Origin of phase stability in Fe with long-period stacking order as an intermediate phase in cyclic $γ$-$ε$ martensitic transformation
A class of Fe-Mn-Si-based alloys exhibits a reversible martensitic transformation between the $γ$ phase with a face-centered cubic~(fcc) structure and an $ε$ phase with a hexagonal close-packed (hcp) structure. During the deformation-induced $γ$--$ε$ transformation, we identified a phase that is different from the $ε$ phase. In this new phase, the electron diffraction spots are located at the 1/3 positions that correspond to the $\{$0002$\}$ plane of the $ε$ (hcp) phase with 2H structure, which suggests long-period stacking order (LPSO). To understand the stacking pattern and explore the possible existence of an LPSO phase as an intermediate between the $γ$ and $ε$ phases, the phase stability of various structural polytypes of iron was examined using first-principles calculations with a spin-polarized form of the generalized gradient approximation in density functional theory. We found that an antiferromagnetic ordered 6H$_2$ structure is the most stable among the candidate LPSO structures and is energetically close to the $ε$ phase, which suggests that the observed LPSO-like phase adopts the 6H$_2$ structure. Furthermore, we determined that the phase stability can be attributed to the valley depth in the density of states, close to the Fermi level.