Tilt grain boundaries in WS₂ from low to high misorientation angles

Grain boundaries (GBs) with low misorientation angles are interfacing lines connecting sparsely distributed dislocation cores, but high-angle GBs could have amorphous atomic arrangements with merged dislocations. Tilt GBs in two-dimensional materials frequently emerge in large-scale specimen production. In graphene, a critical value for differentiating low and high angles is quite big because of its flexibility. However, understanding transition-metal-dichalcogenide GBs meets additional complexities regarding the three-atom thickness and the rigid polar bonds. We construct a series of energetic favorable WS₂ GB models using coincident-site-lattice theory with periodic-boundary conditions. The atomistic structures of four low-energy dislocation cores are identified, consistent with the experiments. Our first-principles simulations reveal an intermediate critical angle of θ _c ≈ 14° for WS₂ GBs. Structural deformations are effectively dissipated via W-S bond distortions especially along the out-of-plane direction, instead of the prominent mesoscale buckling in one-atom-thick graphene. The presented results are informative in studies of the mechanical properties of transition metal dichalcogenide monolayers.