Elastic properties of body-centered cubic iron in Earth's inner core

The solid Earth's inner core (IC) is a sphere with a radius of about 1300 km in the center of the Earth. The information about the IC comes mainly from seismic studies. The composition of the IC is obtained by matching the seismic data and properties of candidate phases subjected to high pressure (P) and temperature (T). The close match between the density of the IC and iron suggests that the main constituent of the IC is iron. However, the stable phase of iron is still a subject of debate. One such iron phase, the body-centered cubic phase (bcc), is dynamically unstable at pressures of the IC (330–364 GPa) and low T but gets stabilized at high T characteristic of the IC (5000–7000 K). So far, ab initio molecular dynamics (AIMD) studies attempted to compute the bcc elastic properties for a small (order of ${10}^2$) number of atoms. The mechanism of the bcc stabilization cannot be enabled in such cells and that has led to erroneous results. Here we apply AIMD to compute elastic moduli and sound velocities of the Fe bcc phase for a 2000 Fe atom computational cell, which is a cell of unprecedented size for ab initio calculations of iron. Unlike in previous ab initio calculations, both the longitudinal and the shear sound velocities of the Fe bcc phase closely match the properties of the IC material at P = 360 GPa and T = 6600 K, likely the PT conditions in the IC. The calculated density of the bcc iron at these PT conditions is just $3\%$ higher than the density of the IC material according to the Preliminary Earth Model. This suggests that the widely assumed amount of light elements in the IC may need a reconsideration. The anisotropy of the bcc phase is an exact match to the most recent seismic studies.

Figure 1

Adiabatic single crystal P-wave and S-wave velocities for bcc Fe at IC conditions as a function of propagation direction: (a) $V_P$, (b) $V_{S1}$, and (c) $V_{S2}$. This figure was generated by Unicef Careware [44].

Figure 2

Size dependence of mean-square displacement (MSD) in bcc Fe. The package lammps [45] was used for these calculations. The MSD is computed as in Ref. [13] using the EAM model [21] at the T = 6600 K and constant volume corresponding to the pressure 360 GPa for the number of particles 2000, 16 million, and 128 million atoms as indicated in the legend (1 time step = 1 fs). The AIMD computed MSD is equal to 0.28 Å ${}^2$ in close agreement to calculated using the EAM model.