bcc-to-hcp transformation pathways for iron versus hydrostatic pressure: Coupled shuffle and shear modes

Abstract

Using density-functional theory, we calculate the potential-energy surface (PES), minimum-energy pathway (MEP), and transition state (TS) versus hydrostatic pressure ${\ensuremath{\sigma}}_{\text{hyd}}$ for the reconstructive transformation in Fe from body-centered cubic (bcc) to hexagonal closed-packed (hcp). At fixed ${\ensuremath{\sigma}}_{\text{hyd}}$, the PES is described by coupled shear $(ϵ)$ and shuffle $(\ensuremath{\eta})$ modes and is determined from structurally minimized hcp-bcc energy differences at a set of $(\ensuremath{\eta},ϵ)$. We fit the PES using symmetry-adapted polynomials, permitting the MEP to be found analytically. The MEP is continuous and fully explains the transformation and its associated magnetization and volume discontinuity at TS. We show that ${\ensuremath{\sigma}}_{\text{hyd}}$ (while not able to induce shear) dramatically alters the MEP to drive reconstruction by a shuffle-only mode at $\ensuremath{\le}30\text{ }\text{GPa}$, as observed. Finally, we relate our polynomial-based results to Landau and nudge-elastic-band approaches and show they yield incorrect MEP in general.