Bravais phases of Fe under pressure from first principles

The structure and stability of four Bravais phases of Fe under pressure are determined by a procedure which first looks for minima of the internal energy E at constant volume V and then tests the states at the minima for stability ( or instability) by showing that the Gibbs free energy G at constant pressure p is a minimum ( or not a minimum) with respect to all possible strains. The phases considered here are either body-centered tetragonal (bct), which includes body-centered cubic (bcc) and face-centered cubic (fcc), or rhombohedral ( rh). The results include showing that bcc Fe becomes unstable at 1500 kbar, that fcc Fe is stable at p = 0, that a phase transition from bcc to fcc is thermodynamically favored at 290 kbar, that a bct phase at c/a = 0.89 is unstable up to 2700 kbar and that a rh phase with angle alpha = 60.5 degrees is stable at p = 0 with E slightly higher than that for fcc Fe.