Reassessment of Birch's Law on hcp-Fe From Ultrasonic Sound Velocity Measurement and Implications on the Velocity Profiles of Earth's Inner Core

We performed in situ X-ray diffraction and ultrasonic sound velocity measurements on hcp-Fe up to 15 GPa, 873 K in a multi-anvil apparatus. The elastic moduli and their pressure and temperature derivatives were determined by fitting the velocity and density data to the third-order finite strain equations, yielding K_S0 = 169.0(57) GPa, K_S0′ = 5.4(6), (∂K_S/∂T)_P = −0.031(3) GPa/K, G₀ = 104.5(27) GPa, G₀′ = 1.7(2), (∂G/∂T)_P = −0.060(2) GPa/K. Within the experimental P-T range, we find significant temperature effect on the density-velocity (ρ − V_{Por S}) relations and caution the use of the temperature-independent Birch's law for extrapolation to core conditions. Furthermore, temperature-induced velocity decrease is more significant in V_S than in V_P, offering a possible explanation for the high Poisson's ratio in the core. Extrapolations based on our results together with previous experimental data suggest that V_P of hcp-Fe aligns with PREM at Earth's core conditions, while Vs and density are approximately 10% and 2.7% higher than PREM, respectively.