Velocity‐Density Systematics of Fe‐5wt%Si: Constraints on Si Content in the Earth's Inner Core

Abstract

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.

Ultrafast X-ray diffraction measurements of shock-compressed iron and iron alloys

“…The measured d-spacing of the transient bcc {110} and {211} reflections corresponds to a hydrostatic pressure of 38 GPa; the high-pressure hcp {002} reflection corresponds to a pressure of 132±26 GPa using the 300 K static compression equation of state from Hirao et al 33 . We make no thermal corrections since the Hirao data agrees well with the shock Hugoniot data reported in Marsh et al 61 , as seen in Fig.4, for Fe-Si 6.9wt% ; measurements of Fe-Si 5wt% at slightly lower pressure by Edmund et al 65 suggest the thermal pressure is ∼15 GPa for our conditions, similar to that found by Fischer et al in Fe-Si 16wt% and less than our error bars. The inferred bcc pressure is consistent with our calculations for the transformation pressure described below.…”

Picosecond Acoustics Technique to Measure the Sound Velocities of Fe-Si Alloys and Si Single-Crystals at High Pressure

“…Irrespective of such considerations, for Fe-5Si, we observed that the acoustic travel time of a sample varied by nearly 50% from ambient pressure to 1 Mbar, while changes in sample volume led to variations in sample thickness of about 10% over the same pressure range [28]. Consequently, the primary contribution to the variation of the sample acoustic travel time over this pressure range was due to the change in sound velocity, rather than the change in thickness.…”

“…The pressure dependence of the sample thickness was taken into account using P-V EoS determined by X-ray diffraction, either after [28] for the bcc and hcp phases of Fe10Si or after [27,29] for Fe5Si. We relate the pressure evolution of the longitudinal sound velocity to the pressure evolution of thickness and acoustic travel time using the following equation:…”

“…On the basis of the determined sound velocities and literature constraints on the shear strength of Ne [34], the pressure gradients that may develop in Ne or Ar are not sufficiently large to induce significant elastic or plastic deformation of the sample in the case of Fe or Fe-alloys relative to experimental uncertainties. Estimations of the Young's moduli of Fe, Fe5Si, and Fe10Si at the highest pressure data points used from these experiments are E = 890 GPa at 152 GPa, E = 810 GPa at 114 GPa, and E = 340 GPa at 36 GPa for these alloys, respectively [27,28,35]. Given that the shear strength of Ar is estimated to be about 3-6 GPa at 150 GPa [36,37] and the shear strength of Ne is less than 1-2 GPa over the pressure ranges investigated in [27,28], deviations from the assumption of purely volumetric variation in thickness are not significant in these systems relative to experimental uncertainties and scatter.…”

“…Estimations of the Young's moduli of Fe, Fe5Si, and Fe10Si at the highest pressure data points used from these experiments are E = 890 GPa at 152 GPa, E = 810 GPa at 114 GPa, and E = 340 GPa at 36 GPa for these alloys, respectively [27,28,35]. Given that the shear strength of Ar is estimated to be about 3-6 GPa at 150 GPa [36,37] and the shear strength of Ne is less than 1-2 GPa over the pressure ranges investigated in [27,28], deviations from the assumption of purely volumetric variation in thickness are not significant in these systems relative to experimental uncertainties and scatter. However, future studies are needed to test this assumption for materials that undergo reconstructive phase transitions at very high pressures, as the rapid loss of shear or compressive strength in a sample under conditions where compression becomes strongly deviatoric may lead to plastic effects that would be important to constrain for more precise velocity determination at multi-Mbar pressures.…”