Sound velocity and density measurements of liquid iron up to 800 GPa: A universal relation between Birch's law coefficients for solid and liquid metals

- Sound velocity and density of liquid iron at pressures up to 800 GPa were measured.
- The sound velocity as a function of density in liquid iron follows Birch's law.
- A slope ratio between the solid and liquid phase is approximately 1.5.
- There are universal relations between solid and liquid for metals along Hugoniot.
- Super-Earth's core has about twice as large density as iron at ambient condition.

We performed compressional sound velocity and density measurements on liquid iron at pressures up to 800 GPa with a newly refined shock-compression method using a high-power laser. We found that sound velocity as a function of density can be fitted to a linear relation following Birch's law for hot dense liquid as well as for the solid phase of iron, with a slope ratio between the solid and liquid of approximately 1.5. A comparison of Birch's law for solid and liquid metals indicates that the sound velocity in the liquid phase is about 10% lower than that in the solid phase at melting point density, which is about 1.5 times larger than the initial density. We suggest that these relations between Birch's law coefficients for solid and liquid phases along the Hugoniot are universal for metals.