Extended Data Fig. 2: Tubular edge structure.

(a) Atomically resolved the curvature of tubular edge. (b) The height profile of the green line in (a). (c) Analogy with paper model for demonstration folded-over graphene wrinkle. (d) Schematic view showing folded-over graphene wrinkle. The cracking tubular edge energy profile as a function of the number of carbon atoms cracking is shown in (e). (f) The corresponding atomistic models used to calculate energies of the tubular edge cracking along zigzag direction (for details of the calculation, refer to the Methods section). Note: The DFT calculations were carried out to model the graphene cracking step on the basis of experimentally obtained values for the curvature of the tubular edge (a, b). (f) shows the modelled hydrogen etching process, in which an H2 molecule was attached at the point of the highest curvature; this attachment ultimately results in graphene cracking. The total energies of representative steps in the etching process (e) indicates the cracking is energetically favourable and further verifies the proposed graphene cracking mechanism.