Order-Disorder in Fe-Si Alloys: Implications for Seismic and Transport Properties of Earth's Inner Core

Abstract

Understanding the structure and dynamics of Earth's inner core is essential for constraining its composition, thermal evolution, and seismic behavior. Silicon is widely considered a major light element in the core. Here, we use first-principles molecular dynamics and thermodynamic modeling to investigate the structural, elastic, and transport properties of iron-silicon (Fe-Si) alloys under inner-core conditions. By computing the Gibbs free energies of multiple solid phases, including ordered B2, hexagonal close-packed (hcp), face-centered cubic (fcc), and body-centered cubic (bcc) Fe-Si, we construct a phase diagram relevant to inner-core pressures and temperatures. We identify a pronounced miscibility gap between hcp and cubic Fe--Si phases, with phase coexistence over approximately 6--11 wt\% Si at 6000 K. The cubic phase exhibits a strong order-dependent elastic response, with disordered bcc showing a large intrinsic shear anisotropy (22.9\% at 6000 K), in contrast to the nearly isotropic hcp phase (0.6\%). Meanwhile, disordered bcc Fe--Si produces shear wave velocities ($V_S=3.73$ km$\cdot$s${}^{-1}$) and Poisson's ratios comparable with seismological constraints. In addition, disordered bcc Fe--Si exhibits a lower thermal conductivity than hcp Fe--Si, providing a quantitative constraint on phase-dependent electronic heat transport. These results demonstrate that chemical ordering strongly controls the stability and physical properties of cubic Fe--Si alloys, and suggest that metastable or localized cubic Fe--Si phases may contribute to the structural and transport complexity of Earth's inner core.