Stacking-disordered phase of iron in the Earth’s inner core from first principles

We propose a stacking-disordered phase defined as a thermally equilibrated planar defective hexagonal-closed-packed structure for a stable state of iron under the Earth’s inner core condition. A multiple configuration sampling technique based on first-principles calculations shows that a stacking fault concentration reaches approximately 40% at a pressure of 400 GPa and a temperature of 6000 K. In addition, the stacking disordering is found to enhance elastic anisotropy, which is expected to explain seismologically observed P-wave anisotropy at the Earth’s inner core.

Figure 1

An example of crystal structures with different stacking sequences for a 12 close-packed-layer supercell. (a) ABAB stacking sequence corresponding to the hexagonal-close-packed (hcp) structure, (b) ABACABCBCBCB stacking sequence, (c) ABCACBCBACAB stacking sequence, (d) ABACBCABACBC stacking sequence, and (e) ABCABC stacking sequence corresponding to the face-centered-cubic (fcc) structure.

Figure 2

Statistics for the stacking disordering. (a) Configuration density of states (CDOS) (spectral density) obtained at 400 GPa for 4098 stacking structures related to a 12 close-packed-layer supercell. Filled diamonds show a stacking fault concentration, $n$. ABAB stacking structure (hcp) and ABCABC stacking structure (fcc) correspond to $n=0$ and $1$, respectively. (b) Temperature dependencies of a thermal expectation value of the stacking fault concentration, $\langle n\rangle$, at 200, 300, and 400 GPa.

Figure 3

Compressional ($V_{\text{P}}$) and shear ($V_{\text{S}}$) wave velocities as a function of the propagation direction. The velocities of the stacking-disordered phase with $\langle n\rangle =0.42$ are compared with those of the hcp and fcc phases at 400 GPa. Panel (a) shows $V_{\text{P}}$, and panels (b) and (c) represent the faster and slower $V_{\text{S}}$’s, respectively. The $z$ axis corresponds to the stacking direction of the close-packed layers.