Fig. 1. (a) Schematic illustration of the initial configurations viewed along the a axis (the green dashed lines highlighted the (10 $\bar{1}$ 2) plane), (b) final Zr (10 $\bar{1}$ 2) grain boundary structure, (c) Zr (10 $\bar{1}$ 2) free surface (FS) and (d) bulk Zr with the same dimensions. The atom color distinguishes the two different stacking sequence of (0001) planes.

Fig. 2. Schematic illustration showing (a) interstitial configurations and Wyckoff positions of impurity atoms X in bulk Zr crystal, (b) the distribution of four typical interstitial sites in Zr (10 $\bar{1}$ 2) grain boundary (the bulk sites used in segregation are also depicted by green and purple circles) and (c) interstitial sites used in Sections 3.2 are labeled by numbers (1-22).

Fig. 3. Calculated formation energy of the stable interstitial sites (octahedral (O), tetrahedral (T), hexahedral (H) and crowdions (C) for all considered impurities).

Fig. 4. Calculated formation energy landscape of the impurity atoms X in octahedral and tetrahedral sites of Zr (10 $\bar{1}$ 2) GB: (a) C-doped; (b) N-doped; (c) H-doped; (d) O-doped; (e) the total view of X-doped. Note that from left to right in each panel showing the interstitial configurations, 2D contour plots and 3D maps of the formation energy, at the same time, the contour line values are also displayed on the left vertical axis in each 3D maps.

Fig. 5. Calculated segregation energy (a) and strengthening energy (b) of the Zr (10 $\bar{1}$ 2) GB with impurities in different sites. The abscissa represents the numbers of the interstitial sites as displayed in Fig. 2(c). The vertical lines indicate the positions of the bulk and GBs.

Fig. 6. Calculated separation energy and tensile stress vs. separation distance of the clean Zr (10 $\bar{1}$ 2) GB and the doped Zr (10 $\bar{1}$ 2) GBs: (a) separation energies from rigid calculations; (b) separation energies from relaxed calculations; (c) tensile stresses from rigid calculations; (d) tensile stress from relaxed calculations.

Fig. 7. Calculated charge density distributions of (a) clean GB, (b) the GB with C at OCT site1 and (c) the GB with H at TET site2 in the (010) plane. The separation distance during tensile testing from relaxtion methodology is given below each frame. (d) Schematic illustration of the bonds region around the GB plane, which are highlighted by red boxes in (a)-(c). Six considered bonds in Fig. 8 are simply labelled by d11-d66, as depicted in the left frame.

Fig. 8. Collected bond lengths around the GB plane as a function of separation distances: (a) all considered bonds for the clean GB, the GB with C at OCT site1 and the GB with H at TET site2; (b) comparative analyses of each bond for the three representative GBs (Clean, C-doped, H-doped).