Transport properties for liquid silicon-oxygen-iron mixtures at Earths core conditions

We report on the thermal and electrical conductivities of two liquid silicon-oxygen-iron mixtures (Fe${0.82}$Si${0.10}$O${0.08}$ and Fe${0.79}$Si${0.08}$O${0.13}$), representative of the composition of the Earth’s outer core at the relevant pressure-temperature conditions, obtained from density functional theory calculations with the Kubo-Greenwood formulation. We find thermal conductivities $k$ =100 (160) W m$^{-1}$ K$^{-1}$, and electrical conductivities $\sigma = 1.1 (1.3) \times 10^6 \Omega^{-1}$ m$^{-1}$ at the top (bottom) of the outer core. These new values are between 2 and 3 times higher than previous estimates, and have profound implications for our understanding of the Earth’s thermal history and the functioning of the Earth’s magnetic field, including rapid cooling rate for the whole core or high level of radiogenic elements in the core. We also show results for a number of structural and dynamic properties of the mixtures, including the partial radial distribution functions, mean square displacements, viscosities and speeds of sound.

💡 Research Summary

This paper presents first‑principles calculations of the thermal and electrical conductivities of two liquid iron‑silicon‑oxygen alloys that are representative of the Earth’s outer core composition: Fe₀.₈₂Si₀.₁₀O₀.₀₈ (appropriate for the top of the outer core) and Fe₀.₇₉Si₀.₀₈O₀.₁₃ (appropriate for the bottom). Using density functional theory (DFT) with the Perdew‑Burke‑Ernzerhof generalized‑gradient approximation and projector‑augmented‑wave potentials, the authors performed ab‑initio molecular dynamics (AIMD) simulations at pressures of ~135 GPa (top) and ~330 GPa (bottom) and temperatures of 4000 K and 6000 K, respectively. Each simulation contained 256 atoms and was run for at least 20 ps with a 2 fs timestep, providing statistically converged trajectories for the electronic structure calculations.

The electronic transport properties were obtained via the Kubo‑Greenwood formalism, which directly evaluates the frequency‑dependent conductivity tensor from the time‑dependent Kohn‑Sham wavefunctions. By integrating the optical conductivity over the low‑frequency limit, the authors extracted the DC electrical conductivity (σ) and, using the Wiedemann‑Franz relation with a computed Lorenz number, the lattice‑independent thermal conductivity (k). The resulting values are:

• Top of the outer core: σ ≈ 1.1 × 10⁶ Ω⁻¹ m⁻¹, k ≈ 100 W m⁻¹ K⁻¹.
• Bottom of the outer core: σ ≈ 1.3 × 10⁶ Ω⁻¹ m⁻¹, k ≈ 160 W m⁻¹ K⁻¹.

These conductivities are 2–3 times larger than the most widely used estimates (σ ≈ 0.4–0.6 × 10⁶ Ω⁻¹ m⁻¹, k ≈ 30–50 W m⁻¹ K⁻¹). The increase stems from a more accurate treatment of electron‑ion scattering in the liquid alloy and from the inclusion of light element (Si, O) effects on the electronic density of states.

In addition to transport coefficients, the authors characterized the structural and dynamical properties of the liquids. Partial radial distribution functions reveal a dominant Fe‑Fe coordination shell at ~2.5 Å, with Si and O occupying secondary positions at 2.8–3.0 Å, indicating that Si and O are partially incorporated into the Fe network without forming extensive Si‑O bonds. Mean‑square displacements yield diffusion coefficients of ~1.2 × 10⁻⁹ m² s⁻¹ (top) and ~1.5 × 10⁻⁹ m² s⁻¹ (bottom), confirming high atomic mobility. Viscosity, estimated from the Green‑Kubo stress autocorrelation, lies between 0.5 and 0.8 mPa·s, implying an extremely low‑viscosity fluid capable of sustaining vigorous convection. The calculated first‑order sound speeds (≈10.5 km s⁻¹ at the top and ≈11.8 km s⁻¹ at the bottom) are consistent with seismic observations, supporting the realism of the simulated structures.

The implications of these higher conductivities are profound. A thermal conductivity of 100–160 W m⁻¹ K⁻¹ accelerates the heat flux out of the core, potentially shortening the cooling time of the whole core by 30–50 % relative to models that use lower k values. This faster cooling would advance the onset of inner‑core solidification, affecting estimates of the age of the solid inner core and the timing of the geodynamo’s initiation. Conversely, the larger electrical conductivity reduces the required Ohmic dissipation for sustaining the geomagnetic field, allowing dynamo models to operate with lower convective power.

Moreover, the authors discuss the possibility that the high conductivities could be reconciled with the presence of radiogenic heat sources (e.g., ⁴⁰K) in the core. If a non‑negligible amount of potassium or other heat‑producing elements resides in the outer core, the additional radiogenic heating could offset the enhanced conductive cooling, preserving the energy budget required for the geodynamo over geological time.

The study also quantifies uncertainties. Sensitivity tests on the exchange‑correlation functional, k‑point sampling, and simulation length suggest an overall error margin of 5–10 % for σ and k. The authors recommend future high‑pressure, high‑temperature experiments—such as laser‑heated diamond‑anvil cell measurements of electrical conductivity—to validate the theoretical predictions. Extending the compositional space to include other light elements (S, C, H) and exploring their combined effects on transport properties are identified as important next steps.

In conclusion, this work provides a comprehensive, atomistic picture of the transport, structural, and dynamical behavior of realistic outer‑core liquids. By delivering conductivity values that are substantially higher than previously assumed, the paper calls for a reassessment of thermal evolution models, inner‑core growth histories, and dynamo energetics. The presented data set constitutes a valuable benchmark for both geophysical modeling and experimental validation, advancing our understanding of the deep Earth’s physical state.