Fig. 5: Quantifying elastic energy for the Σ13b GB with dislocations using linear anisotropic elasticity theory.

a, b Segregation energy profiles along the lines marked by red arrows in Fig. 4c: a Line S1 at GB1 and b Line S2 at GB2, illustrating variations in segregation energy along these GBs. Horizontal dashed lines in a and b indicate the mean segregation energy of GB1 and GB2, respectively, serving as references. c, d The stress field surrounds secondary GB dislocations for GB2 (Σ13b, see Fig. 3f–i) with the DSC-lattice vectors as Burgers vectors: c DSC-a: \({{{{\bf{b}}}}}_{{{{\bf{\alpha 5}}}}}=\frac{a}{13}[\bar{1}4\bar{3}]\) and d DSC-b: \({{{{\bf{b}}}}}_{{{{\bf{\alpha 5}}}}}=\frac{a}{13}[\bar{3}\bar{1}4]\). Here, a is the lattice constant of BCC Fe. e The change in segregation energy (P ^XSΔV) aligns along the GB (averaged within a 0.5 nm distance from the GB plane), corresponding to (c, d). Here, DSC-a and DSC-b have the same Burgers vectors as those stress fields in (c, d). The modulation factor is defined as \(\exp \left(\frac{-{P}^{{{{\rm{XS}}}}}\Delta V}{RT}\right)\). f Maximum change in segregation energy (ΔSeg. Energy) caused by DSC-a or DSC-b dislocations as a function of inclination ϕ. The blue and red circles indicate the experimentally relevant inclinations. g Dislocation density maps for DSC-a and DSC-b types as a function of inclination ϕ and misorientation deviation θ from the ideal Σ13b GB (rotation axis [111]), derived using the Frank-Bilby equation. h Dislocation densities for DSC-a and DSC-b as a function of misorientation deviation θ at a fixed inclination of ϕ = 15.6^∘. i Calculated segregation energy profiles for the Σ13b GB with a misorientation deviation of θ = 0.6^∘, showing contributions from DSC-a, DSC-b secondary GB dislocations, and their combined effect.