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We report the thermal Equation of State (EoS) of the non-magnetic Fe 3 C phase based on in situ X‑ray difraction (XRD) experiments to 117 GPa and 2100 K. High-pressure and temperature unit-cell volume measurements of Fe 3 C were conducted in a laser-heated diamond-anvil cell. Our pressure-volume-temperature ( P-V-T ) data together with existing data were fit to the Vinet equation of state with the Mie-Grüneisen-Debye thermal pressure model, yielding  V  0  = 151.6(12) Å 3 ,  K  0  = 232(24) GPa,  K  0  = 5.09(46), γ 0  = 2.3(3), and q = 3.4 (9) with θ 0  = 407 K (fixed). The high- T  data were also fit to the thermal pressure model with a constant α K  T  term,  P  Th  = α K  T (Δ T ), and there is no observable pressure or temperature dependence, which implies minor contributions from the anharmonic and electronic terms. Using the established EoS for Fe 3 C, we made thermodynamic calculations on the  P-T  locations of the breakdown reaction of Fe 3 C into Fe 7 C 3  and Fe. The reaction is located at 87 GPa and 300 K and 251 GPa and 3000 K. An invariant point occurs where Fe, Fe 3 C, Fe 7 C 3 , and liquid are stable, which places constraints on the liquidus temperature of the outer core, namely inner core crystallization temperature, as the inner core would be comprised by the liquidus phase. Two possible  P-T  locations for the invariant point were predicted from existing experimental data and the reaction calculated in this study. The two models result in different liquidus “phases” at the outer core-inner core boundary pressure: Fe 3 C at 5300 K and Fe 7 C 3  at 3700 K. The Fe 7 C 3  inner core can account for the density, as observed by seismology, while the Fe 3 C inner core cannot. The relevance of the system Fe-C to Earth’s core can be resolved by constructing a thermodynamic model for melting relations under core conditions as the two models predict very different liquidus temperatures.

P-V-T measurements of Fe 3 C to 117 GPa and 2100 K: Implications for stability of Fe 3 C phase at core conditions