Hugoniot Sound Velocities in Metals with Applications to the Earth's Inner Core

Abstract

Hugoniot sound velocities in metals can be used to study the elastic properties of materials at high pressure. Both compressional and bulk sound velocities along the Hugoniot satisfy Birch's Law over the density range 2–27 g/cm^3. That is, velocities are linear in density with slopes proportional to atomic weight. This result provides empirical support for the validity of Birch's Law over the entire range of density distributions in the Earth's interior. Measured Hugoniot velocities are generally consistent with finite strain extrapolations of low pressure data. Differences between measured and extrapolated data can be attributed to thermal effects. Bulk sound velocities allow the volume dependence of the Gruneisen parameter, γ, to be constrained. In agreement with previous results for porous metals, the sound speed data for both solid and liquid metals are consistent with q = ∂lnγ/∂lnV = 1, where V is the volume. Shear velocity, V_S , can be constrained to ∼4% along the Hugoniot in the best cases but more generally uncertainties exceed 10%. At compressions above V_0/V ≈︁ 1.43, 3d‐and 4d‐series transition metals are characterized by negative dV_S/dP slopes ranging between −0.01 and −0.001 km/s/GPa. the low shear velocities result in values of Poisson's ratio above 0.4 for these materials, significantly greater than zero pressure values of 0.3–0.35. This suggests that the shear properties of the inner core are not anomalous but rather are characteristic of the type of behavior observed in 3d‐and 4d‐series metals at high pressure and temperature.