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The elastic constant tensors for the hcp phases of three transition metals (Co, Re, and Fe) are computed as functions of pressure using the Linearized Augmented Plane Wave method with both the local density and generalized gradient approximations. Spin-polarized states are found to be stable for Co (ferromagnetic) and Fe (antiferromagnetic at low pressure). The elastic constants of Co and Re are compared to experimental measurements near ambient conditions and excellent agreement is found. Recent measurements of the lattice strain in high pressure experiments when interpreted in terms of elastic constants for Re and Fe are inconsistent with the calculated moduli.

Earth’s magnetic field is sustained by magnetohydrodynamic convection within the metallic liquid core. In a thermally advecting core, the fraction of heat available to drive the geodynamo is reduced by heat conducted along the core geotherm, which depends sensitively on the thermal conductivity of liquid iron and its alloys with candidate light elements. The thermal conductivity for Earth’s core is very poorly constrained, with current estimates based on a set of scaling relations that were not previously tested at high pressures. We perform first-principles electronic structure computations to determine the thermal conductivity and electrical resistivity for Fe, Fe–Si, and Fe–O liquid alloys. Computed resistivity agrees very well with existing shock compression measurements and shows strong dependence on light element concentration and type. Thermal conductivity at pressure and temperature conditions characteristic of Earth’s core is higher than previous extrapolations. Conductive heat flux near the core–mantle boundary is comparable to estimates of the total heat flux from the core but decreases with depth, so that thermally driven flow would be constrained to greater depths in the absence of an inner core.

Seismological body-wave and free-oscillation studies of the Earth's solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature. By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.

[1] We study a new class of high-resolution mantle circulation models and predict their corresponding elastic heterogeneity. Absolute temperatures are converted to seismic velocities using published thermodynamically self-consistent models of mantle mineralogy for a pyrolite composition. A grid spacing of $25 km globally allows us to explore mantle flow at Earth-like convective vigor so that modeled temperature variations are consistent with the underlying mineralogy. We concentrate on isochemical convection and the relative importance of internal and bottom heating in order to isolate the thermal effects on elasticity. Models with a large temperature contrast on the order of 1000 K across the core-mantle boundary, corresponding to a substantial core heat loss of up to 12 TW, result in elastic structures that agree well with tomography for a number of quantitative measures: These include spectral power and histograms of heterogeneity as well as radial profiles of root-mean-square amplitudes. In particular, high plume excess temperatures of +1000-1500 K in the lowermost mantle lead to significant negative anomalies of shear wave velocity of up to À4%. These are comparable to strong velocity reductions mapped by seismic tomography in the prominent low-velocity regions of the lower mantle. We note that the inference of a large core heat flux is supported by a number of geophysical studies arguing for a substantial core contribution to the mantle energy budget. Additionally, we find significant differences between the characteristics of thermal heterogeneity and the characteristics of elastic heterogeneity in the transition zone due to phase transformations of upper mantle minerals. Our results underline the necessity to include mineral physics information in the geodynamic interpretation of tomographic models.

More than a third of all exoplanets can be classified as super-Earths based on radius (1´2 R C ) and mass (< 10 M C ).Here we model mass-radius relations based on silicate mantle and iron core equations of state to infer to first order the structure and composition range of rocky super-Earths assuming insignificant gas envelopes. As their core pressures exceed those in the Earth by an order of magnitude, significant extrapolations of equations of state for iron are required. We develop a new equation of state of hexagonal close packed (hcp) iron for super-Earth conditions (SEOS) based on density functional theory results for pressures up to 137 TPa. A comparison of SEOS and extrapolated equations of state for iron from the literature reveals differences in density of up to 4% at 1 TPa and up to 20% at 10 TPa. Such density differences significantly affect mass-radius relations. On mass, the effect is as large as 10% for Earth-like super-Earths (core radius fraction of 0.5) and 20% for Mercury-like super-Earths (core radius fraction of 0.8). We also quantify the effects of other modeling assumptions such as temperature and composition by considering extreme cases. We find that the effect of temperature on mass (< 5%) is smaller than that resulting from the extrapolation of the equations of state of iron and lower mantle temperatures are too low to allow for rock and iron miscibility for R < 1.75 R C . Our end-member cases of core and mantle compositions create a spread in mass-radius curves reaching more than 50% in terms of mass for a given planetary radius, implying that modeling uncertainties dominate over observational uncertainties for many observed super-Earths. We illustrate these uncertainties explicitly for Kepler-36b with well-constrained mass and radius. Assuming a core composition of 0.8ρ Fe (equivalent to 50 mol% S) instead of pure Fe leads to an increase of the core radius fraction from 0.53 to 0.64. Using a mantle composition of Mg 0.5 Fe 0.5 SiO 3 instead of MgSiO 3 leads to a decrease of the core radius fraction to 0.33. Effects of thermal structure and the choice of equation of state for the core material on the core radius of Kepler-36b are small but non-negligible, reaching 2% and 5%, respectively.

[1] Carbon is a plausible light element candidate in the Earth's core owing to its cosmic abundance and its chemical affinity for iron. Recent experimental studies on Fe-C phase relations at high pressures have demonstrated that Fe 7 C 3 iron carbide is a likely candidate for the Earth's inner core. Using electronic structure calculations, we determine the equation of state, the full elastic constant tensor, and the sound wave velocities for Fe 7 C 3 , up to inner core pressures. We find that Fe 7 C 3 is ferromagnetic (fm) at low pressure, and that its compression behavior is well represented by a third-order Birch Murnaghan finite strain expression with V 0 fm = 9.1 Å 3 /atom, K 0 fm = 231 GPa, and K′ 0 fm = 4.4. Under compression the magnetic moments of the Fe atoms gradually decrease, and at ∼67 GPa the magnetic moment is lost. The high-pressure nonmagnetic phase (nm) has distinct finite strain parameters with V 0 nm = 8.8 Å 3 /atom, K 0 nm = 291 GPa, and K′ 0 nm = 4.5. Calculated elastic constants show softening associated with the loss of magnetization. In addition, we have conducted nuclear resonant inelastic X-ray scattering experiments on 57 Fe enriched Fe 7 C 3 at 1 bar and 300 K. On the basis of our nuclear resonant inelastic X-ray scattering spectra we have derived a Debye sound velocity of 3.18 km/s. The experimentally determined value is in good agreement with the computational predictions, based on athermal single elastic constants. The static P wave velocity at inner core pressures agrees well with seismological constraints, whereas the S wave velocity is greater by 30%. On the basis of the density of Fe 7 C 3 at inner core conditions, we predict that the maximum possible carbon content of the inner core is around 1.5 wt %.

The magnetic state of hexagonal close-packed iron has been the subject of debate for more than three decades. Although Mö ssbauer measurements find no evidence of the hyperfine splitting that can signal the presence of magnetic moments, density functional theory predicts an antiferromagnetic (afm) ground state. This discrepancy between theory and experiment is now particularly important because of recent experimental findings of anomalous splitting in the Raman spectra and the presence of superconductivity in hexagonal close-packed iron, which may be caused by magnetic correlations. Here, we report results from first principles calculations on the previously predicted theoretical collinear afm ground state that strongly support the presence of afm correlations in hexagonal close-packed iron. We show that anomalous splitting of the Raman mode can be explained by spinphonon interactions. Moreover, we find that the calculated hyperfine field is very weak and would lead to hyperfine splitting below the resolution of Mö ssbauer experiments. P hysical properties of iron are of great importance to many fields in the sciences, as iron is one of the most abundant and stable elements in the universe and the very basis for the steel industry. Hexagonal close-packed (hcp) iron, the form stable at high pressure, plays a central role in geophysics, as the Earth's inner core is thought to be primarily composed of this phase (1, 2), and in our understanding of impact and explosive phenomena in iron and steel (3). The magnetic state of iron has a major influence on the physics of iron and iron alloys, including the relative stability of the iron polymorphs (4, 5). The magnetic structure of the hcp phase has been the subject of a scientific debate for three decades (6), leading to contradictory results from experiments and theory. Although experiments are interpreted to show the absence of magnetism in hcp iron (6-10), computations based on density functional theory find an antiferromagnetic (afm) ground state stable to Ϸ50 GPa (11), similar to magnetism in the double hcp phase (5). The possible presence of magnetism in hcp iron as further substantiated in this article has important implications. In geophysics many experiments are carried out on potentially magnetic hcp iron and are then extrapolated to pressures of Earth's core, into the nonmagnetic region of the hcp stability field at high pressure, and may consequently not be valid. The possible presence of magnetism in hcp iron also plays an important role in the discussion of the recently observed superconductivity of hcp iron (12, 13): Magnetic correlations in hcp iron appear to be necessary to explain the observed pressure dependence of its superconductivity (14-16).The two lower-pressure polymorphs of iron are both magnetic. The phase stable around ambient conditions, body-centered cubic (bcc), owes its stability entirely to the presence of ferromagnetism (4). Heating above the Curie temperature causes the spins to disorder and the net magnetization to vanish, but the ind...