First-principles determination of theα−α′interfacial energy in Fe-Cr alloys

Abstract

The interfacial energies $(\ensuremath{\gamma})$ between the Cr-rich ${\ensuremath{\alpha}}^{\ensuremath{'}}{\text{-Fe}}_{x}{\text{Cr}}_{1\ensuremath{-}x}$ and Fe-rich $\ensuremath{\alpha}{\text{-Fe}}_{1\ensuremath{-}y}{\text{Cr}}_{y}$ phases $(0<x,y<0.35)$ are calculated to be between $\ensuremath{\sim}0.02$ and $\ensuremath{\sim}0.33\text{ }\text{J}\text{ }{\text{m}}^{\ensuremath{-}2}$ for the ferromagnetic state and between $\ensuremath{\sim}0.02$ and $\ensuremath{\sim}0.27\text{ }\text{J}\text{ }{\text{m}}^{\ensuremath{-}2}$ for the paramagnetic state. Although for both magnetic states, the interfacial energy follows a general decreasing trend with increasing $x$ and $y$, the fine structures of the $\ensuremath{\gamma}(x,y)$ maps exhibit a marked magnetic state dependence. The subtleties are shown to be ascribed to the magnetic interaction between the Fe and Cr atoms near the interface. The theoretical results are applied to estimate the critical grain size for nucleation and growth in Fe-Cr stainless steel alloys.