Earth's inner core (IC), as revealed by seismological observations, exhibits heterogeneity and anisotropy, characterized by faster seismic velocities in the polar direction compared to equatorial directions, significant anisotropy changes with depth, and hemispherical dichotomy. Understanding the mechanisms behind this complex structure is crucial for comprehending the IC's history and its relationship with the outer core. While lattice-preferred orientation (LPO) of Fe crystals has been proposed to explain the observed anisotropy, existing models struggle to fully account for the complexities. Models involving different Fe phases and orientations attempt to explain hemispherical variations, but the driving forces remain elusive. The formation of the anisotropic structure during solidification is challenged by the fact that solidified anisotropic textures tend to disappear after prolonged annealing. Alternative hypotheses, such as anisotropic growth driven by flow or Maxwell stress, also struggle to account for the isotropic uppermost inner core (UIC) and the highly anisotropic innermost inner core (IMIC). The quasi-hemispherical variations in the UIC are attributed to asymmetric solidification/melting at the inner core boundary (ICB), further highlighting the need for a comprehensive model. The current study seeks to address these challenges by proposing a novel mechanism involving superionic Fe-H alloys and the influence of the geomagnetic field.

Previous research has explored various mechanisms to explain the anisotropic and heterogeneous structure of the Earth's inner core. The lattice-preferred orientation (LPO) of iron crystals, with variations in hexagonal close-packed (hcp) and body-centered cubic (bcc) structures, has been a prominent explanation, particularly focusing on the differing seismic velocities along the polar and equatorial directions. However, these models often require complex combinations of Fe phases and orientations to fully capture the observed hemispherical anisotropy variations. The role of solidification processes in establishing this structure has also been investigated, but the stability of such textures over geological timescales is questionable. Alternative mechanisms, like the flow of Fe crystals driven by differential growth, requiring high viscosity, or the influence of Maxwell stresses, have been suggested, but these struggle to account for observations such as the isotropic upper inner core and the highly anisotropic innermost inner core. Models that incorporate inner core boundary (ICB) processes like asymmetric solidification and melting attempt to address the complexities but fail to provide a complete picture. The challenges posed by the lack of a comprehensive, unifying mechanism for the inner core's observed features necessitate further exploration.

This study utilizes ab initio molecular dynamics (AIMD) simulations and neural network potential (NNP)-based molecular dynamics (MD) simulations to investigate the behavior of superionic Fe-H alloys under inner core conditions. AIMD simulations were used to calculate seismic wave velocities along different crystallographic directions in superionic hcp-FeH0.25 at varying temperatures (0-6000 K) and hydrogen contents. The climbing-image nudged elastic band (CINEB) method was employed to determine the energy barriers for hydrogen ion migration along different paths in the hcp-Fe lattice. The anisotropic diffusion behavior was analyzed considering temperature effects and the non-ideal c/a ratio. To investigate the influence of an external electric field, NNP-based MD simulations were performed on larger supercells of FeH0.25 at 360 GPa and 6000 K. Nonequilibrium molecular dynamics (NEMD) simulations were used to assess the orientational H-ion diffusion under external electric fields. The internal energy changes were analyzed to determine the preferred orientation of the c-axis with respect to the electric field. The study also explored the influence of the Earth's geomagnetic field by considering its poloidal and toroidal components. The diffusion of H-ions was modeled and related to the observed anisotropic seismic velocities. Elastic constants (C11, C12, C13, C33, and C44) were calculated using distortion matrices to examine the relationship between stress, strain, and elastic moduli. The Voigt average scheme was used to calculate bulk modulus (B) and shear modulus (G). Compressional wave velocity (Vp), shear wave velocity (Vs), and bulk sound velocity (Vφ) were calculated using standard formulas. Azimuthal angle-dependent velocities were determined by solving the Christoffel equation. Finally, the calculated velocity anisotropies were compared with seismic observations to validate the proposed mechanism.

The study's key findings include: 1) Superionic hcp-FeH0.25 exhibits anisotropic seismic velocities, with the fastest direction shifting from the c-axis at lower temperatures to the a-axis at higher temperatures. This reversal is influenced by H-ion distribution in the basal planes. 2) Hydrogen ion (H-ion) diffusion in hcp-FeH0.25 is anisotropic, with the lowest energy barrier along the c-axis. This is consistent with the calculated diffusion activation enthalpies. 3) An external electric field promotes H-ion diffusion along its direction, leading to a lower internal energy when the c-axis is aligned with the field. This effect is driven by diffusion-induced stress (DIS). 4) The Earth's geomagnetic field, specifically its poloidal component, can penetrate the inner core and induce electrical currents. These currents can drive the anisotropic alignment of Fe-H crystals, with their c-axes oriented parallel to the equatorial plane. This alignment is more pronounced at greater depths. 5) The isotropic uppermost inner core can be explained by the combined effects of the poloidal and toroidal magnetic fields and other mass fluxes near the ICB. 6) The calculated velocity anisotropies in the model using superionic Fe-H alloys show good agreement with observations from seismic data, supporting the proposed mechanism. Specifically, the model successfully replicates the observed anisotropy in both the average equatorial plane and inner equatorial plane (IEP), and matches anisotropic IMIC models. The data from the South Sandwich Islands to Alaska was also correlated to the anisotropy model.

This study provides a novel mechanism to explain the complex anisotropic structure of Earth's inner core. By considering the superionic nature of Fe-H alloys and the influence of the geomagnetic field, the model successfully accounts for the observed anisotropic seismic velocities, including the transition from an isotropic upper inner core to a highly anisotropic innermost inner core. The alignment of Fe-H crystals driven by the geomagnetic field provides a plausible explanation for the observed texture without the need for high-viscosity flow or invoking solely solidification processes. The good agreement between the calculated velocity anisotropies and seismic observations strengthens the proposed mechanism and suggests a strong coupling between the inner core's structure and the Earth's magnetic field. This work significantly advances our understanding of the inner core's formation and evolution, highlighting the importance of considering superionic effects and the long-term influence of the geomagnetic field in geodynamic processes.

This study demonstrates that the anisotropic texture in Earth's inner core can be explained by the anisotropic diffusion of hydrogen ions in superionic Fe-H alloys, driven by the Earth's geomagnetic field. The model successfully reproduces observed seismic anisotropy variations. Future research could focus on refining the model by incorporating other light elements, improving the resolution of geomagnetic field models, and exploring the dynamic interplay between the inner and outer cores under the influence of superionic processes. The findings provide critical insight into the evolution and dynamic processes of Earth's inner core.

The model simplifies the complex chemical composition of the inner core, primarily focusing on Fe-H alloys. The exact nature and intensity of the geomagnetic field within the inner core remains uncertain, which may introduce uncertainties in the model's predictions. While the model successfully replicates key features of seismic anisotropy, it does not explicitly address all aspects of the inner core's heterogeneity. Further research incorporating a broader range of compositional and physical parameters could improve the model's accuracy and predictive power.