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The observed shear-wave velocity VS in Earth's core is much lower than expected from mineralogical models derived from both calculations and experiments. A number of explanations have been proposed, but none sufficiently explain the seismological observations. Using ab initio molecular dynamics simulations, we obtained the elastic properties of hexagonal close-packed iron (hcp-Fe) at 360 gigapascals up to its melting temperature Tm. We found that Fe shows a strong nonlinear shear weakening just before melting (when T/Tm > 0.96), with a corresponding reduction in VS. Because temperatures range from T/Tm = 1 at the inner-outer core boundary to T/Tm ≈ 0.99 at the center, this strong nonlinear effect on VS should occur in the inner core, providing a compelling explanation for the low VS observed.

The cementite phase of Fe 3 C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The ferromagnetic phase transition, with T c 9 480 K, greatly affects the thermal expansion coef®cient of the material. The average volumetric coef®cient of thermal expansion above T c was found to be 4.1 (1) Â 10 À5 K À1; below T c it is considerably lower (< 1.8 Â 10 À5 K À1) and varies greatly with temperature. The behaviour of the volume over the full temperature range of the experiment may be modelled by a thirdorder Gru È neisen approximation to the zero-pressure equation of state, combined with a magnetostrictive correction based on mean-®eld theory.