Origin of the Low Rigidity of the Earth's Inner Core

Shear softening of earth's inner core as indicated by its high poisson ratio and elastic anisotropy

Earth's inner core exhibits an unusually high Poisson ratio and noticeable elastic anisotropy. The mechanisms responsible for these features are crucial to understanding the nature of Earth's core. Although different mechanisms have been proposed, few can explain both observations simultaneously. The results of this study indicated that the crystal with noticeable shear softening would have strong anisotropy and an exceptionally high Poisson ratio simultaneously. Body-centered-cubic (bcc) iron exhibits shear instability at inner-core pressures and can be dynamically stabilized by high temperature and the presence of light elements. The bcc-lattice iron alloy could have strong anisotropy and a Poisson ratio of Earth's inner core before shear instability. Identifying which light elements can stabilize the bcc-lattice iron alloy will provide an independent constraint on the chemical composition of the inner core.

An estimate of absolute shear-wave speed in the Earth's inner core

Observations of seismic body waves that traverse the Earth's inner core (IC) as shear (J) waves are critical for understanding the IC shear properties, advancing our knowledge of the Earth's internal structure and evolution. Here, we present several seismological observations of J phases detected in the earthquake late-coda correlation wavefield at periods of 15-50 s, notably via the correlation feature I-J, found to be independent of the Earth reference velocity model. Because I-J is unaffected by compressional wave speeds of the Earth's inner core, outer core, and mantle, it represents an autonomous class of seismological measurements to benchmark the inner core properties. We estimate the absolute shear-wave speed in the IC to be 3.39 ± 0.02 km/s near the top and 3.54 ± 0.02 km/s in the center, lower than recently reported values. This is a 3.4 ± 0.5% reduction from the Preliminary Reference Earth Model (PREM), suggesting a less rigid IC than previously estimated from the normal mode data. Such a low shear-wave speed requires re-evaluating IC composition, including the abundance of light elements, the atomic properties and stable crystallographic phase of iron, and the IC solidification process.

Superionic effect and anisotropic texture in Earth's inner core driven by geomagnetic field

Seismological observations suggest that Earth's inner core (IC) is heterogeneous and anisotropic. Increasing seismological observations make the understanding of the mineralogy and mechanism for the complex IC texture extremely challenging, and the driving force for the anisotropic texture remains unclear. Under IC conditions, hydrogen becomes highly diffusive like liquid in the hexagonal-close-packed (hcp) solid Fe lattice, which is known as the superionic state. Here, we reveal that H-ion diffusion in superionic Fe-H alloy is anisotropic with the lowest barrier energy along the c-axis. In the presence of an external electric field, the alignment of the Fe-H lattice with the c-axis pointing to the field direction is energetically favorable. Due to this effect, Fe-H alloys are aligned with the c-axis parallel to the equatorial plane by the diffusion of the north-south dipole geomagnetic field into the inner core. The aligned texture driven by the geomagnetic field presents significant seismic anisotropy, which explains the anisotropic seismic velocities in the IC, suggesting a strong coupling between the IC structure and geomagnetic field.

Cooperative diffusion in body-centered cubic iron in Earth and super-Earths' inner core conditions

The physical chemistry of iron at the inner-core conditions is key to understanding the evolution and habitability of Earth and super-Earth planets. Based on full first-principles simulations, we report cooperative diffusion along the longitudinally fast⟨111⟩directions of body-centered cubic (bcc) iron in temperature ranges of up to 2000-4000 K below melting and pressures of ∼300-4000 GPa. The diffusion is due to the low energy barrier in the corresponding direction and is accompanied by mechanical and dynamical stability, as well as strong elastic anisotropy of bcc iron. These findings provide a possible explanation for seismological signatures of the Earth's inner core, particularly the positive correlation between P wave velocity and attenuation. The diffusion can also change the detailed mechanism of core convection by increasing the diffusivity and electrical conductivity and lowering the viscosity. The results need to be considered in future geophysical and planetary models and should motivate future studies of materials under extreme conditions.

Low viscosity of the Earth's inner core

The Earth's solid inner core is a highly attenuating medium. It consists mainly of iron. The high attenuation of sound wave propagation in the inner core is at odds with the widely accepted paradigm of hexagonal close-packed phase stability under inner core conditions, because sound waves propagate through the hexagonal iron without energy dissipation. Here we show by first-principles molecular dynamics that the body-centered cubic phase of iron, recently demonstrated to be thermodynamically stable under the inner core conditions, is considerably less elastic than the hexagonal phase. Being a crystalline phase, the body-centered cubic phase of iron possesses the viscosity close to that of a liquid iron. The high attenuation of sound in the inner core is due to the unique diffusion characteristic of the body-centered cubic phase. The low viscosity of iron in the inner core enables the convection and resolves a number of controversies.

Shear properties of Earth's inner core constrained by a detection of J waves in global correlation wavefield

Seismic J waves, shear waves that traverse Earth's inner core, provide direct constraints on the inner core's solidity and shear properties. However, these waves have been elusive in the direct seismic wavefield because of their small amplitudes. We devised a new method to detect J waves in the earthquake coda correlation wavefield. They manifest through the similarity with other compressional core-sensitive signals. The inner core is solid, but relatively soft, with shear-wave speeds and shear moduli of 3.42 ± 0.02 kilometers per second and 149.0 ± 1.6 gigapascals (GPa) near the inner core boundary and 3.58 ± 0.02 kilometers per second and 167.4 ± 1.6 GPa in Earth's center. The values are 2.5% lower than the widely used Preliminary Earth Reference Model. This provides new constraints on the dynamical interpretation of Earth's inner core.

The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

On the basis of ab initio computer simulations, pre-melting phenomena have been suggested to occur in the elastic properties of hexagonal close-packed iron under the conditions of the Earth's inner core just before melting. The extent to which these pre-melting effects might also occur in the physical properties of face-centred cubic metals has been investigated here under more experimentally accessible conditions for gold, allowing for comparison with future computer simulations of this material. The thermal expansion of gold has been determined by X-ray powder diffraction from 40 K up to the melting point (1337 K). For the entire temperature range investigated, the unit-cell volume can be represented in the following way: a second-order Grüneisen approximation to the zero-pressure volumetric equation of state, with the internal energy calculated via a Debye model, is used to represent the thermal expansion of the 'perfect crystal'. Gold shows a nonlinear increase in thermal expansion that departs from this Grüneisen-Debye model prior to melting, which is probably a result of the generation of point defects over a large range of temperatures, beginning at T/Tm > 0.75 (a similar homologous T to where softening has been observed in the elastic moduli of Au). Therefore, the thermodynamic theory of point defects was used to include the additional volume of the vacancies at high temperatures ('real crystal'), resulting in the following fitted parameters: Q = (V0K0)/γ = 4.04 (1) × 10-18 J, V0 = 67.1671 (3) Å3, b = (K0' - 1)/2 = 3.84 (9), θD = 182 (2) K, (vf/Ω)exp(sf/kB) = 1.8 (23) and hf = 0.9 (2) eV, where V0 is the unit-cell volume at 0 K, K0 and K0' are the isothermal incompressibility and its first derivative with respect to pressure (evaluated at zero pressure), γ is a Grüneisen parameter, θD is the Debye temperature, vf, hf and sf are the vacancy formation volume, enthalpy and entropy, respectively, Ω is the average volume per atom, and kB is Boltzmann's constant.

Candy Wrapper for the Earth's inner core

Recent global expansion of seismic data motivated a number of seismological studies of the Earth's inner core that proposed the existence of increasingly complex structure and anisotropy. In the meantime, new hypotheses of dynamic mechanisms have been put forward to interpret seismological results. Here, the nature of hemispherical dichotomy and anisotropy is re-investigated by bridging the observations of PKP(bc-df) differential travel-times with the iron bcc/hcp elastic properties computed from first-principles methods.The Candy Wrapper velocity model introduced here accounts for a dynamic picture of the inner core (i.e., the eastward drift of material), where different iron crystal shapes can be stabilized at the two hemispheres. We show that seismological data are best explained by a rather complicated, mosaic-like, structure of the inner core, where well-separated patches of different iron crystals compose the anisotropic western hemispherical region, and a conglomerate of almost indistinguishable iron phases builds-up the weakly anisotropic eastern side.

An ab initio molecular dynamics study of iron phases at high pressure and temperature

The crystal structure of iron, the major component of the Earth's inner core (IC), is unknown for the IC high pressure (P; 3.3-3.6 Mbar) and temperature (T; 5000-7000 K). There is mounting evidence that the hexagonal close-packed (hcp) phase of iron, stable at the high P of the IC and a low T, might be unstable under the IC conditions due to the impact of high T and impurities. Experiments at the IC P and T are difficult and do not provide a conclusive answer as regards the iron stability at the pressure of the IC and temperatures close to the iron melting curve. Recent theory provides contradictory results regarding the nature of the stable Fe phase. We investigated the possibility of body-centered cubic (bcc) phase stabilization at the P and T in the vicinity of the Fe melting curve by using ab initio molecular dynamics. Thermodynamic calculations, relying on the model of uncorrelated harmonic oscillators, provide nearly identical free energies within the error bars of our calculations. However, direct simulation of iron crystallization demonstrates that liquid iron freezes in the bcc structure at the P of the IC and T = 6000 K. All attempts to grow the hcp phase from the liquid failed. The mechanism of bcc stabilization is explained. This resolves most of the earlier confusion.

Shear relaxation in iron under the conditions of earth's inner core

Large scale molecular dynamics simulations of iron at high pressure and temperature are performed to investigate the physics of shear softening. A solid 16×10(6) atoms sample of iron is grown out of the liquid with a small solid immersed in it at the start of simulation. We observe that diffusion in the sheared solid is similar to that in liquid, even though at different time scales. This allows us to describe the time dependence of shear stress in terms of elastic and hydrodynamic relaxation. The elastic response of the sample is close to the elastic response of Earth's inner core. This explains the abnormally low shear modulus in the core. The reason for the low shear modulus is the presence of defects of the crystal structure.

Hemispherical anisotropic patterns of the Earth's inner core

It has been shown that the Earth's inner core has an axisymmetric anisotropic structure with seismic waves traveling approximately 3% faster along polar paths than along equatorial directions. Hemispherical anisotropic patterns of the solid Earth's core are rather complex, and the commonly used hexagonal-close-packed iron phase might be insufficient to account for seismological observations. We show that the data we collected are in good agreement with the presence of two anisotropically specular east and west core hemispheres. The detected travel-time anomalies can only be disclosed by a lattice-preferred orientation of a body-centered-cubic iron aggregate, having a fraction of their [111] crystal axes parallel to the Earth's rotation axis. This is compelling evidence for the presence of a body-centered-cubic Fe phase at the top of the Earth's inner core.

Dynamical stability of body center cubic iron at the Earth's core conditions

Here, using self-consistent ab initio lattice dynamical calculations that go beyond the quasiharmonic approximation, we show that the high-pressure high-temperature bcc-Fe phase is dynamically stable. In this treatment the temperature-dependent phonon spectra are derived by exciting all the lattice vibrations, in which the phonon-phonon interactions are considered. The high-pressure and high-temperature bcc-Fe phase shows standard bcc-type phonon dispersion curves except for the transverse branch, which is overdamped along the high symmetry direction Gamma-N, at temperatures below 4,500 K. When lowering the temperature down to a critical value T(C), the lattice instability of the bcc structure is reached. The pressure dependence of this critical temperature is studied at conditions relevant for the Earth's core.

Stability of body-centered cubic iron-magnesium alloys in the Earth's inner core

The composition and the structure of the Earth's solid inner core are still unknown. Iron is accepted to be the main component of the core. Lately, the body-centered cubic (bcc) phase of iron was suggested to be present in the inner core, although its stability at core conditions is still in discussion. The higher density of pure iron compared with that of the Earth's core indicates the presence of light element(s) in this region, which could be responsible for the stability of the bcc phase. However, so far, none of the proposed composition models were in full agreement with seismic observations. The solubility of magnesium in hexagonal Fe has been found to increase significantly with increasing pressure, suggesting that Mg can also be an important element in the core. Here, we report a first-principles density functional study of bcc Fe-Mg alloys at core pressures and temperatures. We show that at core conditions, 5-10 atomic percent Mg stabilizes the bcc Fe both dynamically and thermodynamically. Our calculated density, elastic moduli, and sound velocities of bcc Fe-Mg alloys are consistent with those obtained from seismology, indicating that the bcc-structured Fe-Mg alloy is a possible model for the Earth's inner core.