silicate melt is exceptionally low under reduced conditions19,20, a significant amount of excess carbon should have been available to contribute to the formation of a graphite flotation crust.

It has so far been assumed that the pressure-temperature profile of Mercury’s mantle and magma ocean did not enter the diamond stability field due to the lower pressure at Mercury’s core-mantle boundary (CMB) and the absence of accurate constraints on the magma ocean liquidus temperature. As such it was considered that graphite was the only stable carbon-bearing phase during magma ocean crystallization21. Because graphite (ρ ≈ 2200 kg m−3) is less dense than a magma ocean melt (ρ ≈ 2700 kg m−3), it is expected to have floated and contributed to the formation of Mercury’s primordial crust13,20, analogous to the formation of the primordial anorthosite crust on the Moon22,23. However, the nature of the C-bearing phase requires reassessment in light of the most recent gravity field models for Mercury24–26. A smaller normalized polar moment of inertia (MOI) of the entire planet has been proposed (0.333 ± 0.00524). Although this latter value is close to the −1σ error value of the classical estimate (0.346 ± 0.01427), a model with a lower MOI would provide a deeper core-mantle boundary (CMB), and thus assumedly a deeper interface between the core and the magma ocean: 485 ± 20 km25 (similar to values of Steinbrügge et al.28) compared to 436 ± 25 km26 when using a higher MOI, similar to other studies29,30 (Mercury’s mean radius being 2440 km31). Such a change in the depth of the CMB will influence the pressure at the CMB that remained to be quantified and thus an effect on the stability of carbon phases.

Here, we propose a new thermodynamic estimate of Mercury’s magma ocean temperature accounting for the depression of the silicate melt liquidus in the presence of significant amounts of sulfur. Based on the revised geodetic calculations, we also recalculate the temperature and pressure at Mercury’s CMB. Informed by experiments at the relevant conditions and our new thermodynamic models, we revise the relative stability of graphite and diamond at the present CMB and in the magma ocean. We also evaluate the role of core crystallization and the implications for the exsolution of a carbon-bearing phase from the molten outer core. The unique reduced conditions of Mercury, the saturation of carbon phase in different reservoirs, and the formation of a solid inner core allow for different scenarios capable of producing a diamond layer at Mercury’s CMB.

Results
Pressure at the CMB and the liquidus of the deep magma ocean
We used planetary interior structure models that satisfy the various measurements of MOI25 to calculate that the pressure at Mercury’s CMB is 5.77 ± 0.31 GPa with a low MOI24 and 5.38 ± 0.37 GPa with a high MOI26 (Methods and Supplementary Fig. S1). According to our calculations, the highest possible pressure of Mercury’s CMB is 7 GPa. We here provide experimental melting relations at 7 GPa to determine experimentally the carbon speciation at the most extreme pressure conditions of Mercury’s magma ocean. Experiments are then combined with thermodynamic modelling to investigate how phase relations change for lower pressure CMB conditions which would still match Mercury’s MOI.

The most relevant estimate for the composition of the primordial Mercurian mantle is the silicate fraction of enstatite chondrites (EH-EL chondrites32,33). Thus, we compiled the chemical compositions of EH-EL meteorites34,35, excluding iron metal and decreasing phosphorous concentration (to 0.1 wt% P2O5) relative to the bulk EH-EL contents because of its siderophile behavior at reduced conditions36. Because silicon is known to partition more readily into metallic melts under highly reduced conditions11,37, we selected two starting compositions representing the partitioning of 8 and 15 wt% Si into the metallic core (Mer8 and Mer15, respectively; Supplementary Table S1). These values span the range of the most consistent interior structure and thermal models for Mercury25,38. Because sulfur is present in significant amounts at the surface of Mercury39,40 and has lithophile behavior under reduced conditions10,41, we considered sulfur as a potential major element in the Mercurian magma ocean (and a minor element in Mercury’s core) and added FeS to the starting materials to ensure sulfide saturation in the silicate melts. Experiments were performed at 7 GPa using a cubic multi-anvil press to understand melting relations at the greatest depths within the magma ocean (Methods and Supplementary Fig. S2). This pressure corresponds to the maximum value of potential CMB pressures predicted by interior models25. The liquidi of the Mer8 and Mer15 compositions at 7 GPa were 2188 ± 15 K and 2213 ± 10 K, respectively (Fig. 1a). Mer8 was in the stability field of orthopyroxene whereas Mer15 first crystallized olivine. With cooling, both compositions reached a cotectic surface with olivine + orthopyroxene, followed by garnet and clinopyroxene. A sulfide phase was present in all experiments (FeS + MgCaFeS). The solidi of Mer8 and Mer15 at 7 GPa were 2023 ± 50 K and 2113 ± 35 K, respectively. The calculated oxygen fugacities in our experiments were IW−3.9 to IW−5.1 (Methods, Supplementary Fig. S3, and Supplementary Data 1).

The role of sulfur on liquidus depression
Using the MAGEMin thermodynamic calculator42 implementing the most recent THERMOCALC thermodynamic model43, and assuming that the pressure at the bottom of Mercury’s magma ocean was similar to the present CMB pressure of 5.77 ± 0.41 GPa, we calculated the silicate melt liquidi across the pressure range relevant to Mercury’s magma ocean. Thermodynamic models have previously been shown to be very accurate to reproduce phase equilibria of sulfur-free Mercury-like magmas44. We used the composition of a magma ocean in equilibrium with a core containing 8 wt% Si. We then used our experimental dataset to parametrize the effect of sulfur on the liquidus (Methods, Supplementary Fig. S5, S6). The incorporation of 1 wt% S into the silicate melt under the reduced conditions of Mercury depresses the liquidus by 59 K, and the liquidus is depressed further, but by a decreasing degree, with increasing S content (Fig. 1b). Our experimental liquids contained 3.08–16.23 wt% S and the Mercurian magma ocean is predicted to contain up to 11 wt% S10, depressing the liquidus by up to 358 K compared to the S-free system (Fig. 1b). It has been shown previously that sulfur solubility in reduced silicate melts is not pressure sensitive10 so that the liquidus depression we calculate as a function of sulfur content is independent on pressure conditions. Although iron is partitioned into the core under the reduced conditions of Mercury, making the magma ocean Mg-rich, the major effect on the liquidus is the incorporation of sulfur as a major element. Carbon solubility in the reduced magma ocean is orders of magnitude lower than that of sulfur10,19 which implies that carbon has no effect on the magma ocean liquidus temperature.

Diamond in Mercury’s magma ocean
Based on the pressure-temperature conditions at the onset of crystallization in a carbon-saturated magma ocean, we calculated whether graphite or diamond was likely to be stable using the thermodynamic model of Day45. Temperature was obtained using the equation for the liquidus with 7 and 11 wt% S, pressure was calculated for each interior structure model (Methods). For a S-free magma ocean, all CMB pressure estimates plot in the graphite stability field. In contrast, if the silicate melt contained 7 or 11 wt% S, 0.6% or 8.9% of the pressure estimates, respectively, plot in the diamond stability field. We also tested the probability that diamond was stable at 50% crystallization if solidification of the magma ocean was governed by equilibrium crystallization46–48. Under those conditions, 2.5% and 20.6% of the models produce diamond at 7 and 11 wt% S, respectively. Therefore, most models support graphite precipitation during magma ocean solidification and thus a primordial graphite flotation crust21. Although not impossible, the production of diamond from the silicate magma ocean and its sinking to the CMB is statistically improbable. Carbon solubility in reduced magma ocean (<IW-3) is low when considering CO and CO2 solubility (<3 ppm; Supplementary Fig. S7). Recent experiments have shown that it could be slightly higher (up to 15 ppm) under very reduced conditions compared to thermodynamic models19. This may be due to a minor CH4 species in the melt. Nevertheless, the low solubility of carbon under reduced conditions19,20 means that any amount of diamond produced during the early stages of magma ocean crystallization would have been minor: we calculated that diamond crystallization in the magma ocean within 1 GPa above the CMB at IW−7 to IW−3 could only have produced a diamond layer 0.1 to 200 m thick, respectively and depending on the considered C solubility model (Methods, Supplementary Fig. S8). We also constrained the thickness of the graphite layer that could have been produced by carbon saturation during magma ocean crystallization to 2 to 2000 m, also depending on oxygen fugacity and the considered C solubility model (Methods, Supplementary Fig. S7). However, carbon solubility in the magma ocean does fix the lower limit for the thickness of the primordial graphite crust as graphite delivered to Mercury by the building blocks may have accumulated at the surface of the molten planet at carbon-saturation6.

Diamond from the core
Excess graphite present at the surface of Mercury suggests that the entire planet, including its core, was saturated in carbon during its primordial stage. The carbon concentration in the core of a C-saturated Mercury can be constrained by the anticorrelation between the abundances of silicon and carbon in the iron-rich metallic core [e.g., refs. 13, 14]. Using a compilation of experiments on metal-silicate equilibration (Methods, Supplementary Fig. S9), we calculated a probability density distribution for carbon concentrations in the core based on the silicon concentration in the core25 and obtained an average value of 3.4 ± 1.0 wt% C using MOI=0.333 ± 0.00524 and 1.67 ± 1.0 wt% C using MOI=0.343 ± 0.00626 (Methods, Supplementary Fig. S10). Geodetic measurements support the existence of an inner solid core with a radius 30–70% that of the outer core24,29,49. Experimental studies have shown that the inner core should be a FeSi phase50–52. The formation of the solid inner core would have caused diamond to crystallize from the residual metallic molten core. This is because crystallization of C-poor phases52 into the solid core would have for effect to enrich the liquid outer core in C. However, the whole core being at C-saturation implies that the C-enrichment will be accommodated by forming diamond in thermodynamic equilibrium with the liquid core which would then have floated to the CMB due to the much lower density of diamond compared to the liquid iron (+Si, +C, +S) alloy. Using the size of the inner core from interior model25 and considering it to be made of FeSi solid phase with 2.1 wt% C52 and the total carbon content of the fully molten core (Methods), we calculate a CMB diamond layer thickness of 14.9 ± 10.6 km using a MOI=0.333 ± 0.00524 and 18.3 ± 10.6 km with MOI=0.343 ± 0.00626 (Fig. 2). Carbides (Fe3C and Fe7C3) have also been proposed as potential products of core crystallization on Earth53,54. Because the crystallization regime in the molten core of Mercury involves the formation of Fe(Si) snow55,56, the shallow pressure and temperature conditions at CMB must be considered when evaluating the nature of crystallization products. Fe7C3 may be stable below 7 GPa and is replaced by Fe3C at higher pressure54–59. However, it has been shown that Fe3C melts in a peritectic reaction to form liquid + diamond at 1688 K at 5.7 GPa60. This is further supported by other studies which shows that at 5 GPa, Fe3C melts at ca. 1650 K57,58. All these studies support that, as compared to Earth, low-pressure core conditions on Mercury do not favor the formation of carbides which would be stable at lower temperatures.

Any diamond formed at the inner core interface and floated to the CMB very early on in the cooling history of Mercury might have transformed into graphite if CMB temperature was too high. However, compared to the primordial stage of magma ocean crystallization, the CMB today is colder61. Consequently, although the temperature at the CMB 4.5 Ga was at the upper limit for diamond stability, the CMB may now be within the diamond stability field due to secular cooling, even at the lowest estimated CMB pressure. Indeed, the probability distribution of present-day CMB temperatures25, which is consistent with independent estimates based on thermal evolution models61, nearly matches the graphite-diamond transition at the pressure of the CMB (Methods, Supplementary Fig. S11). We thus propose that the CMB today may be at the graphite-diamond transition, which may buffer the CMB temperature. The potential diamond layer thicknesses shown in Fig. 2 are thus maximum values because the extent of the graphite to diamond reaction cannot be predicted and because some early formed graphite may have been redistributed in the mantle due to strong convection and density contrast between graphite and silicate mantle minerals. In addition, convection in the lower mantle may have disrupted the diamond layer and redistributed diamond in the mantle or even in the crust. However, we believe that graphite and diamond redistribution in the silicate part of the planet was likely minimal. This is because strong convection in the lower mantle stopped at 3.7 Ga44 and that inner crystallization only started at about 4 Ga62. Most of the diamond layer or its graphite precursor therefore formed after strong mantle convection stopped which limits the extent to which the diamond layer may have been disrupted and the extent to which graphite may have been redistributed by gravitational instability. Diamond is not expected to be affected by gravitational instability because it is denser than forsterite and enstatite, the main silicate minerals of the present-day mantle. Future work should investigate how the presence of a km-scale diamond layer at the CMB would affect the thermal evolution of the silicate fraction of Mercury61. We however believe that such a thin layer could not be unambiguously confirmed using interior models fitting Mercury’s MOI and tidal Love numbers30 given the current large uncertainties on the physical properties of Mercury’s mantle and core24,25,30.

Based on geodetic data, it has been suggested that a 100 km-thick FeS layer at Mercury’s present day CMB may also exist63. The physical state (solid vs. liquid) of such a layer is unknown and experimental studies combined with geochemical data have shown that this layer, if present, should be much thinner than initially suggested from geophysics10,64,65. The occurrence of a diamond layer at the CMB is compatible with the presence of a FeS layer as both relate to the saturation of an element (C and S) during planetary differentiation. We propose that if the FeS layer is in a liquid state, the diamond layer would lie at the interface between the FeS layer and the silicate mantle. If the FeS layer is solid, the diamond layer would likely lie at the interface between the liquid outer metallic core and the solid FeS layer. Note however that given the strong density contrast between diamond (3500 kg/m3 and solid FeS 4840 kg/m3 in standard conditions) and the likely low viscosity of a hot, solid, FeS layer, gravitational instability may lead to overturn between the FeS layer and the diamond layer.

Carbon cycle on a reduced terrestrial planet
Diamond is commonly reported in meteorites and is interpreted to have been transformed from graphite by shocks on their parent bodies66. Alternatively, diamond may grow up under high-pressure within parent bodies, as reported for ureilites67, although this interpretation is debated68. It has been suggested that diamond formed during magma ocean crystallization on Earth69,70, although diamonds found at the surface are metasomatic71. Exoplanets and their compositional diversities, including potential carbon-enrichment and high C/O ratios72, may allow a variety of processes to produce diamond, from direct crystallization in the interior to impact processes at the surface73, and hydrocarbons may even play a potential role74,75. On Mercury, diamond most likely formed during core crystallization and is now stored at the CMB, and it may have also formed in the deep magma ocean. Additionally, any graphite trapped in deep magma ocean cumulates may have transformed into diamond as the interior cooled. As discussed above, disruption of the diamond layer is only plausible during the early magmatic history of Mercury. As such we believe bringing those diamonds to the surface by remelting of the deep mantle could have happened during the production of high-Mg lavas that require deep melting sources44. This could potentially be investigated by detailed observation of the High-Mg province of Mercury by BepiColombo. At the surface, though, because of the high abundance of graphite from the primordial flotation crust, we consider impacts as the main process capable of forming any significant volume of diamond via the transformation of graphite76.

These new views on the evolution of the carbon cycle on a terrestrial planet have implications for the deep storage of this life-forming volatile element77,78. Compared to other terrestrial planets, Mercury differentiated under unique reduced conditions that modify the behaviors of many chemical elements79. The partitioning of elements between reservoirs to form a Si-rich iron core and a sulfur-rich, iron-poor silicate portion makes Mercury unique. The peculiar conditions at the CMB, the formation of the solid inner core, and the saturation of the planet with carbon have likely resulted in the formation of a diamond layer at the CMB (Fig. 3). Whereas the previously proposed FeS layer at the CMB29,63,80,81 would insulate the core from cooling82, its unlikely occurrence64,65 and the evidence provided here for the presence of a highly conductive diamond layer imply that heat transfer from the liquid outer core may favor thermal stratification at the top of Mercury’s core, with potential implications for the generation of its magnetic field83.

Methods
Mercury’s core-mantle boundary
Mercury is in Cassini state 184,85, in which the obliquity of the body is directly related to its moments of inertia as:

K1(θ) (C−A)/C + K2(θ) (B−A)/C = K3(θ) (1)

where K1, K2 and K3 are constants involving the orbital eccentricity, inclination, mean motion, and planetary spin angular velocity, and explicitly the obliquity θ. A < B < C are the principal moments of inertia which are related to the amplitude of the 88-day librations (ϕ) as:

ϕ = 3(B−A)/2C (1−11e2 + 959/48 e4 +...) (2)

In Eq. 2, C should be replaced by Cm+cr, the value appropriate for the mantle (m) and crust (cr) if the mantle is decoupled from a molten core that is not involved in the 88-day librations.

The gravity field of a body of mass M and radius R can be described with spherical harmonics. Obliquity in combination with degree-2 gravity information thus provides a direct constraint on the polar moment of inertia C:

C/MR2 = (C20/(C22(B−A)/4MR2)) (3)

(B−A)/C = 4C22 / (C/MR2) (4)

Combining Eqs. 1, 3 and 4, we obtain:

C/MR2 = (C20 + 2C22) K1(θ) / K3(θ) + 4C22 K2(θ) / K3(θ) (5)

Based on the most recent estimates of MESSENGER orbital tracking data24, Mercury’s gravitational parameter (GM) is (2.20318636 ± 0.000000060) × 1013 m3 s−2. With G, the gravitational constant, being (6.67408 ± 0.00031) × 10−11 m3 kg−1 s−2, we obtain Mercury’s mass to be:

M = 3.3011 × 1023 kg (6)

The most recent gravitational field solution for Mercury (HgM008) places new constraints on C20 = (0.80415 ± 0.0003) × 10−5 and C22 = (0.80415 ± 0.0002) × 10−5. Different approaches have been followed by24,26 to obtain the obliquity and libration amplitude of Mercury, providing different estimates of Mercury’s normalized polar moment of inertia are C/MR2 = 0.333 ± 0.00524 and 0.343 ± 0.00626. We calculated the pressure conditions at Mercury’s core-mantle boundary (CMB) using the results of the Markov Chain Monte Carlo simulation of Mercury’s internal layering24.

The pressure at the CMB is calculated as:

P(r) = ∫0r ρ(x)g(x)dx (7)

with, g, the local gravity inside a sphere of radius r, defined as:

g(r) = G M(r)/r2 = G/r2 ∫0r 4π ρ(x)x2dx (8)

with M(r) being the mass within the same sphere. For these calculations, we consider that the densities of the crust (ρcr) and the mantle (ρm) are constant throughout the thickness of these two layers. We calculated Mercury’s CMB pressure conditions using the results of 439,000 simulations25. We obtained CMB pressures of 5.77 ± 0.31 GPa using the MOI of Genova et al. (2019) and 5.38 ± 0.37 GPa using Bertone et al.26 (Supplementary Fig. S1).

Experiments
Starting compositions. Synthetic silicate starting materials (Supplementary Table S1) were prepared from high-purity oxide powders: SiO2, TiO2, Al2O3, Cr2O3, MnO, MgO, CaSiO3, Na2SiO3, K2Si2O5, and AlPO4. These powders were mixed in appropriate proportions in an agate mortar. Silicon was added both as SiO2 and metallic Si (Si/SiO2 = 0.2) in order to reduce the starting material. Sulfur was added as FeS (20 wt%) to the starting silicate material (Table S1). A graphite capsule was used to ensure carbon saturation.

Experimental methods. Experiments were performed in a six-anvil cubic press with a maximum load of about 2700 tons on every WC anvil (6 × 27 MN)86. The maximum oil pressure is about 110 MPa using the diameter of the individual ram of 0.56 m. To create high pressure, six WC anvils with a square-shaped truncation and driven from three perpendicular dimensions by a computer-controlled hydraulic system pressurize the central pyrophyllite cubic block (38.5 × 38.5 × 38.5 mm3). The pyrophyllite cubic block serves as both the pressure medium and the gasket material (Supplementary Fig. S2).

Cell pressures were determined using the phase transitions of Bi (I–II transition at 2.55 GPa and III–V at 7.7 GPa), Tl (II–III at 3.68 GPa), and Ba (I–II transition at 5.5 GPa87,88. The phase transitions were detected using the resistance measurement method89. For these experiments, a hand-machined graphite bucket with an I.D. of 0.7 mm, O.D. of ∼1.7 mm, and a length of 3–4 mm, was filled with starting material and closed with a graphite lid. Temperature was monitored using a W97Re3–W75Re25 (type-D) thermocouple and Eurotherm 2404 programmable controller. The capsule was placed in the hotspot of the assembly and adjacent to the thermocouple conjunction point (less than 1 mm) to minimize the thermal gradient and obtain accurate thermocouple readings; sample temperatures were within 5 K of the thermocouple reading90. Experiments were pressurized cold to the target pressure, then heated while maintaining pressure. Experimental pressures were 7 ± 0.5 GPa and temperatures ranged from 1973 to 2273 K. Experimental durations varied between 5 min and 6 h depending on the temperature and degree of melting. Upon completion of an experiment, runs were quenched by cutting power to the heater and the temperature typically dropped to below the glass transition within 5 s.

Analytical methods. Experimental run products were mounted in epoxy and dry polished with 1 µm diamond paste. The surfaces of polished specimens were carbon-coated for backscattered electron (BSE) imagery to assess the texture and mineralogy, and for electron microprobe analysis (EMPA) to obtain accurate chemical compositions for each phase. The chemical compositions of the run product phase (silicate minerals, silicate glasses, sulfides, and metallic alloys) were determined using a JEOL JXA-8230 Electron Microprobe at the Testing Center of Shandong Bureau of China Metallurgical Geology Bureau. Major and minor elements of all phases were determined using a 15 kV accelerating voltage. A focused beam with a current of 20 nA was used to analyze silicate mineral phases. Large melt pools with quench textures were analyzed with a 20 nA beam defocused to a diameter of 20 µm. A defocused beam with a diameter size of 5–10 µm and 5–10 nA was used to analyze small melt pools in order to minimize beam damage and avoid alkali migration. Sulfides and metallic alloys were analyzed with 15 kV and 20 nA focused beam. The standards were natural minerals and synthetic oxides for silicate phases (Si and Na, Jadeite; Ti, Rutile; Al, Garnet; Fe, Fayalite; Mg, Forsterite; Ca, Diopside; K, Sanidine; Cr, Chromite; Mn, Rhodonite; P, Apatite; S, pyrrhotite). Natural sulfide minerals and pure metals were used as standards for sulfide and metallic alloys to minimize the matrix effect. Peak and background counting times were between 10 and 20 s depending on the concentration of each element. Compositions reported here are based on 3–10 analyses per phase. The average compositions and standard deviations of analyzed phases of all experiments are shown in Supplementary Data 1. BSE images of representative run products are shown in Supplementary Fig. S3. Mineral and melt proportions were determined by mass balance using the EMPA data for run product phases. Raman spectroscopic measurements were carried out using a Raman micro-scope equipped with a Renishaw inVia Raman spectrometer, a 532 nm laser, and a 20× objective. The instrument was routinely calibrated using a silicon standard. Analyses were performed using 2400 grooves mm−1, an exposure time of 10 s, and 2 accumulations. The backscattered Raman radiation was collected on a polished sample surface over the range 100–2000 cm−1 (Supplementary Fig. S4).

Calculation of oxygen fugacity. Oxygen fugacity (fO2) in the experiments were calculated relative to the iron-wüstite (Fe-FeO; see below) using the following expression:

ΔIW = 2 log(asilicateFeO / ametalFe) (9)

Where asilicateFeO and ametalFe are the activities of FeO in the silicate melt and Fe in the molten metal, respectively. Activities should be calculated using the activity coefficient (γ) and the mole fraction (χ). In this study, we however assumed ideal solutions so that γFeO = 1.0 and γFe = 1.0.

Mercury’s magma ocean liquidus
We calculated the most likely distribution of Si in Mercury’s core using the results of Goossens et al.25 to be 3.4 ± 1.0 wt% (x ± 1σ) using MOI=0.333 ± 0.00524 and 1.67 ± 1.0 wt% (x ± 1σ) using MOI=0.343 ± 0.00626. We thus calculated the liquidus curve of three S-free bulk silicate compositions (EH-EL (BSM), with no Si in the core; SiCore4, with 4 mol% Si in the core; and SiCore8, with 8 mol% Si in the core; Supplementary Table S1). We tracked the liquidus curve using the thermodynamic model of Holland et al.43 as implemented in the MAGEMin Gibbs free energy minimization software42.

Calculations were performed over six successive iterations to track the boundaries between melt and forsterite and/or enstatite. Following the approach of 91, we parameterized the liquidus equations as:

Tliq,BSM = 2092 + 3.40P + 16.88P2 − 2.43P3 + 0.14P4 (10a)

Tliq,BSM-SiCore4 = 2106 − 7.46P + 25.93P2 − 4.47P3 + 0.27P4 (10b)

Tliq,BSM-SiCore8 = 2124 + 5.58P + 14.28P2 − 2.23P3 + 0.14P4 (10c)

The calculated liquidus curves from 0 to 8 GPa are shown in Supplementary Fig. S5. Comparison of these calculated liquidus curves for S-free compositions allows us to estimate the impact of S on depressing the liquidus. At 7 GPa, the pressure of the experiments performed in this study, the three S-free bulk compositions had very similar liquidus temperatures of ∼2450 K. At the same pressure, our experiments with 6 wt% S had a liquidus temperature of ∼2215 K. Because pressure has no significant effect on sulfur solubility in reduced magmas10, a single non-linear expression is used to define the liquidus depression per wt% S as:

dT/dS = 59.2 XS0.75 (11)

In Eq. 11, we used a power factor identical to that determined for H2O92,93. The liquidus depression trend that we calculate is of the same order of magnitude as that determined for the effect of H2O on the olivine or plagioclase liquidi in basalt92,94 (Supplementary Fig. S6).

Graphite–diamond transition
Graphite and diamonds are two polymorphs of elemental C; diamond is the high-pressure polymorph whereas graphite is the low-pressure polymorph. The transition between the two phases was calculated using the model of Day45 for the reaction:

CGraphite = CDiamond (12)

The Gibbs free energy of reaction (Eq. 12) in standard conditions (ΔGor) is the enthalpy of formation (ΔHof) and entropy (So):

ΔGor = ΔHof − TΔSof (13)

Enthalpy and entropy terms were calculated at the temperature of the reaction using a Maier-Kelly polynomial expression of the heat capacity (CP):

CP = a + bT + cT−2 + dT−0.5 + eT2 + fT−3 + gT−4 + hT3 (14)

The contribution to the Gibbs free energy due to variations in pressure (VδP) is calculated using an equation of state following the formalism of Murnaghan95:

V = V0 (1 + nB0 P)−1/n (15)

where V is volume, V0 is the volume at zero pressure, P is pressure, B0 is the initial bulk modulus and n is the pressure derivative of the bulk modulus.

For both phases, V is calculated at a given temperature using expressions of thermal expansion:

(V/V0)Gr = 1 + α0(T−298) − 20α0(T0.5−2980.5) (16a)

(V/V0)Dia = exp(3 ∫ θ=T θ=T0 exp(θ/T)−1) (16b)

All thermodynamic parameters used in Eq. 13, 14, 15, 16a and 16b are given in Day45.

Carbon in Mercury’s mantle
Carbon solubility. We calculated the solubility of C in Mercury’s mantle, i.e., the maximum C content at graphite or diamond saturation, using two models. In the first, we used the experimental regression of Li et al.19:

log C [ppm] = 0.96 log XH2O − 0.25 ΔIW + 2.83 (17)

with ΔIW being the oxygen fugacity (fO2) relative to the Fe–FeO buffer. We calculated the fO2 of IW using the Gibbs free energy of formation (ΔGof) of FeO listed in the NIST-JANAF Thermochemical Tables. We considered XH2O = 0.01.

In the second model, we calculated the solubility of C based on the following two thermodynamic equilibria:

2C + O2 = 2CO (18a)

C + O2 = CO2 (18b)

We calculated fCO and fCO2 as a function of fO2 using the ΔGof values for CO and CO2 listed in the NIST-JANAF Thermochemical Tables. Fugacities were then linked to the total C content of Mercury’s magma ocean using the expression:

C [ppm] = KCO fCO + KCO2 fCO2 (19)

where KCO and KCO2 are Henry’s constants of CO and CO2 provided by Keppler and Golabek20. Results of the two calculation methods are provided in Supplementary Fig. S10.

Using the model of Li et al.19 and considering that Mercury differentiated at fO2 between IW-5 and IW-610, we calculate a total carbon content of 7-15 ppm C in the magma ocean. Thermodynamic calculations of CO and CO2 solubility20 are 1 or 2 order of magnitudes lower (0.06 to 0.2 ppm). We are not aware of any study evaluating the effect of C content on the liquidus of mafic magmas. However, by analogy with H2O93, we calculate that C depresses the liquidus by less than 1 K. This is obviously insignificant on comparison to the large effect of S on the liquidus depression.

Thickness of graphite or diamond layers from the magma ocean
We calculated the thickness that a floated graphite layer would have if all carbon dissolved in the magma ocean formed graphite during cooling and crystallization. For these calculations, we considered a core radius of 1950 km25, a magma ocean density (ρ) of 3000 kg m−3, and a graphite density of 2100 kg m−321. Results are shown in the right panel of Supplementary Fig. S7.

We also hypothesized that the deepest part of Mercury’s magma ocean might crystallize diamond instead of graphite. We considered that only the lowest ∼79 km of the magma ocean, corresponding to 4.77–5.77 GPa, could be in the stability field of diamond. Using a diamond density of 3500 kg m−3 and considering that diamond would accumulate at the interface between the liquid core and the magma ocean, we calculated the thickness of the diamond layer as shown in Supplementary Fig. S8.

Carbon in FeSi metal
The carbon content in carbon-saturated FeSi metal was recently investigated13 based on new high-temperature, low-pressure experiments and a review of the metallurgic literature. We extended this review by compiling 598 experiments containing metal in C-saturated systems. We ultimately used only 244 experiments with metal containing 0.25–25 wt% Si to ensure that all metals were well within the Fe-Si-C system and had C and Si concentrations above the detection limits for bulk and in situ analytical methods. Using these experiments, we observed a coherent trend of decreasing bulk C content with increasing Si content in the metal (Supplementary Fig. S9). We do not observe any temperature-dependency on C solubility in FeSi metal as already suggested13. We therefore modeled C solubility [wt%] as a function of the metal Si content [wt%] as:

CFe-Si = 5.48 − 0.45 Si + 0.009 Si2 (20)

Using Eq. 20 and the geophysical results25, we defined the distribution of plausible C concentrations in the metallic alloy if C-saturated (Supplementary Fig. S10). We also consider the incorporation of carbon in the FeSi solid inner core by using a liquid/solid partition coefficient of 0.352.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_2": "Review of “A diamond-bearing core-mantle boundary on Mercury” by Xu et al. submitted to Nature\nCommunications\nThis manuscript is well written and organized. The authors present new high P-T experimental data on\nthe liquidus of Mercury’s magma ocean analog combined with thermodynamic modeling and revised\ngeodetic calculations to evaluate the stability of graphite/diamond at Mercury’s core-mantle boundary\n(CMB) conditions. The authors claim that with sulfur as a major element in the magma ocean, it is likely\nalthough not statically favorable that diamond could have crystallized at the bottom of the magma\nocean. In addition, the authors also suggest that the crystallization of a FeSi solid inner core would\nexsolve C as diamond, which would float to CMB and become stable with secular cooling. This study\ndefinitely presents a very interesting story that may significantly improve our understanding of the\ninternal structure and evolution of Mercury, particularly for diamond formation processes on planetary\nbodies, and is expected to interest a broad range of readers in Earth and planetary science. While I\nrecognize the importance and novelty of this study, I do have some concerns about the experimental\ndetails, as well as some interpretations of the data. As such, I think this paper would be suitable for\npublication in Nature Communications, given that the authors could address the comments raised below\n.\nDetailed comments:\n(1) As stated throughout the whole manuscript, the authors assumed that the early magma ocean and\nthe core of Mercury were saturated with carbon. However, the starting materials for the experiments\nsimulating Mercury’s magma ocean do not have any carbon (Table S1). So I am a bit confused, how the\nliquidus T of a magma ocean with compositions that could not crystallize any carbon-bearing phases can\nbe used to place constraints on the occurrence and thermodynamic stability of diamond during the\nmagma ocean crystallization? I might have missed something in the manuscript, but the authors have\nnot clearly discussed this in the experimental section. The authors added FeS to the starting materials to\naccount for the potential of sulfur as a major element in the magma ocean due to its abundance on\nMercury’s surface, although the exact amount of added FeS is not given in the manuscript. But for\ncarbon, it was not clearly discussed. Although carbon solubility in silicate melts may be low, the magma\nocean should have some in order to generate graphite/diamond. And also, whether the presence of\ntrace amount of carbon can affect the liquidus of the magma ocean also needs to be discussed. Overall, I\nthink the choice of starting materials needs more justification if a revision is extended by the editor.\n(2) The experiments were performed only at 7 GPa, which is higher than the estimated pressure range at\nCMB, I am curious why the authors chose a higher pressure. Higher pressure tends to favor the\nstabilization of diamond, and may also affect the solubility of sulfur as well, would this introduce any\nbias in the model without any relatively lower pressure experimental data point? Speaking of sulfur\ncontent, I couldn’t find in Figure 1 or Table S1 the sulfur content in the experiments, neither the amount\nof S added to the starting materials nor the measured S content in the quenched melt. As these are critical\nparameters for evaluating the effect of sulfur on the liquidus depression, they should be reported either\nin the table or labelled in the figure for each experiment.\n(3) Related to the above comment, it seems like the experimental results were mainly used to estimate\nthe effect of sulfur on the liquidus depression at 7 GPa, compared with sulfur-free liquidus obtained\nfrom thermodynamic models. I am wondering why the authors did not perform an experiment on sulfur-\nfree composition so that the effect of sulfur can be evaluated in a more consistent way, and then the\nthermodynamic model can also be compared with and calibrated by the sulfur-free experiments. To me,\nthermodynamic models always have inherent uncertainty that might be different than those from the\nexperiments, particularly if the model has not been calibrated by compositions and conditions relevant\nto Mercury’s interior. So using the modeled liquidus as a basis for evaluating experimental results,\nalthough still useful, is probably less convincing if the calculated liquidus has not been compared with\nexperiment.\n(4) As I am an experimentalist, I might be a bit picky about the experimental details presented in this\npaper. I am a bit surprised that the authors could achieve ~7 GPa using such a large cell assembly (~52.5\nmm). A large cell assembly will inevitably have large thermal gradient cross the sample. I wonder if the\nauthors have calibrated the thermal gradient in the cell, either by experiments or thermal modeling?\nSince the reported T is close to the boundary of graphite/diamond transition and all the rest discussions\nrely on the degree of liquidus depression, accurate determination of the T within the sample is crucial.\nAnd also, please provide a schematic drawing of the cell assembly used for the experiments, which\nwould help the readers easily get the information on the experiments. In addition, the authors\nmentioned the pressures were calibrated by several phase transitions, but those phase transitions listed\nin the paper are all for room-T calibration. Has any high-T phase transition been used in the\ncalibration? As the current experimental T is high (>2000 K), the pressure change due to thermal\npressure and thermal relaxation of the cell at high T would be significant. If the pressure was only\nestimated from room-T calibration, it might significantly deviate from the estimated room-T value at\nhigh T. Such uncertainties also need to be considered when evaluating the P-T conditions of the magma\nocean.\n(5) In terms of the carbon content in Mercury’s mantle, it looks like the two approaches the authors\nemployed predict totally different fO2 dependence of the carbon content, as well as the resulting\nthickness of the graphite/diamond layer (e.g., Fig. S8). I wonder if the authors could compare the\nestimated carbon content in the magma ocean with the measured carbon content in the crust, not just\nthe thickness, assuming all carbon in the magma ocean turned into graphite in the crust. Since we have\na relatively good knowledge of the abundance of carbon in the crust, such comparison may help evaluate\nwhich model predicts the carbon content more precisely. And, we can also evaluate from this\ncomparison whether the carbon exsolution from the core, according to the authors’ hypothesis, might\nhave also contributed to the graphite crust formation in the early stage when the T at CMB was high.\nSome minor issues:\n(1) Quite a few figures and tables are cited incorrectly in the main text. The authors should check the\norder of their figures/tables, and make sure they are mentioned correctly in the appropriate position in\nthe text.\nFor example,\nLine 93: Table S1 does not provide any info on the oxygen fugacity\nLine 136: I think Fig. S8 here should be Fig. S9\nLine 139: Fig. S7 should be Fig. S8\nLine 147: Fig. S5 should be replaced by Fig. S6\nLine 155: I don’t know which figure the authors refer to (Fig. S7?), but there’s no Fig. 2a in the\nmanuscript.\nLine 305: No Table S2 (Appendix) provided\nLine 321 and 330: Table 2 should be Table S2 in the Supplementary Materials\nLine 452: Is the Supplementary Table S1 refer to the attached excel file which the authors sometimes\nrefer as Appendix? Please unify the naming of all supporting figures and tables in a consistent way to\navoid confusion.\n(2) Figure S10, the legend in the figure and the description in the caption do not match\n(3) Lines 127-130: I think a figure is needed for this description\n(4) Line 196: I think a word is missing here. It should be “reduced conditions”\n(5) Table S2. This table reports sulfur-free magma ocean compositions used in the thermodynamic\nmodeling, and Table S1 also reports sulfur-free compositions used in the experiments (the added\namount of FeS is not given!). So I suppose the composition for Mer8 in Table S1 should be similar to that\nof BSM-SiCore8 in Table S2. I think it might be better to merge the two tables into one and use the same\nunit for the composition or report both mol% and wt% to facilitate comparison.\n(6) Line 380: Please check the equation to make sure it’s correct\n(7) The excel file Table S1 Summary of experimental results. I think the added FeS amount for each\nexperiment should also be listed. A quick look at the table shows that the glass composition with the\nhighest sulfur content (~16.23%, run Mer8-2) is significantly different than the glass composition in other\nexperiments (much lower MgO content, significantly higher CaO, Na2O and K2O content), probably due\nto its small fraction causing difficulty in analyzing? Would this affect the interpretation of the sulfur effect\non melt liquidus?", "reviewer_3": "Summary:\nThe manuscript Xu et al. presents novel high-temperature and high-pressure experiments and liquidus\nthermodynamic modelling to understand the stability of graphite vs. diamond, finding diamond was\npossibly, though statistically unlikely, to be stable in Mercury’s silicate magma ocean, but would be\npredicted to form a thick layer at the current core-mantle-boundary (CMB). A conductive diamond layer\non top of the CMB would have significant implications for Mercury’s thermochemical evolution given its\nopposite properties to an unlikely insulating FeS layer. The manuscript is extremely well written and\nthorough in its incorporation of literature data and plentiful supplementary figures. I recommend\nacceptance.\nQuantifying the effect of S on melting T in itself is a super interesting result worth highlighting and\nfurther study (either adding to the main text or in another manuscript rather than hidden in the\nsupplementary). Please expand on the form of equation 12 to define the liquidus depression per wt% S.\nIt is interesting that it is on the same order of magnitude of the effect of H2O on olivine or plagioclase\nliquidi in basalt. Would be interesting to comment on whether the S effect changes with pressure too.", "reviewer_4": "In this manuscript, Xu et al. explore the possibility of a diamond-bearing layer at the core-mantle\nboundary in Mercury. They utilized experimental techniques to understand the geochemistry and phase\nstability of Mercury relevant compositions, paring the results with geophysical models to estimate the\ndynamics of diamond growth and mobility in the mantle and core. This is a novel idea and has the\npotential to have an impact on Mercury science. However, there are several major points that I believe\nneed to be addressed before this can be suitable for publication.\n-Other work has suggested that there would be an FeS layer at the core-mantle boundary (CMB) (e.g.,\nHarder & Schubert, 2001; Smith et al., 2012; Hauck et al., 2013) as a way to explain the moment of\ninertia (MOI) and the abundance of S on the surface. This seems to be taking a similar approach, just\nfrom the perspective of C. Is this an alternative to the FeS hypothesis? Do these analyses fit with the\nMOI measurements better than a possible FeS layer? I think evidence as to how this is a more plausible\nhypothesis (if this is indeed the case) will strengthen this work.\n[https://doi.org/10.1006/icar.2001.6586 https://doi.org/10.1126/science.1218809\nhttps://doi.org/10.1002/jgre.20091]\n-Please provide a pressure scale on Figure 3.\n-Regarding lines 152-154, are the diamonds growing and mobilizing from what is interpreted to be the\nliquid outer core or are diamonds co-crystallizing as the core solidifies? Clarification would be helpful.\nRelated to this point, at what timescale would this occur at and when would a diamond layer be\nexpected to be present at the CMB?\n-In the section starting at Line 70, the CMB pressure is calculated to be 5.77 GPa and in lines 108-109\nit is stated that the pressure at the bottom of Mercury’s magma ocean was similar to present CMB,\nbut the experiments are run at 7 GPa. What is the rationale for this- why weren’t experiments conducted at\na pressure that is more similar to the predicted CMB pressure calculated in this work?\n-At Mercurian CMB pressure conditions and a range of relevant temperature (early and present) this is\nsitting at metastability for diamond and graphite which is mentioned in line 176. I am not convinced at\nthe possible longevity of this layer, lasting long enough to be measurable via MOI today. If some of the\nlayer were to transform to graphite, it would be gravitationally unstable and reduce the thickness of the\nlayer, thus dampening the effect of this diamond bearing layer. Additionally, convection in the first Ga\nof Mercury’s history could disrupt a diamond layer and redistribute in the mantle.\n-The density of the solidified magma ocean and diamonds needs to be scaled with pressure. With the\nminerals being considered (e.g., opx, cpx, garnet, olivine) the density is likely greater than the 3000\nkg/m3 being considered when solidified. This could be an issue thinking about gravitational stability of\ndiamond below a potentially denser silicate at the CMB after the magma ocean stage.\n-Figure S2a- it looks like there is a mid-gray phase surrounding the large phase that is labeled “Sf” (and\nsome of the smaller sulfides). In experiments that are rich in Fe and S that are at lower temperatures\n(which S2a is the lowest T) there is phase separation of a sulfide-rich rim with a metal (Fe)-rich core,\nevolving to a single phase with increasing temperature. Is this the case for this experiment that there\nare indeed two phases? If so, it would be beneficial to label the two phases appropriately.\n-Lines 275-275- what assembly was used (e.g., 14/8)? Were WC cubes used for these experiments?"}, "author_response": "Response to reviewer comments\n[Referee comments in italics, responses in normal font and blue]\nReviewer #2 (Comments for the Author):\nReview of “A diamond-bearing core-mantle boundary on Mercury” by Xu et al. submitted to Nature\nCommunications\nThis manuscript is well written and organized. The authors present new high P-T experimental data on\nthe liquidus of Mercury’s magma ocean analog combined with thermodynamic modeling and revised\ngeodetic calculations to evaluate the stability of graphite/diamond at Mercury’s core-mantle boundary\n(CMB) conditions. The authors claim that with sulfur as a major element in the magma ocean, it is\nlikely although not statically favorable that diamond could have crystallized at the bottom of the magma\nocean. In addition, the authors also suggest that the crystallization of a FeSi solid inner core would\nexsolve C as diamond, which would float to CMB and become stable with secular cooling. This study\ndefinitely presents a very interesting story that may significantly improve our understanding of the\ninternal structure and evolution of Mercury, particularly for diamond formation processes on planetary\nbodies, and is expected to interest a broad range of readers in Earth and planetary science. While I\nrecognize the importance and novelty of this study, I do have some concerns about the experimental\ndetails, as well as some interpretations of the data. As such, I think this paper would be suitable for\npublication in Nature Communications, given that the authors could address the comments raised\nbelow.\nReply: We appreciate that reviewer #2 recognizes the importance and novelty of our study and for\nrecommending publication of our paper after revision. Below we provide detailed replies to all points\nthe reviewer raises. Comments made by reviewer #2 enable us to explain more carefully the\nexperimental approach and the relevance of P-T conditions we investigated. However, the main\nconclusions of our study remain unchanged.\nDetailed comments:\n(1) As stated throughout the whole manuscript, the authors assumed that the early magma ocean and\nthe core of Mercury were saturated with carbon. However, the starting materials for the\nexperiments simulating Mercury’s magma ocean do not have any carbon (Table S1). So I am a bit\nconfused, how the liquidus T of a magma ocean with compositions that could not crystallize any\ncarbon-bearing phases can be used to place constraints on the occurrence and thermodynamic\nstability of diamond during the magma ocean crystallization? I might have missed something in the\nmanuscript, but the authors have not clearly discussed this in the experimental section. The authors\nadded FeS to the starting materials to account for the potential of sulfur as a major element in the\nmagma ocean due to its abundance on Mercury’s surface, although the exact amount of added FeS\nis not given in the manuscript. But for carbon, it was not clearly discussed. Although carbon\nsolubility in silicate melts may be low, the magma ocean should have some in order to generate\ngraphite/diamond. And also, whether the presence of trace amount of carbon can affect the liquidus\nof the magma ocean also needs to be discussed. Overall, I think the choice of starting materials\nneeds more justification if a revision is extended by the editor.\nReply: We thank the reviewer for pointing this out. A graphite capsule was used in our experiments to\nensure carbon saturation in the starting material. The addition of carbon to the starting powder is thus\nnot necessary. The use of a graphite capsule was already mentioned in the caption of Figure 1 and\nreported also in the Methods section (in Experimental methods). Nevertheless, we added the sentence\n“A graphite capsule was used to ensure carbon saturation.” to the section on “Methods – Starting\ncomposition”.\nThe exact amount of FeS added to the starting materials has also been reported in “Methods – Starting\ncomposition”. We also added the relative fraction of Si and SiO used in the starting silicate material.\ncarbon solubility in the silicate melt in the section on “Carbon in Mercury’s mantle – Carbon solubility”.\nIn the revised version, we now provide additional information on the concentration of carbon to be\nexpected in the magma ocean and show that those very low values cannot have any significant effect\non the liquidus of the magma ocean as compared to the effect of sulfur. The following paragraph has\nbeen added at the end of the section “Carbon in Mercury’s mantle – Carbon solubility”.\nUsing the model of 19 and considering that Mercury differentiated at a fO between IW-5 and IW-\n2\n610, we calculate a total carbon content of 7-15 ppm C in the magma ocean. Thermodynamic\ncalculations of CO and CO solubility20 are 1 or 2 order of magnitudes lower (0.06 to 0.2 ppm). We\n2\nare not aware of any study evaluating the effect of C content on the liquidus of mafic magmas.\nHowever, by analogy with H O94, we calculate that C depresses the liquidus by less than 1K. This is\n2\nobviously insignificant on comparison to the large effect of S on the liquidus depression.\nIn the main text we added the following sentence: ‘Carbon solubility in the reduced magma ocean is\norders of magnitude lower than that of sulfur10,14 which implies that carbon has no effect on the\nmagma ocean liquidus temperature.’\nsilicate melts: Implications for the speciation and distribution of sulfur on Mercury. Earth and Planetary\nScience Letters 448, 102-114, doi:http://dx.doi.org/10.1016/j.epsl.2016.05.024 (2016).\nImplications for the degassing of Mars, Mercury, and the Moon. Journal of Geophysical Research:\nPlanets 122, 1300-1320, doi:https://doi.org/10.1002/2017JE005289 (2017).\nformation. Geochemical Perspectives Letters 11, 12-17, doi:https://doi.org/10.7185/geochemlet.1918\n(2019).\nGeochem. Geophys. Geosyst. 4, 1073, doi:10.1029/2002gc000433 (2003).\n(2) The experiments were performed only at 7 GPa, which is higher than the estimated pressure range\nat CMB, I am curious why the authors chose a higher pressure. Higher pressure tends to favor the\nstabilization of diamond, and may also affect the solubility of sulfur as well, would this introduce any\nbias in the model without any relatively lower pressure experimental data point? Speaking of sulfur\ncontent, I couldn’t find in Figure 1 or Table S1 the sulfur content in the experiments, neither the amount\nof S added to the starting materials nor the measured S content in the quenched melt. As these are\ncritical parameters for evaluating the effect of sulfur on the liquidus depression, they should be reported\neither in the table or labelled in the figure for each experiment.\nReply: 7 GPa is actually not higher than the estimated pressure range at CMB, but corresponds to the\nmaximum value of potential pressures predicted by models of Goossens et al. (2022) using the\nnormalized polar moment of inertia of Genova et al. (2019) (the model actually predicts values up to\n7.19 GPa). It is true that pressure tends to favor the stabilization of diamond (at constant temperature).\nBut a higher pressure also implies a higher liquidus temperature of the silicate melt which does not\nfavor diamond stability (but favors graphite stability).\nRunning experiments at 7 GPa does not introduce any bias to the main conclusion of the paper\nbecause our results are based not only on experiments but on the combination between\nexperimental results and careful modelling to cover the full P-T range of CMB conditions. It is\ntrue that running experiments at 7 GPa enabled us to test the most favorable experimental conditions to\nproduce diamond. This does not imply that our conclusions are forced to support diamond stability\nbecause our experimental results are implemented into models to interpolate the diamond-graphite\nstability for the whole range of potential CMB pressures predicted by models of Goossens et al. (2022).\nAs shown in Figure 1a of the paper, the temperature of the diamond-graphite transition is also close to\nthe liquidus of the two starting compositions (Mer8 and Mer15). Additionally, a suite of experiments\non sulfur solubility under reduced conditions were already available at pressure <4GPa, enabling us to\ninterpolate any results between our experimental pressure (7 GPa) and those of Namur et al. (2016).\nWe added this sentence to the main text to make this clear: “This pressure corresponds to the maximum\nvalue of potential CMB pressures predicted by interior models25.”\nWe changed the first part of the result section by adding the following sentence: “We used planetary\ninterior structure models that satisfy the various measurements of MOI25 to calculate that the pressure\nat Mercury’s CMB is 5.77 ± 0.31 GPa with a low MOI24 and 5.38 ± 0.37 GPa with a high MOI26\n(Methods and Supplementary Fig. S1). According to our calculations, the highest possible pressure of\nMercury’s CMB is 7 GPa. We here provide experimental melting relations at 7 GPa to determine\nexperimentally the carbon speciation at the most extreme pressure conditions of Mercury’s magma\nocean. Experiments are then combined with thermodynamic modelling to investigate how phase\nrelations change for lower pressure CMB conditions which would still match Mercury’s MOI.”\nThe role of pressure on sulfur solubility was discussed in Namur et al. (2016) who did not identify any\nsignificant effect as compared to oxygen fugacity, temperature, and melt composition. There is thus no\nreason to suspect that a slightly lower pressure (e.g. 5.5 GPa vs. 7 GPa) would have any effect on the\nconclusions of this study. Anyway, the effect of pressure on the liquidus temperature is considered in\nthus study, as well as the effect of sulfur content. Any effect of pressure on sulfur solubility would not\naffect the model.\nWe have slightly modified the manuscript to make this clear by adding “Because pressure has no\nsignificant effect on sulfur solubility in reduced magmas10, a single non-linear expression is used to\ndefine the liquidus depression per wt% S”.\nIn the main text we added the following sentences: “It has been shown previously that sulfur solubility\nin reduced silicate melts is not pressure sensitive10 so that the liquidus depression we calculate as a\nfunction of sulfur content is independent on pressure conditions.”\nFinally, the S content for each experiment was reported in the Table S1 of the submitted manuscript.\nWe do not know if the format was changed from an excel table to a pdf version. We apologize for this\npotential confusion.\n(3) Related to the above comment, it seems like the experimental results were mainly used to estimate\nthe effect of sulfur on the liquidus depression at 7 GPa, compared with sulfur-free liquidus obtained\nfrom thermodynamic models. I am wondering why the authors did not perform an experiment on sulfur-\nfree composition so that the effect of sulfur can be evaluated in a more consistent way, and then the\nthermodynamic model can also be compared with and calibrated by the sulfur-free experiments. To me,\nthermodynamic models always have inherent uncertainty that might be different than those from the\nexperiments, particularly if the model has not been calibrated by compositions and conditions relevant\nto Mercury’s interior. So using the modeled liquidus as a basis for evaluating experimental results,\nalthough still useful, is probably less convincing if the calculated liquidus has not been compared with\nexperiment.\nReply: This comment by reviewer #2 seems fully relevant at first sight but is confronted with the reality\nof the experimental approach that would not enable us to test experimentally the difference in\ntemperature of the liquidus for a sulfur-free vs. a sulfur-bearing experiments.\nIn our study, we did not produce experiments just at the liquidus of the starting compositions. Instead,\nwe have produced a suite of experiments for two starting compositions over a range of temperature. For\neach of those experiments, we have obtained a silicate glass with a composition varying with\ntemperature (and the degree of crystallinity). In order to obtain the liquidus of each specific sulfur-free\ncompositions, it would have been necessary to synthetize a new starting composition for each\nexperiment (18 in total). For each of those starting compositions, it would have been necessary to run\nat least 4 experiments at different temperatures to identify precisely the liquidus, meaning that 72\nexperiments would have been necessary to follow the approach recommended by reviewer #2. This is\nunrealistic.\nWe decided to use the liquidus temperature of sulfur-free compositions predicted by the MAGEMin\nthermodynamic calculator because, in a previous study by Namur et al. (2016), it was clearly proved\nthat liquidus temperature predicted by available Gibbs free minimization models give accurate results\n(within +- 21°C (see figure below from the supplementary materials of Namur O, Collinet M, Charlier\nB, Grove TL, Holtz F, McCammon C (2016) Melting processes and mantle sources of lavas on Mercury.\nEarth and Planetary Science Letters 439:117-128 doi:http://dx.doi.org/10.1016/j.epsl.2016.01.030). As\ncompared to a liquidus depression of ca. 250-350°C for sulfur-bearing Mercury-like compositions, the\nerror resulting from thermodynamic models is less than 10% of the absolute temperature depression.\nThis minor error would not justify the need for running sulfur-free experiments.\n[Redacted]\nWe added the following sentence in the manuscript: ‘Thermodynamic models have previously been\nshown to be very accurate to reproduce phase equilibria of sulfur-free Mercury-like magmas45.’\n(4) As I am an experimentalist, I might be a bit picky about the experimental details presented in this\npaper. I am a bit surprised that the authors could achieve ~7 GPa using such a large cell assembly\n(~52.5 mm). A large cell assembly will inevitably have large thermal gradient cross the sample. I\nwonder if the authors have calibrated the thermal gradient in the cell, either by experiments or thermal\nmodeling? Since the reported T is close to the boundary of graphite/diamond transition and all the rest\ndiscussions rely on the degree of liquidus depression, accurate determination of the T within the sample\nis crucial. And also, please provide a schematic drawing of the cell assembly used for the experiments,\nwhich would help the readers easily get the information on the experiments. In addition, the authors\nmentioned the pressures were calibrated by several phase transitions, but those phase transitions listed\nin the paper are all for room-T calibration. Has any high-T phase transition been used in the\ncalibration? As the current experimental T is high (>2000 K), the pressure change due to thermal\npressure and thermal relaxation of the cell at high T would be significant. If the pressure was only\nestimated from room-T calibration, it might significantly deviate from the estimated room-T value at\nhigh T. Such uncertainties also need to be considered when evaluating the P-T conditions of the magma\nocean.\nReply: We thank the reviewer for pointing these out. In general, a higher temperature is observed at the\ncenter of the experimental assemblage and gradually decreases towards the edge in a commonly used\n14/8 assembly in a multi-anvil press. The larger assembly we used in a Cubic press (a bit different than\na common multi-anvil press) does not necessarily result in a thermal gradient through the sample.\nActually, a larger assembly has thicker thermal insulation material than the assembly used in a common\nmulti-anvil press, which can efficiently prevent the heat loss from the center and create a smaller thermal\ngradient at the hot-spot region. In our assembly, the graphite capsule itself serves as a heater, and the\nthermocouple junction penetrates the heater and is adjacent to the sample capsule. The thermal gradient\nis generally thought to be insignificant. We provide a schematic drawing of the cell assembly used for\nour experiments as a new Fig. S2. A detailed description of this assembly is shown in Fig. 3 in Wu et\nal. (2024) [this paper has just been published in Wu P, Xu Y, Lin Y (2024) A novel rapid cooling\nassembly design in a high-pressure cubic press apparatus. Matter and Radiation at Extremes 9, 027402.\ndoi:10.1063/5.0176025\nFig. S2: Cubic press experimental assembly shown in vertical section, cross section, and 3D model. A\nslim graphite rod (2.5 mm in diameter) is placed vertically in the center of the assembly, and sample\ncapsules are inserted into this rod. In addition, two sample capsules can be done at the same time, and\nthe thermocouple junction is placed between the capsules in the center of the assembly. The length of\ncube edge is 38.5 mm.\nWe also did the pressure calibration at high-T with the phase transition diamond-graphite at 7 GPa (Day,\n2012; A revised diamond-graphite transition curve, American Mineralogist). In our manuscript., the\ndashed line in Fig. 1a shows that the diamond-graphite transition is constrained at 2348±25 K and 7\nGPa by our experiments, which is consistent with the temperature of diamond-graphite transition at 7\nGPa in the Fig. 7 shown in Day (2012). This demonstrates that our experimental pressure calibration is\nreliable. We clarify this in lines 108-111.\nThe vertical dashed line at 2356 K is the diamond-graphite transition at 7 GPa42, consistent with Raman\nspectra of ‘graphite’ capsules in our experiments at 2323 and 2373 K (Supplementary Fig. S4),\ndemonstrating that the experimental pressure is reliable.\n(5) In terms of the carbon content in Mercury’s mantle, it looks like the two approaches the authors\nemployed predict totally different fO2 dependence of the carbon content, as well as the resulting\nthickness of the graphite/diamond layer (e.g., Fig. S8). I wonder if the authors could compare the\nestimated carbon content in the magma ocean with the measured carbon content in the crust, not just\nthe thickness, assuming all carbon in the magma ocean turned into graphite in the crust. Since we have\na relatively good knowledge of the abundance of carbon in the crust, such comparison may help\nevaluate which model predicts the carbon content more precisely. And, we can also evaluate from this\ncomparison whether the carbon exsolution from the core, according to the authors’ hypothesis, might\nhave also contributed to the graphite crust formation in the early stage when the T at CMB was high.\nReply: Comparing the estimated carbon content in the magma ocean with the measured carbon content\nin the crust is not relevant to us for one major reason: the amount of graphite produced by solidification\nof dissolved carbon in the magma ocean should be considered as the minimum amount of graphite in\nthe crust because any carbon/graphite delivered to Mercury by building blocks above the saturation\nvalue for the planet would remain undissolved at the surface of the planet to form the primordial crust\n(possible reprocessed in the secondary volcanic crust).\nThis was explained in the manuscript by this sentence “However carbon solubility in the magma ocean\ndoes fix the lower limit for the thickness of the primordial graphite crust as graphite delivered to\nMercury by the building blocks may have accumulated at the surface of the molten planet at carbon-\nsaturation5.”\nMoreover, the idea that “we have a relatively good knowledge of the abundance of carbon in the crust”\nis not that obvious to us when considering at the range of values proposed by different authors (<1 to >\n3 wt.%). It is also unknown whether these values are laterally and vertically heterogeneous. Calculating\na bulk C content for the crust seems impossible.\nXu R, Xiao Z, Wang Y, Cui J (2024) Less than one weight percent of graphite on the surface of Mercury.\nNature Astronomy doi:10.1038/s41550-023-02169-5 (this recent reference has been added to the\nmanuscript)\nPeplowski, P. N. et al. Constraints on the abundance of carbon in near-surface materials on Mercury:\nResults from the MESSENGER Gamma-Ray Spectrometer. Planetary and Space Science 108, 98-\n107, doi:https://doi.org/10.1016/j.pss.2015.01.008 (2015).\nPeplowski, P. N. et al. Remote sensing evidence for an ancient carbon-bearing crust on Mercury.\nNature Geosci 9, 273-276, doi:10.1038/ngeo2669 (2016).\nWe added the following sentences in the main text: ‘Carbon solubility in reduced magma ocean (<\nIW-3) is extremely low when considering CO and CO solubility (< 3ppm; Supplementary Fig. S8).\nconditions compared to thermodynamic models19. This may be due to a minor CH species in the\n4\nmelt.’\nSome minor issues:\n(1) Quite a few figures and tables are cited incorrectly in the main text. The authors should check the\norder of their figures/tables, and make sure they are mentioned correctly in the appropriate position\nin the text.\nFor example,\nLine 93: Table S1 does not provide any info on the oxygen fugacity\nReply: Calculated fO2 were reported in column E of Table S1.\nLine 136: I think Fig. S8 here should be Fig. S9\nReply: Correct.\nLine 139: Fig. S7 should be Fig. S8\nReply: Correct.\nLine 147: Fig. S5 should be replaced by Fig. S6\nReply: Correct.\nLine 155: I don’t know which figure the authors refer to (Fig. S7?), but there’s no Fig. 2a in the\nmanuscript.\nReply: Correct. Reference has been made to Fig. S7\nLine 305: No Table S2 (Appendix) provided\nReply: Correct. The previous sentence was modified to “The average compositions and standard\ndeviations of analyzed phases of all experiments are shown in Table S1 (Appendix).”\nLine 321 and 330: Table 2 should be Table S2 in the Supplementary Materials\nReply: Correct.\nLine 452: Is the Supplementary Table S1 refer to the attached excel file which the authors sometimes\nrefer as Appendix? Please unify the naming of all supporting figures and tables in a consistent way\nto avoid confusion.\nReply: Yes, the naming has been unified.\n(2) Figure S10, the legend in the figure and the description in the caption do not match\nReply: Correct. The legend in the figure has been modified.\n(3) Lines 127-130: I think a figure is needed for this description\nReply: We have not been able to identify any meaningful way to illustrate those probabilities. Also\nbecause those probabilities are very low, we believe that reporting the numbers gives a clearer\nview that most models support graphite precipitation during magma ocean solidification.\n(4) Line 196: I think a word is missing here. It should be “reduced conditions”\nReply: Added as suggested, Thanks.\n(5) Table S2. This table reports sulfur-free magma ocean compositions used in the thermodynamic\nmodeling, and Table S1 also reports sulfur-free compositions used in the experiments (the added\namount of FeS is not given!). So I suppose the composition for Mer8 in Table S1 should be similar\nto that of BSM-SiCore8 in Table S2. I think it might be better to merge the two tables into one and\nuse the same unit for the composition or report both mol% and wt% to facilitate comparison.\nReply: A single Table S1 has been prepared. All data are expressed as wt%.\n(6) Line 380: Please check the equation to make sure it’s correct\nReply: The equation has been corrected for the typo (0 after alpha0)\n(7) The excel file Table S1 Summary of experimental results. I think the added FeS amount for each\nexperiment should also be listed. A quick look at the table shows that the glass composition with\nthe highest sulfur content (~16.23%, run Mer8-2) is significantly different than the glass\ncomposition in other experiments (much lower MgO content, significantly higher CaO, Na2O and\nK2O content), probably due to its small fraction causing difficulty in analyzing? Would this affect\nthe interpretation of the sulfur effect on melt liquidus?\nReply: The amount of sulfur added to the starting silicate material in each experiment was fixed\n(20 wt% FeS). This is now reported in the description of starting compositions. Regarding Run\nMer8-2, the reviewer is correct and the high sulfur content is due to a very small percentage of melt\n(near-solidus experiment). The composition of this low-degree partial melt is expected to be\ndifferent from high-degree partial melt, not because of difficulty in analyzing but because of\ndifferent temperature, melt composition, and fO2. More reduced conditions in that experiment are\ndue to the high crystallization degree (phase with high SiO ) and the relative enrichment with Si\n2\n(more reduced) in the residual melt. This results in higher S solubility in the melt.\nReviewer #3 (Comments for the Author):\nSummary:\nThe manuscript Xu et al. presents novel high-temperature and high-pressure experiments and liquidus\nthermodynamic modelling to understand the stability of graphite vs. diamond, finding diamond was\npossibly, though statistically unlikely, to be stable in Mercury’s silicate magma ocean, but would be\npredicted to form a thick layer at the current core-mantle-boundary (CMB). A conductive diamond\nlayer on top of the CMB would have significant implications for Mercury’s thermochemical evolution\ngiven its opposite properties to an unlikely insulating FeS layer. The manuscript is extremely well\nwritten and thorough in its incorporation of literature data and plentiful supplementary figures. I\nrecommend acceptance.\nReply: We thank the reviewer for summarizing our manuscript as a novel study and also appreciate for\nrecommending acceptance of our paper.\nQuantifying the effect of S on melting T in itself is a super interesting result worth highlighting and\nfurther study (either adding to the main text or in another manuscript rather than hidden in the\nsupplementary). Please expand on the form of equation 12 to define the liquidus depression per wt% S.\nIt is interesting that it is on the same order of magnitude of the effect of H O on olivine or plagioclase\n2\nliquidi in basalt. Would be interesting to comment on whether the S effect changes with pressure too.\nReply: The form of equation 12 is non-linear (exponential) so that expressing the liquidus depression\nper wt% S is inappropriate. As mentioned previously, the effect of pressure on sulfur solubility was\ndiscussed in Namur et al. (2016) who did not identify any significant effect of pressure on sulfur\nsolubility as compared to oxygen fugacity, temperature, and melt composition. Understanding precisely\nthe (potentially minor) effect of pressure on sulfur solubility would request a specific experimental\nsetup over a larger range of pressure conditions, which is beyond the scope of the present study. The\nmanuscript has been modified to report that study on the effect of pressure.\nWe added the following sentence in the manuscript: ‘It has been shown previously that sulfur solubility\nin reduced silicate melts is not pressure sensitive10 so that the liquidus depression we calculate as a\nfunction of sulfur content is independent on pressure conditions.”\nReviewer #4 (Comments for the Author):\nIn this manuscript, Xu et al. explore the possibility of a diamond-bearing layer at the core-mantle\nboundary in Mercury. They utilized experimental techniques to understand the geochemistry and phase\nstability of Mercury relevant compositions, paring the results with geophysical models to estimate the\ndynamics of diamond growth and mobility in the mantle and core. This is a novel idea and has the\npotential to have an impact on Mercury science. However, there are several major points that I believe\nneed to be addressed before this can be suitable for publication.\nReply: We thank reviewer #4 for summarizing our manuscript as a novel idea with important impact\non Mercury science. We also appreciate the recommendation to publish our paper after revision. Below\nwe provide detailed replies to all other points the reviewer raises.\nOther work has suggested that there would be an FeS layer at the core-mantle boundary (CMB) (e.g.,\nHarder & Schubert, 2001; Smith et al., 2012; Hauck et al., 2013) as a way to explain the moment of\ninertia (MOI) and the abundance of S on the surface. This seems to be taking a similar approach, just\nfrom the perspective of C. Is this an alternative to the FeS hypothesis? Do these analyses fit with the\nMOI measurements better than a possible FeS layer? I think evidence as to how this is a more plausible\nhypothesis (if this is indeed the case) will strengthen this work.\n[https://doi.org/10.1006/icar.2001.6586 https://doi.org/10.1126/science.1218809 https://doi.org/10.10\n02/jgre.20091]\nReply: The hypothesis of the FeS layer was discussed at the end of the manuscript. References to these\ntwo papers have been added:\nHarder, H. & Schubert, G. Sulfur in Mercury's Core? Icarus 151, 118-122, (2001)\ndoi:https://doi.org/10.1006/icar.2001.6586.\nHauck, S. A. et al. The curious case of Mercury's internal structure. Journal of Geophysical Research:\nPlanets 118, 1204-1220, doi:10.1002/jgre.20091 (2013).\nThe diamond/graphite layer at CMB is not an alternative to the FeS layer. Both layers could actually\ncoexist. In this study and in the previous work on the FeS layer (Namur et al., 2016; Cartier et al. 2020),\nthe nature of the CMB was investigated based on phase equilibria in silicate and metallic systems, and\ngeochemical evidence (surface composition). We believe that the thin diamond layer that we calculate\nwould have no significant effect on the MOI. This is because the density of diamond is close to that of\nthe lower mantle and the range of MOI values estimated for Mercury can accommodate a significant\nvariability in mantle thickness (see Hauck et al., 2013 and Goossens et al., 2022).\nCartier, C. et al. No FeS layer in Mercury? Evidence from Ti/Al measured by MESSENGER. Earth and\nPlanetary Science Letters 534, 116108, doi:https://doi.org/10.1016/j.epsl.2020.116108 (2020).\nWe added the following section to the main text: “Based on geodetic data, it has been suggested that a\n100 km-thick FeS layer at Mercury’s present day CMB may also exist63. The physical state (solid vs.\nliquid) of such a layer is unknown and experimental studies combined with geochemical data have\nshown that this layer, if present, should be much thinner than initially suggested from geophysics10,64,65.\nThe occurrence of a diamond layer at the CMB is compatible with the presence of a FeS layer as both\nrelate to the saturation of an element (C and S) during planetary differentiation. We propose that if the\nFeS layer is in a liquid state, the diamond layer would lie at the interface between the FeS layer and the\nsilicate mantle. If the FeS layer is solid, the diamond layer would likely lie at the interface between the\nliquid outer metallic core and the solid FeS layer. Note however that given the strong density contrast\nbetween diamond (3500 kg/m3 and solid FeS 4840 kg/m3 in standard conditions) and the likely low\nviscosity of a hot, solid, FeS layer, gravitational instability may lead to overturn between the FeS layer\nand the diamond layer.”\n-Please provide a pressure scale on Figure 3.\nReply: We would find confusing to report a pressure scale while a range of pressures at the CMB is\nactually possible depending on many parameters reported in Goossens et al. (2002), including the value\nof the MOI. Also regarding the boundary between the solid inner core and the molten outer core, Fig.3b\nillustrates a snapshot of a continuous process from fully molten at t0 (4.5 Gyr)to a range of possible\nICB today (radius inner core / radius whole core = 0.445 ± 0.181; Goossens et al., 2022). Consequently,\nwe prefer not to follow this recommendation.\nRegarding lines 152-154, are the diamonds growing and mobilizing from what is interpreted to be the\nliquid outer core or are diamonds co-crystallizing as the core solidifies? Clarification would be helpful.\nRelated to this point, at what timescale would this occur at and when would a diamond layer be expected\nto be present at the CMB?\nReply: We are not sure to fully understand this comment. Yes, the diamonds are growing in the liquid\nouter core AND are crystallizing continuously as the core solidifies (because of carbon saturation in the\nmolten metal; i.e. core solidification by crystallization of C poor phases enrich the residual liquid in C\nwhich becomes diamond saturated). Regarding the timescale, diamond would be formed as soon as the\ncore starts crystallizing and will continue until the core is completely solid. In this paper, we discuss\nthe graphite/diamond transition as a function of temperature at CMB. We have no way to link core\ncrystallization to time, except by using thermochemical models (e.g. Tosi et al., 2013; Knibbe & van\nWestrenen, 2018). However, these thermochemical models also give a range of potential paths for\ntemperature vs. time so that a large range of solutions may be obtained.\nTosi, N., Grott, M., Plesa, A. C. & Breuer, D. Thermochemical evolution of Mercury's interior. Journal\nof Geophysical Research: Planets 118, 2474-2487, doi:10.1002/jgre.20168 (2013).\nKnibbe, J. S., & van Westrenen, W. (2018). The thermal evolution of Mercury's Fe–Si core. Earth and\nPlanetary Science Letters, 482, 147-159.\nTo make this section clearer, we added the following section to the manuscript: ‘The formation of the\nsolid inner core would have caused diamond to crystallize from the residual metallic molten core. This\nis because crystallization of C-poor phases52 in the solid core would have for effect to enrich the liquid\nouter core in C. However, the whole core being at C-saturation implies that the C-enrichment will be\naccommodated by forming diamond in thermodynamic equilibrium with the liquid core which would\nthen have floated to the CMB due to the much lower density of diamond compared to the liquid iron\n(+Si, +C, +S) alloy.’\nIn the section starting at Line 70, the CMB pressure is calculated to be 5.77 GPa and in lines 108-109\nit is stated that the pressure at the bottom of Mercury’s magma ocean was similar to present CMB,\nbut the experiments are run at 7 GPa. What is the rationale for this- why weren’t experiments conducted at\na pressure that is more similar to the predicted CMB pressure calculated in this work?\nReply: Here we refer to the answer we provided to comment (2) made by reviewer #2.\nvalue of potential pressures predicted by models of Goossens et al. (2022) using the normalized polar\nmoment of inertia of Genova et al. (2019). It is true that pressure tends to favor the stabilization of\ndiamond at constant temperature. But a higher pressure also implies a higher liquidus temperature which\ndoes not favor diamond stability (but favors graphite stability).\nRunning experiments at 7 GPa enabled us to test the most favorable conditions to produce diamond.\nThis does not imply that our conclusions are forced to support diamond stability because our\nexperimental results into models to interpolate the diamond-graphite stability for the whole range of\npotential pressures predicted by models of Goossens et al. (2022).\nAs shown in Figure 1a of the paper, the temperature of the diamond-graphite transition is also close to\nthe liquidus of the two starting compositions (Mer8 and Mer15) and allowed us to calibrate the pressure\nof our experimental setup (by identifying a graphite to diamond transition of the graphite capsule).\nAdditionally, a suite of experiments on sulfur solubility under reduced conditions were already available\nat pressure <4GPa, enabling us to interpolate any results between our experimental pressure (7GPa) and\nthose of Namur et al. (2016).\n-At Mercurian CMB pressure conditions and a range of relevant temperature (early and present) this is\nsitting at metastability for diamond and graphite which is mentioned in line 176. I am not convinced at\nthe possible longevity of this layer, lasting long enough to be measurable via MOI today. If some of the\nlayer were to transform to graphite, it would be gravitationally unstable and reduce the thickness of the\nlayer, thus dampening the effect of this diamond bearing layer. Additionally, convection in the first Ga\nof Mercury’s history could disrupt a diamond layer and redistribute in the mantle.\nReply: We thank the reviewer for pointing out this interesting idea. We agree with reviewer #4 that\nMOI measurements may not be able to identify the occurrence of such a layer at CMB. Actually we\nbelieve that a diamond layer would have no effect on the MOI. Here we use constraints from phase\nequilibria and surface composition (carbon saturation of the planet) to discuss the speciation of carbon\nat CMB, i.e. graphite vs. diamond.\nWe changed as follows: ‘Future work should investigate how the presence of a km-scale diamond layer\nat the CMB would affect the thermal evolution of the silicate fraction of Mercury60. We however believe\nthat such a thin layer could not be unambiguously confirmed using interior models fitting Mercury’s\nMOI and tidal Love numbers30 given the current large uncertainties on the physical properties of\nMercury’s mantle and core24,25,30.’\nGravitational instability of an early graphite layer accumulated at CMB (before transition to diamond)\nis indeed an interesting working hypothesis that will be inspired by the work we propose. But again,\nthis question is beyond the scope of this study. In addition, transformation of diamond deep in the mantle\nto a thinner graphite layer at the top of the mantle would have a non-measurable effect on the MOI.\nWe added the following section: ‘The potential diamond layer thicknesses shown in Fig. 2 are thus\nmaximum values because the extent of the graphite to diamond reaction cannot be predicted and because\nsome early formed graphite may have been redistributed in the mantle due to strong convection and\ndensity contrast between graphite and silicate’.\nThe last part of the comment “Additionally, convection in the first Ga of Mercury’s history could disrupt\na diamond layer and redistribute in the mantle.” is actually discussed in lines 213-215 of the paper.\nWe added the following section to the manuscript: In addition, convection in the lower mantle may have\ndisrupted the diamond layer and redistributed diamond in the mantle or even in the crust. However, we\nbelieve that graphite and diamond redistribution in the silicate part of the planet was likely minimal.\nThis is because strong convection in the lower mantle stopped at 3.7 Ga45 and that inner crystallization\nonly started at about 4 Ga62. Most of the diamond layer or its graphite precursor therefore formed after\nstrong mantle convection stopped which limits the extent to which the diamond layer may have been\ndisrupted and the extent to which graphite may have been redistributed by gravitational instability.\nThe density of the solidified magma ocean and diamonds needs to be scaled with pressure. With the\nminerals being considered (e.g., opx, cpx, garnet, olivine) the density is likely greater than the 3000\nkg/m3 being considered when solidified. This could be an issue thinking about gravitational stability of\ndiamond below a potentially denser silicate at the CMB after the magma ocean stage.”\nReply: We agree that the density of the silicate mantle should be in the range 3000-3200 kg/m3. Indeed,\nthe mantle of Mercury is made up forsterite (density at 5.5 GPa and 1700 K is 3200 kg/m3), enstatite\n(density at 5.5 GPa and 1700 K is 3243 kg/m3) and sulfides (density ca. 2800 kg/m3). The density of\ndiamond at the CMB is at 5.5 GPa and 1700 K is 3490 kg/m3. There is thus no reason to expect any\ngravitational instability between a dense lower layer of diamond and a less dense upper layer made of\nsilicate minerals. It seems from this comment that the reviewer believes diamond is a light phase.\nWe added the following sentence: ‘Diamond is not expected to be affected by gravitational instability\nbecause this phase is denser than forsterite and enstatite, the main silicate minerals of the present day\nmantle.’\nFigure S2a- it looks like there is a mid-gray phase surrounding the large phase that is labeled “Sf” (and\nsome of the smaller sulfides). In experiments that are rich in Fe and S that are at lower temperatures\n(which S2a is the lowest T) there is phase separation of a sulfide-rich rim with a metal (Fe)-rich core,\nevolving to a single phase with increasing temperature. Is this the case for this experiment that there\nare indeed two phases? If so, it would be beneficial to label the two phases appropriately.\nReply: We thank the reviewer for pointing this out. The mid-gray phase surrounding the Sf phase is a\n(Mg,Fe,Ca)S sulfide. It is labelled in the Figure and note in the caption as well.\nLines 275-275- what assembly was used (e.g., 14/8)? Were WC cubes used for these experiments?\nReply: We apologize for this unclear description of our experimental assembly. The assembly consist\nof a natural pyrophyllite cubic block (the cube edge length: 38.5 mm), semi-sintered magnesium oxide\nsleeves, and a 10 mm inner diameter graphite furnace, which is a typical assembly for the cubic press –\nit is different with an oft-used multi-anvil press. Yes, the six anvils of cubic press are made of WC,\nwhich serve as WC cubes and directly touch the experimental assembly. The detailed description of this\nkind of press can be found in Wu et al. (2024) [A novel rapid cooling assembly design in a high-pressure\ncubic press apparatus, Matter Radiat. Extremes 9, 027402]. The ref. is cited now.\nREVIEWERS' COMMENTS\nReviewer #2 (Remarks to the Author):\nThe authors did a great job in responding to the reviewers’ comments. All my comments/suggestions\nhave been satisfactorily addressed. Thus, I think the manuscript can be accepted for publication in its\ncurrent form.\nReviewer #2 (Remarks on code availability):\nIt seems like enough information is provided for the code in the repository, but I haven't tried to run the\ncode myself.\nReviewer #4 (Remarks to the Author):\nThis is my second review of the manuscript from Xu et al. on \"A diamond-bearing core-mantle boundary\non Mercury\". The authors provided thorough responses to my comments and addressed any issues. I\nhave no further comments, thus I recommend that this manuscript be accepted.\nResponse to reviewer comments\n[Referee comments in italics, responses in normal font and blue]\nReviewer #1 (Remarks to the Author):\nThe authors did a great job in responding to the reviewers’ comments. All my\ncomments/suggestions have been satisfactorily addressed. Thus, I think the manuscript can be\naccepted for publication in its current form.\nReply: We thank that the reviewer for satisfying our responses to all of his/her comments and appreciate\nthat reviewer #1 to recommend for accepting our paper in its current form.\nReviewer #2 (Remarks on code availability):\nIt seems like enough information is provided for the code in the repository, but I haven't tried\nto run the code myself.\nReply: We thank that the reviewer for satisfying our responses to his/her comments. We double check\nthe code and confirm the code can run well.\nReviewer #4 (Remarks to the Author):\nThis is my second review of the manuscript from Xu et al. on \"A diamond-bearing core-mantle\nboundary on Mercury\". The authors provided thorough responses to my comments and\naddressed any issues. I have no further comments, thus I recommend that this manuscript be\naccepted.\nReply: We thank that the reviewer for agreeing that we provided thorough responses to all of his/her\ncomments and addressed all issues, and thanks for recommending our manuscript for acceptance."}]

Decision letter