  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 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 incorrect 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.
