Fig. 4: Mapping and analysis of GB properties in the Fe-1 at% W specimen.

a Integral profiles across GB1 for quantifying the interfacial excess (IE) of W segregation at the Fe GB^40,41. We plot measurements from two points: Point 1 for high W regions (colored pink) and Point 2 for low W segregation regions (colored orange). In each plot, the solid lines show the cumulative relationship between all atoms and solute atoms, while the dashed lines are the fittings within the two grains adjacent to the GB plane. \({N}_{W}^{\,{\mbox{excess}}\,}\) represents the accumulation of excess atoms across the GB interface. IE values are calculated by dividing \({N}_{W}^{\,{\mbox{excess}}\,}\) by the corresponding interface areas, which are approximately 8.0 nm² for Point 1 and Point 2. We indicate the locations of Point 1 and Point 2 in the embedded image, consistent with Fig. 3d. b IE mapping on GBs, as identified from the correlative characterization in Fig. 2c, d. We labeled the locations of all investigated GBs from GB1 to GB12 in (b). c Segregation energy mapping on the same GBs as in b, calculated based on the Langmuir-McLean isotherm, Eq. (1)^11,36. The locations where 1D line profiles of segregation energy values were measured are marked by red lines S1 and S2, details of which will be presented in the following section. d Correlation between the misorientation and segregation energy of all investigated GBs: This scatter plot displays the average segregation energy (in kJ/mol) for various GBs, plotted against their misorientation (in degrees). Each point represents a different GB (GB1–GB12), with colors indicating the rotation axis of misorientation related to the cubic crystal symmetry (\(m\bar{3}m\)), as shown in the color triangle legend. Experimental GB segregation energy spectra for e GB1, f GB2, and g all GBs. Here, n represents the sample size used to derive statistics. The fitting plots, overlaid onto the histograms, generally follow the skew-normal function³⁷ but with local deviations highlighted by the black arrows, see (e, f). The used fitting parameters are: characteristic energy (μ) in kJ/mol, width (σ) in kJ/mol, and shape parameter (α) along with each plot. The sharp peak appearing near 0 kJ/mol in (g) results from the contribution of the GBs without solute segregation and the inevitable minor inclusion of the bulk regions adjacent to the GBs.