Fig. 1. (a) Schematic illustration showing the variation of crystal orientations caused by the presence of GNDs in EBSD-acquired orientation maps. The GND density was calculated from the measurements within the high angle grain boundaries (HAGBs). Moreover, a misorientation angle of 15° was used as the criterion between HAGBs and low angle grain boundaries (LAGBs). Note that because the SSD type dislocations have a net-zero Burger vector, the existence of SSDs has no effect on the lattice curvature. (b) The schematic 3D view of the lattice curvature calculated between points 1 and 2 in Fig. 1(a) with the common axis of [uvw]c and a misorientation angle of ∆θ.

Fig. 2. (a) Schematic illustration of scanning strategy applied in the present work. (b) Schematic 3D overview of the sample for microstructural characterization, hardness measurement and method for determination of GND and SSD densities. BD: building direction, WD: wall direction, TD: transverse direction.

Fig. 3. Typical microstructures of the as-built HX alloy. (a?d) SEM micrographs showing the morphologies of semi-elliptical MPBs, highly serrated GBs, submicron cellular structures. (e) Bright-field STEM micrograph showing high density of tangled dislocations on the cellular boundaries and some nanoparticles with an average size of 65 nm precipitating nearby the boundaries. (f) and (g) Inverse pole figure (IPF) coloring maps acquired from X-Z and X-Y planes, respectively. (h) Distribution of grain size in X-Z and X-Y planes in Fig. 3(f) and (g), respectively. (i) and (j) Qualitative distribution of GND density in the dashed boxes in Fig. 3(f) and (g), respectively. (k) The (100), (110) and (111) pole figures from the same measuring region in Fig. 3(g). (l) Schematic showing the difference between large grains and the surrounding small grains from the aspects of GB density, GND density and grain orientation.

Fig. 4. (a) The schematic illustration of the slip trace (or trace of slip plane) on the sample surface. (b) Indentation of the maximum load of 0.1 kgf in the as-built HX alloy demonstrates that planar slip mode is apparent from the thin and straight slip traces on the sample surface. (c) EBSD IPF coloring map acquired from the same region in Fig. 4(b). (d) GND density map shows the effect of indent on the microstructure. (e) Enlarged region of the white box in Fig. 4(b) and (c) illustrates the occurrence of slip transfer. (f) The change of misorientation angle as a function of the distance from point A in Fig. 4(g). (g, h) Enlarged regions of white and red boxes in Fig. 4(b) and (c) show that two-line directions of slip steps present in the {001} orientated grains.

Fig. 5. (a, b) Hardness as a function of applied stress and indentation depth for the as-built L-PBF HX alloy and (c) corresponding N/G plot for the data in Fig. 5(a) and (b). (d) Relationship between indentation depth and corresponding GND density.

Fig. 6. (a, b) Magnified EBSD-BC and GB distribution maps. (c) Frequency histograms of the total screw, total edge and total GND density distribution in the HX alloy. (d) The total screw, total edge and total GND density map, respectively. (e) Bright-field STEM micrograph of the as-built HX alloy, showing that dislocations with high density segregate at cellular walls. (f) Enlarged regions of the red box in Fig. 6(e). (g) A high-angle annular dark-field (HAADF) STEM image, showing dense dislocation tangled cell structures formed in the as-built microstructure. (h) Peak broadening of reflection 422 in the as-built HX alloy. Full width at half maximum (FHWM) is also indicated, and instrumental broadening has been removed. (i) Relationship between ∆K and $K{{\bar{C}}^{1/2}}$ by fitting Eq. (30). The slope of m-WH plot generally represents the magnitude of total dislocation density.