Breyite inclusions in diamond: experimental evidence for possible dual origin

Inclusions of breyite (previously known as walstromite-structured CaSiO3) in diamond are usually interpreted as retrogressed CaSiO3 perovskite trapped in the transition zone or the lower mantle. However, the thermodynamic stability field of breyite does not preclude its crystallization together with diamond under uppermantle conditions (6–10 GPa). The possibility of breyite forming in subducted sedimentary material through the reaction CaCO3 + SiO2 = CaSiO3 + C + O2 was experimentally evaluated in the CaO–SiO2–C–O2 ± H2O system at 6–10 GPa, 900–1500 C and oxygen fugacity 0.5–1.0 log units below the Fe–FeO (IW) buffer. One experimental series was conducted in the anhydrous subsystem and aimed at determining the melting temperature of the aragonite–coesite (or stishovite) assemblage. It was found that melting occurs at a lower temperature (∼ 1500 C) than the decarbonation reaction, which indicates that breyite cannot be formed from aragonite and silica under anhydrous conditions and an oxygen fugacity above IW – 1. In the second experimental series, we investigated partial melting of an aragonite–coesite mixture under hydrous conditions at the same pressures and redox conditions. The melting temperature in the presence of water decreased strongly (to 900–1200 C), and the melt had a hydrous silicate composition. The reduction of melt resulted in graphite crystallization in equilibrium with titanite-structured CaSi2O5 and breyite at ∼ 1000 C. The maximum pressure of possible breyite formation is limited by the reaction CaSiO3 + SiO2 = CaSi2O5 at ∼ 8 GPa. Based on the experimental results, it is concluded that breyite inclusions found in natural diamond may be formed from an aragonite–coesite assemblage or carbonate melt at 6–8 GPa via reduction at high water activity.

their relative stability relations are unknown (Dörsam et al., 2009). Therefore, the terms wollastonite II and walstromitestructured CaSiO 3 have often been used synonymously. The name breyite was recently proposed for the latter phase and approved by IMA in 2018(IMA no. 2018. Calcium metasilicate CaSiO 3 occurs in a number of structural modifications, and its phase diagram has been extensively studied. Ringwood and Major (1967) converted wollastonite to a denser phase (breyite) at 3 GPa and ∼ 900 • C. The wollastonite-breyite boundary was then tightly constrained by experiments (e.g., Essene, 1974;Gasparik et al., 1994;Akaogi et al., 2004). Kanzaki et al. (1991) observed breyite decomposition to larnite (Ca 2 SiO 4 ) and titanitestructured CaSi 2 O 5 at 12 GPa and 1500 • C. This reaction was studied in detail by Kubo et al. (1997) and Akaogi et al. (2004). Sueda et al. (2006) experimentally demonstrated that the larnite + CaSi 2 O 5 assemblage transforms to CaSiO 3 perovskite at a pressure of ∼ 14 GPa. Gasparik et al. (1994) determined the melting temperatures of CaSiO 3 polymorphs at pressures of 8-16 GPa. Phase relations of CaSiO 3 are summarized in Fig. 1.
It is clear from the phase diagram ( Fig. 1) that the interpretation of monomineralic breyite inclusions in diamond may be ambiguous. The more common scenario implies the entrapment of CaSiO 3 perovskite in the transition zone or lower mantle and its conversion to breyite upon decompression (e.g., Joswig et al., 1999;Brenker et al., 2007;Harte, 2010;Kaminsky, 2012;Burnham et al., 2016). This interpretation is favored by the ubiquity of CaSiO 3 perovskite in the lower mantle (e.g., Wood, 2000;Irifune and Tsuchiya, 2007), the occurrence of breyite together with ferropericlase ± bridgmanite in a single diamond (Stachel et al., 2000) and coexistence of breyite with ringwoodite in a diamond (Pearson et al., 2014). One problem is the enormous volume change of the CaSiO 3 perovskite to breyite transformation of ∼ 38 % (Akaogi et al., 2004). Anzolini et al. (2016) estimated a minimum entrapment pressure of breyite in Juína diamond as 5.7 GPa at 1500 K and argued that the inclusion could not have converted from CaSiO 3 perovskite because of the large volume change involved. To accommodate such a volume change, diamond had to have experienced cracking or considerable plastic deformation, features not detected by Anzolini et al. (2016). In contrast, plastic and brittle deformations were observed around breyite inclusions in diamond by Cayzer et al. (2008), Zedgenizov et al. (2015, Burnham et al. (2015Burnham et al. ( , 2016 and Anzolini et al. (2018), which emphasizes the possibility of the dual origin of breyite inclusions in diamond.
The suggestion that a breyite inclusion can form through direct entrapment at 4-10 GPa rather than from a perovskite precursor is consistent with the CaSiO 3 phase diagram (Fig. 1). In this study we explore this possibility by highpressure experiments in the simple CaO-SiO 2 -C-O 2 system with or without H 2 O.

Problem formulation
In contrast to CaSiO 3 perovskite, breyite is not stable in a peridotitic mantle because of the reaction with low-Ca pyroxene: High-Ca pyroxene is stable up to ∼ 17-18 GPa (Akaogi et al., 2004), i.e., above the breyite stability field. There are no CaSiO 3 phases in subducted basaltic crust (MORB) up to ∼ 20 GPa (e.g., Perrillat et al., 2006). Hence, another lithology for breyite crystallization must be looked for. Wollastonite occurs very rarely in high-pressure rocks (Chopin et al., 2008;Galvez et al., 2013a, b) and is absent in subducted sediments (Li and Schoonmaker, 2003). However, the association of calcite and silica is very common in oceanic sediments (Li and Schoonmaker, 2003) and could be a viable source of CaSiO 3 formation via the decarbonation reaction Hence, the system CaO-SiO 2 -C-O 2 rather than CaSiO 3 -C should be considered. Litasov et al. (2017) calculated the position of Reaction (R2) at high pressures under fluid-saturated conditions (Fig. 2). They showed that Reaction (R2) intersects the melting curve of CaCO 3 at pressure close to the graphite-diamond transformation. However, Reaction (R2) becomes metastable even at significantly lower pressures because of the occurrence of the melting reaction as indicated by experiments in the CaO-SiO 2 -CO 2 system by Wyllie and Huang (1976) and Huang et al. (1980). These studies showed that Reaction (R2) terminates in an invariant point at ∼ 1.8 GPa and 1320 • C and is metastable at higher pressures. The position of Reaction (R3) in the diamond stability field was not studied experimentally, but it is clear that breyite cannot be produced by decarbonation Reaction (R2) in the presence of a CO 2 fluid or, more precisely, a CO 2 -CO fluid whose composition depends on oxygen fugacity (f O 2 ). Decarbonation is possible at lower temperatures, if CO 2 activity is lower than that in the presence of CO 2 fluid or, alternatively, at a f O 2 below the C-CO-CO 2 buffer, via the reaction Another reaction limiting the possible conditions of breyite crystallization in the diamond stability field is Experiments in the CaSiO 3 -CaTiO 3 (Kubo et al., 1997) and CaTiSiO 5 -CaSi 2 O 5 systems (Knoche et al., 1998) at 5.3-16 GPa and 1200 and 1350 • C, respectively, showed that the breyite-coesite assemblage transforms to CaSi 2 O 5 in the Tifree system between 5.3 and 8.7 GPa. Calculations using the thermodynamic data of Holland and Powell (2011) indicate that equilibrium (Reaction R5) lies ∼ 3.0 GPa above the graphite-diamond boundary (Fig. 2). It is evident that Reaction (R5) limits the pressure range where breyite can form in metasedimentary (silica-saturated) assemblages. With these considerations in mind, our experimental study had the following goals: 1. to constrain the temperature dependence of melting Reaction (R3) at 6-10 GPa and its position relative to redox Reaction (R4) at low but geologically realistic oxygen fugacities near the iron-wüstite (IW) buffer, 2. to model the formation of CaSiO 3 at low CO 2 activity in the presence of mixed C-O-H fluid, and 3. to obtain experimental constraints for the lower stability limit of Reaction (R5).

Experiments
Two types of experiments were conducted.
(1) One configuration consisted of three layers (from bottom to top): Fe  Kennedy and Kennedy (1976). The reaction CaCO 3 + SiO 2 = CaSiO 3 + CO 2 was calculated by Litasov et al. (2017) for fluidsaturated conditions; kinks on the reaction line are related to the quartz-coesite and wollastonite-breyite transformations. The reaction lines CaCO 3 + SiO 2 = CaSiO 3 + C + O 2 were calculated using thermodynamic data from Holland and Powell (2011) for logf O 2 values CCO -2 and CCO -3 in the absence of fluid. Melting of CaCO 3 + SiO 2 was experimentally studied up to 3 GPa (Wyllie and Huang, 1976;Huang et al., 1980) and is extrapolated arbitrarily to higher pressures as a dashed line. Circles show melting experiments in hydrous and anhydrous systems in which coexisting CaCO 3 and SiO 2 were observed (Hammouda, 2003;Yaxley and Brey, 2004;Grassi and Schmidt, 2011a, b;Tsuno and Dasgupta, 2012;Kiseeva et al., 2012Kiseeva et al., , 2013Poli, 2015;Brey et al., 2015;Mann and Schmidt, 2015;Martin and Hermann, 2018). The shaded field shows the conditions of possible formation of breyite inclusions in diamond.
metal, SiO 2 and CaCO 3 . These experiments simulated melting of CaCO 3 (aragonite) + SiO 2 (coesite or stishovite) under anhydrous conditions with simultaneous carbonate reduction at a f O 2 near IW.
(2) The second configuration comprised two layers, a mixture of Fe metal and Mg(OH) 2 in the lower part of the sample and a SiO 2 -CaCO 3 mixture in the upper part, nonhermetically separated by a Pt disc. These experiments simulated the interaction of CaCO 3 and SiO 2 with a mixed reduced fluid produced by the reaction Fe + Mg(OH) 2 = 2(Fe, Mg)O + H 2 (R6) and subsequent interaction of H-bearing species with CaCO 3 in the upper zone. Starting materials for the experiments were prepared from Fe, SiO 2 and Mg(OH) 2 reagents along with natural calcite (Icelandic spar). The initial components were pulverized in an agate mortar to a grain size < 20 µm and mixed, when necessary, by grinding under ethanol. Sample powders were packed into Pt capsules with a 1.4 mm inner diameter and ∼ 2.5 mm long.
The experiments were performed in a Walker-type multianvil apparatus using tungsten carbide cubes with a truncation edge length of 8 mm. The pressure assembly consisted of a 95 % MgO + 5 % Cr 2 O 3 octahedron, a zirconia sleeve, a Re foil heater and MgO inserts around the capsule. Any free space was filled with Al 2 O 3 -based cement of W. Haldenwager Technische Keramic GmbH. Pressure was calibrated against the Mg 2 SiO 4 olivine-wadsleyite phase transition at 1200 • C and 13.6 GPa (Morishima et al., 1994), the coesite-stishovite transition at 1650 • C and 10.6 GPa , and the CaGeO 3 garnet-perovskite transition at 1200 • C and 5.6 GPa (Ross et al., 1986). The experimental apparatus and pressure calibration were described in detail by Brey et al. (2008). The uncertainty in pressure was estimated as ±0.3 GPa. Temperature was measured with a W 95 Re 5 -W 74 Re 26 thermocouple inserted through an Al 2 O 3 ceramic tube at the top end of the capsule. Temperature fluctuations during the experiments were no higher than ±3 • C. The duration of the experiments was 1 to 45 h ( Table 1). The experiments were terminated by shutting off the power supply. After the experiment, the capsule was mounted into epoxy, sectioned lengthwise and polished with oil-based diamond pastes. The products were analyzed with a Jeol 8900 Superprobe electron microprobe in wavelength dispersive mode. The microprobe is equipped with five spectrometers along with an energy-dispersive spectroscopy (EDS) system. The following natural and synthetic phases were used as standards: wollastonite for Si and Ca, Al 2 O 3 for Al, fayalite for Fe, forsterite for Mg, and albite for Na. The analytical conditions were as follows: 15 kV accelerating voltage, 20 nA beam current, and 20-40 s counting time for peak and background. Minerals were analyzed with a focused beam and quenched melts, with a beam defocused to a 20 µm spot size. Some experiments were analyzed with a Jeol JSM-6490 scanning electron microscope equipped with an INCA analytical system. The accuracy of INCA EDS analysis was inferior to that of the electron microprobe, and these analyses were considered semiquantitative. However, the quality of these analyses was sufficient for identification of experimental phases, most of which were of fixed composition.
In all anhydrous experiments (type 1), metallic iron coexisted with wüstite (pure FeO), which indicates that the f O 2 was close to the IW buffer reaction: However, careful inspection of the experimental products revealed that the actual f O 2 could differ from IW. In most cases, the association of metallic iron and wüstite was observed in the central part of the metal zone, whereas its outer part consisted only of pure iron, suggesting that the f O 2 was below IW. Some oxygen fugacity gradient existed evidently between the inner and outer parts of the metal zone. It is reasonable to suggest that the oxygen fugacity in the carbonate zone was controlled by equilibria at the interface between the iron and silica zones. Ferrosilite and fayalite were observed in most experiments of this series between iron metal and silica. Hence, the oxygen fugacity was controlled by the reactions or, when fayalite was absent, Reactions (R8) and (R9) are sums of equilibrium (Reaction R7) and the following reactions: respectively. Therefore, the logf O 2 relative to the IW buffer can be calculated as for the fayalite-ferrosilite-iron assemblage and for the iron-ferrosilite-silica (coesite or stishovite), where G(i) is the Gibbs free energy change of the respective reaction, T is the absolute temperature and R is the universal gas constant. The f O 2 was calculated using the thermodynamic properties of phases from the dataset of Holland and Powell (2011). In most cases, the resulting f O 2 values lie 0.5-1.0 log units below IW (Table 1). To further decrease the f O 2 in one experiment (M753), San Carlos olivine (Mg no. ∼ 0.9) was added to the starting Fe layer. This produced Fe-Mg olivine and orthopyroxene solid solutions in the Fe zone, which imposed a f O 2 of ∼IW -1.
In the hydrous experiments (type 2), the buffer assemblage consisted always of metallic Fe free of measurable Pt or any other admixture and ferropericlase with Mg/(Mg+Fe) of approximately 0.3-0.4 (Table 1). The composition of ferropericlase was rather uniform in all experiments, with no systematic variations occurring in contact with the capsule. For these experiments, the f O 2 relative to IW was calculated as IW = 2 ln(a FeO )/2.303RT , where a FeO is the activity of FeO in ferropericlase, calculated using the model of O'Neill et al. (2003). The resulting f O 2 values are lower than IW by 0.2-0.3 log units.  4 Experimental results

Anhydrous aragonite-SiO 2 melting
In the subsolidus experiments at temperatures ≤ 1300 • C, the three layers remained separated with only minor interaction between Fe metal and SiO 2 that produced ferrosilite and fayalite, whereas no interaction was observed between aragonite and SiO 2 . At higher temperatures, quenched melt appeared at the contacts between aragonite and SiO 2 (Fig. 3). The first melt portion appears near the walls of capsules, in the zones of highest temperature. The amount of melt increases rapidly between 1400 and 1500 • C (Fig. 4). Minor graphite grains were observed in some experiments in or near the melt pools.
Their occasional presence within carbonate crystals suggests that graphite was present during the experiment and is not a quench phase. In the most reduced experiment with olivine in the Fe zone (M753 at 8 GPa, 1300 • C and logf O 2 ∼IW -1), more extensive graphite formation was observed (Fig. 5). In this experiment, graphite formed a continuous band of small crystals near the coesite-aragonite contact. Despite the considerable amount of graphite, breyite was not observed in this run, indicating that Reaction (R2) remains metastable under such conditions.

Hydrous experiments
Melt was always present as a major phase in these experiments. The quench texture was very different from that observed in the anhydrous experiments and consisted of a very fine-grained or even glassy matrix and acicular quench coesite or stishovite crystals (Fig. 6). Equilibrium growth of crystals often occurred along the walls or bottom of the capsule. CaSi 2 O 5 formed large euhedral crystals up to 30-50 µm across (Fig. 6a, b). Stishovite crystallized as long prismatic crystals, which were easily distinguished from isometric coesite grains. Breyite was observed in minor amounts at 6-8 GPa (Fig. 7) as short-to-long prismatic grains up to 20 µm long ( Fig. 6b-d). Diopside occurred in some of the experiments due to Mg contamination from the lower buffer zone. Graphite was present in all experiments both within the melt phase and as inclusions in silicate crystals.

Phase compositions
The solid phases mostly have constant compositions and approach ideal stoichiometric element ratios (Table 2). Through contamination with the buffer materials, minor amounts of Mg and Fe were occasionally present in the calcium silicate phases. Aragonite and silica minerals were almost always free of Fe and Mg.  The melt composition from the anhydrous melting experiments was rather variable, especially at low temperatures and low melt fractions (Table 2, Fig. 8). This is related to contamination of the CaCO 3 -SiO 2 system by Fe from the buffer mixture and, possibly, other chemical components from the starting reagents. The influence of these components was most significant at low melt fractions, as indicated by significant FeO and MgO contents in the melt from some experiments. Melt from run M770 (6 GPa, 1300 • C) contained up to 18 wt % FeO, and its SiO 2 content was also unusually high, ∼ 30 wt %. At higher temperatures, the amount of impurities decreased and the melt shifted to a Ca carbonate composition with 5-10 wt % SiO 2 (Fig. 8). The melt composition is essentially insensitive to temperature above 1300 • C. The SiO 2 content seems to decrease with increasing pressure, although the available data are insufficient for a quantitative assessment.
The compositions of melts from the hydrous experiments are different and can be qualified as hydrous calcium silicate liquids. The content of carbonate species is probably low, which is suggested by the absence of quench carbonates and the abundance of graphite produced by the reduction of starting CaCO 3 . The SiO 2 content ranges from ∼ 35 to 55 wt % and is insensitive to temperature but decreases with increasing pressure (Fig. 8).

Decarbonation versus melting reactions
The position of melting Reaction (R3) can be only approximately constrained by our experiments. Its eutectic nature is supported by the absence of additional phases over the melting interval and the independence of melt composition on the degree of melting at high temperatures. However, there are obviously departures from the eutectic behavior. The solid assemblage is transformed to melt (until exhaustion of either silica of aragonite) over a considerable temperature interval rather than at a constant temperature (Fig. 4). There are several reasons for such behavior. First, there is a temperature gradient within the capsule. Our estimates (Woodland et al., 2018) indicate that temperature variation within the short capsules used in the experiments could be up to 50 • C. This explains the gradual propagation of the melt zone from capsule walls toward the center of the sample. Secondly, Fe contamination was observed in many experiments, and significant amounts of FeO were dissolved in melts at low melt fraction. This explains the appearance of small amounts of melt very far from the liquidus and the slow increase in the degree of melting at temperatures 100-200 • C below the liquidus. Thirdly, the presence of minor amounts of graphite in some experiments indicates that the melting was at least not always eutectic but peritectic in nature via the reaction Finally, the presence of minor amounts of H 2 O and/or CH 4 cannot be excluded because of impurities in the starting materials and possible hydrogen migration into the capsule during the experiment. Hence, the melt composition was not constant but changed with increasing temperature, causing melting to occur over a finite temperature interval. However, at high melt fractions, the influence of contamination decreases, and the position of disappearance of aragonite should be close to the position of the eutectic reaction. Our results suggest that Reaction (R3) occurs at temperatures slightly higher than 1500 • C at 6-8 GPa and at ∼ 1500 • C at 10 GPa. The increase in melt fraction as pressure increases from 6 to 8 GPa at 1500 • C suggests that Reaction (R3) could have a negative slope in the coesite stability field. This is in line with a very weak to negligible pressure effect on the melting temperature of CaCO 3 above 5 GPa (Li et al., 2017). At 10 GPa, stishovite occurs instead of coesite, which results in a larger volume change of the melting reaction and a different (though unconstrained) slope of this melting reaction.
The absence of CaSiO 3 in all experiments of this series implies that Reaction (2) is metastable under CO 2undersaturated conditions at a f O 2 ≈ IW -0.5. This result is at odds with calculations of Reaction (R2) using the thermodynamic properties of phases from Holland and Powell (2011). These calculations indicate that a decrease in f CO 2 and, correspondingly, f O 2 shifts Reaction (R2) to lower temperatures. As depicted in Fig. 2, already at f O 2 values 3 log units below the C-CO-CO 2 (CCO) equilibrium (0.5-3.0 log units above the IW buffer), Reaction (R2) occurs at lower temperatures than CaCO 3 -SiO 2 melting over the whole pressure range of breyite stability. Hence, breyite should have been stable rather than aragonite and coesite at least in our highest temperature experiments. The absence of CaSiO 3 in the experimental products could be related to the low melting temperature of the CaSiO 3 + CaCO 3 assemblage. At 3 GPa, the eutectic melting of this assemblage occurs ∼ 100 • C below the CaCO 3 + SiO 2 eutectic melting point (Huang and Wyllie, 1974). The melting relations of CaSiO 3 + CaCO 3 at 6 GPa were recently studied by Fedoraeva et al. (2019). They determined the aragonite-breyite eutectic temperature to be 1400 • C at 6 GPa, which is lower than the temperature of melting Reactions (R3) and (R12) at this pressure.
The metastability of the aragonite-coesite-breyite assemblage is indirectly supported by the results of other experimental studies. Figure 2 shows the pressure-temperature conditions of melting experiments in various systems in which silica and aragonite (calcite) are present. The silicacalcite-wollastonite assemblage was observed in a single experiment on calcite assimilation in dacitic melt at 0.5 GPa and 1000 • C (Carter and Dasgupta, 2016). In all previous experiments above 3 GPa, the CaCO 3 + SiO 2 assemblage remained stable up to 1400 • C under uncontrolled f O 2 . Thus, we conclude that at a f O 2 0.5-1.0 log units below IW, decarbonation Reaction (R2) is metastable owing to the occurrence of eutectic melting.

The equilibrium CaSiO 3 + SiO 2 = CaSi 2 O 5
Equilibrium (Reaction R5) additionally limits the conditions of possible breyite formation from CaCO 3 and SiO 2 . Although it has not been systematically studied experimentally, the position of this equilibrium in pressure-temperature space can be estimated from the thermodynamic data of Holland and Powell (2011). For example, CaSi 2 O 5 should become stable at 1100 • C at a pressure of 7.3 GPa. As plotted in Fig. 2, it is apparent that the stability field of breyite is reduced by ∼ 2 GPa if the metasedimentary assemblage is SiO 2 -saturated. However, the results of our hydrous experiments can provide some additional constraints on the actual position of this reaction. Of three experiments per-formed at 8 GPa and 1100 • C, one produced CaSi 2 O 5 (Table 1, Fig. 7). The other two experiments at this temperature produced either breyite + SiO 2 or only breyite. In an additional experiment at 1000 • C, CaSi 2 O 5 was found to coexist with breyite but without coesite (Table 1). Thus, the equilibrium (Reaction R5) must lie very close to 8 GPa at 1100 • C, i.e., ∼ 0.7 GPa higher than its position calculated using the Holland and Powell (2011) data (Fig. 7). This discrepancy is equivalent to a difference in the H of Reaction (R5) of 5.5 kJ, which is approximately equal to the 2σ uncertainty in the H of CaSi 2 O 5 as given by Holland and Powell (2011) (2.8 kJ). The uncertainties in H for SiO 2 and CaSiO 3 are much smaller (0.5 kJ). Therefore, it can be concluded that the data of Holland and Powell (2011) are consistent within their 2σ uncertainty with our experimental observations. On the other hand, our results do significantly extend the pressure range of possible breyite crystallization in SiO 2 -saturated bulk compositions (Fig. 7).   (Table 2).
Under natural conditions, equilibrium (Reaction R5) can be affected by the presence of TiO 2 . The titanite-structured CaSi 2 O 5 phase from inclusions in diamond is enriched in TiO 2 relative to coexisting breyite. This can be exemplified by the TiO 2 contents of CaSiO 3 (0.02 wt %) and CaSi 2 O 5 (0.15 wt %) inclusions in diamond reported by Joswig et al. (1999). There is no direct experimental evidence on the effect of Ti on Reaction (R5). The experiments of Kubo et al. (1997) on the CaSiO 3 -CaTiO 3 system indicate that the pressure of breyite transformation to larnite + CaSi 2 O 5 is reduced by ∼ 0.7 GPa at 1200 • C and a CaTiSiO 5 mole fraction in titanite-structured Ca(Ti, Si)SiO 5 of ∼ 0.15. If the effect of TiO 2 on Reaction (R5) is of the same order, the presence of ∼ 0.5 % of CaTiSiO 5 in the titanite-structured phase will have a negligible effect on the breyite stability field.

Breyite crystallization under hydrous conditions
In the hydrous experiments, the iron-brucite starting mixture served as a source of fluid and an oxygen buffer. Interaction of brucite with iron produced a ferropericlase solid solution along with a reduced H 2 O-H 2 fluid. The latter reacted with the adjacent CaCO 3 -SiO 2 mixture to form C-O-H fluid species. The high chemical potential of H 2 O acted to significantly depress the melting temperature of the CaCO 3 -SiO 2 mixture, resulting in complete melting already at 1100 • C and 6 GPa and very high degrees of melting at 1100 • C and 8-10 GPa. No separate fluid phase was observed in these experiments, indicating that all fluid components were dissolved in the melt. The hydrous melt is strongly enriched in SiO 2 compared with the carbonate-dominated melt from the anhydrous experiments (Fig. 8).
The hydrous melt contained abundant suspended graphite crystals. Their nature is uncertain, and some could have formed during quenching. However, most graphite grains probably crystallized in equilibrium with the melt, which is indicated by their nonrandom distribution and very high content in some areas. The identification of equilibrium CaSi 2 O 5 and SiO 2 crystals is unambiguous because these phases always occur as euhedral crystals up to 20 µm in size, usually in the lower part of the samples (Fig. 6). In contrast, a quench nature of some breyite crystals might be suspected because of their needle-like morphology (Fig. 6). However, there are several arguments supporting a subliquidus equilibrium origin of most breyite crystals. (1) Their amount is always low and the grains are observed locally near the walls or bottom of a capsule. Here, breyite content might be locally very high (> 50 vol %), whereas isolated CaSiO 3 crystals were never found in the free melt volume. (2) There is a continuous transition from acicular to euhedral isometric breyite grains. The latter can hardly be interpreted as a quench phase (Fig. 6).
(3) In one sample, a large isometric breyite crystal was observed between the Pt capsule and a continuous coesite layer. In this case, the local melt fraction was obviously too low to produce a large quench crystal.
Thus, our experiments demonstrated that simultaneous crystallization of breyite and diamond is possible as a result of interaction between CaCO 3 and SiO 2 in a metasedimentary source in the presence of reduced H 2 O-rich fluid or melt. Although our experiments were made in a strongly simplified system compared with real metasediments, they are directly applicable to interactions in natural environments. Both arag- onite and coesite/stishovite are practically pure phases in metasediments under high-pressure, high-temperature conditions (e.g., Brey et al., 2015). Natural breyite contains up to 0.2 wt % FeO and much lower amounts of other components (Joswig et al., 1999;Burnham et al., 2015). Hence, Reactions (R2) and (R4) are not affected by the presence of other components in natural materials. Moreover, melting in natural metasediments occurs at lower temperatures compared with the experimental CaO-SiO 2 -CO 2 system because of the fluxing influence of alkalis, which must enhance the metastability of decarbonation Reaction (R2).
The pressure range of breyite inclusion formation is limited by the diamond-graphite transformation at ∼ 4 GPa and 1100 • C and Reaction (R5) at ∼ 8 GPa and 1100 • C (Fig. 7). These conditions are slightly above the solidus of hydrous carbonated sediment similar to GLOSS (global subducting sediment) of Plank and Langmuir (1998) coexisting with graphite or diamond (Brey et al., 2015). Hence, hydrous carbonate-silicate melt (or supercritical fluid) can be obtained from subducted sediment, if the temperature of the slab is not high and does not prevent hydrous silicate (lawsonite and phengite) transport to great depths. Such conditions are characteristic of cold subducted slabs (Syracuse et al., 2010).
It is evident from the above discussion that f O 2 is a very important parameter for breyite and diamond crystallization. To quantitatively evaluate a possible scenario for the formation of diamond-hosted breyite inclusions, mineral reactions in sedimentary and peridotitic materials were modeled using the dataset of Holland and Powell (2011). The calculated f O 2 values are expressed in logarithmic units relative to the Fe-FeO buffer (IW).
A proposed scenario of simultaneous breyite and diamond formation at 6-8 GPa and ∼ 1000 • C is presented diagrammatically in Fig. 9. It involves melt formation in subducted sediments and its subsequent interaction with peridotite. At these depths and temperatures, the mineral assemblage of an hydrous carbonated and C-bearing sediment (GLOSS) includes coesite, kyanite, Ca-rich garnet, aragonite, lawsonite, phengite, graphite and accessory phases (Brey et al., 2015). The f O 2 is controlled by the reaction 3CaCO 3 (Arg) + Al 2 SiO 5 (Ky) + 2SiO 2 (Coe) = Ca 3 Al 2 Si 3 O 12 (Grt) + 3C(Dia) + 3O 2 (R13) and is relatively high (logf O 2 ≈ IW +5.5). The mole fraction of grossular in garnet in metasediment at 8 GPa and 1000 • C is 0.3-0.4 (Brey et al., 2015). Accounting for garnet composition using the Berman (1990) model for Ca-Mg-Fe garnet yields even slightly higher logf O 2 values of ∼IW +5.7. Melt produced from such a metasediment will have the same f O 2 . It will be saturated with respect to diamond but undersaturated in breyite, because such a redox potential will provide a CO 2 activity that is too high for decarbonation Reaction (R4) to proceed. However, the produced melt can be subsequently reduced through interaction with mantle peridotite, which will eventually result in diamond formation and redox freezing (Rohrbach and Schmidt, 2011). The redox conditions of mantle peridotite can be constrained by the appearance of Fe metal from below and magnesite from above, i.e., the reactions 2Fe 2 SiO 4 (Ol) = Fe 2 Si 2 O 6 (Opx) + 2Fe(Metal) + O 2 , MgCO 3 (Mst) + 1/2Mg 2 Si 2 O 6 (Opx) = Mg 2 SiO 4 (Ol) + C(Dia) + O 2 .
This yields a wide range of logf O 2 values, from IW to IW +4, which is more reduced than the initial metasedimentderived melt. Note that all the f O 2 values imposed by Reactions (R15)-(R17) are much lower than the CCO buffer at these pressures and temperatures (CCO ≈ IW +8 at 1000-1100 • C and 6 GPa; Jacobsson and Oskarsson, 1994). This implies that a CO 2 -rich gas phase is absent, and diamond will remain stable in both metasediment and peridotite. Interaction of metasediment-derived melt with peridotite will result in reduction accompanied by Fe and Mg transfer from peridotite to melt and SiO 2 transfer from melt to peridotite (Bulatov et al., 2014). If the melt is saturated in diamond (melt is derived in a diamond-bearing metasediment), its reduction will immediately result in diamond crystallization. The reduction-induced crystallization of silicate phases will begin later via two possible paths. If transport of O 2 is much faster than that of Fe and Mg, melt reduction and diamond crystallization will eventually result in breyite (or CaSi 2 O 5 ) crystallization and its possible entrapment by growing diamond crystals. Otherwise, in the case of rapid Fe and Mg transport, breyite formation will be suppressed, and clinopyroxene, garnet or merwinite (e.g., Sharygin et al., 2018) will form instead. The obtained results allow us to speculate about the difference in the origins of breyite inclusions either being trapped at conditions within the breyite stability field or those that formed by retrogression of trapped CaSiO 3 perovskite. Anzolini et al. (2016) emphasized the importance of the very large difference in molar volume between CaSiO 3 perovskite and breyite. They argued that breyite inclusions without any evidence for diamond deformation and/or cracking were probably trapped initially as breyite. Moreover, the large volume change will result in an initial CaSiO 3 perovskite inclusion converting to polymineralic aggregates containing larnite and CaSi 2 O 5 (e.g., Joswig et al., 1999) rather than monomineralic breyite. Inspection of the phase diagram in Fig. 2 indicates that CaSiO 3 inclusions coexisting with larnite or stishovite most probably had a perovskite precursor. In contrast, CaSi 2 O 5 can be trapped together with breyite at a pressure of ∼ 8 GPa. Finally, the formation of breyite through reaction of CaCO 3 and SiO 2 implies a metasedimentary precursor, whereas CaSiO 3 perovskite is a phase stable in a peridotitic mantle. Therefore, the two types of breyite inclusions should have specific geochemical and isotopic signatures. It is interesting in this respect that at least some calcium perovskite inclusions in diamond exhibit geochemical signatures of subducted oceanic crust rather than primitive or depleted peridotites (e.g., Walter et al., 2008). Data availability. All data derived from this research are presented in the enclosed Tables and Figures. Author contributions. All authors contributed to the problem formation, experimental strategy and results interpretation. VKB and ABW conducted the experiments. The analytical work was performed by AVG and HEH. The manuscript was prepared by AVG and ABW.