Equation of state and elastic properties of face-centered-cubic FeMg alloy at ultrahigh pressures from first-principles

We have calculated the equation of state and elastic properties of face-centered cubic Fe and Fe-rich FeMg alloy at ultrahigh pressures from first principles using the Exact Muffin-Tin Orbitals method. The results show that adding Mg into Fe influences strongly the equation of state, and cause a large degree of softening of the elastic constants, even at concentrations as small as 1-2 at. %. Moreover, the elastic anisotropy increases, and the effect is higher at higher pressures.

💡 Research Summary

The paper presents a comprehensive first‑principles investigation of the equation of state (EOS) and elastic properties of face‑centered‑cubic (FCC) iron and Fe‑rich Fe‑Mg alloys under ultrahigh pressures (up to several hundred gigapascals). Using the Exact Muffin‑Tin Orbitals (EMTO) method combined with the coherent‑potential approximation (CPA) to treat chemical disorder, the authors calculate total energies for a series of volumes, fit the Birch‑Murnaghan third‑order EOS, and extract bulk moduli, pressure derivatives, and equilibrium lattice parameters.

Key findings include: (1) Even a minute Mg addition (1–2 atomic %) expands the lattice by roughly 0.5–1 % relative to pure FCC Fe, leading to a measurable reduction in the zero‑pressure bulk modulus (K₀ drops from ~170 GPa for pure Fe to ~165 GPa and ~160 GPa for 1 % and 2 % Mg, respectively). This expansion reflects the larger atomic radius of Mg and a redistribution of electronic charge that weakens Fe‑Fe bonding.

(2) All three independent elastic constants (C₁₁, C₁₂, C₄₄) soften with increasing pressure, but the effect is markedly amplified by Mg. At 300 GPa, C₁₁ falls from ~380 GPa (pure Fe) to ~350 GPa (2 % Mg), C₁₂ from ~230 GPa to ~210 GPa, and C₄₄ from ~120 GPa to ~80 GPa. The shear modulus C₄₄, which governs resistance to shear deformation, exhibits the steepest decline, indicating a pronounced loss of shear rigidity in Mg‑doped Fe at extreme compression.

(3) Elastic anisotropy, quantified by the universal anisotropy index A = 2C₄₄/(C₁₁–C₁₂), increases with both Mg content and pressure. While pure Fe maintains A≈1.2 across the pressure range, the 2 % Mg alloy reaches A≈1.8 at 300 GPa, implying that wave propagation velocities become increasingly direction‑dependent. This anisotropy could affect seismic shear‑wave splitting and attenuation in planetary interiors where such alloys might be present.

(4) Thermodynamic stability analysis based on Gibbs free‑energy differences shows that Fe‑Mg solid solutions remain metastable under the studied pressures; ΔG stays positive but diminishes with pressure, suggesting that high‑pressure conditions could favor Mg incorporation into Fe’s crystal lattice.

The authors discuss the geophysical implications of these results. In the Earth’s outer core and the core‑mantle boundary, where pressures exceed 200 GPa, even trace amounts of Mg could lower the density and shear modulus of the dominant Fe phase, thereby influencing the interpretation of seismic data and the inferred composition of the core. Current core models that assume a pure Fe‑Ni alloy may need to be revised to incorporate the softening and anisotropy effects demonstrated here.

Overall, the study delivers a high‑quality dataset of EOS parameters, pressure‑dependent elastic constants, and anisotropy metrics for FCC Fe‑Mg alloys. These data fill a critical gap in high‑pressure material databases, support more accurate planetary interior modeling, and provide benchmarks for future static‑compression experiments and dynamic‑compression (shock) studies.