Graphene is a single atomic layer of sp2-hybridized carbon arranged in a honeycomb lattice. Defect-free graphene is the strongest material in the world, but current techniques to synthesize graphene sheets large enough to use in applications invariably produce grain boundary defects. Grain boundary defects can be likened to the seams in patchwork quilts, made of pieces of fabric that have been sewn together.

Although researchers now understand fairly well how defects like dislocations and grain boundaries affect the strength of three-dimensional polycrystals, very little is known about how such defects interact in two-dimensional structures like graphene and affect the mechanical properties of these materials. "Our research goes someway in addressing these unknowns and reveals that interactions between defects are important for graphene's mechanical strength," say team members Yujie Wei and Ronggui Yang of the Chinese Academy of Science and the University of Colorado.

Wei, Yang and colleagues, who report their work in Nature Materials, came to their conclusions by using a multiscale analysis approach with quantum-mechanical-based density functional theory and molecular dynamics simulations together with continuum mechanics calculations.

Tilt grain boundaries

The team, led by Mildred Dresselhaus of the Massachusetts Institute of Technology, began by studying how tilted grain boundaries at which the sheets meet influence the material's overall strength. These tilt grain boundaries are symmetrical, with one grain being the mirror image of another on the opposite side of the grain boundary line, explains Wei. The tilt grain boundaries are made by cutting a "V" notch into a rectangular single-crystalline graphene sheet. The two sides of the notch are then stitched together to form a tilt grain boundary with its tilt angle equal to the open angle of the V notch. At the atomic level, tilt grain boundaries in graphene are usually formed by pentagon-heptagon rings in the material.

"We found that grain boundary strength can either increase or decrease with tilt angle," said Wei. "Moreover, the strengths of tilt grain boundaries appear to increase as the square of the tilt angles if pentagon-heptagon rings are evenly spaced, but this trend breaks down if the defects are unevenly spaced." The researchers also discovered that mechanical failure in graphene always starts in the bonds shared by hexagon-heptagon rings in the material.

"Since defects are inevitably present in engineering materials, and there is growing interests in two-dimensional materials, our results will help us better understand how strong these structures really are," Yang told "The results could be important when designing high-strength and stretchable graphene membranes for biological, energy and electronic applications."

The researchers are now busy looking at how defects in graphene affect its electrical and thermal properties.