LAUSR

The anisotropic fracture toughness G(θ) is an intrinsic feature of graphene and is fundamental for fabrication, functioning, and robustness of graphene-based devices. However, existing results show significant discrepancies on the anisotropic factor, i.e., the ratio between zigzag (ZZ) and armchair (AC) directions, G_{ZZ}/G_{AC}, both qualitatively and quantitatively. Here, we investigate the anisotropic fracture of graphene by atomic steps on cleaved graphite surfaces. Depending on the relation between the peeling direction and local lattice orientation, two categories of steps with different structures and behaviors are observed. In one category are straight steps well aligned with local ZZ directions, while in the other are steps consisting of nanoscale ZZ and AC segments. Combined with an analysis on fracture mechanics, the microscale morphology of steps and statistics of their directions provides a measurement on the anisotropic factor of G_{ZZ}/G_{AC}=0.971, suggesting that the ZZ direction has a slightly lower fracture toughness. The results provide an experimental benchmark for the widely scattered existing results, and offer constraints on future models of graphene fracture.