### Phase equilibria and phase compositions

Experiments at 2 GPa, 1500°C (G#2) and 10 GPa, 1700°C (G#6) resulted in equilibrated olivine + orthopyroxene + SiC plus iron silicides (Table 1, Figure 1). The experiment at 10 GPa, 1500°C (G#3) resulted in coarse opx + SiC plus three iron silicides (FeSi, FeSi_{2}, and FeSi_{4}) and olivine that did not develop equilibrium rims large enough for measurement. These charges did not contain any residual silicates from the starting material, but in both the 1500°C and 1700°C experiments at 10 GPa, most of the San Carlos olivine disintegrated to an almost Fe-free olivine containing many submicron iron silicide inclusions (Figure 1b). These inclusions are too small to determine their stoichiometry. The equilibrium *X*
_{
Mg
} of olivine and opx in these experiments are 0.993-0.998 (Table 1). Initially, we added Ir metal as internal oxygen fugacity monitor (Woodland and O’Neill, [1997]; Stagno and Frost, [2010]), this experiment (G#1) at 1300°C, 2 GPa yielded opx (*X*
_{
Mg
} = 0.982) and quartz. However, abundant residual starting material San Carlos olivine testifies for incomplete equilibration questioning whether the *X*
_{
Mg
} of the opx of this experiment corresponds to equilibrium with SiC. We have thus only used experiments #2, #3 and #6 for oxygen fugacity calculations.

### Oxygen fugacity (*f*
_{
O2
}) in the experiments

For the experiments, which yielded iron silicides and equilibrium compositions of olivine and orthopyroxene, oxygen fugacities were calculated from equilibrium (1) and (2), employing the olivine and orthopyroxene activity formulations from O’Neill and Wall ([1987]).

1\phantom{\rule{0.25em}{0ex}}\mathrm{ferrosilite}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}2\phantom{\rule{0.25em}{0ex}}\mathrm{FeSi}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}3\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(1)

1\phantom{\rule{0.25em}{0ex}}\mathrm{fayalite}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{\mathrm{F}\mathrm{e}}_{2}\mathrm{S}\mathrm{i}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}2\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(2)

At equilibrium,

0=2\phantom{\rule{0.12em}{0ex}}{G}_{\mathrm{FeSi}}^{P,T}+3\phantom{\rule{0.24em}{0ex}}{G}_{\mathrm{O}2}^{P,T}-{G}_{\mathrm{fs}}^{P,T}-\mathrm{R}\phantom{\rule{0.24em}{0ex}}T\phantom{\rule{0.24em}{0ex}}ln\frac{{a}_{\mathrm{O}2}^{3}}{{a}_{\mathrm{fs}}^{\mathrm{opx}}}\text{,}

(3)

FeSi being a pure phase and

0={G}_{\mathrm{F}\mathrm{e}2\mathrm{S}\mathrm{i}}^{P,T}+2\phantom{\rule{0.12em}{0ex}}{G}_{\mathrm{O}2}^{P,T}-{G}_{\mathrm{fay}}^{P,T}+\mathrm{R}\phantom{\rule{0.24em}{0ex}}T\phantom{\rule{0.12em}{0ex}}ln\frac{{a}_{\mathrm{O}2}^{2}}{{a}_{\mathrm{fay}}^{\mathrm{olivine}}}\text{,}

(4)

Fe_{2}Si being a pure phase. This leads to

\mathit{\text{log}}{f}_{\mathrm{O}2}=\left(-\phantom{\rule{0.25em}{0ex}}\frac{\left(2\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{FeSi}}^{P,T}+3\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{O}2}^{P,T}-\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{fs}}^{P,T}\right)}{2.3025\phantom{\rule{0.25em}{0ex}}\mathit{R}\phantom{\rule{0.25em}{0ex}}T}+\phantom{\rule{0.25em}{0ex}}\mathit{\text{log}}{a}_{\mathrm{fs}}^{\mathrm{o}\mathrm{p}\mathrm{x}}\right)/3\text{,}

(5)

using the measured opx composition, log *f*
_{
O 2} = − 11.2 (5) or \Delta \mathit{\text{log}}{f}_{O2}^{IW}=\phantom{\rule{0.25em}{0ex}}-4.9 results for G#3 at 10 GPa, 1500°C. For the Fe_{2}Si equilibrium (4)

log{f}_{\mathrm{O}2}=\left(\phantom{\rule{0.25em}{0ex}}-\phantom{\rule{0.25em}{0ex}}\frac{\left({G}_{\mathrm{F}\mathrm{e}2\mathrm{S}\mathrm{i}}^{P,T}+2\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{O}2}^{P,T}-\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{fay}}^{P,T}\right)}{2.3025\phantom{\rule{0.25em}{0ex}}\mathrm{R}\phantom{\rule{0.25em}{0ex}}T}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}log{a}_{\mathrm{fay}}^{\mathrm{olivine}}\phantom{\rule{0.25em}{0ex}}\right)/2\text{,}

(6)

measured olivine compositions yield log *f*
_{
O 2} = − 13.3 (10a, 10b) or \mathit{\Delta}\mathit{\text{log}}{f}_{O2}^{IW}=\phantom{\rule{0.25em}{0ex}}-4.6 for G#2 at 2 GPa, 1500°C; and log *f*
_{
O 2} = − 11.9 (4) or \Delta \mathit{\text{log}}{f}_{O2}^{\mathrm{I}\mathrm{W}}=\phantom{\rule{0.25em}{0ex}}-5.8 for G#6 at 10 GPa, 1700°C. For the two experiments G#2 and G#6, which resulted in equilibrated olivine and orthopyroxene, oxygen fugacities were also calculated from

1\phantom{\rule{0.25em}{0ex}}\mathrm{ferrosilite}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{graphite}/\mathrm{diamond}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{fayalite}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{SiC}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(7)

At equilibrium

0\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{SiC}}^{P,T}+1\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{O}2}^{P,T}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{fay}}^{P,T}-1\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{fs}}^{P,T}-\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{graph}/\mathrm{diam}}^{P,T}+\mathrm{R}\phantom{\rule{0.25em}{0ex}}\mathrm{T}ln\phantom{\rule{0.25em}{0ex}}\frac{{a}_{\mathrm{O}2}\bullet {a}_{\mathrm{fay}}^{\mathrm{olivine}}}{{a}_{\mathrm{fs}}^{\mathrm{o}\mathrm{p}\mathrm{x}}}

(8)

and

\mathit{\text{log}}{f}_{O2}=\phantom{\rule{0.25em}{0ex}}\frac{\left({G}_{\mathrm{fs}}^{P,T}+{G}_{\mathrm{graph}/\mathrm{diam}}^{P,T}-\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{fay}}^{P,T}-\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{SiC}}^{P,T}-\phantom{\rule{0.25em}{0ex}}{G}_{\mathrm{O}2}^{P,T}\right)}{2.3025\phantom{\rule{0.25em}{0ex}}\mathrm{R}\phantom{\rule{0.25em}{0ex}}T}\phantom{\rule{0.25em}{0ex}}-\phantom{\rule{0.25em}{0ex}}\mathit{\text{log}}{a}_{\mathrm{fay}}^{\mathrm{olivine}}+\phantom{\rule{0.25em}{0ex}}\mathit{\text{log}}{a}_{\mathrm{fs}}^{\mathrm{o}\mathrm{p}\mathrm{x}}\text{.}

(9)

SiC and graphite or diamond being pure phases. The resulting oxygen fugacities are log *f*
_{
O 2} = − 15.1. (6) or \Delta \mathit{\text{log}}{f}_{O2}^{IW}=\phantom{\rule{0.25em}{0ex}}-6.4. at 2 GPa, 1500°C (G#2), and log *f*
_{
O 2} = − 10.6 (4) or \Delta \mathit{\text{log}}{f}_{O2}^{IW}=\phantom{\rule{0.25em}{0ex}}-5.6 at 10 GPa, 1700°C (G#2).

### Calculation of *T-f*
_{
O2
}sections

#### Reactions governing reduced phases in the mantle

To understand the succession of phase assemblages with decreasing oxygen fugacity, we calculated *f*
_{
O 2}-temperature diagrams (Figure 2) and phase compositions (Figures 3 and 4) for a model harzburgite at 2 and 10 GPa. For reference, we also give the quartz-fayalite-magnetite (QFM), the graphite/diamond-CO_{2}-CO equilibrium (CCO), and the iron-wustite buffer (IW), even if these do not occur as reactions in the harzburgite phase diagram. The position of the iron-wustite buffer is calculated from Campbell et al. ([2009]), which yields about half a log-unit lower values than the formulation of O'Neill ([1988]).

In the carbon-bearing upper mantle, the iron-wustite equilibrium does not occur, its equivalent leading to the appearance of reduced Fe^{0} are the iron carbide forming reactions

6\phantom{\rule{0.25em}{0ex}}\mathrm{olivine}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}2\phantom{\rule{0.25em}{0ex}}\mathrm{graphite}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}3\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{p}\mathrm{x}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}2\phantom{\rule{0.25em}{0ex}}\mathrm{cementite}\phantom{\rule{0.25em}{0ex}}\left({\mathrm{F}\mathrm{e}}_{3}\mathrm{C}\right)\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}3\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(10a)

and

14\phantom{\rule{0.25em}{0ex}}\mathrm{olivine}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}3\phantom{\rule{0.25em}{0ex}}\mathrm{diamond}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}7\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{p}\mathrm{x}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}2\phantom{\rule{0.25em}{0ex}}{\mathrm{F}\mathrm{e}}_{7}{\mathrm{C}}_{3}+\phantom{\rule{0.25em}{0ex}}7\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(10b)

which are only stable at relatively low temperatures, i.e. 1140 to 1260°C at 2 to 10 GPa. At higher temperatures, carbides do not form but a metal alloy results from

2\phantom{\rule{0.25em}{0ex}}\mathrm{olivine}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}2\mathrm{x}\phantom{\rule{0.25em}{0ex}}\mathrm{graphite}/\mathrm{diamond}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{p}\mathrm{x}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}\left(2+2\mathrm{x}\right)\phantom{\rule{0.25em}{0ex}}{\mathrm{FeSiC}}^{\mathrm{alloy}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(11)

where FeSiC^{alloy} is a ternary metal solid solution. The stoichiometry of reaction (11) depends on the alloy composition. The molar fraction of C in the alloy ranges from 0.13 to 0.33 at 2-10 GPa, 1150-1700°C. At oxygen fugacities of initial metal formation, Si-fractions are <0.1 mol% in the alloy. For a graphite/diamond saturated mantle with a bulk *X*
_{
Mg
} of 0.9, reactions (10a, 10b) and (11) occur at 2 GPa about one log-unit below the iron-wustite buffer and about one log-unit above IW at 10 GPa (Figure 2a,b). About 5-9 log-units below the carbide-forming reactions, increasing chemical potential of Si leads to the replacement of Fe_{3}C or Fe_{7}C_{3} by the FeSiC-alloy then containing significant Si (Figure 5b,d). Silicon contents in the alloy increase with decreasing oxygen fugacity leading to a phase transition from a face centered to a body centered metal structure (fcc and bcc in Figure 5).

Silica carbide forms principally through a reaction involving moissanite, olivine, orthopyroxene and elemental carbon as graphite or diamond (moissanite-olivine-opx-carbon: MOOC)

1\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{p}\mathrm{x}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{graphite}/\mathrm{diamond}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{olivine}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{SiC}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(12)

at 2 GPa at 7.7-4.8 log-units (1100-1700°C) below equilibria (10a, 10b) and (11). At 10 GPa this difference is 9.9-6.5 log units (1100-1700°C). This corresponds to a Δlog*f*
_{
O2
} of IW-9 to IW-6, the difference decreasing with temperature. Along a mantle adiabat, moissanite forms at IW-8.0 at 2 GPa and at IW-6.7 at 10 GPa. Reaction (12) was previously identified as being responsible for the appearance of moissanite in the upper mantle (Mathez et al. [1995]; Ulmer et al. [1998]).

Further reduction causes the FeSiC-alloy to be replaced by stoichiometric iron silicide FeSi. At 2 GPa this happens about ½ a log-unit below the SiC-buffer (12), while at 10 GPa, the FeSi-forming reaction intersects reaction (12) leading to an invariant point. At about 3 and 5 log-units below the SiC-forming reaction (12), opx and then olivine (at these conditions pure enstatite and forsterite, respectively) become unstable and a ternary metal alloy of almost pure Si forms through

1\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{p}\mathrm{x}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}0.01\phantom{\rule{0.25em}{0ex}}\mathrm{SiC}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{olivine}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1.01\phantom{\rule{0.25em}{0ex}}{\mathrm{S}\mathrm{i}}^{\mathrm{alloy}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(13)

1\phantom{\rule{0.25em}{0ex}}\mathrm{olivine}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}0.01\phantom{\rule{0.25em}{0ex}}\mathrm{SiC}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}\mathrm{periclase}\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}1.01\phantom{\rule{0.25em}{0ex}}{\mathrm{S}\mathrm{i}}^{\mathrm{alloy}}+\phantom{\rule{0.25em}{0ex}}1\phantom{\rule{0.25em}{0ex}}{\mathrm{O}}_{2}

(14)

where the Si-alloy has 1 mol% C. Completion of reactions (13) and (14) would leave no oxidized Si. The calculations do not indicate any Fe in the Si metal and only 0.2 to 1.3% C. Reaction (13) is relevant in nature as pure Si-metal attached to SiC has been reported by Trumbull et al. ([2009]).

Summarizing, a harzburgitic mantle would have the following succession of reduced phases: graphite/diamond → (Fe_{3}C/Fe_{7}C_{3}) → Fe-rich FeSiC^{alloy} → SiC → FeSi → Si^{alloy}. At pressures ≥10 GPa, FeSi may form before moissanite.

Note that our calculations do not include liquids and that at high temperatures FeSiC^{alloy} and FeSi become metastable with respect to liquid. This is of particular relevance at oxygen fugacities just below the metal-forming reaction (11) where a *de facto* binary FeC-alloy is almost Si-free. The Fe-C eutectic is located at 1150°C, 1 atm (Chipman [1972]) and 1210°C, 10 GPa (Hirayama et al. [1993]; Rohrbach et al. [2014]), although this location is not entirely unambiguous as Lord et al. ([2009]) report the eutectic at 10 GPa at 1420°C. In a graphite/diamond-saturated system, the ternary FeSiC-alloy would then be replaced by a metallic melt phase. FeSi has a temperature of congruent melting of 1410°C at 1 atm (Lacaze and Sundman [1991]), but to our knowledge its high pressure melting is unknown.

### Mineral compositions at reduced conditions

The above reactions are discontinuous reactions that delineate the various stability fields. For the silicate mantle the continuous reactions consuming the fayalite and ferrosilite components in olivine and orthopyroxene are more dramatic. As illustrated in Figures 3 and 4, *X*
_{
Mg
} in olivine is almost invariant in each field of coexistence with magnesite or graphite/diamond. Immediately below the metal forming reaction, Fe^{2+} becomes strongly reduced, within only 2 log-units, the *X*
_{
Mg
} of olivine (and similarly opx) in equilibrium with metal or Fe_{3}C/Fe_{7}C_{3} and graphite/diamond increases to ~0.99 (Figures 3 and 4). When oxygen contents corresponding to the oxygen fugacities of SiC are reached, the equilibrium *X*
_{
Mg
} in the silicates is >0.999, almost invariant with pressure and temperature (at least for 1100-1700°C, 2-10 GPa). This confirms the experimental findings. Concomitant with the increase in *X*
_{
Mg
} of the silicates, an increase of the Si-content of the FeSiC-alloy is predicted (Figures 4 and 5), mirrored by a decrease of *X*
_{
Fe
}
^{metal} from ~0.90 to 0.70 at 2 GPa and from 0.76 to 0.66 at 10 GPa.

### Silica carbide stability with temperature and pressure

A major question concerning the stability of SiC in the mantle regards the evolution of the difference in oxygen fugacity between the metal or Fe-carbide forming (10a, 10b, 11) and the SiC-forming reactions (12). This difference, Δlog*f*
_{
O 2}
^{(12)-(10a,10b,11)}, decreases with increasing temperature but at near-adiabatic temperatures only by -0.1 log-units per 100°C. With increasing pressure there is a slight increase of Δlog*f*
_{
O 2} between the moissanite forming reaction and the equivalent of IW in the mantle such that along a mantle adiabat Δlog*f*
_{
O 2}
^{(12)-(10a,10b,11)} remains almost constant at ~ -4.5.