Ab initio equation of state for the body-centered-cubic phase of iron at high pressure and temperature

The solid inner core of the Earth consists mostly of iron. There is accumulating evidence that, at the extreme pressures and temperatures of the deep Earth interior, iron stabilizes in the body-centered-cubic phase. However, experimental study of iron at those conditions is very difficult at best. We demonstrate that our ab initio approach is capable of providing volumetric data on iron in very good agreement with experiment at low temperature and high pressure. Since our approach treats high-temperature effects explicitly, this allows us to count on similar precision also at high temperature and high pressure. We perform ab initio molecular-dynamics simulations at a number of volume-temperature conditions and compute the corresponding pressures. These points are then fitted with an equation of state. A number of parameters are computed and compared with existing data. The obtained equation of state for high pressure and temperature nonmagnetic body-centered-cubic phase allows the computation of properties of iron under extreme conditions of the Earth’s inner core.

Figure 1

(Color online) High-pressure iron phase diagram as computed from embedded-atom method tuned to full potential linear-muffin-tin orbitals method (Ref. 8). Continuous curves represent phase boundaries as provided in the legend. The open circles correspond to the low melting curve (Ref. 7), the star is the most recently measured melting temperature (Ref. 6), and the diamonds with error bars are solid-solid and melting transitions. The points where we computed $PVT$ points on bcc iron (with 54 atoms supercells) are shown by filled circles. Two open squares show the points, computed with 128 atoms (see text for discussion).

Figure 2

(Color online) Comparison of two hcp EOS as provided by Dewaele et al. (Ref. 27) and Dubrovinsky et al. (Ref. 20) with computed, in this work, cold hcp $PV$ points.

Figure 3

(Color online) Pressure and temperature time evolutions during a productive stage of molecular-dynamics run for $V=7.0{\text{Å}}^3/\text{atom}$. Pressure curves show the pressure trace (thick continuous curve) as well as $P_{xx}$, $P_{yy}$, and $P_{zz}$ components (dotted, dashed, and long-dashed curves) of the pressure tensor. Temperature is shown by the continuous curve with diamonds. The running over 100 time steps average is shown by the thick continuous curve.

Figure 4

(Color online) Difference between original (AIMD) computed pressures for the given volumes (see legends; volumes are given in ${\text{Å}}^3/\text{atom}$) and fitted ones. The fitted points are calculated at the corresponding (Table ) temperatures.

Figure 5

(Color online) Properties of the bcc phase (this work) (thick curves with open symbols) compared to hcp phase (Ref. 27) (thin curves with filled symbols). (a) Thermal expansion coefficient; (b) Grüneisen parameter $\gamma$; (c) heat capacity at constant pressure; (d) bulk modulus. Comparison is provided at 4 pressures: 100, 200, 300, and 400 GPa as a function of temperature. Note the field of stability of bcc and hcp phases (Fig. 1).