The particle-in-cell model for ab initio thermodynamics: implications for the elastic anisotropy of the Earth’s inner core

We assess the quantitative accuracy of the particle-in-cell (PIC) approximation used in recent ab initio predictions of the thermodynamic properties of hexagonal-close-packed (hcp) iron at the conditions of the Earth’s inner core. The assessment is made by comparing PIC predictions for a range of thermodynamic properties with the results of more exact calculations that avoid the PIC approximation. It is shown that PIC gives very accurate results for some properties, but that it gives an unreliable treatment of anharmonic lattice vibrations. In addition, our assessment does not support recent PIC-based predictions that the hexagonal c/a ratio increases strongly with increasing temperature, and we point out that this casts doubt on a proposed re-interpretation of the elastic anisotropy of the inner core.