An Efficient Way to Model Complex Iron Carbides: A Benchmark Study of DFTB2 against DFT

Iron carbides have attracted increasing attention in recent years due to their enormous potential in catalytic fields, such as Fischer-Tropsch synthesis and the growth of carbon nanotubes. Theoretical calculations can provide a more thorough understanding of these reactions at the atomic scale. However, due to the extreme complexity of the active phases and surface structures of iron carbides at the operando conditions, calculations based on density functional theory (DFT) are too costly for realistically large models of iron carbide particles. Therefore, a cheap and efficient quantum mechanical simulation method with accuracy comparable to DFT is desired. In this work, we adopt the spin-polarized self-consistent charge density functional tight-binding (DFTB2) method for iron carbides by reparametrization of the repulsive part of the Fe-C interactions. To assess the performance of the improved parameters, the structural and electronic properties of iron carbide bulks and clusters obtained with DFTB2 method are compared with the previous experimental values and the results obtained with DFT approach. Calculated lattice parameters and density of states are close to DFT predictions. The benchmark results show that the proposed parametrization of Fe-C interactions provides transferable and balanced description of iron carbide systems. Therefore, spin-polarized DFTB2 is valued as an efficient and reliable method for the description of iron carbide systems.

Carbon sequestration during core formation implied by complex carbon polymerization

Current estimates of the carbon flux between the surface and mantle are highly variable, and the total amount of carbon stored in closed hidden reservoirs is unknown. Understanding the forms in which carbon existed in the molten early Earth is a critical step towards quantifying the carbon budget of Earth's deep interior. Here we employ first-principles molecular dynamics to study the evolution of carbon species as a function of pressure in a pyrolite melt. We find that with increasing pressure, the abundance of CO₂ and CO₃ species decreases at the expense of CO₄ and complex oxo-carbon polymers (C_xO_y) displaying multiple C-C bonds. We anticipate that polymerized oxo-carbon species were a significant reservoir for carbon in the terrestrial magma ocean. The presence of Fe-C clusters suggests that upon segregation, Fe-rich metal may partition a significant fraction of carbon from the silicate liquid, leading to carbon transport into the Earth's core.

The amount of carbon stored in closed hidden reservoirs is unknown. Here the authors use a computational approach to study the evolution of carbon species and observe polymerization of carbon atoms at high pressures, illustrating the potential for a significant carbon reservoir in the Earth’s deep interior.

New high-pressure phases of Fe7N3 and Fe7C3 stable at Earth's core conditions: evidences for carbon–nitrogen isomorphism in Fe-compounds

We carried out ab initio calculations on the crystal structure prediction and determination of P–T diagrams within the quasi-harmonic approximation for Fe₇N₃ and Fe₇C₃. Two new isostructural phases Fe₇N₃-C2/m and Fe₇C₃-C2/m which are dynamically and thermodynamically stable under the Earth's core conditions were predicted. The Fe₇C₃-C2/m phase stabilizes preferentially to the known h-Fe₇C₃ at 253–344 GPa in the temperature range of 0–5000 K, and the Fe₇N₃-C2/m stabilizes preferentially relative to the β-Fe₇N₃ – at ∼305 GPa over the entire temperature range. This indicate that carbon and nitrogen can mutually coexist and replace each other in the Earth's and other planetary cores similarly to low pressure phases of the same compounds.

We carried out ab initio calculations on the crystal structure prediction and determination of P–T diagrams within the quasi-harmonic approximation for Fe₇N₃ and Fe₇C₃.

Mössbauer Spectroscopy of Iron Carbides: From Prediction to Experimental Confirmation

The Mössbauer spectroscopy of iron carbides (α-Fe, γ'-FeC, η-Fe2C, ζ-Fe2C, χ-Fe5C2, h-Fe7C3, θ-Fe3C, o-Fe7C3, γ'-Fe4C, γ''-Fe4C, and α'-Fe16C2) is predicted utilizing the all electron full-potential linearized augmented plane wave (FLAPW) approach across various functionals from LDA to GGA (PBE, PBEsol, and GGA + U) to meta-GGA to hybrid functionals. To validate the predicted MES from different functionals, the single-phase χ-Fe5C2 and θ-Fe3C are synthesized in experiment and their experimental MES under different temperature (from 13 K to 298 K) are determined. The result indicates that the GGA functional (especially, the PBEsol) shows remarkable success on the prediction of Mössbauer spectroscopy of α-Fe, χ-Fe5C2 and θ-Fe3C with delocalized d electrons. From the reliable simulations, we propose a linear relationship between Bhf and μB with a slope of 12.81 T/μB for iron carbide systems and that the proportionality constant may vary from structure to structure.

Carbon-depleted outer core revealed by sound velocity measurements of liquid iron-carbon alloy

The relative abundance of light elements in the Earth's core has long been controversial. Recently, the presence of carbon in the core has been emphasized, because the density and sound velocities of the inner core may be consistent with solid Fe₇C₃. Here we report the longitudinal wave velocity of liquid Fe₈₄C₁₆ up to 70 GPa based on inelastic X-ray scattering measurements. We find the velocity to be substantially slower than that of solid iron and Fe₃C and to be faster than that of liquid iron. The thermodynamic equation of state for liquid Fe₈₄C₁₆ is also obtained from the velocity data combined with previous density measurements at 1 bar. The longitudinal velocity of the outer core, about 4% faster than that of liquid iron, is consistent with the presence of 4–5 at.% carbon. However, that amount of carbon is too small to account for the outer core density deficit, suggesting that carbon cannot be a predominant light element in the core.

The composition of the Earth's core, particularly the light elements present, is not well constrained. Here, the authors report sound velocities of liquid iron-carbon alloy as measured at very high pressures using inelastic X-ray scattering and suggest that carbon cannot be predominant in the outer core.

Hidden carbon in Earth's inner core revealed by shear softening in dense Fe7C3

Earth's inner core is known to consist of crystalline iron alloyed with a small amount of nickel and lighter elements, but the shear wave (S wave) travels through the inner core at about half the speed expected for most iron-rich alloys under relevant pressures. The anomalously low S-wave velocity (vS) has been attributed to the presence of liquid, hence questioning the solidity of the inner core. Here we report new experimental data up to core pressures on iron carbide Fe7C3, a candidate component of the inner core, showing that its sound velocities dropped significantly near the end of a pressure-induced spin-pairing transition, which took place gradually between 10 GPa and 53 GPa. Following the transition, the sound velocities increased with density at an exceptionally low rate. Extrapolating the data to the inner core pressure and accounting for the temperature effect, we found that low-spin Fe7C3 can reproduce the observed vS of the inner core, thus eliminating the need to invoke partial melting or a postulated large temperature effect. The model of a carbon-rich inner core may be consistent with existing constraints on the Earth's carbon budget and would imply that as much as two thirds of the planet's carbon is hidden in its center sphere.

Carbon and other light element contents in the Earth's core based on first-principles molecular dynamics

Carbon (C) is one of the candidate light elements proposed to account for the density deficit of the Earth's core. In addition, C significantly affects siderophile and chalcophile element partitioning between metal and silicate and thus the distribution of these elements in the Earth's core and mantle. Derivation of the accretion and core-mantle segregation history of the Earth requires, therefore, an accurate knowledge of the C abundance in the Earth's core. Previous estimates of the C content of the core differ by a factor of ∼20 due to differences in assumptions and methods, and because the metal-silicate partition coefficient of C was previously unknown. Here we use two-phase first-principles molecular dynamics to derive this partition coefficient of C between liquid iron and silicate melt. We calculate a value of 9 ± 3 at 3,200 K and 40 GPa. Using this partition coefficient and the most recent estimates of bulk Earth or mantle C contents, we infer that the Earth's core contains 0.1-0.7 wt% of C. Carbon thus plays a moderate role in the density deficit of the core and in the distribution of siderophile and chalcophile elements during core-mantle segregation processes. The partition coefficients of nitrogen (N), hydrogen, helium, phosphorus, magnesium, oxygen, and silicon are also inferred and found to be in close agreement with experiments and other geochemical constraints. Contents of these elements in the core derived from applying these partition coefficients match those derived by using the cosmochemical volatility curve and geochemical mass balance arguments. N is an exception, indicating its retention in a mantle phase instead of in the core.

Sound velocities of Fe and Fe-Si alloy in the Earth's core

Compressional wave velocity-density (V(P)--ρ) relations of candidate Fe alloys at relevant pressure-temperature conditions of the Earth's core are critically needed to evaluate the composition, seismic signatures, and geodynamics of the planet's remotest region. Specifically, comparison between seismic V(P)--ρ profiles of the core and candidate Fe alloys provides first-order information on the amount and type of potential light elements--including H, C, O, Si, and/or S-needed to compensate the density deficit of the core. To address this issue, here we have surveyed and analyzed the literature results in conjunction with newly measured V(P)--ρ results of hexagonal closest-packed (hcp) Fe and hcp-Fe(0.85)Si(0.15) alloy using in situ high-energy resolution inelastic X-ray scattering and X-ray diffraction. The nature of the Fe-Si alloy where Si is readily soluble in Fe represents an ideal solid-solution case to better understand the light-element alloying effects. Our results show that high temperature significantly decreases the V(P) of hcp-Fe at high pressures, and the Fe-Si alloy exhibits similar high-pressure V(P)--ρ behavior to hcp-Fe via a constant density offset. These V(P)--ρ data at a given temperature can be better described by an empirical power-law function with a concave behavior at higher densities than with a linear approximation. Our new datasets, together with literature results, allow us to build new V(P)--ρ models of Fe alloys in order to determine the chemical composition of the core. Our models show that the V(P)--ρ profile of Fe with 8 wt % Si at 6,000 K matches well with the Preliminary Reference Earth Model of the inner core.

Synthesis of Binary Transition Metal Nitrides, Carbides and Borides from the Elements in the Laser-Heated Diamond Anvil Cell and Their Structure-Property Relations

Transition metal nitrides, carbides and borides have a high potential for industrial applications as they not only have a high melting point but are generally harder and less compressible than the pure metals. Here we summarize recent advances in the synthesis of binary transition metal nitrides, carbides and borides focusing on the reaction of the elements at extreme conditions generated within the laser-heated diamond anvil cell. The current knowledge of their structures and high-pressure properties like high-(p,T) stability, compressibility and hardness is described as obtained from experiments.