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Thermal equation of state and thermodynamic properties of iron carbide Fe 3 C to 31 GPa and 1473 K
Author(s) -
Litasov Konstantin D.,
Sharygin Igor S.,
Dorogokupets Peter I.,
Shatskiy Anton,
Gavryushkin Pavel N.,
Sokolova Tatiana S.,
Ohtani Eiji,
Li Jie,
Funakoshi Kenichi
Publication year - 2013
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2013jb010270
Subject(s) - orthorhombic crystal system , thermoelastic damping , equation of state , thermodynamics , grüneisen parameter , materials science , debye model , phase (matter) , phase transition , paramagnetism , analytical chemistry (journal) , crystallography , chemistry , thermal expansion , condensed matter physics , thermal , physics , crystal structure , organic chemistry , chromatography
Abstract Resent experimental and theoretical studies suggested preferential stability of Fe 3 C over Fe 7 C 3 at the condition of the Earth's inner core. Previous studies showed that Fe 3 C remains in an orthorhombic structure with the space group Pnma to 250 GPa, but it undergoes ferromagnetic (FM) to paramagnetic (PM) and PM to nonmagnetic (NM) phase transitions at 6–8 and 55–60 GPa, respectively. These transitions cause uncertainties in the calculation of the thermoelastic and thermodynamic parameters of Fe 3 C at core conditions. In this work we determined P‐V‐T equation of state of Fe 3 C using the multianvil technique and synchrotron radiation at pressures up to 31 GPa and temperatures up to 1473 K. A fit of our P‐V‐T data to a Mie‐Gruneisen‐Debye equation of state produce the following thermoelastic parameters for the PM‐phase of Fe 3 C: V 0 = 154.6 (1) Å 3 , K T 0 = 192 (3) GPa, K T ′ = 4.5 (1), γ 0 = 2.09 (4), θ 0 = 490 (120) К, and q = −0.1 (3). Optimization of the P‐V‐T data for the PM phase along with existing reference data for thermal expansion and heat capacity using a Kunc‐Einstein equation of state yielded the following parameters: V 0 = 2.327 cm 3 /mol (154.56 Å 3 ), K T 0 = 190.8 GPa, K T ′ = 4.68, Θ E10 = 305 K (which corresponds to θ 0 = 407 K), γ 0 = 2.10, e 0 = 9.2 × 10 −5 K −1 , m = 4.3, and g = 0.66 with fixed parameters m E 1 = 3 n = 12, γ ∞ = 0, β = 0.3, and a 0 = 0. This formulation allows for calculations of any thermodynamic functions of Fe 3 C versus T and V or versus T and P . Assuming carbon as the sole light element in the inner core, extrapolation of our equation of state of the NM phase of Fe 3 C suggests that 3.3 ± 0.9 wt % С at 5000 К and 2.3 ± 0.8 wt % С at 7000 К matches the density at the inner core boundary.