High Poisson's ratio of Earth's inner core explained by carbon alloying

Prescher, Clemens; Dubrovinsky, Leonid; Bykova, Elena; Kupenko, Ilya; Glazyrin, Konstantin; Kantor, A.; McCammon, Catherine; Mookherjee, Mainak; Nakajima, Yoichi; Miyajima, Nobuyoshi; Sinmyo, Ryosuke; Cerantola, Valerio; Dubrovinskaia, Natalia; Prakapenka, Vitali B.; Rüffer, R.; Chumakov, A. I.; Hanfland, Michael

doi:10.1038/ngeo2370

Cited by 127 publications

(172 citation statements)

References 28 publications

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“…Mössbauer spectroscopy indicates a ferromagnetic to paramagnetic transition at 16 GPa and a paramagnetic to nonmagnetic transition at 70 GPa [20]. Although pressure of the transition to a nonmagnetic state is considerably overestimated here, conflicts between theoretical and experimental magnetic transition pressures are a common problem for iron carbides, in particular for cementite Fe 3 C [7,27].…”

Section: A Crystal Structure and Magnetismmentioning

confidence: 71%

“…1) [20]. The PBE-optimized structure at zero pressure has lattice parameters a = 10.80, b = 3.95, and c = 12.50, corresponding to a volume of 533.7Å 3 .…”

Section: A Crystal Structure and Magnetismmentioning

confidence: 99%

“…A new orthorhombic phase of Fe 7 C 3 (referred to as oFe 7 C 3 ) has very recently been discovered [20]. High pressure diamond anvil cell experiments suggest that o-Fe 7 C 3 is the crystallizing phase at the conditions of the Earth's outer core, rather than h-Fe 7 C 3 .…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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A recently discovered phase of orthorhombic iron carbide o-Fe 7 C 3 [Prescher et al., Nat. Geosci. 8, 220 (2015)] is assessed as a potentially important phase for interpretation of the properties of the Earth's core. In this paper, we carry out first-principles calculations on o-Fe 7 C 3 , finding properties to be in broad agreement with recent experiments, including a high Poisson's ratio (0.38). Our enthalpy calculations suggest that o-Fe 7 C 3 is more stable than Eckstrom-Adcock hexagonal iron carbide (h-Fe 7 C 3 ) below approximately 100 GPa. However, at 150 GPa, the two phases are essentially degenerate in terms of Gibbs free energy, and further increasing the pressure towards Earth's core conditions stabilizes h-Fe 7 C 3 with respect to the orthorhombic phase. Increasing the temperature tends to stabilize the hexagonal phase at 360 GPa, but this trend may change beyond the limit of the quasiharmonic approximation.

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Section: A Crystal Structure and Magnetismmentioning

confidence: 71%

“…1) [20]. The PBE-optimized structure at zero pressure has lattice parameters a = 10.80, b = 3.95, and c = 12.50, corresponding to a volume of 533.7Å 3 .…”

Section: A Crystal Structure and Magnetismmentioning

confidence: 99%

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

et al. 2015

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“…and v p = 10.7 kms −1 at 158 GPa and 300 K, 27 despite the fact that we only consider single-crystal elastic constants computed at zero Kelvin. Here, the v s components are averaged since only one component is experimentally reported.…”

Section: 4 1 S Tat I C E L a S T I C C O N S Ta N T S O F I R O Nmentioning

confidence: 99%

“…Recently, a new orthorhombic phase of Fe 7 C 3 has been prepared in experiments, and it has a Poisson's ratio that is more similar to that of the Earth's core than any other phase. 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.…”

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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Stability and compressibility of a new iron‐nitride β‐Fe₇N₃ to core pressures

Minobe

Nakajima

Hirose

et al. 2015

Geophysical Research Letters

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We have examined the phase relations in the iron‐rich portion of the Fe‐N binary system up to 150 GPa and 2720 K in a laser‐heated diamond anvil cell. Synchrotron X‐ray diffraction measurements revealed the formation of a new phase (β‐Fe7N3) above 41 GPa and ~1000 K. The β phase is structurally identical or very close to Fe7C3 and the most iron‐rich Fe‐N intermediate compound at its stability field. We also measured the volume of β‐Fe7N3 to 132 GPa and found its elastic property very similar to that of Fe7C3. Recently, it has been proposed that the density and sound velocities, in particular, shear wave velocity, in the Earth's inner core are reconciled with Fe7C3, but such properties could be explained by β‐Fe7N3 equally well. It is therefore possible that the inner core consists of Fe7(C,N)3, which is found as diamond inclusions and likely stable under inner core conditions.

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High Poisson's ratio of Earth's inner core explained by carbon alloying

Cited by 127 publications

References 28 publications

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

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

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

Stability and compressibility of a new iron‐nitride β‐Fe₇N₃ to core pressures

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High Poisson's ratio of Earth's inner core explained by carbon alloying

Cited by 127 publications

References 28 publications

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

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

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

Stability and compressibility of a new iron‐nitride β‐Fe7N3 to core pressures

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Product

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Stability and compressibility of a new iron‐nitride β‐Fe₇N₃ to core pressures