Fig. 2: Dislocation analysis in dual-scale shell-lattice metamaterials.

a High-angle angular dark field scanning transmission electron microscopy (HAADF-STEM) cross-section images contrasting the morphology of dislocation-starved grain structure in layer-by-layer growth mode and the dislocation-rich grain structure in screw dislocation growth mode. The sharp steps (red line) penetrated by multiple dislocation arrays (green line). Scale bar: 500 nm. b Diffraction contrast TEM imaging of the dislocation under two-beam conditions of [110] zone axis. TEM images with selected area electron diffraction (SAED) patterns inset under strong two-beam conditions of \((\bar{1}11)\), \((0\bar{2}2)\), and \((1\bar{1}1)\), respectively. The diffraction contrast was strong when the \({{{\bf{g}}}}\) vector parallel to the dislocation direction, while became invisible when the g vector was excited in \((1\bar{1}1)\). The calculated Burgers vector direction was [110], suggesting the Burgers vector of this dislocation had a large screw component. Scale bar: 300 nm. c HAADF-STEM images and corresponding schematic present the distribution of different dislocation line types. Scale bar: 500 nm. d Statistical result revealing the total dislocation density, geometrically necessary dislocation (GND), and the percentage of different dislocation types. e Three-dimensional Kernel average misorientation (KAM) map showing the high-density dislocations in shell-lattice metamaterials. The color scale indicates the misorientation angle range. High-resolution TEM (HRTEM) image displaying the typical (f) edge dislocation and (g) screw dislocation, as well as their corresponding Burgers vector and geometric phase analysis (GPA) strain analysis. The yellow arrow represents the Burgers circuit. The white circle indicates the position of the screw dislocation. Scale bar: 2 nm. The color scale represents normalized strain values from compressive (negative) to tensile (positive). Source data are provided as a Source Data file.