Shear softening of Earths inner core indicated by its high Poissons ratio and elastic anisotropy

Earth’s inner core exhibits an unusually high Poisson’s ratio and noticeable elastic anisotropy. The mechanisms responsible for these features are critical for understanding the evolution of the Earth but remain unclear. This study indicates that once the correct formula for the shear modulus is used, shear softening can simultaneously explain the high Poisson’s ratio and strong anisotropy of the inner core. Body-centred-cubic (bcc) iron shows shear instability at the pressures found in the inner-core and can be dynamically stabilized by temperature and light elements. It is very likely that some combinations of light elements stabilize the bcc iron alloy under inner-core conditions. Such a bcc phase would exhibit significant shear softening and match the geophysical constraints of the inner core. Identifying which light elements and what concentrations of these elements stabilize the bcc phase will provide critical information on the light elements of the inner core.

💡 Research Summary

The paper tackles two long‑standing geophysical puzzles: the unusually high Poisson’s ratio (≈ 0.44) and the pronounced elastic anisotropy of Earth’s solid inner core. Traditional models, which assume a hexagonal‑close‑packed (hcp) iron alloy, struggle to reproduce both features simultaneously because they rely on an isotropic formulation of the shear modulus (G) that overestimates G under the extreme pressures of the inner core. The authors first point out that the standard G‑formula is only exact for isotropic media; in a transversely‑anisotropic material, a reduction of G—known as shear softening—drastically raises the Poisson’s ratio according to the exact relation v = (3K − 2G)/(6K + 2G). When G becomes a small fraction of the bulk modulus K, v climbs into the 0.44–0.48 range, matching seismic inferences.

Having established the theoretical link, the study turns to mineral physics. First‑principles calculations show that body‑centred‑cubic (bcc) iron is shear‑unstable at inner‑core pressures (≈ 330 GPa) because its elastic constant C′ = (C11 − C12)/2 is negative. However, the authors demonstrate that high temperature (≈ 6000 K) and the presence of light alloying elements (sulfur, silicon, oxygen, carbon) can dynamically stabilize the bcc phase. Light elements modify the electronic structure, reducing the shear‑related elastic constants (C′ and C44) and thereby producing a substantial shear‑softening effect—often a 30–50 % drop in G relative to pure bcc Fe. Phonon calculations confirm that the softened lattice remains dynamically stable when these elements are present at a few atomic percent.

The softened bcc alloy naturally generates the observed seismic anisotropy. Because shear wave velocity V_S scales with √G, a lowered G leads to a pronounced directional dependence of V_S, reproducing the measured ∆V_S ≈ 5 % and ∆V_P ≈ 3–4 % anisotropy. Moreover, shear softening promotes the development of crystallographic texture: grains tend to align their easy‑shear planes parallel to the rotation axis, which explains why seismic waves travel faster along the Earth’s spin axis than equatorially.

In summary, the paper argues that shear softening, arising from a temperature‑ and light‑element‑stabilized bcc iron alloy, simultaneously accounts for the inner core’s high Poisson’s ratio and its strong elastic anisotropy—features that hcp‑Fe models cannot reconcile. The authors call for systematic experimental and computational investigations to identify the specific light‑element combinations and concentrations that stabilize the bcc phase under core conditions. Determining these compositional constraints will not only refine our picture of the inner core’s mineralogy but also shed light on its thermal evolution, growth history, and the dynamics that sustain Earth’s magnetic field.