Sound velocity measurements in dhcp-FeH up to 70 GPa with inelastic X-ray scattering: Implications for the composition of the Earthʹs core

We have determined the density evolution of the sound velocity of dhcp-FeHx (x ≈ 1) up to 70 GPa at room temperature, by inelastic X-ray scattering and by X-ray diffraction. We find that the variation of VP with density is different for the ferromagnetic and nonmagnetic dhcp-FeHx, and that only nonmagnetic dhcp-FeHx follows Birchʹs law. Combining our results with Birchʹs law for iron and assuming an ideal two-component mixing model, we obtain an upper bound of the hydrogen content in the Earthʹs inner core, 0.23(6) wt.% H, corresponding to FeH0.13(3). The iron alloy with 0.23(6) wt.% H can satisfy the density, and compressional and shear sound velocities of the PREM inner core, assuming that there are no other light elements in the inner core.