Phonon softening in paramagnetic bcc Fe and its relationship to the pressure-induced phase transition

The structural stability of paramagnetic (PM) body-centered-cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasirandom structure with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered-cubic (fcc) and hexagonal-close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N-4(-) mode), which corresponds to a bcc-hcp phase transition pathway, exhibits strong softening under isotropic volume compression. The frequency of this mode becomes zero by a 2% volume decrease within the harmonic approximation. This result is not consistent with the experimental fact that the phase transition from the PM bcc to hcp phases does not occur under volume compression. The seeming contradiction can be explained only when the anharmonic behavior of the N-4(-) mode is taken into consideration; A potential energy curve along the N-4(-) mode becomes closer to a double-well shape for the PM phase under volume compression. On the other hand, softening of the longitudinal mode at the 2/3[111] point under volume compression is also found for the PM phase, which indicates the pressure-induced bcc-fcc phase transition along this mode. Such behaviors are not seen in ferromagnetic bcc Fe, implying that the magnetic structure plays an essential role on the phase transition mechanism.