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A class of Fe-Mn-Si-based alloys exhibits a reversible martensitictransformation between the $\gamma$ phase with a face-centered cubic~(fcc)structure and an $\epsilon$ phase with a hexagonal close-packed (hcp)structure. During the deformation-induced $\gamma$--$\epsilon$ transformation,we identified a phase that is different from the $\epsilon$ phase. In this newphase, the electron diffraction spots are located at the 1/3 positions thatcorrespond to the $\{$0002$\}$ plane of the $\epsilon$ (hcp) phase with 2Hstructure, which suggests long-period stacking order (LPSO). To understand thestacking pattern and explore the possible existence of an LPSO phase as anintermediate between the $\gamma$ and $\epsilon$ phases, the phase stability ofvarious structural polytypes of iron was examined using first-principlescalculations with a spin-polarized form of the generalized gradientapproximation in density functional theory. We found that an antiferromagneticordered 6H$_2$ structure is the most stable among the candidate LPSO structuresand is energetically close to the $\epsilon$ phase, which suggests that theobserved LPSO-like phase adopts the 6H$_2$ structure. Furthermore, wedetermined that the phase stability can be attributed to the valley depth inthe density of states, close to the Fermi level.

Origin of phase stability in Fe with long-period stacking order as an intermediate phase in cyclic $\gamma$-$\epsilon$ martensitic transformation