Folding and Fracture of Single-Crystal Graphene Grown on a Cu(111) Foil

A single-crystal graphene film grown on a Cu(111) foil by chemical vapor deposition (CVD) has ribbon-like fold structures. These graphene folds are highly oriented and essentially parallel to each other. Cu surface steps underneath the graphene are along the <110> and <211> directions, leading to the formation of the arrays of folds. The folds in the single-layer graphene (SLG) are not continuous but break up into alternating patterns. A "joint" (an AB-stacked bilayer graphene) region connects two neighboring alternating regions, and the breaks are always along zigzag or armchair directions. Folds formed in bilayer or few-layer graphene are continuous with no breaks. Molecular dynamics simulations show that SLG suffers a significantly higher compressive stress compared to bilayer graphene when both are under the same compression, thus leading to the rupture of SLG in these fold regions. The fracture strength of a CVD-grown single-crystal SLG film is simulated to be about 70 GPa. This study greatly deepens the understanding of the mechanics of CVD-grown single-crystal graphene and such folds, and sheds light on the fabrication of various graphene origami/kirigami structures by substrate engineering. Such oriented folds can be used in a variety of further studies.