Order-Disorder in Fe-Si Alloys: Implications for Seismic Anisotropy and Thermal Evolution 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 properties. Silicon is a probable major component of Earth's core. Using first-principles molecular dynamics and thermodynamic modeling, we investigate the structural, elastic, and transport properties of Fe-Si alloys at high pressures and temperatures. By computing the Gibbs free energies of B2, hcp, fcc, and bcc solid solutions, we construct the Fe-Si phase diagram applicable to the Earth's inner core. Our results reveal a pronounced miscibility gap between hcp and B2 Fe-Si, with the two phases coexisting over the compositional range of 6-11 wt% Si at 6000 K. The B2 Fe-Si alloy exhibits strong single-crystal shear anisotropy (22.9% at 6000 K) compared to the nearly isotropic hcp phase (0.6%), and yields a shear wave velocity (3.73 km/s) and Poisson's ratio consistent with seismological observations. Moreover, the computed transport properties reveal substantially lower thermal conductivity of B2 Fe-Si relative to pure iron or hcp Fe-Si under inner-core conditions. These results imply that Earth's inner core likely comprises multiple phases, whose distribution and crystallographic texture critically influence its seismic and thermal properties.

Figures (18)

• Figure 1: Effects of order parameter in B2 Fe–Si alloys. Illustrated for a representative composition of Fe$_{0.875}$Si$_{0.125}$ (12.5 mol% Si), where $Q=0$ and $Q=1$ denote completely disordered (bcc) and fully ordered (B2) states, respectively. a Enthalpy at 330 GPa 6000 K, b configurational entropy, c vibrational entropy at 330 GPa and 6000 K, and d Gibbs free energy at 330 GPa and 6000 K as functions of order parameter $Q$. The enthalpies and Gibbs free energy at Q=0 have been shifted to zero for illustration.
• Figure 2: Order–disorder phase transition in Fe–Si alloys. Temperature dependence of the order parameter ($Q$) for the B2 (red), hcp (blue), and fcc (green) phases of Fe–Si alloys at Si content of a 12.5, b 25.0, c 37.5, and d 50 mol%, corresponding to Fe$_{0.875}$Si$_{0.125}$, Fe$_{0.75}$Si$_{0.25}$, Fe$_{0.625}$Si$_{0.375}$, and Fe$_{0.5}$Si$_{0.5}$, respectively. The yellow shaded region indicates the estimated temperature range of Earth’s inner core anzelliniMeltingIronEarths2013. The disordered phase ($Q=0$) of the B2 phase corresponds to the bcc structure.
• Figure 3: Composition–temperature phase diagram of Fe–Si alloys at 330 GPa. Red points denote phase boundaries separating hcp (blue), coexisting hcp+B2 (yellow), and B2 (magenta) regions, determined from common-tangent constructions between Gibbs free energy curves of the B2 and hcp phases at different temperatures. The ordered B2–Fe–Si alloy transforms into a disordered bcc phase ($Q = 0$) above the dashed cyan line. The dashed black lines represent the phase boundaries (hcp, coexistence, B2, and fluid) determined in Ref. liShortrangeOrderStabilizes2025. The shaded grey regions indicate the constraints imposed by melting curves beyond the range of our simulations. The blue diamond indicates the experimental constraints tatenoStructureFeSi2015 defining the boundary between the hcp phase and the hcp/B2 mixture for Fe–9Si at 330 GPa. The open red diamond is extrapolated from lower-pressure experiments fischerPhaseRelationsFe2013a.
• Figure 4: Electrical transport properties of Fe–Si alloys at $\sim$330 GPa and 6000 K.a Electrical resistivity ($\rho$), b thermal conductivity ($\kappa$), and c Lorenz number ($L$) for B2 and hcp Fe–Si alloys with Si contents of 12.5 mol% and 25 mol% (Fe$_{0.875}$Si$_{0.125}$ and Fe$_{0.75}$Si$_{0.25}$). The order parameter $Q$ varies from 0 (bcc, disordered) to 1 (B2, ordered). The ideal Lorenz number ($L_0 = 2.45\times10^{-8}$ W$\Omega$K$^{-2}$) is indicated by the dotted horizontal line. d Total electronic density of states (DOS) of Fe$_{0.875}$Si$_{0.125}$, with the Fermi energy shifted to zero. In the B2 structure, Fe$_{0.875}$Si$_{0.125}$ stabilizes in the disordered ($Q=0$, bcc-like) phase, while Fe$_{0.75}$Si$_{0.25}$ remains ordered ($Q=1$) at 6000 K.
• Figure 5: Seismic velocities of Fe–Si alloys as a function of density and composition. Calculated compressional-wave ($V_P$) and shear-wave ($V_S$) velocities of Fe$_{0.875}$Si$_{0.125}$ alloys in the B2 (a) and hcp (b) phases are compared with the Preliminary Reference Earth Model (PREM) dziewonskiPreliminaryReferenceEarth1981 values for the inner core (open red stars) and with previous simulations (open triangles)liShortrangeOrderStabilizes2025. Panels (c) and (d) show the composition dependence of seismic velocities for B2 and hcp phases at 5000 K and 6000 K, including pure Fe, Fe$_{0.875}$Si$_{0.125}$, and Fe$_{0.75}$Si$_{0.25}$. In the B2 structure, Fe$_{0.875}$Si$_{0.125}$ is stabilized in the disordered ($Q=0$, bcc-like) phase, whereas Fe$_{0.75}$Si$_{0.25}$ remains ordered ($Q=1$) at 5000 K and 6000 K.