First-principles calculations of properties of orthorhombic iron carbide<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>7</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>at the Earth's core conditions

Raza, Zamaan; Shulumba, Nina; Caffrey, Nuala M.; Dubrovinsky, Leonid; Abrikosov, Igor A.

doi:10.1103/physrevb.91.214112

Cited by 22 publications

(21 citation statements)

References 35 publications

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“…A possible solution to this puzzle, as indicated by Raza et al . [], is that Fe 7 C 3 may decompose to more stable stoichiometries such as Fe 2 C and Fe 3 C. However, this conjecture is based on zero temperature calculation, which is questionable at a high temperature that corresponds to that of Earth's inner core.…”

Section: Resultsmentioning

confidence: 99%

“…In the absence of Si doping, we find h‐Fe 7 C 3 to be more stable compared to o‐Fe 7 C 3 in agreement with the conclusion of Raza et al . [] based on DFT study. Having ascertained thermodynamic stability at Earth's core condition, we moved forward to calculate their elastic properties as a function of pressure, which were compared to the data put forth by the PREM.…”

Section: Discussionmentioning

confidence: 99%

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First‐principles prediction of Si‐doped Fe carbide as one of the possible constituents of Earth's inner core

Das

Chatterjee

Ghosh

et al. 2017

Geophysical Research Letters

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We perform a computational study based on first‐principles calculations to investigate the relative stability and elastic properties of the doped and undoped Fe carbide compounds at 200–364 GPa. We find that upon doping a few weight percent of Si impurities at the carbon sites in Fe7C3 carbide phases, the values of Poisson's ratio and density increase while VP, and VS decrease compared to their undoped counterparts. This leads to marked improvement in the agreement of seismic parameters such as P wave and S wave velocity, Poisson's ratio, and density with the Preliminary Reference Earth Model (PREM) data. The agreement with PREM data is found to be better for the orthorhombic phase of iron carbide (o‐Fe7C3) compared to hexagonal phase (h‐Fe7C3). Our theoretical analysis indicates that Fe carbide containing Si impurities can be a possible constituent of the Earth's inner core. Since the density of undoped Fe7C3 is low compared to that of inner core, as discussed in a recent theoretical study, our proposal of Si‐doped Fe7C3 can provide an alternative solution as an important component of the Earth's inner core.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

First‐principles prediction of Si‐doped Fe carbide as one of the possible constituents of Earth's inner core

Das

Chatterjee

Ghosh

et al. 2017

Geophysical Research Letters

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“…Exchange‐correlation effects were treated in the generalized gradient approximation with the Perdew, Burke, and Ernzerhof (PBE) scheme [ Perdew et al ., ]. As shown in previous studies, PBE works well for the description of the Fe‐C system [ Mookherjee et al ., ; Oganov et al ., ; Raza et al ., ]. Both experiments [ Prescher et al ., ; Chen et al ., ] and calculations [ Mookherjee et al ., ; Raza et al ., ] show the disappearance of magnetic moments at high pressures (53 GPa h ‐Fe 7 C 3 and 70 GPa for o ‐Fe 7 C 3 ), so we performed nonspin polarized calculations for pressures above 70 GPa.…”

Section: Methodsmentioning

confidence: 99%

Thermoelasticity of Fe₇C₃ under inner core conditions

Vočadlo

Brodholt

et al. 2016

JGR Solid Earth

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It has recently been reported, on the basis of extrapolated experimental data, that the iron carbide, Fe7C3, has shear wave velocities and a Poisson's ratio consistent with the seismological values for the Earth's inner core and thus that Fe7C3 is a strong candidate for the inner core composition. In this study, using ab initio molecular dynamics simulations, we report the thermoelastic properties of Fe7C3 at 350 GPa up to its melting temperature. Due to significant elastic softening prior to melting, the calculated elastic properties, including wave velocities, do indeed agree well with those from seismology. However, the density was found to be much too low (by ~8%) when compared to geophysical data, and therefore, Fe7C3 must be ruled out as a major component of the Earth's inner core.

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“…Quasiharmonic calculations suggest that this phase is stable compared to the well known hexagonal phase at experimental conditions, but also suggest that it is considerably less stable than hexagonal at Earth's core conditions. 28 Preliminary anharmonic calculations using TDEP suggest that the orthorhombic phase is, in fact, stabilised at high temperatures at the pressure of the Earth's core. In addition to affecting phase stability, I also demonstrate that temperature and anharmonicity can have a tremendous effect on the mechanical properties of a material.…”

Section: Temperature Dependent Electronic Structure Of Aluminium Nitridementioning

confidence: 99%

“…27 Static calculations suggest that the new orthorhombic phase is more stable than the hexagonal below approximately 100 GPa, but it is not sufficient to merely consider zero temperature calculations when we are interested in stability at the Earth's core, which has a temperature in excess of 5000 K. As a first approximation, we compute the Gibbs free energy of both phases at experimental (150 GPa) and Earth's core pressures (360 GPa), finding that at 150 GPa the orthorhombic phase is marginally less stable but becomes more stable with increasing temperature, and at 360 GPa the hexagonal phase is significantly more stable, a trend that is not changed by increasing the temperature. 28 However, as a first approximation, these calculations do not take anharmonicity into account, and at such high temperatures, anharmonicity is likely to have a decisive effect. One particularly difficult problem is the finite-temperature modelling of random alloys, i.e.…”

Section: Introductionmentioning

confidence: 99%

Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

Shulumba¹

2015

Linköping Studies in Science and Technology. Dissertations

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In this thesis I introduce a new method for calculating the temperature dependent vibrational contribution to the free energy of a substitutionally disordered alloy that accounts for anharmonicity at high temperatures. This method exploits the underlying crystal symmetries in an alloy to make the calculations tractable. The validity of this approach is demonstrated by constructing the phase diagram via direct minimization of the Gibbs free energy of a notoriously awkward and technologically important system, Ti 1-x Al x N. The vibrational entropy including anharmonic effects is shown to be large and comparable to the configurational entropy at high temperatures, and with its inclusion, the theoretical miscibility gap of Ti 1-x Al x N is reduced from 6560 K to 2860 K, in line with atom probe experiments. A similar treatment of Zr 1-x Al x N and Hf 1-x Al x N alloys suggests that mass disorder has a minimal effect on phase stability compared with chemical ordering. My method is also capable of demonstrating that Hf 1-x Al x N, which is dynamically unstable at room temperature, is stabilised at high temperatures. Moreover I develop a new method of computing temperature dependent elastic constants for alloys from their phonon spectra, and show that for Ti 1-x Al x N, the elastic anisotropy is found to increase with temperature, helping to explain the spinodal decomposition.The effects of lattice dynamics on phase stability, mechanical, magnetic and transport properties on other materials are also examined. Four specific systems are discussed in detail. Firstly, in the case of CrN, lattice vibrations are shown to decrease the antiferromagnetic to paramagnetic phase transition temperature from 500 K to 380 K, in line with experimental evidence. Secondly, a temperature/pressure induced phase transition in AlN becomes much more facile than in the quasiharmonic approximation, and the thermal conductivity of the rocksalt phase is shown to be much lower than that of the wurtzite phase, as a result of the increased anharmonicity in the rocksalt structure. Thirdly, the temperature dependence of elastic constants of TiN becomes more isotropic as the temperature increases. Finally, iron carbides are evaluated as potentially important phases at the Earth's core; specifically, calculating the Gibbs free energy of a recently discovered orthorhombic phase of Fe 7 C 3 demonstrates that it is not stable relative to the known hexagonal phase at extreme pressure and temperatures.V Popular science summary Solid materials can be described using a simple mathematical model from the theory of lattice dynamics. In a solid, atoms are arranged in a regular and repeating structure (a lattice), and the forces between them can essentially be modelled as springs. Despite the simplicity of this model, it is possible to derive a surprising amount of information on materials from it. One can determine which arrangements of atoms, or phases, form the stable microscopic structures that we encounter in the real world, their mechanical properti...

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First-principles calculations of properties of orthorhombic iron carbideFe7C3at the Earth's core conditions

Cited by 22 publications

References 35 publications

First‐principles prediction of Si‐doped Fe carbide as one of the possible constituents of Earth's inner core

First‐principles prediction of Si‐doped Fe carbide as one of the possible constituents of Earth's inner core

Thermoelasticity of Fe₇C₃ under inner core conditions

Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

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First-principles calculations of properties of orthorhombic iron carbideFe7C3at the Earth's core conditions

Cited by 22 publications

References 35 publications

First‐principles prediction of Si‐doped Fe carbide as one of the possible constituents of Earth's inner core

First‐principles prediction of Si‐doped Fe carbide as one of the possible constituents of Earth's inner core

Thermoelasticity of Fe7C3 under inner core conditions

Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

Contact Info

Product

Resources

About

Thermoelasticity of Fe₇C₃ under inner core conditions