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

Abstract

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 KS0 = 169.0(57) GPa, KS0′ = 5.4(6), (∂KS/∂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 − VP or 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 VS than in VP, 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 VP 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.