Quasihydrostatic Equation of State of Iron above 2 Mbar

The compression curve of iron is measured up to 205 GPa at 298 K, under quasihydrostatic conditions in a diamond anvil cell. Above 150 GPa, the compression of this metal is significantly higher than previously measured under nonhydrostatic conditions. The same compression curve is also calculated ab initio and the deviation between experiment and theory is clearly established. A formulation of the equation of state of iron over a large pressure and temperature range, based on the current data and existing shock-wave data, is also proposed. Implications for the Earth’s core are discussed.

Figure 1

(a) Measured atomic volume of iron ($\alpha$-Fe for $P\le 14.6\mathrm{GPa}$ and $ϵ$-Fe for $P\ge 17.7\mathrm{GPa}$) as a function of the pressure (pressure gauge: see Table ), compared with literature data. Inset: evolution of the $c/a$ ratio for hexagonal closed packed $ϵ$-Fe. (b) Difference between measured and fitted volume, Vinet formulation with $V_0=11.214{\AA }^3$, $K_0=163.4\mathrm{GPa}$, $K_0^{\prime }=5.38$.

Figure 2

Comparison between calculated DFT-GGA EOS (this work and Ref. 20 ) and measured EOS. 298 K thermal pressure, calculated using Eq. (2), has been added to DFT-GGA pressure in order to be compared to $P_{\exp }$. $P_{\mathrm{Abinit}}\mathrm{\text{−}}{P}_{\exp }$ is calculated for a given atomic volume $V$. The hatched area represents the uncertainty on $P_{\exp }$ caused by uncertainty on pressure calibration in the diamond anvil cell.

Figure 3

Specific volume of $ϵ$-Fe as a function of pressure on several isotherms, calculated using Eqs. (1, 2). The isotherms are plotted as continuous lines in the estimated domains of stability of solid iron [31]. Specific volume profile in the Earth’s core, according to the PREM seismic model [28], is shown for comparison.