Twinning pathways in Fe and Fe–Cr alloys from first-principles theory

Using density-functional theory, we determine the generalized stacking fault energy (GSFE) for the $\left\{1\overline{1}2\right\}〈\overline{1}11〉$ twinning system in ferromagnetic (FM) body-centered cubic Fe and Fe–Cr alloys with molar fraction of Cr $\le 0.5$. We adopt both reflection and isosceles twinning pathways and reveal the magnetic ordering effects on the GSFE by contrasting the FM results to those obtained for the magnetically disordered paramagnetic (PM) state. The results show that the isosceles twin boundary configuration is energetically preferred in this binary. The loss of long-range magnetic order lowers the GSFE amplitude but increases the twin boundary migration (TBM) energy regardless of the Cr content. The twin boundary formation (TBF) energy and the TBM energy show non-linear dependences on Cr content in the FM and PM states, and the effect of Cr on these properties critically depends on the magnetic state. We discuss our results in regard to the stable twin boundary structure and deformation twinning experimentally observed in homogeneous Fe-50 wt.% Cr alloy up to temperatures slightly above the magnetic ordering temperature.