Phase Relations in the FeO-Fe3C-Fe3N System at 7.8 GPa and 1350 °C: Implications for Oxidation of Native Iron at 250 km

Oxidation of native iron in the mantle at a depth about 250 km and its influence on the stability of main carbon and nitrogen hosts have been reconstructed from the isothermal section of the ternary phase diagram for the FeO-Fe3C-Fe3N system. The results of experiments at 7.8 GPa and 1350 °C show that oxygen increase in the system to > 0.5 wt % provides the stability of FeO and leads to changes in the phase diagram: the Fe3C, L, and Fe3N single-phase fields change to two-phase ones, while the Fe3C + L and Fe3N + L two-phase fields become three-phase. Сarbon in iron carbide (Fe3C, space group Pnma) is slightly below the ideal value and nitrogen is below the EMPA (Electron microprobe analysis) detection limit. Iron nitride (ε-Fe3N, space group P63/mmc) contains up to 2.7 wt % С and 4.4 wt % N in equilibrium with both melt and wüstite but 2.1 wt % С and 5.4 wt % N when equilibrated with wüstite alone. Impurities in wüstite (space group Fmm) are within the EMPA detection limit. The contents of oxygen, carbon, and nitrogen in the metal melt equilibrated with different iron compounds are within 0.5–0.8 wt % O even in FeO-rich samples; 3.8 wt % C and 1.2 wt % N for Fe3C + FeO; and 2.9 wt % C and 3.5 wt % N for Fe3N + FeO. Co-crystallization of Fe3C and Fe3N from the O-bearing metal melt is impossible because the fields of associated C- and N-rich compounds are separated by that of FeO + L. Additional experiments with excess oxygen added to the system show that metal melt, which is the main host of carbon and nitrogen in the metal-saturated (~0.1 wt %) mantle at a depth of ~250 km and a normal heat flux of 40 mW/m2, has the greatest oxygen affinity. Its partial oxidation produces FeO and causes crystallization of iron carbides (Fe3C and Fe7C3) and increases the nitrogen enrichment of the residual melt. Thus, the oxidation of metal melt in the mantle enriched in volatiles may lead to successive crystallization of iron carbides and nitrides. In these conditions, magnetite remains unstable till complete oxidation of iron carbide, iron nitride, and the melt. Iron carbides and nitrides discovered as inclusions in mantle diamonds may result from partial oxidation of metal melt which originally contained relatively low concentrations of carbon and nitrogen.


Introduction
Metal saturation at mantle depths below 250 (± 30) km has been supported by multiple lines of theoretical and experimental evidence [1][2][3][4]. The mechanism of stable metal saturation consists in progressive disproportionation by the reaction 3Fe 2+ →2Fe 3+ + Fe 0 maintained by the stability of Fe 3+ in silicate phases (subcalcic pyroxene or majoritic garnet) increasing with pressure [1,2]. The stability of the metal phase in the mantle was proven by findings of metallic iron in inclusions from diamonds

Materials and Methods
The experiments with the FeO-Fe 3 C-Fe 3 N system followed the same basic approaches as in our previous work with the system Fe-Fe 3 C-Fe 3 N [20]. In the same way, the samples saturated or undersaturated with respect to carbon were placed into graphite and ceramic containers, respectively. Proceeding from the previous experience, the 1 h run duration was chosen to minimize the loss of volatiles.

Starting Composition
The starting composition included FeO powder, iron carbide (Fe 3 C) synthesized at 6.3 GPa and 1400 • C from iron and graphite, and iron nitride (Fe 2-4 N); all components were of >99.9% pure chemical grade. The iron nitride we used contained 7.1 wt % N, according to quantitative analysis on a Carlo Erba-1106 (La Métairie, France) CHN analyzer. This content of nitrogen was assumed later when plotting the ternary phase diagram. The powders were stored in a vacuum desiccator at~100 mbar.
In an additional series of experiments, > 99.9% pure chemical grade Fe 2 O 3 powder was used instead of FeO.
The starting mixtures (Table 1 and Figure 1) were prepared immediately before the experiments (to avoid oxidation), placed in thick-walled graphite or ceramic capsules, and then loaded in the high-pressure cell. The graphite capsules were made from >99.99% pure graphite, and the ceramic capsules were made from high-quality natural talc from the Onot deposit (Irkutsk region, Russia) converted to quartz-enstatite ceramics by annealing at 900 • C. The capsules were 2.4 mm high cylinders 7 mm in diameter, with two 2.0 mm holes (for charges) in each, sealed with 0.5 mm discs of the same material on both sides. Two capsules, of the 6.8 mm total height, were stacked upside down into the center of a low gradient furnace zone.

High-Pressure Apparatus
Experiments at 7.8 GPa were carried out in a split-sphere multi-anvil high-pressure apparatus [28]. The multi-anvil sphere of 8/6-type consisted of two anvils with square faces on top and bottom and four side anvils with rectangular faces placed in an octahedral cavity formed by truncating the vertices of eight steel anvils. The size of the high-pressure cells was 19 × 19 × 22 mm; graphite heaters had inner diameters of 9.2 mm and heights of 14.8 mm. Pressure was calibrated by recording the change in the resistance of Bi at 2.55 GPa and PbSe at 4.0 and 6.8 GPa [29] at room temperature and at 1350 • C by bracketing the graphite-diamond equilibrium [30] in the Ni 0.7 -Fe 0.3 -C system. Temperature was monitored in each run with a PtRh 6 /PtRh 30 thermocouple calibrated at 6.3 GPa using the melting points of Al, Ag [31]. The pressure and temperature measurements were accurate to ± 0.1 GPa and ± 20 • C, respectively.

Analytical Methods
After experiments, the samples were treated following the method from [32] and then examined on a Tescan MIRA 3 LMU (Brno, Czech Republic) scanning electron microscope (SEM) and under a Carl Zeiss Stemi 2000-C optical microscope. To make the analysis easier, the polished surfaces were etched using Nital (5 vol % nitric acid in ethanol) containing 0.1 vol % HCl [33].
Element abundances in the samples were determined by electron microprobe analysis (EMPA) on a Jeol JXA-8100 (Tokyo, Japan) microanalyzer at 15 kV accelerating voltage, 200 nA beam current, and 1 to 2 µm beam diameters for solids and 100 µm for quenched liquids. The samples were coated with 10 nm gold or chromium. The results were checked against Fe 3 N, Fe 3 C, Fe, and Fe 2 O 3 standards. Measured intensities were converted to concentrations by the ZAF method. The C and N contents in solid phases were estimated to an accuracy of 5 rel %, and Fe and O were accurate to 2 rel %. The detection limit for C, N, and O was 0.1 wt % at the applied analytical conditions. The errors in element contents were larger for quenched liquids because of enclosed coarse dendritic crystals. For this reason, the analytical quality was low even with the beam diameter 100 µm. Additionally, the metal phase compositions were analyzed using a Tescan MIRA 3 LMU scanning electron microscope coupled with an INCA EDS microanalysis system 450 with an Oxford Instruments liquid nitrogen-free large area EDS X-Max-80 Silicon Drift Detector (High Wycombe, UK). The instruments were operated at an accelerating voltage of 20 keV, a beam current of 1 nA, and a spot diameter of~3-10 µm; the count time for spectra collection was 20 s. The EDS spectra were optimized for quantification using the standard XPP procedure built into the INCA Energy 450 software.
The synthesized phases were identified by X-ray powder diffraction on a Stoe IPDS-2T (Darmstadt, Germany) diffractometer (MoKα radiation, graphite monochromator) in the Gandolfi mode. Two-dimensional X-ray patterns were radially integrated using the XArea software package. The diffraction profiles were processed in WinXPow (Stoe). For the phase analysis, the database of PDF-4 Minerals was used.
X-ray single-crystal diffraction (XRD) analysis of the synthesized phases was performed on a Stoe IPDS-2T diffractometer (MoKα radiation, graphite monochromator). Diffraction data were collected with ω scans, at a step of 1 • and 240 s per frame, and processed in CrysAlis Pro [34]. A semi-empirical absorption correction was applied using the multi-scan technique. The structure was determined with the SHELX program package [35]. Analytical studies were performed in the Sobolev Institute of Geology and Mineralogy SB RAS and at the analytical center for multi-elemental and isotope research SB RAS.

Textures of Experimental Samples
The obtained quenched melts generally produced a dendritic network, with blades and an interstitial lamellar quench texture (Figure 2b-d). In a few samples, however, no quench textures appeared in SEM images though a dendritic network came out upon etching with 5% Nital for 2-4 min (Figure 2e

Crystal Structure and Compositions of Phases
The results of single-crystal experiments in the system FeO-Fe 3 C-Fe 3 N are presented in Tables 3 and 4; Figure 3 shows the unit-cell parameters of iron nitride per formula unit, with the respective values for FeN x obtained earlier [20,21] given for comparison. The previous and new data fall within the same trend, except for two points with low contents of nitrogen in iron nitride in run 1036_7_2 of [20], which may result from bad choice of quench crystals. Without these two points, the approximating relationship V fu (N x ) plotted using data of three experimental series in the systems Fe-Fe 3 C-Fe 3 N, FeO-Fe 3 C-Fe 3 N, and Fe (Fe 3 C)-fluid receives solid grounds. According to single-crystal XRD, the Fe x O number of Fe (x) in wüstite increases from 0.863 to 1.000 while the unit-cell volume slightly decreases (Table 4). Table 3. Results of X-ray single-crystal analysis of Fe(C,N) n .

Sample
Unit   The phases in the two-phase region FeO + Fe 3 C have a fixed composition revealed by EMPA, because of low solubilities: nitrogen in Fe 3 C (at the level of detection limit), as well as carbon and nitrogen in FeO. The solubility of carbon in Fe 3 N is quite high and reaches 2.7 wt % in association with FeO, which marks the respective solid solution limit. In the three-phase region FeO + Fe 3 C + L, the concentrations of C and N in Fe 3 C and quench melt fit two points in the diagram with a deviation around ± 0.1 wt % ( Table 2). These points limit the respective two-phase fields in the ternary diagram ( Figure 4). The quenched melt of four samples with different relative percentages of FeO, Fe 3 C and L contains 3.7 wt % C and 1.2 wt % N. The composition of iron carbide in these samples is identical, within the error, to that in the two-phase association FeO + Fe 3 C. The situation with the three-phase region FeO + Fe 3 N + L is the same. The compositions of Fe 3 N and L, with errors of ± 0.2 wt % for C and ± 0.1 wt % for N, fit the points in the diagram. The quenched melt equilibrated with FeO and Fe 3 N consists of 91.0-92.5 wt % Fe, 2.7 wt % C, and 3.5 wt % N in three samples, while the composition of iron nitride in these samples is 92.0-92.5 wt % Fe, 2.1 wt % C, and 4.5 wt % N. On the other hand, the concentrations of carbon and nitrogen in the melt from two-phase samples FeO + L vary from 2.1 to 3.7 wt % and 1.2 to 3.5 wt %, respectively. Oxygen in the melt equilibrated with FeO varies from 0.4 to 0.6 wt % in all cases.
Melts that formed in three runs of the additional experimental series (Table 2; Figure 5), with excess oxygen added to the Fe-Fe 3 C-Fe 3 N system, fit into the field FeO + L (3-4 wt % C and 1.5-3.5 wt % N), but contain Fe 3 C and Fe 7 C 3 in two cases. The composition of Fe 3 C is close to ideal, with a minor nitrogen impurity (0.2 wt % N) and Fe 7 C 3. The phase compositions of samples obtained in two runs with the greatest oxygen enrichment (1606_3_5 and 1806_3_6) correspond to the fields Fe 3 N + FeO and Fe 3 C + FeO, while the phases approach the equilibrium.

Phase Relations in System FeO-Fe 3 C-Fe 3 N
The experimental results have revealed phase relations in the FeO-Fe 3 C-Fe 3 N system and were used to plot the isothermal section in the respective ternary diagram. The boundaries of one-, two-, and three-phase fields were outlined according to changes in the set of equilibrium phases (Figures 1  and 4). Specifically, the boundaries of the fields of phases associated with liquid were reconstructed from data on the compositions of the quenched melt equilibrated with solids. Wüstite is unstable in the system at 7.8 GPa and 1350 • C, at ≤0.5 wt % O. At these conditions, the phase relations in the FeO-Fe 3 C-Fe 3 N system (Figures 1 and 4) become similar to those in the Fe-Fe 3 C-Fe 3 N system we studied before [20]. As oxygen increases to exceed 0.5-0.8 wt %, the Fe 3 C, L, and Fe 3 N single-phase fields change to those of two phases (FeO-Fe 3 C, FeO + L, and FeO-Fe 3 N), while the originally two-phase fields Fe 3 C + L and Fe 3 N + L move to three phases: Fe 3 C + FeO + L and Fe 3 N + FeO+L in the regions of high C and N, respectively (Figures 1 and 4).
The synthesized wüstite (space group Fm3m) lacks impurities exceeding the detection limit of EMPA. The concentration of nitrogen in iron carbide was likewise below the EMPA detection limit. It was hard to select relatively large fragments from the samples consisting of fine-grained aggregates. Single-crystal analysis of one suitable carbide grain revealed unit-cell parameters of Fe 3 C, space group Pnma. According to our previous data of the CHN analyzer [20], iron carbide in the Fe-Fe 3 C-Fe 3 N system at 7.8 GPa and 1350 • C in equilibrium with an N-rich melt contained 0.3 to 0.5 wt % nitrogen. N-bearing iron carbide of this kind had a 7-11% larger formula-unit volume than the initial N-free carbide. In EMPA data, carbon in the FeO-Fe 3 C-Fe 3 N system was slightly below the ideal value for Fe 3 C. The concentrations of N and C in phase ε-Fe 3 N, space group P6 3 /mmc (Table 3), vary in a large range. The phase is identical to iron nitride obtained earlier in experiments with the Fe-Fe 3 C-Fe 3 N system under the same P-T conditions. It contains up to 2.7 wt % C and 4.4 wt % N in equilibrium with both C-rich melt and wüstite but 2.1 wt % C and 5.4 wt % N in the case of equilibrium with wüstite alone. Note that at 1 atm ε-Fe 3 N can accommodate a large amount of carbon within the octahedral interstices of the structure, which leads to its transformation to ε-Fe 3 (C/N) [36]. C-bearing iron nitride obtained at high pressure should be considered as carbonitride.
Iron carbide and nitride equilibrated with melt in the FeO-Fe 3 C-Fe 3 N system have their stability fields separated by a two-phase field of FeO + L and thus cannot be co-crystallized from the same melt. Metal melt enriched in carbon and nitrogen is stable within the FeO range from a few fractions of percent to 90 wt % (Figures 1 and 4). The contents of carbon and nitrogen in this melt are, respectively, 3.8 wt % C and 1.2 wt % N if it is in equilibrium with Fe 3 C and FeO but 2.9-3.0 wt % C and 3.5-3.6 wt % N in the case of equilibrium with Fe 3 N and FeO. Oxygen in the melt remains within 0.5-0.8 wt % at any bulk contents of O, C, and N. Thus, oxygen increase leads to greater FeO percentages in the run products but not to the formation of magnetite (Fe 3 O 4 ).

Formation Conditions of Iron Oxide, Carbide, and Nitride Inclusions in Natural Diamonds
The conditions P = 7.8 GPa and T = 1350 • C used for the experiments in our work correspond to the 1300 • C adiabat [23] at a depth of 250 km. Thus, our data can be used to reconstruct the mechanism of native iron oxidation in the upwelling process in the sublithospheric mantle at adiabatic temperatures. Potential temperatures in the near subduction slab zones can be significantly lower. Therefore, additional research is needed to investigate phase equilibria in the FeO-Fe 3 C-Fe 3 N system in the temperature range from 1000 • C to 1350 • C. The obtained experimental evidence demonstrates that partial oxidation of a metal phase containing low carbon and nitrogen in the mantle depleted in volatiles at a depth about 250 km can produce FeO with minor amounts of Fe 3 C; the latter then becomes fully oxidized with release of C 0 [22]. If the mantle is rich in volatiles, the process may lead to the formation of a FeO + Fe 3 C + L association. According to experiments with additional oxygen inputs to the system, oxidation begins with the melt, because it has the greatest oxygen affinity. The melt exposed to oxidation loses iron but gains carbon and nitrogen, which is favorable for the onset of crystallization of Fe 3 C and even Fe 7 C 3 . Therefore, it is reasonable to hypothesize that diamond may crystallize from the melt which undergoes rapid oxidation and becomes supersaturated with respect to carbon. Fe 3 C and Fe 7 C 3 can become unstable as the content of Ni in the metal phase increases to 10 at % at 5.7 GPa [37] and to 20 at % at 10 GPa [15]. Upon further oxidation of the system, it may acquire ever more FeO while the percentage of melt decreases. Note that the concentration of nitrogen in the system increases as well, while the contents of carbon and oxygen remain invariable due to crystallization of FeO and iron carbides. Proceeding from nitrogen partitioning between diamond and iron melt rich in volatiles at D N Dm/Met = 0.013-0.024 [38], one can expect nitrogen increase in diamond that crystallizes from the oxidizing metal melt. Accumulation of nitrogen in the melt subject to oxidation may lead to crystallization of iron nitride and complete melt consumption. At normal thermal conditions in the mantle, crystallization of C-bearing iron nitride (or carbonitride) is possible in the presence of an N-and C-bearing melt within the three-phase field FeO + Fe 3 N + L. This mechanism can explain the formation of coexisting iron nitrides and oxides found as inclusions in mantle diamonds [11,12]. Complete oxidation of the melt and iron nitride can liberate nitrogen which remained fixed in metal phases before. In this case, it can release in the form of N 2 and, being almost insoluble in silicates at high fO 2 [39], rise to the surface as part of a fluid by degassing. Such behavior of nitrogen differs markedly from the fate of carbon after the oxidation of iron carbide or the metal melt which are the main carbon hosts in the reduced mantle. As the metal phases become oxidized, carbon remains in mantle rocks either in the elemental form C 0 (graphite or diamond) or being bound in carbonates or carbonate-silicate melts.
Inclusions in both peridotitic and eclogitic natural diamonds often contain magnetite along with iron carbide and metallic iron [5,7,8,[10][11][12]. Some authors [10][11][12] infer that magnetite can crystallize from a metal growth medium of diamond before the encapsulation of inclusions. Note that magnetite inclusions were found in diamonds synthesized in the Fe-Ni-C system at 1400 • C and 5.0-6.5 GPa [40]. Our data on phase relations in the FeO-Fe 3 C-Fe 3 N system and on oxidation of its different phases in the presence of excess oxygen provide direct evidence that metal melt is stable at 7.8 GPa and 1350 • C, i.e., at the P-T parameters corresponding to the conditions near the metal phase precipitation boundary at a depth of 250 km. However, only FeO can crystallize from the melt subject to oxidation until complete consumption of the latter.
It is pertinent to discuss the formation mechanism of magnetite in diamond-hosted inclusions. As it was shown by [41], magnetite is out of equilibrium with C 0 and begins to reduce until wüstite at 7.7 GPa and >1150 • C. Thus, the reverse process of wüstite oxidation to magnetite is possible at ≤ 1150 • C. The lowest temperature, at which diamond can crystallize from the metal melt which compositionally corresponds to inclusions of native iron, has been a subject of extensive research.
In the system Fe-Fe 3 C, the estimated eutectic temperature was slightly below 1350 • C at 5.7 GPa [37] and was inferred to be 1364 • C at 7.8 GPa by interpolation of data from [17]. Inclusions of native iron in diamond often contain nickel and sulfur impurities [5,7,8,[10][11][12] which can extend considerably the stability field of the metal melt, both in temperature and composition. Eutectic temperatures in systems that simulate native iron can fall below 1200 • C at high contents of sulfur [42]. At 6 GPa and <1200 • C, magnetite potentially can crystallize together with iron carbides from a metal melt containing 18-23 wt % S [42]. However, diamond cannot crystallize from such an S-rich melt at these P-T conditions [43], and metastable graphite crystallizes instead. Meanwhile, oxygen excess in the metal melt causes no influence on its diamond-forming ability [44]. Thus, magnetite, at the temperature of its stability, hardly can co-crystallize with diamond from a metal melt corresponding in composition to metal inclusions.
A more realistic hypothesis is that magnetite crystallizes at temperatures below the iron alloy solidus. Then, the final crystallization of diamond at ≤1200 • C is possible from a relatively oxidized H 2 O-CO 2 fluid or from a carbonate-silicate melt [14,[45][46][47][48][49][50][51]. In this case, the diamond growth medium can be at the same time a source of oxygen for the reaction 3FeO + 1/2O 2 →Fe 3 O 4 . The formation of oxidized fluids or carbonate melts can result from upwelling of metal-bearing peridotite to the depths where majorite garnet is unstable [4] or from oxidized carbonate-bearing metapelite in subduction zones [16]. Note that the formation of magnetite from wüstite by the disproportionation reaction 4FeO→Fe 3 O 4 +Fe 0 does not require additional oxygen sources. This reaction can easily occur within an already entrapped inclusion but is possible only below 700 • C at pressures below 10 GPa [51]. However, the disproportionation of wüstite, or wüstite associated with metallic iron, would produce a mixture of phases with ≤ 0.5 mole fraction of magnetite, which does not occur in reality judging by data of [10].

Conclusions
The phase relations in the FeO-Fe 3 C-Fe 3 N system revealed in experiments at 7.8 GPa and 1350 • C have implications for the process of native iron oxidation in the mantle near the 250 km boundary. Wüstite (space group Fm3m) turns out to be the only stable iron oxide in equilibrium with iron carbide. Its co-crystallization with Fe 3 C (space group Pnma), ε-Fe 3 N (space group P6 3 /mmc), or with metal melt begins if the system contains > 0.5 wt % O and stops once the system attains complete oxidation. No magnetite has been found in the run products. At pressures and temperatures corresponding to thẽ 250 km mantle depth and at a normal heat flux of 40 mW/m 2 , the metal melt is less stable to oxidation than iron carbide or nitride. Co-crystallization of Fe 3 C and Fe 3 N from an oxidizing melt is impossible because the fields of coexisting phases rich in carbon and nitrogen are separated by that of FeO + L. Additional inputs of oxygen into the system lead to the formation of FeO, to the crystallization of Fe 3 C and Fe 7 C 3 , and to nitrogen enrichment of the residual melt. In the mantle containing 250 ppm C and 100 ppm N, this process can induce crystallization of iron nitride. The reported results show that iron carbides and nitrides found enclosed in mantle diamonds may have formed by oxidation of metal melts that originally contained quite small amounts of carbon and nitrogen. Funding: This research was funded by the Russian Science Foundation, grant number 16-17-10041, and by state assignment of IGM SB RAS (effect of excess oxygen on phase equilibrium in the system).