The Structure of Iron in Earth’s Inner Core

Tateno, Shigehiko; Hirose, Kei; Ohishi, Yasuo; Tatsumi, Yoshiyuki

doi:10.1126/science.1194662

Cited by 434 publications

(306 citation statements)

References 27 publications

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“…In order to interpret seismic data and build geophysical models, 4 knowing the core composition and structure is of high priority. It is generally to 380 GPa and 5700 K (Tateno et al, 2010), whilst increasing temperature 14 at moderate pressure has been shown to stabilise an fcc phase (Lin et al,15 2002). The fcc phase was also found to be stabilised by increased Ni con-16 tent (Mao et al, 2006;Kuwayama et al, 2008) at temperatures up to 3500 17 K and pressures of 200 GPa.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the c/a-ratio has been previously 81 been found rather insensitive to temperature (Tateno et al, 2010). In or-82 der to limit the computational burden in our alloy configuration calculations 83 (Sections 3.1 and 3.2), we therefore used equilibrium c/a-ratios obtained at 84 T = 0 K and P = 0 GPa also at elevated temperature and pressure for our 85 studies of mixing enthalpy and short-range order.…”

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confidence: 99%

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Configurational thermodynamics of Fe–Ni alloys at Earth's core conditions

Ekholm

Mikhaylushkin

Simak

et al. 2011

Earth and Planetary Science Letters

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By means of ab-initio calculations, we perform an analysis of the configurational thermodynamics, effects of disorder, and structural energy differences in Fe-Ni alloys at the pressure and temperature conditions of the Earth's core. We show from ab-initio calculations that the ordering energies of fccand hcp-structured Fe-Ni solid solutions at these conditions depend sensitively on the alloy configuration, i.e., on the degree of chemical disorder, and are on a scale comparable with the structural energy differences. From configurational thermodynamics simulations we find that a distribution of Fe and Ni atoms in the solutions should be very close to completely disordered at these conditions. Using this model of the Fe-Ni system, we have calculated the fcc-hcp structural free energy difference in a wide pressure-temperature range of 120-360 GPa and 1000-6600 K. Our calculations show that alloying of Fe with Ni below 3000 K favours stabilisation of the fcc phase over the

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Configurational thermodynamics of Fe–Ni alloys at Earth's core conditions

Ekholm

Mikhaylushkin

Simak

et al. 2011

Earth and Planetary Science Letters

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“…However, the FE calculation is based on integration from low temperature, and it is necessary that a harmonic treatment be appropriate there for the method (in the basic form presented here) to be applicable. For the demonstration, we calculate the absolute FE of the high-pressure hcp phase of iron (which is a candidate structure in the Earth's inner core 49 ) for a single isochore (7.0Å 3 /atom) up to temperatures near melting (5000 K), with full inclusion of anharmonicity, electronic excitation, and the change of equilibrium c/a ratio with temperature. At the conditions of interest, iron is paramagnetic, and we neglect contributions to the FE from magnetic properties.…”

Section: Introductionmentioning

confidence: 99%

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

et al. 2017

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A framework for computing the anharmonic free energy (FE) of metallic crystals using BornOppenheimer ab initio molecular dynamics (AIMD) simulation, with unprecedented efficiency, is introduced and demonstrated for the hcp phase of iron at extreme conditions (up to ≈ 290 GPa and 5000 K). The advances underlying this work are: (1) A recently introduced harmonically-mapped averaging temperature integration (HMA-TI) method reduces the computational cost by order(s) of magnitude compared to the conventional TI approach. The TI path starts from zero Kelvin, where it assumes the behavior is given exactly by a harmonic treatment; this feature restricts application to systems that have no imaginary phonons in this limit. (2) A Langevin thermostat with the HMA-TI method allows use of a relatively large MD time step (4 fs, which is about eight times larger than the size needed for the Andersen thermostat) without loss of accuracy. (3) AIMD sampling is accelerated by using density functional theory (DFT) with a low-level parameter set, then the measured quantities of selected configurations are robustly reweighted to a higher level of DFT. This introduces a speedup of about 20-30× compared to directly simulating the accurate system. (4a) The temperature (T ) dependence of the hcp equilibrium shape (i.e. c/a axial ratio) is determined (including anharmonicity), with uncertainty less than ±0.001. (4b) Electronic excitation is included through Mermin's finite-temperature extension of the T = 0 K DFT. A simple FE perturbation method is introduced to handle the difficulty associated with applying the TI method with a Tdependent geometry and (due to electronic excitation) potential-energy surface. (5) The FE in the thermodynamic limit is attained through extrapolation of only the (computationally inexpensive) quasiharmonic FE, because the anharmonic FE contribution has negligible finite-size effects. All methods introduced here do not affect the AIMD sampling -results are obtained through postprocessing -so established AIMD codes can be employed without modification. Analytical formulas fitted to the results for the variation of the equilibrium c/a ratio and FE components with T are provided. Notably, effects of magnetic excitations are not included, and may yet prove important to the overall FE; if so, it is plausible that such contributions can be added perturbatively to the FE values reported here. Notwithstanding these considerations, FE values are obtained with an estimated accuracy and precision of 2 meV/atom, suggesting that the capability to compute the phase diagram of iron at Earth's inner core conditions is within reach.

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“…Pioneering powder X-ray diffraction experiments have now reached the extreme conditions of the inner core 10 . But much work remains to identify the exact composition of the iron alloy in the core and how its crystal structure and physical properties connect to the seismic observations.…”

Section: Core Puzzlesmentioning

confidence: 99%

Earth science: Crystallography's journey to the deep Earth

Duffy

2014

Nature

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The Structure of Iron in Earth’s Inner Core

Cited by 434 publications

References 27 publications

Configurational thermodynamics of Fe–Ni alloys at Earth's core conditions

Configurational thermodynamics of Fe–Ni alloys at Earth's core conditions

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

Earth science: Crystallography's journey to the deep Earth

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