fig5

Figure 5. (A) The occupation probability of Ti at each metallic site, with noticeable Ti segregation around grain boundaries. Ti forms a monolayer at the grain boundary plane in the 010_21 grain boundary, while it forms an off-center bilayer pattern in the 210_11 grain boundary. Gray atoms are B, and colored atoms are metals; (B) The concentration profile of Ti (R_Ti) at the metallic site surrounding various grain boundaries, displaying prominent Ti segregation around most of these boundaries. The unit of the horizontal axis is Å; (C) A comparison of the ideal grain boundary strength between pure ZrB₂ and medium-entropy Ti_1/3Zr_1/3Hf_1/3B₂ (ME-TMB₂) after MC/MD simulation. Ideal grain boundary strength values are listed in Supplementary Table 3. MC/MD: Hybrid Monte Carlo/molecular dynamics.