Grain boundary energy function for 𝛼 iron

Polycrystalline 𝛼 iron has been used in various applications, yet its microstructure design via grain boundary engineering (GBE) is not well established. One limiting factor is that while there are many different grain bound- aries in the five-dimensional space of grain boundary types, relatively few of the energies have been determined. In this study, a piece-wise continuous grain boundary energy function for 𝛼 iron is constructed to fill the entire five-dimensional space of grain boundary types using scaffolding subsets with lower dimensionality. Because the energies interpolated from the grain boundary energy function are consistent with the 408 boundaries that have been calculated using atomistic simulations, the energy function is then employed to generate a larger set of grain boundary energies. Comparisons between the interpolated energies and the measured grain boundary population indicate that they are inversely correlated for the high-energy anisotropy misorientations (those for which the difference between the maximum and minimum grain boundary energies is greater than 0.4 J/m2). The results suggest that GBE in the 𝛼 iron should consider the high-energy anisotropy misorientations, rather than the twinning-related grain boundaries (Σ3, Σ9, Σ27a, and Σ27b) as in the case of fcc metals.