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# Superionic iron alloys and their seismic velocities in Earth’s inner core

## Abstract

Earth’s inner core (IC) is less dense than pure iron, indicating the existence of light elements within it1. Silicon, sulfur, carbon, oxygen and hydrogen have been suggested to be the candidates2,3, and the properties of iron–light-element alloys have been studied to constrain the IC composition4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. Light elements have a substantial influence on the seismic velocities4,5,6,7,8,9,10,11,12,13, the melting temperatures14,15,16,17 and the thermal conductivities18,19 of iron alloys. However, the state of the light elements in the IC is rarely considered. Here, using ab initio molecular dynamics simulations, we find that hydrogen, oxygen and carbon in hexagonal close-packed iron transform to a superionic state under the IC conditions, showing high diffusion coefficients like a liquid. This suggests that the IC can be in a superionic state rather than a normal solid state. The liquid-like light elements lead to a substantial reduction in the seismic velocities, which approach the seismological observations of the IC20,21. The substantial decrease in shear-wave velocity provides an explanation for the soft IC21. In addition, the light-element convection has a potential influence on the IC seismological structure and magnetic field.

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## Data availability

The data supporting the findings of this study have been deposited at the 4TU Center for Research Data: https://doi.org/10.4121/12932588.v2. Any additional data are available upon request from the corresponding author. Source data are provided with this paper.

## Code availability

The Vienna Ab initio Simulation Package is a proprietary software available for purchase at https://www.vasp.at/. Phonopy code is available at http://phonopy.github.io/phonopy/. WIEN2k is available at http://www.wien2k.at/. The WIEN2k+eDMFT package is available at http://hauleweb.rutgers.edu/tutorials/.

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## Acknowledgements

This study was supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB 18010401). We acknowledge the support of the National Natural Science Foundation of China (42074104, 41774101, 11774015, U1930401) and the Youth Innovation Promotion Association of CAS (2020394). Numerical computations were performed at the Hefei Advanced Computing Center, the Shanghai Supercomputer Center and the National Supercomputer Center in Guangzhou.

## Author information

Authors

### Contributions

Y.H. and S.S. contributed equally to this work, conducted the calculations, analysed the data and wrote the manuscript. Y.H., D.Y.K. and H.-k.M. initiated and designed the project. Y.H. conducted calculations on phase transition, melting temperatures and diffusion properties. S.S. performed simulations on elastic properties. B.G.J. performed electronic conductivity calculations. Y.H., D.Y.K. and H.L. discussed the geophysical implications. All authors discussed the data interpretation and commented on the manuscript.

### Corresponding author

Correspondence to Yu He.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Trajectories and mean square displacements (MSDs) of H, O, C and Fe in Fe-light-element alloys.

Trajectories of a, H and Fe in FeH0.25; b, O and Fe in FeO0.0625; c, C and Fe in FeC0.0625 at the superionic state under the IC conditions (~360 GPa and ~5000 K). Small pink, red, black and brown spheres represent the trajectories of H, O, C and Fe, respectively. MSDs of d, H and Fe in FeH0.25; e, O and Fe in FeO0.0625; f, C and Fe in FeC0.0625.

### Extended Data Fig. 2 The evolution of temperature and pressure with respect to simulation time in the two-phase coexisting systems for Fe-H, Fe-O and Fe-C alloys.

a, Temperatures and b, pressures for Fe-H, Fe-O and Fe-C alloys are shown with light grey, pink and cyan curves, and the averaged data over a 0.5 ps period are shown with thick black, red, and blue curves.

### Extended Data Fig. 3 Ionic conductivities of superionic Fe alloys at the core conditions.

Diffusion coefficients calculated using 4 × 4 × 2 supercells and 10 ps simulation time are shown with open symbols. Blue squares: FeH0.25 at ~260 GPa; red squares: FeH0.25 at ~360 GPa; cyan triangles: FeO0.0625 at ~260 GPa; orange triangles: FeO0.0625 at ~360 GPa; green circles: FeC0.0625 at ~260 GPa; pink circles: FeC0.0625 at ~360 GPa. The convergence test results using 4 × 4 × 6 supercell and 100 ps simulation time are labeled by crosses and bars. The results of convergence test are presented with yellow, magenta, and cyan symbols for FeH0.25, FeO0.0625, and FeC0.0625, respectively.

### Extended Data Fig. 4 Electronic conductivities of Fe and Fe alloys at 360 GPa with increasing temperature.

The electronic conductivities of Fe, FeH0.25, FeO0.0625, and FeC0.0625 calculated by DFT + DMFT method are shown by black, blue, red, and magenta symbols.

### Extended Data Fig. 5 Calculated Poisson’s ratios of FeH0.25, FeC0.0625 and FeO0.0625 at various temperatures and 360 GPa.

Increasing temperature leads to obvious increases in Poisson’s ratios approaching the value of the inner core (~0.44).

### Extended Data Fig. 6

Calculated chemical potentials of X (X = H, O, C, S, and Si) in hcp-Fe with different configurations at 360 GPa and 0 K. The chemical potentials are shown with blue bars. The superscripts s and i denote the substitutional and interstitial defects. Separated(sub. + inter.) and correlated (dimer) configurations are noted.

### Extended Data Fig. 7 The stability of interstitial and substitutional H, C and O in hcp-Fe under inner core conditions.

a, The MSD of Fe in Fe60H4 at 360 GPa and 5000 K; The relative formation energy of b, C and c, O at interstitial and substitutional site at 340 GPa and 360 GPa, respectively.

### Extended Data Fig. 8 MSDs of Si, S, and Fe in FeSi0.0625 and FeS0.0625 at ~330 GPa and 3000 K.

MSDs of a, Si and Fe in FeSi0.0625; b, S and Fe in FeS0.0625. The MSDs of Si, S and Fe increase obviously with simulation time indicating a liquid state.

### Extended Data Fig. 9 The structures of two-phase systems of Fe-H, Fe-O and Fe-C after the AIMD simulations.

These structures suggest the coexistence of solid and liquid Fe alloys. Pink, red, black and brown spheres represent H, O, C and Fe atoms, respectively.

## Supplementary information

### Supplementary Information

Supplementary Discussion, Figs. 1–4, Table 1 and References.

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He, Y., Sun, S., Kim, D.Y. et al. Superionic iron alloys and their seismic velocities in Earth’s inner core. Nature 602, 258–262 (2022). https://doi.org/10.1038/s41586-021-04361-x

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• DOI: https://doi.org/10.1038/s41586-021-04361-x

• ### Compressional wave velocity for iron hydrides to 100 gigapascals via picosecond acoustics

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