Figure 1

Phase diagram of iron. Bold black lines show the results of our calculations including the $\mathrm{fcc}=\mathrm{hcp}$ and $\mathrm{fcc}=\mathrm{bcc}$ phase coexistence lines. Thin black lines show the experimental phase boundaries. Superimposed on the phase diagram are (red lines) the calculated isentrope (lower) and Hugoniot (upper). Pressure-temperature conditions at the center of Earth, a super-Earth with 5 times Earth’s mass [36], and Jupiter [4] are shown by the blue circles. The calculated $\mathrm{fcc}=\mathrm{hcp}$ coexistence line is dashed at low pressure where the slope is influenced by magnetic contributions that we have neglected. The stability field of liquid, indicated with gray hatching, is estimated from our computed vibrational frequencies via the Lindemann law [38].Reuse & Permissions

Figure 2

Static contribution to the energy: the difference fcc-hcp (red), bcc-hcp (blue), and bct-hcp (green) are shown. Pressure is indicated along the top axis. Downward-pointing arrows indicate the volumes at which band structures are shown in Fig. 3. Properties of phase transformations, including the phase transition pressure $P_{\mathrm{tr}}$, the volume of the low pressure phase $V_1$, and the volume contrast $\Delta V$ are hcp to fcc: $P_{\mathrm{tr}}=60\mathrm{Mbar}$, $V_1=18.5\mathrm{a}.\mathrm{u}.$ ($33.9\mathrm{g}/{\mathrm{cm}}^3$), $\Delta V=0.15\%$; fcc to bcc: $P_{\mathrm{tr}}=383\mathrm{Mbar}$, $V_1=9.4\mathrm{a}.\mathrm{u}.$ ($66.7\mathrm{g}/{\mathrm{cm}}^3$), $\Delta V=0.1\%$. The dashed blue line and open blue symbols are for ferromagnetic bcc iron from our previous work [11] and show the influence of magnetism on the stability of iron at low pressure.Reuse & Permissions

Figure 3

Band structure of iron at high pressure in the stability field of hcp (left), fcc (middle), and bcc (right). The Fermi energy is denoted by the dashed black line. Bands are color-coded according to the amount of $d$ character in the eigenstates as indicated. Bands are well separated in the middle panel in order of increasing energy: $3s$, $3p$, $3d$, and $4s$. Band structures are calculated in the fcc structure.Reuse & Permissions

Figure 4

Finite temperature contributions to the free energy including the electronic (top) and phonon (bottom) terms; pressure is indicated along the top axis. The top panel shows the difference in electronic free energy between fcc and hcp phases over a range of temperatures as indicated (1000–20 000 K). The inset shows that the electronic density of states at the Fermi level is higher in fcc than in hcp at high pressure. The bottom panel shows the difference in the logarithm of the geometric mean vibrational frequency, which is directly proportional to the phonon contribution to the free energy.Reuse & Permissions