L Vocadlo

Possible thermal and chemical stabilization of body-centred-cubic iron in the Earth's core

The nature of the stable phase of iron in the Earths solid inner core is still highly controversial. Laboratory experiments suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations have indicated the possible presence of complex, inner-core layering. Theoretical studies currently suggest that the hexagonal close packed (h.c.p.) phase of iron is stable at core pressures and that the body centred cubic (b.c.c.) phase of iron becomes elastically unstable at high pressure. In other h.c.p. metals, however, a high-pressure b.c.c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b.c.c. phase will be stabilized with respect to the h.c.p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner core.

Thermal expansion and crystal structure of cementite, Fe3C, between 4 and 600 K determined by time-of-flight neutron powder diffraction

The cementite phase of Fe3C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The ferromagnetic phase transition, with Tc ≃ 480 K, greatly affects the thermal expansion coefficient of the material. The average volumetric coefficient of thermal expansion above Tc was found to be 4.1 (1) × 10−5 K−1; below Tc it is considerably lower (< 1.8 × 10−5 K−1) and varies greatly with temperature. The behaviour of the volume over the full temperature range of the experiment may be modelled by a third-order Gruneisen approximation to the zero-pressure equation of state, combined with a magnetostrictive correction based on mean-field theory.

Ab initio free energy calculations on the polymorphs of iron at core conditions

Abstract In order to predict the stable polymorph of iron under core conditions, calculations have been performed on all the candidate phases proposed for inner core conditions, namely, body-centred cubic (bcc), body-centred tetragonal (bct), hexagonal close-packed (hcp), double-hexagonal close-packed (dhcp) and an orthorhombically distorted hcp polymorph. Our simulations are ab initio free energy electronic structure calculations, based upon density functional theory, within the generalised gradient approximation; we use Vanderbilt ultrasoft non-normconserving pseudopotentials to describe the core interactions, and the frozen phonon technique to obtain the vibrational characteristics of the candidate structures. Our results show that under conditions of hydrostatic stress, the orthorhombic, bcc and bct structures are mechanically unstable. The relative free energies of the remaining phases indicate that dhcp and fcc Fe are thermodynamically less stable than hcp Fe, therefore, we predict that the stable phase of iron at core conditions is hcp-Fe.

First principles calculations on crystalline and liquid iron at Earth's core conditions

Ab initio electronic structure calculations, based upon density functional theory within the generalised gradient approximation using ultrasoft non-norm-conserving Vanderbilt pseudopotentials, have been used to predict the structure and properties of crystalline and liquid iron and solid FeSi at conditions found in the Earths core. The quality of the pseudopotentials used was assessed by calculating well documented properties of the solid phase: we have accurately modelled the equation of state of bcc and hcp Fe and FeSi, the bcc→hcp phase transition, the magnetic moment of bcc Fe, the elastic constants of bcc Fe, the bcc→bct distortive phase transition and the phonon frequencies for fcc Fe; the results show good agreement with both theory and experiment. Simulations were also performed on liquid iron and we present the first abinitio quantum molecular dynamics calculations on the structure and transport properties of liquid iron under core conditions. Our calculations show that the structure of liquid iron at the conditions to be found in the outer core is highly compressed with a first-neighbour coordination number inferred from the radial distribution function of ca. 12. We have also predicted a diffusion coefficient of 0.5×10-4 cm2 s-1 indicative of a core viscosity of ca. 0.026 Pa s, in line with current estimates.

Strong Premelting Effect in the Elastic Properties of hcp-Fe Under Inner-Core Conditions

On the Brink of Melting The considerable pressures and temperatures of Earths iron-rich inner core make it a challenge to compare measurements made in experimental systems with observed seismic data. Computational simulations of core materials may reconcile any apparent differences. Martorell et al. (p. 466, published online 10 October) used ab initio simulations to predict the elastic properties of iron at core pressures. As temperatures approached the melting point of pure iron, the material was predicted to weaken to the point that seismic waves would be slowed considerably. An inner core with a small percentage of light elements like oxygen and silicon near its melting temperature would correspond well with measured seismic velocities. Elastic weakening of iron just before melting explains variations in the seismic structure of Earth’s inner core. The observed shear-wave velocity VS in Earth’s core is much lower than expected from mineralogical models derived from both calculations and experiments. A number of explanations have been proposed, but none sufficiently explain the seismological observations. Using ab initio molecular dynamics simulations, we obtained the elastic properties of hexagonal close-packed iron (hcp-Fe) at 360 gigapascals up to its melting temperature Tm. We found that Fe shows a strong nonlinear shear weakening just before melting (when T/Tm > 0.96), with a corresponding reduction in VS. Because temperatures range from T/Tm = 1 at the inner-outer core boundary to T/Tm ≈ 0.99 at the center, this strong nonlinear effect on VS should occur in the inner core, providing a compelling explanation for the low VS observed.

First principles calculations on the diffusivity and viscosity of liquid Fe-S at experimentally accessible conditions

Ab initio molecular dynamics calculations, based upon density functional theory within the generalised gradient approximation (GGA) using ultrasoft non-norm conserving Vanderbilt pseudopotentials, have been used to predict the transport properties of liquid Fe–S. In order to compare our simulations with experimental data, the simulations were performed for the eutectic composition of Fe–S at the experimentally accessible conditions of 5 GPa and of 1300 and 1500 K. Our results give values for Fe and S diffusion of a few times 10−5 cm2 s−1. Our calculated viscosities, obtained directly from the simulations, are 11±5 and 4±1 mPa s at 1300 and 1500 K, respectively. Our calculated diffusion and viscosity coefficients agree well with recent experiments at similar pressures and temperatures, supporting a high diffusivity and low viscosity in liquid Fe–S at temperatures up to a few hundred Kelvin above the eutectic temperature. Furthermore, an extensive study of the liquid structure shows no evidence for sulphur polymerisation or the existence of any large viscous flow units. These results are in direct conflict with the previously reported experimental results of Le Blanc and Secco [LeBlanc, G.E., Secco, R.A., 1996. Viscosity of an Fe–S liquid up to 1300°C and 5 GPa, Geophys. Res. Lett., 23, 213–216.].

Grüneisen parameters and isothermal equations of state

Abstract The Grüneisen parameter (γ) is of considerable importance to Earth scientists because it sets limitations on the thermoelastic properties of the lower mantle and core. However, there are several formulations of the Grüneisen parameter in frequent use which not only give different values for γ at ambient pressure but also predict a varying dependence of γ as a function of compression. The Grüneisen parameter is directly related to the equation of state (EOS), yet it is often the case that both the form of γ and the EOS are chosen independently of each other and somewhat arbitrarily. In this paper we have assessed some of the more common definitions of the Grüneisen parameter and the EOS, and have applied them to a test material. Of the EOS considered, when compared against ab initio compressional data for hcp-Fe as our exemplar, we find that the fourth order logarithmic and Vinet relations describe the material with the highest accuracy. Of the expressions for γ considered, it has been suggested, on theoretical grounds, that the modified free-volume formulation should be expected to give the most realistic description of the thermoelastic behavior of a material. However, when we use the fourth order logarithmic EOS to obtain the compressional behavior of the various Grüneisen parameters, we find that there is, in fact, poor agreement between the modifiedfree- volume formulation and the Mie-Grüneisen parameter obtained directly from ab initio free energy calculations on hcp-Fe. We conclude that none of the analytical forms of gamma are sufficiently sophisticated to describe the thermoelastic behavior of real materials with great accuracy, and care must therefore be taken when attempting to model the thermoelastic behavior of solids to ensure that the appropriate γ (ideally obtained from experiments or ab initio calculations) and equations of state are used

The equation of state of CsCl‐structured FeSi to 40 GPa: Implications for silicon in the Earth's core

21.74 ± 0.02 Au, with a K0 of 184 ± 5 GPa and K 0 = 4.2 ± 0.3. The measured density and elastic properties of CsClFeSi are consistent with silicon being a major element in the Earth’s core. INDEX TERMS: 1212 Geodesy and Gravity: Earth’s interior—composition and state (8105); 3919 Mineral Physics: Equations of state; 8124 Tectonophysics: Earth’s interior—composition and state (old 8105). Citation: Dobson,

The structure of iron under the conditions of the Earth's inner core

The inferred density of the solid inner core indicates that it is predominantly made of iron. In order to interpret the observed seismic anisotropy and understand the high pressure and temperature behaviour of the core, it is essential to establish the crystal structure of iron under core conditions. On the basis of extrapolated experimental data, a number of candidate structures for the high P/T iron phase have been proposed, namely, body-centred cubic (bcc), body-centred tetragonal (bct), hexagonal close-packed (hcp), double-hexagonal close-packed (dhcp) and an orthorhombically distorted hcp polymorph (Matsui, 1993; Stixrude and Cohen, 1995; Boehler, 1993; Saxena et al., 1996; Andrault et al., 1997). Here we present the results of the first fully ab initio free energy calculations for all of these polymorphs of iron at core pressures and temperatures. Our results show that hcp-Fe is the most stable polymorph of iron under the conditions of the Earths inner core.

The high-pressure phase diagram of ammonia dihydrate

We have investigated the P–T phase diagram of ammonia dihydrate (ADH), ND3·2D2O, using powder neutron diffraction methods over the range 0–9 GPa, 170–300 K. In addition to the ambient pressure phase, ADH I, we have identified three high-pressure phases, ADH II, III, and IV, each of which has been reproduced in at least three separate experiments. Another, apparently body-centred-cubic, phase of ADH has been observed on a single occasion above 6 GPa at 170 K. The existence of a dehydration boundary has been confirmed where, upon compression or warming, ADH IV decomposes to a high-pressure ice phase (ice VII or VIII) and a high-pressure phase of ammonia monohydrate (AMH V or VI).