Fig. 1: Secondary GB dislocations in the Fe-1 at% W specimen.

a Illustration of grain boundaries (GBs) in a three-dimensional (3D) polycrystalline structure. b Magnification of a selected high-angle GB (HAGB) showing curved GB plane. c Illustration of steps and secondary GB dislocations on the GB. d Bright-field image of a transmission electron microscopy (TEM) lamella prepared from the body-centered cubic (BCC) Fe-1 at% W specimen, featuring multiple GBs, one of which is labeled as a HAGB. This HAGB is a Σ11 GB that deviates by 2. 2° from the theoretical misorientation. e Corresponding weak-beam dark-field (WBDF) image of the same area, imaged under the two-beam condition with \({{{\bf{g}}}}=[1\bar{3}0]\). The inset image in the right side of e displays the diffraction pattern collected from the left grain ([100] zone axis). Scale bar: 1/0.1 nm. f High magnification bright-field image displaying the steps and secondary GB dislocations of the GB. g Bright-field image of a Σ3 GB with a 2^∘ deviation from the ideal misorientation. h Corresponding dark-field image of the Σ3 GB with \({{{\bf{g}}}}=[0\bar{1}1]\), revealing secondary GB dislocations. i Bright-field image of a Σ5 GB that deviates by 2. 5^∘ from the ideal misorientation. j Dark-field images of the Σ5 GB acquired at various α tilt angles. Scale bar: 50 nm. k Magnified view of the area at 0^∘ tilt angle, with semi-transparent red dots highlighting the atomic column configuration near the GB. See additional details in Supplementary Fig. 5. l The region in k overlaid with a displacement shift complete (DSC) lattice and a Frank circuit, illustrating the presence of a secondary GB dislocation characterized by the Burgers vector (b).