The elasticity of hcp-Fe-5wt%Si has been investigated by synchrotron X-ray diffraction up to 110 GPa and 2,100 K and by picosecond acoustics measurements at ambient temperature up to 115 GPa. The established Pressure-Volume-Temperature equation of state shows that the density of the Earth's inner core can be matched by an Fe-Si alloy with 5wt% Si for all reasonable core temperatures, but that its compressional and shear velocities remain too high with respect to seismological observations. On the other hand, Fe-Si alloys whose velocities are expected to get close to seismological observations are too dense at relevant temperatures. Thus, based on these combined velocity-density measurements, silicon is not likely to be the sole light element in the inner core.

International audienceWe carried out sound velocity and density measurements on solid hcp-Fe and an hcp-Fe–Si alloy with 9 wt.% Si at 300 K up to ∼170 and ∼140 GPa, respectively. The results allow us to assess the density (ρ ) dependence of the compressional sound velocity (VPVP) and of the shear sound velocity (VSVS) for pure Fe and the Fe–Si alloy. The established VPVP–ρ and VSVS–ρ relations are used to address the effect of Si on the velocities in the Fe–FeSi system in the range of Si concentrations 0 to 9 wt.% applicable to the Earth's core. Assuming an ideal linear mixing model, velocities vary with respect to those of pure Fe by ∼+80 m/s∼+80 m/s for VPVP and ∼−80 m/s∼−80 m/s for VSVS for each wt.% of Si at the inner core density of 13 000 kg/m3. The possible presence of Si in the inner core and the quantification of its amount strongly depend on anharmonic effects at high temperature and on actual core temperature